A Reappraisal of the Allocation Puzzle through the

Portfolio Approach ∗

Kenza Benhima †

University of Lausanne

This version: May 2010

Abstract

Paradoxically, high-investment and high-growth developing countries tend to

experience capital outows. This paper shows that this allocation puzzle can be

explained simply by introducing uninsurable idiosyncratic investment risk in the

neoclassical growth model. Using a sample of 67 countries between 1980 and 2003,

we show that the model predicts accurately the allocation of capital ows in this

sample. This is because the model accounts for two main facts: (i) TFP growth is

positively correlated with capital outows in a sample including creditor countries;

(ii) the long-run level of capital per ecient unit of labor is positively correlated

with capital outows.

Key Words: Capital ows, Global imbalances, Investment risk.

JEL Class.: F36, F41, F43.

∗I would like to thank Mark Aguiar, Philippe Bacchetta, Agnès Bénassy-Quéré, Nicolas Berman,Daniel Cohen, Jean Imbs, Imen Ghattassi, Pierre-Olivier Gourinchas, Sebnem Kalemli-Özcan, GuyLaroque, Philippe Martin, Valérie Mignon, Romain Rancière and Hélène Rey for helpful comments. Ialso thank seminar participants at Banque de France, CREST, GREQAM, Paris School of Economics,the University of Lausanne, the University of Le Mans, the University of Evry, the European EconomicAssociation 2009 (Barcelona), Theories and Methods of Macroeconomics (T2M) 2009 (Strasbourg),Research in International Economics and Finance 2009 (Aix-Marseilles) and the North American WinterMeeting of the Econometic Society 2010 (Atlanta).†University of Lausanne, UNIL-Dorigny, Extranef, room 250, 1015 Lausanne. TEL: (+41) (0)

21.692.36.92. Email: Kenza.Benhima@unil.ch

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1 Introduction

Empirical studies on capital ows to developing countries suggest that the predictionsof the neoclassical growth model (Ramsey-Cass-Koopmans) are not veried in the data.This model predicts that capital should ow to countries with high growth, both totake advantage of investment opportunities and to smooth consumption. However, theopposite holds in reality: as Aizenman and Pinto (2007) and Prasad et al. (2007) showcapital ows to countries with low growth and low investment. Consequently, as Gour-inchas and Jeanne (2007) show, capital outows predicted by the neoclassical model arenegatively correlated with actual outows. Providing an explanation to this puzzle isthe objective of this paper. Explaining the allocation puzzle would also help understandthe phenomenon of global imbalances, and especially their structure. In particular, whyare surpluses originated in Asia and not in Latin America or Africa? Indeed, Asia hasexperienced relatively high growth rates and should have imported capital instead ofexporting it.

The contribution of this paper is twofold. Theoretically, it provides a frameworkgenerating a positive correlation between growth and capital outows and gives the con-ditions and channels through which such a correlation emerges. This framework involvessimply an extension of the neoclassical growth model that accounts for uninsurable id-iosyncratic investment risk. Empirically, using a sample of 67 countries between 1980and 2003, we show that the model predicts accurately the allocation of capital ows inthis sample. This is because the model accounts for two main facts: (i) TFP growthis positively correlated with capital outows in a sample including creditor countries;(ii) the long-run level of capital per ecient unit of labor is positively correlated withcapital outows.

The theoretical part of this paper builds on Gourinchas and Jeanne (2007) but de-viates from their approach in two important aspects. First, while they focus on the roleof TFP in channelling the correlation between growth and capital outows, we enlargethe set of potential channels by taking into account the role of capital per ecient unitof labor. Indeed, if TFP is the only source of growth, the stock of capital per ecientunit of labor should be equal across countries in the long run. However, this variabledoes dier substantially across countries.1 Gourinchas and Jeanne do introduce a capi-tal wedge (i.e. a distortion between the private and social return to capital) in order toaccount for these dierences in capital stock, but only for robustness purposes. In ourmodel and because of the presence of risk, it plays a crucial role.

Figures 1 and 2 illustrate and motivate this point, using our sample of developingcountries. They represent the cross-country correlation of capital outows between 1980

1See Lucas (1990), Hsieh and Klenow (2007) and Caselli and Feyrer (2007). The volatility of thecapital stock per ecient units of labor is reected in Caselli and Feyrer by the volatility of their naiveestimates of the marginal product of capital and by the volatility of investment rates in Hsieh andKlenow.

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and 2003 respectively with TFP growth and with the end-of-period capital per ecientunit of labor, where TFP growth and the capital per ecient unit of labor are estimatedusing a growth-accounting method.2 The correlation is positive for both variables, but itis more robust for the capital-labor ratio than for TFP growth. Actually, the correlationof capital outows with TFP growth seems to be driven by a few outliers, which is notthe case with capital per ecient unit of labor. The latter seems then to be a bettercandidate to explain the positive empirical correlation of growth and investment withcapital outows.

The second deviation from Gourinchas and Jeanne's approach is the introductionof uninsurable individual investment risk. As compared to the standard model, thepresence of investment risk has a crucial implication: the composition of the portfoliomatters. In particular, when capital and therefore risk-taking increases, capital outowsmay result from a precautionary need for buer-stock assets. However, whether such aneect actually emerges depends on the sources of growth.

The role of the dierent sources of growth in explaining the puzzle are studied usingAngeletos and Panousi (2009)'s framework, which boils down to a Merton-Samuelsonportfolio choice problem between risky capital and safe assets, including human wealthand external bonds. This framework allows to nest both the riskless approach andthe approach with risk, which we call the portfolio approach. This model is extendedto allow, as in Gourinchas and Jeanne (2007), for TFP growth and a capital wedgeaccounting for the dierences in the long-run capital stock per ecient units of labor.

In this framework, the domestic capital stock is a constant fraction of total wealth inthe long run, and this desired portfolio composition dominates the traditional investmentand consumption smoothing eects. More specically, if individual risk is relatively high,which is the case in developing countries, then the fraction of capital in total wealth islower than one. This means that risk-taking through capital accumulation should becompensated by a proportional increase in non-capital wealth, which is used as a buerstock to face that risk. Importantly, in the neoclassical growth model, non-capital wealthis composed of foreign assets, but also of human wealth, that is the discounted sum offuture labor revenues. Capital outows should then follow growth only if the increasein the capital stock is not matched by a sucient increase in human wealth.

Consequently, since the relationship between capital and human wealth depends onthe sources of growth (i.e. TFP versus capital wedge), the relationship between growthand capital outows depends also on the sources of growth. TFP does not aect thecomposition of domestic assets between capital and human wealth and therefore doesnot aect the ratio between capital and foreign assets. As a result, an increase in thecapital stock stemming from TFP growth translates into capital inows if the country isa net debtor and into capital outows if the country is a net creditor. On the opposite,the capital wedge aects the composition of domestic assets. For example, a country

2The data and calibration method are described fully in Section 3.

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with a lower capital wedge will have a higher capital stock. But, because capital hasdecreasing marginal returns, the eect on labor income and therefore human wealth islimited. As a consequence, capital outows may arise in order to maintain a constantratio of capital to non-capital assets, even if the country is a net debtor.

This simple extension of the standard neoclassical growth model provides us with aninterpretation of the preliminary evidence given in Figures 1 and 2. First, the correlationbetween capital outows and TFP growth is conditional on the sign of the externalposition. An explanation of the instability of the empirical correlation would then bethat it is driven by a few creditor countries, and should become negative if we excludethem. Second, the correlation between capital outows and the long-run capital stockper ecient units of labor should be more robust to the exclusion of countries withpositive external positions.

These predictions are tested, and conrmed, on a sample of 67 developing countriesbetween 1980 and 2003. We then use this evidence to reinterpret the allocation puzzle,that is the observed positive correlation of capital outows with GDP growth and in-vestment. We nd that the capital stock per ecient units of labor is the main channelof these correlations.

Finally, we perform a calibration analysis where the amount of capital ows pre-dicted by the model are computed and compared to the data. While, consistently withGourinchas and Jeanne (2007), predicted capital ows are negatively correlated with theactual ones in the riskless approach, the correlation becomes positive in the portfolioapproach. The portfolio approach also reproduces accurately the patterns of capitalows across regions.

Our approach based on portfolio choice is close to Kraay and Ventura (2000). Theyexplain the current account dynamics by using a portfolio choice rule similar to ours:capital is a constant fraction of total wealth. However, in their model, domestic wealthincludes only capital, whereas we take into account human wealth, which plays a crucialrole in our approach. Indeed, the way the dierent channels of growth relate to thecomposition of domestic wealth is essential in generating our results. In the case ofTFP-driven growth, we nd an eect similar to their New Rule, that is: the correlationbetween investment and capital outows depends on the sign of the net foreign assetposition. However, this eect arises because TFP aects proportionally the dierentcomponents of domestic wealth, which is not the case when investment is driven by alower capital wedge.

Some theoretical papers, like Mendoza et al. (2009) and Sandri (2008), explain globalimbalances by the presence of investment risk, or more generally by the weakness ofnancial development in emerging countries.3 However, the structure of these imbalances

3See, among others, Dooley et al. (2005), Matsuyama (2007), Ju and Wei (2006, 2007), Caballeroet al. (2008), Song et al. (2009).

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and the allocation puzzle have been overlooked. Indeed, to explain global imbalances,most researchers either consider emerging markets as a whole or take Asia (and especiallyChina) in isolation. Aguiar and Amador (2009) are an exception. They explain whycountries that grow rapidly tend to accumulate net foreign assets rather than liabilitiesby introducing political economy and contracting frictions. However, their approach issilent on the respective role of the factors of growth.

The remainder of the paper is organized as ows: Section 2 presents the neoclassicalgrowth model with investment risk and its predictions; Section 3 presents the dataand the calibration method; Section 4 tests the predictions of the model regarding thedeterminants of capital ows and reinterprets the allocation puzzle by investigating thechannels of the positive correlation of capital outows with investment and growth; andnally, Section 5 performs a calibration analysis by comparing actual and predictedows.

2 The neoclassical growth model with idiosyncratic in-

vestment risk

In this section, we study the implications in terms of capital ows of the neoclassi-cal growth model with investment risk. To achieve this, we use Angeletos and Panousi(2009)'s model, which generalizes the tractable Merton-Samuelson portfolio choice prob-lem to account for human wealth. This model is extended here to account, as in Gour-inchas and Jeanne (2007), for TFP growth and a capital wedge, that is a distortionbetween the private and social return to capital.

The model is then used to infer the amount of capital ows between an initial periodand the steady state and to study the impact of the dierent factors of growth (TFPcatch-up and the capital wedge) on these capital ows.

2.1 The household's program

Consider a small open economy with a continuum of length 1 of innitely-lived house-holds, or families, indexed by i. Time is continuous, indexed by t ∈ [0,∞). Eachhousehold owns a rm which produces a homogeneous good using two factors, labor andcapital, according to a Cobb-Douglas technology:

Y it = F (Ki

t , AtNit ) = Kiα

t (AtNit )

1−α, 0 < α < 1

where Kit is the amount of private capital invested in rm i at date t, N i

t the amount oflabor hired in the rm and At the deterministic domestic level of technology.

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Financial markets are incomplete: households can invest only in their own rm andcannot trade equity. They face an idiosyncratic investment risk, but cannot diversifyaway this risk through equity or any other means. The only freely traded asset, domes-tically and internationally, is the riskless bond Bi

t whose return is xed internationallyto R∗.

Denote household i's net capital income by dQit. It is dened as follows:

dQit = (1− τ)[F (Ki

t , AtNit )− wtN i

t ]dt− δKitdt+ σKi

tdvit (1)

where wt the wage rate, which is not rm-specic since the labor market is competitive.δ is the depreciation rate.

τ is a wedge on the gross capital return. Following Gourinchas and Jeanne (2006,2007), it is introduced in order to account for the cross-country dierences in capital-labor ratios that are not attributable to TFP. This wedge can be interpreted as a taxon capital income, or as the result of other distortions that would introduce a dier-ence between social and private returns. We assume that the product of this tax Zt isdistributed equally among households:

Zt =

∫ 1

0

τ [Kiαt (AtN

it )

1−α − wtN it ]di

The technology is exactly identical to Gourinchas and Jeanne (2007), except thattime is continuous and that rms face investment risk. This risk is introduced herethrough a standard Wiener process dvit. This process is iid across agents and time andsatises E[dvit = 0]. This risk can be interpreted as a production or a depreciation shockthat aects the return on capital. It is assumed that this shock is averaged out acrosshouseholds, that is:

∫ 1

0dvit = 0. The parameter σ measures the amount of individual risk.

Gourinchas and Jeanne (2007)'s specication is nested when σ = 0. In the case with risk,market incompleteness is important: if households were able to diversify perfectly theirinvestment risk, then the model would boil down to the standard neoclassical modelwithout risk.4

Each household is composed of Nt members, and each member is endowed with 1unit of labor which he supplies inelastically in the competitive labor market. Since,additionally, there is no aggregate risk, all aggregate variables are deterministic, includ-ing the competitive individual wage wt. There is neither unemployment risk nor anyother shock that would introduce an income risk besides investment risk. Therefore,labor income is deterministic. Moreover, the tax product is by assumption redistributedequally among households, and is thus also deterministic. The absence of labor incomerisk and, more generally, of any endowment risk is useful to make the model tractable.

4A certain amount of contingent claims could be introduced in order to allow households to decreasetheir eective level of risk σ. But what is important for our results is that the nal amount of riskremains positive.

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Since the labor market is competitive, then kit, the capital per ecient unit of laborKit/(AtN

it ), is constant across rms. Since, additionally, the production function has

constant returns to scale, the capital income is linear in Kit , and we can write it as

follows:dQi

t = rtKitdt+ σKi

tdvit

where rt = (1−τ)f ′(kt)−δ is the private net return on capital, with f(k) = F (k, 1) = kα.

As in Barro and Sala-i Martin (1995), the household maximizes the following dis-counted expected welfare of the family members:

U it = Et

∫ ∞t

Ns ln cise−ρ(s−t)ds (2)

where ρ > 0 is the discount rate and cit is the individual consumption of the members ofhousehold i in period t. The population growth rate is supposed to be exogenous andequal to n, with n < ρ:

Nt = N0ent

We now turn to the household's budget constraint. The evolution of the household'snancial wealth Bi

t +Kit obeys to:

d(Bit +Ki

t) = dQit + [R∗Bi

t +Ntwt + Zt − Cit ]dt (3)

However, this expression of the budget constraint misses some aspects of household'swealth. Indeed, the household's eective wealth Ωi

t includes his nancial wealth, butalso human wealth, that is the present discounted value of future labor income and taxproduct, dened as H i

t = Ht =∫∞te−(s−t)R∗

(Nsws+Zs)ds. Therefore, Ωit = Ki

t+Bit+Ht.

In order to include human wealth in the budget constraint, we follow Angeletos andPanousi (2009) and use the denition of human wealth to write:

dHt = (R∗Ht −Ntwt − Zt)dt (4)

It follows from (1), (4) and (3), that the evolution of eective wealth, in per capitaterms, can be described by:

dωit = [rtkit +R∗(bit + ht)− cit − nωit]dt+ σkitdv

it (5)

with ωit = kit + bit + ht. Lower case letters, except n, the population's growth rate, standfor per capita (i.e. per family member) values. For each variable X i

t (Xt), xit (xt) standsfor X i

t/Nt (Xt/Nt).

The household maximizes (2) subject to his budget constraint (5), which states thathousehold's wealth is increased by the revenues from capital, whose return rt + σdvit isrisky, and from safe assets, bit and ht, whose return is R

∗, minus consumption. Populationgrowth additionally diminishes the value of wealth per capita. Thanks to the linearity

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of the budget constraint with respect to wealth, this problem boils down to a tractableMerton-Samuelson portfolio choice problem.

Kraay and Ventura (2000) and Kraay et al. (2005) also applied this portfolio choiceapproach to the study of capital ows, but in an AK context without human wealth,which is an important variable in this paper. Here, we use a transformation of thebudget constraint introduced by Angeletos and Panousi (2009) in order to make humanwealth explicitly appear, without impairing the tractability of the problem.

2.2 Technology

The country has an exogenous, deterministic productivity path Att=0,...,∞, which isbounded by the world productivity frontier:

At ≤ A∗t = A∗0eg∗t

The world productivity frontier is assumed to grow at rate g∗. Following Gourin-chas and Jeanne (2007), we dene TFP catch-up πt as the dierence between domesticproductivity and the productivity conditional on no technological catch-up:

eπt =At

A0eg∗t

(6)

We assume that π = limt→∞πt is well dened. Therefore, the growth rate of domesticproductivity converges to g∗.

2.3 Household's behavior

In line with the Merton-Samuelson approach, it follows from the linearity of the budgetconstraint and the homotheticity of preferences that the capital stock and consumptionchoices are linear in wealth.5 Dene φit = kit/ω

it, the fraction of eective wealth invested

in private capital. For a given interest rate R∗ and a given sequence of wages Wt, theoptimal choices of household i are given by:

cit = (ρ− n)ωit (7)

rt −R∗ = φtσ2 (8)

5See Kraay and Ventura (2000), Kraay et al. (2005) or Angeletos and Panousi (2009) for a fullderivation.

8

Equation (7) shows the familiar result that consumption per capita equals the annual-ized value of wealth, taking into account population growth. This is a direct consequenceof log utility.

Equation (8) provides a portfolio choice rule. It states that the excess return tocapital rt−R∗ is equal to the risk premium. With logarithmic households, the coecientof risk aversion is equal to one and the risk premium is the covariance between the returnon capital and the return on the portfolio, which is equal here to the variance of thereturn to capital multiplied by the share of capital in the the portfolio.

2.4 Steady state

The saving rule (7) and the portfolio rule kit = φtωit, with φt dened by (8), are linear in

wealth and can therefore be written in aggregate terms: ct = (ρ − n)ωt and kt = φtωt,where ωt =

∫ 1

0ωitdi is the aggregate value for ω

it. By dividing each side by At, they can

also be written in terms of ecient units of labor, denoted ct, kt and ωt.

Capital per ecient units of labor at the rm level, kt = Kit/AtN

it is constant across

rms as a result of competitive labor market. Since the labor market clears (∫N itdi =

Nt), it is equal to its aggregate value kt = Kt/AtNt.

Equations (7) and (5), when expressed in aggregate terms and divided by At, alongwith the no-Ponzi conditions and the equilibrium values for wt, rt and φt, characterizethe dynamics of ct and ωt. Once the paths of these variables are known, kt = φtωt,ht =

∫∞0e−(R∗−(n+g∗))s+πs−πt(1−α+ τα)kαt+sds and bt = ωt− kt− ht can be determined.

We assume no domestic supply of bonds, so the aggregate demand for bonds btrepresents the country's external position.

These equations are used to determine the steady state. We dene the steady stateby ˙c/c = 0 and πt = 0. The following proposition characterizes the steady state.6

Proposition 1: The open economy steady state exists if and only if n+ g∗ < R∗ <ρ+ g∗ and is dened by:

(1− τ)f ′(k∗)− δ −R∗ =√σ2(ρ+ g∗ −R∗) (9)

k∗ = φ∗ω∗ (10)

with φ∗ =√

ρ+g∗−R∗

σ2 , ω∗ = k∗ + b∗ + h∗ and h∗ = (1−α+ατ)f(k)R∗−g∗−n .

6See the Appendix for the proof, originally provided in Angeletos and Panousi (2009). We repeatthis material in order to make the paper self-contained, but also to take into account the capital wedge,which is absent in Angeletos and Panousi (2009).

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The condition that the interest rate R∗ should be strictly lower than the growth-adjusted discount rate ρ+g∗ is a standard condition to insure stationarity in the presenceof risk (Aiyagari, 1994; Angeletos and Panousi, 2009). The interest rate should not betoo low either: R∗ > n + g∗. Otherwise, the long-run human wealth would not be welldened.

The steady-state level of capital is dened through Equation (9) by the equalitybetween the excess return and the steady-state risk premium. Importantly, this linksthe capital wedge τ to the long-run capital stock. A lower τ leads to a higher capitalper eent unit of labor k∗.

The steady-state share of capital in the portfolio is dened by Equation (10). Indeed,in steady state, the risk premium and therefore the long-run composition between safeand risky assets is dened by the equality between the return of the portfolio and thepropensity to consume.

Equation (10) gives also the steady-state external demand for bonds:

b∗ =1− φ∗

φ∗k∗ − (1− α + ατ)f(k∗)

R∗ − g∗ − n(11)

The rst term is the amount of non-capital wealth that is needed to achieve thedesired capital-to-wealth ratio φ∗. This non-capital wealth is composed of safe assets,bonds and human wealth. This demand for safe assets is positive if φ∗ < 1 which isequivalent to σ2 > ρ+ g∗ −R∗. This condition is satised as long as the level of risk inthe country is greater than in the rest of the world.7 Assuming that the country has arelatively high level of risk is consistent with the fact that we are dealing with developingcountries. We therefore maintain this assumption in the rest of the paper.

The second term represents human wealth. External bond holdings represent theneed for non-capital wealth that is not satised by domestic human wealth.

7Formally, this argument runs as follows. The constraint that φ∗/(1−φ∗) > 0 and equivalently thatφ∗ < 1 can be rationalized by the a general equilibrium argument. The world as a whole is in autarky,that is b∗W = 0. According to (10), we have:

k∗W =φ∗W

1− φ∗W(1− α+ ατW )(k∗W )α

R∗ − g∗ − nW

Since k∗W is positive, φ∗W /(1− φ∗W ) is necessarily positive and therefore φ∗W < 1. This is made possibleby the adjustment of the world interest rate R∗ in order to clear the world bond market. If we assume,as in the calibration section, that σ > σW , then φ∗ < φ∗W . It is therefore consistent with the portfolioapproach to assume that φ∗ < 1.

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2.5 Capital ows

Here we explicit capital outows over a nite period [0, T ] as a function of the parameters,especially those at the source of growth and investment, π and k∗, which is a function ofτ . This is for the purpose of confronting the model with the data, following Gourinchasand Jeanne (2007).

Before deriving the level of bonds predicted by the model, some assumptions mustbe made. First, we abstract from unobserved future developments in productivity byassuming that all countries have the same productivity growth rate g∗ after T .

Assumption 1: πt = π for all t ≥ T .

Besides, it is assumed that T is suciently large to be able to make the followingapproximation: kt = k∗ for all t ≥ T .

Denote by ∆BP/Y0 = (BT−B0)/Y0 the predicted amount of capital outows between0 and T . Under Assumption 1 and for T large, it can be written as follows:

∆BP

Y0

= eπ+(n+g∗)T b∗

y0

− b0

y0

(12)

where b∗ satises Equation (11). Notice that b∗, according to Equation (11), is indepen-dent of π. The eect of π on ∆BP

Y0depends therefore only on the sign of b∗. This gives

the following proposition:

Proposition 2: Suppose that σ2 > ρ−R∗ + g∗, that T is suciently large, that thestationarity conditions of Proposition 1 and Assumption 1 are satised. Consider twocountries A and B, identical except for their long-run productivity catch-up π. Thenthere are two cases:

(i) If A and B have a positive long-run external position (b∗ > 0), then country A sendsmore capital outows than country B if and only if country A catches up fasterthan country B towards the world technology frontier:

∆BA > ∆BB ⇔ πA > πB

(ii) If A and B have a negative long-run external position (b∗ < 0), then the oppositeholds:

∆BA > ∆BB ⇔ πA < πB

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This result is the cross-country, growth-accounting counterpart of the New Ruleintroduced by Kraay and Ventura (2000). TFP growth explains the puzzle only tothe extent that countries with positive long-run external positions drive the observedpositive correlation between growth and capital outows.

To understand this, consider the ratio of external assets to capital, given by Equation(11):

b∗

k∗=Ab∗

Ak∗=b∗

k∗=

1− φ∗

φ∗− (1− α + ατ)f(k∗)

(R∗ − g∗ − n)k∗(13)

The ratio of external assets to capital is the ratio of non-capital wealth to capital, whichis constant, minus the ratio of human wealth to capital.

The level of TFP A aects proportionally capital k∗ = Ak∗ and human wealthh∗ = Ah∗ = A(1−α+ατ)f(k∗)

R∗−g∗−n because it benets to both factors of production, capital and

labor. Thus, it does not aect the composition of domestic assets (1−α+ατ)f(k∗)

(R∗−g∗−n)k∗. As a

result, it does not aect the ratio between external assets and capital: An increase in Aleads to an increase in b∗ = A b∗

k∗k∗ only if b∗

k∗is positive, through a pure portfolio growth

eect.

In the following proposition, we show that the stock of capital per ecient unit oflabor aects capital ows dierently than TFP does, which could contribute to solvethe puzzle. In our model, this variable is isomorphic to the capital wedge τ , for givenrisk σ (see Equation(9)). The capital wedge explains precisely the amount of capital perhead that is not accounted for by TFP. The following proposition examines the eect ofa variation in τ on capital ows.

Proposition 3: Suppose that σ2 > ρ−R∗ + g∗, that T is suciently large, that thestationarity conditions of Proposition 1 and Assumption 1 are satised. Consider twocountries A and B, identical except for their capital wedge τ , then there are two cases:

(i) If A and B satisfy b∗ ≥ −(1−α) f(k∗)R∗−n−g∗ , then country A sends more capital outows

than country B (∆BA > ∆BB) if and only if country A has a lower capital wedgethan country B (τA < τB):

∆BA > ∆BB ⇔ τA < τB

(ii) If A and B do not satisfy b∗ ≥ −(1− α) f(k∗)R∗−n−g∗ , the opposite holds.

∆BA > ∆BB ⇔ τA > τB

The proof is provided in the appendix. The way capital outows are related tocapital per ecient unit of labor (i.e. to the capital wedge) depends on a condition onb∗, that is the long-run external position, as in the case of TFP-driven growth.

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However, the condition for capital per ecient unit of labor to generate capitaloutows (b∗ ≥ 0) is less restrictive than the condition for TFP catch-up to generatecapital outows (b∗ ≥ −(1 − α) f(k∗)

R∗−n−g∗ ). In particular, a positive correlation betweencapital outows and investment is compatible now with negative external positions indeveloping countries.

The intuition is based again on Equation (13). A decrease in the capital wedgeincreases capital k∗ = Ak∗ through the ratio of capital per ecient unit of labor k∗.Because capital has a positive eect on production, it aects also positively labor incomeand human wealth h∗ = Ah∗ = A(1−α+ατ)f(k∗)

R∗−g∗−n . A portfolio growth eect is therefore atplay, as for TFP. However, the capital wedge aects also the composition of domesticassets between capital and human wealth (1−α+ατ)f(k∗)

(R∗−g∗−n)k∗. Because the capital stock has

decreasing returns, the portfolio composition is tilted towards capital. In order to restorethe desired ratio between non-capital and capital assets 1−φ∗

φ∗, external bond holdings

must increase. Capital outows emerge then as the result of a portfolio compositioneect.

2.6 Comparison with the riskless case

Here we compute the amount of capital outows that the model generates in the absenceof risk (σ = 0) in order to compare them with the case with risk. These capital owswill be calibrated in Section 6 in order to compare predicted ows in the riskless andportfolio approaches.

In the case without risk, the condition for stationarity is R∗ = ρ + g∗. In that case,capital outows, denoted by ∆B

Y0

R, are dened by:

∆B

Y0

R

= − k∗ − k0

kα0e(n+g∗)T − (eπ − 1)

k∗

kα0e(n+g∗)T

−eπ+(n+g∗)T (1− α + ατ)k∗α

kα0

∫ T

0

e−(ρ−n)t(1− eπt−π)dt+(e(n+g∗)T − 1

) b0

kα0(14)

which is the continuous-time version of Gourinchas and Jeanne's decomposition (see theAppendix for a complete derivation).

The rst two terms reect the eect of domestic investment on capital ows. Anyinvestment takes place through foreign borrowing, whether it comes from convergence(that is when k∗ > k0) or through TFP catch up (that is when π > 0). The third termrepresents consumption smoothing. Following Gourinchas and Jeanne, it can be shownthat this term, under some mild assumptions (π < 100%), is negatively correlated toTFP catch-up π. The fourth term is a trend component that represents the amountof capital outows that are necessary to maintain constant the initial external position.

13

According to the second and third terms, capital outows should then be negativelycorrelated to TFP growth through both an investment and a consumption smoothingeect. Why are these eects absent in the portfolio approach?

Note that, in the case with risk, capital outows in (12) can also be decomposed intosimilar terms:

∆BP

Y0

=1− φ∗

φ∗k∗ − k0

kα0e(n+g∗)T +

1− φ∗

φ∗(eπ − 1)

k∗

kα0e(n+g∗)T

−eπ+(n+g∗)T (1− α + ατ)k∗α

kα0

∫ T

0

e−(ρ−n)t

(1− f(kt)

f(k∗)eπt−π

)dt+

(e(n+g∗)T − 1

) b0

kα0(15)

+

(1

φ∗− 1

φ0

)e(n+g∗)T k0

kα0

See the Appendix for the derivation. The rst four terms are identical to the casewithout risk, except that the coecients in front of the investment terms (rst two terms)are positive, because φ∗ < 1. They correspond to the need for safe assets necessary toself-insure against the additional capital stock due either to TFP catch-up (rst term)or to convergence (second term). The consumption smoothing component and the trendcomponent (respectively the third and fourth components) are identical.

Additionally, in the portfolio approach, a fth term representing the long-run adjust-ment of the portfolio towards the desired composition appears. If φ∗ < φ0, that is if thelong-run desired share of capital in the portfolio is lower than the current one, then, for agiven capital stock, the external position should increase in the long-run. In the risklessapproach, because the composition of the portfolio is undetermined, this last term isabsent. The rst four terms then persist in the long run. In the portfolio approach, theinvestment and consumption smoothing eects may still appear in the short run, but, inthe long run, the desired portfolio composition prevails and might oset these short-runeects.

3 Calibration

In order to perform our empirical analysis, we need either to measure or calibrate theparameters of the model.

14

3.1 Data and calibration method

We use the same sample of 69 emerging countries as in Gourinchas and Jeanne (2007).8

However, Jordan and Angola are removed from this sample because their working-agepopulation does not satisfy n < ρ. The sample is therefore reduced to 67 countries.

The parameters which are common across countries also follow their paper: thedepreciation rate δ is set to 6%, the capital share of output α to 0.3 and the growthrate of world productivity g∗ to 1.7%. Only the discount rate ρ is set to a higher valueof 5% (instead of 4%) in order to accommodate high growth rates of labor in the data.9

The time span is extended to 1980-2003 (instead of 1980-2000) in order to encompassthe recent surge in capital outows from developing countries and to shed some light onthe global imbalances debate.

In order to determine the exogenous interest rate, we make the hypothesis that eachcountry is too small to inuence the world's demand for bonds. We also assume thatthe world is composed exclusively of developed countries with zero labor growth andno distorsions to the marginal capital return. The world interest rate then correspondsto the autarky steady-state interest rate with n = 0 and τ = 0. In the portfolioapproach, the amount of risk σ in developed countries is set to 0.3, which is the amountof entrepreneurial risk commonly reported by empirical studies in the US and the Euroarea (Campbell et al., 2001; Kearney and Poti, 2006). This gives φ∗ = 13.1% andR∗ = 6.55%. If we extend this calibration approach to the case without risk, we getR∗ = ρ+g∗ = 6.7%, which is the long-run value of the autarky interest rate when σ = 0.

The amount of risk in emerging countries is set to σ = 0.6, in line with Koren andTenreyro (2007), who nd that the amount of both macroeconomic and idiosyncratic(sectoral) risk is roughly twice as large in developing countries as in industrial ones.

The country-specic data are the paths for output, capital, productivity and working-age population. These data come from Version 6.2 of the Penn World Tables (Hestonet al., 2006). Following Gourinchas and Jeanne (2007) and Caselli (2004), the capitalstock is constructed with the perpetual inventory method from time series data on realinvestment. The level of productivity At is calculated as (yt/k

αt )1/(1−α) and the level

8This sample includes: Angola, Argentina, Bangladesh, Benin, Bolivia, Botswana, Brazil, BurkinaFaso, Cameroon, Chile, China, Colombia, the Republic of Congo, Costa Rica, Cyprus, Côte d'Ivoire,Dominican Republic, Ecuador, Egypt, Arab Republic, El Salvador, Ethiopia, Fiji, Gabon, Ghana,Guatemala, Haiti, Honduras, Hong Kong, India, Indonesia, Iran, Israel, Jamaica, Jordan, Kenya,Republic of Korea, Madagascar, Malawi, Malaysia, Mali, Mauritius, Mexico, Morocco, Mozambique,Nepal, Niger, Nigeria, Pakistan, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Rwanda,Senegal, Singapore, South Africa, Sri Lanka, Syrian Arab Republic, Taiwan,Tanzania, Thailand, Togo,Trinidad and Tobago, Tunisia, Turkey, Uganda, Uruguay and Venezuela.

9Indeed, in the portfolio approach, the world interest rate (i.e. R∗) is lower than ρ+ g∗. If ρ is toosmall, then we could have R∗ − (g∗ + n) negative or very close to zero. In the rst case, capital owsare not well dened; in the second, their variance goes to innity.

15

of capital per ecient unit of labor kt as (yt/kt)1/(1−α). The level of TFP At and the

capital per ecient unit of labor kt are ltered using the Hodrik-Prescott method inorder to suppress business cycles. The parameter n is measured as the annual growthrate of the working-age population. Under Assumption 1, the long-term catch-up π canbe measured as ln(AT )− ln(A0)− Tg∗.

The capital wedge τ is calibrated in order to account exactly for the steady-statestock of capital per ecient unit of labor. We use the fact that, assuming that T = 23is a suciently large number, k∗ is approximately equal to kT . We thus take k∗ = kT .Then τ is used to adjust the private marginal return on capital to the world interest

rate: τ = 1 − k(1−α)T

R∗+δ+√σ2(ρ+g∗−R∗)

α. This method assigns a high capital wedge to

countries with low end-of-period capital per ecient unit of labor.

Finally, actual capital ows are taken from Lane and Milesi-Ferretti (2006)'s netforeign asset data. They provide estimates for the net external position in current USdollars.10 Actual capital outows during the period, as a share of initial output, aredenoted ∆B

Y0.

3.2 Some key variables

Table 1 sums up some key parameters given by the calibration method. Consider thelong-run productivity catch-up π in column (1) of Table 1. On average, non-OECDcountries have fallen behind the world frontier in terms of productivity. When lookinginto details, only Asian countries have caught up with the world productivity. BothAfrica and Latin America fell behind.

Column (3) presents the average growth rate of capital ∆kT y0

. The main observation isthat the capital stock decreased on average. Consistently with Gourinchas and Jeanne(2006, 2007), emerging countries were not capital-scarce but capital-abundant. Amongregions, only Asia increased its capital per ecient unit of labor.

Consider now column (5). When calibrated inside the riskless framework, the averagewedge τ on the net capital return is equal to 38%, which is consistent with the averagewedge on gross capital return of 12% found in Gourinchas and Jeanne (2007). Africa,which has the smallest end-of-period capital level (column (4)), has therefore the highestestimated capital wedge, while Asia's estimated capital wedge is the smallest, since it hasthe highest end-of-period capital level. The capital wedge calibrated inside the portfolioframework is given by column (6). It is lower than the one reported in column (4)

10These estimates are calculated using the cumulated current account data and are adjusted forvaluation eects. In order to be consistent with the PPP-adjusted data used here, a PPP deator isextracted from the Penn World Table and is used to calculate a PPP-adjusted measure of net externalposition.

16

because the risk premium accounts partially for the low levels of capital in developingcountries. This leaves unchanged the regions' ranking.

4 Determinants of capital ows

The objective of this section is to examine whether the predictions of the model aresatised in the data. First, according to the model, the correlation between TFP catch-up and capital outows should be negative in a sample of countries with negative externalposition, and positive in a sample of countries with positive external positions. Second,the correlation between capital per ecient unit of labor and capital outows can bepositive even in a sample of countries with negative external positions. These predictionsare consistent with the preliminary evidence showing that the positive correlation ofcapital outows with TFP catch-up is unstable and that their correlation with capital perecient unit of labor is more robust. This section consists in examining the robustnessof this preliminary evidence.

4.1 Methodology

The decomposition of capital ows in the portfolio approach (12) can be log-linearizedas follows around the cross-country averages π, (n+ g∗)T , ln(y0) and ln(k∗):

∆BP

Y0

=B

Y0

+B

Y0

[(π + (n+ g∗)T − ln(y0))− (π + (n+ g∗)T − ln(y0))

]+

B + κH

Y0

(ln(k∗)− ln(k∗)

)− B0

Y0

(16)

where BY0

and HY0

are respectively the implied end-of-period net foreign assets and humanwealth over initial output evaluated at the country averages and κ = (1− α)/(1− α +ατ) ' 1. Based on this approximation, the following structural equation can be testedin our sample:

∆B

Y0 i

= γ1 + γ2πi + γ3 ln(k∗)i + γ4(n+ g∗)Ti + γ5 ln(y0))i + γ6B0

Y0 i

+ εi (17)

with i the country index, γ1 − γ6 the coecients to estimate and εi an error term.According to Equation 16, we should have: γ2 = B

Y0and γ3 = B+H

Y0. Therefore, we

should verify that γ2 is sensitive to the sample average of BY0

and that γ3 > γ2.

17

4.2 Results

Table 2 gives the regression results for Equation (17) with the observed ows between1980 and 2003 for the same sample as the one used for the calibration analysis.

First, consider the impact of TFP growth π on capital outows, given by γ2. Accord-ing to the portfolio approach, it should depend on the sign of the average net foreignasset position B

Y0, which is sample-dependent.

Consider the results given in Table 2. When abstracting from the other correlates,the impact of π on the observed ows is signicantly positive at the 10% level if estimatedon the whole sample but it turns signicantly negative at the same level if restrictingthe sample to countries with negative external positions (respectively, columns (1) and(2)). This suggests that the coecient is, as predicted by the portfolio approach, highlysample-dependent. The same happens when we control for the other determinants, onlythe coecients are not signicant (columns (3) and (4)). In this case, in line with theportfolio approach, the estimated values are not signicantly dierent from the actualaverages of B

Y0.11

This suggests that the positive correlation between capital outows and TFP growthpresented as preliminary evidence in Figure 1 was driven by a few countries with positiveend-of-period external positions, among which Asia is well represented. These countriesare: Botswana, China, Hong-Kong, Iran, Mauritius, Singapore, Taiwan and Venezuela.In particular, Botswana and Hong-Kong appear clearly as outliers in the gure.12

Second, consider the impact of capital per ecient unit of labor ln(k∗), which isisomorphic to the capital wedge τ , on capital outows. In the model, it depends bothon the external position and on human wealth, as suggested also by Equation (16).This means that its impact should be more robustly positive than that of TFP catch-up. The results are reported in columns (3) and (4) of Table 2. The impact of ln(k∗)is signicantly positive (at the 10% level), whether we estimate it on the whole sample(column (3)) or on the sample of countries with negative end-of-period external positions(column (4)). These results imply that γ3−γ2 are equal respectively to 0.49 and 0.77. Inline with the portfolio approach, these quantities, which are estimates of H

Y0, are greater

than zero respectively at the 10% and 1% level.13

These estimates of HY0

imply end-of-period ratios of human wealth to output HY

ofrespectively 0.20 and 0.34. This is much lower than what the model predicts. According

11The actual average BY0

is equal to -79% in the whole sample with a standard error of 156%. When

we exclude countries with positive external positions, the actual average BY0

is equal to -120% with astandard error of 74%.

12Alfaro et al. (2010) also highlight the role of these outliers in driving the correlation between growthand capital outows, but do not provide an explanation for their behavior.

13Standard errors are equal respectively to 0.38 and 0.28.

18

to the model, this value should be greater than (1 − α)/R∗ ' 10. However, our modelnaturally overestimates human wealth because it assumes that household can potentiallyshort-sell all their future income, which supposes no frictions in the bond market. Inreality, many agents do not have access to nancial markets. These values should thenbe interpreted as eective human wealth, that takes into account the limited access tonancial markets. The discrepancy between our estimates and the model is actually anassessment of the lack of nancial development in developing countries.

Note that the fact that human wealth is relatively larger in the sample with negativeend-of-period external positions is consistent with the portfolio approach: according tothe theory, countries with a high level of human wealth do not need to export capitaland are more likely to end up with negative foreign assets.

4.3 Robustness

As we have seen, the variations in the long-run capital per ecient unit of labor k∗ acrosscountries are crucial to explain capital ows. However, this long-run level is proxied bythe end-of-period level and is then subject to measurement errors. In this section, weuse the relative price of capital and its share in production as alternative proxies for thelong-run capital stock k∗. We then investigate whether these proxies still explain capitalows.

To understand the role of the relative price of capital and of its share in production,we follow Caselli and Feyrer (2007). Production is dened as follows:

Y =t A

1−αkt Kαk

t XαxN1−αk−αxt

withX denoting non-reproducible capital and αx its share in production. Non-reproduciblecapital is introduced in order to estimate the share of reproducible capital in productionαk more accurately. Equalization between the private marginal return to capital andthe risk-adjusted return to capital implies then:

(1− τ)αkk∗αk−1

Pk= R∗ + δ +

√σ2(ρ+ g∗ −R∗)

where Pk is the price of investment goods in terms of nal goods. In this more generalsetting, countries with large αk and low Pk will have a higher long-run capital ratio k∗.We can then use αk and Pk as proxies for k∗.

We estimate the relative price of capital Pk as the ratio of the investment price indexto the GDP price index from the Penn World Tables 6.2 (Heston et al., 2006). Weuse the data of 1996, which is the year where the broadest number of countries weresurveyed.

19

To measure αk, following Caselli and Feyrer (2007), we obtain the labor share 1 −αk − αx from Bernanke and Gurkaynak (2001) and derive the total share of capital(reproducible and non-reproducible) αw = αk+αx. We then use the equality between thesteady-state perceived private returns on reproducible capital and on non-reproduciblecapital. Assuming that τ = 0, the former is equal to αk Y

PkK− δ−

√σ2(ρ+ g∗ −R∗). To

infer the private return on non-reproducible capital, we must make assumptions aboutits risk. For simplicity, we assume that non-reproducible capital is not risky. In thatcase, its private return is

(αx

YX

+ ∂Px∂t

)/Px, where Px is the price of non-reproducible

capital in terms of nal goods. In steady state, the rate of price appreciation for non-reproducible capital should be equal to g∗ + n1−αw

αw. Equality between returns then

yields:

αk =

[αw +

(g∗ +

1− αwαw

+ δ +√σ2(ρ+ g∗ −R∗)

)PxY

]PkK

PxX + PkK

By considering Table 1, we can see how these measures relate to the capital stockacross regions. Latin America benets both from a lower price of reproducible capitalPk (column (8)) and from a higher share αk (column (9)) than Africa, which explains itsrelatively higher capital stock (column (4)). Asia has the same share as Latin America,but faces a lower price of capital, which explains why Asia has the highest capital stock.

Columns (5) and (6) of Table 2 give the determinants of capital outows where ln(k∗)is replaced by Pk and αk repectively for the whole sample and for the sample of countrieswith negative net foreign assets. In both regressions, the coecients of Pk and αk aresignicant at least at the 10% level and have the expected signs: respectively negativeand positive. Interestingly, π is signicantly negative in the sample of net creditors,which is also in line with the portfolio approach.

4.4 Reinterpreting the allocation puzzle

In the literature, the phenomenon labelled allocation puzzle by Gourinchas and Jeanne(2007) covers several aspects. In its narrow denition, it refers to the positive cross-country correlation between TFP growth and capital outows. We take it here in abroader sense, that is as the positive correlation between per-capita GDP growth andcapital outows (Prasad et al., 2007) and as the correlation between investment andcapital outows (Aizenman and Pinto, 2007). Here, we check whether the portfolioapproach can account for this corpus of evidence.

Both TFP catch-up π and capital per ecient unit of labor ln(k∗) are potentialchannels of growth and investment. However, according to the above empirical anal-ysis and consistently with the portfolio approach, only ln(k∗) correlates robustly withcapital outows. This suggests that the correlation of capital outows with investment

20

and growth that has been documented in the empirical literature is channelled mainlythrough ln(k∗).

However, the fact that capital outows, investment and growth are related separatelyto capital per ecient unit of labor is not sucient to explain the allocation puzzle.Indeed, the positive correlation between, say, investment and capital outows couldbe driven by other common factors. In that case, the allocation puzzle would not besolved. To test this, we estimate the cross-country correlation between capital outowsand investment as follows:

∆B

Y0 i

= γ∆K

Y0 i

+ νi

where ∆KY0 i

= KTi−K0i

Y0irefers to investment between 1980 and 2003 and νt is the error

term. We then add π and ln(k∗) and ask if any of these variables soak the signicance ofγ. We conduct the same analysis by replacing investment ∆K

Y0 iby GDP growth between

1980 and 2003 ∆YY0 i

= YTi−Y0iY0i

.

The results are provided in Tables 3 and 4. As column (1) of Table 3 shows, theunconditional correlation between ∆B

Y0and ∆K

Y0is positive and signicant at the 10%

level. This is the allocation puzzle. When we add π, this coecient remains stable andsignicant (column (2)). This means that TFP catch-up is not at the source of theallocation puzzle for investment. However, when ln(k∗) is added, both with and withoutπ (respectively columns (4) and (3)), the signicance of γ is soaked up. The same resultshold when ln(k∗) is replaced with Pk and αk (columns (5) and (6)). This suggests thatthe stock of capital per ecient unit of labor is at the origin of the positive correlationbetween capital outows and investment across countries.

Column (1) of Table 4 shows that the unconditional correlation between ∆BY0

and ∆YY0

is signicantly positive at the 10% level. When we add π and ln(k∗), respectively incolumns (2) and (3), the signicance of this correlation drops. Interestingly, the coe-cient of ∆Y

Y0is smaller when we add both variables than when we add them separately.

This suggests that both drive the allocation puzzle. However, only ln(k∗) remains sig-nicant, indicating that it play a more important role in driving the positive correlationbetween growth and capital outows. Again, the same results hold when we replaceln(k∗) by Pk and αk (columns (5) and (6)).

5 Predicted ows

In this section, we adopt the same approach as Gourinchas and Jeanne (2007): wecompute the amount of capital ows predicted by the model and then compare thesepredicted ows to the actual ones. Gourinchas and Jeanne found that the neoclassicalgrowth model without risk failed in predicting accurately the allocation of capital ows

21

between countries. However, we showed in Section 3 that, contrary to the model witoutrisk, the predictions of the model with risk were satised in the data. We check herewhether this is sucient to predict the accurate direction of ows between emergingcountries.

5.1 The riskless approach

In this subsection, for comparison purposes, we reproduce the results of Gourinchasand Jeanne on the performances of the neoclassical growth model without risk. Figure3 summarizes the outcome of the riskless approach across regions. The upper panelreports the actual net capital outows as a share of initial output ∆B/Y0: their sizeis −46% on average, which means that emerging countries have received net capitalinows during the period. The middle panel reports the predicted capital outowsbased on equation (2.6). These estimates are constructed under the hypothesis thatthe productivity catch-up follows a linear trend: πt = πmint/T, 1. According to themodel, non-OECD countries should have received capital inows on average, which isthe case. Moreover, average predicted ows in non-OECD countries are of the sameorder of magnitude as the actual ones.

However, while satisfying in terms of global trends, the picture is more contrastedwhen considering the direction and magnitude of ows inside the sample. Accordingto the predictions, Africa and Latin America should have exported capital while Asiashould have received capital inows (middle panel of Figure 3). This is because Asia hasbeneted from high TFP catch-up during the period while the other regions have fallenbehind the world frontier (see Table 1). Asia should have borrowed from the rest ofthe world both to take advantage of local investment opportunities and to smooth con-sumption in the face of rising revenues. Africa and Latin America should have exportedcapital to seek better returns and to smooth consumption in the face of decreasing rev-enues relatively to the rest of the world. In the data, the opposite happens (upper panelof the same gure).

However, if we abstract from the sign of capital ows, Latin America and Africa arecorrectly ranked by the model. Latin America experienced slower TFP growth thanAfrica and should then have exported more capital, which is consistent with the data.Therefore, Asia appears as an outlier inside the riskless approach.

On the whole, capital seems to ow in the right direction, except for Asia. The sameidea emerges from Figure 4, which shows the scatter plot of actual versus predictedows. The correlation appears as negative on the whole, which represents the allocationpuzzle. However, this negative correlation is driven by a set of countries dominated byAsia, in the upper left of the graph. If we excluded these countries, the correlation wouldbe positive. Explaining the allocation puzzle therefore entails to explain the peculiarbehavior of Asian countries.

22

5.2 The portfolio approach

We have shown that the model without risk reproduces the allocation puzzle, and thatthis allocation puzzle is mainly driven by Asia. We now turn to the extension with risk,and examine whether it solves this anomaly. It appears that, contrary to the risklessapproach, Asia is not an outlier in the portfolio approach. More importantly, this isnot at the expense of another outlier, since Latin America and Africa are still correctlyranked. This is because the portfolio approach does not simply reverse the link betweengrowth and capital ows. This link depends in a complex way on the dierent factorsof growth.

The lower panel of Figure 3 reports the estimated predicted net outows according toequation (10). The estimates are computed under the assumption that the productivitycatch-up follows a linear path, as in the riskless approach. The path of capital perecient unit of labor kt implied by the model is approximated by the following formula:kt = k0e

ln(k∗/k0)(1−λt), where 1− λ is the convergence rate estimated from the data (thatis 1− λ = 0.3).14

Note rst that the magnitude of predicted ows is above the actual ones (upperpanel) by several orders of magnitude. This is a shortcoming of the portfolio approachthat has been already highlighted in Kraay et al. (2005).15 It can also be related to thehome bias in portfolio (Lewis, 1999). But this shortcoming is accentuated here by thepresence of potentially huge human wealth, due to labor and productivity growth.

When abstracting from the magnitude issue, it appears that the predicted outowsin the lower panel of Figure 3 exhibit the right sign, which is negative, and, contraryto the riskless approach, the right ranking between regions. According to the model'spredictions, Africa and Latin America should receive capital inows while Asia shouldexport capital, as in the data. Additionally, the model predicts accurately that Africashould receive more capital inows than Latin America.

This analysis sheds some light on a neglected issue in the studies on global imbalances.Namely: why are these imbalances originated in Asia and not in other developing regions.An answer suggested here is that Asian growth is originated not only in TFP growth,but also, importantly, in a larger long-run capital per ecient unit of labor. As aconsequence, growth had beneted both to capital and labor income, but this growth hasbeen slightly tilted towards capital. Therefore, the asset demand due to a large capitalaccumulation has not been compensated by a matching increase in human wealth -although human wealth has grown a lot. This resulted in capital outows. On theopposite, Africa and Latin America face large frictions on the return to capital, which

14The assumed trend is a good proxy for the capital dynamics since the theory predicts that it movessmoothly from k0 to k∗.

15In their paper, the magnitude of capital ows becomes more realistic when they introduce sovereignrisk.

23

implies that their human wealth is large relative to their capital stock. Their assetdemand is then low relative to their domestic human wealth, leading to capital inows.

Not only does the portfolio approach rationalize the behavior of Asia relative toother regions, but it also explains the dierence between Africa and Latin America.Both regions have low capital per ecient unit of labor, but this is especially true forAfrica. Human wealth is then particularly disproportionate as compared to capital inAfrica. This results in larger capital inows in Africa than in Latin America.

The portfolio approach seems therefore to be a better predictor, if not of the magni-tude of ows, at least of their direction. Figure 5 sums up this idea by plotting predictedows according to the portfolio approach against the actual ones. A positive correla-tion appears. Besides, this correlation is not driven by Asian countries, contrary to theriskless approach.

5.3 Sensitivity analysis

In this subsection, we perform sensitivity analysis on the portfolio approach.

5.3.1 No redistribution of the tax product

In the model, the wedge between the social and private return to capital is represented bya tax on capital income that is redistributed equally among agents through a lump-sumtax Zt. While this capital wedge is meant at rationalizing the unwillingness to accu-mulate capital in developing countries, it also introduces a de facto insurance meansin the economy. Indeed, by redistributing a fraction of capital income, the tax trans-formes a risky income into a safe one. This insurance eect is another source of positivecorrelation between capital outows and growth.

However, the benets of the capital wedge do not necessarily go to the public inreality. If it results from the preemptive action of the government, it is not redistributedto households. If it arises from nancial frictions, it can be in the form of a rent thatgoes to private agents who might not be able to diversify this source of income. Theassumption that the tax product Zt is redistributed must be then taken with a grain ofsalt. In order to check whether our results rely on this assumption, we assume that thetax product is not redistributed but is sunk (e.g. it is consumed by the government).This will aect exclusively the estimated human wealth, which will be lower than in thebaseline when the capital wedge is positive because it does not include the tax product.

The resulting predicted capital ows are represented in Graph (a) of Figure 6 againstthe observed ones. Most predicted values are shifted to the right, except some very

24

positive values, which are shifted to the left. This is because most developing countrieshave a positive capital wedge, except a few countries with a high stock of capital and thuslarge estimated capital outows. For the former, a lower human wealth translates intolarger capital outows and for the latter, a higher human wealth translates into smalleroutows. As a result, estimated outows are less volatile but they are still correlatedpositively with the observed ones.

5.3.2 Alternative values of risk

Idiosyncratic risk is a very dicult parameter to assess, in particular in developing coun-tries. The value that we assigned to σ in the calibration, 0.6, is then highly questionable.In Graph (b) of Figure 6, the scatter plots of observed versus predicted ows for dif-ferent values of σ are represented. According to the graph, the higher σ, the larger thepredicted capital outows for each country. Indeed, σ aects negatively φ∗, the share ofcapital in the portfolio: σ increases the need for precautionary savings for a given levelof capital. As a result, the plots are shifted to the left or to the right relative to thebaseline but the correlation is still positive.

The value of σ in developed countries, 0.3, must be challenged as well. This isachieved by making the world interest rate R∗ vary. Indeed, the channel through whicha higher risk in developed countries manifests itsef is a lower world interest rate. Graph(c) of Figure 6 provides the scatter plots with dierent levels of interest rate. It appearsthat lower risk in the rest of the world (i.e. higher interest rate) has the same eect ashigher risk in developing countries: it increases predicted outows but does not alterthe correlation.

In the calibration analysis, we assumed that all developing countries faced the sameamount of risk. This is arguably a strength of the model since it generates heterogeneityin capital outows without contending heterogeneity in risk. However, domestic nancialdevelopment varies a lot across emerging countries and in a direction that does not seemfavorable to our approach: it is believed to be stronger in Asia, which has experiencedlarger capital outows. To check whether this is an issue, predicted capital ows arecomputed with σ = 0.3 in Asiatic countries, which is the amount of risk assigned todeveloped countries, and σ = 0.6 - the baseline - in the other emerging countries. Graph(d) of Figure 6 provides the scatter plot of these predicted ows against the observedvalues, along with the baseline. Clearly, predicted ows exhibit less excessively largevalues, which were composed of Asiatic countries. Still, the correlation remains positive.

25

5.3.3 Alternative measures of the capital wedge

In our model, the variations in capital per ecient unit of labor k∗ are accounted for bya capital wedge τ . It is set in order to equalize the private marginal returns to capitalacross countries, thus shutting down the Lucas (1990) puzzle. However, this capitalwedge is a black box: it does not say anything about the sources of the dierences incapital per ecient unit of labor across countries and thus about the sources of theallocation puzzle. Besides, as in the empirical section, it might be sensitive to thecalibration procedure and therefore subject to measurement errors. In this section, weuse the relative price of capital and its share in production computed in the previoussection as alternative measures of the capital wedge. We then investigate whether thepuzzle is still solved, that is: does the model still predicts accurately the cross-countrydirection of ows?

Caselli and Feyrer show in their paper that allowing for diering relative price ofinvestment Pk and share of capital αk across countries is sucient to account for thecross-country dierences in capital-labor ratio. Indeed, as reported in Table 1, if wecalculate the capital wedge τ that would equalize the new private return to capitalto the world's interest rate, we nd that the new capital wedge (column (6)) is muchsmaller (8% on average) than in the baseline calibration. This is in line with the ndingsof Caselli and Feyrer (2007).

Capital ows are then computed under the hypothesis that τ = 0 but with Pk andαk taken into account. Graph (e) of Figure 6 plots actual capital outows against thesepredicted values. As compared to the baseline, the predicted values are higher on average(the scatter plot is shifted to the right), but their correlation with observed ows is stillpositive.

6 Conclusion

This paper develops an extension of the traditional neoclassical growth model to riskyinvestment that contributes to match the actual capital ows and to solve the allocationpuzzle. It also provides an explanation to global imbalances and to their regional struc-ture. Namely, it explains why capital ows to the North come from Asia and not fromother regions with poor nancial development as Africa and Latin America. The advan-tage of this approach is that it does not constitute a great departure from the textbookmodel and therefore allows the adoption of a development accounting approach.

The portfolio approach fares better than the riskless one in predicting capital owsto developing countries because it accounts for two main facts: (i) countries with highTFP catch-up experienced larger capital outows, but conditional on a positive externalposition; (ii) countries with higher long-run capital per ecient unit of labor experienced

26

more capital outows.

One further step in this line of research would consist in studying whether the port-folio approach can also account for the composition of ows. Extending the model to thepossibility to trade equity, at least partially, could help predict both equity and bondholdings. We could then check whether the portfolio approach is consistent with thefact that direct foreign investment is positively correlated with growth, while securitiesare not, as shown by Prasad et al. (2007). Another question is the role of labor incomerisk, which is an important feature of developing countries, as well as investment risk.This is left for future research.

References

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Alfaro, L., S. Kalemli-Ozcan and V. Volosovych (2010), `International capital mobilitythrough the lens of the neoclassical growth model', mimeo.

Angeletos, G.-M. and V. Panousi (2009), `Revisiting the supply side eects of governmentspending', Journal of Monetary Economics 56(2), 137153.

Barro, R. J. and X. Sala-i Martin (1995), Economic Growth, McGraw Hill, New York.

Bernanke, B. and R. Gurkaynak (2001), N.B.E.R. Macroeconomics Annual, MIT PressCambridge MA, chapter Is Growth Exogenous? Taking Mankiw, Romer and Weilseriously, pp. 1172.

Caballero, R. J., E. Farhi and P.-O. Gourinchas (2008), `An equilibrium model of "globalimbalances" and low interest rates', American Economic Review 98(1), 35893.

Campbell, J.Y., M. Lettau, B.J. Malkiel and Y. Xu (2001), `Have individual stocksbecome more volatile? an empirical exploration of idiosyncratic risk', Journal ofFinance 56(1), 143.

Caselli, F. (2004), `Accounting for cross-country income dierences', NBER WorkingPaper No 10828.

Caselli, F. and J. Feyrer (2007), `The marginal product of capital', Quarterly Journal ofEconomics 122, 53568.

27

Dooley, M. P., D. Folkerts-Landau and P. Garber (2005), `The us current account decitand economic development: Collateral for a total return swap', Proceedings, FederalReserve Bank of San Francisco, Issue Feb.

Gourinchas, P-O. and O. Jeanne (2006), `The elusive gains from international nancialintegration', Review of Economic Studies 73, 71541.

Gourinchas, P.-O. and O. Jeanne (2007), `Capital ows to developing countries: Theallocation puzzle', NBER Working Paper No 13602.

Heston, A., R. Summers and B. Aten (2006), `Penn world table version 6.2', Centerfor International Comparisons of Production, Income and Prices at the University ofPennsylvania.

Hsieh, C.-T. and P.J. Klenow (2007), `Relative prices and relative prosperity', AmericanEcnomic Review 97(3), 56285.

Ju, J. and S.-J. Wei (2006), `A solution to two paradoxes of international capital ows',NBER Working Paper No 12668.

Ju, J. and S.-J. Wei (2007), `Domestic institutions and the bypass eect of nancialglobalization', NBER Working Paper No 13148.

Kearney, C. and V. Poti (2006), `Have european stocks become more volatile? an em-pirical investigation of idiosyncratic and market risk in the euro area', The Institutefor International Integration Studies Discussion Paper Series iiisdp132, IIIS.

Koren, M. and S. Tenreyro (2007), `Volatility and development', Quarterly Journal ofEconomics 122(1), 24387.

Kraay, AArt and Jaume Ventura (2000), `Current accounts in debtor and creditor coun-tries', The Quarterly Journal of Economics 115(4), 11371166.

Kraay, AArt, Norman Loayza, Luis Serven and Jaume Ventura (2005), `Country port-folios', Journal of the European Economic Association 3(4), 914945.

Lane, Philip R. and Gian Maria Milesi-Ferretti (2006), `The external wealth of nationsmark ii: Revised and extended estimates of foreign assets and liabilities for industrialand developing countries, 1970-2004', IMF Working Paper (69).

Lewis, K. (1999), `Trying to explain home bias in equities and consumption', Journal ofEconomic Literature 37(2), 571608.

Lucas, R. E. Jr. (1990), `Why doesn't capital ow from rich to poor countries?', AmericanEconomic Review 80, 9296.

Matsuyama, K. (2007), `Credit traps and credit cycles', American Economic Review97(1), 503516.

28

Mendoza, E. G., V. Quadrini and J.-V. Ríos-Rull (2009), `Financial integration, nancialdevelopment, and global imbalances', Journal of Political Economy 117(3), 371416.

Prasad, E., R. Rajan and A. Subramanian (2007), `Foreign capital and economic growth',Brookings Papers on Economic Activity 1(2007-1), 153230.

Sandri, D. (2008), `Growth and capital ows with risky entrepreneurship', Mimeo, JHUDepartment of Economics.

Song, Z.M., K. Storesletten and F. Zilibotti (2009), `Growing like china', CEPRWorkingPaper No DP7149.

7 Appendix

Proof of Proposition 1

In order to prove Proposition 1, we rst establish the following Lemma:

Lemma 1: Let xt = Xt/(AtNt) denote the value of Xt in ecient labor terms at theaggregate level. For a given interest rate R∗, the aggregate dynamics of the economy ischaracterized by:

ct = (ρ− n)ωt (18)

˙ωtωt

= rtφt +R∗(1− φt)− (ρ+ g∗ + πt) (19)

where rt = r(φtωt) = (1− τ)α(φtωt)α−1 − δ and φt dened by equation (8).

Equation (18) is the counterpart of Equation (7) in terms of ecient units of labor.

Equation (19) is obtained from the aggregation of the individual budget constraints(5) written in terms of ecient units of labor and where the wage clears the labor market.

Equations (18) and (19), along with the no-Ponzi conditions and the denitions ofrt and φt, characterize the dynamics of ct and ωt. Once the paths of these variables areknown, kt = φtωt, ht =

∫∞0e−(R∗−(n+g∗))s+πs−πt(1− α + τα)kαt+sds and bt = ωt − kt − ht

can be determined. However, these equations are used here only to determine steadystate.

We now characterize stationarity.

29

Since, according to Equation (18), consumption is proportional to wealth, the station-arity of consumption ˙c/c = 0 implies the stationarity of wealth ˙ω/ω = 0. Additionally,the stationarity of catch-up ˙π = 0, along with the aggregate budget constraint, impliesthat the long-run share of capital φ∗ satises:

r∗φ∗ +R∗(1− φ∗)− (ρ+ g∗) = 0

which is equivalent to:(r∗ −R∗)2

σ2= ρ+ g∗ −R∗ (20)

Therefore, for the steady state to exist, we must have R∗ ≤ ρ+ n.

Since the share of capital in wealth φ is necessarily non-negative, then r−R∗ is alsonon-negative. Equation (20) therefore yields the expression of the return dierential:

r∗ −R∗ =√σ2(ρ+ g∗ −R∗)

This equation is equivalent to Equation (9).

Equation (10) derives from the denition of φ at steady state:

φ∗ = k∗/(k∗ + b∗ + h∗) (21)

To establish Equation (10), we must then derive the value of the steady-state share ofcapital φ∗ and the steady-state human wealth h∗.

First, when σ > 0, we must have necessarily R∗ < ρ + n. This can be shown bynoticing that Equation (20) can be rewritten as follows:

σ2φ∗2 = ρ+ g∗ −R∗

Suppose that R∗ = ρ + g∗, this would imply, when σ > 0, that φ∗ = 0. If wealth isstationary, this means that the stock of capital converges towards zero. Given the Cobb-Douglas specication, this implies that the return to capital would tend to innity, whichcontradicts the fact that the return dierential is constant, as suggested by Equation(9). Since, as shown above, R∗ ≤ ρ+ g∗ for the steady state to exist, then we must haveR∗ < ρ+ g∗. As a consequence, Equation (20) implies that:

φ∗ =

√ρ+ g∗ −R∗

σ2

Second, to complete Equation (10), we have to determine h at steady state. ht =∫∞0e−R

∗s Nt+sAtt+sNtAtt

(1−α+τα)kαt+sds =∫∞

0e−(R∗−(n+g∗))s+πs−πt(1−α+τα)kαt+sds. Equa-

tion (9) gives k∗, the steady-state value of k. We have also πt = π in the long run.Therefore,

h∗ =(1− α + τα)k∗α

R∗ − (n+ g∗)

Replacing h∗ in Equation (21) with the steady-state φ∗ yields Equation (10).

30

Proof of Proposition 3

Notice that the predicted capital ows must satisfy (12). According to this equation thederivative of ∆B

Y0with respect to τ depends only on the derivative of b∗.

Dierentiating (10) with respect to τ , we obtain:

∂b∗

∂τ=∂k∗

∂τ

[1− φ∗

φ∗− (1− α + τα)αk∗(α−1)

R∗ − n− g∗

]− αk∗α

R∗ − n− g∗

In order to infer ∂k∗

∂τ, we dierentiate Equation (9) with respect to τ and get:

∂k∗

∂τ=

k∗

(1− τ)(1− α)

Replacing in ∂b∗

∂τ, we can show that:

∂b∗

∂τ=

1

(1− τ)(1− α)

[−b∗ − (1− α)

k∗α

R∗ − n− g∗

]

Therefore, ∂b∗

∂τ≤ 0 if and only if b∗ ≥ −(1− α) k∗α

R∗−n−g∗ .

Derivation of Equation (14)

When σ = 0, the no-arbitrage condition rt = R∗ is necessarily satised for all t. Oth-erwise, according to the expression of φt (8), the stock of capital would be innite.Therefore, the stationarity of wealth implies:

R∗ = ρ+ g∗

Using (18) and (19) in per capita terms, along with the fact that rt = R∗ andR∗ = ρ+ g∗, we obtain the following Euler condition:

ctct

= g∗ (22)

Therefore, ct = c0eg∗t, and ct = c0e

g∗tA0/At = c0e−πt . As a consequence, we obtain at

steady state: c∗ = c0e−π. We know also that kt = k∗ always because of the no-arbitrage

31

condition. The stationarity of wealth therefore implies that b∗ is also constant in thelong run and satises:

ω∗ = k∗ + b∗ + h∗

Since c∗ = (ρ−n)ω∗ and, as we have shown above, h∗ = (1−α+τα)k∗α/(R∗−(n+g∗)),this equation can be rewritten as follows:

b∗ = −k∗ − (1− α + τα)k∗α

ρ− n+c0e−π

ρ− n

Replacing c0 using c0 = (ρ− n)ω0, we obtain:

b∗ = −k∗ − (1− α + τα)k∗α

ρ− n+ e−π

[h0 + k0 + b0

]

Replacing this expression for b∗ in Equation (12) and substituting for h0 = (1− α+ατ)k∗α

∫∞0e−(ρ−n)t+πtdt, we obtain:

∆B

Y0

R

= − k∗ − k0

kα0e(n+g∗)T − (eπ − 1)

k∗

kα0e(n+g∗)T

−eπ+(n+g∗)T (1− α + ατ)k∗α

kα0

(1

ρ− n−∫ ∞

0

e−(ρ−n)t+πt−πdt

)+(e(n+g∗)T − 1

) b0

kα0

Since 1/(ρ− n) =∫∞

0e−(ρ−n)tdt, this expression leads to Equation (14).

Productivity and consumption smoothing

When σ = 0, under Assumption 3, the third term of Equation (2.6) can be written asfollows:

∆Bs

Y0

= −e(n+g∗)T (1− α + ατ)k∗α

kα0

∫ T

0

e−(ρ−n)t(eπ − eπf(t))dt

A sucient condition for ∆Bs

Y0to be decreasing in π is that eπ − eπf(t) is increasing

in π. We have:∂[eπ − eπf(t)

]∂π

= eπ[1− f(t)eπ(f(t)−1)

]Consider the term between brackets:

∂[1− f(t)eπ(f(t)−1)

]∂f(t)

= −eπ(1−f(t))[1 + πf(t)]

32

A sucient condition for this derivative to be negative is π ≥ −1. If it is the case, thenfor 0 ≤ f(t) ≤ 1:

1− f(t)eπ(f(t)−1) ≥ 0

which implies that∂[eπ−eπf(t)]

∂π≥ 0. As a consequence, if π ≥ −1, then ∆Bs

Y0is decreasing

in π.

Derivation of Equation (15)

In (12), we replace b∗ using (11) and − b0kα0

with b0kα0

((e(n+g∗)T − 1

)b0kα0− e(n+g∗)T

). After

rearranging using b0 = 1−φ0φ0

k0 − h0, we get:

∆BP

Y0

=1− φ∗

φ∗k∗ − k0

kα0e(n+g∗)T +

1− φ∗

φ∗(eπ − 1)

k∗

kα0e(n+g∗)T

−eπ+(n+g∗)T (1− α + ατ)f(k∗)

kα0

(1

R∗ − (n+ g∗)−∫ ∞

0

e−(R∗−(n+g∗))t+πt−πdtf(kt)

f(k∗)

)

+(e(n+g∗)T − 1

) b0

kα0+

(1

φ∗− 1

φ0

)e(n+g∗)T k0

kα0

Since 1/(R∗ − (n+ g∗)) =∫∞

0e−(R∗−(n+g∗))tdt, this expression leads to Equation (15).

33

Table1:

Long-term

capitalpere

cientun

itof

labor,capitalwedge

andpotentialdeterm

inants

ofcapitalows

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

πb 0 y0

∆k

Ty0

kT

τ[

τ\

τ]

Pk

αk

Obs.

Non-O

ECD†

-10%

-31%

-0.65%

1.8

38%

28%

9%

2.61

35%

67

Sub-SaharanAfrica

-16%

-40%

-1.34%

1.2

55%

47%

10%

3.43

31%

28

LatinAmerica

-37%

-35%

-0.75%

2.0

32%

20%

13%

2.13

37%

22

Asia

34%

-11%

0.61%

2.6

19%

6%

2%

1.89

37%

17

Asia(ExcludingChina)

24%

-12%

0.8%

2.6

20%

6%

4%

1.91

38%

16

Theguresare

unweightedcountryaverages.

† :Includes

alsoKorea,MexicoandTurkey.

[ :calculatedwithin

theriskless

approach.

\ :calculatedwithin

theportfolioapproach.

] :calculatedwithin

theportfolioapproach

andwiththeadjustmentforPkandαk

34

Table2:

Determinants

ofobserved

andpredictedcapitaloutow

s

(1)

(2)

(3)

(4)

(5)

(6)

Dependent

variable:

∆BY0

∆BY0

∆BY0

∆BY0

∆BY0

∆BY0

All

BT<

0All

BT<

0All

BT<

0

π0.565*

-0.417*

0.339

-0.380

0.007

-0.629**

(0.313)

(0.220)

(0.355)

(0.231)

(0.307)

(0.310)

ln(k∗ )

0.831*

0.385*

(0.432)

(0.224)

Pk

-0.288*

-0.208*

(0.146)

(0.110)

αk

5.156**

1.606*

(2.420)

(0.900)

b0

y0

0.898

-0.135

1.186

-0.205

(0.735)

(0.257)

(0.927)

(0.312)

ln(y

0)

-0.779

-0.426

-0.252

-0.213***

(1.160)

(0.678)

(0.182)

(0.073)

(n+g∗ )∗T

-0.422

-0.266

-1.099

-0.551

(0.835)

(0.507)

(0.853)

(0.547)

Constant

-0.420**

-0.928***

0.055

-0.767

-0.180

-0.466

(0.200)

(0.114)

(0.769)

(0.474)

(1.198)

(0.742)

Observations

6759

6759

6255

R-squared

0.037

0.057

0.228

0.173

0.270

0.220

Robuststandard

errors

inparentheses

***p<

0.01,**

p<0.05,*p<

0.1

35

Table3:

The

channelsof

theallocation

puzzle-Investment

Dependent

variable:

∆BY0

(1)

(2)

(3)

(4)

(5)

(6)

∆KY0

0.122*

0.131*

0.066

0.036

0.066

0.071

(0.063)

(0.072)

(0.047)

(0.060)

(0.040)

(0.059)

π-0.092

0.274

-0.064

(0.386)

(0.419)

(0.450)

ln(k∗ )

0.544***

0.584***

(0.182)

(0.202)

Pk

-0.259*

-0.262*

(0.137)

(0.140)

αk

2.963*

2.933*

(1.521)

(1.564)

Constant

-0.755***

-0.784***

-0.805***

-0.722***

-1.125**

-1.122*

(0.141)

(0.225)

(0.124)

(0.214)

(0.559)

(0.575)

Observations

6767

6767

6262

R-squared

0.091

0.092

0.167

0.171

0.182

0.182

Robuststandard

errors

inparentheses

***p<

0.01,**

p<0.05,*p<

0.1

36

Table4:

The

channelsof

theallocation

puzzle-GDPgrow

th

Dependent

variable:

∆BY0

(1)

(2)

(3)

(4)

(5)

(6)

∆YY0

0.175*

0.070

0.122

-0.004

0.114

0.145

(0.102)

(0.163)

(0.095)

(0.156)

(0.075)

(0.158)

π0.380

0.453

-0.126

(0.596)

(0.573)

(0.603)

ln(k∗ )

0.638***

0.643***

(0.207)

(0.209)

Pk

-0.304**

-0.313**

(0.152)

(0.155)

αk

3.173**

3.149*

(1.578)

(1.621)

Constant

-0.740***

-0.544

-0.869***

-0.636*

-1.118*

-1.143*

(0.154)

(0.404)

(0.146)

(0.354)

(0.584)

(0.641)

Observations

6767

6767

6262

R-squared

0.034

0.038

0.162

0.168

0.171

0.172

Robuststandard

errors

inparentheses

***p<

0.01,**

p<0.05,*p<

0.1

37

Figure 1: Capital outows against TFP catch-up - 1980-2003

ArgentinaBangladesh Benin

Bolivia

Botswana

Brazil Burkina FasoCameroon ChileColombia

Congo RepCosta Rica CyprusDominican RepublicEcuador

Egypt Arab Rep

El Salvador

Ethiopia

FijiGabon

Ghana

GuatemalaHaitiHonduras

Hong Kong China

India

Indonesia

Iran Islamic Rep

IsraelIvory Coast

JamaicaKenyaKorea Rep

Madagascar

Malawi

MalaysiaMali

Mauritius

Mexico Morocco

Mozambique

NepalNiger

Nigeria

PakistanPanama

Papua New Guinea

ParaguayPeruPhilippinesRwanda

Senegal

Singapore

South Africa

Sri LankaSyrian Arab Republic

Taiwan China

TanzaniaThailand

Togo

Trinidad and Tobago

Tunisia

Turkey

Uganda

UruguayVenezuela

-20

24

68

Cap

ital o

utflo

ws

(198

0-20

03)

-.5 0 .5 1TFP growth

Fitted values (t=1.45) Fitted values excluding outliers (t= 0.48)

Source: Penn World Tables 6.2 (Heston et al., 2006), Lane and Milesi-Ferretti (2006), author's calcula-tions.Outliers are Hong Kong and Botswana. China is excluded from the gure.TFP growth is estimated as π = ln(AT ) − ln(A0), where At is the trend of TFP, measured through agrowth accounting method. See Section 3 for details.

38

Figure 2: Capital outows against the long-term capital stock per ecient unit of labor- 1980-2003

ArgentinaBangladeshBenin

Bolivia

Botswana

BrazilBurkina FasoCameroon ChileColombia

Congo RepCosta Rica CyprusDominican Republic Ecuador

Egypt Arab Rep

El Salvador

Ethiopia

FijiGabon

Ghana

GuatemalaHaitiHonduras

Hong Kong China

India

Indonesia

Iran Islamic Rep

IsraelIvory Coast

JamaicaKenyaKorea Rep

Madagascar

Malawi

MalaysiaMali

Mauritius

MexicoMorocco

Mozambique

NepalNiger

Nigeria

PakistanPanama

Papua New Guinea

Paraguay PeruPhilippinesRwanda

Senegal

Singapore

South Africa

Sri LankaSyrian Arab Republic

Taiwan China

Tanzania Thailand

Togo

Trinidad and Tobago

Tunisia

Turkey

Uganda

UruguayVenezuela

-20

24

68

Cap

ital o

utflo

ws

(198

0-20

03)

-2 -1 0 1 2Long-term capital per efficient unit of labor

Fitted values (t=3.12) Fitted values excluding outliers (t=3.16)

Source: Penn World Tables 6.2 (Heston et al., 2006), Lane and Milesi-Ferretti (2006), author's calcula-tions.Outliers are Hong Kong and Botswana. China is excluded from the gure.The long-term capital stock per ecient unit of labor is the TFP-adjusted capital/labor ratio at theend of the sample. It is measured as kt = Kt/(AtNt), where Kt is the aggregate capital stock, At isTFP and Lt is the labor force, and then cleaned from short-run uctuations. See Section 3 for details.

39

Figure 3: Observed and predicted capital ows by region

Observed capital outflows

-0.80 -0.70 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10

All non-OECD

Africa

Latin America

Asia

Asia (Excluding China)

Share of initial output

Predicted capital outflows (riskless approach)

-15.00 -10.00 -5.00 0.00 5.00 10.00

All non-OECD

Africa

Latin America

Asia

Asia (Excluding China)

Share of initial output

Predicted capital outflows (portfolio approach)

-70 -60 -50 -40 -30 -20 -10 0 10 20

All non-OECD

Africa

Latin America

Asia

Asia (Excluding China)

Share of initial output

Source: Penn World Tables 6.2 (Heston et al., 2006), Lane and Milesi-Ferretti (2006), author's calcula-tions.Observed capital ows are the observed ratio of net capital outows to initial output, predicted capitalows in the riskless and portfolio approaches are respectively ∆BR

Y0as dened by Equation (2.6) and

∆BP

Y0as given by Equation (12).

The gures are unweighted country averages.Non-OECD countries include also Korea, Mexico and Turkey.

40

Figure 4: Actual capital outows (as a share of initial GDP) against their predictedvalue, according to the riskless approach, 1980-2003

Bangladesh

Hong Kong China

India

Indonesia

Korea Rep

Malaysia NepalPakistanPhilippines

Singapore

Sri LankaThailandArgentina

Bolivia

BrazilChile ColombiaCosta RicaDominican Republic EcuadorEl Salvador

FijiGuatemalaHaiti

HondurasJamaica

Mexico

Mozambique

Panama

Papua New Guinea

ParaguayPeru

Taiwan China

Trinidad and Tobago

UruguayVenezuela

Egypt Arab RepIran Islamic Rep

IsraelMorocco

Syrian Arab Republic

Tunisia

Cyprus TurkeyBenin

Botswana

Burkina FasoCameroon

Congo Rep

Ethiopia

Gabon

Ghana

Ivory CoastKenya

Madagascar

Malawi

Mali

Mauritius

Niger

NigeriaRwanda

Senegal

South Africa

Tanzania

Togo

Uganda

-20

24

68

Act

ual c

apita

l out

flow

s

-30 -20 -10 0 10 20Predicted capital outflows - Riskless approach

coeff.=-.0314837, robust se=.0196067, t=-1.61

Source: Penn World Tables 6.2 (Heston et al., 2006), Lane and Milesi-Ferretti (2006), author's calcula-tions.Note: China is excluded.

41

Figure 5: Actual capital outows (as a share of initial GDP) against their predictedvalue, according to the portfolio approach, 1980-2003

Bangladesh

China

Hong Kong China

India

Indonesia

Korea Rep

MalaysiaNepalPakistanPhilippines

Singapore

Sri Lanka ThailandArgentina

Bolivia

BrazilChileColombiaCosta RicaDominican RepublicEcuadorEl Salvador

FijiGuatemalaHaiti

HondurasJamaica

Mexico

Mozambique

Panama

Papua New Guinea

ParaguayPeru

Taiwan China

Trinidad and Tobago

UruguayVenezuela

Egypt Arab RepIran Islamic Rep

IsraelMorocco

Syrian Arab Republic

Tunisia

CyprusTurkeyBenin

Botswana

Burkina FasoCameroon

Congo Rep

Ethiopia

Gabon

Ghana

Ivory CoastKenya

Madagascar

Malawi

Mali

Mauritius

Niger

NigeriaRwanda

Senegal

South Africa

Tanzania

Togo

Uganda

-20

24

68

Act

ual c

apita

l out

flow

s

-200 -100 0 100 200Predicted capital outflows - Portfolio approach

coeff.=.0093646, robust se=.0038073, t=2.46

Source: Penn World Tables 6.2 (Heston et al., 2006), Lane and Milesi-Ferretti (2006), author's calcula-tions.

42

Figure 6: Actual capital outows (as a share of initial GDP) against their predictedvalue, according to the portfolio approach, 1980-2003 - Robustness

(a) (b)

-20

24

68

Act

ual c

apita

l out

flow

s

-200 -100 0 100 200 300Predicted capital outflows - Portfolio approach

Baseline Fitted values (t=2.49)After adjusting for alphak and Pk Fitted values (t=2.43)

-20

24

68

Act

ual c

apita

l out

flow

s

-200 -100 0 100 200Predicted capital outflows - Portfolio approach

Sigma=0.4 Fitted values (t=2.02)Sigma=0.6 (baseline) Fitted values (t=2.46)Sigma=0.8 Fitted values (t=2.53)

(c) (d)

-20

24

68

Act

ual c

apita

l out

flow

s

-200 -100 0 100 200Predicted capital outflows - Portfolio approach

R*=6.4% Fitted values (t=2.10)R*=6.5% (baseline) Fitted values (t=2.42)R*=6.6% Fitted values (t=2.52)

-20

24

68

Act

ual c

apita

l out

flow

s

-200 -100 0 100 200Predicted capital outflows - Portfolio approach

Baseline Fitted values (t=2.46)Sigma=0.3 in Asia Fitted values (t=2.62)

(e)

-20

24

68

Act

ual c

apita

l out

flow

s

-200 -100 0 100 200 300Predicted capital outflows - Portfolio approach

Baseline Fitted values (t=2.49)After adjusting for alphak and Pk Fitted values (t=2.43)

Source: Penn World Tables 6.2 (Heston et al., 2006), Lane and Milesi-Ferretti (2006), Bernanke andGurkaynak (2001), author's calculations.

43