1

Using gravity models to calculate trade potentials

for developing countries

Jean-Michel Pasteels (ITC)

Workshop on Tools and Methods for Trade and Trade Policy Analysis, Geneva, September 2006

version 1.2

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Applications of gravity models:

1) Analysis of elasticities of trade volumes - Regional Trade Agreements (RTA), "natural regionalism"

(Frankel & Wei, 1993, Baier & Bergstrand 2005)

- WTO membership

- Impact of NTBs on trade (Fontagné et al. 2005)

- Cost of the border (Mac Callum, Anderson & van Wincoop 2003)

- Impact of conflicts on trade

- FDI & trade: complements or substitute (Eaton & Tamura, 1994; Fontagné, 2000)

- Effect of single currency on trade (Rose, 2000)

- Trade patterns: inter and intra-industry trade (Fontagné, Freudenberg & Péridy, 1998)

- Diasporas (community of immigrants)- Internet

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Applications of gravity models:

2) Analyse predicted trade flows and observe differences between predicted and observed flows (analysis of residuals)

- Trade potentials of economies in transition (out-of sample predictions, ref...)

- Identify the natural markets and markets with an untapped trade potential

- Predicted values are used in some cases as an input for CGE modeling (Kuiper and van Tongeren, 2006)

- Use of confidence intervals in addition to predicted values, in order to take into account the residual variance

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Gravity Equation (1) can be transformed in to a stochastic logarithmic form:

;ln*

ln)1(ln)1(lnlnln*ln

00

1210

with

PPzYYX ijjimij

M

mmjiij

(2)

1

ji

ij

w

jiij PP

t

y

yyx(1)

The Gravity Equation

Pi and Pj are the multilateral resistance terms, capturing the resistance of country i and country j to trade with all regions. Highlighted by Anderson & Van Wincoop (2003) earlier gravity models were mispecified

These terms are not observable (function of trade barriers and consumer prices)

1

1

1)(i

ii

ijj

tP(3)

5

This implies for a cross-section model, that the equation can only include bilateral variables (perfect correlation between country fixed effects and any other country specific variable). What should we do with Yi (GDP)? Anderson & van Wincoop suggest an unitary income elasticity.

ijjiijmij

M

mmjiij tzYYX

lnlnlnln*ln1

210

Pi and Pj are estimated using country fixed effects (dummy variables):

(4)

ijjiijmij

M

mmjiij tzYYX

lnln)/ln(1

0(5)

ijjiijtmijt

M

mmjtitijt tzYYX

lnlnlnln*ln1

210

(4)bis: panneldata

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• Some practical and conceptual problems:– colinearity

– heteroscedaticity

– zero values (Ln(0))

– endogeneity & simultaneity: RTA, conflicts

– autocorrelation: (pannel models)

– Data availability and reliability: production at the industry-level, SPS/TBT, FDI, export subsidies

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• Colinearity: – affects the estimated parameters

(elasticities and their variances)– not so much a problem if the focus is

on the fitted values and residuals

the model can include many variables

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• Heteroscedasticity:

- Affects the estimated variances- For a log-log model, the elasticities are also affected

The expected value of the log of a random variable is different from the log of its expected value. Jensen inequality:

E(ln ) ln E() Silva and Tenreyro (2005) proposed to use a pseudo-maximum likelihood (PML) technique to estimate gravity models

- Alternative solution: robust estimation techniques (robust option in stat-a)

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• Problem of zero values (Ln(0)) – Concern in particular large data samples

(many counries and sectoral data)– Throwing observations– Ln(Xij + 0.0001)– Tobit with (Xij + 1) as a dependent variable

(inconsistent estimator)– Pseudo-Maximum Likelihood (PML).

Proposed by Silva & Tenreyro (2005)– Heckmann

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• Endogeneity & simultaneity– RTA, cultural factors and borders

(neighbouring countries and countries with the same official language often belong to the same regional block)

– Conflicts & trade. (conflicts have a negative impact on trade. In addition, a nation will avoid to enter into a conflict with a significant trading partner, trade has also a positive impact on conflict)

Use of instrumental variables (2SLS and 3SLS) and use of dynamic models (panel data in first difference, Baier & Bergstrand 2005)

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• Data availability and reliability- Trade data: 2 observations (exp ij, imp j i),

aspects of reliability and transhipments should be taken into account

- Production at the industry-level: only available for a limited number of countries

- SPS/TBT, quotas- FDI (stock)- Export subsidies

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Example of a gravity model: TradeSim, version 3

• Public version available on http://www.intracen.org/menus/countries.htm

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Download the background paper

Download the main results by country

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TradeSim, version 3• Different versions of gravity models. The results from

the base model are available to the public domain • Country sample

- 133 exporters- 154 importers

• Sector-level data (19 sectors ISIC), cross section (average 2002-2003)

• Trade data, average of export and import figures (two third rule)

• Explanatory variables- Distances, borders, common language, Southern-

hemisphere dummy- Market access measure (tariffs) (ITC MacMap)- Conflict measure (HIIK)- FDI stock, not used in the model but provided

when available in the output tables

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where:i : the exporting countryj: the importing country k: sectorXij : trade from country i to country j

Dij: distance between i and j

Borderij: i and j are neighbouring countries (=1) or not (=0)

Tariffij: bilateral market access measure (for trade from i to j)

Languageij: bilateral measure of common language

Conflictij: bilateral measure of conflict

Geoij : bilateral measure of geographical location

: multilateral resistance terms in form of fixed effects. Capture both industrial production and multilateral resistance

ijijijijijijkijjiijk GeoConflictLanguageBorderTariffDX 6543210 lnlnln

ji ,

Estimation by Pseudo Maximum Likelihood (PML)

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Regression results for some sectors

 

   

Variables S1 S2 S3 S4 S5 S6 S7 S8

ln tariff-4.312(0.00)

-16.28(0.00)

-19.91(0.00)

-20.84(0.00)

-2.422(0.38)

-7.357(0.06)

-26.83(0.00)

-12.86(0.00)

ln distance-0.792(0.00)

-0.761(0.00)

-0.929(0.00)

-0.889(0.00)

-1.093(0.00)

-0.845(0.00)

-0.862(0.00)

-0.878(0.00)

ln conflict0.138(0.39

0.384(0.04

-0.361(0.13

-0.806(0.00)

-0.177(0.51)

-0.126(0.44)

-0.183(0.21)

0.098(0.45)

Bilateral measure of common language

0.736(0.00)

0.881(0.00)

0.558(0.00)

1.079(0.00)

0.468(0.00)

0.317(0.01)

0.658(0.00)

0.672(0.00)

Common border dummy variable

0.509(0.00)

0.217(0.02)

0.526(0.00)

0.681(0.00)

0.865(0.00)

0.174(0.04)

0.586(0.00)

0.733(0.00)

Bilateral measure of Southern hemisphere

.. .. .. .. .. .. .. ..

Pseudo R2 0.91 0.93 0.95 0.93 0.84 0.95 0.96 0.94

S1 Food, beverages and tobacco S5 Coke, petroleum products and nuclear fuel

S2 Textiles, clothing and leather S6 Chemicals and chemical products

S3 Wood and wood products S7 Rubber and plastic products

S4Publishing, printing and reproduction of recorded media

S8 Non-metallic mineral products

Note: Pr>|z| in parenthesis; Number of observations for all sectors: 20356

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Current exports and export potential of South Africa to its main markets (USD th unless specified)

Rank Importer Rank SectorCurrent Exports

2002-2003

share in ZAF 's

exports of sector, in

%

Relative Trade PotentialTotal FDI outward

stock 2003

Share in Total FDI Outstock,

in %

Tariff applied by

importer, in %

1 USA TOTAL 3,547,392 11.8% 5. High untapped trade potential 2,249 11.5%

1 USA 1 Metal and metal products 1,250,985 16.5% 4. Untapped trade potential . . 0 to 5%

1 USA 2Motor vehicles and other transport equipment

576,453 17.4% 5. High untapped trade potential . . 0 to 5%

1 USA 3 Chemicals and chemical products 351,172 15.0% 5. High untapped trade potential . . 0 to 5%

1 USA 4 Mining and quarrying 346,719 6.7% 3. Predicted = Current or low values . . 0 to 5%

1 USA 5 Textiles, clothing and leather 228,463 28.7% 5. High untapped trade potential . . 0 to 5%

1 USA 6 Machinery and equipment 210,137 10.2% 5. High untapped trade potential . . 0 to 5%

1 USA 7 Other manufacturing 175,451 15.9% 5. High untapped trade potential . . 0 to 5%

1 USA 8 Food, beverages and tobacco 109,322 5.6% 5. High untapped trade potential . . 0 to 5%

1 USA 9 Coke, petroleum products and nuclear fuel 62,988 8.3% 5. High untapped trade potential . . 0 to 5%

1 USA 10 Agriculture and hunting 59,526 4.0% 5. High untapped trade potential . . 0 to 5%

1 USA 11 Wood and wood products 55,280 4.7% 5. High untapped trade potential . . 0 to 5%

1 USA 12 Rubber and plastic products 37,470 8.7% 5. High untapped trade potential . . 0 to 5%

1 USA 13 Electrical and electronic equipment 34,614 4.0% 5. High untapped trade potential . . 0 to 5%

1 USA 14 Non-metallic mineral products 23,460 8.9% 5. High untapped trade potential . . 0 to 5%

1 USA 15 Precision instruments 10,437 6.0% 4. Untapped trade potential . . 0 to 5%

2 UK TOTAL 3,379,180 11.3% 2. Strong current trade (above predicted) 6,639 33.8%

2 UK 1 Mining and quarrying 1,407,548 27.3% 3. Predicted = Current or low values . . 0 to 5%

2 UK 2 Motor vehicles and other transport equipment 465,426 14.0% 1. Very strong current trade (above predicted)

. . 0 to 5%

2 UK 3 Metal and metal products 298,752 3.9% 4. Untapped trade potential . . 0 to 5%

2 UK 4 Agriculture and hunting 235,030 15.9% 1. Very strong current trade (above predicted)

. . 0 to 5%

Example of an output table

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Trade potentials

- Within-sample predictions based on gravity estimations- Residuals in relative terms (varies between –100% and

+100%)

100ˆ

ˆReRe

ijkijk

ijkijk

XX

XXsiduallative

If 0%, predicted trade is close to current tradeIf > 30% untapped trade potentialIf < -30% strong current trade (above predicted). Bilateral FDI

often explains those type of discrepancies

- Alternative measure: use 95% prediction intervals

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TradeSim should be seen as an interesting input and/or point of departure for asking the right questions and for stimulating in-depth analysis related to:

trade policy issues and strategies (design, negociations) ex post.

trade development programmes (South-South trade, export promotion)

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• Within sample predictions

=> Predictions depend on the sample choice

(multilateral resistance term)• Other possible determinants of trade flows,

such as FDI, SPS/TBT, export subsidies and quantitative restrictions (quotas) are not taken into account

• Specialization patterns of small countries difficult to capture (mono-exporters)

Some caveats

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Annex 1: Regression results by sectorSecondary Sector (Tradesim, version 3)

 

   

Variables S1 S2 S3 S4 S5 S6 S7 S8

ln tariff-4.312(0.00)

-16.28(0.00)

-19.91(0.00)

-20.84(0.00)

-2.422(0.38)

-7.357(0.06)

-26.83(0.00)

-12.86(0.00)

ln distance-0.792(0.00)

-0.761(0.00)

-0.929(0.00)

-0.889(0.00)

-1.093(0.00)

-0.845(0.00)

-0.862(0.00)

-0.878(0.00)

ln conflict0.138(0.39

0.384(0.04

-0.361(0.13

-0.806(0.00)

-0.177(0.51)

-0.126(0.44)

-0.183(0.21)

0.098(0.45)

Bilateral measure of common language

0.736(0.00)

0.881(0.00)

0.558(0.00)

1.079(0.00)

0.468(0.00)

0.317(0.01)

0.658(0.00)

0.672(0.00)

Common border dummy variable

0.509(0.00)

0.217(0.02)

0.526(0.00)

0.681(0.00)

0.865(0.00)

0.174(0.04)

0.586(0.00)

0.733(0.00)

Bilateral measure of Southern hemisphere

.. .. .. .. .. .. .. ..

Pseudo R2 0.91 0.93 0.95 0.93 0.84 0.95 0.96 0.94

S1 Food, beverages and tobacco S5 Coke, petroleum products and nuclear fuel

S2 Textiles, clothing and leather S6 Chemicals and chemical products

S3 Wood and wood products S7 Rubber and plastic products

S4Publishing, printing and reproduction of recorded media

S8 Non-metallic mineral products

Note: Pr>|z| in parenthesis; Number of observations for all sectors: 20356

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Comparing trade potentials including FDI inthe Gravity Equation

100)(

*

jGDP

stockFDI

100)(

*

jGDP

stockFDI

  

Excluding FDI Including FDI

Importing country

Current trade 2002-2003, US$ mio.

TOTAL FDI stock 2003, US$ mio.

Trade Potential, US$ mio.

Relative residual

Trade Potential, US$ mio.

Relative residual

Primary sector

USA 414 2249 0.02 223 29.9 1023 -42.4

United Kingdom

1645 6639 0.37 135 84.8 1124 18.8

Mauritius 33 618 11.83 116 -54.9 342 -82.0

Mozambique 58 764 17.68 562 -81.4 1644 -93.2

Zimbabwe 87 306 1.72 291 -53.9 440 -66.9

Zambia 52 62 1.43 291 -69.6 186 -53.6

Secondary sector

USA 3133 2249 0.02 187 88.7 924 54.5

United Kingdom

1734 6639 0.37 192 79.9 1385 11.2

Mauritius 232 618 11.83 135 26.4 374 -23.4

Mozambique 613 764 17.68 311 32.5 1163 -30.9

Zimbabwe 855 306 1.72 359 40.8 498 26.4

Zambia 511 62 1.43 289 27.7 185 46.7

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Annex 2: deriving the gravity equation (Armington + CES):

111

max

iji

i c

i

jijij ycpts ..

With: ijcConsumption by region j consumers of goods from region i

Consumers in region j maximize:

Subject to their budget constraint:

σ Elasticity of substitution between all goods

iPositive distribution parameter

jy

ijpNominal income of region j residents

Price of region i goods for region j consumers

(1)

(2)

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assuming

ijiij tpp

and

ijijijiijijiij cpcptcpx )1(

and

j

iji xy

Substituting in (1) and (2) and maximizing yields the nominal demand for region i goods by region j consumers:

jj

ijiiij y

P

tpx

1

(3)

With the consumer price index of region j

1

1

1)(i

ijiij tpP(4)

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The sum of i’s exports to all countries must equal i’s GDP

jj j

ijiij

j j

iiji

jiji y

P

tpy

P

ptxy

1

1

1

)()()((5)

Substituting (5) into (3)

jjjij

jij

w

jiij Pt

Pt

y

yyx

1

1

)(

)(with j

wj yy

defining

(6)

1

1

1)(j

jj

iji P

t(7)

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Substituting (7) into (6)

1

ji

ij

w

jiij P

t

y

yyx(8)

And substituting (5) into (4)

1

1

1)(i

ii

ijj

tP(9)

Assuming symmetric trade barriers, i.e. jiij tt , (7) and (9) can be solved, yielding

iiP (10)

1

ji

ij

w

jiij PP

t

y

yyx(11)

Yielding the Gravity Equation