Topic Gravity 2014-2

8/12/2019 Topic Gravity 2014-2

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Topic 2:

The gravity equation


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Overview

Short introduction Theory in gravity Empirical estimationApplication: Does WTO membership affect

trade?


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Gravity equation

Gravity models explain trade flowsbetween countriesjand kusing marketsize and distance as explanatory variables

Very successful in empirical work (highexplanatory power)

Augmented gravity equation to investigaterole of border effects, free tradeagreements, common language, etc. onbilateral trade


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The origins

Isaac Newtons Law of UniversalGravitation(1687)

Attractive force Fbetween two objects iandjisgiven by

F is the attractive force, M are the masses, Dis distance between objects, G is gravitationalconstant depending on units of measurement formass and force

2

ij

ji

ijD

MMGF =


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Gravity equation in trade

Jan Tinbergen in 1962 proposed similar form toexplain trade flows

Fij trade flows from i to j Miand Mjare economic masses(size) D

ij

is distance between the two locations

G is a constant (equal to Newtons law if !=!=1 and "=2)

!

"#

ij

ji

ij

D

MMGF =


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Gravity equation in trade

Take logs to arrive at estimable equationlnFij= !lnMi+ !lnMj "lnDij+ lnG+ eit

If eis classical error term, equation can beestimated using OLS

Mi supply of goods Mj demand for goods Dij frictionsin trade (trade costs)


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Theory in gravity?

Starting with Anderson (AER 1979)theoretical models have been derived thatlead to gravity-like equations

Mainly based on monopolistic competition


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The simplest model

Countries i,jspecialised in different varieties k Identical demand No trade costs Country GDP: Yi= "k yik World GDP: Yw= "iyi Exports from i to j: Xijk= sjyik

X

ij

= "kXij

k= sj

"k yi

k = sj

Yi

== sj si Yw = Xji

Xij+ Xji= 2 (sj si Yw ) = (2/ Yw )Yi Yj


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The role of distance

Prices

CES utility function

Budget constraint Demand for each product

iijijpTp =

!=

"=

C

i

ijjcU

1

/)1()( ##

!=

=

C

i

ijijij

cpNY1

)/()/( jjjijij PYPpc !"=


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Price index inj

Total exports

)1/(1

1

)1()(

!

!

"

=

"

#$

%&'

(= )

C

i

ijijpNP

ijijiijcpNX =

( ) !"

=

1/

jijjiijppYNX


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Prices are difficult to measure, hencemodel difference between pijand pias

Anderson and van Wincoop (2003): If Tij=Tji, then

ijijijij dT !"# ++= lnln

!"

##$

%

&&'

(

##$

%

&&'

(=

1

~~ ji

ij

w

jiij

PP

T

Y

YY

X


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Estimable equation

Estimation strategy 1: Solve for priceindices

Estimation strategy 2: Use fixed effects tocontrol for unobserved price indices

ijwji

ijiijiij

YPP

dYYX

!"

"#$"

"" )1()/1ln()~

ln()~

ln(

ln)1()1()/ln(11

%++++

%

+%

=

%%


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Empirical uses of gravity

Particularly useful / popular because it canbe easily augmented with other variables

lnXij= !lnYi+ !lnYj "lndij+ #Zij+ eit

In the context of the earlier model, Zproxies factors that impact on transportcosts


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Data requirements

Dependent variable: Trade flows betweencountry iandj

Economic mass

Generally measured as GDP

Widely available Distance

Generally measured as great circledistancebetween two capitals (minimum distance along thesurface)

Data available from some data sources, e.g.,http://www.macalester.edu/research/economics/PAGE/HAVEMAN/Trade.Resources/TradeData.html


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The identificationproblem

Do variables really capture what they aresupposed to capture?

Unobserved bilateral country paircharacteristics

Time trends in panel datalnXijt= !lnYit+ !lnYjt "lndij+ #Zijt+

+ !ij+ "t+ eijt


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Brief Review: RE Estimation

! Random effects estimation puts uijin the error term! Assume

yit= #xit+ vit where vit= ui+ eit

! RE amounts to estimating(yit- $!yi) = #(xit- $!xi) + (vit - $!vi)

! where $= 1 - $[%2e/(%2e+ T%2u)]! Special cases if $= 0 and $= 1


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Brief Review: RE vs FE

! FE cannot estimate time invariant variables! RE based on assumption that E(ui| xi) = 0! Choose using a Hausman test! FE is consistent if assumption fails, RE is not! Statistically significant difference between the estimates

is interpreted as evidence against RE

! where H is distributed asymptotically as &2M! If only one parameter of interest, use t statistic

( )( ) ( )REFEREFEREFE !!VV!!

1

!!"

!=

!

H

( ) ( )22

)

()

(/

REFEREFE

seseH

!!!! ""=


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Illustration

Using data for OECD countries, 1980 -2000


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(1) (2) (3) (4) (5) (6)

panel panel OLS with

countrydummies

OLS with

countrydummiesand timedummies

FE with

country-pairdummiesand timedummies

RE with

country-pairdummiesand timedummies

Log distance -0.979 -0.885 -1.122 -1.133 Notestimated

-0.964

(0.008)*** (0.009)*** (0.012)*** (0.012)*** (0.028)***

Y home 0.948 0.950 0.596 0.466 0.403 0.801

(0.006)*** (0.006)*** (0.042)*** (0.059)*** (0.031)*** (0.018)***Y partner 0.882 0.882 1.040 0.919 0.907 0.912

(0.006)*** (0.006)*** (0.039)*** (0.050)*** (0.027)*** (0.017)***

fta 0.469 0.310 0.243 0.123 0.137

(0.023)*** (0.021)*** (0.020)*** (0.016)*** (0.016)***

Constant -20.267 -21.190 -13.129 -5.747 -14.264 -17.782

(0.227)*** (0.228)*** (0.804)*** (2.291)** (1.109)*** (0.677)***

Observations 13284 13284 13284 13284 13284 13284R-squared 0.81 0.82 0.89 0.89 0.61

Standard errors in parentheses

* significant at 10%; ** significant at 5%; *** significant at 1%


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Prob>chi2 = 0.0000 = 479.22 chi2(22) = (b-B)'[(V_b-V_B)^(-1)](b-B) Test: Ho: difference in coefficients not systematic

B = inconsistent under Ha, efficient under Ho; obtained from xtreg b = consistent under Ho and Ha; obtained from xtreg

time21 .1192557 .7052175 .5859618 . time19 .0283487 .6014997 .573151 . time18 .073328 .4956382 .5689662 . time17 .2078112 .3416377 .549449 . time16 .2948453 .264275 .5591202 . time15 .3452295 .2585844 .603814 . time14 .3733772 .2489987 .6223759 . time13 .3876499 .204316 .5919659 . time12 .3953121 .2085065 .6038186 . time11 .329257 .2784265 .6076835 .

time10.3170783 .3449739 .6620522 .0040154

time9 .3945857 .26442 .6590057 .0038288 time8 .3297571 .3645879 .694345 .0109167 time7 .3248091 .437687 .762496 .0188515 time6 .2360411 .6229433 .8589844 .0280628 time5 .3475799 .5126343 .8602142 .0281149 time4 .4956576 .3466562 .8423138 .0266676 time3 .6001653 .214024 .8141893 .0237784 time2 .6584187 .1201724 .7785912 .0200937 fta .1233579 .1369302 .0135723 .l_gdp_USD_pa .9073102 .9117582 .004448 .0206251l_gdp_USD_co .4033102 .8008224 .3975122 .0256198

fixed . Difference S.E. (b) (B) (b-B) sqrt(diag(V_b-V_B)) Coefficients

Hausman test of FE vs RE


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A note on interpretation

FTA is a dummy variable in a log-linearmodel

Effect of switching dummy from 0 to 1:exp()-1

i.e., (exp(0.137)-1) = 0.147 %being member of a FTA is associated

with 15% higher trade


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Application

Does WTO membership increase trade?Andrew Rose,American Economic

Review, 2004

Related work on currency unions byAndrew Rose and co-authors


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Research question

What is the effect of WTO membership oninternational trade?

Two different aspects: How much more do countries within WTO

trade compared to non-members?

What is the trade effect of a country joining(or leaving) WTO?


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Equation to be tested


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GSP: Generalized System of Preferences

GSP exempts WTO member countries from the most favoured nationprinciple for the purpose of lowering tariffs for the least developing countries

(without also doing so for rich countries).


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Data Sources

IMF Direction of Trade data covering 178entities(territories) between 1948 to 1999

X includes exports + imports, deflated using US CPI WTO information to create WTO and GSP variables GDP and population from World Bank World

Development Indicators or IMF

WTO data to create FTA dummy: EU, US-Israel, NAFTA,CARICOM, PATCRA, ANZCERTA, Mercosur

Currency Union: Currency interchangeable between twocountries at a 1:1 par for extended period of time CIAWorld Factbook for other control variables

Data available on Andrew Roses website


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Estimation approach

Pooled panel OLS (including year controlsand robust standard errors)

Cross section OLS on individual years Panel estimation controlling for

unobservable country pair effects

Sensitivity analysis


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Conclusion on Rose

Rose claims to find no effect of WTOmembership on trade

Is this the correct estimation of a gravitymodel?


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The problem of zeros

General gravity modellnXij= !lnYi+ !lnYj "lndij+ #Zij+ eit

Only estimated on country pairs where trade isnon-zero.

Potentially biased results if conclusions areapplied to all countries (okay if conclusions are

based on sample with only positive trade values)


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The problem of zeros

Example: The distance puzzle Generally studies find that distance coefficient

changes over time

At odds with idea that transport costs decreasedand that distance is dead

One explanation (Felbermayr and Kohler 2004):model is mis-specified (extensive vs. intensivemargin)

Reduction in transport costs affects extensivemargin, mainly small volumes Need to take zeros into account


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Two views on zeros

Censoring (corner solution) ytake on 0 with positive probability, but is a

continuous random variable over strictly

positive valuesy* = x!+ u, u|x ~ Normal(0,%2)

y = max(0, x!+ u)

Estimation using Maximum Likelihood (Tobitmodel due to Tobin (1956)) Practical problem in gravity: ln(0) on LHS


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Two views on zeros

Selection (incidental truncation) trade data are available only for a clearly

defined subset of the population. Trade values

are missing as a result of the outcome ofanother variable, namely, the decisiontotrade.

y = x1!+ u

d = 1[x"+ v > 0] Do not set y = 0 if d = 0! If d = 0, y is missing Estimation using Selection Model


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Two views on zeros

Selection (incidental truncation) E(y|x, d = 1) = x1!+ &$(x")

where $(x") = '(x") / ((x") is inverted Mills

ratio Estimation of equation using OLS on selected

sample omits IMR ("not observed)

Consistent estimator of "is available from firststage probit estimation

Probit: P(d = 1 | x) = ((x") OLS: y = x1!+ &!$(x") + e


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Applications

Felbermayr and Kohler (2004) Corner Solution Model using Tobit estimation Solves distance puzzle!

Helpman, Melitz, Rubinstein (2008) Selection model


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Implementation in Stata

Random effects: tsset (panelunit) (time) xtreg y X, re

Tobit: tobit xttobit

Selection heckman


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Reading

Feenstra, Robert C. (2004),Chapter 5 Head, K. (2003), Gravity for Beginners, mimeo Baltagi, B., P. Egger, M. Pfaffermayr (2014), Panel

data gravity models of international trade, CESIfoWorking Paper 4616

Rose, A.K. (2002), Do we really know that the WTOincreases trade?, NBER Working Paper 9273(published in AER 2004)

Felbermayr, G and W. Kohler (2006), Exploring theintensive and extensive margins of world trade,Review of World Economics, 142(4)

Helpman, E., M. Melitz, Y. Rubinstein (2008),Estimating trade flows: trading partners and tradingvolumes, Quarterly Journal of Economics, 123(2)

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Topic Gravity 2014-2