Essays in Open Economy Macroeconomics

Nikhil Patel

Submitted in partial fulfillment of the

requirements for the degree

of Doctor of Philosophy

in the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY

2015

a

©2015

Nikhil Patel

All Rights Reserved

ABSTRACT

Essays in Open Economy Macroeconomics

Nikhil Patel

This dissertation comprises of three essays in open economy macroeconomics. The

main contribution in these essays lies in incorporating insights from the literature

on international trade in macroeconomic models to enhance their ability to explain

transmission of business cycle fluctuations across countries.

The motivation for this research comes from the observation that international trade

plays a key role in open economy macroeconomic models, and is the primary (and in

some cases the only) channel through which shocks can be transmitted across countries.

My doing so, the open economy macro literature has given a central role to international

trade in explaining business cycle comovement across countries. However, even in the

most sophisticated open economy models, international trade continues to be modeled

in a highly stylized manner, and key insights and characteristics specific to international

trade are ignored. These essays explore the role of two such features in international

trade which have received widespread empirical support in the trade literature but

continue to be overlooked as far as the macro literature in concerned-namely trade

finance (or the dependence of international trade on external finance) and trade in

intermediate inputs and re-export of imported goods.

Chapter 1 explicitly incorporates a role for international trade finance by modeling

the link between external finance and the cost channel of monetary policy in a two

country new keynesian Dynamic Stochastic General Equilibrium (DSGE) model and

shows that trade finance affects the propagation of all shocks that are known to be

important drivers of business cycles in advanced economies. It further shows that the

degree and extent to which trade finance affects the propagation of shocks depends

critically on certain key parameters that characterize the external sectors of countries

including the degree of flexibility of import prices.

Motivated by the theoretical insights gained from chapter 1, chapter 2 takes a more

quantitative approach by estimating the two country model with trade finance using

data from the US and Eurozone (EZ) for the great moderation period. Apart from

providing parameter estimates for the critical parameters identified in chapter 1, it

documents how bayesian model comparison exercises provide evidence in favor of models

incorporating a role for trade finance, and that trade finance matters more for spillover

effects of shocks rather than the effects on the respective country of origin.

Chapter 3 (joint work with Zhi Wang and Shang-Jin Wei) examines the issue of

measurement of competitiveness as defined by the real effective exchange rate and

argues in favor of accounting for the distinction between intermediate and final goods

trade flows and the need for considering sector level heterogeneities. On the theoretical

front, it provides a multi-country multi-sector model which is solved and used to define

competitiveness at both the country and country-sector level. On the empirical front,

it provides estimates of elasticity of substitution across different countries, sectors and

categories (production inputs vs final consumption goods) and compiles an annual

database of real effective exchange rates for 40 countries and 35 sectors within each

country for 1995-2009.

Contents

List of Figures iii

1 Credit Constraints, Trade Finance and the Cost Channel of Monetary Policy inOpen Economies 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131.4 Understanding the Role of Novel Features in the Model . . . . . . . . . . . . . . . . . . 281.5 Calibration and Assessment of the Role of External Finance: . . . . . . . . . . . . . . . 311.6 Model Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2 Quantifying the Trade Finance Channel in an Estimated Two Country Model 722.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752.3 Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 802.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 852.6 Implications for Monetary Policy and Beyond . . . . . . . . . . . . . . . . . . . . . . . . 972.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

3 Global Value Chains and Effective Exchange Rates at the Country-Sector Level(With Zhi Wang and Shang-Jin Wei) 1043.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053.2 The Concept of REER as a Measure of Competitiveness . . . . . . . . . . . . . . . . . . 1123.3 A Stylized Three Country Global Value Chain . . . . . . . . . . . . . . . . . . . . . . . 1163.4 The General Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1223.5 Computation of Effective Exchange Rate Weighting Matrices . . . . . . . . . . . . . . . 1253.6 Relationship to other REER Weighting Matrices in the Literature . . . . . . . . . . . . 1303.7 Building Country-level REER From Ground Up . . . . . . . . . . . . . . . . . . . . . . . 1333.8 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1383.9 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1463.10 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

i

3.11 Application: Bilateral Real Exchange Rates: . . . . . . . . . . . . . . . . . . . . . . . . . 1573.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

Bibliography 162

Appendices 173

A Appendix: Chapter 1 173

B Appendix: Chapter 2 174B.1 Model With Sticky Wages: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174B.2 Parameter Estimates for Model With Importer Interest Rate Trade Finance . . . . . . . 176B.3 Data: Definitions and Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

C Appendix: Chapter 3 179C.1 Stylized 3 by 2 GVC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179C.2 Solution of the general model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189C.3 Derivations of the expressions (3.21) and (3.25) . . . . . . . . . . . . . . . . . . . . . . . 198C.4 Proofs of Propositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199C.5 Illustration of Role of Elasticities: Example 3.1 . . . . . . . . . . . . . . . . . . . . . . . 208C.6 Estimation of elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208C.7 Bootstrap moments of elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211C.8 Inspecting the China–US bilateral Real Exchange Rate: . . . . . . . . . . . . . . . . . . 211C.9 Expressions for matrices with n = m = 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 216C.10 General algebra and results with Armington aggregators . . . . . . . . . . . . . . . . . . 225C.11 List of countries and sectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226C.12 Divergence Index for 1435 country- sectors pairs . . . . . . . . . . . . . . . . . . . . . . 226C.13 REER indices plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

ii

List of Figures

1.1 The Great Trade Collapse and Interest Rate Spreads . . . . . . . . . . . . . . . . . . . . 91.2 Home Monetary Contraction: θfh = θhf = 0.1 . . . . . . . . . . . . . . . . . . . . . . . 361.3 Home Monetary Contraction: θfh = θhf = 0.1 . . . . . . . . . . . . . . . . . . . . . . . . 371.4 Home Monetary Contraction: θfh = 0.1, θhf = 0.7 . . . . . . . . . . . . . . . . . . . . . 421.5 Home Monetary Contraction: θfh = 0.1, θhf = 0.7 . . . . . . . . . . . . . . . . . . . . . 431.6 Home Monetary Contraction: θfh = 0.7, θhf = 0.1 . . . . . . . . . . . . . . . . . . . . . 451.7 Home Monetary Contraction: θfh = 0.7, θhf = 0.1 . . . . . . . . . . . . . . . . . . . . . 461.8 Home Monetary Contraction: θfh = 0.7, θhf = 0.7 . . . . . . . . . . . . . . . . . . . . . 481.9 Home Monetary Contraction: θfh = 0.7, θhf = 0.7 . . . . . . . . . . . . . . . . . . . . . 491.10 Home Monetary Contraction with labor cost: θfh = θhf = 0.1 . . . . . . . . . . . . . . 521.11 Home Monetary Contraction with labor cost: θfh = 0.1, θhf = 0.7 . . . . . . . . . . . . 531.12 Home Government Spending Shock: θfh = 0.7, θhf = 0.1 . . . . . . . . . . . . . . . . . . 551.13 Home Government Spending Shock: θfh = 0.7, θhf = 0.1 . . . . . . . . . . . . . . . . . . 561.14 Home Government Speeding Shock: θfh = 0.1, θhf = 0.7 . . . . . . . . . . . . . . . . . . 581.15 Home Government Spending Shock: θfh = 0.1, θhf = 0.7 . . . . . . . . . . . . . . . . . . 591.16 Home Government Spending Shock: θfh = 0.7, θhf = 0.7 . . . . . . . . . . . . . . . . . . 601.17 Home Government Spending Shock: θfh = 0.7, θhf = 0.7 . . . . . . . . . . . . . . . . . . 611.18 Home Productivity Shock: θfh = 0.1, θhf = 0.7 . . . . . . . . . . . . . . . . . . . . . . . 631.19 Home Productivity Shock: θfh = 0.1, θhf = 0.7 . . . . . . . . . . . . . . . . . . . . . . . 641.20 Home Productivity Shock: θfh = 0.7, θhf = 0.1 . . . . . . . . . . . . . . . . . . . . . . . 651.21 Home Productivity Shock: θfh = 0.7, θhf = 0.1 . . . . . . . . . . . . . . . . . . . . . . . 661.22 Home Productivity Shock: θfh = 0.7, θhf = 0.7 . . . . . . . . . . . . . . . . . . . . . . . 671.23 Home Productivity Shock: θfh = 0.7, θhf = 0.7 . . . . . . . . . . . . . . . . . . . . . . . 682.1 Time series Plots of Data Used in Estimation . . . . . . . . . . . . . . . . . . . . . . . . 842.2 US Monetary Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922.3 US Monetary Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 932.4 US Labor Supply Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 942.5 US Productivity Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.1 REER indices for USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1513.2 Sector level Exchange rates along with Aggregate country REER for select countries . . 1523.3 The role of heterogenous elasticities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1533.4 Examples with high divergence between uniform elasticity and heterogenous elasticity

GVC-REER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1553.5 The role of sector level price indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1563.6 Comparison of GVC-RER and standard RER bilateral exchange rates for China . . . . 160A.1 Expansionary Monetary Contractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

iii

C.1 Illustration of Role of Elasticities: Example 3.1 . . . . . . . . . . . . . . . . . . . . . . . 209C.2 Divergence index at the country-sector level . . . . . . . . . . . . . . . . . . . . . . . . . 228C.3 GVC-REER and Q-REER indices for all countries . . . . . . . . . . . . . . . . . . . . . 229C.4 GVC-REER and Q-REER indices for all countries cont. . . . . . . . . . . . . . . . . . . 230C.5 GVC-REER and Q-REER indices for all countries cont. . . . . . . . . . . . . . . . . . . 231C.6 GVC-REER and Q-REER indices for all countries cont. . . . . . . . . . . . . . . . . . . 232C.7 GVC-REER and Q-REER indices for all countries cont. . . . . . . . . . . . . . . . . . . 233

iv

Acknowledgements

I am extremely grateful to my supervisor Shang-Jin Wei for his guidance and support

throughout the PhD. His high standards have always pushed me to strive towards

improving the quality of my work. He has truly been an inspiration, and words fail me

as I attempt to express my gratitude towards him.

I am also immensely grateful to my advisors Stephanie-Schmitt-Grohe and Martin

Uribe. Their guidance throughout my years as a graduate student has been an important

part of my intellectual development.

My research has also benefitted greatly from the discussions and suggestions that I

have received from Jon Steinsson and David Weinstein (who are also members in my

dissertation committee) as well as Frederic Mishkin, Emi Nakamura, Jaromir Nosal,

Ricardo Reis, Zhi Wang and numerous colleagues at Columbia University. In particular

I would like to thank Pablo Ottonello for introducing me to the field of international

macroeconomics. My interest in the subject developed in large part due to his enthusiastic

teaching and insightful discussions.

Part of the research in this dissertation was conducted while I was an intern at

the Hong Kong Institute for Monetary Research (HKIMR) and Hong Kong Monetary

Authority (HKMA). I am extremely grateful to them for their hospitality and financial

support. The views expressed here are my own and do not correspond to the views of

the HKIMR or HKMA.

Finally, I express my deepest gratitude to my family and friends for being a pillar of

support. Their encouragement, trust, and faith in my abilities has been an invaluable

asset throughout my doctoral studies.

v

1 Credit Constraints, Trade Finance and the Cost Channel of

Monetary Policy in Open Economies

1

1.1 Introduction

The empirical literature on international trade flows has firmly established that

international trade is heavily reliant on external finance. Infact, Bekaert et al. (2009)

identify trade finance as the “fundamental problem in international trade”.1 While the

empirical literature on trade finance is extensive, its macroeconomic implications, in

particular its role in affecting the propagation (or even generation) of macroeconomic

shocks in general equilibrium settings is less well understood. This paper undertakes this

task by explicitly modeling trade finance constraints in a two country New Keynesian

model with nominal rigidities. Since an important determinant of external finance is

the stance of monetary policy,2 the approach taken in the paper would be to treat trade

finance as a supply side mechanism that augments the credit channel of monetary policy.

As emphasized in Bernanke and Gertler (1995) and Mishkin (1995), monetary policy

and interest rates affect economies in a variety of ways. However, in standard New

Keynesian DSGE models used by researchers and central banks around the world prior

to the great recession, monetary policy was modeled solely as a channel than influenced

aggregate demand by altering the consumption-saving decision of households.3 While

the presence of the cost channel of monetary policy was acknowledged in the literature,1 According to the estimates of the Committee on the Global Financial System, $6.5–8

trillion worth of bank-intermediated trade finance was provided during the year 2011,which, at around 10 percent of global GDP and 30 percent of global trade, is a fairlysizable number in itself, even though it does not include letters of credit and other formsof trade finance not explicitly involving bank loans

2In fact, Ju et al. (2013) provide direct evidence on the adverse effects of contractionarymonetary policy on exports.

3See for instance Erceg et al. (2006) and Smets and Wouters (2003), the DSGE modelsused at the Board of Governors and ECB respectively prior to the crisis.

2

these features were typically ignored due to their limited quantitative importance in

business cycle models in closed economy settings.4 Recognizing the important role played

by financial factors in the great recession, models incorporating financial accelerators

have witnessed a resurgence in both academia and central banks.5

Although models in this vein have been extended to open economy settings (see for

instance Gilchrist, 2003 and Gertler et al., 2007), these models do not distinguish between

the external finance dependence of international and intra-national trade, something

that the international trade literature has strongly emphasized. This paper models

this distinction and argues that it is important to take it into account for two reasons.

Firstly, as argued before, there is extensive empirical evidence from around the world

suggesting that international trade is disproportionately more reliant on external finance

than intra-national trade. Secondly, as this paper will show, this distinction matters

not only quantitatively, but also qualitatively in terms of the sign of the effect that

they generate. For instance, standard cost side channels of monetary policy (either in

their mild form through simple working capital constraints or in a stronger form via

the financial accelerator) typically play the role of amplifying the effect of domestic

shocks that hit the economy.6 On the other hand, this paper shows that in principle

trade finance can either amplify or mitigate the effects of shocks. Consider a monetary

contraction in the home economy, which leads to a fall in domestic aggregate demand

and prices. If importing firms are constrained to borrow at their respective home4See Barth III and Ramey (2002), Christiano et al. (2005) Ravenna and Walsh (2006).

A more comprehensive literature review follow in the next section.5See for instance Christiano et al. (2008) for a medium scale closed economy DSGE

model with the financial accelerator. The DSGE models used at various regional FederalReserve Banks all now have the financial accelerator in them. See for instance Negroet al. (2013) and Campbell et al. (2010) and the PRISM model of the Philadelphia Fed.

6This is always true for shocks that move output and prices in the same direction, likea monetary policy shock, but may also be true for shocks that imply opposite movementsin output and prices.

3

interest rates, then foreign imports into the home country become more expensive

whereas imports into the foreign country (i.e home exports) become cheaper for foreign

consumers, leading to a higher demand for the latter and a lower demand for the former.

As a result, the trade finance constraints play the role of cushioning the effect of the

original monetary contraction on home output. Unlike the financial accelerator channel

however, the trade finance channel is not limited in the qualitative effects that it can

generate. If for instance exporting firms are financially constrained and borrow in their

domestic interest rate, then the trade finance constraints can amplify the effect of the

monetary contraction on home GDP. This paper further shows that unlike the domestic

aspect of the cost channel of monetary policy which has been studied in the literature so

far, international trade finance can have a significant impact on propagation of shocks

even without an amplification mechanism like the financial accelerator.7

Motivated by these aspects that distinguish open economies and international trade

finance, this paper provides the first incorporation of trade finance in a two country

dynamic stochastic general equilibrium framework within the New Keynesian paradigm.

On the theoretical front, it studies how the transmission mechanism of shocks is altered

in the presence of these additional features. Because monetary policy has both an

exogenous and endogenous component (in the form of a Taylor Rule) these additional

features affect not just the propagation of monetary policy shocks (the exogenous

component of monetary policy) but also influence the propagation of all other shocks

via the endogenous component of monetary policy. The paper shows that the effect7Kaufmann and Scharler, 2009 and Gilchrist (2002) in (response to (Barth III and

Ramey, 2002)) show that the cost channel modeled in the form of working capitalconstraints for firms leads to only negligible effects in a general equilibrium setting, andhence models assigning a significant role to the credit channel of monetary policy relyon devices like the financial accelerator.

4

of external finance constraints on propagation of shocks depends critically on certain

key parameters in the model including the degree of price stickiness (and asymmetry

across countries in this parameter) and parameters quantifying the external finance

dependence of trade flows.

Given the tight link between trade finance and monetary policy in the model, the effect

of trade finance on propagation of shocks can be illustrated most clearly by considering

the effects of exogenous monetary policy shocks. To this end, table 2 summarizes the

standard channels governing the transmission mechanism of monetary policy in open

economies that have been studied in the literature and introduces the new channel

that will be developed and explored in this paper. Irrespective of whether the economy

is open or closed, the direct impact of a monetary contraction is a fall in aggregate

demand, which leads to a fall in home GDP. If the economy is open, the effect spills over

and leads to a fall in demand for foreign GDP as well. In open economies, there is an

additional channel coming via the real exchange rate. Monetary contraction leads to an

appreciation of the exchange rate which makes home goods more expensive than foreign

goods. Both home and foreign consumers thus shift away from home goods and towards

foreign produced goods. This leads to a further fall in home GDP and a rise in foreign

GDP. The third channel is the standard cost or credit channel which works through the

supply side by altering the cost function of firms (which depends on the nominal interest

rate). The net effect of a monetary contraction on home and foreign GDP depends on

which of these channels dominates. If for instance the expenditure switching channel

dominates, then a monetary contraction at home leads to a rise in foreign output.

In addition to these standard channels, this paper introduces a new channel for

monetary transmission through international trade finance. Import/Export or trade

5

firms are assumed to be credit constraint and are required to borrow in order to maintain

working capital . When interest rates are high, imported goods become expensive and

both countries shift away from imports and towards domestically produced goods. The

net effect on home and foreign GDP is ambiguous and depends on parameters that

determine the relative strengths of these effects.

This paper also links the literature on vertical specialization, trade in intermediate

inputs and trade intermediaries with the credit channel of monetary policy in an open

economy setting.8 Although ignored in majority of the literature in macroeconomics,

recently a growing literature on global value chains and sequential production and trade

has shown that these features are successful in accounting for many stylized facts that

standard models have failed to explain.9 A natural consequence of multiple stages is

that it generates scope for amplification of shocks along value chains in the presence of

financial frictions. In reference to the great trade collapse, Eichengreen (2009) argues

that “The most important factor is probably the growth of global supply chains, which

has magnified the impact of declining final demand on trade”. This paper argues that in

addition to the demand side effects, supply chains can also affect international trade

from the supply side by amplifying the effects of trade finance shocks.10 For instance, it

is reasonable to assume that while domestic firms can sell in the domestic market directly

or through a single intermediary (say a ground transportation firm), the same firm when

selling internationally may need the services of more intermediaries (for instance, it8See Ahn et al. (2011b) for the documented importance of intermediaries in interna-

tional trade9See for instance Huang and Liu (2007) who show that multiple stage trade can

account for the high comovement of output across countries without resorting to highcorrelations in exogenous shocks, a well known failure of standard models based on theseminal international RBC model of Backus et al. (1992).

10These ideas have been explored in closed economy setting before-see for instanceBigio and La’O (2013)

6

Table 1 – Amplification of Financial Constraints with Multiple Stages

Number of stages marginal cost faced by nth stage firm

No external finance [1,∞) pExternal finance 1 (1 + i)pExternal finance n (1 + i)np

may need ground transportation services in both the home and destination country, a

shipping agency, a currency exchange agency etc). If each of these intermediaries are

subject to financial constraints, then even a small shock while propagating through such

a chain can lead to large aggregate effects. Table 1 provides a simple illustration of this

point. Here p denotes the price of input (which could be wage or price of an intermediate

input) which each producer transforms one for one into output. i is the nominal interest

rate. The first row shows that with no external finance constraints, trade is frictionless

and the marginal cost faced by the firm at the nth stage is independent of n and is equal

to the price p. If on the other hand firms are required to borrow and pay for their inputs

in advance, then the cost faced by he nth stage firm is increasing in n and is given by

(1 + i)np.

Researchers studying the great trade collapse characterizing the recent financial crisis

have found it hard to explain the fall in trade to GDP ratios purely on the basis of

demand and compositional effects. Eichengreen (2009) for instance notes that “The

collapse of trade since the summer of 2008 has been absolutely terrifying, more so insofar

as we lack an adequate understanding of its causes”. Trade finance has been conjectured

to be the natural candidate that can fill the void between the data and demand side

predications based on standard models. Figure 1.1 shows the collapse in trade to GDP

7

Table 2 – Transmission Mechanism of Monetary Policy in Open Economies

Home Output Foreign Output

Standard Channels1 Fall in aggregate Demand ↓ ↓2 Appreciation of Exchange Rate ↓ ↑3 Working Capital/Financial Accelerator ↓ ↑

New ChannelTrade Finance ↑↓ ↑↓

ratio for the US alongside the sharp increase in the TED spread, a measure of the

external finance premium. The fact that the most recent spike in the TED spread

coincides with the great trade collapse hints at a possible connection.

Because international trade is by construction more reliant on external finance

than intra-national trade in the model, it can naturally account for the decline in

trade to GDP ratios in response to shocks that raise interest rates (or–more generally

interpreted–interest rate spreads). Several papers including Eaton et al. (2011) have

shown that the demand side effects and product heterogeneity alone cannot fully account

for the collapse in global trade. Trade finance is the natural candidate to bring the

predictions of models more in line with the data and this paper shows that it can do so

quantitatively.

The general nature of the implications that emerge from the model can be summarized

under two scenarios depending on whether the countries are symmetric with resect to each

other in regard to their external sectors.11 External sectors could differ due to the degree

of external finance dependence, price flexibility and currency denomination of trade11The nature of those asymmetries and various factors that determine them will be

discussed in more detail when the model is presented and estimated.

8

Figure 1.1 – The Great Trade Collapse and Interest Rate Spreads

(a) Trade to GDP ratio for the US:(Exports+Imports

2GDP

)

1990 1995 2000 2005 2010

0.08

0.1

0.12

0.14

(b) TED Spread

1990 1995 2000 2005 2010

0.5

1

1.5

2

Notes: TED spread is the difference between 3 month US dollar Libor and 3 month US T bill rate,expressed in annualized percentage points.

finance contracts, all of which in turn could be functions of the nature of export bundles

of countries. When the external sectors are symmetric across countries, incorporation

of trade finance leads to sharp movements in trade volumes but has negligible impact

on GDP. For instance, when global interest rates are high, international trade becomes

more expensive, which leads to higher import prices for both countries. Both countries

shift away from imports and towards their respectively domestically produced goods in

such a way that the net effect on the GDP of both countries is minimal. On the other

hand when countries are asymmetric in any of these dimensions, trade finance can alter

the response of GDP to various shocks that hit the economy.

The model also provides a novel explanation for the phenomenon of expansionary

monetary contractions (or equivalently contractionary devaluations) which has been

documented not only in developing countries but also in the US.12 Typically these are12See for instance Uhlig (2005)

9

explained by either liability dollarization or heterogenous agents (redistribution leads

to concentration of wealth in the hands of agents that have a high propensity to save).

The trade finance channel introduced in this paper, coupled with an amplification effect

coming from multiple stage can very well lead to a situation in which devaluations can

lead to expenditure switching effects that overshadow the aggregate demand effect and

lead to a fall in domestic output.

1.2 Related Literature

The paper is linked to several different strands in the literature at the intersection

of macroeconomics, monetary economics and international trade. The incorporation

of credit constraints in this paper is motivated by the extensive literature on trade

finance and in particular the interaction between trade finance and monetary policy. This

literature has documented–across countries and time– the higher reliance of international

trade on external finance compared to intra-national trade. Ju et al. (2013) employ a

large bilateral sector level trade data set for the years 1970-2000 to study the effect of

monetary policy tightening on export behavior. Given their rich dataset, they are able to

exploit cross-sectional differences and find that sectors relying more on external finance

are disproportionally largely affected by monetary tightening, and that the exporting

behavior is affected more than domestic sales even after controlling for endogeneity.

Using monthly data on US imports, Chor and Manova (2012) also document the impact

on interest rates on trade. In particular, they find that the US imported less from

countries with higher interest rates and tighter credit conditions.

Using a panel of 91 countries from 1980 to 1997, Manova (2008) shows that equity

10

market liberalizations are positively associated with higher exports. Manova et al. (2011)

report similar results using firm level data from China. Based on survey data from

Italian manufacturing firms, Minetti and Zhu (2011) report that credit rationing affects

international sales more than domestic sales. Using transaction level data from a US

exporter of frozen and refrigerated food products, Antràs and Foley (2014) report cash

in advance to be the most common form of payment reported by US exporters from

foreign importers. Using a detailed matched firm level dataset for banks and firms in

Japan, Amiti and Weinstein (2009) find that the health of the banking sector is much

more influential in determining exporting behavior of firms compared to their domestic

sales.

There are two main explanations for why international trade is more reliant on

external finance compared to intra-national trade. Firstly, the time lags associated

with international transactions are substantially high, generating the need for firms

to maintain more working capital. Based on a sample of 180 countries, Djankov et al.

(2006) find that the median time it takes from the moment goods are ready to ship at a

factory until they are loaded on a ship is 21 days, and it takes another 23 days from the

time goods arrive at an import port for them to reach the eventual purchasers warehouse.

These numbers exclude the actual shipping time, which for the typical US import

according to Hummels and Schaur (2013) is another 20 days. Secondly, informational

asymmetries involved in cross-border transactions are likely to be much higher, which

generates more demand for insurance and external finance in the form of instruments

like bank guarantees. Schmidt-Eisenlohr (2013) studies the optimal contracting problem

in the presence of time lags and information asymmetries and Niepmann and Schmidt-

Eisenlohr (2014) study the use of letters of credit by US exporting firms and show how

11

it is sensitive to the perceived riskiness of importing countries as well as aggregate

uncertainty.

An alternative to bank intermediated trade finance is trade credit, or the direct

extension of credit between buyers and suppliers. Although the two are substitutes and

one would expect firms to turn from bank intermediated trade finance to trade credits,

the evidence supporting this hypothesis is mixed.13

In its exploration of the role of the cost channel of monetary policy in open economy

settings, the paper has several precedents in the closed economy literature. Using

industry level data from the US, Barth III and Ramey (2002) provide compelling

evidence in favor of the cost channel of monetary policy. Dedola and Lippi (2005) report

similar conclusions based on a richer dataset containing information on 21 manufacturing

sectors from five OECD countries. Ravenna and Walsh (2006) highlight the presence of

the cost channel on the basis of parameters estimates based on their estimation of the

phillips curve for the US. They also provide a characterization of the optimal monetary

policy problem in the presence of these cost side effects. In advanced economies monetary

policy is primarily conducted via open market operations which affect the balance sheets

of banks directly. If cost side effects of monetary policy are present, one would expect

countries with bank based systems to be more sensitive to monetary policy shocks. This

is exactly what Cecchetti (1999) and Kashyap and Stein (1997) find. Moreover, based on

joint BIS-IMF-OECD-World Bank statistics on external debt, Auboin (2007) documents

that 80 percent percent of the providers of trade finance are private banks.14

The paper also builds on ideas developed in the literature on vertical specialization13See Asmundson et al. (2011) and Choi and Kim (2005) as two examples of the mixed

evidence.14In the Lehman bankruptcy six of the thirty largest unsecured claims against Lehman

were letters of credit.

12

and multiple stage production. Huang and Liu (2007), Huang and Liu (2001) and

Wong and Eng (2012) are among the many papers that have used these features to

explain various empirical stylized facts that standard models have difficulty in accounting

for. This paper will build a model that would allow multiple stage trade to act as

an amplification mechanism for shocks due to borrowing constraints. Similar ideas

incorporating liquidity constraints have been applied in a closed economy setting by

Bigio and La’O (2013) and Kalemli-Ozcan et al. (2013).

More broadly, the paper is motivated by the literature on credit constraints and

their role in amplifying macroeconomic fluctuations. Following the seminal work of

Bernanke et al. (1999) and Kiyotaki and Moore (1995), there has been a large literature

on modeling the effects of endogenous credit constraints in macroeconomic models.

These channels have also been implemented in the open economy literature (see for

instance Bianchi, 2010 and Bianchi and Mendoza, 2010) and production chains (Bigio

and La’O, 2013). This paper differs from the literature in that it explicitly models the

role of interest rates in influencing the borrowing costs of firms, as well as modeling

the dependence of trade on external finance that has been widely documented in the

literature.

1.3 Model

The model in this paper builds on the framework used in Gali and Monacelli (2005)

and Lubik and Schorfheide (2006), which in turn fit into the New Open Economy

Macroeconomics (NOEM) paradigm of Obstfeld et al. (1996).15 The world economy is

assumed to comprise of two countries of equal size. Households have preferences over15See Lane (2001) for a survey of the NOEM literature.

13

domestic and foreign goods and supply labor to firms elastically. There are two sets

of firms in each economy– production firms and trade firms. Prices are assumed to be

sticky and consequently money is not neutral in the short run. The monetary authority

is assumed to conduct monetary policy by using the short term nominal interest rate

as its instrument. The following sections describe each of the sectors in the model in

detail. For brevity, only the home economy is described in detail. The foreign economy

is assumed to be isomorphic.

Households

The household side of the economy is characterized by a representative consumer

with preferences over consumption and leisure given by the following utility function.

U(Cht , H

ht , N

ht ) =

1

1− σc(Cht −Hh

t

At)1−σc − 1

1 + σLNh1+σLt (1.1)

Here Cht is consumption , Nh

t is the labor supply and Hht (=χCh

t−1) is the habit stock

going into period t. At is a non stationary world-wide productivity shock which evolves

according to:

At = Zt (γAt−1) (1.2)

Here Zt is an exogenous component and γ denotes the trend growth rate of world

productivity. Agents are thus assumed to derive utility from effective consumption

relative to the level of global technology.16 Preferences are characterized by internal16This assumption is made to ensure that the model has a balanced growth path along

which hours worked are stationary as is the case in the data.

14

habits.17

I assume a constant elasticity of substitution (CES) aggregator for Cht :

Cht =

[(1− α)

1η(Chht

) η−1η + α

1η

(Cfht

) η−1η

] ηη−1

(1.3)

Here Chht and Cfh

t denote the home and foreign produced components in the con-

sumption bundle of country h. η is the elasticity of substitution between domestic and

foreign aggregates and α parametrizes the home bias in consumption. The associated

price index, which is also the consumer price index (CPI) of the home country is given

by

P h,cpit =

[(1− α)

(P hht

)1−η+ α

(P fht

)1−η] 1

1−η

(1.4)

where P hht and P fh

t denote the domestic and import price indices for the home

country. The bundles Chht and Cfh

t in turn are CES aggregates combining different

home and foreign produced varieties,

Chht =

[ˆj

Chht (j)

ε−1ε dj

] εε−1

, Cfht =

[ˆj

Cfht (j)

ε−1ε dj

] εε−1

(1.5)

where ε is the elasticity of substitution across different varieties produced in the same

country.

The associated price indices are as follows:17With a representative agent internal and external habit formulations yield almost

identical dynamics. Using micro data Ravina (2007) establishes that the internal habitis stronger than external. Note however that although habits are internal, they are not“Deep habits” in the sense considered by Ravn et al. (2006). As is shown in Ravn et al.(2006), Ravn et al. (2010) and Ravn et al. (2012), the move from internal to deep habitsleads to more drastic changes and is beyond the scope of the present paper.

15

P hht =

[ˆj

P hht (j)1−εdj

] 11−ε

, P fht =

[ˆj

P fht (j)1−εdj

] 11−ε

(1.6)

Here P hht (i) and P fh

t (j) denote the prices paid by home consumers for imported

varieties i and j respectively. Markets are assumed to be complete, so that households

can trade in a complete set of state contingent securities in order to smooth consump-

tion fluctuations. While the complete markets assumption is a strong one, it is used

extensively in the literature and incomplete markets have been shown to generate only

minor departures from the complete markets benchmark (see for instance Schmitt-Grohé

and Uribe 2003.)

In the presence of complete markets the household budget constraint is as follows:

P h,cpit Ch

t +

ˆs

µt,t+1(s)Dht+1(s) ≤ W h

t Nht +Dh

t + T ht (1.7)

Here Dt+1 denotes the amount of state contingent securities purchased by households

at price µt,t+1(s) which yield one unit of nominal payoff at time t + 1 if state s is

realized. Wt is the nominal wage, and Tt denotes lump sum transfers to households.

These comprise of net transfers from the government as well as dividends from firms

and financial intermediaries. Each of these components will be described in detail in the

following sections.

Although as a simplification I model a cashless economy with no explicit mention

of money, implicitly there is assumed to be a time invariant one to one relationship

between the nominal interest interest rate and money demand which the central bank

can exploit to set the desired nominal interest rate by changing money supply.

As a simplification, wages are assumed to be flexible and the monetary non neutrality

16

is induced solely via price stickiness. In a closed economy setting, Smets and Wouters

(2007) show that price stickiness is more important in explaining fluctuations in the

US data compared to wage stickiness. Wage stickiness is nevertheless introduced in

standard models to provide a “cost push shock”. In this model however, the working

capital constraints on firms plays that role.18

The first order conditions characterizing the household problem are as follows:

Atλht =

((Ch

t −Hht )

At

)−σc− χγβEt

[AtAt+1

((Ch

t+1 −Hht+1)

At+1

)−σc](1.8)

(Nht )σL = λht

W ht

P h,cpit

(1.9)

βEt

[λht+1

λht

P h,cpit

P h,cpit+1

]=

1

Rht

= µt,t+1 (1.10)

λht is the Lagrange multiplier associated with the budget constraint, which also

captures the marginal utility of consumption. Equation (1.8) is the standard Euler

equation with internal habits in consumption. (1.9) is the labor supply condition which

equates the marginal disutility from work to the increase in income. (1.10) Gives the

price of state contingent bonds, which also equals the inverse of the equilibrium gross

nominal interest rate. Note that (1.10) uses the assumption that the state contingent

bonds are denominated in the home currency. This is without loss of generality and the18It is pertinent to note that the decision to ignore stickiness in wages in made explicitly

based on its limited contribution to a model like the one that is being built here. There isstrong evidence in favor of wage stickiness in the form of downward nominal rigidity andthis has first order implications for open economies–see for instance Schmitt-Grohé andUribe (2011). However the solution technique used in this paper involves linearizationaround a deterministic steady state and is neither equipped to deal with large shocksnor with asymmetries like one sided wage rigidity so these considerations are beyondthe scope of the present paper.

17

corresponding equation for the foreign country is given by

βEt

[λht+1

λht

P f,cpit

P f,cpit+1

EtEt+1

]=

1

Rft

= µt,t+1 (1.11)

Where Et denotes the nominal interest rate, i.e the price of foreign currency in terms

of home currency.19 (1.10) and (1.11) can be used to show that uncovered interest rate

parity condition holds up to a first order.

Rht = Rf

t Et(Et+1

Et

)(1.12)

Firms

The production side of the economy is characterized by a continuum of atomistic

firms, each of which produces a differentiated product. Labor is the only input in

production and the production function of the generic firm is given by:20

Y ht (j) = AtA

htN

ht (j) (1.13)

Here At is a common world wide technology component and Aht is a country-specific

stationary technology shock. Following Christiano et al. (2005) I assume that firms

operate under a working capital constraint and are required to borrow funds at the19Note that as defined here, an increase in the nominal exchange rate corresponds to a

depreciation of the home currency.20I abstract from capital mainly for simplicity. This assumption is not uncommon in

the New Keynesian literature–see for instance Lubik and Schorfheide (2006). Anotherless innocuous reason however for excluding capital is that the introduction of cost sideeffects of monetary policy on investment has non trivial implications for stability andmodel indeterminacy as emphasized by Aksoy et al. (2012).

18

nominal interest rate to pay a fraction of their wage bill21. The cost function of the firm

is thus given by:

Ξht (j) = Rh

L,tWht Y

ht (j) (1.14)

Where RhLt is the firm’s total interest rate factor. I assume that a fraction uhL of

the wage bill has to be financed by intra-period borrowing, which gives the following

relationship defining the external financial dependence of goods producing firms:

RhL,t =

(uhLR

ht + 1− uhL

)(1.15)

uhL = 0 corresponds to the case with no working capital constraints whereas uhL = 1

corresponds to the case that is considered in most papers that model the cost channel,

including Christiano et al. (2005) and Ravenna and Walsh (2006). Goods producing

firms are constrained to borrow at the domestic interest rate (i.e they cannot borrow in

foreign currency).

The market structure is assumed to be monopolistically competitive. Each producer

producing a distinct good faces an elasticity of demand ε. Prices are assumed to be

sticky and pricing contracts are staggered according to the mechanism in Calvo (1983).22

In each period each firm has the opportunity to re-optimize and set its price with21This is a standard channel via which a cost channel for monetary policy can be

introduced. See Barth III and Ramey (2002) for intra industry evidence on the costchannel and Ravenna and Walsh (2006) for a theoretical exploration and more empiricalevidence.

22Alternatively, the more realistic quadratic adjustment costs as proposed in Rotemberg(1982) can be assumed. However, the model is solved by considering a first orderapproximation around a deterministic steady state and it can be shown that the dynamicsimplied by these two mechanisms are identical up to a first order approximation. Inparticular, they both lead to the same Philip’s curve derived below. I choose Calvo(1983) formulation over that of Rotemberg (1982) for its simplicity.

19

probability (1−θh). The firms that do not optimize their price are assumed to keep their

price unchanged from the previous period. 23 Conditional on having the opportunity to

reset its price in period t , firm j would reset its price in order to maximize a discounted

value of its lifetime future expected profits conditional on the prices remaining the same.

The associated maximization problem is given by:

P ht (j)∗ = ArgmaxEt

[∞∑k=0

(θh)kΩt,t+k

[P ht (j)∗Y h

t+k(j)− Ξht+k(j)

]](1.16)

where the demand function for each firm is as follows:

Y ht (j) =

(P ht (j)∗

P ht

)−εY ht (1.17)

The first order conditions associated with this problem yield the following expression

for the optimal price conditional on re-optimization:

P ht (j)∗ = Et

[∑∞k=0(θh)kΩt,t+k

(εε−1

)P ht+kMCh

t+kYht+k∑∞

k=0(θh)kΩt,t+kY ht+k

](1.18)

(1.19)

WhereMCht =

RhLWht

AtAht Phtdenotes the real marginal cost facing each firm. The log linearized

version of (1.18) around the symmetric steady state reads:24

23Alternatively, one could allow for prices to be indexed to past inflation. As shown byAdolfson et al. (2007) and Smets and Wouters (2007) adding this assumption does notchange much in terms of the fit of the model. This is also consistent with the singleequation estimates of Galı et al. (2001).

24Throughout the paper, lower case letters are used to denote log deviations fromsteady state, i.e xt = logXt − log(X)

20

pht (j)∗ = (1− βθh)

∞∑k=0

(βθh)kEt(mcht+k) (1.20)

This leads to the following forward looking phillips curve for PPI inflation:25

πht = βEtπht+1 +(1− βθh)(1− θh)

θhmcht (1.21)

Import-Export Sector

In order to introduce a role for trade finance, an import-export sector characterized

by the presence of trade firms is explicitly introduced, as in Lubik and Schorfheide (2006)

and Monacelli (2005) . While these papers introduce the import sector purely to generate

the scope for incomplete passthrough of exchange rate fluctuations into import prices,

the international trade sector in this model, which is assumed to be credit constrained,

generates a role for trade finance constraints to influence real variables in the economy

in addition to incomplete passthrough. In particular, like the domestic firms, the trade

firms too are assumed to be credit constrained and are required to borrow to pay for an

exogenous (and time invariant) fraction of their costs. For simplicity, I assume that the

the trade firms do not employ any labor.

Sequential trade and vertical fragmentation are key features in the trade data than

have been successful in explaining many empirical stylized facts26. Following this

literature I model the import sector as characterized by a sequence of firms that operate

at different stages. Each firm has a trivial production function which transforms the25The derivation is standard, see for instance Galí (2009).26See for instance Wong and Eng (2012),Huang and Liu (2001) and Huang and Liu

(2007)

21

input into output one for one. Each firm however is credit constrained and is required

to finance a part of its purchase by borrowing at the risk free rate. Multiple processing

stages in the import sector thus play the role of amplifying the cost effects of monetary

policy.

Incorporating these features, the import-export sector is modeled as an n stage

sequential set up. At each stage k, a continuum of atomostic firms operate with the

following production technology:

Y fhk,t (j) = Y fh

k−1,t(j), k ∈ 1, 2, .., n, j ∈ (0, 1) (1.22)

Note that for simplicity it is assumed that these firms neither employ labor nor are

they subject to productivity shocks as is the case with goods producing firms. The cost

function of each firm is given by

Ξfhk,t(j) = Rfh

t (k)P fhk−1,t (1.23)

Where, similar to the goods producing firms, Rfht is the gross interest factor which

characterizes the external finance dependence of the sector. Moreover, in order to allow

for incomplete passthrough of exchange rate into import prices, firms at the final stage

(n) in the import-export sector are assumed to operate under monopolistic competition

like the goods producing firms. Under these assumptions, the real marginal cost of the

import-export sector as a whole can be written as follows:

Φfht =EtP

ft R

fht

P fht

(1.24)

here P fht denotes the local currency price of foreign goods that are sold to home

22

consumers. Note that similar to Lubik and Schorfheide (2006), this real marginal cost

term can be interpreted as a a law of one price gap. However, in this paper this gap

comprises not only of incomplete passthrough because of price stickiness but also an

additional effect coming from trade finance, which implies that in this model there can

be deviations from law of one price even in the absence of market power and flexible

prices on the part of the importing firms.

The gross interest rate factor in equation 1.24 can be written as follows:

Rfht =

[ufhRc

t + (1− ufh)]n (1.25)

Where n is the number of processing stages and 0 < ufh < 1 is the fraction of the

purchases that have to be financed by external borrowing at each stage.27Rct is the

interest rate that is used in trade finance. It would be either the home interest rate (Rft )

or the foreign interest rate Rft

Log linearizing equation (1.25) yields the following approximate relationship between

the number of processing stages, external finance dependence in each stage and the

nominal interest rate

rfht ≈ nufhrht (1.26)

As is evident from (1.26), the impact of changes on nominal interest rate on trade

finance depends on both the external finance dependence (ufh) and the number of pro-

cessing stages (n). The equation also makes it clear however that with this specification

it is not possible to identify these two parameters separately in the data. Moreover, the

relationship between the risk free interest rate and the marginal cost of the retail sector27For simplicity this parameter is assumed to be independent of nas well as t.

23

may depend on other factors that are not modeled explicitly but may nevertheless pay

a role.28. Since the goal of the paper is to study the consequences of this relationship

rather than its micro-foundations, the model is parametrized in terms of an aggregate

parameter (δfh) which can be understood as the elasticity of marginal cost of import

retailers with respect to the risk free rate, i.e

rfht = δfhrht (1.27)

Where δfh = f(n, ufh, Z) is a function of n, ufh and other characteristics Z that are

not explicitly modeled.

Trade finance in the real world (both domestic and international) is operationalized

in a number of different ways including direct lending by banks to the exporter and/or

the importer, inter-firm trade credit, open account (i.e post delivery payment) or cash-in

advance.29. To the extent that all these mechanisms involve atleast one of the parties

engaging in borrowing at an interest rate that is directly affected by changes in monetary

policy (as captured by equation C.94 ), it is important to emphasize that even with this

parsimonious specification of external finance dependence, the model is general enough

to capture all the different trade finance arrangements.

Similar to the case of goods producing firms, the optimal pricing decisions of the

importing firms lead to the following forward looking phillips curve for import consumer

prices.

πfht = βEtπfht+1 +

(1− βθfh)(1− θfh)θfh

φfht (1.28)

28Amplification effects coming via a financial accelerator type mechanism is an exampleof one such scenario

29See Ahn et al. (2011a) , Antras and Foley (2014) Schmidt-Eisenlohr (2013).

24

As θfh → 0 we have the benchmark case of complete passthrough, with the difference

from the standard model being that in addition to exchange rate rate pass thorough,

there is also “interest rate passthrough”, a novel channel not considered in the literature

so far.

For future reference, the CPI inflation in the home country is given by a weighted

sum of πfht and πht . In particular,

πfht = (1− α)πht + απfht (1.29)

Financial Intermediaries

As emphasized above, a key feature in this model is that firms are liquidity constrained.

In particular, they are constrained to finance (partly or fully) their input purchases

(or wages as the case may be) by borrowing at the risk free rate. This financing

could be assumed to be intermediated by banks, which rebate their profits to domestic

households.30 Note that although the paper follows the common approach in the new

Keynesian literature of modeling a cashless economy, implicitly there is a money demand

equation which maps a one to one relationship between money and the nominal interest

rate.

Government

The remaining aspects of the model are standard. There is a government which30This forms part of the term T ht in equation 1.7 along with other dividend payments

from goods producing and trade firms

25

finances current expenditure by imposing lump sum taxes on households. For simplicity

i do not allow for government borrowing or lending and all expenditures are financed

based on current period receipts.31

The government consumption good is assumed to follow the same aggregator as that

for the households. The overall government spending process is stochastic and driven

by persistent shocks.

ght = ρhgght−1 + εhgt (1.30)

Note that although neither the lump sum tax nor the assumption of same consumption

bundle for households and the government is realistic, 32 the goal for introducing the

government in this model is to have a source for exogenous demand shocks. The paper

is not aimed at studying the effects of fiscal policy per se.

Central Bank

The central bank is assumed to set interest rates according to a modified version

of the Taylor rule postulated in Taylor (1993). In particular, I allow for interest rate

smoothing and the possibility of nominal exchange rate stabilization in the central banks

reaction function. 33

31With optimizing households, Ricardian equivalence holds and allowing for governmentborrowing will not alter the results.

32In particular, government consumption is likely to be concentrated towards nontradable and therefore exhibit a higher home bias than households. See Lane (2010) fora discussion of this point.

33In particular, I allow the responses of the central bank to nominal exchange rates todiffer across the two countries. As is shown by Backus et al. (2010), this asymmetry cango a long way in explaining the uncovered interest rate parity puzzle, a robust featureof the data.

26

The central bank’s reaction function is thus given by:

iht = ρhRiht−1 + (1− ρhR)

[φhππ

ht + φhy4yht + φhe4et

]+ εhrt (1.31)

Where iht denotes the nominal interest rate (Rht = 1 + iht ), 4yht denotes the growth

rate of output and 4et denotes the rate of (nominal) depreciation. εht is an idiosyncratic

white noise process to be interpreted as a monetary policy shock.

Finally, the model is closed by imposing the following market clearing condition for

each firm in equilibrium:

Y ht (j) = Chh

t (j) +Ghht (j) +Ghf

t (j) + Chft (j)∀j ∈ (0, 1) (1.32)

Terms of Trade and Real Exchange Rate

Terms of trade for a country is defined as the ratio of the price of domestically

produced good at home relative to the price of imported goods.34 In particular, the

terms of trade for the home country is defined as follows:

totht =P ht

P fht

(1.33)

Analogously, terms of trade for the foreign country is defined as:

totft =P ft

P hft

(1.34)

34Note that typically terms of trade is defined as the ratio of the price of exports toimports. The distinction ceases to matter since most models typically have the featurethat export prices are equal to domestic prices. This however is not the case in thismodel due to imperfect competition as well as trade finance.

27

Using (1.24) and its foreign country counterpart along with (1.33) and (1.34) give:

φfht φhft = totht tot

ftR

fht R

hft (1.35)

This equation shows that even under the assumption of perfect competition (so that

φhft = φfht = 1) the home and foreign terms of trade do not equal each other (inversely).

In this case, the law of one price gap still exists, but depends only on terms relating to

international trade finance.

The real exchange rate (RER) between home and foreign currencies is defined in the

standard way by weighting the nominal exchange rate by the ratio of the consumer price

indices in the two countries.

St =EtP

f,CPI

P h,CPI(1.36)

As with the nominal exchange rate, the real exchange rate is defined in such a way

that an increase corresponds to a depreciation of the home currency. Typically in

open economy models the real exchange rate as defined above is used an a gauge of

competitiveness, i.e a falling RER denotes lower competitiveness of home goods and

vice-versa. As the next section shows however, this interpretation of the RER can be

flawed in the presence of frictions like trade finance constraints and the terms of trade

is more relevant as a measure of competitiveness.

1.4 Understanding the Role of Novel Features in the Model

At this point it is instructive to pause and summarize how the model fits into the

extant literature, where it differs and what implications these departures are likely to

28

have on the propagation mechanism of shocks. The two new features added to the model

are external finance requirements on international trade and domestic firms in the form

of working capital constraints. If these two features are removed, the model reduces

to something that closely resembles the standard two country model of Lubik and

Schorfheide (2006) and will be treated as a baseline case against which the augmented

models will be compared.

In addition to their effect on aggregate demand, interest rates in this model directly

enter the cost functions of both the goods producing and trade firms. This gives rise to

new channels through which interest rates interact with and influence prices and real

variables in the economy and these impacts depend on certain key parameters in the

model. In order to delineate the role of interest rates, it is useful to isolate the channels

thorough which cost side effects in interest rates enter the model by looking at goods

firms and trade firms separately.

Regarding the cost channel in goods production, since firms are subject to working

capital constraints and are required to borrow funds in the open market to finance part

of their wage bill, interest rates have a direct impact on the marginal cost of firms. When

interest rates increase, firms face a higher marginal cost. This effect tends to make the

firms increase their desired prices, or–in the case of a contractionary monetary policy

shock–reduce their prices by less. This additional channel serves to amplify the effects

of the monetary policy shock since the supply side effects work in the same direction as

the demand side effect.

This however is not always the case for trade finance. When global interest rates are

high, firms face a reduced demand for their exports from abroad, and as a consequence

an increase in the demand for their output from domestic consumers. The net effect

29

on GDP is thus ambiguous and depends on two factors. Firstly, the impact on trade is

determined by the interaction of the interest rate differential along with the parameters

governing the external finance dependance.35 Secondly, the impact also depends on the

degree of price stickiness in the import sector. Most models in the NOEM (New Open

Economy Macroeconomics) literature that assume producer currency pricing implicitly

model the import sector as perfectly competitive. The resultant complete passthrough

of exchange rates into import prices leads to relatively large spillover effects. However,

as is documented in the trade literature (see for instance Bernard et al. 2007) exporting

and importing firms are typically large and are likely to exercise market power. While

in the New Keynesian tradition the model continues to have atomistic firms, it does

allow for market power but assumes that firms are small enough so that their desired

markup remains constant over the business cycle.36

Equilibrium and Solution method

The equilibrium conditions characterized above along with the shock processes

comprise a dynamic system with a unique non stochastic steady state.37 The model is35This effect would be explained in more detail in the context of simulation examples

in the next section.36I make this assumption to avoid the nature of desired markups over the business

cycle influencing the results in the paper. There is no consensus on the cyclical behaviorof markups over the business cycle and there are theoretical and empirical justificationsfor both pro-cyclical and counter-cyclical markups. While Ravn et al. (2010) and Ravnet al. (2012) show that the dynamic effects of monetary and fiscal policy shocks aremore consistent with counter-cyclical markups, Nekarda and Ramey (2011) provideindustry level evidence in favor of pro-cyclical markups and Davis and Huang (2011) showthat market power and pro-cyclical markups are successful in explaining internationalcomovement of output.

37All parameter restrictions required for uniqueness, including the taylor principleproposed in Woodford and Walsh (2005) are imposed to allow a unique solution. (Thefocus of the paper is not on indeterminacy and sunspot equilibria. See Aksoy et al.

30

solved by log-linearizing the equilibrium conditions characterizing the model around

this non stochastic steady state.38 In addition to the monetary policy, productivity

and government spending shocks, the model also features a shock to the labor supply

equation and the nominal exchange rate process.

1.5 Calibration and Assessment of the Role of External Finance:

This section discusses some simulation results based on a symmetrically calibrated

version of the model to outline the dynamics of the key model variables and how they

are affected by the presence and degree of external finance dependence in the wake of

exogenous shocks. The model is calibrated to a symmetric two country case with most

parameter values picked from the previous literature-in particular Lubik and Schorfheide

(2006), Smets and Wouters (2003) and Smets and Wouters (2007), but the values are

kept the same for both home and foreign countries so as to illustrate the mechanics in

the model more clearly. 39

Table 5 shows the values used in the calibration exercise. Although most of the

values are standard, there are a few parameters that merit further discussion. The

(2012) for a summary of these issues in the presence of cost channel of monetary policy).Steps will be taken to restrict priors to the region so that the posterior distribution alsocontinues to satisfy these constraints.

38Note that as in most New-Keynesian models, prices and nominal exchange ratesare not stationary in the model. However, it can be shown that the model specified interms of the remaining (real) variables as well as the first difference of prices (inflation)and exchange rates (depreciation) is stationary. While is its possible to solve and evenestimate models with unit roots, I will work with a stationary version of the model forsimplicity. Note also that as in the standard new Keynesian model, it can be shownthat this model too has a minimal representation that fits the canonical three equationform (for each country) comprising of a forward looking IS curve, a forward lookingPhillips curve and a monetary policy rule. Since this representation fails to providemuch insight, I omit it for brevity.

39These restrictions will be lifted in the empirical section and most parameters will beestimated without imposing these symmetry restrictions.

31

intra-temporal elasticity of substitution between home and foreign goods is a parameter

that, despite extensive empirical research has failed to yield a consensus, leading to

the “Elasticity Puzzle” ( see (Ruhl, 2008)). Typically, the elasticity estimates are found

to fall with the level of aggregation, as documented in Disdier and Head (2008) and

Hummels (1999). While calibrated models typically rely on evidence from the trade

literature and pick values greater than one,40 estimates based on macro data typically

yield much lower values, most often less than one.41 Although this paper too finds

estimates of elasticity to be small in line with the macro literature, these estimates could

be susceptible to the downward aggregation bias discussed in Imbs and Méjean (2012),

who show that when elasticities are heterogenous, aggregation leads to a downward bias.

Indeed the evidence on heterogeneity of elasticities is substantial, as documented in

Patel et al. (2014) and Broda and Weinstein (2006) among others. The value chosen for

the simulation results η = 1 is a compromise between the estimated obtained from the

micro and macro literatures and is more in line with the latter.42

The only asymmetries introduced in the calibration are in the external sectors in

the two countries in order to study their interaction with trade finance constraints.

The external sectors of the two countries can be asymmetric along several dimensions.

Firstly, they could differ in the degree of their external finance dependence, i.e δfh 6= δhf .

As argued above, this implies that the asymmetry is either in the average external

finance dependence per stage and/or the number of stages involved in transporting

the good from one country to another. For instance, Amiti and Weinstein (2011) find40See for instance Obstfeld and Rogoff (2005). For micro studies that typically yield

values greater than 2 see Broda and Weinstein (2006), Feenstra (1994) and Soderbery(2010).

41See for instance Justiniano and Preston (2010) and Lubik and Schorfheide (2006).42Recently, Drozd et al. (2014) have shown how allowing for dynamic elasticities (i.e

different elasticity in the short vs long run) can help reconcile the business cycle andtrade literatures.

32

that external finance dependence is much higher for goods shipped by sea compared

to those shipped by air. Secondly, countries could differ in the degree of their import

price passthroughs, which could be a function of the nature of goods themselves. For

instance, Peneva (2009) shows that prices of labor intensive goods are stickier than

capital intensive goods. If countries export goods with substantially different factor

intensities, this could lead to an asymmetry in import prices. Lastly, countries can also

differ in the interest rate/currency that they are constrained to borrow in. The first

two asymmetries are likely to be linked to differences in export bundles of countries.

A country exporting high end luxury products is likely to have lower competitiveness,

higher markups and hence lower price flexibility in its prices compared to a commodity

exporting country that exports a homogenous product. The third source of asymmetry,

the currency denomination of debt, is likely to be an institutional feature that I assume

is fixed in the short run.43 The two parameters governing import price stickiness will be

varied in the simulations to show how they affect the propagation mechanism of shocks.

In order to determine plausible values for the external finance dependence parameters, I

rely on two different approaches. Firstly, I consider the model’s predication regarding

the fall in trade to GDP ratios in response to a trade finance shock, which in the context

of this paper is best understood as a shock to the interest rate spread. Figure 1.1 shows

the collapse in the global trade to GDP ratio in the recent financial crisis, along with

the TED spread.44 Table 3 shows the peak response of trade to GDP ratio (the model

analogue to the data based measure plotted in figure 1.1 ). The corresponding number

in the data is of the order of 20 to 30 percent. Eaton et al. (2011) argue that about 80

percent of the fall in trade to GDP ratio can be accounted for by demand side effects

and heterogeneity in traded vs non traded goods. This leaves 20 percent of the collapse,

or about 4-6 percent fall in trade to GDP ratios unexplained. Table 3 shows the peak43A large fraction of international trade in conducted in US dollars and hence the dollar

is the primary currency not only for settling trade transactions but also in facilitatingtrade finance. However, local currency debt in countries like Europe and Japan are alsofairly likely–see for instance Gopinath et al. (2010)and Amiti and Weinstein (2011).

44The TED spread, as currently defined in the difference between the 3 month Liborand the 3 month T bill rate

33

Table 3 – Peak Response of trade to GDP ratio to an interest rate spread shock of 300 basis points

η = 2 δ = 2 δ = 4

θhf = θhf = 0.1 -10.0366 -23.0467θhf = θhf = 0.7 -2.8278 -5.8697

η = 0.5 δ = 2 δ = 4

θhf = θhf = 0.1 -2.5092 -5.7617θhf = θhf = 0.7 -0.707 -1.467

response of trade to GDP ratios under different assumption on elasticity of substitution

and import price flexibility. Since there is no consensus on the value of elasticity of

substitution (although values closer to and even below 1 are typically preferred by the

macro data), a value of δ around 2 seems to be a plausible (if somewhat conservative)

value for this parameter.45

As discussed above, the parameter δ captures not just external financial dependence

of sectors but rather also the number of stages involved in the process from actual

production to eventual consumption. Regarding this interpretation, one can get a

sense of the length of the chain by considering a statistic like the average propagation

length (APL). The APL between A and B measures the number of stages it takes for

the good produced in A to reach B. As an example, consider a world in which global

trade comprises of an upstream country (say Japan) exporting intermediate goods to a

downstream country (say China) which in turn exports them to the consuming country

(say the US). In this simple example, the APL between Japan and the US would be 2,

which the APL between Japan and China would be 1.45The maximum response if generates is -10 percent which might seem high, but neither

this elasticity nor this passthrough specification seems plausible and is rejected by thedata. Based on the other three numbers, it seems to be a conservative estimate.

34

Table 4 – Average Propagation Length: Summary Statistics For Benchmark Year 2007

(a) Average Propagation Length (APL) Summary Statistics

Country Level APL Country-Sector Level APL

Number of countries 41 Number of Country-Sectors 1435Mean APL 2.8465 Mean APL 3.61Median APL 2.7396 Median APL 3.62

St. Dev 0.5 St. Dev 0.9

(b) APL for select Country Pairs

US Germany ChinaUS 1.70 2.85 3.65

Germany 2.83 1.62 3.54China 3.42 3.53 2.48

Source: World Input Output Database (wiod.org) and author calculations.

Table 5 – Parameter Calibration for Simulation Exercises

θh 0.7 σc 2θf 0.7 σL 2θhf 0.1,0.7 h 0.7θfh 0.1,0.7 η 1

φπ 1.5 α 0.15φy 0.5 β 0.99φe 0 δ 0,2ρR 0.7

35

Figure 1.2 – Home Monetary Contraction: θfh = θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(b) Foreign GDP

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

(e) Home TOT

1 2 3 4 5 6 7 8

0.2

0.4

0.6

0.8

1

1.2

(f) Foreign TOT

1 2 3 4 5 6 7 8

−2

−1.5

−1

−0.5

0

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

(i) Home Inflation

1 2 3 4 5 6 7 8

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

36

Figure 1.3 – Home Monetary Contraction: θfh = θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(b) Foreign GDP

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

0.25

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

0.6

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

(e) Home TOT

1 2 3 4 5 6 7 8

0.2

0.4

0.6

0.8

1

1.2

(f) Foreign TOT

1 2 3 4 5 6 7 8

−2

−1.5

−1

−0.5

0

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−1

−0.8

−0.6

−0.4

−0.2

0

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−2

−1.5

−1

−0.5

0

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

37

More generally, APLs can be computed using input-output tables using the procedure

outlined in Dietzenbacher and Romero (2007). Table 4 displays summary statistics for

APLs computed at the country and country-sector level using detailed inter-country

input output data from the World Input Output Database for the benchmark year

2007.46 While the country level APLs are likely to be biased downwards since they

ignore within country flows and the heterogeneity is substantial, the values in the range

2 to 5 seem to be a reasonable based on these statistics, which are also in line with the

range of plausible values obtained using the behavior of trade to GDP ratios.

1.6 Model Simulations

Monetary Shocks

Figure 1.2 plots impulse responses of nine endogenous variables to a contractionary

home monetary policy shock in the symmetric case where both home and foreign import

price exhibit high flexibility (θhf = θfh = 0.1). The three lines correspond to models

without trade finance, the model in which all trade finance is driven by home interest

rates and a model in which all trade finance is driven by foreign interest rates respectively.

As the figure shows, as far as foreign GDP is concerned, in all these three cases the

expenditure switching effect dominates the aggregate demand effect and a monetary

contraction leads to an increase in foreign GDP. As is also evident from the diagrams,

the net effect of trade finance constraints on home and foreign GDP is minimal. This

is a consequence of two opposing effects which tend to cancel each other out in this

symmetric setting. Since global interest rates are high, the external finance channel46See Timmer and Erumban (2012) for s detailed description of the database and

Dietzenbacher and Romero (2007) for a detailed discussion of APL.

38

makes imports more expensive for both countries, leading to a shift towards domestically

produced goods by both home and foreign consumers. The two sides of this shift imply

that in a symmetric setting the fall in demand for imports is compensated by the rise in

demand for domestically produced goods, implying a negligible net effect on both home

and foreign GDP. The impulse responses of terms of trade for both home and foreign

countries as well as the global trade to GDP ratio show that although the net effect

on GDP is negligible, the movements in terms of trade indicate a substantial decline

in global trade, since in the case with trade finance constraints on trade the effect on

both home and foreign terms of trade is lower, signaling the rise in competitiveness of

domestically produced goods and fall in competitiveness of imports in both the home

and foreign markets.

There are at least three interesting implications captured in these results. Firstly,

note that although GDP is not significantly affected in this case, the model with trade

finance constraints does imply a larger fall in global trade, and hence lower welfare

for both domestic and foreign agents, so the negligible differences in the response of

GDP should not be interpreted to mean that the trade finance constraints no not

contribute significantly to the mechanics of the model.47 Secondly, this analysis shows

that the model with trade finance constraints has the potential to explain phenomena

like the great trade collapse which characterized the great recession and the subsequent

recovery48 since the model with trade finance constraints leads to a much sharper fall in

trade to GDP ratio compared to the model without trade finance constraints. Although

monetary policy may not have been the primary cause of the increase in external finance47The model is analytically intractable and the simulation results are based on a first

order approximation and a full quantitative characterization of the welfare is beyondthe scope of the paper.

48See for instance Bems et al. (2010)

39

premia (and may have in fact mitigated their rise), financial intermediation, and in

particular trade finance did take a big hit in the aftermath of the great recession for many

different reasons including increase in uncertainty and tougher capital requirements

on banks. Although this paper models external finance premia solely as captured by

changes in interest rates, changes in trade finance premia for other reasons are likely

to generate the same effects. Thirdly, these pictures emphasize the difference and

provide a comparison between the real exchange rate and terms of trade and measures of

competitiveness. The real exchange rate (RER) in its many forms is typically used as a

measure of competitiveness.49 However, when the law of one price does not hold–as is the

case in this model–competitiveness in the home and foreign markets become de-linked

from one another and a single measure like the RER becomes insufficient to quantify

competitiveness movements. Terms of trade, separately defined for the two countries to

account for the disparity in prices, are the right quantities to examine in order to make

inferences regarding competitiveness. This also allows for the possibility of simultaneous

increase and/or decrease in competitiveness in the two countries, something that an

RER measure by construction cannot accommodate.

Figure 1.8 shows impulse responses to the same endogenous variables and the same

shock as above but for the case in which both home and foreign import prices have lower

passthrough (θhf = θfh = 0.7). In this case the aggregate demand effect dominates the

expenditure switching effect and foreign GDP falls in response to a home monetary

contraction. With regard to trade finance constraints however, the message from this

picture is the same as above, i.e with symmetric passthrough trade finance constraints

imply a large drop in international trade (and terms of trade) but have a minimal net

effect on both home and foreign GDP. The results are similar if trade is assumed to49See for instance Chinn (2006) and Patel et al. (2014).

40

be financed by borrowing at the foreign risk free rate instead of home, although the

magnitude of the effect is less.

The main conclusion that emerges from the analysis so far is that when the external

sectors of the two countries are symmetric (with regard to their passthrough as well

as external finance dependence), the presence of trade finance constraints affects the

response of trade and terms of trade variables but has minimal impact on the GDP of

two countries. The remainder of this section will show that if the external sectors of the

two countries are asymmetric, then trade finance constraints alter not just the response

of trade variables, but also the responses of home and foreign GDP to various shocks.

Figure 1.4 shows how the domestic and spillover effects of contractionary monetary

policy at home are altered in the presence of of trade finance requirements in the case

in which home import prices are more flexible than foreign import prices. As a starting

point, the dotted line (without trade finance constraints) shows that this parameter

specification implies that the expenditure switching effect dominates the aggregate

demand effect and the net effect of the shock is to cause an increase in foreign output

accompanied by a fall in domestic output.50 Comparing the impulse responses with and

without trade finance constraints also serves to show that trade finance constraints tend

to generate a positive effect on home GDP and a negative effect on foreign GDP. This

is due to the fact that trade finance constraints coupled with a higher interest rates

imply that imports become more expensive. Since home import prices are more flexible,

this effect is felt more in the form of a shift towards home produced goods by home

consumers, whereas the low passthrough to foreign import prices that the consumers

end up paying implies that the corresponding shift in the foreign country is minimal.

Together these two effects lead to a lower fall in the demand for goods produced at50i.e, with this parameters specification monetary expansions are “beggar thy neighbor”

41

Figure 1.4 – Home Monetary Contraction: θfh = 0.1, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

−0.2

−0.18

−0.16

−0.14

−0.12

−0.1

−0.08

−0.06

−0.04

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.02

0

0.02

0.04

0.06

0.08

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

0.6

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

(e) Home TOT

1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

1.2

1.4

(f) Foreign TOT

1 2 3 4 5 6 7 8

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−0.2

0

0.2

0.4

0.6

0.8

1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−2.5

−2

−1.5

−1

−0.5

0

0.5

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

42

Figure 1.5 – Home Monetary Contraction: θfh = 0.1, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

−0.22

−0.2

−0.18

−0.16

−0.14

−0.12

−0.1

−0.08

−0.06

−0.04

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.04

−0.02

0

0.02

0.04

0.06

0.08

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

0.6

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

(e) Home TOT

1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

1.2

1.4

(f) Foreign TOT

1 2 3 4 5 6 7 8

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−2.5

−2

−1.5

−1

−0.5

0

0.5

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

43

home compared to the case in which trade is not dependent on external finance. The

remaining plots in figure 1.4 illustrate how the transmission mechanism in altered is the

presence of trade finance constraints. As argued above, the key relative price governing

the allocation of expenditure between domestically produced goods and imports in this

model is the terms of trade, which is defined as the ratio of the price of domestically

produced goods to the price of imports. As seen in figure 1.4 the home terms of trade

increase by less in the presence of trade finance constraints. This is due to the interest

rate component which enters the denominator of terms of trade (via the import price)

and tends to reduce the expenditure switching towards foreign produced goods. Foreign

terms of trade, which show lower impact because of high price stickiness in foreign

imports, exhibit the same pattern qualitatively. In standard open economy models, the

real exchange rate is the quantity that determines the relative expenditure shares across

home and imported goods and serves as a measure of competitiveness. However as the

impulse responses of the real exchange rate in figure 1.4 show, this is not the case in

the present model. With trade finance, the real exchange rate appreciates more, which

in the absence of the interest rate channel would imply a larger spillover effect. The

distinction between terms of trade and the real exchange rate becomes more relevant in

a setting like this and it is the former quantity that is more relevant in gauging the shift

in relative demand.

Figure 1.6 presents the other case of asymmetric passthrough in which foreign import

prices are highly flexible while domestic import prices are sticky. In this case the trade

finance constraints generate a negative impact on home GDP and a positive impact on

foreign GDP. The intuition is the same as above. Once again the higher interest rates

translate into higher import prices as before, but now the impact on foreign import

44

Figure 1.6 – Home Monetary Contraction: θfh = 0.7, θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(b) Foreign GDP

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

(c) Home Nominal Interest

1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

(e) Home TOT

1 2 3 4 5 6 7 8

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(f) Foreign TOT

1 2 3 4 5 6 7 8

−2.5

−2

−1.5

−1

−0.5

0

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−2

−1.5

−1

−0.5

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−2.5

−2

−1.5

−1

−0.5

0

0.5

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

45

Figure 1.7 – Home Monetary Contraction: θfh = 0.7, θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(b) Foreign GDP

1 2 3 4 5 6 7 8−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

(c) Home Nominal Interest

1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

(e) TOT

1 2 3 4 5 6 7 8

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(f) Foreign TOT

1 2 3 4 5 6 7 8

−2.5

−2

−1.5

−1

−0.5

0

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−2.2

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−2.5

−2

−1.5

−1

−0.5

0

0.5

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

46

prices is much higher due to greater price flexibility in that sector. As a result, demand

for home exports decline to a greater extent leading to a greater fall in home GDP

and a higher rise in foreign GDP. Figure 1.6 also shows the differences in transmission

mechanism across the different models as manifested in the terms of trade, which

experience much larger movements in the presence of trade finance constraints in this

case.

As emphasized above, import price flexibility (or passthrough) is not the only

dimension along which the external sectors of the two countries can differ. So far it was

assumed that within each model there is only one interest rate (i.e the risk free rate of

one of the two countries) that governs external finance premia for all trade firms. A

priori there is no reason to believe that this would necessarily be the case. Because of

institutional constraints or other frictions, trade firms may be constrained to borrow

only in the risk free rate of a particular country. As two extreme cases, we may have a

scenario in which all bilateral trade finance is governed by either the exporter’s risk free

interest rate or the importer’s risk free rate. In comparison to figure 1.2, figure 1.3 shows

that if this is the case, then even if passthrough is symmetric in both countries, trade

finance constraints can alter the response of GDP to monetary shocks. Consider for

instance the impulse responses of home and foreign GDP in figure 1.3. The baseline case

(without trade finance constraints) is represented by the dotted line. If trade finance is

governed by the exporting country’s monetary policy (blue/dashed lines), then the figure

shows that trade finance constraints generate a negative impact on home GDP and a

positive impact on foreign GDP. The intuition is as follows: as a result of the home

monetary shock, home interest rate rises significantly more than foreign interest rate. 51

51Which also rises in this case, but may actually fall for different calibration ofparameters as seen in figure 1.9 .

47

Figure 1.8 – Home Monetary Contraction: θfh = 0.7, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

−0.01

−0.005

0

0.005

0.01

0.015

(e) Home TOT

1 2 3 4 5 6 7 8

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(f) Foreign TOT

1 2 3 4 5 6 7 8

−0.55

−0.5

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−2.5

−2

−1.5

−1

−0.5

0

0.5

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

48

Figure 1.9 – Home Monetary Contraction: θfh = 0.7, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

−0.14

−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

0

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.14

−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

0

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

−0.015

−0.01

−0.005

0

0.005

0.01

0.015

0.02

(e) Home TOT

1 2 3 4 5 6 7 8

−0.25

−0.2

−0.15

−0.1

−0.05

(f) Foreign TOT

1 2 3 4 5 6 7 8

−0.5

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−0.55

−0.5

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

0

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−2.5

−2

−1.5

−1

−0.5

0

0.5

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

49

This affects trade flows from home to foreign country more than from foreign to home

country, since the latter set of trade flows are dependent on the foreign interest rates. As

a result, the demand for home goods from abroad falls sharply, with little countervailing

increase coming from domestic demand since foreign interest rates rise only moderately.

The net effect is a sharper fall in home GDP and a reduced spillover effect on foreign

GDP. The scenario reverses itself when trade finance is governed by the importing

country’s nominal interest rate (green/solid line). Now the trade finance constrains

generate a positive impact on home GDP and a negative effect on foreign GDP. More

generally, trade finance in either direction could be governed by a combination of home

and foreign interest rates. This possibility will also be considered in the estimation

section.

There is potentially a third source of asymmetry vis-a-vis the the external sectors of

the two countries as they could differ in their external finance dependence parameters

themselves (i.e δhf 6= δhf). The mechanics in this scenario will be much like the ones

discussed above for the exporter vs importer trade finance scenarios.

Table 6 summarizes the impact of trade finance constraints on the transmission of

home monetary contraction to home and foreign GDP. When home import prices are

more flexible than foreign import prices, trade finance constraints tend to increase home

GDP at the expense of foreign GDP. The opposite happens when foreign import prices

are more flexible than home import prices.

Labor hiring costs

External finance dependence of goods producing firms (in the form of labor financing)

is another channel through which monetary policy generates a cost-push effect in this

50

Table 6 – Summary of Transmission of Monetary Policy with Trade Finance Constraints andAsymmetric Passthrough

θfh θhf Home GDP Foreign GDP

Symmetric

High High Negligible NegligibleLow Low Negligible Negligible

Asymmetric Passthrough

low high ↑ ↓high low ↓ ↑

Asymmetric Interest rate dependence for trade finance

Exporter interest rate trade finance ↓ ↑Importer interest rate trade finance ↑ ↓

model.52 Figure 1.10 displays the impulse responses to a contractionary monetary

policy shock at home in which both home and foreign import passthrough is high

(θhf = θhf = 0.1). The top row shows that the effect on GDP is minimal, much like the

case with symmetric passthrough and trade finance constraints. However, unlike the

latter, in this case the difference in the response of terms of trade and trade to GDP

ratios across the two models are also minimal, indicating that there is little effect of

these constraints on international trade as well. This confirms the results obtained in

closed economy settings by Gilchrist (2002) and Kaufmann and Scharler (2009), that the

cost side effects of monetary policy-as captured by labor financing constraints-have little

quantitative impact over and above the aggregate demand effects of monetary policy.

Figure 1.11 further shows that the response of GDP to a monetary contraction52Infact this is the only channel through which cost side effects of monetary policy are

modeled in closed economy settings-see for instance Ravenna and Walsh (2006)

51

Figure 1.10 – Home Monetary Contraction with labor cost: θfh = θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(b) Foreign GDP

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

(e) Home TOT

1 2 3 4 5 6 7 8

0.2

0.4

0.6

0.8

1

1.2

(f) Foreign TOT

1 2 3 4 5 6 7 8−1.4

−1.2

−1

−0.8

−0.6

−0.4

−0.2

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−0.025

−0.02

−0.015

−0.01

−0.005

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.2

−1

−0.8

−0.6

−0.4

−0.2

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−2

−1.5

−1

−0.5

0

Baseline(No EF)

Only Domestic EF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

52

Figure 1.11 – Home Monetary Contraction with labor cost: θfh = 0.1, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

−0.22

−0.2

−0.18

−0.16

−0.14

−0.12

−0.1

−0.08

−0.06

−0.04

(b) Foreign GDP

1 2 3 4 5 6 7 8

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

(e) Home TOT

1 2 3 4 5 6 7 80

0.5

1

1.5

(f) Foreign TOT

1 2 3 4 5 6 7 8

−0.25

−0.2

−0.15

−0.1

−0.05

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

0

0.2

0.4

0.6

0.8

1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.5

−1

−0.5

0

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8−2.5

−2

−1.5

−1

−0.5

0

0.5

Baseline(No EF)

Only Domestic EF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

53

continues to be minimal even under an asymmetric passthrough. The results are similar

to the ones reported above and the main conclusion that emerges from this exercise

is that labor financing constraints, which is the primary means through which cost

side effects of monetary policy have been introduced in the literature so far, are not

quantitatively important.

Effects of External Finance Constraints on Propagation of Non-Monetary Shocks

The main theoretical contribution of this paper is the incorporation of cost side

effects of interest rates through trade and labor finance constraints. While the impact

of these features shows up most clearly in the case of propagation of monetary policy

shocks, they also affect the propagation mechanism of all other shocks in the economy

via their effects on global interest rates through the endogenous component of monetary

policy represented by the interest rate rule. For instance, following a positive aggregate

demand shock the central bank is likely to respond by raising interest rates. In the model

with financial constraints, this change would trigger cost side effects that are absent

in the standard model and that can significantly alter the transmission mechanism of

the original demand shock in both the home and the foreign economy. This section

illustrates some such effects for two non monetary shocks in the model–a supply shock

(rise in home productivity) and a demand shock (rise in home government spending).

Government Spending Shocks:

Figure 1.16 show the impulse response to a home government spending shock in the

symmetric case for three models that differ in their trade finance setup as indicated.

54

Figure 1.12 – Home Government Spending Shock: θfh = 0.7, θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

0.6

0.8

1

1.2

1.4

1.6

(b) Foreign GDP

1 2 3 4 5 6 7 8

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0.2

0.25

0.3

0.35

0.4

0.45

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.05

0.1

0.15

(e) Home TOT

1 2 3 4 5 6 7 8

0.4

0.5

0.6

0.7

0.8

0.9

1

(f) Foreign TOT

1 2 3 4 5 6 7 8

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−3

−2.5

−2

−1.5

−1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−0.8

−0.6

−0.4

−0.2

0

0.2

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

55

Figure 1.13 – Home Government Spending Shock: θfh = 0.7, θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

0.6

0.8

1

1.2

1.4

1.6

(b) Foreign GDP

1 2 3 4 5 6 7 8

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

0.15

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0.2

0.25

0.3

0.35

0.4

0.45

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.04

0.06

0.08

0.1

0.12

0.14

0.16

(e) Home TOT

1 2 3 4 5 6 7 80.4

0.5

0.6

0.7

0.8

0.9

1

(f) Foreign TOT

1 2 3 4 5 6 7 8−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−3

−2.5

−2

−1.5

−1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−0.8

−0.6

−0.4

−0.2

0

0.2

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

56

Some of the observations in this figure are in line with the intuition developed in the

case of propagation of monetary policy shocks discussed above. In particular, the

introduction of trade finance constraints has minimal effect on the response of home

GDP and the real and nominal exchange rates, and alters the response of the different

trade variables. However, unlike the case with monetary shocks in a symmetric setting,

in this case trade finance constraints have a larger impact on the response of foreign

GDP. This is attributable to the higher inflation in the foreign country which leads to

a stronger response of the nominal interest rate via the taylor rule, reducing foreign

aggregate demand in the process. This channel becomes more evidence when we compare

response under the same price stickiness assumptions but under different assumption of

the trade financing interest rate in figure 1.17. If international trade finance is governed

by exporter’s interest rate, then demand for imports from the home country rises by

more, leading to a sharper rise in foreign GDP compared to the model without trade

finance constraints (this rise in demand from abroad is not compensated by the fall in

domestic demand in the foreign country since foreign imports become more expensive

under exporter ). The effect runs in the opposite direction when trade is financed by

importing country interest rates.

Figures 1.12 -1.14 illustrate the impact of trade finance constraints in altering

the propagation mechanism of government spending shocks in the two cases with

asymmetric passthrough. The results are in line with the corresponding ones for

monetary contractions and can be summarized is the same was as in table 6.

Productivity Shocks

Positive productivity shocks present the opposite scenario to the one operational in

57

Figure 1.14 – Home Government Speeding Shock: θfh = 0.1, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

0.6

0.8

1

1.2

1.4

1.6

(b) Foreign GDP

1 2 3 4 5 6 7 8

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0.2

0.25

0.3

0.35

0.4

0.45

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.035

0.04

0.045

0.05

0.055

0.06

0.065

(e) Home TOT

1 2 3 4 5 6 7 8

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

(f) Foreign TOT

1 2 3 4 5 6 7 8−1.3

−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−2

−1.8

−1.6

−1.4

−1.2

−1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.4

−1.3

−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

58

Figure 1.15 – Home Government Spending Shock: θfh = 0.1, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

0.6

0.8

1

1.2

1.4

1.6

(b) Foreign GDP

1 2 3 4 5 6 7 80

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0.2

0.25

0.3

0.35

0.4

0.45

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

0.07

0.075

(e) Home TOT

1 2 3 4 5 6 7 8

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

(f) Foreign TOT

1 2 3 4 5 6 7 8−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

−0.4

(g)(TradeGDP

)

1 2 3 4 5 6 7 8−1.8

−1.7

−1.6

−1.5

−1.4

−1.3

−1.2

−1.1

−1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.5

−1.4

−1.3

−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

59

Figure 1.16 – Home Government Spending Shock: θfh = 0.7, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

0.6

0.8

1

1.2

1.4

1.6

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0.2

0.25

0.3

0.35

0.4

0.45

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

0.06

0.065

(e) Home TOT

1 2 3 4 5 6 7 8

0.5

0.6

0.7

0.8

0.9

1

1.1

(f) Foreign TOT

1 2 3 4 5 6 7 8

−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

(g)(TradeGDP

)

1 2 3 4 5 6 7 8−2.2

−2

−1.8

−1.6

−1.4

−1.2

−1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.4

−1.3

−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

60

Figure 1.17 – Home Government Spending Shock: θfh = 0.7, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

0.6

0.8

1

1.2

1.4

1.6

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.02

0

0.02

0.04

0.06

0.08

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0.2

0.25

0.3

0.35

0.4

0.45

0.5

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

0.02

0.03

0.04

0.05

0.06

0.07

(e) Home TOT

1 2 3 4 5 6 7 8

0.5

0.6

0.7

0.8

0.9

1

1.1

(f) Foreign TOT

1 2 3 4 5 6 7 8

−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−2

−1.8

−1.6

−1.4

−1.2

−1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

−1.5

−1.4

−1.3

−1.2

−1.1

−1

−0.9

−0.8

−0.7

−0.6

−0.5

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

61

the case of monetary contractions and positive aggregate demand shocks since with the

interest rule modeled in the paper they typically lead to a fall in interest rates following

a positive shock. Figures 1.18 through 1.23 illustrate the impulse responses of different

variables in the model to a positive home productivity shock under different model

assumptions as before.

The results are in line with those reported above (and summarized in table 6 ), but

operational in reverse, so that when home import prices are more flexible than their

foreign counterpart, trade finance constraints end up increasing the demand for foreign

goods compared to the model without trade finance constraints. (see figure 1.18).

To summarize, the main conclusion that emerges from the analysis of different shocks

in this section is that to the extent that the introduction of trade finance constraints

affects the propagation of shocks via interest rates, their effect is analogous to the case

with monetary policy shocks. Unlike the monetary contraction for which the exogenous

component of monetary policy generates the differences across models, for the other real

shocks in the economy it is endogenous component imbedded in the interest rate rule

that alters the propagation mechanism of shocks.

1.7 Conclusion

An extensive literature in international trade has documented the heavy reliance

of international trade flows on external finance and has shown that this phenomenon

matters much more for international trade as opposed to intra-national trade. This

paper assesses how this feature affects business cycle fluctuations in open economies

by modeling the link between trade finance and the cost channel of monetary policy in

62

Figure 1.18 – Home Productivity Shock: θfh = 0.1, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

0.25

0.3

0.35

0.4

0.45

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.065

−0.06

−0.055

−0.05

−0.045

−0.04

−0.035

−0.03

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

−0.18

−0.17

−0.16

−0.15

−0.14

−0.13

−0.12

−0.11

−0.1

−0.09

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

−0.045

−0.04

−0.035

−0.03

−0.025

(e) Home TOT

1 2 3 4 5 6 7 8

−0.95

−0.9

−0.85

−0.8

−0.75

−0.7

−0.65

−0.6

−0.55

−0.5

−0.45

(f) Foreign TOT

1 2 3 4 5 6 7 8

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−0.4

−0.3

−0.2

−0.1

0

0.1

0.2

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

63

Figure 1.19 – Home Productivity Shock: θfh = 0.1, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 80.2

0.25

0.3

0.35

0.4

0.45

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.065

−0.06

−0.055

−0.05

−0.045

−0.04

−0.035

−0.03

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

−0.18

−0.17

−0.16

−0.15

−0.14

−0.13

−0.12

−0.11

−0.1

−0.09

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

−0.05

−0.045

−0.04

−0.035

−0.03

−0.025

(e) Home TOT

1 2 3 4 5 6 7 8

−0.95

−0.9

−0.85

−0.8

−0.75

−0.7

−0.65

−0.6

−0.55

−0.5

−0.45

(f) Foreign TOT

1 2 3 4 5 6 7 8

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−0.4

−0.3

−0.2

−0.1

0

0.1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−0.1

0

0.1

0.2

0.3

0.4

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

64

Figure 1.20 – Home Productivity Shock: θfh = 0.7, θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

0.25

0.3

0.35

0.4

0.45

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.085

−0.08

−0.075

−0.07

−0.065

−0.06

−0.055

−0.05

−0.045

−0.04

(c) Home Nominal Interest

1 2 3 4 5 6 7 8−0.17

−0.16

−0.15

−0.14

−0.13

−0.12

−0.11

−0.1

−0.09

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

−0.09

−0.08

−0.07

−0.06

−0.05

−0.04

(e) Home TOT

1 2 3 4 5 6 7 8

−0.8

−0.75

−0.7

−0.65

−0.6

−0.55

−0.5

−0.45

−0.4

(f) Foreign TOT

1 2 3 4 5 6 7 8

0.6

0.7

0.8

0.9

1

1.1

1.2

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

0

0.1

0.2

0.3

0.4

0.5

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

0.4

0.45

0.5

0.55

0.6

0.65

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

65

Figure 1.21 – Home Productivity Shock: θfh = 0.7, θhf = 0.1

(a) Home GDP

1 2 3 4 5 6 7 8

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.09

−0.085

−0.08

−0.075

−0.07

−0.065

−0.06

−0.055

−0.05

−0.045

−0.04

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

−0.17

−0.16

−0.15

−0.14

−0.13

−0.12

−0.11

−0.1

−0.09

−0.08

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

−0.09

−0.08

−0.07

−0.06

−0.05

−0.04

(e) Home TOT

1 2 3 4 5 6 7 8

−0.8

−0.75

−0.7

−0.65

−0.6

−0.55

−0.5

−0.45

−0.4

(f) Foreign TOT

1 2 3 4 5 6 7 8

0.6

0.7

0.8

0.9

1

1.1

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

0.4

0.45

0.5

0.55

0.6

0.65

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

66

Figure 1.22 – Home Productivity Shock: θfh = 0.7, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

0.2

0.25

0.3

0.35

0.4

0.45

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.055

−0.05

−0.045

−0.04

−0.035

−0.03

−0.025

−0.02

−0.015

−0.01

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

−0.19

−0.18

−0.17

−0.16

−0.15

−0.14

−0.13

−0.12

−0.11

−0.1

−0.09

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

−0.045

−0.04

−0.035

−0.03

−0.025

−0.02

−0.015

(e) Home TOT

1 2 3 4 5 6 7 8

−0.8

−0.75

−0.7

−0.65

−0.6

−0.55

−0.5

−0.45

(f) Foreign TOT

1 2 3 4 5 6 7 8

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−0.1

0

0.1

0.2

0.3

0.4

Baseline(No TF)

Home TF

Foreign TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

67

Figure 1.23 – Home Productivity Shock: θfh = 0.7, θhf = 0.7

(a) Home GDP

1 2 3 4 5 6 7 8

0.2

0.25

0.3

0.35

0.4

0.45

(b) Foreign GDP

1 2 3 4 5 6 7 8

−0.06

−0.05

−0.04

−0.03

−0.02

−0.01

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

−0.19

−0.18

−0.17

−0.16

−0.15

−0.14

−0.13

−0.12

−0.11

−0.1

−0.09

(d) Foreign Nominal Interest

1 2 3 4 5 6 7 8

−0.045

−0.04

−0.035

−0.03

−0.025

−0.02

−0.015

(e) Home TOT

1 2 3 4 5 6 7 8

−0.8

−0.75

−0.7

−0.65

−0.6

−0.55

−0.5

−0.45

(f) Foreign TOT

1 2 3 4 5 6 7 8

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

(g)(TradeGDP

)

1 2 3 4 5 6 7 8

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

(h) Real Exchange Rate

1 2 3 4 5 6 7 8

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

(i) Nominal Exchange Rate

1 2 3 4 5 6 7 8

−0.1

0

0.1

0.2

0.3

0.4

Baseline(No TF)

Exporter TF

Importer TF

Notes: The impulse responses are computed through simulations using the values in table 5. Thehorizontal axis measures time in quarters. The vertical axis units are deviations from the unshockedpath. Inflation and nominal interest rate are given in annualized percentage points. The other variablesare in percentages.

68

an otherwise standard two country model with nominal rigidities. Unlike the domestic

component of the cost channel of monetary policy which has been studied extensively in

the literature, this paper shows that the cost channel when combined with trade finance

has much richer implications for business cycles, both qualitatively and quantitatively.

More specifically, the paper shows that when external sectors are symmetric across

countries, trade finance constraints lead to sharp movements in terms of trade and trade

volumes, but do not significantly alter the response of GDP to shocks in either the

home country or abroad. On the other hand, if external sectors are asymmetric, trade

finance constraints significantly change the response of GDP to both monetary and non

monetary shocks. Various sources of this asymmetry (including differences in import

price flexibility) are identified and their implications are explored.

The paper also hints that incorporation of trade finance constraints has a larger impact

on spillover as opposed to domestic effects of shocks. This makes the incorporation of

trade finance constraints especially important for understanding business cycles in small

open economies and countries that face a sizable fraction of their fluctuations due to

shocks origination beyond their borders. On the other hand, omission of trade finance

in a large open economy like the US may indeed be innocuous.

The credit channel of monetary policy has thus far been primarily incorporated in

closed economy settings. Although the literature has considered extensions to open

economy settings (see for instance Gertler et al. (2007) and Gilchrist (2003)), the

important role of trade finance has not been incorporated in line with empirical evidence

from the behavior of international trade flows. This is the first paper to incorporate

trade finance in an open economy macroeconomic framework and generates several

avenues for future research and inquiry. A central message in the paper is that relative

69

differences in external sectors and bilateral trade flows across countries are critical in

determining the impact of trade finance constraints on propagation of shocks. Given

that these effects can be large, more empirical investigation into the nature and range

of these asymmetries is likely to be an important contribution towards understanding

the propagation of macroeconomic shocks, especially for small open economies.

Models incorporating the financial accelerator have become prominent in the DSGE

literature, especially since the financial crisis. In order to isolate the role of trade finance

in the simplest possible setting, this paper abstracted from the interaction between firm

value and external finance premia. Endogenizing the external finance premium while

maintaining the international vs intra-national trade distinction would be an extension

worth pursuing in future research.

The approach in this paper is primarily positive and is focused on analyzing the role

of trade finance constraints in affecting the propagation mechanism of shocks. Given

that the data exhibits a strong preference for incorporation of the cost side features

studied in this paper, normative aspects are also worthy of consideration in future

research. Most important amongst these is likely to be a characterization of optimal

monetary policy in models incorporating trade finance constraints. Although Ravenna

and Walsh (2006) characterize the optimal monetary policy problem in the presence of

the cost channel, they do so in a closed economy setting in which the cost side effects

come exclusively from labor financing constraints. As emphasized above, the more

important cost side effects are likely to come from international trade finance constraints

and their incorporation into an optimal monetary policy problem is likely to be a fruitful

avenue for future research, especially for economies that face a larger fraction of their

fluctuations from foreign shocks. The paper also outlines means through which fiscal

70

policy in the form of variations in import tariffs can act as a stabilization device in

conjunction with monetary policy. These and other normative aspects of the model are

likely to be promising avenues for future research.

71

2 Quantifying the Trade Finance Channel in an Estimated Two

Country Model

72

2.1 Introduction

Trade finance is identified as the “fundamental problem in international trade” by

Bekaert et al. (2009). An extensive literature in international trade has documented that

international trade is heavily reliant on external finance. In particular, these papers have

found that external finance is much more important for international trade as opposed

to intra-national trade. Several explanations for this phenomenon have been explored

in the literature. The most common explanation hinges on the fact that international

shipments take more time than domestic shipments (both travel time and time taken

for documentation and clearances),53 which implies that producers have to incur costs

of production much before revenues are obtained. Feenstra et al. (2011) provide a

theoretical model incorporating these ideas. International trade is also likely to be more

intensive in external finance because of higher information asymmetries associated with

cross border transactions.54

While the literature on trade finance is extensive, the implications of trade finance,

and in particular its link to monetary policy have not been explored in the literature.

This omission is particularly questionable given the fact that open economy models

that are commonly used in both academia and by central banks for policy analysis and

forecasting typically give a central role to international trade, which is the primary

and in some cases the only channel through which shocks can be transmitted across

countries.

Chapter 1 of this dissertation took the first step towards addressing this void in the

literature by introducing a role for trade finance and linking it to monetary policy in a53See Hummels and Schaur (2013) and Djankov et al. (2006).54See Schmidt-Eisenlohr (2013) for a theoretical exploration of this point.

73

two country Dynamic Stochastic general Equilibrium (DSGE) framework. It showed

how trade finance affects the propagation of business cycle shocks and identified key

parameters that are critical in determining the degree and extent to which trade finance

matters for business cycle fluctuations and hinted that trade finance is likely to matter

more for spillover effects of shocks to other countries rather than the effect of shocks on

their country of origin itself. Being the first attempt to understand the link between

trade finance and business cycles, that chapter however raises more questions than

it answers. In particular, it shows how the influence of trade finance can depend on

different model parameters, but for some of these parameters it does not provide good

insights into what reasonable values are likely to be (for instance the import price

flexibility). Uncovering these parameters from both micro and macro sources, and

quantitatively assessing open economy business cycle models incorporating trade finance

is thus likely to be a fruitful avenue for future research.

This chapter takes a first step in this direction by estimating a two country DSGE

model with trade finance using data from two regions that constitute one of the largest

trading relationships in the world-the US and Euro zone (EZ). The focus in this chapter

is three fold: (a) parameter estimation (b) model comparison and (c) a quantitative

analysis of the role played by trade finance in business cycle fluctuations.

Regarding parameter estimation, particular emphasis will be given to parameters that

were identified in the previous chapter as critical in determining the influence of trade

finance in business cycle fluctuations. These include parameters governing the import

price flexibility as well as the elasticity of marginal cost of retailers with respect to the

risk free rate (δ). One question motivating this research was the fact that while open

economy macro models typically give a central role to international trade, they ignore an

74

important feature of international trade (namely trade finance) which has been shown to

be important in the trade literature. How significant is this omission, and should there

be a move towards incorporating models involving trade finance? The model comparison

exercises in this paper will address these questions and discuss scenarios under which

the case for incorporating trade finance in macro models is strongest. Lastly, based

on the results of various versions of the estimated model, the chapter will try to show

how important trade finance is, in quantitative terms, in accounting for business cycle

fluctuations after controlling for model and parameter uncertainty.

The main findings of the chapter can be summarized as follows. The estimation

results reveal robust evidence in favor of there being an asymmetry in the import price

flexibility between the US and EZ. In particular, US import prices are found to be

much more flexible compared to EZ.55. The estimates for the other key parameter-the

elasticity of marginal cost of import retailers with respect to the risk free rate, are also

consistent with values postulated in chapter 1. Moreover estimation of different versions

of the model (in particular ones with and without trade finance) provide evidence in

favor of models incorporating trade finance and shows that trade finance is indeed

quantitatively important in accounting for business cycle fluctuations.

2.2 Model

In order to quantitatively assess the implications of trade finance for business cycle

fluctuations in both the domestic and foreign countries, a two country DSGE model

will be used. The model is outlined in chapter 1 of this dissertation. It falls within55This is also in line with some prior evidence from Lubik and Schorfheide (2006), although, as will be argued and

shown later, the evidence in this paper is more robust

75

the NOEM (New Open Economy Macroeconomics) and builds on the work of Gali and

Monacelli (2005), Monacelli (2005) and Lubik and Schorfheide (2006). To summarize,

the model is a standard two country DSGE model augmented with the cost channel of

monetary policy in the form of trade finance. On the household side, a representative

agent makes decisions of behalf of households in each country and chooses labor supply,

consumption and bond holdings in order to maximize a time separable utility function.

Markets are complete (both within and across countries). Two sets of firms comprise

the production and retail side of the economy. Goods producing firms hire labor and

produce output according to a constant returns to scale technology. They sell their

goods directly to domestic consumers or to firms in the import/export sector. The

import -export sector comprises of firms which are responsible for shipping goods across

international borders and delivering them to consumers in countries different form the

country of production. Multiple intermediation stages may be involved in this process.

Some or all of these firms are assumed to be credit constrained and are required to

borrow at the risk free rate (or a rate linked to the risk free rate) in order to satisfy

their working capital needs. Monetary policy is governed by a central bank that sets

interest rates according to a standard interest rate feedback rule.56

2.3 Estimation

The different models in this paper are estimated using bayesian techniques. While

in principle the model can be estimated using frequentist likelihood based methods,

two aspects of the nature of the problem at hand make the bayesian framework more

suited for the purpose of this paper. Firstly, the bayesian framework allows for explicit56A detailed description of the model can be found in chapter 1.

76

incorporation of information from outside the model in the form of prior distributions.

Likelihoods in highly non linear (in terms of parameters) models like this are likely to be

multi-modal and not well behaved in certain regions of the parameter space. Hence even

in a frequentist setting the researcher has to guide the estimation routine by providing

appropriate set of starting values. The bayesian framework makes this more explicit in

the form of prior distributions. Moreover, the model is not stable for all values in the

parameter space. For instance, the coefficient on inflation in the taylor rule has to be

high enough (typically greater than one) for the model to have a unique solution with a

non explosive path for inflation. 57 Priors can be used to ensure that the unstable regions

of the parameter space are assigned low or zero probability. Secondly, the bayesian

framework is much more amenable to post-estimation analysis including model selection

and comparison (especially for non-nested models). Since a major aim in the empirical

part of the paper is to document evidence for or against models incorporating trade

finance, model comparisons will be used extensively, making the bayesian framework

more appealing.

Within the Bayesian estimation setting, the estimation is based on a full information

approach which considers the likelihood of the data for each model in the presence of

multiple shocks that have been identified in the prior DSGE literature as important

drivers of business cycles. Since impulse responses to shocks are a useful and intuitive

way of summarizing the properties of DSGE models, a common estimation routine in

the literature involves impulse response matching-where parameters of the model are

chosen to minimize the distance between impulse responses to a shock in the model and

impulse responses obtained from the data using an identified empirical model (like a57See Blanchard and Kahn (1980) for conditions under which linearized rational

expectations models of the form considered here have unique and stable solutions.

77

structural vector autoregression). 58. Since as emphasized in chapter 1 the influence

of trade finance is most noticeable in the case of monetary policy shocks, impulse

response matching vis-a vis monetary policy shocks seems to be a natural candidate

for estimation. However, as has been shown in the prior DSGE literature, monetary

policy shocks account for only a small fraction of fluctuations in advanced economies,

and restricting attention to them would come at the cost of ignoring the insights that

can be gained from looking at a broad array of shocks that account for majority of

business cycle fluctuations. Moreover, identifying monetary policy shocks in the data

has been the subject of much contentious debate and no consensus has emerged in the

literature.59Paradoxical results across sample periods, as documented in Ilzetzki and Jin

(2013) and Crowe and Barakchian (2010) have further questioned common identification

schemes for monetary policy shocks, and Fernández-Villaverde et al. (2005) too have

cautioned against the VAR based impulse response matching approach. The remainder

of this section provides a brief summary of the bayesian estimation approach that will

be used. 60

Preliminaries

Let M denote a generic model and let θM be the vector of parameters associated with

it. Let Y denote the data that is used to estimate the model (note that Y does not have58See for instance Christiano et al. (2005), Miyamoto and Nguyen (2014) and Ravn

et al. (2010)59In broadly the same sample period, while Christiano et al. (2005) find a moderate

and persistent fall in GDP in response to a monetary contraction while ROMER andROMER (2004) find a much sharper fall (more than twice compared to Christiano et al.(2005)). Using an identification scheme based on sign restrictions, Uhlig (2005) on theother hand finds a positive response of GDP in response to a monetary contraction.

60For a detailed discussion of Bayesian Estimation in the context of models like thethe present one see Schorfheide (2011).

78

an M subscript, i.e it is assumed that the data used is the estimation routine is constant

across models). Bayesian estimation proceeds by specifying a prior distribution over

θM which is denoted here by P(M, θM). The prior is then combined with the likelihood

computed using the data to form the posterior distribution of parameters as follows:

P(θM|M,Y) ∝ P(Y|M, θM)P(M, θM) (2.1)

Draws from the posterior distribution are generated by applying the Gibbs Sampler

using standard Markov Chain Monte Carlo (MCMC) techniques.61

Model Selection

The marginal density of the data given the model M is given by:

P(Y|M) =

ˆθM

P(Y|M, θM)P(M, θM) (2.2)

This quantity has the interpretation of being the probability of observing the data

given the true model is M. In order to compare two models M1 and M2 , first the prior

odds are specified for both models. These are then combined with the marginal densities

to obtain posterior odds ratios which are used for the purpose of model comparison.

PO1|2 =P(Y|M1)P(M1)

P(Y|M2)P(M2)(2.3)

One advantage of the bayesian framework is that the models do not have to be

nested.62 Throughout this paper, a non informative prior is assumed on the models61See Koop et al. (2007) for an overview of MCMC techniques.62Note however that in order for the data densities to be comparable, the data used

79

(P(M1) = P(M2) = 0.5) so that the ratio of marginal data densities is equal to the

posterior odds ratio, which in this case is also equal to the frequently quoted statistic

called the bayes factor.

2.4 Data

The model is matched to the data by treating the US and Eurozone as the two

countries comprising the world economy. The sample period is 1983Q1-2007Q4. The

period from 2007 onwards has been characterized by abnormally low interest rates

with US interest rates stuck at zero and the European interest rates exhibiting a wide

divergence across countries. Since the focus of the paper is to capture external finance

premia as captured by interest rates, the period since the financial crisis is not suited

for the study for both the reasons mentioned above.

Table 7 lists the variables used as observables in the estimation (A more detailed

description along with data sources can be found in appendix B.3). These comprise of

short term nominal interest rates, the euro-dollar nominal exchange rate, GDP growth

rates and various inflation rates for the two countries, as well as the change in bilateral

trade to GDP ratio. Compared to previous studies like Lubik and Schorfheide (2006)

that have used only one measure of prices (namely the CPI inflation) I use both CPI

and GDP deflator based inflation as well as trade data (and an import price index for

the US in some specifications). This is done in order to make the likelihood of the model

more informative regarding the new features and parameters introduced in the model.

The US data is taken from the Bureau of Economic Analysis and the European data is

in estimating the two models should be the same and the priors should be proper (i.ethey should define a valid distribution that integrates to one). These conditions will beimposed throughout the paper in order to keep the model comparisons valid

80

taken from the European Central Bank’s Area Wide Model (AWM) database. Bilateral

Trade data comes from the IMF’s Direction of Trade Statistics (Database). The DOTS

covers only merchandise trade which in the absence of more comprehensive data will

be used as a proxy for aggregate trade.63 Prior to estimation, all the data is seasonally

adjusted and demeaned.

Table 8 provides the correlation matrix for some observables used in the estimation.

Note that although the GDP deflators and the US import price deflators are positively

correlated with their respective CPI inflation rates, the correlation is not perfect64,

indicating that the addition of these additional series is indeed likely to provide more

information in the likelihood and hence the posterior of the model. Figure 2.1 plots

some of time series used in the estimation. As is evident in figure 2.1a, the volatility of

import price inflation far exceeds the volatility of other inflation series. to account for

this the estimation procedure would allow for the possibility of measurement error with

a relatively high prior variance, as discussed later. The main results in the paper are

also robust to the exclusion of this variable.

Shocks

All estimated models allow for a minimum of 10 shocks. These include government

spending shocks, idiosyncratic (country specific) productivity shocks, labor supply shocks

and monetary policy shocks for each country, as well as a global productivity shock

and a shock to the nominal exchange rate depreciation rate. Moreover, since import63Since DOTS does not explicitly have Eurozone imports from the US, I take the

difference between European Union imports and imports by Britain.64The highest correlation amongst these variables is between the US CPI and GDP

deflator based inflation with a value of 0.63.

81

Table 7 – Observables and Data Sources

Interest RatesRUS Effective Federal Funds RateREU EURO Area nominal interest rate

PricesπUS,CPI CPI inflation,USπUS,GDP GDP deflator Inflation. USπEU,CPI CPI inflation,EUπEU,GDP GDP deflator Inflation. EUπUS,IMP Import price inflation, US

Exchange Rate%4E Nominal Depreciation rate of UD dollar against EURO65

Output4Y US GDP growth Rate, US4Y EU GDP growth Rate, EU

Trade4(TradeGDP

)Change in Trade/GDP ratio

4(ImportGDP

)Change in Imports/GDP ratio

82

Table 8 – Correlations Between Observables Used in Estimation

4Y US iUS πCPI,US πGDP,US πIM,US 4Y EU iEU πCPI,EU πGDP,EU 4E

4Y US 1

iUS 0.142 1

πCPI,US -0.042 0.311 1

πGDP,US -0.015 0.368 0.627 1

πIM,US -0.098 -0.199 0.606 0.155 1

4Y EU 0.126 0.236 0.039 0.047 0.048 1

iEU 0.088 0.698 0.323 0.384 -0.16 -0.063 1

πCPI,EU 0.157 0.498 0.459 0.552 0.025 -0.124 0.649 1

πGDP,EU -0.056 0.287 0.499 0.732 0.124 0.113 0.185 0.416 1

4E -0.156 -0.107 0.011 -0.195 0.409 -0.009 -0.067 -0.242 -0.243 1

83

Figure 2.1 – Time series Plots of Data Used in Estimation

(a) US Inflation Rates

1985 1990 1995 2000 2005

−10

−5

0

5

10

15

20

CPI

GDP

IMPORT

(b) EU Inflation Rates

1985 1990 1995 2000 2005

−2

−1

0

1

2

3

4

5

CPI

GDP

(c) US GDP Growth Rate

1985 1990 1995 2000 2005

−1.5

−1

−0.5

0

0.5

1

(d) EU GDP Growth Rate

1985 1990 1995 2000 2005

−1

−0.5

0

0.5

1

(e) Nominal Interest Rates

1985 1990 1995 2000 2005

−4

−3

−2

−1

0

1

2

3

4

5

US

EU

(f) Nominal Depreciation

1985 1990 1995 2000 2005−12

−10

−8

−6

−4

−2

0

2

4

6

8

Notes: This figure plots the 10 time series used in the estimation. All data is at quarterly frequencyfrom 2003Q1-2007Q4 and is seasonally adjusted and demeaned.

84

and export prices are particularly vulnerable to miscalculation, 66 I explicitly introduce

measurement errors in this variable whenever it is included in the estimation exercise.

Another reason to introduce measurement error in this equation is evident from 1.29,

which shows that there is a linear relationship between three observables and hence

stochastic singularity would arise in the absence of such a measurement error.

Priors

The first four columns of table 9 list the priors used in the estimation prices. Most of

the priors are based on priors and estimates from Lubik and Schorfheide (2006), Smets

and Wouters (2007) and Smets and Wouters (2003). There are two parameters that

quantify trade finance dependence which are new in the paper (δhf and δfh). Regarding

δhf and δfh, no off-the-shelf parameter estimates are available as reliable benchmarks.

Relaying on the observations from calibration results a value of 2 is used as the mean

for the prior. A fairly high standard deviation is allowed in the prior in order to

reflect parameter uncertainty. Regarding the elasticity of substitution (η), a prior of

1 is assumed as a compromise between the macro and micro evidence regarding the

magnitude of this parameter as argued before.

2.5 Results

Parameter Estimates and Model Comparison

Tables 9 and 10 summarize the prior and posterior distribution of the estimated66see for instance Nakamura and Steinsson (2009)

85

parameters for the model in which all trade is financed by borrowing at the US interest

rate. This is the model which has the highest bayes factor, as will be discussed later.

It is pertinent to note that the posterior estimates of the price stickiness parameters

imply that the data supports a model in which there is asymmetry in the passthrough

into import prices across the two countries. While the passthrough into EU import

prices is quite low (θEU Import has a posterior mean of 0.87), the corresponding value

for the US is fairly high (posterior mean of θUS Import is 0.38). The obvious candidate

behind this discrepancy seems to be the US import price index. Since import prices are

known to be highly volatile, and since the estimation uses import prices for only the US,

it is likely to lead to high passthrough estimates (low price stickiness parameters). This

however is not the case, since the passthrough estimates do not change much even if the

US import price inflation is removed from the list of observables used in the estimation,

which is the case in the reported results.67 These results are in line with estimates from

Lubik and Schorfheide (2006) who also find evidence in favor of this asymmetry. Table

11 shows a comparison of the posterior means for the Calvo parameters from table 9. In

their case this difference may also be driven by the choice of their prior distribution,

which is asymmetric and implies higher price flexibility in the US compared to EU for

both domestic and import prices.68 This paper on the other hand does not impose this

asymmetry ex ante.

Table 12 reports the log marginal density for various specifications of the model that

are estimated, along with the bayes factor for each model in comparison to the model

without trade finance. Assuming the prior to be the same across models, numbers in67Even when it is included, the estimation procedure explicitly allows for measurement

error in this variable in order to account for the extremely high volatility of this variablecompared to other prices used in the estimation.

68They rely on Bils and Klenow (2004) and Angeloni et al. (2006) to impose a highprior on Europe and low prior on the US.

86

Table 9 – Summary of Prior and PosteriorPrior and Posterior Distribution of Estimated Param-eters

Parameter Description Prior PosteriorDistribution Mean Stdev Mean 90% C.I

θUS Calvo Domestic beta 0.5 0.05 0.837 0.8 0.874

θUS ImportCalvo Import beta 0.5 0.1 0.377 0.229 0.518

θEU ImportCalvo Import beta 0.5 0.1 0.872 0.726 0.986

θEU Calvo Domestic beta 0.5 0.05 0.75 0.695 0.807

σc Intermemporal Consumption Elasticity gamma 1 0.25 4.512 3.309 5.751

σL Labor supply Elasticity gamma 2 0.5 1.541 0.966 2.092

h Habit Parameter beta 0.5 0.1 0.547 0.395 0.697

η Intra Temporal Elasticity gamma 1 0.3 0.408 0.25 0.558

φUSπ Taylor Rule Parameter gamma 1.5 0.25 1.926 1.591 2.232

φUSy Taylor Rule Parameter gamma 0.5 0.25 0.452 0.206 0.68

φUSe Taylor Rule Parameter gamma 0.1 0.05 0.031 0.01 0.051

φEUπ Taylor Rule Parameter gamma 1.5 0.25 1.862 1.524 2.219

φEUy Taylor Rule Parameter gamma 0.5 0.25 0.546 0.246 0.845

φEUe Taylor Rule Parameter gamma 0.1 0.05 0.03 0.008 0.05

ρUSA US TFP Persistence beta 0.8 0.1 0.996 0.992 0.999

ρUSR US Interest rate Smoothing beta 0.5 0.2 0.821 0.789 0.856

ρUSG US Government spending Persistence beta 0.8 0.1 0.963 0.941 0.985

ρEUA EU TFP Persistence beta 0.6 0.2 0.574 0.259 0.906

ρEUR EU Interest rate Smoothing beta 0.5 0.2 0.867 0.843 0.892

ρEUG EU Government spending Persistence beta 0.8 0.1 0.93 0.891 0.971

ρZ Global Productivity Persistence beta 0.66 0.15 0.461 0.258 0.661

δEU→US Trade Finance Parameter: US gam 2 0.75 2.27 0.991 3.423

δUS→EU Trade Finance Parameter: US gam 2 0.75 1.837 0.735 2.909

ρUSN US Labor Supply Shock persistence beta 0.85 0.1 0.81 0.743 0.878

ρEUN EU Labor Supply Shock persistence beta 0.85 0.1 0.894 0.849 0.939

Notes: The results are based on 200,000 MCMC draws (split across 2 chains) after burnin with the posterior mode used as the starting value for each parameter

87

Table 10 – Summary of Priors and Posterior distributions of Standard Deviations of shocks

Shock Prior PosteriorDistribution Mean Stdev Mean 90% C.I

Ah invg 1.253 0.655 1.167 0.873 1.463Gh invg 1.253 0.655 0.526 0.451 0.6Rh invg 0.501 0.262 0.161 0.139 0.183Af invg 0.501 0.262 0.464 0.224 0.707Gf invg 1.253 0.655 0.502 0.432 0.569Rf invg 0.251 0.131 0.138 0.12 0.156Z invg 0.627 0.328 0.337 0.236 0.4344E invg 4.387 2.293 4.166 3.673 4.643Nh invg 0.101 0.262 1.563 1.355 1.755N f invg 2 0.5 2.608 1.722 3.472

Notes: ’invg’ denotes the inverse gamma distribution. The last two rows correspondto measurement errors of the corresponding observed variables. h denotes the homecountry (US) and f denotes the foreign country (EU)

Table 11 – Comparison of Calvo Parameters with Lubik and Schorfheide (2006)

Lubik and Schorfheide (2006)Posterior Mean Posterior Mean 90 percent C.I Prior Mean

θUS 0.83 0.62 [0.49, 0.77] 0.5θUS Import 0.38 0.45 [ 0.17, 0.72] 0.5θEU Import 0.87 0.9 [ 0.82, 1.00] 0.75

θEU 0.75 0.61 [ 0.43, 0.81] 0.75

88

Table 12 – Marginal Likelihood for different models

Model Marginal data density Bayes Factor wrt No trade finance

1 No trade finance -1236.04 1

2 trade finance: both Interest rates -1233.71 10

3 US interest rate trade finance -1227.37 5825

4 EU interest rate trade finance -1236.15 0.9

5 Importer Interest rate trade finance -1227.42 5541

6 Exporter interest rate trade finance -1232.34 40

Notes: The second model “trade finance: both Interest rates” allows for trade finance to be dependenton both home and foreign interest rates

each column (i.e estimates based on the same number of observables) can be interpreted

as measures of the posterior odds ratios, with higher numbers (i.e lower absolute values)

indicating higher posterior odds for the corresponding model.69 The last column report

bayes factors computed with respect to the baseline model with no trade finance (which

by construction has a bayes factor of 1 with respect to itself.). Bayes factors greater

than one indicate that the respective model is more preferred by the data than the

baseline model. According to Jeffreys (1998) bayes factor greater than 30 is “very strong

” and a bayes factor greater than 20 is “decisive” evidence.

As can be seen from the first row, the models with trade financing with US interest

rates and importer interest rates carry the highest posterior probability and bayes factors.

The first of these is not surprising, given the central role that US monetary policy plays

in the global economy and given the fact that the dollar is also the primary vehicle69Note that this comparison is valid as long as the prior is proper, which is the case

throughout this paper.

89

currency in which international trade is conducted.70. The higher posterior marginal data

density of the model with importer interest rate trade finance is interesting. Although

majority of the empirical literature in trade finance has documented the link between

exporter monetary policy and volume of exports, theoretical justifications given for

these apply equally to the link between imports and interest rates as well. The question

of which channel (or both) is more important is an empirical question that calls for

more research and this paper provides indicative evidence that the link between imports

and external finance conditions in importing countries could be an important aspect

affecting business cycle fluctuations. In the data, the trade finance channel seems to

be governed by the interaction of US interest rates with US imports. Since European

imports play a limited role due to their low price flexibility, the models with US interest

rate and importer interest rate financing both seem to be consistent and the data is not

clearly able to distinguish between the two.71

Comparison of Shock Propagation Mechanism Across Estimated Versions of the Model:

This section illustrates the differences in propagation mechanisms using estimated

impulse responses for two shocks. Figure 2.2 shows the impulse response of a one

standard deviation US monetary contraction (median and 90 percent confidence bands)

using the estimated model with trade finance constraints and US trade finance (the

model with the higher posterior probability than the standard model). For comparison,

the figure also shows two impulse responses corresponding to the standard model.

One of these (labelled “Estimated w/o trade finance (Median)”) corresponds to the70For evidence regarding the latter, see Goldberg and Tille (2008).71The parameter estimates are also quite similar across the two models. Table 29 in

the appendix summarizes the parameter estimates for the latter model.

90

estimated model without trade finance constraints and the second (labelled “Simulated

w/o trade finance”) corresponds to the impulse response from the simulated model with

all parameters at the posterior mean from the model with trade finance constraints

except the trade finance dependence parameters themselves which are set to zero. These

are two alternate ways of comparing the results with the estimated model with trade

finance. Qualitatively, the results in figure 2.2 are broadly in line with the simulation

results discussed in chapter 1. Quantitatively, the figure shows that while the models

generate similar predications for the response of domestic GDP, they differ appreciably

in the response of foreign GDP and terms of trade. This is also true in figure 2.3 which

compares the estimated impulse responses to a monetary contraction with the model

with importer trade finance taken as the benchmark.

Figures 2.4 and 2.5 perform a similar exercise with two non monetary shocks-a one

standard deviation labor supply shock and a one standard deviation productivity shock

respectively. Once again, the results are qualitatively in agreement with the illustrations

in chapter 1. The productivity shock, which has a high persistence (the autoregressive

coefficient being 0.99) provides an opportunity to illustrate that since in line with

evidence form the empirical literature trade finance is modeled in a way such that it has

minimal impact at low frequencies, it is unlikely to make much difference in terms of

the response of variables to persistent shocks, as is found to be the case in figure 2.5.

These results convey that trade finance constraints have a larger impact in altering

the spillover effects of domestic shocks as opposed to the domestic effects themselves.

One implication of this is that for a large open economy like the US whose business

cycle fluctuations are mostly driven by domestic shocks, excluding trade finance from

models might be an innocuous omission. On the other hand, if the object of interest is

to study spillover effects from foreign shocks (as would typically be the case for a small

open economy), ignoring trade finance constraints can lead to severe misrepresentation

91

Figure 2.2 – US Monetary Contraction

1 2 3 4 5 6 7 8

−0.06

−0.05

−0.04

−0.03

−0.02

−0.01

(a) Home GDP1 2 3 4 5 6 7 8

−12

−10

−8

−6

−4

−2

0

2

4x 10

−3

(b) Foreign GDP1 2 3 4 5 6 7 8

0.02

0.04

0.06

0.08

0.1

0.12

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

0.5

1

1.5

2

2.5

3

3.5

4

4.5

x 10−3

(d) Foreign Nominal Interest1 2 3 4 5 6 7 8

0.05

0.1

0.15

0.2

0.25

(e) Home TOT1 2 3 4 5 6 7 8

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

(f) RER

1 2 3 4 5 6 7 8

−0.1

−0.08

−0.06

−0.04

−0.02

(g) US Inflation

Estimated with Trade Finance (Median and 90% CI)

Simulated w/o Trade Finance

Estimated w/o Trade Finance (Median)

Note: Baseline model (dotted line) assumes US interest rate trade finance.

92

Figure 2.3 – US Monetary Contraction

1 2 3 4 5 6 7 8

−0.07

−0.06

−0.05

−0.04

−0.03

−0.02

(a) Home GDP1 2 3 4 5 6 7 8

−12

−10

−8

−6

−4

−2

0

2

4

x 10−3

(b) Foreign GDP1 2 3 4 5 6 7 8

0.02

0.04

0.06

0.08

0.1

0.12

(c) Home Nominal Interest

1 2 3 4 5 6 7 8

1

2

3

4

5

6

x 10−3

(d) Foreign Nominal Interest1 2 3 4 5 6 7 8

0.05

0.1

0.15

0.2

0.25

(e) Home TOT1 2 3 4 5 6 7 8

−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

(f) US Imports

1 2 3 4 5 6 7 8

−0.1

−0.08

−0.06

−0.04

−0.02

(g) US Inflation

Estimated with Trade Finance (Median and 90% CI)

Simulated w/o Trade Finance

Estimated w/o Trade Finance (Median)

Note: Baseline model (dotted line) assumes importer country trade finance.

93

Figure 2.4 – US Labor Supply Shock

1 2 3 4 5 6 7 8

−0.15

−0.1

−0.05

(a) Home GDP1 2 3 4 5 6 7 8

−6

−4

−2

0

2

4

6

8

10

x 10−3

(b) Foreign GDP1 2 3 4 5 6 7 8

0.04

0.05

0.06

0.07

0.08

(c) Home Nominal Interest

1 2 3 4 5 6 7 81

2

3

4

5

6

7

8

9

x 10−3

(d) Foreign Nominal Interest1 2 3 4 5 6 7 8

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

(e) Home TOT1 2 3 4 5 6 7 8

−0.6

−0.5

−0.4

−0.3

−0.2

(f) RER

1 2 3 4 5 6 7 8

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

(g) US Imports

Estimated with Trade Finance (Median and 90% CI)

Simulated w/o Trade Finance

Estimated w/o Trade Finance (Median)

94

Figure 2.5 – US Productivity Shock

2 4 6 8 10 12 14 16

0.2

0.3

0.4

0.5

0.6

(a) Home GDP2 4 6 8 10 12 14 16

−0.06

−0.04

−0.02

0

0.02

(b) Foreign GDP2 4 6 8 10 12 14 16

−0.02

−0.01

0

0.01

0.02

0.03

0.04

(c) Home Nominal Interest

2 4 6 8 10 12 14 16

−2

0

2

4

6

8

10

12

x 10−3

(d) Foreign Nominal Interest2 4 6 8 10 12 14 16

−2.2

−2

−1.8

−1.6

−1.4

−1.2

−1

−0.8

(e) Home TOT2 4 6 8 10 12 14 16

1.2

1.3

1.4

1.5

1.6

1.7

1.8

(f) RER

2 4 6 8 10 12 14 16

−0.5

−0.45

−0.4

−0.35

−0.3

−0.25

−0.2

−0.15

−0.1

(g) US Imports

Estimated with Trade Finance (Median and 90% CI)

Simulated w/o Trade Finance

Note: Baseline model (dotted line) assumes US interest rate trade finance.

95

of the important transmission channels in the model. The intuitive underpinning for

this comes from the fact that trade finance exerts its influence on shock propagation

by affecting terms of trade which translate into changes in trade volumes. As far as

domestic economy is concerned, it is therefore just an additional channel through which

the main effects are likely to come from the domestic impact of shocks in variables only

weakly related to international trade. On the other hand, as far as the foreign economy

and spillover effects are concerned, the entire effect of the domestic shock is transmitted

through the external sector, which in turn is affected by trade finance constraints. As a

result, incorporation of trade finance constraints matters more for spillover effects of

shocks as opposed to domestic effects.

Robustness

The parameters quantifying import price flexibility as well as the elasticity of marginal

cost with respect to the risk free rate are critical in determining the role played by

trade finance in propagation of business cycle shocks. This section conducts a series of

robustness checks with regard to these parameters. Table 13 reports posterior means of

these parameters under different variations of the model. For each of the cases reported

in table 13, the prior mean and standard deviation of the parameters is the same as that

in the benchmark case (table 9) except when indicated in the first column.

Since the elasticity of intertemporal substitution is estimated to be somewhat higher

in comparison to the literature in the baseline case, the first row considers a model with

log utility. The second row considers another restriction on the model by fixing the

intra-temporal elasticity of substitution between domestic and foreign bundles As argued

in chapter 1, there is little consensus in the value of this parameter in the literature

96

Table 13 – Posterior Means of Key Parameters Under Different Model Assumptions/Restrictions

θUS Import θEU Import δEU→US δUS→EU

σc = 1 0.31 0.72 2.02 1.68η = 1 0.33 0.96 2.40 1.94

Domestic Cost Channel 0.33 0.84 2.36 1.89Sticky Wages 0.37 0.84 2.12 1.79

Notes: The prior mean and standard deviation of the parameters is the same as that inthe benchmark case (table 9) except when indicated in the first column.

and a value of 1 can be considered a compromise between the trade and business cycle

literatures.72 The third row considers a model in which the cost channel of monetary

policy is operational even in the domestic sector, i.e even the goods producing firms are

required to borrow in order to finance their wage bill. This is typically how the cost

channel of monetary policy has been modeled in the literature so far.73 As is evident

form the results reported in the table, the estimates of the main parameters of interest

are robust to all these departures from the baseline version of the model.

2.6 Implications for Monetary Policy and Beyond

The issue of spillover effects of monetary policy and the need and scope for monetary

policy coordination across central banks has received renewed interest following the

financial crisis which compelled many central banks to undertake extraordinary monetary72A more thorough approach would be to allow for dynamic elasticities as discussed

in Drozd et al. (2014) and Crucini and Davis (2013). However, this approach is notundertaken since the main message of the paper is robust to the value of the elasticityused.

73See for instance Christiano et al. (2005), Barth III and Ramey (2002) and Ravina(2007)

97

policy actions. In what turned out to be a somewhat controversial speech, Rajan (2014)

emphasized the need for reconsidering the role for monetary policy coordination and

for countries-especially the US-to take into account the effects of their monetary policy

actions on the rest of the world. This analysis lends support to the arguments made in

the speech on several counts. Insofar as trade finance is an important channel through

which monetary policy affects domestic and foreign economies, this paper highlights that

under certain conditions the spillover effects of monetary policy can be fairly large and

can differ both qualitatively and quantitatively from the predictions of standard models.

Moreover, it also shows that trade finance alters the spillover effects of domestic shocks

in significant ways while affecting the domestic economy only mildly. This implies that

although it might be beneficial to re-evaluate the merits of monetary policy coordination

in light of these results, it might not necessarily be in the best interest of the central

country (in this case the US) to do so.

Evidence regarding the importance of US interest rates as the primary determinant

of trade finance conditions uncovered here is in line with the central role that US

monetary policy is acknowledged to play in the global economy.74 To the extent that

US is the primary vehicle currency for international trade (Goldberg and Tille 2008),

US interest rates are likely to be the primary determinants of external finance premia in

international trade, a consequence of the “exorbitant privilege”. Since this is likely to be

the case more generally across countries and especially emerging markets and developing

economies, a new channel through which US monetary policy can affect countries is

uncovered in this analysis, above and beyond traditional trade and financial linkages.

For instance, even if there are two economies that trade with each other but have no74See for instance Rey (2013) for the critical role played by US monetary policy in

driving the global economic cycle.

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trade or financial linkages with the US, US monetary policy can affect these economies

by affecting the external finance conditions that trade firms are subject to. This could

be one explanation behind what has been labelled in the media as the “taper tantrum”,

the sudden and sharp movements in emerging market currencies at the mere mention

of the possibility of US monetary policy tightening in the future, the severity of which

cannot be explained on the basis of fundamentals.

Because interest rates affect external finance premia governing international trade,

competitive devaluations or “currency wars” may not always be a zero sum game and

may actually end up increasing welfare even in the absence of distortions associated

with monopoly power on the part of firms.

Although the focus of the present paper is on international aspects of trade finance,

insights developed here can also enrich our understanding of monetary transmission in

closed economies characterized by complex input output linkages and sectoral hetero-

geneity in external finance dependence. Sectors that are most sensitive to the cost side

effects of monetary policy are the ones that have (a) high external finance dependence

(b) large value of distance to final demand and (c) large values of number of embodied

production stages. Regarding (a), Rajan and Zingales (1998) document substantial

heterogeneity in the external finance dependence of different sectors in the US. (b) and

(c) are statistics defined in Fally (2012) that quantify how deeply a sector is involved in

input output structure of the economy. For instance, if all sectors have equal external

finance dependence, downstream sectors which purchase inputs from other sectors in the

economy are likely to be more vulnerable to monetary tightening, and consequently are

likely to benefit most from monetary easing.75 If recessions are concentrated in certain

key sectors in the economy and if these sectors can be clearly characterized based on the75Similar arguments have been made in Bigio and La’O (2013)

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criteria above, this information can help predict how useful monetary policy is likely to

be in dealing with the recession. For instance, according to the estimates in Antràs et al.

(2012), the automobile industry has a fairly high downstreamness measure amongst

industries in the US. The analysis in this paper seems to suggest that as far as the cost

side effects of monetary policy are concerned, this industry is likely to get high cost side

benefits from monetary easing.

When interest rates affect the cross border movement of goods as in this model,

they play a role similar to the one played by tariffs. This raises the possibility of

using fiscal policy in the form of variations in tariffs on imports as a stabilization tool

to complement monetary policy actions. For instance, consider an economy suffering

from a positive output gap characterized by high inflation. The monetary authority

would like to respond to this situation by raising short term interest rates. However,

in addition to the desired effect of lowering aggregate demand, this would also lead to

the unintended disruption in international trade due to higher financing costs, which

apart from reducing welfare would also have the undesirable effect of shifting some of

the demand for imports towards home goods. Clearly the single instrument of interest

rate cannot address these two concerns simultaneously. In such situations, reductions in

tariffs can serve to mitigate the unintended consequences of the monetary policy action

by reducing the price of imports and hence reducing the fall in volume of international

trade. Similar benefits can also be derived from appropriate management of capital

controls.

The analysis in this paper also has important implications for the implementation of

macro prudential regulations, especially in light of the new Basel II guidelines under

which trade finance instruments are considered “safe assets”. This has several implications

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for business cycle fluctuations and welfare of economies through the trade finance channel

in both the short and the long run. Given the low risk weights, banks would have higher

incentives to hold more trade finance instruments on their balance sheet, some of which

may be a consequence of portfolio rebalancing. Given that international trade in the

real word is much lower than what standard welfare maximizing trade models would

predict76, intuition suggests that higher trade volumes facilitated by easier trade finance

can only be expected to raise welfare. The analysis here however points out that while

this intuition may be true in the medium to long run, in the short run the implications

for higher trade finance could be more subtle, and as shown above, higher trade finance

may sometimes amplify business cycle fluctuations. The lower risk weights are also likely

to lead to higher provision of trade finance going forward due to regulatory reasons.77

These regulations would give banks a greater incentive to fund international trade in

economic downturns and recoveries. While this would help mitigate the fall in trade

(and associated welfare loss), the increase in trade finance provision may come at the

cost of domestic firms being rationed out of the credit market. Since domestic firms

are typically smaller than firms involved in international trade (Bernard et al., 2007)

this may have the undesirable effect of denying bank credit to those firms which need it

the most, since unlike large firms small firms typically don’t have access to the broader

financial market to raise funds and have to rely on bank loans.78

76see for instance Obstfeld and Rogoff (2001) and the extensive literature on home biasin trade.

77 Moreover, letters of credit are typically off-balance sheet assets that don’t consumebank capital.

78Gertler and Gilchrist (1991) show that monetary contractions affect small firmsdisproportionately more than large firms

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2.7 Conclusion

Using bayesian techniques, this paper estimates a two country DSGE model with

trade finance, using data from the US and Eurozone (EZ), two regions which share

one of the largest bilateral trading relationships in the world. Based on formal model

comparison exercises, models that appropriately incorporate trade finance constraints

provide a better characterization of the data. Secondly, trade finance is quantitatively

important, even after accounting for parameter uncertainty. Thirdly, as hinted in chapter

1, trade finance matters more for spillover effects of shocks rather than the effects on

the country of origin. The intuition for this is as follows: Consider each country to

be comprised of a domestic sector and an external sector. because of home bias in

consumption, the domestic sector is typically larger than the external sector. Therefore,

when a shock originates in the domestic sector, its primary impact is through the direct

impact that it has on the domestic sector. For instance, in the case of a monetary

contraction, the primary impact comes from a rise in the risk free rate, which alters

the consumption-saving decision of households and leads to a fall in aggregate demand

and prices. If the economy is open, there might be an additional effect of the shock

which comes from the external sector (in the case of a monetary contraction, this would

be a fall in demand due to an appreciation of the exchange rate). However, since the

external sector is small, the second effect is small as far as the domestic economy is

concerned. Trade finance by its very nature only influences the external sector, and

hence as far as the domestic economy is concerned, it only generates a small effect. This

is no longer true for the spillover effects of the shock to other countries. These spillover

effects are transmitted exclusively through the external sectors of the two countries, so

if trade finance can influence the dynamics of these external sectors, it can make large

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alterations to the spillover effects.

The parameter estimates across models provide compelling evidence for asymmetry

in import price flexibility across these two countries. In particular, US import prices are

found to be more flexible than their european counterparts. In line with the theoretical

results discussed in chapter 1, this distinction implies that trade finance matters not

only for trade volumes and terms of trade, but also for variables like GDP and inflation.

This is the first paper to consider the implications for heterogeneity in import price

flexibility across countries and estimate the relevant parameters. While the estimates are

somewhat in agreement with Lubik and Schorfheide (2006), who also estimate analogous

parameters, they seem to be at odds with the extensive literature on passthrough

into import prices which has found the passthrough (in particular with regards to the

nominal exchange rate) into US import prices to be low, pointing to a very low import

price flexibility estimate for the US.79 Although a thorough exploration of this apparent

discrepancy cannot be complete without detailed examination of micro data and is

beyond the scope of this dissertation, two possible explanations can be conjectured.

Firstly, while the trade literature has focussed for the most part on exchange rate

passthrough, the asymmetry revealed here is with regard to passthrough of marginal

costs into prices more generally, including other components of marginal costs apart

from the nominal exchange rate. Secondly, while the trade literature has focussed on

import prices at the dock, the estimates in the model correspond more to retail price of

imports. Understanding the journey of imports from the dock to eventual retail outlets,

including the characteristics of the different markets and intermediaries involved would

be an important part of interpreting these findings.

79See for instance Gopinath et al. (2010)

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3 Global Value Chains and Effective Exchange Rates at the

Country-Sector Level (With Zhi Wang and Shang-Jin Wei)

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3.1 Introduction

The Real Effective Exchange Rate (REER) is one of the the most quoted indices

in international economics among academics, policy makers and financial market par-

ticipants. A google search on “effective exchange rates” yields close to 58 million hits,

higher than terms like “inflation targeting ”(~5 million) and “comparative advantage”(~9

million). The underlying purpose behind the construction of REER is to have a statistic

that measures competitiveness by quantifying the sensitivity of demand for output

originating from a particular country as a function of changes in world prices. It is

a partial equilibrium construct which takes observed price changes as given and does

not require modeling of primitive shocks that lead to those price changes, or any other

general equilibrium constraints like balanced trade.80 Among the common applications

of REER in international macroeconomics is its use as an indicator to draw inferences

regarding currency manipulation, currency misalignment and vulnerability to crises–see

for instance Chinn (2000) , Goldfajn and Valdés (1999) and Gagnon (2012).

The importance of REER is further evident from the time, effort and resources

devoted to computing REER indices by leading organizations like the International

Monetary Fund (IMF), Bank of International Settlements (BIS), OECD as well as

various central banks around the world.81

Standard REER measures make a number of simplifying assumptions which we

evaluate in this paper. For instance, they assume that every country exports only final

goods which are produced without using imported intermediate goods. The first point80See Chinn (2006) for a primer on the concept of REER and Rogoff (2005) for an

application and discussion.81For the IMF REER computation see McGuirk (1986) and Bayoumi et al. (2005). For

the Federal reserve’s REER measure see Loretan (2005). The BIS’s REER methodologyis summarized in Klau et al. (2008)

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we wish to emphasize is that this assumption is not innocuous, as the following example

shows.

Consider a stylized world with three countries involved in a global value chain–China,

Japan and the US. Suppose Japan manufactures raw materials for the production of

a mobile phone and ships it to China which acts as an assembly point. China in turn

exports the finished product to the US which is then consumed by US consumers.

According to the traditional REER measures like the one used at the IMF, the phone

would be classified as China’s “product” and China would be assumed to be competing

with other providers of phones. Consequently these models would conclude that an

increase in the price of a mobile phone in Japan would lead to an increase in the demand

for China’s mobile phone and hence increase its competitiveness. In reality however,

China is not producing the entire phone but is the producer of assembly services, which

accounts for only a small fraction of the total value of the product. It therefore competes

with other providers of such processing services and not phone manufacturers. Once

we recognize this, it becomes clear that an increase in Japanese prices of mobile phone

components could very well lead to a decline in demand for China’s services and hence

a decline in its competitiveness.

This example shows that REER computed by organizations like the IMF is not only

inaccurate in terms of magnitude, but may also have the wrong sign. Given that trade in

intermediate goods can potentially have a major influence on the REER, it is important

to incorporate it in the model used to compute REER, especially given the prominence

and rising trend in intermediate goods trade in the last two decades.82

82For OECD countries Miroudot et al. (2009) find the share of trade in intermediategoods and services to be 56% and 73% respectively. As emphasized in Baldwin andLopez-Gonzalez (2012), intermediate goods trade and vertical specialization have grownmany fold in developing countries starting in the 1980s (see also Wang et al., 2013) Also

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Another limitation common to all previous work in this literature is that REER is

defined at the level of individual countries.83 With increasing specialization and trade

in intermediate inputs, inter-sectoral linkages between countries differ substantially

from aggregate country level relationships. Wang et al. (2013) (henceforth WWZ)

have documented this heterogeneity substantially. In particular, they find that total

foreign content (VS) sourced from manufacturing and services sectors used in world

manufacturing goods production has increased by 8.3 percentage points from 1995

to 2011 (from 22. 5% in 1995 to 30.8% in 2011). Moreover, they show that this

increase is primarily accounted for by the increase in foreign double counted terms

(FDC) which are a result of back and fourth trading between countries. Once we

take the concept of global value chains seriously, we have to recognize the fact that

different sectors in a country tend to participate in cross-border production sharing by

different extents and in different ways. For example, according to WWZ (2013), some

sectors mostly engage in regional value chains (i.e., buying or selling intermediate inputs

with neighboring countries), whereas others engage in truly global value chains (i.e.,

sourcing and selling a significant amount of inputs to countries on different continents.)

This implies substantial heterogeneity in changes in competitiveness across sectors to a

given change in foreign price vector. An aggregate country level measure is incapable of

capturing these. Indeed, in section 3.10 we document several instances where the REERs

important is the import content of exports, epitomized by the prevalence of processingtrade involving Asian economies, especially China. Koopman et al. (2014) find that theimport content of exports is as high as 90 percent for some sectors in China.

83Although Goldberg (2004) develops sectoral effective exchange rates for the US andKiyotaka et al. (2012) and Kiyotaka et al. (2013) do so for Japan, Korea and China,these papers do not take into account trade in intermediate inputs or differences inelasticity of substitution. In fact they proceed in a reduced form manner and do notallow for even third country competition as is done in our framework as well as in themodels by the IMF and BIS.

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move in opposite directions for different sectors within a country. In these cases where

the country level REER moves in the opposite direction to certain key sectors within the

country, lack of information on the latter can lead to false conclusions and inefficient or

even counter-productive policy measures. For example, we document in figure 3.2 that

Mexico as a whole has experienced a loss in competitiveness (appreciation) starting in

1995. One policy measure this may instigate is (implicit or explicit) subsidies, especially

to exporters. However applying these measures uniformly across all sectors would be

erroneous since there are sectors like the financial intermediation sector that are already

experiencing a gain in competitiveness. This illustrates the usefulness of sector level

exchange rates in enabling countries to better target and manage their producers and

exporters. Although lack of data and absence of the global value chain phenomenon

had prevented the feasibility and need for such measures in the past, in this paper we

emphasize that this is no longer the case.

Recognizing all these shortcomings, this paper proposes a concept of REER that

improves upon the existing REER measures in the literature along four dimensions.

Firstly, by explicitly allowing for trade in intermediate inputs and distinguishing trade

by end use category, our model recognizes that value added and gross output are not the

same. We therefore compute different REER indices for value added (GVC-REER) and

gross output (Q-REER). Secondly, we start at the level of sectors within countries and

build our way up, allowing us to define and compute not just country REERs but also

REERs for sectors within countries. Given our data source (to be discussed in detail

later on in the paper) we can compute REER indices for 35 sectors within each of the 40

countries in the sample. We find substantial heterogeneity in the REER across sectors

within countries and are in a position to talk about competitiveness of individual sectors

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within the same countries. Thirdly, we estimate and explicitly incorporate different

elasticities of substitution across different groups of goods in our REER measure. This

is a significant improvement relative to other attempts to take GVCs into account

which continue to work with a simplified Cobb-Douglas case in which all elasticities are

identically equal to one. Lastly, we compute sector level price indices and use these in

our REER measure instead of the more coarse country level price indices (GDP deflator

or CPI) which have been used in the literature so far.

We show that our model can also be used to construct better measures of bilateral

real exchange rates (RERs). Bilateral RERs are typically used for either price level

comparisons or relative movements in competitiveness (see for example Chinn, 2006).

If the goal is the latter, then we show that the insights gained from our discussion of

REERs can be used to construct measures of bilateral RERs using sector level trade

flows that better reflect movements in relative competitiveness. We find in the data

that our measure of bilateral RER paints a substantially different picture compared to

the standard GDP deflator based RER for certain key country pairs. Section 3.11 for

instance shows that for US-China, we find that although the standard RER displays a

non monotonic pattern for the RER including substantial depreciation of the Chinese

exchange rate prior to the abandonment of the peg in 2005 (which was widely reported

and discussed among academics, financial participants as well as in the media) our RER

measure which exploits sector level linkages shows a secular appreciation during the

sample period.

It is worth emphasizing that our objective is to model relatively short-term and

small-scale movements in competitiveness. We therefore take the nature of GVC and

trade patterns across countries and sectors as given and do not consider the issue of

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endogenous off-shoring and production sharing decisions.84 Moreover, due to the complex

nature of the model we solve it using log linearization techniques. This further reinforces

the view that our REER indices are best suited for short-term movements resulting

from shocks that are not too large so as to affect organization of GVCs.

This paper is related to two different strands of the literature. First and foremost the

paper is a contribution to the literature on international trade and finance. The most

prominent and commonly cited REER measure today is the IMF’s REER measure. This

along with other commonly used REER indices like the ones by the Federal Reserve and

Bank of International Settlements (BIS) do not distinguish between trade in intermediate

and final goods and consider all trade flows to be in the latter category. The consequence

of making this assumption could be quite detrimental, as we have discussed above.

A few recent papers have recognized this drawback and have made attempts to address

them. Bems and Johnson (2012) (henceforth BJ) allow for trade in intermediates and

compute the REER weighting matrix at the country level. Bayoumi et al. (2013) propose

a measure of competitiveness in which they borrow the weighting matrix from the IMF

but adjust the price indices to acknowledge the presence of imported inputs. But these

papers work with the constant elasticity (Cobb Douglas) assumption and country level

(instead of more detailed sector level) price indices. Our attempt to incorporate sector

level price indices and build sector level exchange rates has a precedent in the work of

Bennett and Zarnic (2009). But their work does not incorporate trade in intermediate

goods and uses an IMF-like weighting matrix. Moreover, they use unit labor costs to

proxy for price of value added, whereas we have a more comprehensive measure of value

added price index at the sector level which includes not only labor but also capital.84There is a growing literature on organization of global value chains that looks into

these questions. See for instance Antràs and Chor (2013), Costinot et al. (2013) andJohnson and Moxnes (2012).

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In Table 14 we summarize our contribution to this literature by drawing comparisons

across the most influential as well as the most advanced REER computation frameworks

available. A check mark (√) indicates that the paper attempts to address the particular

attribute, irrespective of whether they achieve the desired objective in our opinion. In

fact, in most cases where there are check marks in the table, we show drawbacks that are

addressed by our framework. As will be shown in the sections to follow, our measure is

not only more comprehensive, but nests most of the common measures in the literature.

Table 14 – Comparison with the literature on computing REER

IMF FED BIS BJ BST BZ This paperValue added competitiveness

√ √

Sector level exchange rates/prices√ √

Trade in intermediate goods√ √ √

Heterogenous elasticities√

Key: BJ: Bems and Johnson (2012); BST: Bayoumi et al. (2013); BZ: Bennett andZarnic (2009);A check mark (√) indicates that the paper attempts to address the particular attribute,irrespective of whether they achieve the desired objective in our opinion

More broadly, the paper is motivated by and is linked to new but rapidly expanding

literature on global value chains and vertical specialization in trade (see Hummels

et al., 2001 and Baldwin and Lopez-Gonzalez, 2012 among many others) as well as

the literature on trade statistics and export accounting in the presence of intermediate

goods trade (Koopman et al., 2012 and Wang et al., 2013).

After briefly reviewing the concept of REER in section 3.2 we start by presenting a

simplified version of our framework in section 3.3 to illustrate some of the features of

our exchange rate measure before moving on to the general model in section 3.4 which

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is discussed in greater detail and applied to the data.

3.2 The Concept of REER as a Measure of Competitiveness

The real effective exchange rate measures change in competitiveness by quantifying

changes in the demand for goods produced by a country as a function of changes in

relative prices.85 To be more precise, if VJ is the demand for the goods produced (or

alternatively, value added) by country J , then the effective exchange rate of country J

is defined as:

4REERJ = 4VJ = GJ (4pni=1) (3.1)

where 4pni=1 is a vector of price changes in all countries including the home country.

Note that no other variables except the prices explicitly enter the function G(.). Hence

by construction REER is a partial equilibrium construct where the primitive shocks

that lead to the observed price changes are not modeled. Moreover the demand side of

the economy is assumed to be exogenous and the aggregate final demand is assumed to

be constant (although relative demands are allowed to change when prices change).

The function GJ(.) is homogenous of degree zero, so that the model satisfies neutrality

in the sense that if all prices (including the home price) double, then the relative demands

remain unchanged (and since by construction aggregate demand is held fixed, the absolute

demand for each good also remains unaffected).85In this literature the use of the word “competitiveness” is appropriate only in conjunc-

tion with the perfect competition assumption. With imperfect competition, an increasein demand for value added may coincide with a decrease in profits for the producers(as would be the case for instance with a monetary policy shock with sticky prices).It seems misleading to label this an increase in competitiveness of the producers. Wethank Charles Engel for pointing this out.

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It is worth pointing out that REER models like ours do not assume balanced trade

or any restrictions on the trade balance. Trade balances are allowed to be non-zero in

the steady state and are calibrated to their observed counterparts in the data. This is

in line with the partial equilibrium setup in which the demand side is exogenous.

Throughout the paper we work with a static partial equilibrium model. Before

describing the model it is pertinent to address concerns regarding its ostensibly restrictive

nature.

Competitiveness is a supply side concept and measures how changes in cost structure

of a producer makes its product more competitive by enabling it to capture demand

from other producers. In order to isolate the role of competitiveness it is therefore

critical to shut out other effects that might be operational, most notably aggregate

demand.

Consider the case of a favorable supply shock like a productivity shock or a tariff

reduction that affects a single producer. In the partial equilibrium setting of this paper,

the shock manifests itself only in the form of a lower price, which leads to an increase in

demand for the good (at the expense of other goods). This is interpreted as an increase

in competitiveness. In a general equilibrium framework, a supply shock of this form

will have additional effects. In particular, it will affect the real incomes of agents which

in turn will affect aggregate demand (and also its distribution in a heterogenous agent

economy). This latter effect, however, is not a direct consequence of the cost advantage

gained by the producer and hence must not be included in the competitiveness measure.

To make the point more precise, consider a two country (A and B), two sector (1 and

2) model and suppose (A, 1) is hit by a positive productivity shock. The direct impact

of this shock would be to lower the price of (A, 1). This in turn would lead to a shift

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in demand towards (A, 1) at the expense of demand going to all the three remaining

sectors. This demand is captured by (A, 1) due to its cost advantage triggered by the

favorable productivity shock. This is the effect that a competitiveness measure should be

designed to capture and our REER measure does exactly this. In addition, the favorable

productivity shock would most likely also lead to an increase overall demand (i.e quantity

demanded) for all goods. This effect may imply an increase in the quantity demanded

for either or all of the three remaining sectors. This latter increase however comes

despite an unfavorable movement in relative costs (i.e a decline in competitiveness),

and hence must not be interpreted as an increase in competitiveness as would be the

case if we measure competitiveness solely by increase in quantity demanded in a general

equilibrium setting. For instance, with home bias in consumption, the transfer effect

leads to an improvement in home terms of trade which in turn leads to an increase in

the absolute demand for foreign goods as well, but this happens despite an increase in

costs, not due to a favorable movement in costs which is what competitiveness in meant

to capture.

It is often relevant for researchers working with partial equilibrium models to justify

that the ignored general equilibrium effects are not likely to overturn their main partial

equilibrium conclusions. The goal in this paper, however, is the construction of statistic

as opposed to forecasting, comparative statics or explaining stylized facts in the data.

We therefore do not need to show robustness with respect to generalization of the model

beyond the partial equilibrium setup. On the contrary we argue that the question at

hand requires us to look precisely at partial equilibrium effects and although general

equilibrium effects might overturn partial equilibrium ones as hinted above, the latter

are not the object of attention as far as measurement of competitiveness is concerned.

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Regarding the static nature of the model, although the model does not have any

inter-temporal features like capital accumulation and investment, it nevertheless imports

the dynamics from the persistence of shocks in the data, which are the observed price

movements. In fact, the model is calibrated to the exact time series of price changes so

that we let the data completely govern the dynamic aspects of our REER measures.

Aside from effective exchange rates, unit labor costs (both at the country and sector

level) are often used as indicators of competitiveness. Although these are widely available

and easy to comprehend, REER, especially if constructed taking into account trade in

intermediate goods and sector level trade flows as in this paper, is superior as a measure

of competitiveness on several counts. Firstly the REER incorporates movements in

relative prices as opposed to looking at individual or a pair of prices in isolation. It

combines information from prices in all countries by weighting them in proportion to how

important they are in affecting the competitiveness of the country or sector in question

based on past trade flows. Looking at individual prices cannot deliver such information.

For instance consider two countries A and B. If prices in A rise by more than prices

in B, this does not automatically make B more competitive than A since they may be

trading with different partners whose prices themselves may have changed differently.

Moreover, B might be using A’s output as an intermediate input in production, in which

case B’s competitiveness might actually fall when A’s price rises. Secondly, a measure

like the unit labor cost considers only one component of value added (namely labor)

and ignores the effect of prices of other inputs (most notably capital) which account for

one third of the total value added on average (and much higher in certain sectors). This

is also a drawback of all effective exchange rate measures that use unit labor costs as

deflators. In this paper we compute price indices for value added which incorporates all

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components of the latter (including labor and capital) to overcome this shortcoming.

3.3 A Stylized Three Country Global Value Chain

We start with a simplified 3 country, 2 sector model capturing the basic Global Value

Chain (GVC) features. There are three countries (J, C and U for Japan, China and

USA respectively) and two sectors indexed by 1, 2. Table 15 displays the input output

table. All boxes with “X” denote non-zero entries while the remaining entries are zero.

Note that the IO matrix is sparse and contains only one (out of a possible 36) non-zero

entries. The global value chain is modeled across two sectors in three different countries.

The upstream sector J1 (sector 1 in country J) produces raw materials that are exported

to country C. Sector 2 in country C combines these intermediate inputs from J along

with its own value added to produce final goods that are then exported to countries J

and U in addition to being consumed internally by country C. All other sectors (i.e J2,

C1, U1 and U2) only produce goods using own value added (i.e no intermediate inputs)

and sell them as final demand in the home country. Sector 2 can be interpreted as the

electronics sector and sector 1 can be interpreted as a (raw) materials sector.

Table 15 – A stylized 3 country 2 sector global value chain set up

J C U JFinal CFinal Ufinal total outputJ1 J2 C1 C2 U1 U2

J J1 0 0 0 X 0 0 X 0 0 XJ2 0 0 0 0 0 0 X 0 0 X

C C1 0 0 0 0 0 0 0 X 0 XC2 0 0 0 0 0 0 X X X X

U U1 0 0 0 0 0 0 0 0 X XU2 0 0 0 0 0 0 0 0 X X

VA X X X X X Xtotal output X X X X X X

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Specifying the model:

We use Qhl to denote the gross output of sector l is country h. 86 Xfh

sl denotes the

intermediate input from country f sector s used in production by (h, l). V hl denotes the

value added by (h, l). We assume a constant elasticity of substitution which is allowed

to differ across consumption and production aggregators as clarified below.

Production:

The production function of (C, 2) is given by

QC2 =

[(wV )

1σ (V C

2 )σ−1σ + (wX)

1σ (XJC

12 )σ−1σ

] σσ−1 (3.2)

where σ is the elasticity of substitution between the two inputs and wV and wX are

weights that can be mapped to the shares of the two inputs.

Since all other production comprises entirely of own value added, the remaining

production functions are of the form:

Qhl = V h

l ∀(h, l) 6= (C, 2) (3.3)

Consumption:

We use F hfl to denote output of (h, l) that is absorbed in country f as final demand.

Based on table 15, the consumption aggregators for the three countries are given as86Throughout this paper, superscripts will be used for countries and subscripts for

sectors.

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follows:

F J = [(κJJ1 )1θ (F JJ

1 )θ−1θ + (κJJ2 )

1θ (F JJ

2 )θ−1θ + (κCJ2 )

1θ (FCJ

2 )θ−1θ ]

θθ−1 (3.4)

FC = [(κCC1 )1θ (FCC

1 )θ−1θ + (κCC2 )

1θ (FCC

2 )θ−1θ ]

θθ−1 (3.5)

FU = [(κUU1 )1θ (FUU

1 )θ−1θ + (κUU2 )

1θ (FUU

2 )θ−1θ + (κCU2 )

1θ (FCU

2 )θ−1θ ]

θθ−1 (3.6)

We use large case P to denote CPI, small case pQ is used to denote price of gross

output; pV will be used to denote price of value added and pX for price of intermediate

goods. θ is the elasticity of substitution between different goods in the final consumption

good bundle and is assumed to be the same across all countries87. κ s are weights that

denote the shares of the different components in the aggregators.

Appendix C.1 shows how the linearized version of the model can be solved to write

the demand for value added for each entity as a function of all the value added prices

assuming that total final demand remains constant (i.e F h = 0∀h), or what we define as

the real exchange rate (GVC-REER) following this partial equilibrium literature88:

4GV C −REERhs = V h

s = w(v)hJs1 p(V )J1 + w(v)hJs2 p(V )J2 + w(v)hCs1 p(V )C1

+w(v)hCs2 p(V )C2 + w(v)hUs1 p(V )U1 + w(v)hUs2 p(V )U2 (3.7)

where h ∈ J,C, U, s ∈ 1, 2

To illustrate the properties of our REER weighting scheme, we focus on the weight

assignment between the two sectors that are involved in the the GVC. We use the87This and many other restrictions imposed so far will be relaxed in the general model

presented later.88In addition to the first order conditions, the only equilibrium conditions we need are

market clearing conditions. These are listed in the appendix.

118

notation p(V )al Vabl to denote the total value added created in (a, l) that is ultimately

absorbed as country b’s final demand. Our model yields the following expression for the

weight assigned by C2 o J1:

w(v)CJ21 = θ

[(p(V )C2 V

CJ2

p(V )C2 VC2

)(p(V )J1 V

JJ1

PJFJ

)+

(p(V )C2 V

CC2

p(V )C2 VC2

)(p(V )J1 V

JC1

PCFC

)+

(p(V )C2 V

CU2

p(V )C2 VC2

)(p(V )J1 V

JU1

PUFU

)]

+

(p(Q)J1X

JC12

p(Q)C2 QC2

)(σ − θ) (3.8)

Several aspects of the weighting schemes now become evident from (C.75). Firstly,

under the constant elasticity assumption (θ = σ = 1)the weight reduces to:

w(v)CJ21 =∑

k=J,C,U

[(p(V )C2 V

Ck2

) (p(V )J1V

Jk1

)(p(V )C2 V

C2 ) (PKF k)

]≥ 0 (3.9)

This is the same as the sum of the three terms inside the bracket in (C.75)89. Each of

these terms can be interpreted as capturing the intensity of competition between (C, 2)

and (J, 1) in the three final goods markets, namely C, J and U . The higher is the intensity

of competition as measured by these terms, the higher would be the weight assigned by

(C, 2) to (J, 1), since in that case a fall in the price of (J, 1)’s value added would hurt

(C, 2) more. As an example, if the last term in (C.75)[(

p(V )C2 VCU2

p(V )C2 VC2

)(p(V )J1 V

JU1

PUFU

)]is high,

it conveys that value added by (C, 2) and (J, 1) are competing intensively in order to

satisfy country U ’s final demand, so a fall in (J, 1)’s price will hurt (C, 2) to a greater

extent.89In fact, under the assumption of constant elasticity, all weights can be represented

by a formula mimicking (3.9), i.e.

w(v)hkls =∑

k=J,C,U

[(p(V )hl V

hkl

) (p(V )csV

cks

)(p(V )hl V

hl

)(PKF k)

]∀h, k, s, l

This is the same as 3.22 in the case of the general model.

119

Secondly, note that w(v)CJ21 is strictly increasing in σ. Intuitively, the lower is the

elasticity of substitution between own value added and Japanese imports in (C, 2)’s

production, the higher will be the co-movement between the value added by (C, 2) and

(J, 1). In this case, the weight assigned by (C, 2) to (J, 1) will be lower, since a fall in

the price of (J, 1) ’s value added, which increases demand for output of (J, 1) , will also

end up exerting a positive effect on the demand for value added by (C, 2).

Thirdly, unlike σ, the effect of an increase in θ is ambiguous. On the one hand an

increase in θ exerts a positive effect on w(v)CJ21 via the standard expenditure switching

effect–if consumers are more willing to substitute between different goods in their

consumption bundle, a fall in the price of a substitute will decrease demand for the

own good to a greater extent. On the other hand, to the extent that the value added

by (C, 2) and (J, 1) are complementary, expenditure switching towards (J, 1)’s value

added indirectly also implies a shift in expenditure towards (C, 2)’s output and hence

towards (C, 2)’s value added which is embodied in its own output. In this example the

two effects run in opposite directions.

Lastly, (C.75) and (3.9)also illustrate the restrictive nature of the weighting scheme

in the constant elasticity case. In particular the complementarity effect discussed above

is not present, and as is evident from (3.9) the weighting scheme is not flexible enough

to accommodate negative weights.

The appendix shows how we can derive REERs for gross output competitiveness (as

opposed to competitiveness for value added which is what GVC-REER measures) and

how it compares to our GVC-REER weighting scheme in this 3 by 2 world.

120

Defining Aggregate Real Effective Exchange Rates for Countries

We compute aggregate country level REERs by exploiting information on sector level

trade flows. For comparison, in the appendix we also compute an alternate measure

that aggregates all trade flows within a country as is commonly done in the literature.

Appendix C.1 shows that the demand for value added produced by country h can be

written as:

V h =∑

f∈(J,C,U)

∑k∈1,2

[(p(V )h1V

h1

p(V )hV h

)w(v)hf1k +

(p(V )h2V

h2

p(V )hV h

)w(v)hf2k

]p(V )fk (3.10)

If sector level price indices are available, then (3.10) provides the most accurate

measure of competitiveness for a country as a whole. Typically however, country level

REER is computed using an aggregate country-wide price index (like the GDP deflator,

CPI or some measure of unit labor cost). To define an analogous measure in our

framework we need to make an assumption regarding the link between sector level prices

and the aggregate GDP deflator of a country. We choose to make the simplest possible

assumption (which is also made implicitly throughout this literature), namely that all

sector level prices change by the same proportion as the change in the aggregate GDP

deflator. In particular,

p(V )h = p(V )h1 = p(V )h2 (3.11)

With this assumption we can simplify (3.10) to write:

121

V h =∑

f∈(J,C,U)

[(p(V )h1V

h1

p(V )hV h

)(w(v)hf11 + w(v)hf12

)+

(p(V )h2V

h2

p(V )hV h

)(w(v)hf21 + w(v)hf21

)]︸ ︷︷ ︸

wA(v)hf

p(V )f

(3.12)

Here wA(v)hf denotes the aggregate (i.e country level) weight assigned by country

h to country f in the real exchange rate of country h. As is evident from (3.12), this

weight is itself a weighted sum of the weights assigned by each sector in h to each sector

in f , with the weights given by the value added shares of the sectors in h.

In the appendix we compare our country level REER measure against the common

approach of aggregating across sectors within each country and show that these two

approaches yield different results except in knife-edge cases.90

3.4 The General Model

Consider a world economy comprising of n countries. There are m sectors within

each country. Each country-sector is called an “entity” so that there are a total of nm

production entities in the world economy. Each entity uses a production function with

its own value added and a composite intermediate input which can contain intermediate

inputs from all mn entities including itself. The output of each entity can be used

either as a final good (consumed in any of the n countries) or as an input by another

entity. Thus there are a total of nm producers and nm + n consumers (nm entities

plus n final goods consumers) in the economy. Both the production function and final

goods consumption aggregators are nested CES (constant elasticity of substitution)90The issue of aggregation is explored in more detail after we present the general model.

122

aggregators which are described in detail next.

Consider the production process for entity (c, l). The production process is assumed

to follow the following three stage hierarchy:

First, for each sector, inputs from all foreign countries from that sector are aggre-

gated (with a constant elasticity of substitution) to form sectoral intermediate inputs

X(f)cslms=1. In other words, X(f)csl is the aggregate sector s foreign intermediate input

used in production by country c sector l

X(f)csl =

[n∑

i=1,i 6=c

(wicsl)1/σ1

s(c,l)(X icsl)

σ1s (c,l)−1

σ1s (c,l)

] σ1s (c,l)

σ1s (c,l)−1

, s = 1, 2, ..m (3.13)

Here X icsl denotes inputs from country i sector s used in production by country c sector

l, the w′s are aggregation weights and σ1s(c, l) is the (constant) elasticity of substitution

between different foreign varieties of the sector s output in the production function of

entity (c, l)

The sector s import bundle is then combined with the domestic sector s input to

form the aggregate sector s input. The elasticity of substitution between these two

inputs is σ1hs (c, l).

Xcsl =

[(wccsl )

1/σ1hs (c,l)(Xcc

sl )σ1hs (c,l)−1

σ1hs (c,l) + (w(f)csl)1/σ1h

s (c,l)(X(f)csl)σ1hs (c,l)−1

σ1hs (c,l)

] σ1hs (c,l)

σ1hs (c,l)−1

(3.14)

With this two step framework we are allowing for a distinction between “macro”

(σ1hs (c, l)) and “micro” (σ1

s(c, l)) elasticities for each sector, which is a feature of the data

123

documented in the literature–see Feenstra et al. (2010) .

Next, these m sectoral aggregates are combined to form the aggregate intermediate

input Xcl

Xcl =

[m∑s=1

(wcsl)1/σ2(c,l)(Xc

sl)σ2(c,l)−1

σ2(c,l)

] σ2(c,l)

σ2(c,l)−1

(3.15)

Finally, the aggregate intermediate input is combined with the entity’s own value

added to form the gross output for entity (c, l) which is used both as intermediate and

final good. This is denoted by Qcl . The elasticity of substitution between value added

and aggregate intermediate is σ3(c, l)

Q.c.l =

[(wvcl )1/σ3(c,l)(V c

l )σ3(c,l)−1

σ3(c,l) + (wXcl )1/σ3(c,l)(Xcl )

σ3(c,l)−1

σ3(c,l)

] σ3(c,l)

σ3(c,l)−1

(3.16)

A country specific final good is obtained by aggregating goods from all nm production

entities in two stages.

Firstly, for each sector s, goods from all foreign countries are aggregated to form

an aggregate sector s final imported good for consuming country c. The elasticity of

substitution for each aggregate is θ1s(c)

F cs (f) =

[n∑

i=1,i 6=c

(κics )1/θ1s(c)(F ics )

θ1s(c)−1

θ1s(c)

] θ1s(c)

θ1s(c)−1

(3.17)

Each of these imported goods is then combined with the domestic goods from its

respective sector to form an aggregate sector s consumption good for country c.

124

Fsc =

[(κccs )1/θ1hs (c)(F cc

s )θ1s(c)−1

θ1s(c) + (κ(f)cs)1/θ1hs (c)(F (f)cs)

θ1hs (c)−1

θ1hs (c)

] θ1hs (c)

θ1hs (c)−1

(3.18)

Market Clearing Finally, these s sectoral aggregates are combined (with constant

elasticity θ2(c)) to form the aggregate consumption good for country c

F c =

[m∑s=1

(κcs)1/ρ2(c)(F c

s)θ2(c)−1

θ2(c)

] θ2(c)

θ2(c)−1

(3.19)

Gross output from an entity is absorbed either as an intermediate input or a final

good (we do not allow for inventory accumulation or any inter-temporal effects). Thus

the following market clearing condition holds ∀(c, l)

Qcl =

n∑i=1

F cil +

m∑j=1

n∑k=1

Xcklj (3.20)

3.5 Computation of Effective Exchange Rate Weighting Matrices

In order to define the exchange rates we take prices and final demands in all countries

as exogenous and compute the demand for value added and gross output of different

entities as functions of prices. This partial equilibrium setup is common in the literature

and requires only one market clearing condition along with the different optimality

conditions for production and consumption.

125

Demand for value added as a function of price of value added:(GVC-REER)

The appendix shows that the demand for value added can be written as

vec(V cl

)= WV vec (p(V )cl ) +WFV vec

(F c)

(3.21)

Here(vec(V cl

))nmX1

is the vector of changes in value added stacked across all

countries and sectors, and WV and WF are nm by nm matrices derived in the appendix.

Putting the change in final demand vec(F c)to zero, the nm by nm matrix premultiply-

ing vec (p(V )cl ) can be interpreted as a matrix of weights for the real effective exchange

rate, as it measures how the demand for value added originating in a country-sector

changes when price of value added changes in any other entity.

Interpretation in the case with constant elasticity:

Appendix C.4 shows that under the constant elasticity assumption the weight assign-

ment by country sector (h, l) to country-sector (c, s) where (h, l) 6= (c, s) can be written

as follows:

whcls =n∑k=1

[(p(V )hl V

hkl

) (p(V )csV

cks

)(p(V )hl V

hl

)(PKF k)

], (h, l) 6= (c, s) (3.22)

where we use lower case w to denote constant elasticity weights. This is a generalized form

of equation 3.9 which was derived in the context of a simplified model and the intuition

is similar. In particular, the weight assigned by country sector (h, l) to country-sector

(c, s) where (h, l) 6= (c, s) is a weighted sum of the value added created by country-sector

(c, s) and absorbed by each of the countries k(= 1, .., n), where the weights are given

by the value added created by (h, l) that is absorbed in the same country k. This

126

captures both mutual and third country competition, because the weight is high if both(p(V )hl V

hkl

)and

(p(V )csV

cks

)are high, which happens when both (h, l) and (c, s) have a

high share of value added exports to country k.

Relaxing the Uniform Elasticity Assumption

Since a full analytical characterization of the role played by different elasticities is

infeasible given the complex nature of the model, we will illustrate the role played by the

different elasticities in a series of examples in section 3.8. However, in order to provide

some intuition the following proposition shows the effect of a small change in elasticity

on the REER weights in the neighborhood of the constant elasticity equilibrium.

Proposition 3.1. Suppose all production and consumption elasticities are constant and

equal to σ and θ respectively91. Then starting at the uniform elasticity equilibrium, the

effect of a change in elasticity on the weight assigned by entity (h, l) to entity (c, s) is

given by:

∂whcls∂θ

= whcls −vhl v

cs

∑nc1=1

∑nc2=1

∑mk=1 b

hc1lk b

cc1sk (p(Q)c1k F

c1c2k )

p(V )hl Vhl

, (h, l) 6= (c, s) (3.23)

Proof(sketch): See appendix C.4.

Here b is used to denote elements of the global Leontief inverse matrix and p(Q)

is used to denote price of gross output.(3.23) shows that an increase in elasticity of

substitution of consumption holding everything else constant(including the production

elasticity) has two opposing effects on the weight assigned by home entity (h, l) to91This is equivalent to assumption (A2) in section 3.6

127

the foreign entity (c, s). The two terms correspond to the expenditure switching and

complementarity effect illustrated earlier with the stylized model. In particular, the

first effect (expenditure switching) is positive and is given by the constant elasticity

weight whcls , which, it should be recalled, is always positive in the constant elasticity case.

In addition, there is the countervailing complementarity effect which comes from the

second term on the right hand side. This term is high when the products bhc1lk bcc1sk are

high for various entities indexed by (c1, k), which in turn happens if the outputs of the

two entities are used together in production (i, e entities such as (c1,k) which use the

output of (c, s) as an input, also uses the output of (h, l) as an input).

Intuitively, when the price of (c, s) decreases, its quantity demanded increases. This

effect is greater the greater is the elasticity of substitution between goods(θ). Moreover,

an increase in demand for (c, s) will end up increasing the output of (h, l) if it is highly

complementary with (c, s).

The corresponding expression for the two GVC sectors in section 3.3 is the following:

∂wCJ21

∂θ|θ=σ=1 = wCJ21 −

(p(Q)J1X

JC12

p(Q)C2 QC2

)(3.24)

We will elaborate more on these mechanisms by the use of stylized examples.

Gross Output Competitiveness

We also derive the demand for aggregate output as a function of price of value added

(this is analogous to the “goods” REER measure proposed in Bayoumi et al. (2013). See

appendix for steps of proof)

128

vec(Qcl

)= WQvec

(ˆp(V )cl

)+WFQvec

(F c)

(3.25)

Here WQ is an nm by nm weighting matrix derived in appendix C.3. Again putting

the change in final demand vec(F c)to be zero, the nm by nm matrix premultiplying

vec (pvcl ) can be interpreted as a matrix of weights for the real effective exchange rate

with regard to gross competitiveness, i.e it measures how the demand for output of

a country-sector changes with changes in prices of other country-sectors. This is in

contrast to the first measure defined above, which looks at change in demand for value

added. (As is shown in 3.2, the two are the same in the special case where gross output

is the same as value added, as is assumed in most of the REER measures including IMF,

FED and BIS).

Bayoumi et al. (2013) define the “Goods REER” as a measure of competitiveness of

a country’s gross output.

4log(GoodsREERi) =∑j 6=i

W ijimf

(pi − pj

)(3.26)

where W ijimf are the IMF weights. The analogous expression in the context of the

framework proposed in this paper (and BJ) can be obtained by setting m = 1, F c = 0∀c

and taking the ith row of the following expression (3.25)

However in general (3.25) and(3.26) are not the same since, as shown in the next

section, the IMF weights coincide with the weights obtained in the present framework

only under fairly restrictive conditions.

The idea behind the Integrated real exchange rate (IRER) measure proposed in

129

Thorbecke (2011)92 is also similar to Bayoumi et al. (2013) with the analogous expression

in the present model given by (3.25) . However they too use the IMF weighting scheme,

which means that their measure only coincides with the measure proposed in the present

paper under fairly restrictive assumptions, which we discuss in detail below.

3.6 Relationship to other REER Weighting Matrices in the Literature

This section shows the link between the two REER measures proposed in the previous

section and some common REER measures in the literature with particular emphasis

on whether and under what conditions the different measures in the literature can be

recovered from the more general measures proposed here. We start by listing the various

REER measures that are compared in this section. With some abuse of terminology, we

refer to the weighting matrix by the same name as the name given to the associated

REER measure by the authors(irrespective of the price index used).

1. GVC-REER and Q-REER are as defined in the previous section

2. IOREER(BJ): Input-output real effective exchange rates as defined by BJ in their

model

3. VAREER(BJ): Value added real effective exchange rates as defined by BJ in

their model. It is a special case of IOREER with all elasticities (production and

consumption) set equal to each other.

4. GOODS-REER: as defined by Bayoumi et al. (2013) .92Thorbecke (2011) defines the IRER measure with lag dependence. However, I ignore

this feature and refer to IRER as the Thorbecke (2011) measure without lag dependencein order to make the measure comparable to the other measures discussed here and inthe following sections

130

5. IRER: Integrated real exchange rate as proposed by Thorbecke (2011), but without

lagged dependence

6. IMF-REER

As shown in Bayoumi et al. (2005) the weight assignment by country i to country

j in the IMF’s REER measure is given by:

W ijimf = (αm + αs)W

ijimfm + (αc)W

ijimfc + (αT )W ij

imfT (3.27)

where αm, αs, αc, andαT are shares of manufactures, (non-tourism) services, com-

modities, and tourism in overall trade.

Assumptions:

(A1)m = 1. i.e, each country has only one sector

(A2) Elasticities are the same across consumption and production entities

1. σ1s(c, l) = σ1∀s, c, l, σ1h

s (c, l) = σ1∀s, c, l, σ2(c, l) = σ2∀c, l, σ3(c, l) = σ3∀c, l

2. θ1s(c) = θ1∀s, c, θ1h

s (c) = θ1∀s, c, θ2(c) = θ2∀c

(A3) All elasticities(in both consumption and production) are the same

• σ1 = σ2 = σ3 = θ1 = θ2=1(wlog)

131

(A4) No intermediates in production and only final goods are traded.

(A5) All trade flows comprise of trade in manufacturers and non tourism services,

i.eαc = αT = 0

Proposition 3.2.

1. Under (A1) and (A2):

GVC-REER =IOREER

2. Under (A1) , (A2) and (A3):

GVC-REER=IOREER=VAREER

3. Under (A1), (A2), (A3) and (A4):

GVC-REER=Q-REER=IOREER=VAREER

4. Under (A1), (A2), (A3), (A4) and (A5)

IMF-REER = GVC-REER=Q-REER=IOREER=VAREER=GOODSREER=IRER93

proof: see appendix.

In general, the GVC-REER measure does not reduce to the common measures

currently is use, such as those of the FED (Loretan, 2005), BIS (Klau et al., 2008) or93As mentioned before, note that the IMF uses CPI to compute REER, but in this

section we will use IMF-REER to denote total effective exchange rates computed withIMF weights but using the GDP deflator, to make the measure comparable with othermeasures proposed here and in BJ

132

IMF (Bayoumi et al., 2005). Certain parallels can, however, be drawn between the IMF

measure and the GVC-REER (and BJ) measure as shown in part 4 of proposition 3.2.

3.7 Building Country-level REER From Ground Up

Value added weights at the country level

This section provides a method to aggregate the country-sector level weights derived

above and defines country level weights analogous to the ones commonly discussed

in the literature. We show that the aggregated weights so derived in general do not

correspond to any of the ones proposed in the literature except in knife-edge cases. This

is attributable to the fact that our measure exploits inter-sectoral linkages between

countries to provide a more comprehensive measure of competitiveness than what can

be obtained by using just country level data.

To derive the expression for country-level value added weights, we start with the

following decomposition of the nominal GDP of country c into its different sectoral

components:

p(V )cV c =m∑l=1

p(V )clVcl (3.28)

log linearizing this equation we get:

p(V )c + V c =m∑l=1

(p(V )clV

cl

p(V )cV c

)[p(V )cl + V c

l

](3.29)

133

Stacking the n equations in (3.29) we can write the system in matrix notation as:

vec (p(V )c)nX1 + vec(V c)nX1

= RV

[vec (p(V )cl )nmX1 + vec

(V cl

)nmX1

](3.30)

where

(RV )nXnm =

SV1 0′m .. 0

′m

0′m SV2 :

: .. :

0′m 0

′m .. SVn

(3.31)

and(SVi)

1Xm=(p(V )i1V

i1

p(V )iV i,p(V )i2V

i2

p(V )iV i, .., p(V )imV

im

p(V )iV i

)and 0m is an m by 1 matrix of zeros.

By definition the change in the GDP deflator is the weighted sum of change in its

components and hence (3.30) reduces to

vec(V c)nX1

= RV

[vec(V cl

)nmX1

](3.32)

using (3.21) in (3.32) and imposing vec(F c)

= 0 as before we get:

vec(V cl

)= RVWV vec (p(V )cl ) (3.33)

Defining the two measures of country level value added exchange rates:

When sector level price indices are available, (C.46) defines the change in the country

level GVC-REER, i.e

4log(GV C −REER) = WV (C)vec (p(V )cl ) (3.34)

134

where the n by nm matrixWV = RVWV is the weighting matrix which can be interpreted

as follows: the weight assigned by country i to country j sector l is itself a weighted

sum of the weights assigned by each sector of country i to (j, l), with the weights being

proportional to the country i sector’s share of value added as a fraction of total value

added by country i

WVijl =

m∑s=1

(p(V )isV

is

p(V )iV i

)(WV )ijsl (3.35)

Sector level prices are often not available for many countries. In such cases we need

a further approximation. In particular, we need to assume a mapping between sector

level prices and GDP deflator, i.e between pvc and pvcl Ml=1. We make the relatively

uninformed assumption that all sectoral level prices change in the same proportion as

the aggregate GDP, i.e we make the following assumption94.

Assumption (AP):

ˆp(V )j = p(V )jl∀l∀j (3.36)

Using this assumption we can define our second measure of country level value added

exchange rate, GVC-REER(GDPdef) as follows:

4log(GV C −REER(GDPdef)) = WV (CG)vec (p(V )c) (3.37)

where WV (GDPdef) = RVWVRg is an n by n matrix of weights and Rg = In ⊗ 1m

94Note that in a world with price rigidity and producer currency pricing this assumptionis satisfied automatically.

135

Link to other measures in the literature:

Our second measure of country level exchange rates which uses only the GDP deflator

(GVC-REER(GDPdef)) has an n by n weighting matrix as all other measures in the

literature and we can hence make a comparison with them.

Given the country-sector level weights(WV ), the country level weights (WV (CG))

have an intuitive interpretation. The weight assigned by country i to country j is a

weighted sum of the weights assigned by each sector of country i to each sector of

country j, with the weights being proportional to the home sector’s share of value added

as a fraction of total home value added.

WV (GDPdef)ij =m∑s=1

(p(V )isV

is

p(V )iV i

)( m∑k=1

(WV )ijsk

)(3.38)

These country level weights defined here are different from others proposed in the

literature in several respects as will be discussed in the following sections. The closest

to our measure is the one by Bems and Johnson (2012) who also take into account the

input-output linkages in their measure and define weights in terms of value added, but

do not exploit sector level linkages across countries. Because of the greater information

used in our measure, it is in general different from their VAREER and IOREER, even

under the assumption of all elasticities being the same. The following proposition shows

that even under the uniform elasticity assumption, GVC-REER and VAREER differ

from each other except in special cases. 95

95We make the comparison with Bems and Johnson (2012) because it is the closest toour framework. Although they do not allow for sector level linkages in their theoreticalmodel, in the empirical implementation of their model they do use sector level linkagesfrom Johnson and Noguera (2012) by making some simplifications. (However theirsimplification only works in the constant elasticity case).

136

Condition 7.1

vin∑c=1

bicF cj =m∑l=1

vis

n∑c=1

m∑s=1

biclsFcjs ∀i, j (3.39)

where vil =p(V )ilV

il

p(Q)ilQilis the value added share for entity (i, l) and b denotes a generic

element of the global inter-country Leontief inverse matrix.

Proposition 3.3.

The country level weights (WV (GDPdef)) defined above reduces to VAREER (and

IOREER) weights defined in Bems and Johnson (2012) if either of the two conditions

below are satisfied.

1. (A2), (A3) and condition 5. 1

2. (A3), (A4) and θ1 = θh1 = θ2

The proof is given in appendix C.4. The first part of the proposition shows that

outside of the knife-edge case in which the above condition is satisfied, the GVC-

REER(GDPdef) weights which exploit inter-sectoral linkages between countries will

dominate the VAREER measure even under the uniform elasticity assumption (they

would of course differ if elasticities are different even if the first condition in the

proposition is satisfied). Intuitively, condition (3.39) is satisfied if different sectors within

a country are “symmetric” with regard to their input-output linkages with the rest of

the world, for in that case aggregation across sectors within a country will be a closer

137

approximation to the behavior of each individual sector. The next section will provide

an example to illustrate the role played by the condition in aggregating weights at the

country level.

The second part of the proposition shows that differences between GVC-REER and

VAREER vanish when there is no trade in intermediates. This shows that if there is no

trade in intermediates, then aggregating trade flows across sectors within a country does

not lead to any loss of information as far as computation of real effective exchange rate

is concerned. Intuitively, if all production by all entities involves only own value added

and no intermediates, then there is no asymmetry between sectors within a country

with regard to the foreign value added embodied in their output (which is zero in all

cases) and hence aggregation does not lead to any loss of relevant information.

Gross output exchange rate at country level

Following a similar procedure to the one used for GVC-REER, we can define weights

and exchange rates for gross output at the country level:

4log(QREER) = WQvec (p(V )cl ) (3.40)

4log(QREER(GDPdef)) = WQ(GDPdef)vec (p(V )c) (3.41)

3.8 Illustrative Examples

This section presents some examples to illustrate the different aspects of the weighting

matrices derived above and compare them to other measures proposed in the literature.

138

Table 16 – Input output table for 3.1

J C U J final C final U final Total outputJ 0 1 0 1 0 0 2C 0 0 0 0.1 0.1 1 1. 2U 0 0 0 0 0 1 1

Value added 2 0.2 1Total output 2 1. 2 1

Example 3.1. Three country world with limited trade in intermediate inputs:

Consider the following 3 country one sector example where the input output linkages

are restricted to just one non-zero entry. Country C imports intermediates from country

J, puts in own value added and sells the output to all the three countries as final output.

Table 16 displays the associated input-output table.

In this simplified example only two elasticities are relevant, namely σ3 (elasticity of

substitution between C’s value added and intermediate input from J in C’s gross output)

and θ1 (elasticity of substitution between final goods in the final consumption basket of

all countries. For simplicity, this elasticity is assumed to be common across countries).

Consider the weight assigned by country C to country J, WCJ , which measures the

change in demand for value added by C when price of value added by J changes. A

decrease in p(V )J affects the demand for C’s value added via two channels. Firstly,

with regard to final goods consumption, a decrease in p(V )J leads to a shift towards

J’s value added (and goods containing value added by J, namely the gross output of

C) in the final goods consumption bundle of all countries. The strength of this effect

depends on θ1. A higher θ1 means that goods are more substitutable in the final goods

consumption bundle of countries and hence the shift towards J’s value added will be

more pronounced when its price decreases.

139

Secondly, with regard to intermediate goods and production mix, a decrease in the

price of J’s value added leads to a shift towards J’s value added and a shift away from

C’s value added in the production function of C. The strength of this effect depends

on σ3. The higher is this elasticity, the higher is the shift towards J’s value added in

C’s production (at the expense of C’s own value added) and hence higher is the fall in

demand for C’s value added.

As a result of these two effects WCJ is an increasing function of σ3 and a decreasing

function of θ1, as was pointed out in proposition (3.1). Interestingly, when θ1 is sufficiently

high and σ3 is sufficiently low, WCJ may indeed be negative, something that the IMF

weights or the value added weights in BJ do not allow for.

Table 17 presents weights based on different schemes for this example when σ3 = 1.5,

θ1 = 5. (as is done by the IMF and others, weights are normalized so that own weight

is -1 and is not reported). Several aspects of the differences in the weighting schemes

are noteworthy. Firstly, note that there are no negative weights in the IMF and the

VAREER weighting matrix. In fact it can be easily shown that these weighting schemes

are not flexible enough to accommodate negative weights under any circumstances. Next,

note from column 1 that WJC and WCJ are negative in the GVC-REER measure. As

discussed above, this is a consequence of the input output structure and a combination

of a relatively high θ1 (=5) and low σ3 (=1. 5). Column 3 illustrates that as far as gross

output is concerned, the magnitude of the negative weight assigned by country C to

country J is much larger. This is because only the first effect discussed above (i.e shift in

final demand) affects gross output, whereas the second effect (shift towards intermediate

composition) does not affect the gross output measure.

The uniform elasticity assumption is overly restrictive can also be noted from the

140

Table 17 – Comparison of weights under different measures for example 3.1

GVC-REER VAREER Q-REER GOODS-REER IMF Weights(PWW) (BJ) (PWW) (BST) (BLS)

WJC -0.04 0.19 -0.04 1.0 1.00WJU 1. 04 0.80 1. 04 0 0WCJ -0.25 0.54 -4.07 -3.40 0.26WCU 1.25 0.45 5.07 4.40 0.73WUJ 0.83 0.83 0.83 0.83 0WUC 0.16 0.16 0.16 0.16 1

keyPWW Patel, Wang, Wei(2014)BJ Bems and Johnson (2012)BST Bayoumi et al. (2013)BLS Bayoumi et al. (2005)

observation that the VAREER(BJ) weight which does take into account trade in

intermediates, does worse than the IMF weight which ignores it, although both have

the wrong sign.

Column 4 shows that the Goods-REER measure of Bayoumi et al. (2013) falls

somewhere in between the GVC-REER and the Q-REER measures (columns 1 and 3) so

that it measures neither gross output competitiveness nor value added competitiveness

but some arbitrary combination of the two. Although the aim in Bayoumi et al. (2013)

is to capture gross competitiveness, they fall short of doing so because their measure

uses the IMF weighting scheme which does not account for trade in intermediates. This

aspect is further illustrated by the fact that the GOODS-REER measure(which in turn

inherits this property from the IMF measure) assigns a value of 0 to WJU because there

is no direct trade between J and U. However, J’s value added does reach U via C and so

the correct weighting matrix must have WJU 6= 0.

Lastly, note from the last two rows of table 17 that the weights assigned by country

U to the remaining two countries are the same in all the measures except IMF. This is

a consequence of the fact that the US trades in only final goods and all its production

141

comprises entirely of its own value added.

Figure C.1 in the appendix shows how the weight assigned by C to J changes with the

elasticities. The top left figure plots WCJ for three measure(GVC-REER, VAREER(BJ)

and IMF) for different values of σ3 with θ1 fixed at 1. 5. The top right picture plots the

same weights for different values of θ1 with σ3 fixed at 5. The bottom left figure shows

a 3D plot of WCJ for the GVC-REER measure for different values of σ3 and θ1 while

the bottom right augments this graph by adding a surface each for VAREER and IMF

weights.

Example 3.2. A three country 2 sector world:

This example is an extension of example 3.1 which will be used to illustrate the role of

aggregation and comment on the practice of normalization of weights. In each country we

now have two distinct production sectors. The main object of attention will be country

C which is assumed to have two sectors that are different with regard to their production

function. Sector 1(C1) uses its own value added and produces only final goods absorbed

at home. Sector 2 (C2) operates downstream and uses intermediates from a different

country and produces only a final good. The elasticities and input-output table is given

in table 18 below.

Table 18 displays the full 6X6 country-sector level weighting matrix (which is not

normalized to illustrate the mechanics of aggregation based on equation (3.38) later

on). In line with the observations made in example 3.1, C2 and J1 are found to attach

negative weights to each other. Table 20 shows the weights at the country level. As

can be seen from the country level weighting matrix, the negative weights disappear

142

Table 18 – IO table and elasticities for example 3.2

J C U JFinal CFinal Ufinal total outputJ1 J2 C1 C2 U1 U2

J J1 0 0 0 2 0 0 1 0 0 3J2 0 0 0 0 0 0 1 0 0 1

C C1 0 0 0 0 0 0 0 2 0 2C2 0 0 0 0 0 0 0.5 0.5 2.5 3.5

U U1 0 0 0 0 0 0 0 0 2 2U2 0 0 0 0 0 0 0 0 1 1

VA 3 1 2 1.5 2 1total output 3 1 2 3.5 2 1

Elasticities:σ1 = 2, σ2 = 2 , σ3 = 2, θ1 = 5, θ2 = 5

Table 19 – GVC-REER weights at country-sector level(raw) for example3.2

J1 J2 C1 C2 U1 U2

J1 -2.36 0.86 0.38 -0.169 0.86 0.43J2 2.57 -3 0 0.43 0 0C1 0.571 0 -1 0.4 0 0C2 -0.338 0.28 0.571 -2.4 1. 3 0.65U1 1.30 0 0 0.97 -3.18 0.90U2 1.30 0 0 0.97 1. 81 -4.0

when sectors are aggregated by country. To understand the intuition behind this, table

21 shows a 2 by 2 sub matrix from table 20 which contains weights assigned by sectors

in C and J to each other, along with the value added and gross output shares of the

respective sectors, derived from table 18.

Note that the aggregate country weight WCJ is a combination of the 4 sector level

weights (in line with (3.38)). Since in value added terms the size of C1 and J1 is higher

compared to C2 and J2 respectively, the country level GVC-REER weight is likely to

Table 20 – GVC-REER weights at country level for example3.2

J C UJ -1.24 0.26 0.97C 0.30 -1.14 0.83U 1.30 0.97 -2.27

143

Table 21 – 2X2 weighting matrix for example 3.2

J1 J2 value added share gross output shareC1 0.571 0 0.57 0.36C2 -0.338 0.28 0.43 0.64

value added share 0.75 0.25gross output share 0.75 0.25

Table 22 – Summary of different weights at country-country (normalized) example 3.2

GVC-REER IO-REER VAREER Q-REER GOODS-REER IMF Weights(PWW) (BJ) (BJ) (PWW) (BST) (BLS)

WJC 0.21 0.41 0.69 0.21 1 1WJU 0.78 0.58 0.30 0.79 0 0WCJ 0.26 0.29 0.56 -0.80 0.25 0.53WCU 0.73 0.71 0.44 1.80 0.75 0.47WUJ 0.57 0.36 0.36 0.57 0.36 0WUC 0.42 0.63 0.63 -0.42 0.63 1

be dominated by WJ1C1 , which is positive (0.57)96

Table 22 provides a summary of country-level weights assigned by different measures

in the literature alongside the weighting matrices proposed in the preceding sections

(now the weights are normalized to make the comparison easier). Unlike the case with

GVC-REER weights, note that Q-REER, which focuses on gross output, does end

up assigning negative weights (see row 3 containing WCJ) even at the country level,

the intuition for which is again clear from noting that in terms of gross output shares

the dominant sectors are J1 and C2 so the country level weight WCJ is likely to be

dominated by the weight assigned by C2 to J1, which is negative(-0.338). However as

in the previous example since the GOODS-REER measure uses IMF weights, it does

not completely account for the input-output linkages and hence offers a different weight

from our Q-REER measure.96the number 0.3 can be recovered from (3.38) as followsWCJ = 0.57(WCJ

11 +WCJ12 )+0.43(WCJ

21 +WCJ22 )=0.57(0.571+0)+0.43(−0.338+0.28) '

0.3

144

Table 23 – Country level IO table for example 3.2

table 6. 2. 6 J C U J final C final U final Total outputJ 0 2 0 2 0 0 4C 0 0 0 0.5 2.5 2.5 5.5U 0 0 0 0 0 3 3

Value added 4 3.5 3Total output 4 5.5 3

Table 24 – GVC-REER and VAREER weights (raw, constant elasticity)

GVC-REERC A-REERWJC 0.18 0.27WJU 0.19 0.12WCJ 0.20 0.32WCU 0.16 0.25WUJ 0.25 0.16WUC 0.19 0.28

More on aggregation:

To focus exclusively on the role of aggregation we now set all elasticities equal to one.

Table 23 shows the country-level input output table derived from the general country-

sector level IO table. The country level IO table is what is used to compute weights

when inter-sectoral flows are ignored, as is common in the literature. Table 24 gives the

weights under the two difference schemes, GVC-REER and the corresponding measure

derived from a country level IO table, which we call A-REER (for aggregate). Note that

in theory the A-REER measure is equivalent to VAREER in Bems and Johnson (2012).

The difference between the 2 weighting matrices can be illustrated using WCU as an

example. WCU is an increasing function of value added by C that is ultimately absorbed

in country U . By exploiting sector level information the GVC-REER measure recognizes

that all the exports from C to U are associated with sector C2, which uses foreign (J)

value added (and therefore less of its own value added) and hence it tends to reduce the

weight assigned by C to U. The aggregate measure on the other hand looks at aggregate

145

Table 25 – Normalization and the role of aggregation

Raw Weights Normalized weightsGVC-REER A-REER(raw) GVC-REER A-REER

WJC 0.18 0.27 0.48 0.69WJU 0.19 0.12 0.51 0.37WCJ 0.20 0.32 0.55 0.56WCU 0.16 0.25 0.44 0.43WUJ 0.25 0.16 0.57 0.36WUC 0.19 0.28 0.43 0.63

country level data and as a result attributes a higher amount of value added by C in

its exports to U (because C2 has a higher fraction of own value added). As a result,

WCU is higher under the aggregate measure compared to GVC-REER. Table 25 shows

a comparison between normalized and raw weights under the two measures. Note that

now the ordering in WCU is reversed and the GVC-REER measure assigned a higher

weight than A-REER. This undesirable feature is a consequence of the arbitrariness

involved in normalization and highlights its drawbacks.

3.9 Data

We use recently released data from the World Input-Output Database(WIOD) which

was developed by a consortium of eleven European research institutions with funding

from the European Commission. The database consists of a time series of input-output

tables covering 40 countries and 35 sectors from 1995-201197. The data is available

in both current and previous year prices which enables us to compute price indices

for different entries in the input-output table. A detailed description of this database

can be found in Timmer and Erumban (2012). As documented by these authors, the

database is more precise than previous attempts in the literature (for instance Johnson97The full set of countries and sectors is listed in appendix C.11

146

and Noguera, 2012) as it uses less approximations and more detailed trade data98.

Estimation of Elasticities

The examples in the previous section have shown that the different elasticities of

substitution are key parameters in computing the REER weights. In the next section

we take up the task of estimating these elasticities. The availability of input output

tables at previous year prices in the World Input Output Database (WIOD) allows

us to estimate elasticities used in the computation of weights instead of assuming all

elasticities to be unity as is done in the literature. We use the framework pioneered in

Feenstra (1994) and subsequently used in Broda and Weinstein (2006) and Soderbery

(2013) to estimate the different elasticities used in the CES aggregators for production

and consumption which also enter the expression for the real exchange rate. Appendix

C.6 provides a brief overview of the framework followed by a discussion of how the

estimation is carried out in the context of our model.

3.10 Results

Elasticity Estimation

We generalize the framework used in Feenstra (1994) and subsequently in Broda

and Weinstein (2006) and Soderbery (2013) to allow for elasticities less than unity. To

minimize the effect of outliers we winsorize the data at the 10th and 90th percentiles.

Further, we propose to use the bootstrap median as our point estimate since we find this

to be more stable than the MLE in our simulations. Table 32 in the appendix reports

the moments of the sample bootstrap distribution obtained using 50 draws. In table 2698For instance, unlike Johnson and Noguera (2012) who use a proportionality assump-

tion to split intermediate and final goods imports, the WIOD uses detailed data fromcom-trade to distinguish trade flow into the different categories.

147

we report estimates across different country and sector groups.

Baseline Calibration

As shown in table 26 we find substantial heterogeneity in the elasticities across

country and sector groups. The p-values for the null of equality of medians across

samples is often insignificantly different from zero. For our baseline calibration of

consumption elasticities we pool across sectors and split countries into two groups,

OECD and non-OECD. For production elasticities we pool across countries and split

sectors into primary, secondary and tertiary. Thus we use 16 different elasticities in

the baseline calibration. These are highlighted in bold in table 26. Although slightly

on the higher side, these numbers are broadly in the range of estimates obtained in

the trade literature (Broda and Weinstein (2006)), but fairly high compared to the

estimates obtained in the macro literature (Justiniano and Preston (2010))99 Table 32

in the appendix reports more details on the estimated elasticities including moments of

the bootstrap distributions.99As shown in Imbs and Méjean (2012), the macro estimates suffer from a downward

bias doe to aggregation.

148

Table 26 – Comparison of median elasticities across different country and sector groups

Consumption Elasticities

θ1 θ1h θ2

OECD(28) 7.75 3.38 1.35

Non-OECD(13) 17.80 9.45 1.925

p(OECD,Non-OECD) 0.00*** 0.074* 0.266

observations 1435 41 41

Production Elasticities

σ1 σ1h σ2 σ3

primary(2) 12.25 8.19 4.76 1.015

secondary(15) 5.81 8.02 4.36 1.015

tertiary(18) 9.14 7.29 3.22 1.015

p(secondary, tertiary) 0.00*** 0.34 0.00***

Notes: p(a, b) denotes the p-value for the null hypothesis that the medians are constantfor a and b using Moods chi squared test. Tests for σ1 are based only on 2 countries(i.e2450 (=2*35*35) observations). Agriculture and mining are classified as primary sectorswhile the rest are split into manufacturing (secondary, 15 sectors) and services (tertiary,18 sectors).For p values, “***”, ”**” and “*” denote significance at 1%, 5% and 10% level respectively

Multilateral Exchange rates

In this section we illustrate the properties of our different REER indices. Figure 3.1

illustrates the different kinds of REER indices that we generate using our framework

taking the example of one country, the United States. The first plot displays eight

different country REER indices that can be constructed using the framework developed

in this paper. Four of these (solid lines) are value added exchange rate indices and

the other four are indices for gross output. The eight indices can also be seen as two

groups of four indices each corresponding to the uniform elasticity elasticity (UE) or

our baseline calibration. Here we use normalized versions of the weighting matrices,

the rationale for which we will discuss below. All indices are in logs and normalized

to zero at the start of the sample period so the value on the y axis can be read as

the percentage deviation from the start of the sample. The second plot illustrates how

each of the 8 indices in the first plot can be split into 35 sectoral components using the

baseline GVC-REER as an example.

149

For reference, figures C.3-C.7 in appendix C.13 show the 8 indices for all 40 countries

in the sample. Several interesting observations are worthy of mention. Firstly, note that

there is substantial heterogeneity across the indices which speaks to the importance

of incorporating trade in intermediate goods. Secondly, we note that the 8 indices,

although different, show high comovement for most countries. The notable exception is

China. Here a comparison of the red dotted line and the pink solid line for instance

shows that although there was an appreciation in China’s value added exchange rate

(GVC-REER) in the initial part of the sample, if we impose the constant elasticity

assumption and look at China’s gross output instead of value added, the conclusion

seems to be the opposite. China is a country that shows the most disparity across REER

indices and we will discuss and illustrate them in the remainder of this section.

As mentioned before, our framework also allows us to compute exchange rates at the

sector level to gauge competitiveness of individual sectors within a country. Figure 3.2

shows some sector level exchange rates for select countries. As can be seen in the figure,

we find evidence of substantial heterogeneity across movements in competitiveness for

sectors within countries. For Mexico for instance we find that although the aggregate

exchange rate appreciates through the sample period, the REER for the financial

intermediation sector indicates depreciation, implying an increase in its competitiveness

even as the overall competitiveness of the economy falls.

We next illustrate the role of different aspects of our REER indices in isolation. Figure

3.3 shows a comparison of uniform elasticity and baseline elasticity GVC-REER indices

for select countries. The figure clearly shows the dramatic increase in the volatility of

REER when moving from Cobb-Douglas case(constant elasticity) to the case where more

realistic elasticities estimated from the data are incorporated 100. This is the reason we100The same pattern holds in a comparison of constant and heterogenous elasticities

150

Figure 3.1 – REER indices for USA

1995 2000 2005 2009

0

0.05

0.1

United States

GVC−REER(UE)GVC−REER(GDPdef,UE)Q−REER(UE)Q−REER(GDPdef,UE)GVC−REERGVC−REER(GDPdef)Q−REERQ−REER(GDPdef)

1995 2000 2005 2010−10

−5

0

5

10

15

20

Sectoral GVC−REER: 35 sectors for the US

Notes: This figure illustrates all the different REER indices that we compute using ourframework taking the case of USA as an example. The first plot shows the 8 indicesat the aggregate (country) level and the second plot shows how each of the 8 can befurther split into 35 sectoral components.All indices are in logs and normalized to zero at the start of the sample period sothe value on the y axis can be read as the percentage deviation from the start of thesample. Further, all own weights are normalized (as done by the IMF) to make a visualcomparison feasible. In this figure the IMF convention is adopted so that an increasecorresponds to an appreciation.

151

Figure 3.2 – Sector level Exchange rates along with Aggregate country REER for select countries

1995 2000 2005 2009

−2

0

2

4

6

8

Australia

Mining and Quarrying

Other Non−Metallic Mineral

Aggregate

1995 2000 2005 20090

1

2

3

4

5

6

7

China

Mining and Quarrying

Renting of M&Eq and Other Business Activities

Aggregate

1995 2000 2005 2009

−3

−2

−1

0

1

2

3

4

Mexico

Renting of M&Eq and Other Business Activities

Financial Intermediation

Aggregate

1995 2000 2005 2009

0

5

10

15

United States

Coke, Refined Petroleum and Nuclear Fuel

Mining and Quarrying

Aggregate

Notes: All indices are in logs and normalized to zero at the start of the sample periodso the reading on the value on the y axis can be read as the percentage deviation fromthe start of the sample. In this figure the IMF convention is adopted so that an increasecorresponds to an appreciation.

152

Figure 3.3 – The role of heterogenous elasticities

1995 2000 2005 20090

0.2

0.4

0.6

China

1995 2000 2005 2009

−0.6

−0.4

−0.2

0Germany

1995 2000 2005 2009

−0.1

0

0.1

United States

GVC−REER(UE)

GVC−REER

Notes: All indices are in logs and normalized to zero at the start of the sample periodso the reading on the value on the y axis can be read as the percentage deviation fromthe start of the sample. In this figure the IMF convention is adopted so that an increasecorresponds to an appreciation.

chose to display indices based on normalized weights in figure 3.1.

Due to the high volatility of the REER with heterogenous elasticities, a mere visual

comparison between the two indices is not informative. Moreover, our focus in this

paper is not on second moments of REER. Therefore, in order to illustrate the role

played by heterogenous elasticities we define a statistic to qualitatively capture the

differences in REER based on uniform and heterogenous elasticity. For each entity (e)

and for each year, we create a variable det which takes the value one if the GVC-REER

uniform elasticity and heterogenous elasticity (with baseline calibration) indices move

in opposite directions and zero otherwise.

indices for gross output competitiveness as well (These results are not reported)

153

Table 27 – Divergence index for Countries

de number of countries0.21 10.14 40.07 150 21

total=41

det = 1 (sign(4GV C −REER(BM)t) 6= sign(4GV C −REER(CE)t)) (3.42)

We then compute the mean of det for each e across all time periods and to define the

“Divergence index” for entity e as follows:

de =

∑Tt=2 d

et

T − 1(3.43)

Note that de takes the value zero if the two REER measures always agree in their

direction of movement and takes the value of 1 if they never agree, i.e always move in

opposite directions.

Table 27 summarizes the distribution of the divergence index for country level GVC-

REER101. A large fraction of countries (21) never see a divergence between the two

measures. The maximum number of times the measures move in opposite directions is

3, which is still a small fraction (20%) of the total number of years. This happens for

Slovenia. Our main takeaway from these statistics is that incorporation of heterogenous

elasticities does not significantly alter the REER indices at the country level, at least

154

qualitatively.

The story however is different when we go to more disaggregated level of sectors

within each country. Here we find examples where the two measures disagree on sign

in as many as 10 (67%) of the time periods. Figure C.2 in the appendix displays a

histogram plot of the divergence index for 1435 country-sector pairs, and figure 3.4

shows some examples where the two measures have the highest disparity.

Figure 3.4 – Examples with high divergence between uniform elasticity and heterogenous elasticityGVC-REER

1995 2000 2005 2009−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

Russia: Retail Trade(WIOD sector 21)Divergence index=0.57

GVC−REER,normalized

GVC−REER(UE),normalized

1995 2000 2005 2009−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Italy: Coke, Refined Petroleum and Nuclear FuelDivergence index=0.71

GVC−REER,normalized

GVC−REER(UE),normalized

Notes: All indices are in logs and normalized to zero at the start of the sample periodso the reading on the value on the y axis can be read as the percentage deviation fromthe start of the sample. In this figure the IMF convention is adopted so that an increasecorresponds to an appreciation.

Next, we consider the role of using sector level price indices in isolation. Figure 3.5

plots the GVC-REER indices based on the baseline calibration using sector level prices

alongside the same indices constructed using an aggregate price index (namely the GDP

deflator) for select countries. While there is very little difference between the two indices

for some countries (Germany) the divergence is substantial for countries like China and101The results for other REERs including Q-REER are qualitatively similar

155

Turkey. The difference is most stark when the indices move in opposite directions (as is

the case for these countries at various points in the sample), as it shows that ignoring

sector level information can lead to an error in computing not only the magnitude but

also the direction of exchange rate movement. For instance, in 2003, while the GDP

deflator based REER indicates a depreciation, the more comprehensive REER based on

sector level prices actually indicates an appreciation of the Chinese GVC-REER. Similar

instances are also observed for other countries, most notably for India and Turkey as

shown in figure 3.5.

Figure 3.5 – The role of sector level price indices

1995 2000 2005 2009

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

China

1995 2000 2005 2009

−0.7

−0.6

−0.5

−0.4

−0.3

−0.2

−0.1

0Germany

1995 2000 2005 2009−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

Turkey

1995 2000 2005 2009

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

India

GVC−REER

GVC−REER(GDP def)

Notes: All indices are in logs and normalized to zero at the start of the sample periodso the reading on the value on the y axis can be read as the percentage deviation fromthe start of the sample. In this figure the IMF convention is adopted so that an increasecorresponds to an appreciation.

156

3.11 Application: Bilateral Real Exchange Rates:

The bilateral real exchange rate (RER) is commonly used to gauge competitiveness

as well as cost of living differentials between countries. In particular, the bilateral real

exchange rate between countries h and f is defined as follows:

RERhf = p(V )f − p(V )h (3.44)

where pf and ph are changes in aggregate (country wide) price indices measured in a

common currency.

Based on the the insights gained from the previous sections we argue that if the

goal is to measure competitiveness of one country against the other then the standard

RER measures computed using an aggregate price index(such as those in Chinn, 2006)

like the GDP deflator and ignoring trade in intermediates can be misleading since they

ignore sector level linkages between the countries.

Consider a two country world where each country has two sectors. There is no trade

in intermediate goods and production comprises entirely of own value added. Table 28

shows how the final demand is distributed across sectors.

Table 28 – IO table for bilateral RER

C U CFinal Ufinal total outputC1 C2 U1 U2

C C1 0 0 0 0 1 1 2C2 0 0 0 0 3 0 3

U U1 0 0 0 0 0 1 1U2 0 0 0 0 0 1 1

VA 2 3 1 1total output 2 3 1 1

Suppose in addition, p(V )C1 = −0.01, p(V )C2 = 0.02, p(V )U1 = 0, p(V )U2 = 0 (all prices

157

are in a common currency, so nominal exchange rate is already incorporated)

Based on the conventional RER definition using an aggregate country level price

index,

ˆRERUS−CH

= p(V )C − p(V )U = 0.008 (3.45)

and hence the conventional RER measure would indicate an increase in competitiveness

of the US. This however is misleading since the entire price increase comes from China’s

sector 2 which does not compete with any of the US sectors. Moreover, the Chinese

sector which does compete with the US is C1, which actually experiences a decrease in

its price, so the correct measure of competitiveness must signal an appreciation of the

US exchange rate against China, not a depreciation as measured by the standard RER

in 3.44.

Our framework to compute effective exchange rates can be easily modified to adjust

these bilateral RERs to better reflect movements in competitiveness. We define our

bilateral RER measure, the “GVC-RER” as follows

GV C −RERhf =m∑i=1

vhi

[m∑j=1

whhij p(V )hj +m∑j=1

whfij p(V )fj

](3.46)

Here,vhi =p(V )hi V

hi∑m

j=1 p(V )hj Vhjis the share of sector i in country h’s total value added, so that∑m

i=1 vhi = 1. The ws are weights that are analogous to the GVC-REER weights. Based

on this measure, we get ˆGV C −RERUS−CH = −0.01. Hence the two measures differ

not just in magnitude but also the sign. The conventional measure shows a depreciation

whereas the new measure shows an appreciation that is consistent with intuition.

Figure 3.6 Shows the comparison of the two RER measures for China against two of

158

its major trading partners–The United States and Germany. In computing these indices,

the weights are normalized so that the sum of the home country and foreign country

weights are equal in magnitude, as is the case with the standard RER measure. Unlike in

the GVC-REER effective exchange rate computation, here the normalization of weights

cannot be avoided, since otherwise the GVC-RER measure would be dominated by

home prices because home sectors (especially the own sector) on average carry much

higher GVC-REER weights.

It can be seen that there are substantial differences between the two measures for

some country pairs. For China’s bilateral exchange rate against the US for instance,

whereas the standard RER shows a U shaped pattern, the GVC-REER shows a secular

appreciation during the sample period, indicating that price movements during this

period have meant that China has lost competitiveness against the US steadily. In

appendix C.8 we take a closer look at this divergence between the two measures by

examining how different sectors and elasticities play a role in generating differences

across the two measures.

159

Figure 3.6 – Comparison of GVC-RER and standard RER bilateral exchange rates for China

1995 2000 2005 2009−0.2

0

0.2

0.4

0.6

0.8

1

1.2

China−US

1995 2000 2005 20090

0.2

0.4

0.6

0.8

1China−Germany

Notes: All indices are in logs and normalized to zero at the start of the sample periodso the reading on the value on the y axis can be read as the percentage deviation fromthe start of the sample. In this figure the IMF convention is adopted so that an increasecorresponds to an appreciation.

3.12 Conclusion

This paper proposes a theoretical framework to compute real effective exchange

rates (REER) as a measure of competitiveness by incorporating four features that

have been typically overlooked in the literature and that we show are likely to lead to

mis-measurement in competitiveness. Firstly, we distinguish between trade by end use

category (i.e intermediate vs final). Recognizing that with trade in intermediate inputs,

value added and gross output become delinked, we define and compute REER indices

to quantify competitiveness both in terms of gross output (Q-REER) and value added

(GVC-REER). Secondly, we go beyond aggregate REERs for countries and compute

REERs for individual sectors within countries. We are able to do so by exploiting

detailed sector level trade flows in the data and by specifying a general multi-country

multi-sector model on the theoretical side. Thirdly, we construct sector level price

160

indices and use these in our REER indices instead of relying on the more coarse country

level price indices like CPI, GDP deflator or some measure of unit labor cost. Fourthly,

we explicitly estimate and incorporate different elasticities of substitution in production

functions and final demand aggregators in our REER indices, which is a significant

improvement from the typical practice of assuming all elasticities to be unity as is

done in the literature. We illustrate the importance of each of these additions using

illustrative examples as well as actual REER indices computed using data from the

World Input-Output Database (WIOD) and outline the conditions under which our

general framework nests the other measures in the literature.

We take our framework to the data by utilizing detailed input-output tables from the

World Input-Output Database (WIOD). We compute REER indices for 40 countries

and 1435 country-sector pairs for the period 1995-2009 and display various aspects of

our REER measures and contrast them with other measures in the literature.

In addition to addressing the issue of competitiveness in a comprehensive manner, we

see two other important auxiliary contributions of the paper. Firstly, our modeling of

the production and consumption aggregators is the most comprehensive in the literature

and allows for features like intermediate inputs and several elasticities of substitution

including a distinction between macro and micro elasticities that has been shown to

be a feature of the data (see Feenstra et al., 2010). Although we worked with a static

partial equilibrium model in this paper in order to best address the primary question

of interest, the model can be extended to a dynamic general equilibrium setting to

study other important issues in international macroeconomics including international

transmission of shocks. Secondly, this is the first paper to our knowledge that has

taken up the task of estimating elasticities of substitution comprehensively by making a

161

distinction between consumption and production elasticities on the one hand and micro

and macro elasticities on the other. Since even the most advanced empirical estimates of

elasticities available in the literature to date do not distinguish between production and

consumption elasticities (see for instance Broda and Weinstein, 2006, Soderbery, 2013 or

Feenstra et al., 2010), DSGE models aiming to study the role of production sharing are

often missing a key component in their calibration102. Our elasticity estimates provide a

first step toward filling this void.

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Appendices

A Appendix: Chapter 1

Application: Expansionary Monetary Contractions

Expansionary monetary contractions (or equivalently contractionary devaluations)

are phenomena that standard macro models are unable to account for, especially

for advanced economies. Although, liability dollarization can explain this puzzle for

developing economies (see for instance (Cook, 2004)), these explanations cannot explain

the evidence in favor of expansionary monetary contractions in the US based on certain

identified vector auto-regressions like those in Uhlig (2005). The trade finance mechanism

173

proposed in this paper can in principle account for this result if the external finance

dependence in relatively high. Figure A.1 displays the impulse responses to a home

monetary contraction with asymmetric passthrough (θhf = 0.9, θfh = 0.1) and varying

degrees of external finance dependence when the elasticity of substitution is 2. It

shows that in this case when δ is high enough, home output actually expands following

a monetary contraction. The reason is that although the exchange rate appreciates,

because of the heavy reliance of imports on external finance import prices increase to

such an extent that demand for home output ands up increasing, even though aggregate

demand by home agent falls.

B Appendix: Chapter 2

B.1 Model With Sticky Wages:

Household Problem is to maximize utility given by:

max

∞∑j=0

(βθhw)jEt(Ut+j(Ct+j , Ht+j , Nt+j(h)) (B.1)

Subject to the per period budget constraint given by:

P ,cpit Ct +

ˆs

µt,t+1(s)Dt+1(s) ≤WtNt +Dt + Tt (B.2)

and the labor demand schedule given by:

Nt(j) =

(Wt(j)

Wht

)−ηNt∀t (B.3)

Here (1− θw) denotes the time invariant probability of readjusting wages in a given period.The first order condition implies the following expression for the wage negotiated by households

who optimize in a given period:

W ∗t =

∑j(βθw)

jEt (Nt+j(h)UN (t+ j))∑j(βθw)

jEt

(Nt+j(h)UC(t+ j)

(η−1η

)1

pc,t+j

) (B.4)

174

Figure A.1 – Expansionary Monetary Contractions

1 2 3 4 5 6 7 8

−0.3

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

Home GDP

δ=0

δ=2

δ=4

(a) Home GDP1 2 3 4 5 6 7 8

−0.3

−0.2

−0.1

0

0.1

0.2

Foreign GDP

δ=0

δ=2

δ=4

(b) Foreign GDP

1 2 3 4 5 6 7 8

−1

−0.5

0

0.5

1

Home Terms of Trade

δ=0

δ=2

δ=4

(c) Home Terms of Trade1 2 3 4 5 6 7 8

−0.2

−0.15

−0.1

−0.05

0

Foreign Terms of Trade

δ=0

δ=2

δ=4

(d) Foreign Terms of Trade

1 2 3 4 5 6 7 8

−2

−1.5

−1

−0.5

0

0.5

Home Import Inflation

δ=0

δ=2

δ=4

(e) Home Import Price Inflation1 2 3 4 5 6 7 8

−2

−1.5

−1

−0.5

0

Real Exchange Rate

δ=0

δ=2

δ=4

(f) Real Exchange RateNotes: θhf = 0.9,θfh = 0.1, η = 2. Remaining parameters are calibrated to values in table 5. The horizontalaxis measures time in quarters. The vertical axis units are deviations from the unshocked path. Inflation and

nominal interest rate are given in annualized percentage points. The other variables are in percentages.

175

Which linearizes to:

w∗t = (βθw)Et( ˆw∗t+1) + (1− βθw)(UN (t)− Uc(t) + pc(t)

)(B.5)

The aggregate wage evolves according to the following equation:

wt = (1− θw)w∗t + θwwt−1 (B.6)

Combining (B.5) and (B.6), we can write the Phillips curve analogue of real wage inflation as follows:

wt =βθw

1 + βθ2wEtwt+1 +

θw1 + βθ2w

wt−1 +(1− βθw)(1− θw)

1 + βθ2w(UN (t)− Uc(t) + pc(t)) (B.7)

B.2 Parameter Estimates for Model With Importer Interest Rate TradeFinance

B.3 Data: Definitions and Sources

This appendix provides the details and sources for the data used in the empirical part of the paper.Unless otherwise mentioned, the data is at quarterly frequency from 1983Q1-2007Q4. It is seasonallyadjusted and demeaned before estimation.

US Data

• RUS : Effective Federal funds Rate, nominal, annualized, percentage

• 4Y US : Quarter to quarter growth rate of GDP per capita computed as follows:

4Y USt = 100[log(GDPtPOPt

)− log

(GDPt−1

POPt−1

)]– Note: Nominal GDP is converted to real using the GDP deflator.

• CPI inflation:

πCPI,USt = 400 [log (CPIt)− log (CPIt−1)]

• GDP Deflator Inflation:

– πGDP,USt = 400 [log (GDPDEFt)− log (GDPDEFt−1)]

• Import Price Inflation

– πIM,USt = 400 [log (PIM,t)− log (PIM,t−1)]

176

Table 29 – Summary of Prior and PosteriorPrior and Posterior Distribution of EstimatedParameters

Parameter Description Prior PosteriorDistribution Mean Stdev Mean 90% C.I

θUS Calvo Domestic beta 0.7 0.05 0.8507 0.815 0.8876

θUS ImportCalvo Import beta 0.5 0.15 0.3525 0.2044 0.5103

θEU ImportCalvo Import beta 0.5 0.15 0.8029 0.6366 0.9809

θEU Calvo Domestic beta 0.7 0.05 0.7494 0.6947 0.8073

σc Intermemporal Elasticity gamma 1 0.5 4.4685 3.288 5.6461

σL Labor supply Elasticity gamma 2 0.5 1.6053 1.0014 2.205

h Habit Parameter beta 0.5 0.1 0.5452 0.3916 0.704

η Intra Temporal Elasticity gamma 1 0.25 0.4044 0.2543 0.5505

φUSπ Taylor Rule Parameter gamma 1.5 0.25 1.8714 1.5407 2.1731

φUSy Taylor Rule Parameter gamma 0.5 0.25 0.4654 0.2106 0.7025

φUSe Taylor Rule Parameter gamma 0.1 0.05 0.0312 0.0099 0.0509

φEUπ Taylor Rule Parameter gamma 1.5 0.25 1.8547 1.5163 2.1842

φEUy Taylor Rule Parameter gamma 0.5 0.25 0.5387 0.2365 0.8255

φEUe Taylor Rule Parameter gamma 0.1 0.05 0.0271 0.0077 0.0448

ρUSA US TFP Persistence beta 0.8 0.1 0.7892 0.7149 0.8681

ρUSR US Interest rate Smoothing beta 0.5 0.2 0.8247 0.794 0.8553

ρUSG US Government spending Persistence beta 0.8 0.1 0.9655 0.9463 0.9848

ρEUA EU TFP Persistence beta 0.6 0.2 0.5841 0.2818 0.9445

ρEUR EU Interest rate Smoothing beta 0.5 0.2 0.8633 0.8372 0.8891

ρEUG EU Government spending Persistence beta 0.8 0.1 0.9275 0.8869 0.9699

ρZ Global Productivity Persistence beta 0.66 0.15 0.4494 0.2541 0.644

δEU→US Trade Finance Parameter: US gamma 2 0.75 2.1414 0.9446 3.2773

δUS→EU Trade Finance Parameter: US gamma 2 0.75 2.1258 0.8294 3.341

ρUSN US Labor Supply Shock persistence beta 0.85 0.1 0.9989 0.9989 0.9989

ρEUN EU Labor Supply Shock persistence beta 0.85 0.1 0.8859 0.8352 0.9416

Notes: The results are based on 200,000 MCMC draws (split across 2 chains) after burnin with the posterior mode used as the starting value for each parameter

177

Data Sources: The data for the US block is taken from the Bureau of Economic Analysis (BEA)National Income and Product Accounts (NIPA). The data on population is taken from Ramey (2011)’spublicly available dataset.

EU data

• REU : Effective Federal funds Rate, nominal, annualized, percentage

• 4Y EU : Quarter to quarter growth rate of GDP per capita computed as follows:

4Y EUt = 100[log(GDPtPOPt

)− log

(GDPt−1

POPt−1

)]– Note: Nominal GDP is converted to real using the GDP deflator.

• CPI inflation:

πCPI,EUt = 400 [log (CPIt)− log (CPIt−1)]

• GDP Deflator Inflation:

– πGDP,EUt = 400 [log (GDPDEFt)− log (GDPDEFt−1)]

• Nominal Exchange rate Depreciation:

– 4Et = log(Et)− log(Et−1)

Data Sources: The data for the EU block is taken from the European Central Bank (ECB) Area WideModel (AWM) database. The nominal effective exchange rate series before 2000 is taken from Lubikand Schorfheide (2006)’s publicly available database.

Trade Data

• Bilateral trade data between US and European Union at quarterly frequency is taken from theIMF’s Direction of Trade Statistics (DOTS). The database only covers merchandise trade and isused in this paper as a proxy for total trade.

4 tradeGDP

= 100

[log

(Exportst + Importst

GDPUSt

)− log

(Exportst−1 + Importst−1

GDPUSt−1

)](B.8)

4ImportGDP

= 100

[log

(ImportstGDPt

)− log

(Importst−1GDPUSt−1

)](B.9)

178

C Appendix: Chapter 3

C.1 Stylized 3 by 2 GVC

The associated price indices for final goods consumption (CPIs) can be computed asfollows:

P J = [(κJJ1 )(p(Q)J1 )1−θ + (κJJ2 )(p(Q)J2 )1−θ + (κCJ2 )(p(Q)C2 )1−θ]1

1−θ (C.1)

PC = [(κCC1 )(p(Q)C1 )1−θ + (κCC2 )(p(Q)C2 )1−θ]1

1−θ (C.2)

PU = [(κUU1 )(p(Q)U1 )1−θ + (κUU2 )(p(Q)U2 )1−θ + (κCU2 )(p(Q)C2 )1−θ]1

1−θ (C.3)

Market clearing conditions:

Output of all entities except (C, 2) is sold only as final good. Table 15 implies thefollowing market clearing conditions:

QJ1 = XJC

12 + F JJ1 (C.4)

QJ2 = F JJ

2 (C.5)

QC1 = FCC

1 (C.6)

QC2 = FCC

2 + FCJ2 + FCU

2 (C.7)

QU1 = FUU

1 (C.8)

QU2 = FUU

2 (C.9)

Solving the model:

We solve the model by combining the log linearized first order conditions with themarket clearing conditions. The first order condition for final good can be written as:

F fhs = κfhs

(p(Q)fsP h

)−θF h, h, f ∈ J,C, U), s ∈ 1, 2 (C.10)

(note that only 8 out of the 18 values of F fhs are positive, as denoted in table 15 ).

We will work with the following log linearized version:

179

F fhs = −θpfs + θP h + F h (C.11)

Linearizing the expressions for the CPIs in the three countries we get:

PU

=

(pC2 F

CU2

PUFU

)p(Q)

C2 +

(p(Q)U1 F

UU1

PUFU

)p(V )

U1 +

(p(Q)U2 F

UU2

PUFU

)p(V )

U2 (C.12)

PC

=

(p(Q)C1 F

CC1

PCFC

)p(Q)

C1 +

(p(Q)C2 F

CC2

PCFC

)p(Q)

C2 (C.13)

PJ

=

(p(Q)J1F

JJ1

PJFJ

)p(Q)

J1 +

(p(Q)J2F

JJ2

PJFJ

)p(Q)

J2 +

(p(Q)C2 F

CJ2

PJFJ

)p(Q)

C2 (C.14)

The first order conditions for production are as follows:

XJC12 = wX

(p(Q)J1p(Q)C2

)−σQC

2

V C2 = = wV2

(p(V )C2p(Q)C2

)−σQC

2

These along with the production function (3.32) and its associated price index canbe linearized as follows:

XJC12 = −σp(Q)J1 + σp(Q)C2 + QC

2 (C.15)

V C2 = −σp(V )C2 + σp(Q)C2 + QC

2 (C.16)

QC2 =

(p(V )C2 V

C2

p(Q)C2 QC2

)V C

2 +

(p(V )J1X

JC12

p(Q)C2 QC2

)XJC

12 (C.17)

pC2 =

(p(V )C2 V

C2

p(Q)C2 QC2

)p(V )C2 +

(p(V )J1X

JC12

p(Q)C2 QC2

)p(V )J1 (C.18)

Next, the non trivial market clearing conditions (C.7) and (C.79) can be linearizedas follows:

180

QC2 =

(p(Q)C2 F

CC2

p(Q)C2 QC2

)FCC

2 +

(p(Q)C2 F

CJ2

p(Q)C2 QC2

)FCJ

2 +

(p(Q)C2 F

CU2

p(Q)C2 QC2

)FCU

2 (C.19)

QJ1 =

(p(Q)J1X

JC12

p(Q)J1QJ1

)XJC

12 +

(p(Q)J1F

JJ1

p(Q)J1QJ1

)F JJ

1 (C.20)

(C.21)

Computation of linearized expression for V C2 and QC

2 in section 3.3.

From (C.80) and (C.46) we get:

QC2 = V C

2 +

(p(Q)J1X

JC12

p(V )C2 VC

2

)(−σp(V )J1 + σp(Q)C2

)(C.22)

Using the linearized first order conditions for final goods consumption (C.23) in themarket clearing condition (C.86) we get:

QC2 =

p(Q)C2 FCC2

p(Q)C2 QC2

FCC2 +

p(Q)C2 FCJ2

p(Q)C2 QC2

FCJ2 +

p(Q)C2 FCU2

p(Q)C2 QC2

FCU2

=

p(Q)C2 FCC2

p(Q)C2 QC2

(−θp(Q)C2 + θP

C+ F

C) +

p(Q)C2 FCJ2

p(Q)C2 QC2

(−θp(Q)C2 + θP

J+ F

J) (C.23)

+

p(Q)C2 FCU2

p(Q)C2 QC2

(−θp(Q)C2 + θP

U+ F

U) (C.24)

Using the expressions for the linearized CPIs ((C.91) (C.92) and (C.107) )) as wellas (C.100) we can write (C.23) as follows:

Qc2 = w(Q)CJ21 p(V )J1 + w(Q)CJ22 p(V )J2 + w(Q)CC21 p(V )C1 + w(Q)CC22 p(V )C2 (C.25)

+w(Q)CU21 p(V )U1 + w(Q)CU22 p(V )U2 (C.26)

where

181

w(Q)CJ21 = −θ(p(Q)J1X

JC12

p(Q)C2 QC2

)+ θ

(p(Q)J1X

JC12

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

PJFJ

)

+θ

(p(V )C2 V

C2

p(Q)C2 QC2

)(p(Q)C2 F

CC2

p(Q)C2 QC2

)(p(Q)C2 F

CC2

PCFC

)(C.27)

+θ

(p(Q)C2 F

CJ2

p(Q)C2 QC2

)(p(Q)J1F

JJ1

PJFJ

)+ θ

(p(Q)J1X

JC12

p(Q)C2 QC2

)(p(Q)C2 F

CU2

p(Q)C2 QC2

)(p(Q)C2 F

CU2

PUFU

)(C.28)

w(Q)CJ22 = θ

(p(Q)C2 F

CJ2

p(Q)C2 QC2

)(p(Q)J2F

JJ2

P JF J

)(C.29)

w(Q)CC21 = θ

(p(Q)C2 F

CC2

p(Q)C2 QC2

)(p(Q)C1 F

CC1

PCFC

)(C.30)

w(Q)CC22 = −θ + θ

(p(V )C2 V

C2

p(Q)C2 QC2

)(p(Q)C2 F

CC2

p(Q)C2 QC2

)(p(Q)C2 F

CC2

PCFC

)+ θ

(p(V )C2 V

C2

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

PJFJ

)

+θ

(p(V )C2 V

C2

p(Q)C2 QC2

)(p(V )C2 F

CU2

p(Q)C2 QC2

)(p(Q)C2 F

CU2

PUFU

)

w(Q)CU21 = θ

(p(Q)C2 F

CU2

p(Q)C2 QC2

)(p(Q)U1 F

UU1

PUFU

)w(Q)CU22 = θ

(p(Q)C2 F

CU2

p(Q)C2 QC2

)(p(Q)U2 F

UU2

PUFU

)From (C.22) and (C.25) we can write the demand for value added by (C, 2) as a

function of prices as follows:

V c2 = w(v)CJ21 p(V )J1 + w(v)CJ22 p(V )J2 + w(v)CC21 p(V )C1 + w(v)CC22 p(V )C2

+w(v)CU21 p(V )U1 + w(v)CU22 p(V )U2

where

182

w(V )CJ21 = w(Q)CJ21 + σ

(p(Q)J1X

JC12

p(Q)C2 QC2

)w(V )CJ22 = w(Q)CJ22

w(V )CC21 = w(Q)CC21

w(V )CC22 = w(Q)CC22 + σ

(p(Q)J1X

JC12

p(Q)C2 QC2

)w(V )CU21 = w(Q)CU21

w(V )CU22 = w(Q)CU22

V c1 = w(v)CJ11 p(V )J1 + w(v)CJ12 p(V )J2 + w(v)CC11 p(V )C1 + w(v)CC12 p(V )C2

+w(v)CU11 p(V )U1 + w(v)CU12 p(V )U2

where

w(V )CC11 = −θ(

1− p(Q)C1 FCC1

PCFC

)w(V )CC12 = θ

(p(Q)C2 F

CC2

PCFC

)(p(V )C2 V

C2

pC2 QC2

)w(V )CJ11 = θ

(p(Q)C2 F

CC2

PCFC

)(p(Q)J1X

JC12

p(Q)C2 QC2

)(C.31)

w(V )CJ12 = w(V )CU11 = w(V )CU12 = 0

The appendix shows that the weight assigned by sector 2 in country C to sector 1 incountry J (its input supplier) is given by

183

w(v)CJ21 =

(p(Q)J1X

JC12

p(Q)C2 QC2

)(σ − θ) + θ

(p(Q)J1X

JC12

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

PJFJ

)︸ ︷︷ ︸

term2

+ θ

(p(V )C2 V

C2

p(Q)C2 QC2

)(p(Q)C2 F

CC2

p(Q)C2 QC2

)(p(Q)C2 F

CC2

PCFC

)︸ ︷︷ ︸

term3

(C.32)

+ θ

(p(Q)C2 F

CJ2

p(Q)C2 QC2

)(p(Q)J1F

JJ1

PJFJ

)︸ ︷︷ ︸

term4

+ θ

(p(Q)J1X

JC12

p(Q)C2 QC2

)(p(Q)C2 F

CU2

p(Q)C2 QC2

)(p(Q)C2 F

CU2

PUFU

)︸ ︷︷ ︸

term5

(C.33)

We can interpret the different terms on the right hand side of the above equation asfollows:

term2 + term4 = θ

(p(Q)J1X

JC12

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

PJFJ

)+ θ

(p(Q)C2 F

CJ2

p(Q)C2 QC2

)(p(Q)J1F

JJ1

PJFJ

)

= θ

[(p(Q)V C2 V C2p(Q)C2 Q

C2

)(p(Q)C2 F

CJ2

p(V )C2 VC2

)][(p(Q)J1X

JC12

p(Q)C2 QC2

)(p(Q)C2 F

CJ2

PJFJ

)+

(pJ(Q)1

FJJ1

PJFJ

)](C.34)(

p(V )C2 VC2

p(Q)C2 QC2

)p(Q)C2 F

CJ2 is the value added created by (C, 2) that is ultimately absorbed

in country J . Similarly(p(Q)J1X

JC12

p(Q)C2 QC2

)p(Q)C2 F

CJ2 + p(Q)J1F

JJ1 is the value added created

in (J, 1) that is ultimately absorbed in country J . Therefore we can simplify (C.34) towrite:103

term2 + term4 = θ

(p(V )C2 V

CJ2

p(V )C2 VC

2

)(p(V )J1V

JJ1

P JF J

)(C.35)

Comparison of GVC-REER and Q-REER

With trade in intermediate inputs, competitiveness in gross output and value addedcan be delinked. The expression for gross output competitiveness in our model is asfollows (We label this measure of gross output competitiveness “Q-REER”).

4Q−REERc2 = Qc2 = w(Q)CJ21 p(V )J1 +w(Q)CJ22 p(V )J2 +w(Q)CC21 p(V )C1 +w(Q)CC22 p(V )C2 +w(Q)CU21 p(V )U1 +w(Q)CU22 p(V )U2(C.36)

where

103The derivation follows by multiplying and dividing both terms by(pV C2 V C2pC2 Q

C2

)and

rearranging.

184

w(Q)CJ21 = θ

p(V )C2 VCJ2

p(V )C2 VC2

p(V )J1 VJJ1

PJFJ

+

p(V )C2 VCC2

p(V )C2 VC2

p(V )J1 VJC1

PCFC

+

p(V )C2 VCU2

p(V )C2 VC2

p(V )J1 VJU1

PUFU

−θ

p(Q)J1XJC12

p(Q)C2 QC2

(C.37)

= w(v)CJ21 − σ

p(Q)J1XJC12

p(Q)C2 QC2

(C.38)

The idea behind the “Goods-REER” measure of Bayoumi et al. (2013) is to measurecompetitiveness of gross output as opposed to value added. The analogous expressionin our framework is given by (C.36), but as will be shown later, the two measures donot coincide except in very restrictive and/or knife-edge cases.

Two differences between the value added weight w(v)CJ21 and gross output weightw(Q)CJ21 are worth highlighting. First, note that as long as the production function isnot Leontief (i.e σ 6= 0) , the gross output competitiveness weight is always lower thenthe value added weight (w(Q)CJ21 < w(V )CJ21 ). This is a consequence of the fact thatsubstitutability in the production function which causes the weight w(V )CJ21 to increasebecause of the possibility of a shift occurring from V C

2 to (J, 1)’s value added(embodiedin XJC

12 ) does not affect the gross output weight w(Q)CJ21 , for as far as gross output isconcerned the substitution between different inputs in production is irrelevant as longas the final demand for the good increases.

Secondly note that when XJC12 = 0, the two weights are equivalent. As will be shown

in the paper later on, this is a general result–that in the absence of intermediate inputsthe gross output and value added weighting matrices are identical.

Computing Aggregate Real Effective Exchange Rates for Countries

To derive the expression for country-level value added weights, we start with thefollowing decomposition of the nominal GDP of country h into its different sectoralcomponents:

p(V )hV h = p(V )h1Vh

1 + p(V )h2Vh

2 (C.39)

where pvh is the GDP deflator of country h. Log linearizing this equation we get:

185

p(V )h + V h =

(p(V )h1V

h1

p(V )hV h

)[p(V )h1 + V h

1

]+

(p(V )h2V

h2

p(V )hV h

)[p(V )h2 + V h

2

](C.40)

Since (up to a first order approximation) the change in GDP deflator is a weightedsum of changes in the different sector level prices, the above equation reduces to

Vh

=

p(V )h1Vh1

p(V )hV h

[V h1 ] +

p(V )h2Vh2

p(V )hV h

[V h2 ]

=

p(V )h1Vh1

p(V )hV h

∑f∈J,C,F

∑k∈1,2

w(v)hf1kp(V )

fk

+

p(V )h2Vh2

p(V )hV h

∑f∈J,C,F

∑k∈1,2

w(v)hf2kp(V )

fk

=

∑f∈(J,C,U)

∑k∈1,2

p(V )h1Vh1

p(V )hV h

w(v)hf1k

+

p(V )h2Vh2

p(V )hV h

w(v)hf2k

p(V )fk

(C.41)

Solution of the single sector version of the model:

Final demand:

F fh = −θp(Q)fs + θP h + F h, (h, f) ∈ (C,C), (J, J), (U,U), (C, J), (C,U) (C.42)

Linearizing the expressions for the CPIs in the three countries((C.87)-(C.88)) we get:

PU =

(p(Q)CFCU

PUFU

)p(V )C +

(p(Q)UFUU

PUFU

)p(V )U (C.43)

PC = p(V )C (C.44)

P J =

(p(Q)JF JJ

P JF J

)p(Q)J +

(p(Q)CFCJ

P JF J

)p(Q)C (C.45)

The first order conditions for production are as follows:

XJC12 = wX

(p(Q)J1p(Q)C2

)−σQc

2

V C2 = = wV2

(p(Q)C2p(Q)C2

)−σQc

2

186

Table 30 – Single sector version of the 3 by 2 model

J C U JFinal CFinal Ufinal total outputJ 0 X 0 X 0 0 XC 0 0 0 X X X XU 0 0 0 0 0 X XVA X X X

total output X X X

These along with the production function (3.32) and its associated price index canbe linearized as follows:

XJC = −σp(Q)J + σp(Q)C + QC (C.46)

V C = −σp(Q)C2 + σp(Q)C2 + QC2 (C.47)

QC =

(p(Q)CV C

p(Q)CQC

)V C

2 +

(p(V )JXJC

p(Q)CQC

)XJC (C.48)

pC =

(p(V )CV C

p(Q)CQC

)p(V )C +

(p(V )JXJC

p(Q)CQC

)p(V )J (C.49)

Next, the market clearing conditions (C.7) and (C.79) can be linearlized as follows:

QC =

(p(Q)CFCC

p(Q)CQC

)FCC +

(p(Q)CFCJ

p(Q)CQC

)FCJ +

(p(Q)C2 F

CU2

p(Q)CQC

)FCU (C.50)

QJ =

(p(Q)J1X

JC

p(Q)JQJ

)XJC +

(p(Q)JF JJ

p(Q)JQJ

)F JJ (C.51)

Using these linearized first order and market clearing conditions we can derive anexpression for change in demand for value added by country C (equation (C.135) and(C.123) )

Country Level exchange rate without exploiting sector level heterogeneity

The production functions, price indices and final demands and market clearingconditions are now given as follows:

Qc =[(wCV )

1σ (V c)

σ−1σ + (wCX)

1σ (XJc)

σ−1σ

] σσ−1 (C.52)

187

p(Q)c =[(wCV )(p(V )c)1−σ + (wCX)(p(Q)J)1−σ] 1

1−σ (C.53)

Qh = V h, h ∈ J, U (C.54)

Consumption

F J = [(κJJ)1θ (F JJ)

θ−1θ + (κCJ)

1θ (FCJ)

θ−1θ ]

θθ−1 (C.55)

FC = FCC (C.56)

FU = [(κUU)1θ (FUU)

θ−1θ + (κCU)

1θ (FCU)

θ−1θ ]

θθ−1 (C.57)

P J = [(κJJ)(p(Q)J)1−θ + (κCJ)(p(Q)C)1−θ]1

1−θ (C.58)

PC = p(Q)C (C.59)

PU = [(κUU)(p(Q)U)1−θ + (κCU)(p(Q)C)1−θ]1

1−θ (C.60)

QJ = XJC + F JJ

QC = FCC + FCJ + FCU

QU = FUU

The appendix shows that the weight assigned by country C to country J in this caseis given by:

V C = w(v)CJ p(V )J + w(v)CC p(V )C + w(v)CU p(V )U (C.61)

188

w(v)CJ

= σ

p(V )JXJC

p(Q)CQC

− θ p(V )JXJC

p(Q)CQC

+ θ

p(V )CFCC

p(Q)CQC

p(V )CFCC

PCFC

(C.62)

+θ

p(V )JXJC

p(Q)CQC

p(V )CFCJ

p(Q)CQC

p(V )CFCJ

PJFJ

+ θ

p(V )CFCJ

p(Q)CQC

p(V )CFCJ

PJFJ

+θ

p(V )JXJC

p(Q)CQC

p(V )CFCU

p(Q)CQC

p(V )CFCU

PUFU

(C.63)

w(v)CC

= −σ

p(V )JXJC

p(Q)CQC

− θ p(V )CVC

p(Q)CQC

+ θ

p(V )CVC

p(Q)CQC

p(V )CFCC

p(Q)CQC

p(V )CFCC

PCFC

+θ

p(V )CVC

p(Q)CQC

p(V )CFCJ

p(Q)CQC

p(V )CFCJ

PJFJ

+θ

p(V )CVC

p(Q)CQC

p(V )CFCU

p(Q)CQC

p(V )CFCU

PUFU

(C.64)

w(v)CU

= θ

p(V )CVC

p(Q)CQC

p(V )CFCU

p(V )CVC

p(V )UFUU

PUFU

(C.65)

It is evident from C.62 and 3.12 that w(v)CJ and wA(v)CJ are not equal. The issueof the non-equivalence of the two weighting matrices will be discussed after we havespecified the general model. For now we just want to emphasize that our weightingmatrix which exploits sector level information is unique in the literature, and so astarting point to begin a comparison with other measures in the literature is to considerthe case where there is only one sector within each country.

We next move on to our general model which builds on the intuition developed fromthis 3 by 2 setting. After discussing the relationship to other measures in the literaturebased on the general model we come back to the 3 by 2 model to show some illustrativeexamples.

C.2 Solution of the general model

189

First order conditions

first order conditions for production:

V cl = wvcl

(p(V )clp(Q)cl

)−σ3(c,l)

Qcl (C.66)

Xcl = wXcl

(p(X)clp(Q)cl

)−σ3(c,l)

Qcl (C.67)

Xcsl = wcsl

(p(X)cslp(X)cl

)−σ2(c,l)

Xcl (C.68)

X icsl = wicsl

(p(Q)is

p(X)(f)sl

c

)−σ1s(c,l)

X(f)csl (C.69)

Xccsl = wccsl

(p(Q)cs

p(X)(f)csl

)−σ1hs (c,l)

Xcsl (C.70)

Xcsl(f) = w(f)csl

(p(X)

(f)csl

p(X)csl

)−σ1hs (c,l)

Xcsl (C.71)

Here qcl and qcsl are price indices corresponding to Xcl and Xc

sl respectively and aregiven by:

p(X)cl =

[m∑s=1

(wcsl)(p(X)csl)1−σ2(c,l)

] 11−σ2(c,l)

(C.72)

p(X)(f)csl =

[n∑

i=1,i 6=c

(wicsl)(p(Q)is)1−σ1

s(c,l)

] 1

1−σ1s (c,l)

(C.73)

p(X)csl =[(wccsl )(p(Q)cs)

1−σ1h(c,l) + (wXcl )(p(X)(f)csl )1−σ1h(c,l)

] 1

1−σ1h(c,l) (C.74)

and price of gross output is given by:

190

p(Q)cl =[(wvcl )(p(V )cl )

1−σ3(c,l) + (wXcl )(p(X)cl )1−σ3(c,l)

] 11−σ3(c,l) (C.75)

where p(V )cl is the price of value added(i.e price of factor of production) of country csector l

First order conditions for final consumption:

F ics = κics

(p(Q)isP (f)cs

)−θ1s(c)F (f)cs (C.76)

F ccs = κccs

(p(Q)csP cs

)−θ1hs (c)

F cs (C.77)

F (f)cs = κ(f)cs

(P (f)csP cs

)−θ1hs (c)

F cs (C.78)

F cs = κcs

(P cs

P c

)−θ2(c)

F c (C.79)

Here P cs and P c are price indices for sector s good and aggregate good consumed by

country c, respectively and are given by

P cs (f) =

[n∑

i=1,i 6=c

(κics )(p(Q)is)1−θ1s(c)

] 1

1−θ1s(c)

(C.80)

P cs =

[(κccs )(p(Q)cs)

1−θ1hs (c) + (κ(f)cl )(P (f)cs)1−θ1hs (c)

] 1

1−θ1hs (c) (C.81)

P c =

[m∑s=1

(κcs)(Pcs)

1−θ2(c)

] 11−θ2(c)

(C.82)

Let [A]nmXnm be the input-output coefficient matrix at the country-sector level, i.ethe (i, j)th block which has dimension mXm is given by

191

[A]ijmXm =

aij11 aij12 .. aij1maij21 aij22 .. aij2m: : : :

aijm1 aijm2 .. aijmm

(C.83)

where aijsl denotes the output of (i, s) used in the production of one unit of (j, l), i.e

aijsl =p(Q)isX

ijsl

p(Q)jlQjl

(C.84)

Let [B]nmXnm be the corresponding total requirement matrix given by

[B]nmXnm = (Inm − [A])−1 (C.85)

Also, define the matrix [DQ]nmxnm to be a diagonal matrix with the (cl)th diagonalentry given by 1

pclQcl

Log Linearization

A note on notation

• for any variable Y abcd , vec

(Y abcd

)denotes a vector with all components of Y ab

cd stackedtogether

• The stacking order is as follows: d, c, b, d. i, e first the home sector index changes,followed by foreign sector, followed by home country and finally foreign country

– vec(Y bcd

), vec

(Y abc

)etc are defined accordingly.

• Examples in a 2 by 2 case (m = n = 2)

– vec(Y abcd

)=(Y 1111 , Y

1112 , Y

1121 , Y

1122 , Y

1211 , Y

1212 , Y

1221 , Y

1222 , Y

2111 , Y

2112 , Y

2121 , Y

2122 , Y

2211 , Y

2212 , Y

2221 , Y

2222

)′

– vec(Y bcd

)= (Y 1

11, Y1

12, Y1

21, Y1

22, Y2

11, Y2

12, Y2

21, Y2

22)′

This appendix contains the log linearized first order and market clearing conditions andorganizes them in stacked matrix notation which will be useful in deriving the resultsthat follow. A variable with a “” denotes log deviation from steady state.

192

Log linearizing and stacking components of production function and price indices:(tosimplify notation further, we omit the parenthesis for gross output prices, i.e theparenthesis containing “Q” is omitted)

Raw expression X(f)csl =

∑ni=1,i 6=c(w

icsl)

1/σ1s(c,l)(Xic

sl)

σ1s(c,l)−1

σ1s(c,l)

σ1s(c,l)

σ1s(c,l)−1

Log linearized expression ˆX(f)c

sl =∑ni=1,i 6=c

(pisX

icsl

P (X)(f)cslX(f)c

sl

)Xicsl

Stacked vector: (vec(X(f)csl)

)= W1XXH︸ ︷︷ ︸nm2Xn2m2

vec(Xicsl ) (C.86)

Raw expression Xcsl =

(wcsl)1/σ1h

s (c,l)(Xccsl )

σ1hs (c,l)−1

σ1hs (c,l) + (w(f)csl)1/σ1h

s (c,l)(X(f)csl)

σ1hs (c,l)−1

σ1hs (c,l)

σ1hs (c,l)

σ1hs (c,l)−1

Log linearized expression Xcsl =

∑ni=1

(pisX

icsl

p(X)cslXcsl

)Xicsl

Stacked Vector: (vec(Xc

sl))= W1XX︸ ︷︷ ︸nm2Xn2m2

vec(Xicsl ) (C.87)

Raw expression Xcl =

[∑ms=1(wcsl)

1/σ2(c,l)(Xcsl)

σ2(c,l)−1

σ2(c,l)

] σ2(c,l)

σ2(c,l)−1

Log linearized expression Xcl =

∑ms=1

(p(X)qcslX

csl

p(X)clXcl

)Xcsl

Stacked vector:vec(Xc

l ) = (W2XX)nmXnm2 vec(Xcsl) (C.88)

Raw expression q(f)csl =[∑n

i=1,i6=c(wicsl)(p

is)

1−σ1s(c,l)

] 11−σ1s(c,l)

Log linearized expression qcsl(f) =∑ni=1,i6=c

(pisX

icsl

p(X)cslXcsl

)pis

Stacked vector:vec(qcsl(f)) = (W1XPH)nm2Xnm vec(p

is) (C.89)

193

Raw expression qcsl =[(wccsl )(p

cs)

1−σ1h(c,l) + (wXcl )(p(X)(f)csl)1−σ1h(c,l)

] 1

1−σ1h(c,l)

Log linearized expression ˆp(X)c

sl =∑ni=1

(pisX

icsl

p(X)cslXcsl

)pis

Stacked vector:vec( ˆp(X)

c

sl) = (W1XP )nm2Xnm vec(pis) (C.90)

Raw expression p(X)cl =[∑m

s=1(wcsl)(p(X)csl)

1−σ2(c,l)] 1

1−σ2(c,l)

Log linearized expression qcl =∑ms=1

(p(X)cslX

csl

p(X)clXcl

)qcsl

Stacked vector:vec(qcl ) = (W2Xp)nmXnm2 vec( ˆp(X)

c

sl) (C.91)

Raw expression P cs (f) =[∑n

i=1,i6=c(κics )(p

is)

1−θ1s(c)] 1

1−θ1s(c)

Log linearized expression ˆP (f)cs =∑ni=1,i6=c

(pisF

ics

P (f)csF (f)cs

)pis

Stacked vector:

vec(P cs

)nmX1

= (W1FPH)nmXnmvec(pis)nmX1

(C.92)

Raw expression P cs =[(κccs )(pccs )1−θ

1hs (c) + (κ(f)cl )(P (f)

cs)

1−θ1hs (c)] 1

1−θ1hs (c)

Log linearized expression P cs =∑ni=1

(pisF

ics

P csFcs

)pis

Stacked vector:

vec(P cs

)nmX1

= (W1FP )nmXnmvec(pis)nmX1

(C.93)

Raw expression P c =[∑m

s=1(κcs)(P

cs)

1−θ2(c)] 1

1−θ2(c)

Log linearized expression P c =∑ms=1

(P csF

cs

P cF c

)P cs

194

Stacked vector:

vec(P c)nX1

= (W2FP )nXnmV ec(P cs

)nmX1

(C.94)

Final goods consumption first order conditions:

F ics = −θ1s(c)(pis − ˆP (f)sc) + ˆF (f)s

c(C.95)

F ccs = −θ1hs (c)(pcs − Psc) + Fs

c(C.96)

ˆF (f)cs = −θ1hs (c)(P (f)cs − Psc) + Fs

c(C.97)

F cs = −θ2(c)(P cs − P c) + F c (C.98)

We can combine these 4 conditions to write:

Fsic

= −θ1s(c)pis +(θ1s(c)− θ1hs (c)

) ˆP (f)c

s +(θ1hs (c)− θ2(c)

)P cs + θ2(c)P c + F c

Fscc

= −θ1hs (c)pcs +(θ1hs (c)− θ2(c)

)P cs + θ2(c)P c + F c

We can now stack the above n2m equations to write a single matrix equation asfollows:

vec(F ics

)n2mX1

= JF (i 6= c)[(Y1)n2mXnmvec(θ

1s(c))nmX1

][(Y2)n2mXnmvec(p

is)nmX1

]− −JF (i = c)

[(Y1)n2mXnmvec(θ

1hs (c))nmX1

][(Y2)n2mXnmvec(p

is)nmX1

]+ JF (i 6= c)

[Y1(vec(θ1s(c))nmX1 − vec(θ1hs (c))nmX1

)][Y1vec(P (f)

cs)nmX1

]+

(Y1vec(θ

1hs (c))nmX1 − (Y3)n2mXnvec(θ

2(c))nmX1

)(Y1vec(P

cs)nmX1

)+

[Y3vec(θ

2(c))nmX1

][Y3vec(P

c)nX1

]+ Y3F

c

where Y1 = 1n⊗ Inm, Y2 = In⊗ 1n⊗ Im, Y3 = 1n⊗ In⊗ 1m, is the element by elementmultiplication operator for two vectors and JF (x) is an n2m by 1 vector with ones in allindices that satisfy the condition x and zero elsewhere.

Combining this with (C.94) and (C.93),

195

vec(F ics

)n2mX1

= ZF vec(pis)nmX1 + Y3F

c (C.99)

where

(ZF )n2mXnm = JF (i 6= c)[(Y1)n2mXnmvec(θ

1s(c))nmX1

] [(Y2)n2mXnm] (C.100)

− −JF (i = c)[(Y1)n2mXnmvec(θ

1hs (c))nmX1

] [(Y2)n2mXnm]

+ JF (i 6= c)[Y1(vec(θ1s(c))nmX1 − vec(θ1hs (c))nmX1

)] [Y1WFH ]

+(Y1vec(θ

1hs (c))nmX1 − (Y3)n2mXnvec(θ

2(c))nmX1

) (Y1W1FP )

+[Y3vec(θ

2(c))nmX1

] [Y3W2FPW1FP ]

Log linearizing Production first order conditions:

V cl = wvcl

(pvclpcl

)−σ3(c,l)

Qcl (C.101)

Xcl = wXcl

(qclpcl

)−σ3(c,l)

Qcl (C.102)

Xcsl = wcsl

(qcslqcl

)−σ2(c,l)

Xcl (C.103)

X icsl = wicsl

(pis

q(f)csl

)−σ1s(c,l)

X(f)csl (C.104)

Xccsl = wccsl

(pcsqcsl

)−σ1hs (c,l)

Xcsl (C.105)

Xcsl(f) = w(f)csl

(q(f)cslqcsl

)−σ1hs (c,l)

Xcsl (C.106)

Xicsl = −σ1

s(c, l)pis + σ1

s(c, l)ˆp(X)

(f)c

sl + X(f)csl

Xccsl = −σ1h

s (c, l)pcs + σ1hs (c, l) ˆp(X)

c

sl + Xcsl

ˆXcsl(f) = −σ1h

s (c, l) ˆp(X)(f)c

sl + σ1hs (c, l) ˆp(X)

c

sl + Xcsl

Xcsl = −σ2(c, l) ˆp(X)csl + σ2h(c, l) ˆp(X)

c

l + Xcl

196

Xicsl = −σ1

s(c, l)pis +

(σ1s(c, l)− σ1h

s (c, l)) ˆp(X) +

(σ1hs (c, l)− σ2(c, l)

) ˆp(X)c

sl

+(σ2(c, l)− σ3(c, l)

) ˆp(X)c

l + σ3(c, l)pcl + Qcl

Xccsl = −σ1h

s (c, l)pcs +(σ1hs (c, l)− σ2(c, l)

) ˆp(X)c

sl

+(σ2(c, l)− σ3(c, l)

)qcl + σ3(c, l)pcl + Qcl

These n2m2 equations can be stacked to write

vec(Xicsl

)n2m2

= −JX(i 6= c)[C1vec

(σ1s(c, l)

)nm2X1

][C3vec(p

is)nmX1

]− JX(i = c)

[C1vec

(σ1hs (c, l)

)nm2X1

][C3vec(p

is)nmX1

]+ JX(i 6= c)

[C1

(vec

(σ1s(c, l)

)nm2X1

− vec(σ1hs (c, l)

)nm2X1

)][C1

ˆp(X)(f)c

sl

]+

[C2

(vec

(σ2(c, l)

)nmX1

− vec(σ3(c, l)

)nmX1

)][C2

ˆp(X)cl

]+

[C1vec

(σ1hs (c, l)

)nm2X1

− C2vec(σ2(c, l)

)nmX1

][C1

ˆp(X)csl

]+

[C2vec

(σ3(c, l)

)nmX1

][C2vec(p

is)nmX1

]+ C2Q

cl

where C1 = 1n ⊗ Inm2 , C2 = 1n ⊗ In ⊗ 1m ⊗ Im, C3 = In ⊗ 1n ⊗ Im ⊗ 1m. JX(y) is ann2m by 1 vector with ones in all indices that satisfy the condition y and zero elsewhere.

Combining this with (C.87) - (C.91) we get:

vec(Xicsl

)n2m2

= ZXvec(pis)nmX1 + C2Ql

c(C.107)

where

ZX = −JX(i 6= c)[C1vec

(σ1s(c, l)

)nm2X1

] [C3] (C.108)

− JX(i = c)[C1vec

(σ1hs (c, l)

)nm2X1

] [C3]

+ JX(i 6= c)[C1

(vec

(σ1s(c, l)

)nm2X1

− vec(σ1hs (c, l)

)nm2X1

)] [C1WXH ]

+[C2

(vec

(σ2(c, l)

)nmX1

− vec(σ3(c, l)

)nmX1

)] [C2W2XPW1XP ]

+[C1vec

(σ1hs (c, l)

)nm2X1

− C2vec(σ2(c, l)

)nmX1

] [C1W1XP ]

+[C2vec

(σ3(c, l)

)nmX1

] [C2]

Next, linearizing the production function we have:

197

vec(Qcl

)= (Dv)nmXnm

(vec(V cl

))nmX1

+ (DX)nmXnm vec(Xcl

)(C.109)

vec(pcl)

= Dvvec (p(V )cl ) +DXvec(

ˆp(X)c

l

)(C.110)

(here Dv and DX are nmXnm diagonal matrices denoting the shares of value addedand intermediate inputs in the production of different goods , i.e the lcth diagonal entryof Dv is p(V )clV

cl

p(Q)clQcland that of DX is p(X)clX

cl

p(Q)clQcl. We can use (C.90) and (C.91) in (C.110)to

obtain the following expression linking price of gross output and price of value added:

vec(pcl)

= (I −DXW2XPW1XP )−1DV vec(

ˆp(V )cl

)(C.111)

The market clearing conditions (C.7) can be linearized as:

Qij =

n∑h=1

m∑l=1

X ihjl

Qij

X ihjl +

n∑h=1

F ihj

Qij

F ihj (C.112)

As before, these can be written in stacked form by creating matrices SX and SF fromthe above equations to yield:

vec(Qcl

)= (SF )nmXn2m vec

(ˆF fcs

)+ (SX)nmXn2m2 vec

(Xfcsl

)(C.113)

C.3 Derivations of the expressions (3.21) and (3.25)

From (C.113) and (C.107) we get

vec(Qcl

)[Inm − SXC2] = (SXZX + SFZF ) vec (pcl ) + SFY3vec

(F c)

(C.114)

Using (C.111) in (C.114)and rearranging we get:

vec(Qcl

)= [Inm − SXC2]−1 (SXZX + SFZF ) (I −DXW2XPW1XP )−1DV vec

(ˆp(V )il

)(C.115)

+ [Inm − SXC2]−1 SFY3vec(F i)

198

This is equation (3.25) in the main text.Next, starting from the linearized production function vec

(Qcl

)= Dvvec

(V cl

)+

DXvec(Xcl

)we first use (C.88) and (C.87) to get:

vec(Qcl

)= Dvvec

(V cl

)+DXW2XXW1XXvec

(X icsl

)(C.116)

substituting (C.107) in (C.116) and rearranging we get:

vec(Qcl

)[I −DXW2XXW1XXC2] = Dvvec

(V cl

)+DXW2XXW1XXZXvec (pcl ) (C.117)

It can be shown that W2XXW1XXC2 = I and hence [I −DXW2XXW1XXZ4Z6] = Dv

so that the above expression simplifies to:

vec(Qcl

)= vec

(V cl

)+D−1

V DXW2XXW1XXZX (I −DXW2XPW1XP )−1DV vec(

ˆp(V )cl

)(C.118)

eliminating vec(Qcl

)from (C.115) and (C.118) we get:

vec(Vcl

)=

(Inm − SXC2

)−1 (SF ZF + SXZX

)−D−1

v DXW2XXW1XXZX

(I −DXW2XPW1XP

)−1DV vec

(pvcl

)(C.119)

+(I − SXZ4Z6

)−1SF Y3vec

(Fc)

It is easy to show the following identities:

(Inm − SXC2)−1 = D−1Q BDQ (C.120)

(I −DXW2XPW1XP )−1 = B′ (C.121)

Substituting (C.120) and (C.121) in (C.119) we get (3.21) in the main text, with:

WV =[D−1Q BDQ(SFZF + SXZX)−D−1V DXW2XXW1XXZX

]B′DV (C.122)

C.4 Proofs of Propositions

199

Sketch of Proof of Proposition 3.1

In this appendix we sketch the proof of proposition 3.1. Since the underlying intuition is preservedin the case with m = 1, we will sketch the proof for this simplified case.

The expression for the weighting matrix is given by:

w =D−1Q BDQ (SFZF + SXZX)−D−1v DXW2XXW1XXZX

B′DV (C.123)

As shown in proposition (3.2), under the constant elasticity assumption and m = 1, the GVC-REERweighting matrix reduces to VAREER weighting matrix defined in Bems and Johnson (2012), whichaccording to equation (18) in that paper is given by

w = −I +D−1Q BDQSFM2B′Dv (C.124)

define the matrices

Z1 = Z4 = 1n ⊗ In ≡M2

Z2 = Z5 = In ⊗ 1n ≡M1

Under the constant elasticity assumption, from (C.108) and (C.100) we have:

ZX = σ(M2 −M1) (C.125)

ZF = θ(M2WFP −M1) (C.126)

Taking the partial derivative of (C.123) wrt θ

∂w

∂θ= D−1Q BDQSF (M2WFP −M1)B

′DV (C.127)

using (C.124) in (C.127) , the following relationship holds for the off diagonal elements of w

∂wij

∂θ= wij −

[D−1Q BDQSFM1B

′DV

]ij, i 6= j (C.128)

Simplifying the last term in the above expression gives (3.23) in the main text.

Proof of Proposition 3.2

Part 1.

the GVC-REER weighting matrix under (A2) is given by:

WV =

(I − SXZ4Z6)−1 −D−1v DXW2XXW1XXZX

(I −DXW2XpW1Xp

)−1DV (C.129)

200

whereZX = σ1(Z4W1XP − Z5) + σ2(Z4Z6W2XPW1XP − Z4W1XP ) + σ3(Z4Z6 − Z4Z6W2XPW1XP )

with

Z1 = 1n ⊗ Inm , Z2 = In ⊗ (1n ⊗ Im), Z3 = In ⊗ 1m, (Z4)n2m2Xnm2 = 1n ⊗Inm2 , (Z5)n2m2Xnm = In ⊗ 1n ⊗ Im ⊗ 1m and Z6 = (In ⊗ 1m)⊗ Im

for m = 1, the different matrices in the above equation simplify as:Z1 = Z4 = 1n ⊗ In ≡M2

104

Z2 = Z5 = In ⊗ 1n ≡M1

Z3 = Z6 = In

W2FP = W2XX = W2XP = In

DXW1Xp = Ω′, where Ω is the country level input output matrix with Ωij =piXijpjQj

ZX = σ1(Z4W1XP − Z5) + σ2(Z4Z6W2XPW1XP − Z4W1XP ) + σ3(Z4Z6 − Z4Z6W2XPW1XP )

= σ1(M2W1XP −M1) + σ2(M2W1XP −M2W1XP ) + σ3(M2 −M2W1XP )

= σ1(M2W1XP −M1) + σ3(M2 −M2W1XP ) (C.130)

ZF = θ1(Z1W1FP − Z2) + θ2 (Z1Z3W2FPW1FP − Z1W1FP )

= θ1(M2WFP −M1)

Substituting all these in the expression for ZV clp we get

W V = −θ1 (I − SXM2)−1 SF (M1 −M2WFP )(I − Ω′)−1DV

+ (I − SXM2)−1 SX [σ1(M2W1XP −M1) + σ3(M2 −M2W1XP )] (I − Ω′)−1DV

− D−1V DXWX [σ1(M2W1XP −M1) + σ3(M2 −M2W1XP )] (I − Ω′)−1DV

104In this section the matrices M1 and M2 are as defined in Bems and Johnson (2012)and are different from the ones defined earlier in this paper.

201

This is the same as equation (33) in section 5 of Bems and Johnson (2012) IOREER-BJ.

Part 2 and 3 follow directly from Bems and Johnson (2012).

Part 4:

The IMF manufacturing weights are given by (Bayoumi et al. (2005))

W ijimfm =

∑k w

iksjk∑k w

ik(1− sik)(C.131)

where sjk = salesjk∑l sales

lk and wik = salesik∑n sales

in (salesij denotes gross sales from country i tocountry j)

Substituting the expressions for sjk and wik in W ij and simplifying we get:

W ijimfm =

1

T imfmi

∑k

(salesik∑n sales

in

)(salesjk∑l sales

lk

)(C.132)

where

T imfmi = 1−∑k

(salesik∑n sales

in

)(salesik∑l sales

lk

)(C.133)

From parts 1-3 we know that under (A1), (A2) TEER and VAREER-BJ are equivalentand given by equation (24) in BJ which is reproduced below.

W ijBJ =

1

TBJi

∑k

(pivV ik

P ivV i

)(pjvV jk

P kF k

)(C.134)

with TBJi =∑

k

(pivV ik

P ivV i

)(pivV ik

PkFk

)Under the assumption of no intermediates (A3)we have:

• piv = pi, Qi = V i, V ik = F ik

• salesik = pivV ik = piV ik

•∑

n salesin =

∑n p

ivV in = pivV i

•∑

l saleslk =

∑l plvV lk = P kF k

Substituting these in (C.132) and (C.133)

202

W ijimfm = W ij

BJ

Finally, using αc = αT = 0 we haveW ijimf = W ij

BJ

The equivalence of IMF-REER to GOOD-SREER and IRER follows in a straight-forward manner from the respective papers (Bayoumi et al. (2013) and Thorbecke(2011))

Proof of Proposition 3.3

Part 1

We start with the following expression for GVC-REER weights at the country-sectorlevel (C.129).

under the constant elasticity assumption:

ZX = −Z5 + Z4Z6 (C.135)

ZF = −Z2 + Z1Z3W2FPW1FP (C.136)

Here, without loss of generality we can assume that the elasticity is 1.

(I − SXZ4Z6)−1 = D−1Q BDQ ≡ λ (C.137)

(I −DXW2XPW1XP )−1 = B′ (C.138)

Substituting (C.135), (C.136), (C.137) and (C.138) in (C.129)

WV =[(λ(SFZF + SXZX)−D−1

V DXW2XXW1XXZX

]B′DV

= λSFZ1Z3W2FPW1FPB′Dv +

[λSXZ4Z6 − λ (SFZ2 + SXZ5)−D−1

V DXW2XXW1XXZX

]B′DV(C.139)

Using the identities SFZ2+SXZ5 = I and DV −DXW2XXW1XXZX = (I−A)′ = B′−1,we can show that the second term in (C.139) is the identity matrix, so that (C.139)reduces to:

203

WV = −Inm + λSFZ1Z3W2FPW1FP [Bcl ]′Dv (C.140)

= −Inm +M1mM2m

where

M1m = λSFZ1Z3

M2m = W2FPW1FP [Bcl ]′Dv

Next, the country level weights (which correspond to VAREER in Bems and Johnson(2012)) are given by:

W 1V =

(I − S1

XZ14Z

16

)−1 (S1FZ

1F + S1

XZ1X

)− (D1

v)−1D1

XW1XXZ1X

(I −D1

XW1Xp

)−1D1V

(C.141)(where the superscript 1 on the matrices on the RHS of (C.141) indicates that the matrixcorresponds to the case where m = 1)

Following steps similar to those used to derive (C.140) we can get an analogousexpression:

W 1V

= −In + λ1S1FZ

11Z

13W

11FP [Bc]′Dv (C.142)

= −In +M1M2

where

M1 = λ1S1FZ

11Z

13 (C.143)

M2 = W 11FP [Bc]′D1

v

The 2 country level weights are equal iff

204

RVWVRg = WV (CG) (C.144)

‘Since RVRg = In, a necessary and sufficient condition for (C.144) to hold is :

(RVM1m)(M2mRg) = M1M2 (C.145)

(RVM1m)ij =n∑c=1

m∑l=1

m∑s=1

(visb

icslF

cjl

pviV i

)

(M2mRg)ij =n∑c=1

m∑l=1

m∑s=1

(vjsb

jcslF

cil

P iF i

)

(M1)ij =n∑c=1

(vibicF cj

pviV i

)(M2)ij =

n∑c=1

(vjbjcF ci

P iF i

)

here vis =(pvis V

is

pisQis

).

From these expressions it is clear that the condition (C.145) is satisfied for all valuesif and only if

vin∑c=1

bicf cj =m∑l=1

vis

n∑c=1

m∑s=1

biclsFcjs ∀i, j (C.146)

or stacking these conditions in matrix notation:

diag[vc]nXn[Bc]nXn[FC ]nXn = (MV )nXnmdiag[vcl ]nmXnm[Bcl ]nmXnm[F c

l ]nmXn (C.147)

which is the same as (3.39) in the main text.

205

Interpretation in the case of constant elasticity

Under the assumption that all elasticities (both in production and consumption) arethe same, we can interpret the country-sector level weights purely in terms of valueadded trade flows. Suppose the common elasticity is η . Without loss of generality wecan assume η to be unity since it factors out. Then the weighting matrix W can bewritten as above:

WV = −Inm +M1M2 (C.148)

The matrix M1 is an nm by n matrix with each row corresponding to a uniqueproduction entity. Along this row, the n columns give the value added created by theproduction entity that is finally absorbed by each country. As an example, the entrycorresponding to row (i, l) and column j gives the value added created by productionentity (i, l) that is eventually absorbed in country j as a fraction of total value addedcreated by the production entity (i, l). Entries in this matrix can thus be interpreted asexport shares in value added terms. The corresponding mathematical expression is105

M1((i, l), j) =vil∑n

c=1

∑ms=1 b

icls (p(Q)csF

cjs )

p(V )ilVil

(C.149)

where vil =pvil V

il

pilQil

. For later, it is convenient to write this expression compactly as:

M1((i, l), j) =p(V )ilV

ijl

p(V )ilVil

(C.150)

where pvil Vijl is the value added created by production entity (i, l) that is finally absorbed

in country j.Matrix M2 is an n by nm matrix with each column corresponding to a unique

production entity and each row containing the value added created by the entitycorresponding to the column that is absorbed in each country, as a fraction of the totalfinal demand in that country. As an example, the entry corresponding to column (i, l)

and row j gives the value added created by production entity (i, l) that is ultimately

105The raw expression of the matrix M1 is∑nc=1

∑ms=1 b

iclsp(Q)csF

cjs

p(Q)ilQil

. Multiplying and dividing

by vil =p(V )ilV

il

p(Q)ilQilyields the expression below.

206

absorbed in country j as a fraction of total final demand of country j. The correspondingmathematical expression is :

M2(j, (i, l)) =vil∑n

c=1

∑ms=1 b

icls (p(Q)csF

cjs )

P jF j(C.151)

As above, it turns out to be more convenient to rewrite the above expression inshort-hand notation as follows:

M2(j, (i, l)) =p(V )ilV

ijl

P jF j(C.152)

Using the generic terms from (C.150) and (C.152)we can write the weight assignmentby country sector (h, l) to country-sector (c, s) where (h, l) 6= (c, s) as follows:

whcls =n∑k=1

[(p(V )hl V

hkl

) (p(V )csV

cks

)(p(V )hl V

hl

)(PKF k)

], (h, l) 6= (c, s) (C.153)

where we use lower case w to denote constant elasticity weights. This is a generalized formof equation 3.9 which was derived in the context of a simplified model and the intuitionis similar. In particular, the weight assigned by country sector (h, l) to country-sector(c, s) where (h, l) 6= (c, s) is a weighted sum of the value added created by country-sector(c, s) and absorbed by each of the countries k(= 1, .., n), where the weights are givenby the value added created by (h, l) that is absorbed in the same country k. Thiscaptures both mutual and third country competition, because the weight is high if both(p(V )hl V

hkl

)and

(p(V )csV

cks

)are high, which happens when both (h, l) and (c, s) have a

high share of value added exports to country k.

Part 2:

Under (A3), (A4) and θ1 = θ2 (=1(wlog)) we have,diag[vc]nXn = [Bc]nXn = In,

diag[vcl ]nmXnm = [Bcl ]nmXnm = Inm

(MV )nXnm[F cl ]nmXn = [FC ]nXn

With these simplifications condition (C.147) is automatically satisfied and henceGVC-REER(CG) is equivalent to VAREER.

207

(C.154)

C.5 Illustration of Role of Elasticities: Example 3.1

C.6 Estimation of elasticities

Framework

The approach used here will be based on recent work by Soderbery (2013) whichoutlines certain drawbacks in the preceding two papers and proposes an estimator whichoutperforms them. Consider a generic CES Armington aggregator defined as follows:

Dt =

[∑k∈K

(wk)1/η(Dkt)

η−1η

] ηη−1

(C.155)

The objective is to estimate the demand elasticity η. The double differenced demandequation in terms of expenditure shares is given by106:

4rln(skt) = −(η − 1)4rln(pkt) + εrkt (C.156)

where 4rln(xkt) = 4ln(xkt)−4ln(xrt) and 4ln(xjt) = ln(xjt)− ln(xj(t−1)), x = s, p r

is called a reference variety and is typically chosen to be the one with the largest share .skt is the expenditure share of the kth variety and is given by:

skt =pktDkt∑k∈K pktDkt

(C.157)

Next, given a supply curve with elasticity ρ, the supply curve in terms of differencedshares and prices can be written as:

4rln(pkt) =

(ρ

1 + ρ

)4rln(skt) + δrkt (C.158)

If the demand and supply disturbances are independent across time, then the 2equations can be multiplied and scaled to yield:106See Soderbery (2013) , Broda and Weinstein (2006) or Feenstra (1994) for furtherdetails including the actual derivation

208

Figure C.1 – Illustration of Role of Elasticities: Example 3.1

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

σ3

W(C

J)

W(CJ) for different σ3 with θ

1 fixed

GVC−REER

VAREER(BJ)

IMF

1 2 3 4 5 6 7 8−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

θ1

W(C

J)

W(CJ) for different theta1 with σ3 fixed

GVC−REER

VAREER(BJ)

IMF

12

34

56

78

1

2

3

4

5

6

−1.5

−1

−0.5

0

0.5

1

θ1

σ3

W(C

J)

0

2

4

6

8

1

2

3

4

5

6

−1.5

−1

−0.5

0

0.5

1

θ1

W(CJ)

σ3

GVC−REER

VAREER

IMF

209

Ykt = θ1Z1kt + θ2Z2kt + ukt (C.159)

where Ykt = (4rln(pkt))2 , Z1kt = (4rln(skt))

2, Z2kt = (4rln(pkt))(4rln(skt)), andukt =

εrktδrkt

1−φ .Further, the parameters of this regression model can be mapped to the primitive

parameters of the demand and supply system as follows:φ = ρ(η−1)

1+ρη∈ [0, σ−1

σ)

θ1 = φ(η−1)2(1−φ)

θ2 = 2φ−1(η−1)(1−φ)

Consistent estimates of θ1 can be obtained by using the moment condition E(ukt) = 0,where consistency relies on T →∞. 107 If standard procedures (2SLS or LIML) yield avalue of θ1 that gives imaginary values for η and ρ or values with the wrong sign, thenthe grid search or the non-linear search method of Soderbery (2013) can be used.

Implementation

We construct sectoral price indices for all cells in the WIOD input output tableusing the tables in previous year prices. For a fixed production entity(identified by thecountry-sector pair (c, l)) and a fixed sector s, table 31 shows how the estimation of thedifferent elasticities in the model maps onto the procedure outlined above.

Table 31 – Elasticity Estimation

D Dk pkProduction elasticities

σ1s(c, l) (X(f)csl) (Xkc

sl ) p(Q)ksσ1hs (c, l) (Xc

sl) (Xccsl ), (X(f)csl) p(Q)ks

σ2(c, l) (Xcl ) (Xc

kl) p(X)cklσ3(c, l) (Qc

l ) (Xcl , V

cl ) (p(Q)cl , p(V )cl )

Consumption elasticitiesθ1s(c) (F (f)cs) (F kc

s ) p(Q)ksθ1hs (c) (F c

s ) (F cs ), (F (f)cs) p(Q)ks

θ1(c) (F c) (F ck ) P c

kThis table shows how the model in section 3.4 maps into the general framework for estimation ofelasticities discussed in section C.6

107Given the nature of the data, the value of T is typically very small. For exampleSoderbery (2013) uses an unbalanced panel with 15 years of data

210

C.7 Bootstrap moments of elasticities

Table 32 – Summary of Bootstrap moments

Consumption Elasticities Production Elasticitiesθ1 θ1h θ2 σ1 σ1h σ2 σ3

15th percentile 1. 774 1. 174 1. 04 1. 65 1. 782 1. 008 0.867median 9. 876 7. 438 1. 527 7. 88 7. 7 3. 816 1. 015

85th percentile 82. 535 65. 550 4. 73 67. 22 37. 607 14. 553 1. 501sample size 1435(=35*41) 41 41 2450 1435 1435 41

Note: the table reports the percentiles of bootstrap medians, for example, for θ1, 1.774 isthe 15th percentile of the distribution of medians of the 1435 θ1 bootstrap distributions.We propose this quantity as our point estimate as they are more stable than the LIMLpoint estimate. The moments reported above are based on 50 iterations.Statistics for σ1 are based only on observations for 2 countries (China and the US), i.e< 5percent of the total number of possible observations.

C.8 Inspecting the China–US bilateral Real Exchange Rate:

As show in section 3.11, the GVC-REER approach implies a much stronger andsecular appreciation of China’s bilateral REER vis-a-vis the US. In this section wesummarize how the weights assigned by our measure differ from the standard GDPdeflator weights and how this difference points towards a higher appreciation of China’sexchange rate when combined with information on sector level price indices. Throughoutthis section we use C to denote China and U to denote the United States. As shown insection 3.11, the expressions for conventional and GVC-REER bilateral exchange ratesare given by the following equations:

GV C −RERCU =m∑i=1

vCi

[m∑j=1

wCCij p(V )Cj +m∑j=1

wCUij p(V )Uj

](C.160)

and

RERCU = p(V )U − p(V )C (C.161)

where vhi =p(V )hi V

hi∑m

j=1 p(V )hj Vhj

is the value added share of sector i in country h. In order tosimplify the comparison, we focus exclusively on the weights assigned by China to the

211

different US sectors under the two schemes. As shown below, for the GVC-REER case,this is a weighted sum of the weights assigned by different Chinese sectors to thedifferent US sectors, with the weights in the sum given by the value added shares of thedifferent Chinese sectors. In other words, by ignoring the weights assigned to the homecomponents, we have a comparison between the following quantities:

gvc− rerCU =m∑i=1

vCi

[m∑j=1

wCUij p(V )Uj

](C.162)

and

rerCU = p(V )U =m∑i=1

vUi p(V )Ui (C.163)

where we use small case letters to denote the part of the respective REER indicesthat rely on changes in the US. Note that (C.162) and (C.163) represent a weightedsum of the different US sector-level price indices. While the conventional approachweighs the different US price indices by their value added shares in the US economy, ourmeasure, which is geared towards capturing information embedded in the US prices thatis relevant for China’s competitiveness, weighs the different US price indices accordingto the GVC-REER scheme outlined in the paper. 108

In order to quantify the contribution of each sector in generating the divergencebetween GVC-RER and conventional RER, we propose to construct a statistic for eachsector based on sample averages of the weights and cumulative price changes. Letw(b)CUs be the weight assignment by China to sector s in the US under the GVC-RERbilateral scheme. (Note that this is exactly a normalized version of the weights appearingin (C.162), with the normalization undertaken to keep the weights comparable to theconventional RER as argued above). We compute the following quantity for each sector:

Ds =(vUs − ¯w(b)CUs

)4p(V )Us (C.164)

A bar above the weights indicates that they are sample averages across the 15 yearsin the sample, and 4p(V )Us in (C.164) denotes the cumulative price change over the108As mentioned in the text, since the magnitudes of these weights are not directlycomparable, we will resort to appropriate normalizations wherever necessary.

212

sample period.Note that a positive value of Ds conveys that sector s contributes more towards a

depreciation of the Chinese exchange rate in the conventional RER compared to theGVC-RER, with a higher magnitude indicating a larger effect. Conversely, a positivevalue Ds implies that sector s contributes less towards the appreciation of Chinese RERunder the conventional RER scheme compared to GVC-RER. Table 33 provides theestimates of Ds for both the estimated and uniform elasticity weights. The columns arearranged in decreasing order of Ds so that sectors at the top are the ones significantin explaining the observed divergence between the two measures. As expected fromthe results in section 3.11 the overall effect is positive, i.e

∑s Ds > 0, which implies

that the GVC-RER measure generates a stronger appreciation of the Chinese currencycompared to the standard RER. Moreover,

∑s Ds >

∑s

¯Ds(UE) which means thatimposing uniform elasticities undermines the appreciation of the RNB.

213

Table 33 – Decomposing the divergence between GVC-RER and conventional bilateral RER forChina-US bilateral real exchange rate

WIOD code Ds Ds(UE) 4Ps

14 10.951 4.818 -1.60831 4.705 1.224 0.53718 3.013 0.805 0.84833 2.462 0.681 0.46929 2.299 0.813 0.39620 1.064 0.199 -0.23622 0.751 0.237 0.46734 0.599 0.234 0.61332 0.464 0.133 0.745 0.105 0.007 -1.12621 0.098 0.032 0.02319 0.048 0.014 0.07235 0.044 0.016 0.58128 0.027 0.098 0.20627 0.026 0.000 -0.1156 0.021 0.004 -0.1617 -0.029 0.058 0.56815 -0.035 -0.043 0.09425 -0.041 -0.017 0.1141 -0.048 -0.022 0.0413 -0.072 0.008 0.7874 -0.089 -0.008 0.07324 -0.104 -0.025 0.59411 -0.128 -0.023 0.49710 -0.131 -0.036 0.23526 -0.244 -0.051 0.27823 -0.312 -0.066 0.3967 -0.348 -0.163 0.58716 -0.498 -0.069 0.62113 -0.831 -0.472 0.4722 -0.876 -0.241 1.57112 -1.024 -0.388 0.4259 -1.194 -0.654 0.57630 -1.604 -0.176 0.2938 -2.055 -0.708 7.251

Note: Sectors are ranked in decreasing order of Ds which is a statistic quantifying the contribution of sector s in thedivergence between standard RER and GVC-RER for China-US bilateral real exchange rate, as defined in (C.164).Ds(UE) is the same statistic computed using weights that impose uniform (constant) elasticity. 4Ps denotes thecumulative price change through the sample period.

214

As an example of a sector that generates stronger appreciation of Chinese currencyunder GVC-RER, consider the first sector in table 33, namely the electrical and opticalequipment sector (WIOD code 14). Over the period 1995-2009, this sector has seen asizable decline in its price (~160 percent). This sector gets a much higher weight underthe GVC-RER scheme than the RER scheme, because although the sector is small as ashare of the US economy, it is much more important as a competitor in internationalmarkets when viewed from China’s perspective. The higher weight under the GVC-RERscheme, coupled with the decline in the price thus implies a much stronger contributionto the appreciation of the Chinese exchange rate compared to the standard RER measure.The third sector in the table (construction, WIOD code 18) provides an example ofthe opposite scenario. This sector has seen a significant increase in its price during thesample period(~84 percent). Moreover, it gets a higher weight under the standard RERmeasure than the GVC-RER measure, since it is a large fraction of the US economybut from the perspective of China is not a large competitor. The high increase in pricecoupled with this difference in the weights under the two schemes implies that the sectoronce again contributes more towards an appreciation of China’s currency against theUS under the GVC-RER scheme compared to the standard RER. As final example, wediscuss a sector with a negative value of Ds. Chemicals and Chemical Products (WIODcode 9) has seen an increase in its price by around 58 percent. Since this sector getsa higher weight under the GVC-RER scheme than the standard RER scheme becauseof its higher importance as a competitor to China compared to its share in the USeconomy, it tends to contribute more towards an appreciation of the standard RERmeasure compared to the GVC RER measure.

We can also see the role played by elasticities in generating the larger differencebetween the two measures. In order to do so we pick the “Agriculture, Hunting, Forestryand Fishing” ’ sector (WIOD code 1). As per the estimates in table (26) , being a primarysector, this sector is characterized by a higher elasticity of substitution compared to theother sectors. The high substitutability, ceteris paribus, would imply that the weightassigned to this sector by China would be higher than in the case with uniform elasticity,since the same change in its price would have a larger impact on competitiveness becauseof high substitutability. Given the increase in the price of this sector through the sampleperiod, this implies that the GVC-RER scheme which takes into account heterogenous

215

elasticities would imply a stronger depreciation of China’s exchange rate compared tothe constant elasticity case. This is exactly what we find based on the estimates in table33.109

Note that although we used the agriculture sector for illustrative purposes, the morecommon case is the opposite, in which accounting for heterogenous elasticities leads toa stronger appreciation of the exchange rate.

C.9 Expressions for matrices with n = m = 2

This appendix includes details of each of the matrices as they appear in the text,including dimension and content. As always, n stands for the number of countries and mfor the number of sectors within each country. An example with n = m = 2 is providedin each case.

Matrix (W1XX)nm2Xn2m2

(W1XX)nm2Xn2m2 = [(W 1

1XX

)nm2Xnm2 ,

(W 2

1XX

)nm2Xnm2 , .., (W

n1XX)nm2Xnm2 ] (C.165)

(Wi1XX )

nm2Xnm2 =

(diag(Wi1

1XX ))m2Xm2 0

m2Xm2 .. 0m2Xm2

0m2Xm2

(diag(Wi2

1XX ))m2Xm2 .. 0

m2Xm2

: : : :

0m2Xm2 0

m2Xm2 ..(diag(Win

1XX ))m2Xm2

(C.166)

(Wij1XX)m2X1 =

[(p11X

ij11

qj11Xj11

),

(p11X

ij12

qj12Xj12

), ..,

(p11X

ij1m

qj1mXj1m

), ..,

(p1mX

ijm1

qjm1Xjm1

),

(p1mX

ijm2

qjm2Xjm2

), ..,

(p1mX

ijmm

qjmmXjmm

)]

109Ds for this sector is -0.048 based on the heterogenous elasticities weights comparedto -0.022 based on the uniform elasticity case, implying a stronger contribution to thedepreciation of the Chinese currency in the former case.

216

Example with n = m = 2

W 111XX =

[(p1

1X1111

q111X

111

),

(p1

1X1112

q112X

112

),

(p1

2X1121

q121X

121

),

(p1

2X1122

q122X

122

)]W 12

1XX =

[(p1

1X1211

q211X

211

),

(p1

1X1212

q212X

212

),

(p1

2X1221

q221X

221

),

(p1

2X1222

q222X

222

)]W 21

1XX =

[(p2

1X2111

q111X

111

),

(p2

1X2112

q112X

112

),

(p2

2X2121

q121X

121

),

(p2

2X2122

q122X

122

)]W 22

1XX =

(p2

1X2211

q211X

211

),

(p2

1X2212

q212X

212

),

(p2

2X2221

q221X

221

),

(p2

2X2222

q222X

222

)

W11XX =

(p11X

1111

q111X111

)0 0 0 0 0 0 0

0

(p11X

1112

q112X112

)0 0 0 0 0 0

0 0

(p12X

1121

q121X121

)0 0 0 0 0

0 0 0

(p12X

1122

q122X122

)0 0 0 0

0 0 0 0

(p11X

1211

q211X211

)0 0 0

0 0 0 0 0

(p11X

1212

q212X212

)0 0

0 0 0 0 0 0

(p12X

1221

q221X221

)0

0 0 0 0 0 0 0

(p12X

1222

q222X222

)

W21XX =

(p21X

2111

q111X111

)0 0 0 0 0 0 0

0

(p21X

2112

q112X112

)0 0 0 0 0 0

0 0

(p22X

21

q121X121

)0 0 0 0 0

0 0 0

(p22X

2122

q122X122

)0 0 0 0

0 0 0 0

(p21X

2211

q211X211

)0 0 0

0 0 0 0 0

(p21X

2212

q212X212

)0 0

0 0 0 0 0 0

(p22X

2221

q221X221

)0

0 0 0 0 0 0 0

(p22X

2222

q222X222

)

WXX = [W 1

1XX ,W21XX ]

217

Matrices (W2XX)nmXnm2 and (W2Xp)nmXnm2 ((W2XP )nmXnm2=(W2XX)nmXnm2)

(W2Xp)nmXnm2 =

(W 1

2Xp

)mXm2 0mXm2 .. 0mXm2

0mXm2

(W 2

2Xp

)mXm2 .. 0mXm2

: : :

0mXm2 0mXm2 ..(W n

2Xp

)mXm2

(C.167)

(W i

2Xp

)mXm2 =

((W i,1

2Xp

)mXm

,(W i,2

2Xp

)mXm

, ..,(W i,m

2Xp

)mXm

)(C.168)

(W i,k

2Xp

)mXm

= diag

(qik1X

ik1

qi1Xi1

,qik2X

ik2

qi2Xi2

, ..,qikmX

ikm

qimXim

)(C.169)

Example with n = m = 2

(W 1,1

2Xp

)mXm

=

(q111X

111

q11X11

0

0q112X

112

q12X12

)(W 1,2

2Xp

)mXm

=

(q121X

121

q11X11

0

0q122X

122

q12X12

)(W 2,1

2Xp

)mXm

=

(q211X

211

q21X21

0

0q212X

212

q22X22

)(W 2,2

2Xp

)mXm

=

(q221X

221

q21X21

0

0q222X

222

q22X22

)

(W 1

2Xp

)mXm2 =

(q111X

111

q11X11

0q121X

121

q11X11

0

0q112X

112

q12X12

0q122X

122

q12X12

)(W 1

2Xp

)mXm2 =

(q211X

211

q21X21

0q221X

221

q21X21

0

0q212X

212

q22X22

0q222X

222

q22X22

)

218

(W2Xp)nmXnm2 =

q111X

111

q11X11

0q121X

121

q11X11

0 0 0 0 0

0q112X

112

q12X12

0q122X

122

q12X12

0 0 0 0

0 0 0 0q211X

211

q21X21

0q221X

221

q21X21

0

0 0 0 0 0q212X

212

q22X22

0q222X

222

q22X22

Matrix (W1XP )nm2Xnm

(W1XP )nm2Xnm =

(W 11

1Xp

)m2Xm

(W 21

1Xp

)m2Xm

..(W n1

1Xp

)m2Xm(

W 121Xp

)m2Xm

(W 22

1Xp

)m2Xm

..(W n2

1Xp

)m2Xm

: : : :(W 1n

1Xp

)m2Xm

(W 2n

1Xp

)m2Xm

(W nn

1Xp

)m2Xm

(C.170)

(W ij

1Xp

)m2Xm

=

(W ij

1Xp

)1

mX10mX1 .. 0mX1

0mX1

(W ij

1Xp

)2

mX1.. 0mX1

: : : :

0mX1 0mX1 ..(W ij

1Xp

)mmX1

(C.171)

(W ij

1Xp

)kmX1

=

(pikX

ijk1

qjk1Xjk1

,pikX

ijk2

qjk2Xjk2

, ..,pikX

ijkm

qjkmXjkm

)′(C.172)

Example with n = m = 2

219

(W 11

1Xp

)1=

(p1

1X1111

q111X

111

,p1

1X1112

q112X

112

)′(W 11

1Xp

)2=

(p1

2X1121

q121X

121

,p1

2X1122

q122X

122

)′(W 21

1Xp

)1=

(p2

1X2111

q111X

111

,p2

1X2112

q112X

112

)′(W 21

1Xp

)2=

(p2

2X2121

q121X

121

,p2

2X2122

q122X

122

)′(W 12

1Xp

)1=

(p1

1X1211

q211X

211

,p1

1X1212

q212X

212

)′(W 12

1Xp

)2=

(p1

2X1221

q221X

221

,p1

2X1222

q222X

222

)′(W 22

1Xp

)1=

(p2

1X2211

q211X

211

,p2

1X2212

q212X

212

)′(W 22

1Xp

)2=

(p2

2X2221

q221X

221

,p2

2X2222

q222X

222

)′

220

(W 11

1XP

)4X2

=

p11X

1111

q111X111

0p11X

1112

q112X112

0

0p12X

1121

q121X121

0p12X

1122

q122X122

(W 21

1XP

)=

p21X

2111

q111X111

0p21X

2112

q112X112

0

0p22X

2121

q121X121

0p22X

2122

q122X122

(W 12

1XP

)=

p11X

1211

q211X211

0p11X

1212

q212X212

0

0p12X

1221

q221X221

0p12X

1222

q222X222

(W 22

1XP

)=

p21X

2211

q211X211

0p21X

2212

q212X212

0

0p22X

2221

q221X221

0p22X

2222

q222X222

W1XP =

p11X1111

q111X111

0p21X

2111

q111X111

0p11X

1112

q112X112

0p21X

2112

q112X112

0

0p12X

1121

q121X121

0p22X

2121

q121X121

0p12X

1122

q122X122

0p22X

2122

q122X122

p11X1211

q211X211

0p21X

2211

q211X211

0p11X

1212

q212X212

0p21X

2212

q212X212

0

0p12X

1221

q221X221

0p22X

2221

q221X221

0p12X

1222

q222X222

0p22X

2222

q222X222

(C.173)

221

Matrix (SX)nmXn2m2

(SX)nmXn2m2 =

(S1

X)mXnm2 0mXnm2 .. 0mXnm2

0mXnm2 (S2X)mXnm2 .. 0mXnm2

: : : :

0mXnm2 0mXnm2 .. (SnX)mXnm2

(C.174)

(SiX)mXnm2 =((Si1X)mXm2 ,

(Si2X)mXm2 , ...,

(SinX)mXm2

)(C.175)

(SijX)mXm2 =

(SijX1

)1Xm

01Xm .. 01Xm

01Xm

(SijX2

)1Xm

.. 01Xm

: : : :

01Xm 01Xm ..(SijXm

)1Xm

(C.176)

(SijXk

)1Xm

=

(X ijk1

Qik

,X ijk2

Qik

, ..,X ijkm

Qik

)(C.177)

Example with n = m = 2:(S11

X1)1X2 =(X11

11

Q11,X11

12

Q11

)(S11

X2) =(X11

21

Q12,X11

22

Q12

)(S12

X1) =(

X1211

Q11,

X1212

Q11

)(S12

X2) =(

X1221

Q12

,X12

22

Q12

)(S21

X1) = (X21

11

Q21,X21

12

Q21

)

(S21X2) =

(X21

21

Q22,X21

22

Q22

)(S22

X1) = (X22

11

Q21,X22

12

Q21

)

(S22X2) = (

X2221

Q22,X22

22

Q22

)

S11X =

(X11

11

Q11

X1112

Q11

0 0

0 0X11

21

Q12

X1122

Q12

)

S12X =

(X12

11

Q11

X1212

Q11

0 0

0 0X12

21

Q12

X1222

Q12

)

222

S21X =

(X21

11

Q21

X2112

Q21

0 0

0 0X21

21

Q22

X2122

Q22

)

S22X =

(X22

11

Q21

X2212

Q21

0 0

0 0X22

21

Q22

X2222

Q22

)

S1X =

(X11

11

Q11

X1112

Q11

0 0X12

11

Q11

X1212

Q11

0 0

0 0X11

21

Q12

X1122

Q12

0 0X12

21

Q12

X1222

Q12

)

S2X =

(X21

11

Q21

X2112

Q21

0 0X22

11

Q21

X2212

Q21

0 0

0 0X21

21

Q22

X2122

Q22

0 0X22

21

Q22

X2222

Q22

)

SX =

X1111Q1

1

X1112Q1

1

0 0X12

11Q1

1

X1212Q1

1

0 0 0 0 0 0 0 0 0 0

0 0X11

21Q1

2

X1122Q1

2

0 0X12

21Q1

2

X1222Q1

2

0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0X21

11Q2

1

X2112Q2

1

0 0X22

11Q2

1

X2212Q2

1

0 0

0 0 0 0 0 0 0 0 0 0X21

21Q2

2

X2122Q2

2

0 0X22

21Q2

2

X2222Q2

2

Matrix (SF )nmXn2m

(SF )nmXn2m =

(S1

F )mXnm 0mXnm .. 0mXnm

0mXnm (S2F )mXnm .. 0mXnm

: : : :

0mXnm 0mXnm .. (SnF )mXnm

(SiF )mXnm = ((Si1F )mXm , (S

i2F )mXm , ..., (S

inF )mXm)

(SijF )mXm =

SijF1 0 .. 0

0 SijF2 .. 0

: : : :

0 0 .. SijFm

(SijFk)

1X1=(F ijkQik

)Example with n = m = 2:S11F1 =

F 111

Q11, S11

F2 =F 112

Q12, S12

F1 =F 121

Q11, S12

F2 =F 122

Q12

S21F1 =

F 211

Q21, S21

F2 =F 212

Q22, S22

F1 =F 221

Q21, S22

F2 =F 222

Q22

S11F =

(F 111

Q11

0

0F 112

Q12

), S12

F =

(F 121

Q11

0

0F 122

Q12

)

223

S21F =

(F 211

Q21

0

0F 212

Q22

), S22

F =

(F 221

Q21

0F 222

Q22

)

S1F =

(F 111

Q11

0F 121

Q11

0

0F 112

Q12

0F 122

Q12

), S2

F =

(F 211

Q21

0F 221

Q21

0

0F 212

Q22

F 222

Q22

)

SF =

F 111

Q11

0F 121

Q11

0 0 0 0 0

0F 112

Q12

0F 122

Q12

0 0 0 0

0 0 0 0F 211

Q21

0F 221

Q21

0

0 0 0 0 0F 212

Q22

F 222

Q22

Matrix (W1FP )nmXnm

W1FP =

(W 1

1FP )mXnm

(W 21FP )mXnm

:

(W n1FP )mXnm

where

(W k

1FP

)=[(W 1k

1FP

)mXm

(W 2k

1FP

)mXm

...(W nk

1FP

)mXm

](W jk

1FP

)mXm

= diag(pj1F

jk1

Pk1 Fk1,pj2F

jk2

Pk2 Fk2, ..., p

jmF

jkm

PkmFkm

)Example with n = m = 2

W1FP =

p11F

111

P 11 F

11

0p21F

211

P 11 F

11

0

0p12F

112

P 12 F

12

0p22F

212

P 12 F

12

p11F121

P 21 F

21

0p21F

221

P 21 F

21

0

0p12F

122

P 22 F

22

0p22F

222

P 22 F

22

Matrix (W2FP )nXnm

W2FP = [(W 12FP )nXm (W 2

2FP )nXm , .., (Wn2FP )nXm]

(W i2FP )nXm is a matrix with the ith row given by

(P i1F

i1

P iF i,P i2F

i2

P iF i, ..., P

imF

im

P iF i

)Example with n = m = 2

W2FP =

(P 11 F

11

P 1F 1

P 12 F

12

P 1F 1 0 0

0 0P 21 F

21

P 2F 2

P 22 F

22

P 2F 2

)

224

Matrix (DV )nmXnm

(DV

)nmXnm = diag

pv11 V 1

1

p11Q11

,pv12 V 1

2

p12Q12

, ...,pv1m V 1

m

p1mQ1m︸ ︷︷ ︸

mX1

,pv21 V 2

1

p21Q21

,pv22 V 2

2

p22Q22

, ...,pv2m V 2

m

p2mQ2m︸ ︷︷ ︸

mX1

, ..,pvn1 V n1

pn1Qn1

,pvn2 V n2

pn2Qn2

, ...,pvnm V nm

pnmQnm︸ ︷︷ ︸

mX1

Example with m = n = 2

(DV )4X4 = diag

pv11 V

11

p11Q

11

,pv1

2 V1

2

p12Q

12︸ ︷︷ ︸

2X1

,pv2

1 V2

1

p21Q

21

,pv2

2 V2

2

p22Q

22︸ ︷︷ ︸

2X1

Matrix (DX)nmXnm

(DX

)nmXnm = diag

q11X

11

p11Q11

,q12X

12

p12Q12

, ...,q1mX

1m

p1mQ1m︸ ︷︷ ︸

mX1

,q21X

21

p21Q21

,q22X

22

p22Q22

, ...,q2mX

2m

p2mQ2m︸ ︷︷ ︸

mX1

, ..,qn1 X

n1

pn1Qn1

,qn2 X

n2

pn2Qn2

, ...,qnmX

nm

pnmQnm︸ ︷︷ ︸

mX1

Example with n = m = 2

(DX)4X4 = diag

q11X

11

p11Q

11

,q1

2X12

p12Q

12︸ ︷︷ ︸

2X1

,q2

1X21

p21Q

21

,q2

2X22

p22Q

22︸ ︷︷ ︸

2X1

C.10 General algebra and results with Armington aggregators

M =

[∑g

(wg)1/δ(mg)

δ−1δ

] δδ−1

(C.178)

foc:

mg = wg

(pgpM

)−δM (C.179)

price index:

PM =

[∑g

(wg)(pg)1−δ

] 11−δ

(C.180)

linearized version:

M =∑g

(pgmg

PMM

)mg (C.181)

PM =∑g

(pgmg

PMM

)pg (C.182)

225

Table 34 – List of Countries in WIOD

WIOD Code Country Name WIOD Code Country Name

1 ’Australia’ 21 ’Ireland’2 ’Austria’ 22 ’Italy’3 ’Belgium’ 23 ’Japan’4 ’Bulgaria’ 24 ’Korea’5 ’Brazil’ 25 ’Lithuania’6 ’Canada’ 26 ’Luxembourg’7 ’China’ 27 ’Latvia’8 ’Cyprus’ 28 ’Mexico’9 ’Czech Republic’ 29 ’Malta’10 ’Germany’ 30 ’Netherlands’11 ’Denmark’ 31 ’Poland’12 ’Spain’ 32 ’Portugal’13 ’Estonia’ 33 ’Romania’14 ’Finland’ 34 ’Russia’15 ’France’ 35 ’Slovak Republic’16 ’United Kingdom’ 36 ’Slovenia’17 ’Greece’ 37 ’Sweden’18 ’Hungary’ 38 ’Turkey’19 ’Indonesia’ 39 ’Taiwan’20 ’India’ 40 ’United States’

/

C.11 List of countries and sectors

C.12 Divergence Index for 1435 country- sectors pairs

226

Table 35 – List of Sectors in WIOD

WIOD code Sector Description

1 ’Agriculture, Hunting, Forestry and Fishing’2 ’Mining and Quarrying’3 ’Food, Beverages and Tobacco’4 ’Textiles and Textile Products’5 ’Leather, Leather and Footwear’6 ’Wood and Products of Wood and Cork’7 ’Pulp, Paper, Paper , Printing and Publishing’8 ’Coke, Refined Petroleum and Nuclear Fuel’9 ’Chemicals and Chemical Products’10 ’Rubber and Plastics’11 ’Other Non-Metallic Mineral’12 ’Basic Metals and Fabricated Metal’13 ’Machinery, Nec’14 ’Electrical and Optical Equipment’15 ’Transport Equipment’16 ’Manufacturing, Nec; Recycling’17 ’Electricity, Gas and Water Supply’18 ’Construction’19 ’Sale, Maintenance and Repair of Motor Vehicles and Motorcycles; Retail Sale of Fuel’20 ’Wholesale Trade and Commission Trade, Except of Motor Vehicles and Motorcycles’21 ’Retail Trade, Except of Motor Vehicles and Motorcycles; Repair of Household Goods’22 ’Hotels and Restaurants’23 ’Inland Transport’24 ’Water Transport’25 ’Air Transport’26 ’Other Supporting and Auxiliary Transport Activities; Activities of Travel Agencies’27 ’Post and Telecommunications’28 ’Financial Intermediation’29 ’Real Estate Activities’30 ’Renting of M&Eq and Other Business Activities’31 ’Public Admin and Defense; Compulsory Social Security’32 ’Education’33 ’Health and Social Work’34 ’Other Community, Social and Personal Services’35 ’Private Households with Employed Persons’

227

Figure C.2 – Divergence index at the country-sector level

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

200

400

600

800

1000Histogram of divergence index for 1435 country−sectors

228

C.13 REER indices plots

Figure C.3 – GVC-REER and Q-REER indices for all countries

1995 2000 2005 2009

−0.1

0

0.1

0.2

0.3

Australia

1995 2000 2005 2009

−0.2

−0.1

0Austria

1995 2000 2005 2009

−0.4

−0.2

0

Belgium

1995 2000 2005 20090

1

2

Bulgaria

1995 2000 2005 2009

−0.2

0

0.2

0.4

0.6

Brazil

1995 2000 2005 2009

0

0.1

0.2

Canada

1995 2000 2005 2009

−0.10

0.10.20.3

China

GVC−REER(UE)

GVC−REER(GDPdef,UE)

Q−REER(UE)

Q−REER(GDPdef,UE)

GVC−REER

GVC−REER(GDPdef)

Q−REER

Q−REER(GDPdef)

229

Figure C.4 – GVC-REER and Q-REER indices for all countries cont.

1995 2000 2005 2009

0

0.1

0.2

Cyprus

1995 2000 2005 20090

0.5

Czech Republic

1995 2000 2005 2009

−0.2

−0.1

0Germany

1995 2000 2005 2009

−0.1

0

0.1

0.2

Denmark

1995 2000 2005 2009

−0.1

0

0.1

0.2

Spain

1995 2000 2005 20090

0.5

1

Estonia

1995 2000 2005 2009

−0.2

−0.1

0Finland

GVC−REER(UE)

GVC−REER(GDPdef,UE)

Q−REER(UE)

Q−REER(GDPdef,UE)

GVC−REER

GVC−REER(GDPdef)

Q−REER

Q−REER(GDPdef)

230

Figure C.5 – GVC-REER and Q-REER indices for all countries cont.

1995 2000 2005 2009

−0.2

−0.1

0

France

1995 2000 2005 2009

0

0.1

0.2

United Kingdom

1995 2000 2005 2009

−0.05

0

0.05

0.1

Greece

1995 2000 2005 2009

−0.2

0

0.2

0.4

0.6

Hungary

1995 2000 2005 2009

−0.6−0.4−0.2

00.2

Indonesia

1995 2000 2005 2009−0.1

0

0.1

India

1995 2000 2005 20090

0.2

0.4

Ireland

GVC−REER(UE)

GVC−REER(GDPdef,UE)

Q−REER(UE)

Q−REER(GDPdef,UE)

GVC−REER

GVC−REER(GDPdef)

Q−REER

Q−REER(GDPdef)

231

Figure C.6 – GVC-REER and Q-REER indices for all countries cont.

1995 2000 2005 2009

0

0.1

0.2

Italy

1995 2000 2005 2009

−0.2

0Japan

1995 2000 2005 2009

−0.6

−0.4

−0.2

0

Korea

1995 2000 2005 20090

0.5

1

Lithuania

1995 2000 2005 2009

0

0.5

1

Luxembourg

1995 2000 2005 20090

0.5

1

Latvia

1995 2000 2005 2009

0

0.2

0.4

Mexico

GVC−REER(UE)

GVC−REER(GDPdef,UE)

Q−REER(UE)

Q−REER(GDPdef,UE)

GVC−REER

GVC−REER(GDPdef)

Q−REER

Q−REER(GDPdef)

232

Figure C.7 – GVC-REER and Q-REER indices for all countries cont.

1995 2000 2005 2009

0

0.2

0.4

Malta

1995 2000 2005 2009−0.3

−0.2

−0.1

0

0.1Netherlands

1995 2000 2005 2009

0

0.2

0.4

Poland

1995 2000 2005 2009

0

0.1

0.2

Portugal

1995 2000 2005 20090

0.5

1

Romania

1995 2000 2005 2009

−0.4−0.2

00.20.40.6

Russia

1995 2000 2005 20090

0.5

1

Slovak Republic

GVC−REER(UE)

GVC−REER(GDPdef,UE)

Q−REER(UE)

Q−REER(GDPdef,UE)

GVC−REER

GVC−REER(GDPdef)

Q−REER

Q−REER(GDPdef)

233