The Gravity Model of Trade

The Gravity Model of Trade During the past 40 years, the volume of international trade has increased markedly across the world. The rise in trade flows has led to an increase in the number of studies investigating the sources of trade. The gravity model has long been the workhorse model used to explain bilateral trade. Based upon Newton s Law of Gravitation, the gravity model predicts that the volume of trade between two economies should increase with their economic size and decrease with distance. 1-1

The Gravity Model of Trade The gravity model initially suffered from a weak theoretical foundation. It has recently become extremely popular in the empirical trade literature. Why? 1. Modern theories of trade based on differentiated products provide an improved theoretical foundation for the gravity equation. 2. The gravity model has proved quite successful in estimating bilateral trade flows. 3. There has been an increased interest in empirically testing the trade effects of regional trading arrangements. 4. There has been a new interest among economists in the subject of geography and trade. 1-2

Preview Who trades with whom? The basic gravity equation Influence of an economy s size on trade Distance Estimation of the gravity equation Empirical model and data Results for the basic gravity variables Augmenting the gravity equation income per capita, common language and colonial links, Geographic factors, trade policy, relative development, relative factor endowments, exchange rate risk, regional trade agreements Economic integration Stages of economic integration Trade diversion and trade creation 1-3

Who Trades with Whom? The 5 largest trading partners with the US are Canada, Mexico, China Japan and Germany. The largest 10 trading partners with the US account for about 70% of the value of U.S. trade. 1-4

Size Matters: The Gravity Model 3 of the top 10 trading partners with the U.S. are also the 3 largest European economies: Germany, UK, and France. These countries have the largest gross domestic product (GDP) in Europe. GDP measures the value of goods and services produced in an economy. Why does the U.S. trade most with these European countries and not other European countries? 1-5

Size Matters: The Gravity Model The size of an economy is directly related to the volume of imports and exports. Larger economies produce more goods and services, so they have more to sell in the export market. Larger economies generate more income from the goods and services sold, so people are able to buy more imports. 1-6

The Size of European Economies, and the Value of Their Trade with the United States 1-7

The Gravity Model In its basic form, the gravity model assumes that only size and distance are important for trade in the following way: T ij = A x Y i x Y j / D ij where T ij is the value of trade between country i and country j A is a constant Y i the GDP of country i Y j is the GDP of country j D ij is the distance between country i and country j 1-8

The Gravity Model In a slightly more general form, the gravity model that is commonly estimated is T ij = A x Y ia x Y jb / D ij c where a, b, and c are allowed to differ from 1. Perhaps surprisingly, the gravity model works fairly well in predicting actual trade flows, as the figure above representing U.S. EU trade flows suggested. 1-9

The Gravity Model: Looking for Anomalies Netherlands, Belgium, and Ireland trade considerably more with the United States than the standard gravity would have predicted Why? 1-10

Impediments to Trade: Distance, Barriers, and Borders Why do the United States North American neighbors trade so much more with the United States than its European partners? 1-11

Impediments to Trade: Distance, Barriers, and Borders Estimates of the effect of distance from the gravity model predict that a 1% increase in the distance between countries is associated with a decrease in the volume of trade of 0.7% to 1.5%. This drop partly reflects increased costs of transporting and services. Economists also believe that less tangible factors play a crucial role: Trade tends to be intense when countries have close personal contact, and this contact tends to diminish when distances are large. 1-12

Impediments to Trade: Distance, Barriers, and Borders Besides distance, borders increase the cost and time needed to trade. Trade agreements between countries are intended to reduce the formalities and tariffs needed to cross borders, and therefore to increase trade. The U.S. signed a free trade agreement with Mexico and Canada in 1994, the North American Free Trade Agreement (NAFTA). Because of NAFTA and because Mexico and Canada are close to the U.S., the amount of trade between the U.S. and its northern and southern neighbors as a fraction of GDP is larger than between the U.S. and European countries. 1-13

Estimation of the Gravity Equation Empirical Model TRADE ij = ( RGDPi RGDP A b2 DIST ij j ) b 1 log( TRADEij ) A + b1 log( RGDPij ) + b2 = log( DIST ) + ε ij ij The regression equation form is logarithmic-linear, meaning that the equation is linear when all variables are expressed as logarithms. The regression coefficients can be interpreted as elasticities, measuring the percentage change of the dependent variable in response to a one percent change of the explanatory variables. 1-14

Variables and Data The dependent variable is the natural log of the sum of exports and imports. Real bilateral trade is measured in international prices. GDP is also measured in real terms. Bilateral distance is measured as the great-circle distance between the two capital cities (or economic centres) of the trading partners. Great circle distance is distance measured between any two latitude-longitude combinations that is, as the crow flies between two cities. The data set consists of annual observations for 186 developing and developed countries in 1995. The data set is from Gosh and Yamarik (2004). 1-15

Results for the Basic Gravity Variables Coefficient Std. Error t-statistic Prob. C -28.41464 0.655097-43.37473 0.0000 LOGRGDP 1.013139 0.012436 81.47117 0.0000 LOGDIST -1.465580 0.039328-37.26548 0.0000 R-squared 0.612923 The core variables of the gravity model explain explain about 60 percent of the variation in bilateral trade flows (R 2 = 0.61). Each variable enters in with its predicted sign and is significant at the 1% level. The coefficients imply an elasticity with respect to real GDP of about 1 and an elasticity with respect to distance of -1.466. 1-16

Why does distance matter so much? Distance can be seen as a proxy for transport costs. Distance indicates the time elapsed during shipment. For perishable goods the probability of surviving intact is a decreasing function of time in transit. Perishability may by interpreted quite broadly to include the following risks: Damage or loss of the good due to whether mishandling (e.g. ship sinks in a storm). Decomposition and spoiling of organic materials (e.g. maggot infestation). Loss of the market (the intended purchaser becomes unwilling or unable to make payment). Synchronization costs. Sourcing inputs from nearby lowers synchronization costs. 1-17

Why does distance matter so much? Communication costs. Distance proxies for the possibilities of personal contact between managers, customers, and so on; (much business depends on the ability to exchange more information of a less formal kind than can be sent over a wire). Transaction costs. Distance may also be correlated with the costs of searching for trading opportunities and the establishment of trust between potential trading partners. Cultural distance. It may also be that greater geographic distances are correlated with larger cultural differences. Cultural differences can impede trade in many ways such as inhibiting communication, generating misunderstandings, clashes in negotiation styles, etc. 1-18

Income Per Capita Countries with higher income levels have better infrastructure and transportation systems which allow them to trade more. High-income countries generally have institutions and resources needed to tax domestic economic activity, and thus do not have to rely on tariffs to finance government spending. High-income countries tend to demand a greater variety of products that are traded internationally. High-income countries typically offer more opportunities for firms to acquire the knowledge and resources necessary to enter export markets. 1-19

Income Per Capita Coefficient Std. Error t-statistic Prob. C -34.31923 0.590396-58.12914 0.0000 LOGRGDP 0.860467 0.011527 74.64950 0.0000 LOGDIST -1.391240 0.034280-40.58509 0.0000 LOGRGDPPC 0.761965 0.019808 38.46826 0.0000 R-squared 0.706920 Potential endogeneity of real GDP and real GDP per capita!!! 1-20

Common Language and Colonial Links One explanation for the trade impeding effects of distance was transaction costs caused by inability to communicate and cultural differences. Common language is seen to directly lower translation costs and, thereby, transaction costs. Colonial ties enhance both trading partners understanding of each other s culture and legal system. We consider three measures of linguistic and historical ties: 1. COMLANG is a dummy variable that is one if both countries share a common language and zero otherwise. 2. COMCOL is a dummy variable that is unity if both countries share a common colonizer 3. COLONIAL is a dummy variable that is unity if one country was a former colony of the other 1-21

Common Language and Colonial Links Coefficient Std. Error t-statistic Prob. C -37.05617 0.616537-60.10374 0.0000 LOGRGDP 0.898593 0.011682 76.92340 0.0000 LOGDIST -1.312385 0.033884-38.73201 0.0000 LOGRGDPPC 0.763136 0.019331 39.47683 0.0000 COMLANG 0.610760 0.077799 7.850475 0.0000 COMCOL 0.867379 0.108351 8.005299 0.0000 COLONIAL 1.705009 0.212757 8.013876 0.0000 R-squared 0.722864 1-22

Trade policy Sachs-Warner openness index Dummy variable that takes a value of one if a country is classified as open and zero otherwise. An economy is open if all five of the following conditions are met: 1. an average tariff rate of less than 40 percent, 2. average non-tariff barriers equivalent to a tariff rate of less than 40 percent; 3. a black market exchange rate premium of less than 20 percent; 4. no communistic government, 5. no state monopoly of major exports. We include the sum of the Sachs-Warner openness index of the two trading partners 1-23

Trade policy Coefficient Std. Error t-statistic Prob. C -39.88678 0.672391-59.32078 0.0000 LOGRGDP 1.085700 0.018087 60.02707 0.0000 LOGDIST -1.181982 0.036576-32.31604 0.0000 LOGRGDPPC 0.582110 0.030126 19.32219 0.0000 COMLANG 0.666684 0.082689 8.062554 0.0000 COMCOL 0.474944 0.129302 3.673133 0.0002 COLONIAL 1.452882 0.224094 6.483349 0.0000 LOGAREAP -0.179617 0.013054-13.75970 0.0000 SACHSS -0.043422 0.056457-0.769109 0.4419 R-squared 0.783089 1-24

Geographic factors The cost of moving goods between two adjacent locations is lower than the cost of moving those goods through a third country. The cost of shipping goods across water is lower than over land. Countries with larger surface areas should have higher transportation costs ceteris paribus than those with smaller surface areas. Several studies include a remoteness variable to capture the effect of an additional geographic factor on bilateral trade. 1-25

Geographic factors We consider a vector of four variables to measure geographic factors 1. BORDER is a dummy variable that is unity if the two countries share a common border. 2. Remoteness, log(remote), is the inverse of the product of the average distance of country i from all other trading partners besides the trading partner, country j. 3. LANDLOCK is 0 if both the importing and the exporting nations border a navigable sea or ocean, 1 if one nation borders water and the other is landlocked and 2 if both are landlocked. 4. Log(AREAP) is the log product of the surface areas of both countries 1-26

Coefficient Std. Error t-statistic Prob. C -38.83472 0.698892-55.56611 0.0000 LOGRGDP 1.065294 0.018318 58.15691 0.0000 LOGDIST -1.177105 0.040603-28.99072 0.0000 LOGRGDPPC 0.562604 0.030310 18.56193 0.0000 COMLANG 0.619335 0.084583 7.322203 0.0000 COMCOL 0.443854 0.129855 3.418067 0.0006 COLONIAL 1.465580 0.226867 6.460092 0.0000 SACHSS -0.025713 0.056715-0.453370 0.6503 BORDER 0.477048 0.200928 2.374222 0.0176 LOGREMOTE 222.6474 72.55618 3.068620 0.0022 LOGAREAP -0.173656 0.013214-13.14169 0.0000 LANDLOCK -0.452101 0.062224-7.265653 0.0000 The way to interpret the coefficient on a dummy variable is to take the exponent: exp(0.48) = 1.62. Two countries that share a common border engage in 62 percent (exp(0.48) 1 = 62) more trade than two otherwise similar countries. 1-27

Relative Development Heckscher-Ohlin theory: The more countries differ the more they will trade with each other. Linder hypothesis: Countries with similar levels of development will have similar preferences. Therefore, the more alike countries are the more trade will occur. To measure relative development, we include the absolute difference in per capita GDP between trading partners, log(gdppcd). The coefficient on log(gdppcd) is positive, suggesting that trade is driven more by the theory of comparative advantage than by the Linder hypothesis. 1-28

Relative Development Coefficient Std. Error t-statistic Prob. C -39.93018 0.696060-57.36599 0.0000 LOGRGDP 1.080658 0.018092 59.73129 0.0000 LOGDIST -1.220663 0.040189-30.37333 0.0000 LOGRGDPPC 0.570369 0.029845 19.11127 0.0000 COMLANG 0.599092 0.083282 7.193498 0.0000 COMCOL 0.532355 0.128109 4.155481 0.0000 COLONIAL 1.225828 0.224516 5.459867 0.0000 SACHSS 0.062713 0.056478 1.110384 0.2669 BORDER 0.641789 0.198424 3.234434 0.0012 LOGREMOTE 321.3475 72.05539 4.459729 0.0000 LANDLOCK -0.539746 0.061834-8.728950 0.0000 LOGAREAP -0.175665 0.013009-13.50358 0.0000 LOGGDPPCD 0.290749 0.028112 10.34235 0.0000 R-squared 0.793704 1-29

Relative Factor Endowments Relative factor endowments are an important source of inter-industry trade. In the Heckscher-Ohlin model, greater difference in factor endowments between the two countries increases specialization and thus raises the volume of trade across industries. The variable log(school) is the absolute log difference of average years of secondary schooling in the 25+ population and measures relative human capital endowments. The variable log(density) is the absolute log difference of the population density and reflects the relative endowment of land between the two countries. The coefficients on log(school) and log(density) are positive and significant, suggesting differences in factor endowments increase the volume of trade. 1-30

Relative Factor Endowments Variable Coefficient Std. Error t-statistic Prob. C -40.69447 0.750760-54.20438 0.0000 LOGRGDP 1.085824 0.019466 55.78069 0.0000 LOGDIST -1.241731 0.042116-29.48361 0.0000 LOGRGDPPC 0.560674 0.033713 16.63076 0.0000 COMLANG 0.633749 0.086686 7.310885 0.0000 COMCOL 0.419082 0.144457 2.901087 0.0037 COLONIAL 1.180014 0.249459 4.730283 0.0000 SACHSS 0.130089 0.061725 2.107545 0.0352 BORDER 0.636015 0.195899 3.246642 0.0012 LOGREMOTE 332.2596 76.84818 4.323585 0.0000 LANDLOCK -0.533399 0.066407-8.032224 0.0000 LOGAREAP -0.157671 0.013985-11.27471 0.0000 LOGGDPPCD 0.218707 0.042316 5.168483 0.0000 LOGSCHOOL 0.127000 0.052639 2.412679 0.0159 LOGDENSITY 0.148759 0.022821 6.518378 0.0000 R-squared 0.810676 1-31

Exchange Rate Risk Variable Coefficient Std. Error t-statistic Prob. C -40.57620 0.766088-52.96548 0.0000 LOGRGDP 1.083854 0.019579 55.35842 0.0000 LOGDIST -1.240927 0.042714-29.05212 0.0000 LOGRGDPPC 0.551333 0.034228 16.10746 0.0000 COMLANG 0.625130 0.087416 7.151248 0.0000 COMCOL 0.396081 0.145650 2.719393 0.0066 COLONIAL 1.155522 0.253909 4.550925 0.0000 SACHSS 0.146564 0.062671 2.338633 0.0194 BORDER 0.656411 0.196714 3.336873 0.0009 LOGREMOTE 342.4716 77.25834 4.432811 0.0000 LANDLOCK -0.552351 0.067034-8.239909 0.0000 LOGAREAP -0.151707 0.014298-10.61044 0.0000 LOGGDPPCD 0.222486 0.042914 5.184522 0.0000 LOGSCHOOL 0.121711 0.053015 2.295782 0.0218 LOGDENSITY 0.154184 0.023076 6.681469 0.0000 VOLATD -0.134009 0.064753-2.069545 0.0386 1-32

Regional Trade Agreements Stages of Economic Integration Preferential Trade Agreement (PTA) Countries offer tariff reductions (though perhaps not eliminations) to a set of partner countries in some product categories. Free Trade Area (FTA) A free trade area occurs when a group of countries agree to eliminate tariffs between themselves, but maintain their own external tariff on imports from the rest of the world. Customs Union A customs union occurs when a group of countries agree to eliminate tariffs between themselves and set a common external tariff on imports from the rest of the world. 1-33

Common Market While the FTA and the customs union concerns flow of goods only, common market also covers flow of production factors, such as capital and labor. Economic Union Under the economic union, member countries coordinate fiscal and monetary policy, too. Monetary Union Monetary union establishes a common currency among a group of countries. This involves the formation of a central monetary authority which will determine monetary policy for the entire group. Complete Economic Union This is the final stage of economic integration, where super-national institutions enforce economic policies on member countries. 1-34

Regional Trade Agreements Trade Diversion and Trade Creation Trade diversion and trade creation can occur regardless of whether a preferential trade agreement, a free trade area or a customs union is formed. Three countries: A, B and C. The attention in this analysis will be on country A. Country A is a small country in international markets (which means that it takes international prices as given). Countries B and C are assumed to be large countries. Thus, country A can export or import as much of a product as desired with countries B and C at whatever price prevails in those markets. 1-35

Regional Trade Agreements Trade Diversion and Trade Creation Trade diversion means that a free trade area diverts trade, away from a more efficient supplier outside the FTA, towards a less efficient supplier within the FTA. Original imports from world markets are replaced by imports from a more expensive member country. Trade creation means that a free trade area creates trade that would not have existed otherwise. It means the replacement of higher cost domestic products by lower cost imports from member countries As a result, supply occurs from a more efficient producer of the product. 1-36

Trade Diversion P Country A S is supply and D is demand for country A. S P B T P C T a b c d P B e S 2 S 1 D 1 D 2 Q P C D Country A eliminates the tariff on imports from country B; countries A and B form a free trade area (FTA). S 2 D 2 Imports from B Since the non-distorted (free trade) price in country C is less than the price in country B, trade is said to be diverted from a more efficient supplier to a less efficient supplier. P B and P C represent the free trade supply prices of the good from country s B and C, respectively. (Country C is assumed capable of supplying the product at a lower price than country B.) A has a specific tariff t B = t C = t* set on imports from both countries B and C (the green dotted lines). The tariff raises the domestic supply prices to P BT and P CT, respectively. S 1 D 1 Imports from C 1-37

Trade Diversion P Country A S T P B T P C a b c d P B e P C D S 2 S 1 D 1 D 2 Q Country A Consumer surplus + (a + b + c + d) Producer surplus Government revenue (Tariff revenue) National welfare (net effect) - a - (c + e) + (b + d) - e 1-38

Trade Creation P Country A S T P B T P C P B a b c d P C D Country A eliminates the tariff on imports from country C; countries A and C form a free trade area (FTA). S 2 D 2 Imports from C Since trade now occurs with the FTA, and it did not occur before, trade is said to be created. S 2 S 1 D 1 D 2 Q S is supply and D is demand for country A. P B and P C represent the free trade supply prices of the good from country s B and C, respectively. (Country C is assumed capable of supplying the product at a lower price than country B.) A has a specific tariff t B = t C = t* set on imports from both countries B and C (the green dotted lines). The tariff raises the domestic supply prices to P BT and P CT, respectively. S 1 D 1 Imports from C 1-39

Trade Creation P Country A S T P B T P C P B a b c d P C D S 2 S 1 D 1 D 2 Q Country A Consumer surplus + (a + b + c + d) Producer surplus Government revenue (Tariff revenue) National welfare (net effect) - a - c + (b + d) - c 1-40

Regional Trade Agreements The international trade literature estimates the amount of trade creation by augmenting the gravity model equation with a set of dummy variables, RTAij, as follows: log( TRADE ij ) = A + b1 log( RGDPij ) + b2 log( DISTij ) + b3 X ij + b4 RTA ij + ε ij where Xij is a vector of control variables, and RTAij is a vector of variables which measures whether both countries i and j belong to the same regional trading arrangement. RTAij, takes a value of unity when both countries are current members of the bloc. A positive value for b 4 indicates that the two countries trade more with one another than predicted by the core factors and other variables, and is thus taken as evidence of trade creation. 1-41

Regional Trade Agreements The amount of trade diversion is estimated by augmenting the gravity model with a set of dummy variables, RTAi: log( TRADE ij ) = A + b1 log( RGDPij ) + b2 log( DISTij ) + b3 X ij + b4rtaij + + b5 RTA i + ε ij RTAi measures current membership of either country i or j in a regional trade agreement. RTAi takes a value of unity if only one of the two countries is a current member of the bloc. A positive value for b 5 implies that trade between a country within the bloc and countries outside the bloc is more than a random pair of countries, and is interpreted as openness of that region to imports from outside the region. A negative value for b 5 indicates less trade with nonmembers and is thus interpreted as evidence of trade diversion 1-42

Regional Trade Agreements Variable Coefficient Std. Error t-statistic Prob. C -17.59646 0.704536-24.97595 0.0000 LOGRGDP 0.802770 0.013217 60.73667 0.0000 LOGDIST -1.690857 0.041595-40.65024 0.0000 EUIJ 2.244804 0.213063 10.53584 0.0000 EFTAIJ 2.787553 1.036541 2.689285 0.0072 MERCIJ 2.565568 0.735360 3.488860 0.0005 NAFTAIJ -0.375693 1.050136-0.357756 0.7205 CACMIJ 1.138446 0.577261 1.972152 0.0487 APECIJ 3.673448 0.185299 19.82447 0.0000 EUI 1.958008 0.066698 29.35651 0.0000 EFTAI 1.099785 0.108311 10.15399 0.0000 MERCI 0.750149 0.102599 7.311473 0.0000 NAFTAI -0.468624 0.109317-4.286827 0.0000 CACMI -0.054289 0.107270-0.506095 0.6128 APECI 1.944969 0.075551 25.74364 0.0000 RTAij is positive and statistically significant for EU, EFTA, Mercosur (MERC), CACM, and APEC. RTAi is negative and statistically significant for the North American block. 1-43