United States 

Department of 

Agriculture

Economic

Research

Service

Thomas L. Vollrath and Charles B. Hallahan

Reciprocal Trade Agreements

Impacts on Bilateral Trade Expansion 

and Contraction in the World 

Agricultural Marketplace Economic

Research 

Report

Number 113

April 2011
www.ers.usda.gov

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Recommended citation format for this publication:

Vollrath, Thomas L., and Charles B. Hallahan. Reciprocal Trade Agreements: 

Impacts on Bilateral Trade Expansion and Contraction in the World Agricultural 

Marketplace. ERR-113. U.S. Dept. of Agriculture, Econ. Res. Serv. April 2011.

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A Report from the Economic Research Service

Abstract

The rapid increase in the number of bilateral and regional free-trade agreements 

since 1995 is a striking development. The proliferation of these agreements has raised 

questions about whether they have, in fact, opened markets, created trade, promoted 

economic growth, and/or distorted trade. This study uses panel data from 1975 to 

2005 and a gravity framework model to identify the infl uence of reciprocal trade 

agreements (RTAs) on bilateral trade in the world agricultural marketplace. A benchmark, Heckman sample-selection and two generalized models, one of which accounts 

for RTA phase-in effects, are used to gauge the impact on partner trade of mutual as 

well as asymmetric RTA membership. Empirical results show that RTAs increase 

agricultural trade between member countries but decrease trade between member and 

nonmember countries. Interestingly, RTAs were found to be particularly effective at 

expanding agricultural trade and opening markets in developing countries when developing-country trading partners are part of the same agreement.

Keywords: trade policy, reciprocal trade agreements, bilateral, regional, missing 

trade, gravity models.

Acknowledgments

The authors thank Mary Anne Normile, Ralph Seeley, and Danny Pick of USDA’s 

Economic Research Service; Jason Grant of Virginia Polytechnic and State 

University; Jeffrey Reimer of Oregon State University; and anonymous reviewers for 

their insights, critiques, and comments and absolve them from any errors or omissions. 

Thanks also to John Weber and Curtia Taylor for editorial and design assistance.

Thomas L. Vollrath, thomasv@ers.usda.gov

Charles B. Hallahan, hallahan@ers.usda.gov

Reciprocal Trade Agreements

Impacts on Bilateral Trade Expansion 

and Contraction in the World 

Agricultural Marketplace 

Economic

Research

Report

Number 113

April 2011
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Contents

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Econometric Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Empirical Findings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Model Tradeoffs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Summary of Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Appendix: Economic Trade Theory and Advances 

in Applied Analyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Also see the recently released ERS report Selected Trade Agreements and 

Implications for U.S. Agriculture, by John Wainio, Mark Gehlhar, and John Dyck 

(www.ers.usda.gov/publications/err115). This study (ERR-115) uses the computable general equilibrium framework to examine how free trade agreements between 

ASEAN (Southeast Asia) countries and China and Australia/New Zealand, as 

well as pending agreements between the United States and Korea, Colombia, and 

Panama, are likely to affect U.S. agricultural trade. Empirical results fi nd that trade 

created under these agreements exceeds trade diverted, but that results depend on 

the specifi c circumstances of each agreement. The RTA study (ERR-113) uses panel 

data and econometric models to examine the impact on partner trade in agriculture 

of all types of bilateral and regional trade agreements in which members agree to 

open their markets to each other’s exports by lowering trade barriers.
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Summary

What Is the Issue?

Countries use bilateral/regional trade agreements to increase market access 

and expand trade in foreign markets. These agreements are called reciprocal trade agreements (RTAs) because members grant special advantages 

to each other. RTAs include many types of agreements, such as preferential 

arrangements, free trade agreements, customs unions, and common markets, 

in which members agree to open their markets to each other’s exports by 

lowering trade barriers. They have become an increasingly prominent feature 

of the multilateral trading system in recent years, in part, because of stalled 

global negotiations taking place under the auspices of the World Trade 

Organization (WTO). 

Many observers believe that RTAs deepen market integration and complement efforts by the WTO to liberalize international markets. While acknowledging that RTAs can open up markets, other observers contend that these 

agreements also distort trade and discriminate against nonmember countries. 

Many studies have examined the degree to which RTAs increase trade 

between member countries. Relatively few, however, have attempted to quantify the extent to which RTAs curtail trade between member and nonmember 

countries. In this study, ERS empirically examines the bilateral trade expansion/contraction effects of RTAs in the world agricultural marketplace. 

What Did the Study Find?

• Model results estimate that RTA membership boosts agricultural trade 

between member countries, on average, between 34 and 93 percent in the 

long run. 

• The expansion of trade between RTA members typically comes at the 

expense of trade with nonmember countries. Empirical results show that 

agricultural trade falls, on average, between 26 and 46 percent in the long 

run between two countries when one of them does not belong to an RTA 

to which the other is a member.

• The trade impacts of RTAs grow as producers and consumers adjust to 

policy-induced changes in market structure and as the implementing 

provisions of these agreements are phased in over time. Models that 

account for the cumulative, phase-in effects of RTAs show that, on 

average, agricultural trade increases 105 percent between two trading 

partners that belong to the same agreement in the long run but falls 49 

percent between an RTA member country and a nonmember trading 

partner. 

• RTAs boost trade in agricultural markets. The percentage increase in 

partner trade expansion induced by mutual RTA membership exceeds 

the percentage decline in partner trade characterizing asymmetric RTA 

membership. 
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• RTAs are particularly effective at expanding agricultural trade and 

opening markets in developing countries when both developing-country 

trading partners are members of the same agreement. 

How Was the Study Conducted?

ERS developed econometric models to isolate the impacts of RTAs on bilateral trade in agriculture. Researchers adopted various approaches to control 

for the infl uence of the many factors affecting bilateral trade, such as the 

capacity of suppliers to export, the size of demand in importing countries, 

transaction costs, and characteristics that induce two countries to trade 

with each other (e.g., differences in resource endowments). The trade data 

deployed in model estimations included bilateral trade fl ows reported by UN 

Comtrade between 69 countries covering the 1975 to 2005 time frame.

The empirical models identifi ed statistical regularities, controlled for the 

unique institutional and physical characteristics of each country pair, and 

allowed for dynamic pricing and RTA phase-in effects. They yielded quantitative estimates of the impacts on partner trade of mutual and asymmetric 

RTA membership.
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Introduction

Trade agreements, whether multilateral, regional, or bilateral in scope, are 

policy instruments that can increase market effi ciency, expand trade, and 

enhance economic welfare of participant countries. Economists hold a particularly favorable view of the World Trade Organization (WTO), the global 

organization dealing with the rules of trade between nations, and its predecessor, the General Agreement on Tariffs and Trade (GATT). The GATT/

WTO provides an international forum to supervise and liberalize trade 

worldwide and to ensure that trade fl ows as freely as possible. The guiding 

principle is open and free trade enunciated in the WTO’s most-favored-nation 

(MFN) clause. The granting of MFN status means that a country should not 

discriminate among trading partners. 

Acceptable rules and regulations of bilateral/regional trade agreements 

(RTAs) are identifi ed in Article XXIV of the GATT/WTO. This Article 

establishes conditions governing cross-border barriers both within bilateral/

regional trade agreements and between bilateral/regional-trade-agreement 

members and nonmembers. One condition eliminates or removes trade 

barriers on “substantially all the trade” within bilateral/regional trade agreements. Another prohibits member countries from raising trade barriers 

against non-member countries above their pre-agreement levels.

Since the Annecy Round in 1949, the GATT/WTO has progressively reduced 

trade barriers in the world marketplace. Agriculture, however, was largely 

exempt from the trade-liberalizing rules that applied to most products under 

the GATT; that is, until the Uruguay Round Agricultural Agreement (URAA) 

in 1994. Still, many countries continue to use a variety of instruments to 

protect domestic agriculture and to curtail imports of agricultural goods in 

the post-URAA era. Examples include special safeguards, special and differential treatment for developing countries, relatively high tariffs, and comparatively modest access within tariff-rate quotas.

The Doha Round of the WTO was launched in 2001 with the aim of further 

opening up agricultural markets and increasing exporter access to both developed and developing country markets. However, no tangible breakthrough 

has been achieved after 9 years of negotiations. Stalled multilateral talks have 

provided opportunities for some countries to reduce trade barriers via reciprocal trade agreements (RTAs). These agreements arise when members agree 

to open their markets to each other’s exports by lowering trade barriers. They 

can take various forms, such as preferential arrangements, free trade agreements, customs unions, and common markets.

RTAs have become an increasingly prominent feature of the multilateral 

trading system in recent years. According to the WTO, there were 186 such 

agreements in force in 2005, up from 50 just prior to the Uruguay Round in 

1994, less than 25 in 1985, and just 13 agreements in 1975 (fi g. 1).1 As the 

number of agreements expanded, the RTA share of world trade rose from 22 

percent in 1975 to over 50 percent in 2005.

Some economists believe that RTAs can be powerful forces promoting 

market liberalization that not only complement, but go beyond, multilateral 

1According to the WTO’s Committee 

on Regional Trade Agreements 

(CRTA), as of July 31, 2010, there are 

a total of 474 bilateral/regional trade 

agreements in force (World Trade 

Organization, 2010).
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trade efforts in the WTO to open international markets (Bergsten, 1998). 

While the WTO has progressively lowered tariffs worldwide, it has made 

little progress addressing other trade barriers, such as food safety concerns, 

domestic regulations, and incompatible technical standards. Harmonization 

of nontariff barriers is a source of trade and welfare gains of RTAs. For 

example, negotiations leading to the establishment of the North American 

Free Trade Agreement (NAFTA) addressed many contentious issues inhibiting trade. One result of these discussions was the removal import-licensing 

requirements for grapes in Mexico. The lifting of these requirements 

increased U.S. grape exports (Zahniser et al., 2004). 

Other economists are less convinced about the positive effects of bilateral/

regional trade agreements. They acknowledge that the formation and growth 

of RTAs can foster trade liberalization, deepen economic integration, and 

generate economic opportunities, but they also express concerns that these 

agreements can distort trade, increase discrimination against nonmember 

countries, and lower overall economic welfare (Bhagwati and Panagariya, 

1996; Fiorentino et al., 2006). 

Trade theory does not provide a defi nitive answer as to whether RTAs 

enhance economic welfare. Increases in partner trade of RTA members may 

be benefi cial whenever production shifts toward the most effi cient producers 

of specifi c goods within the trading bloc. Consumers are better off in countries belonging to a bilateral/regional trade agreement when they substitute 

lower priced imported goods from RTA partners for higher priced domestic 

goods. But while RTAs often increase trade among partner countries, 

they may also discriminate and favor relatively high-cost member-country 

suppliers at the expense of more effi cient nonmember suppliers.

The impacts of RTAs on the direction and fl ow of agricultural trade in the 

world marketplace depend not just upon trade expansion within member 

blocs but also on trade contraction between RTA and non-RTA members, 

a byproduct of these agreements. In this study, we empirically examine the 

Figure 1

Growth in bilateral/regional trade agreements (RTAs) and their prominence in global markets

RTA share of world trade Numbers of RTAs in force

Source: USDA, Economic Research Service using Wainio (2006) and Grant and Lambert (2008b)

0

50

100

150

200

0

10

20

30

40

50

60

1975 1980 1985 1990 1995 2000 2005

Share of trade occurring under RTAs RTA agreements in force
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effects on bilateral trade of RTAs in agriculture using Viner/Meade’s notions 

of trade creation and trade diversion.

According to Viner (1950), trade creation arises when RTAs induce shifts 

from domestic to partner country sources of supply. He posits that trade 

expansion occurs because low-cost products from producers in member countries displace high-cost domestic products. Trade diversion occurs, according 

to Viner, when RTAs trigger a shift in the source of production from 

nonmember suppliers to member countries. This happens when bloc partners 

reorient their imports away from low-cost, nonmember countries toward 

higher cost, member countries. Meade (1956) elaborated on Viner’s production-oriented explanation to include RTA’s effects on consumption. Meade 

points out that even if production in two countries belonging to the same RTA 

does not change, both countries may gain because lower prices enable their 

citizens to consume more of the goods for which they express a preference.

Applied research is needed to clarify the economic tradeoffs of bilateral/

regional trade agreements. To date, most econometric studies have focused on 

quantifying the extent to which mutual RTA membership has expanded trade. 

Relatively few studies have examined how asymmetric RTA membership may 

also have lowered trade. 

In this study, the primary objective of ERS is to empirically examine the 

impacts of RTAs on bilateral trade in agriculture where restrictive domestic 

and border policies continue to pose signifi cant impediments to free and open 

trade. We use the gravity framework and panel data to quantify the degree 

to which these agreements have affected partner trade, both positively and 

negatively. 
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Econometric Models

Clearly, many economic forces besides the establishment of bilateral/regional 

free-trade agreements shape the direction and volume of trade in the global 

market. When attempting to empirically isolate the ex-post impact of RTAs, it 

is, therefore, important to control for the many other determinants affecting 

partner trade. The gravity framework, which can account for myriad infl uences, is well suited to identify how these agreements shape cross-border 

trade.2 See the appendix for a summary of advances in applied analyses and 

theoretical linkages underlying the gravity framework.

The gravity framework has been widely used in applied research to assess the 

RTA impacts on trade between member countries. For example, the following 

studies have deployed the commonly used RTA dummy variable—defi ned 

as equaling one when both the exporter and importer are members of the 

same agreement, and zero otherwise: Aitken, 1973; Sapir, 2001; Rose and 

van Wincoop, 2001; Cheng and Wall, 2005; Vollrath et al., 2006; Sandberg 

et al., 2006; Eicher and Henn, 2009; Subramanian and Wei, 2007; Baier and 

Bergstrand, 2007; Baier et al., 2008; Grant and Lambert, 2008a. 

Soloaga and Winters (2001) developed a model designed to control for relative openness of RTA member countries with the objective of removing the 

potential bias in intrabloc coeffi cients. The gravity equations used in their 

study (as well as in studies by Clarete et al., 2003, and Lambert and McKoy, 

2009) include dummy variables to denote mutual RTA membership as well 

as two dummy variables to control for systematic openness of RTA members, 

one for the exporter and one for the importer. The exporter openness dummy 

equals one should the exporter be a member of a designated RTA regardless of the status of the importing country. The importer openness dummy 

is defi ned similarly. It equals one should the importing country belong to an 

RTA, regardless of the status of the exporting country. 

In addition to estimating the intrabloc effects on unidirectional trade fl ows, 

applied research has been used to determine whether trade agreements 

increase two-way trade, advance trade liberalization, and/or lead to market 

distortions. Eichengreen and Irwin (1995); Bayoumi and Eichengreen (1997); 

Wei and Frankel (1997); and Ghosh and Yamarik (2004) sought to determine 

whether individual RTAs were open or closed trading blocs in models where 

the dependent variable was the “sum of exports and imports.” Rose (2004) 

and Tomz et al. (2007) addressed whether trade agreements increase the 

“average value of bilateral trade,” using dummy variables to denote mutual 

membership in these agreements. Vicard (2009) examined whether different 

types of RTAs (i.e., preferential arrangements, free trade agreements, custom 

unions, and common markets) affect “total bilateral trade” differentially. 

Several studies have developed models designed explicitly to estimate both 

trade creation and trade diversion. Endoh (1999) developed a model that 

focused on the European Economic Community, the Latin American Free 

Trade Association, and the Council of Mutual Economic Assistance. Tang 

(2005) directed attention to NAFTA, the Closer Economic Relations trade 

agreement between Australia and New Zealand, and the Association of 

Southeast Asian Nations (ASEAN) trade agreement. Koo et al. (2006) 

2One reviewer expressed skepticism that any useful information could 

be generated from highly aggregate 

gravity models. Our view is that 

applied research is needed across 

numerous levels of aggregation if 

economists are to provide information 

about economic relationships that can 

be helpful to policymakers and can help 

educate the public. It is important to 

be able to generalize about the effect 

of policy instruments, such as bilateral/regional trade agreements, on the 

patterns of world trade and economic 

welfare. It is also important to gain 

insight about the impact of such policy 

instruments on individual sectors, 

commodities, periods, and specifi c 

agreements. Additional research is 

needed that focuses attention on the 

impacts of specifi c agreements on trade 

in agriculture, both at the sector level 

and across individual commodities and 

also on the impacts of RTAs on exports 

(imports) of individual countries.
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focused attention on the European Union, NAFTA, the ASEAN, and the 

Andean Community. Magee (2008) and Vollrath et al. (2009) developed 

generic indexes to quantify overall trade creation and trade diversion. All of 

the gravity model studies enumerated here, with the exception of Tang and 

Magee, were estimated using cross-sectional data.3

The use of panel, rather than cross-sectional data, is generally preferred, 

especially in a gravity model incorporating RTA dummy variables. In crosssectional estimates, the RTA dummies account for everything specifi c to the 

bilateral pairs not captured by the invariant fi xed effects (e.g., distance) specifi ed in the model. As a result, the RTA dummies in such models do not really 

isolate the trade-creation and trade-diversion effects. Panel-based models also 

offer a better opportunity to account for changes (e.g., changes in income) 

taking place within and between countries over time. Moreover, they generate 

more effi cient parameter estimates. Importantly, they enable the researcher 

to enrich model specifi cation with fi xed effects that mitigate omitted-variable 

and heterogeneity bias, which more effectively isolates the impacts of RTAs. 

In this study, ERS uses panel data and information about mutual and asymmetric RTA membership to estimate gravity models that contain generic RTA 

indices designed to approximate Viner/Meade’s trade creation and trade 

diversion effects in the global marketplace.4 The binary mutual-agreement 

index (MA) takes a value of one whenever two countries jointly belong to the 

same RTA, otherwise MA equals zero. The asymmetric-agreement index 

(AA) takes a value of one whenever the exporter is not a member of an RTA 

to which the importer belongs and zero otherwise. A positive and statistically 

signifi cant MA coeffi cient indicates that bilateral trade between two countries 

belonging to the same RTA increases as a result of the removal of tariffs and 

nontariff restrictions. A negative and signifi cant AA coeffi cient indicates that 

imports by an RTA member from a nonmember falls as a result of asymmetric membership. 

MA and AA capture, respectively, bilateral trade expansion and trade contraction in the global marketplace due to RTAs. They do not measure the welfare 

effects of these agreements, for such effects depend not only on the amount 

of trade created and diverted but also on relative effi ciencies or differences 

in unit costs. As noted in Palgrave (1987), trade creation increases economic 

welfare when higher cost domestic sources of supply are replaced by lower 

cost imports from partner countries that had been constrained by tariffs 

and nontariff barriers. Trade diversion has a welfare cost when trade-policy 

discrimination against nonmember countries leads to the replacement of 

lower cost sources of supply in these countries by higher cost partner country 

sources.

We estimate two conventional and two generalized gravity models using 

fi xed effects.5 The conventional models are based upon commonly used 

benchmark equations as well as Heckman’s sample-selection framework. 

The generalized models are structured to conform to Anderson and van 

Wincoop’s (2003; 2004) analytical framework. The fi rst generalized model 

is a dummy-intensive fi xed-effects model that incorporates exporter-by-time, 

importer-by-time, and export-import pair dummies. The second includes 

the same set of fi xed effects as the fi rst, but adds RTA phase-in variables 

to complement the contemporaneous RTA variable. To address the issue of 

3The trade-diversion variables used 

in the Tang and Magee studies equal 

one when either country i or j belongs 

to an RTA. These dummies depart 

from Viner’s concept of trade diversion in that Viner restricted attention 

to imports by an RTA member country 

from a nonmember supplier.

4Other studies that have used generic 

RTA indexes in a panel setting include 

Rose (2006), Tomz et al. (2007), 

Subramanian and Wei (2007), Baier 

and Bergstrand (2007), and Grant and 

Lambert (2008a). But these indexes 

have been restricted to portray trade 

creation, not trade diversion.

 5A reviewer asked why we never 

tried random-effects estimation. We did 

not use this approach, as others have 

rejected it for theoretical and empirical 

reasons. Baier et al. (2008) reject using 

the random-effects model in gravity 

analyses on conceptual grounds. They 

point out that unobserved time-invariant 

variables infl uence both the presence of 

RTAs as well as the volume of trade. In 

the fi xed-effects model, these unobservable variables are controlled by using 

country-pair fi xed effects. The problem 

with the random-effects model is that 

it assumes zero correlation between 

these bilateral fi xed effects and RTAs. 

Moreover, Egger (2000) tested for fi xed 

versus random effects after estimating 

gravity equations with panel data. 

Using the Hausman test, he found 

overwhelming empirical evidence for 

the rejection of random-effects gravity 

model relative to a fi xed-effects model.
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heterogeneity of partner trade, we ran the generalized model not only on the 

global sample of bilateral trade fl ows between 69 countries but also on eight 

subsamples, consisting of various combinations of developed and developing 

countries exporting and importing from each other.

The benchmark model

The basic gravity framework using panel data relates exports by country i to 

country j in year t to the market size of both countries in year t and economic 

distance or trade costs separating the two countries. In our conventional 

gravity models, we follow the literature and use Gross Domestic Product 

(GDP) to quantify market size. The time-varying GDP of the exporting 

country, (Yit), represents the potential supply of goods from that country. The 

GDP of the importing country, (Yjt), refl ects the potential demand of the 

goods being traded.6 Since data on trade costs are not readily available, our 

basic model includes observable variables to refl ect different aspects of bilateral trade costs, namely transportation costs, cultural proximity, and partner 

trade policies.

Our benchmark gravity equation takes the following form:

 ln( ) ln( ) ln( ) ln( ) ln( ) ( ) ijt t it jt ijt ij ij 01 2 1 2 3 12 1 2 ) () ( ) ( ) ( ) (3 ) CBi l( ) l( ) l( ) l( ) βββ l( ) l( ) 01 2 1 2 1 21 2 ln( ) ln( ) ln( ) ln( ) ) l( ) l( ) l( ln( ) ln( ) 01 2 1 2 1 21 2 ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ) ln( ) ln( ) ln( 01 2 1 2 1 2 1 2 1 21 2

45 6 7 ( ) ( ) ( ) ( ) (1) +++ ++ ββ β βε LL LS CH TP ij ij ij ijt ijt

factor endowments are captured by (FEijt), a measure of exporter-to-importer 

arable-land/total-labor ratios in year t. The indicators for transportation costs 

include physical distance (DTij) and two dummy variables to refl ect 

geographical adjacency, (CBij) which equals 1 when i and j share a contiguous border and 0 otherwise and landlockedness (LLij), which equals 1 when 

either i or j are landlocked and 0 otherwise. The measures for cultural proximity include language similarity (LSij) a dummy variable which equals 1 

whenever 9 percent or more of the population in both countries share a 

common language and 0 otherwise;7 and colonial heritage (CHij), a dummy 

variable which equals 1 if two countries have established colonial ties since 

1945 and 0 otherwise.8 Time dummies (γt

) account for factors common to all 

countries, including worldwide infl ation, increases in trade attributable to 

globalization, and general shocks affecting the world economy.9 We include 

two dummy variables to represent domestic trade policies (TPijt) in each 

model type: (1) a dummy variable denoting mutual membership in RTAs 

(MAijt), which equals 1 in year t when two trading partners are both 

members of the same bilateral/regional trade agreement and 0 otherwise; 

and/or (2) a dummy variable denoting asymmetric membership in these 

agreements (AAijt), which equals 1 in year t when i is not a member of an 

RTA to which j belongs and 0 otherwise.10

Most gravity models are specifi ed in log-linear terms because of ease of 

calculation and interpretation. This specifi cation is not, however, without its 

problems. Taking logarithms often removes observations from the sample 

because the log of zero is undefi ned. Omitting zero-fl ow or missing observations implies that information is lost on the causes of no or very low trade. 

Moreover, the practice of dropping observations may produce downwardly 

biased and inconsistent parameter estimates. Consequently, the dependent 

6A reviewer expressed concern 

that the GDP variables in our model 

may induce endogeneity. Baier and 

Bergstrand (2007) addressed this issue, 

as well as other possible sources of 

endogeneity, in gravity equations. 

They contend that while GDP is a function of total exports and total imports, 

the inclusion of country i’s income 

and country j’s income as independent 

variables in gravity equations is not a 

likely cause of endogeneity because 

each importer has many suppliers and 

each exporter sends its goods to many 

destination markets. 

7The 9-percent threshold serves to 

denote the level at which the ability to 

communicate is viewed as not imposing 

substantial transaction costs. 

8Rose identifi es four types of dummy 

variables that can be used to control for 

colonial heritage in gravity models: (1) 

a binary variable which is unity if i and 

j were ever colonies after 1945 with the 

same colonizer, (2) a binary variable 

which is unity if i is a colony of j at 

time t or vice versa, (3) a binary variable which is unity if i ever colonized j

or vice versa, and (4) a binary variable 

is unity if i and j remained part of the 

same nation during the sample. We 

arbitrarily chose the fi rst type of binary 

variable to depict colonial heritage in 

our models.

9The γt

 = 1 when year is equal to 

t and 0 otherwise, where t = 1975, 

1980,......2005.

10The two RTA dummies were 

constructed using “full-year” enforcement, with full year referring to at least 

8 months of agreement implementation. 
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variable in gravity models estimated using samples where no trade is 

recorded for some export-to-import partners is no longer bilateral trade; 

rather, it is bilateral trade contingent on the existence of trading relationships. 

The Heckman model

Heckman’s (1979) sample-selection model offers a theoretically sound and 

econometrically elegant way to include zero fl ows in models of bilateral trade 

(Linders and de Groot, 2006).11 The sample selection gravity model allows 

for the correlation between (1) the joint decision of whether i chooses to 

export to j and j chooses to import from i and (2) the amount, if any, of unidirectional trade between i and j. In other words, this model accounts for the 

relationship between expected profi tability and conditional expected trade. A 

“selection equation” is used to incorporate the binary decision of whether or 

not to trade based on expected profi tability. Then, an “outcome equation” 

determines the volume of bilateral trade. 

To circumvent problems associated with zero trade fl ows, we estimate 

conventional gravity equations using Heckman’s sample-selection framework. 

We chose the maximum likelihood estimator (MLE), as research has shown 

that MLE is preferred over the Heckman two-step estimator to jointly estimate the selection and outcome equations (Martin and Pham, 2008). 

Formally, the Heckman model distinguishes between the selection and 

outcome processes:

 s*

ij = zijδ + vij (selection mechanism)

 yij = xijβ+ μij (outcome mechanism)

where zij and xij are the vectors of variables affecting the selection and 

outcome mechanisms, respectively; s* is the underlying latent variable representing the decision whether to trade (s is observed to be 1 if trade occurs and 

0 otherwise); y is the log of trade when trade occurs (s = 1); and the μ and 

errors are assumed to be jointly normally distributed with correlation ρ. 

The expected value of y, given that it is observed, is

 E[ y | s = 1 ] = xβ + ρλ(zδ)

where λ(zδ) is the Inverse Mills Ratio (IMR).12

The fi rst set of covariates in the sample-selection model determine the probability of whether the two countries engage in trade. The second set of covariates determines the intensity of bilateral trade, conditional on the existence of 

a trade relationship. MLE estimation allows for the probability of trade and 

the size of potential trade to be explained jointly.

Our sample-selection model for bilateral agricultural trade is specifi ed as 

follows:

11Linders and de Groot (2006) 

investigated other methods for dealing 

with zero-trade fl ows, including 

various extensions of Tobit estimation, 

truncated regression, probit regression, 

and replacement of zero fl ows with 

arbitrary numbers. They found the 

sample-selection model econometrically preferable to these alternative 

approaches.

12OLS parameter estimates are likely 

to be downwardly biased and inconsistent should incidental truncation 

arise (ρ ≠ 0). In such situations, the 

OLS regression is misspecifi ed as it 

excludes the Inverse Mills Ratio as an 

independent variable. As a result, OLS 

coeffi cients are attenuated (i.e., biased 

toward zero) and the error variance 

(σ2

U) is underestimated.
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The selection equation

* ln( ) ln( ) ( ) ln( ) ln( ) ijt t it jt ijt ij ij 01 2 3 4 5 12 3 4 ln( ) ln( ) ( ) ln( ) ln( 234* ln( 5 δδδ δ δ δ δ l( ) l( ) ( ) l( ) 01 2 3 4 1 23 ln( ) ln( ) ( ) ln( ) ) l( ) ( ) l( 01 2 3 4 1 23 ln( ) ln( ) ( ) ln( ) ln( ) ln( ) ( ) ) ln( ) ( ) ln( 01 2 3 4 1 2 3 4 1 23

6 ln( ) ln( ) ( ) ( ) (2) ij ij ij ijt ijt 7 89 ( ) 6 δ δ δδ ln( ) ln( ) ( ) ( ) 7 89 ) l( ) ( ) ( l( ) ( ) ( 7 89 ln( 6 ) ln( ) ( ) ( ln( ) ( ) ) 7 89 ( 7 89

where 

sijt = 1 if s*

ijt > 0

sijt = 0 if s*

ijt ≤ 0 

The outcome equation13

* ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ijt t it jt ijt ij ij 01 2 3 4 5 12 3 4 ) ln( ) ln( ) ln( ) ln( ) ln( 5 ) * βββ β β β β l( ) l( ) l( ) l( ) ln( 01 2 3 4 1 23 4 ln( ) ln( ) ln( ) ln( ) ) l( ) l( ) l( 01 2 3 4 1 23 4 ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) ) ln( ) ln( ) ln( 01 2 3 4 1 2 3 4 1 23 4

6 ln( ) ( ) ( ) (3) β β βμ 6 ij ij ijt ijt 7 8 ln( ) ( ) ( ) 7 8 ijt ln( ) ()( ) 6 ) ()( 7 8 

where

 (μijt, νijt) – bivariate normal [0,0,1,σ 2

υ, ρvμ]

The generalized gravity models

Anderson and van Wincoop (AvW) developed a generalized gravity model 

in which prices play a central equilibrating role. Baier and Bergstrand (BB) 

extended the AvW framework to a panel setting and estimated models that 

controlled for the effects of changes in multilateral prices through time via 

the use of exporter-by-time and importer-by-time fi xed effects. BB’s generalized gravity model also controls for partner heterogeneity via the use of 

exporter-to-importer fi xed effects. These country-pair dummies account 

for the whole host of time-invariant dyadic determinants (e.g., the special 

relationship established between Japan and the United States) that mutually 

affect the volume of trade for each partner pair. Baier and Bergstrand also 

developed a model that includes RTA lags in order to gauge the phase-in 

effects of these agreements on member countries’ trade over time. 

Generalized gravity models address the concerns about proper specifi cation 

identifi ed earlier. Following AvW and BB, the fi rst such model we estimate is 

as follows: 

 ln( ) ( ) (4) ijt ij it jt ijt ijt 0 1 X ) () ijt β ( ) 0 1 ij it jt ijt ( )

where γit denotes exporter-by-time fi xed effects, γjt signifi es importer-by-time 

fi xed effects, and γij represents exporter-to-importer fi xed effects.14 Equation 

(4) does not include either ln(Yit) or ln(Yit), as these regressors are absorbed 

by γit and γit, respectively. Similarly, specifi c dyadic variables, such as 

distance and contiguity, are absorbed by γij. 

Equation (4) overcomes many of the shortcomings of conventional gravity 

models. The country-by-time dummies control for multilateral resistances à 

13To circumvent a possible identifi cation problem, we followed common 

practice by excluding an exogenous 

variable in the outcome equation that 

is included in the selection equation. 

One reviewer was critical of our choice 

of dropping the language-similarity 

variable. However, William Greene 

of New York University informed us 

(in personal communication) that the 

identifi cation restriction was not only 

a “nonissue” when using the MLE, but 

that, if a restriction was imposed, it 

made little difference which variable 

was chosen to exclude from the selection equation. Moreover, we did not 

estimate the Heckman model in two 

stages, but rather simultaneously, using 

maximum likelihood estimator. 

14γit = 1 for exporter i in year t and 

0 otherwise, γit = 1 for importer j in 

year t and 0 otherwise, and γij = 1 for 

country i exporting to importer j and 0 

otherwise (where i = 1, 2, ... 69, j = 1, 

2, ... 69, and t = 1975, 1980 ... 2005). 

A reviewer asked why γij did not pick 

up the effects of RTAs. The answer is 

that the TP indices, unlike the countrypair fi xed effects, are not invariant over 

the 31-year time period of the analysis. 

MA and AA are coded dynamically to 

account for the changing composition 

of RTAs through time as countries join/

depart from the specifi c agreements.
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la AvW. These dummies not only account for time-varying export and import 

price indexes that infl uence bilateral trading decisions but also sweep away 

country-specifi c time-varying effects, such as shifts in domestic policies and 

macroeconomic shocks. The exporter-to-importer dummies provide a way 

to more thoroughly control for cultural and physical heterogeneity among 

country pairs than determinants commonly found in conventional gravity 

models (e.g., distance, contiguity, language similarity, and common colonial 

heritage). 

RTAs typically take time to mature. Their effects on trade cannot, therefore, 

be completely captured with binary variables using the date RTAs entered 

into force. The second generalized model we estimate follows Baier and 

Bergstrand’s framework and incorporates lagged RTA dummies to address 

this problem. This framework includes the same set of fi xed effects as the 

fi rst, but adds RTA phase-in variables. 

Our RTA phase-in model includes contemporaneous and lagged RTA dummy 

variables at 5 and 10 years as follows:

ln( ) ( ) ( ) ( ) (5) ijt ij it jt ij t ij t ij t ijt 0 1 , 2 , 5 3 , 10 1 , 2 ,5 3 , ) ()( )( ) ) ()( )( ) 0 1 , 2 , 5 3 , 10 ij it jt ij t ij t ij t 1 , 2 ,5 3 , 1 , 2 ,5 ()( )( ) 1 , 2 ,5 3 , 1 , 2 ,5 3 ()( )( ) 0 1 2 5 3 10 1 2 53 10 ()( )( 0 1 2 53 1 2 53 

The lagged variables mitigate measurement errors typically found in gravity 

models that include RTAs as explanatory variables that arise due to the 

inability of contemporaneous 0-1 dummy variables to account for the phasein effects of these agreements. In recognition of heterogeneity characterizing partner trade, equation (5) was run not only on the global sample of 69 

countries trading with each other but also on 8 subsamples, categorized by 

various combinations of high and low per capita incomes of the exporting and 

importing countries.
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Data

The panel dataset developed for this study includes bilateral trade fl ows for 

agriculture among 69 countries at 5-year intervals beginning in 1975 and 

ending in 2005.15 Most, but not all, countries export (import) to every other 

country. However, 20 percent of the cells are “missing” in the agricultural 

trade matrix.16 Summary statistics for the variables in the panel dataset are 

shown in table 1.

Bilateral trade data were obtained from the United Nations Commodity Trade 

Statistics (UN Statistical Offi ce, 2008) database, UN Comtrade, the primary 

international data source for partner- and product-specifi c trade that includes 

most countries and products. The WTO’s defi nition of agriculture is used 

to quantify total agricultural trade. Distances between capital cities and/

or the major commercial center closest to partner countries were calculated 

using the great circle method obtained from USDA’s Agricultural Research 

Service. Data on colonial heritage and landlockedness were obtained from 

Andrew Rose’s (2006) website. Data on language similarity were obtained 

from the Centre d’Etudes Prospectives et d’Informations Internationales 

(2005) website. Information about arable land was obtained from the United 

Nations Food and Agricultural Organization’s (2008) FAOSTAT database. 

Data on bilateral/regional trade agreements and their date of entry into force 

were compiled by scrutinizing multiple sources, including Oh (2006) and the 

WTO website (see box, “MA and AA: Two Generic RTA Variables Denoting 

Bilateral Trade Policies”). All other data were obtained from World 

Development Indicators (see World Bank, 2005).

15The 69 countries include Algeria, 

Argentina, Australia, Austria, 

Bangladesh, Belgium-Luxembourg, 

Brazil, Cameroon, Canada, Chile, 

China (mainland), Colombia, 

Costa Rica, Denmark, Dominican 

Republic, Egypt, El Salvador, Finland, 

France, Germany, Ghana, Greece, 

Guatemala, Honduras, Hong Kong, 

India, Indonesia, Ireland, Israel, Italy, 

Ivory Coast, Jamaica, Japan, Jordan, 

Kenya, Malaysia, Mexico, Morocco, 

Netherlands, New Zealand, Nicaragua, 

Nigeria, Norway, Pakistan, Panama, 

Paraguay Philippines, Poland, Portugal, 

Saudi Arabia, Senegal, Singapore, 

South African Customs Union 

(Botswana, Lesotho, Namibia, South 

Africa, and Swaziland), South Korea, 

Spain, Sri Lanka, Sweden, Switzerland, 

Taiwan, Thailand, Trinidad-Tobago, 

Tunisia, Turkey, United Kingdom, 

United States, Uruguay, Venezuela, and 

Zambia.

16We assume that empty cells are due 

to no trade actually having taken place.

The proliferation of bilateral and regional trade agreements 

in recent years raises the question of the impact of this 

phenomenon on agricultural trade in the world marketplace. 

This study examines this phenomenon and gauges its impact 

on partner trade in cases of mutual and asymmetric RTA 

membership using two generic indices. The MA index is 

used to quantify trade creation characterizing joint RTA 

membership. The AA index is used to compute trade 

diversion typifying partners when the exporter is not a 

member of an RTA to which the importer belongs. Both 

measures incorporate the following reciprocal preferential 

arrangements, free-trade agreements, customs unions, and 

common markets: Andean Community, Association of 

Southeast Asian Nations (ASEAN), Australia-Singapore 

Agreement, Australia-Thailand Agreement, Canada-Chile 

Agreement, Canada-Costa Rica Agreement, CanadaIsrael Agreement, Canada-U.S. Free Trade Agreement, 

Caribbean Community, Central American Common 

Market, Chile-Costa Rica Agreement, Chile-El Salvador 

Agreement, Chile-Israel Agreement, China-Hong Kong 

Agreement, Closer Economic Relations, Common Market 

for Eastern and Southern Africa, European Free Trade 

Agreement (EFTA), EFTA-Chile Agreement, EFTA-Israel 

Agreement, EFTA-Jordan Agreement, EFTA-Mexico 

Agreement, EFTA-Morocco Agreement, EFTA-Poland 

Agreement, EFTA-Singapore Agreement, EFTA-Turkey 

Agreement, European Union (EU), EU-Algeria Agreement, 

EU-Chile Agreement, EU-Egypt Agreement, EU-Israel 

Agreement, EU-Jordan Agreement, EU-Mexico Agreement, 

EU-Morocco Agreement, EU-Norway Agreement, EU-South 

Africa Agreement, EU-Switzerland Agreement, EU-Tunisia 

Agreement, EU-Turkey Agreement, G-3 Free Trade Area, 

Greater Arab Free Trade Area, Gulf Cooperation Council, 

India-Sri Lanka Agreement, Japan-Singapore Agreement, 

Latin American Integration Agreement, MERCOSUR, 

MERCOSUR-Chile Agreement, Mexico-Chile Agreement, 

Mexico-Costa Rica Agreement, Mexico-El Salvador 

Agreement, Mexico-Guatemala Agreement, MexicoHonduras Agreement, Mexico-Israel Agreement, MexicoJapan Agreement, Mexico-Nicaragua Agreement, New 

Zealand-Singapore Agreement, North American Free Trade 

Agreement, Panama-El Salvador Agreement, Poland-Israel 

Agreement, Poland-Turkey Agreement, South African 

Development Community, South Asian Preferential Trade 

Arrangement, Turkey-Israel Agreement, U.S.-Australia 

Free Trade Agreement, U.S.-Chile Free Trade Agreement, 

U.S.-Israel Free Trade Agreement, U.S.-Jordan Free Trade 

Agreement, and the U.S.-Singapore Free Trade Agreement.

MA and AA: Two Generic RTA Variables Denoting Bilateral Trade Policies 
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Table 1

Summary statistics for variables in panel dataset

Variable Statistics1 Description 

Xij

70

(355) Agricultural trade between i and j (millions of U.S. dollars)

Yi

377

(1,105) GDP of exporter i (billions of U.S. dollars)

Yj

370

(1,105) GDP of importer j (billions of U.S. dollars)

FEij

24

(218)

Relative factor endowment: exporter-to-importer 0.1 hectare of 

arable land per worker in the total labor force

DTij

7,910

(4,666)

Kilometers between exporter i's and importer j's major 

commercial cities

CBij

0.03

(0.17) Dummy: both countries share a common border

LLij

0.13

(0.33) Dummy: if either or both countries are landlocked

LSij

0.21

(0.41)

Dummy: 9 percent or more of the population in both countries 

share a common language

CHij

0.01

(0.12) Dummy: existence of a colonial linkage after 1945

MAij

0.10

(0.29) Dummy: mutual RTA membership

AAij

0.90

(0.30) Dummy: asymmetric RTA membership

No. of observations 25,931

1Sample means with standard deviations in parentheses.

Source: USDA, Economic Research Service.
12

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Empirical Findings

Econometric results for the applied gravity models are displayed in tables 

2-6. Tables 2 and 3 contain the statistical results for the benchmark and 

Heckman models. Table 4 presents empirical fi ndings from the dummy-intensive generalized model focused on contemporaneous RTA variables. Tables 5 

and 6 exhibit statistics from the generalized-gravity models that account for 

contemporaneous as well as RTA phase-in effects. 

Findings from benchmark and Heckman models 

Most parameter estimates in the benchmark models and the Heckman output 

equations are similar in magnitude and statistical signifi cance (tables 2 and 

3).17 The size of the exporter-income, importer-income, and factor-endowment coeffi cients are virtually identical and statistically signifi cant at the 0.01 

level in both models. Interestingly, the absolute size of the coeffi cients for 

distance, common border, landlockedness, and colonial heritage are slightly 

smaller in the benchmark than in the Heckman models. By contrast, the MA

and AA parameter estimates are somewhat larger. Given that incidental truncation was found to characterize agricultural trade in the sample-selection 

model, these results are not surprising.18 They point to parameter bias in loglinear models due to omitted observations.19 This bias is not, however, severe.

Both models generated correct signs for the basic gravity variables, income 

and distance. The magnitude of the parameter estimates for these two determinants fall within conventionally acceptable levels. The statistically signifi -

cant distance elasticities equal -0.78 in the benchmark models and -0.84 in 

the outcome equations of the sample-selection model. The generated income 

elasticities with respect to agricultural trade range from 0.71 for exporters to 

0.79 for importers. The higher elasticity for imports is not unexpected given 

the relatively high demand for food in the developing countries. 

The factor-endowment elasticity with respect to agricultural trade equals 

0.18. The fi nding of a positive parameter estimate for the exporter-to-importer 

land/labor ratio shows that national resources are an important determinant 

of cross-border trade in agriculture. It provides empirical validation of the 

relevance of economic trade theory and the Heckscher-Ohlin (H-O) explanation of trade. H-O theory leads one to expect that the uni-directional fl ow of 

agricultural trade from i and j would be positively related to the relative land/

labor ratio because the production of agricultural goods requires relative 

intensive use of arable land.

Coeffi cients for the invariant dyadic variables—landlockedness, common 

borders, language similarity, and colonial heritage—are statistically signifi -

cant at the 0.01 level, and each has the hypothesized sign in tables 2 and 3. 

The cost to trade whenever either the exporter or the importer is landlocked 

imposes an ad valorem tax equivalent of 4 to 10 percent, given parameter 

estimates in the benchmark and Heckman models and the assumption that 

the elasticities of substitution range between 5 and 10.20 Sharing a common 

border generates a competitive trade advantage for contiguous partners, 

providing them effectively with an ad valorem subsidy equivalent between 

17The correlation between MA and 

AA is high. Classic signs of multicollinearity arose when both MA and AA

variables were included in the same 

equation. The magnitude, sign, and 

statistical signifi cance of these variables often changed upon removal of 

either one of them. To circumvent such 

statistical problems, we ran separate 

equations for (1) trade creation by 

including MA but not AA and (2) trade 

diversion by including AA but not MA.

18Rejection of the null hypothesis 

that ρ = 0 confi rms the existence of 

correlation between the output and 

selection equations.

19Unfortunately, it was not possible 

to draw inferences about possible 

bias associated with missing observations and zero trade in our generalized 

gravity models. When attempting to 

apply the Heckman framework to these 

models, the Hessian became unstable, 

precluding convergence. 

20According to Rose and van 

Wincoop and the theoretical underpinnings of the gravity framework identifi ed by Anderson and van Wincoop, 

the coeffi cient of a time-invariant 

coeffi cient, such as landlockedness, is 

an estimate of (σ – 1)ln m, where (m 

– 1) is its tariff equivalent and σ is the 

elasticity of substitution.
13

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Table 2

Benchmark gravity model (OLS)

Variables Symbols

Coeffi cients

MA and AA MA only AA only

Exporter's income ln(Yi

) 0.71**

(0.01)

0.71**

(0.01)

0.71**

(0.01)

Importer's income ln(Yj) 0.79**

(0.01)

0.79**

(0.01)

0.79**

(0.01)

Relative land/labor ln(FEij) 0.18**

(0.01)

0.18**

(0.01)

0.18**

(0.01)

Distance ln(DTij) -0.78**

(0.02)

-0.78**

(0.02)

-0.78**

(0.02)

Common border CBij

0.59**

(0.08)

0.59**

(0.08)

0.59**

(0.08)

Landlockedness LLij

-0.41**

(0.04)

-0.40**

(0.04)

-0.40**

(0.04)

Language similarity LSij

0.62**

(0.04)

0.62**

(0.04)

0.62**

(0.04)

Colonial heritage CHij

1.43**

(0.09)

1.43**

(0.09)

1.42**

(0.09)

Mutual RTA membership MAij

0.82**

(0.24)

0.66**

(0.05)

Asymmetrical RTA membership AAij

0.16

(0.24)

-0.61**

(0.05)

Constant C 15.49**

(0.29)

15.64**

(0.18)

16.30**

(0.16)

Adjusted R2 0.446 0.446 0.446

F-statistic 1,754 1,871 1,852

Root MSE 2.341 2.341 2.341

No. of observations 25,931 25,931 25,931

Notes: The dependent variable is the natural log of agricultural bilateral trade (lnXijt) from country i to country j in year t. RTA = reciprocal 

trade agreement. MA = mutual-agreement index. AA = Asymmetric-agreement index. All regressions are estimated using 5-year panel data 

from 1975 to 2005. Coeffi cient estimates for the fi xed time effects are not reported for brevity. Standard errors are in parentheses. They are 

calculated using White’s heteroskedastic robust standard errors. ** denotes the null hypothesis is rejected at the 0.01 level.

Source: USDA, Economic Research Service.
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Table 3

Heckman’s sample selection model (MLE) 

Variables Symbols

Coeffi cients

MA and AA MA only AA only

Outcome Selection Outcome Selection Outcome Selection

Exporter's income ln(Yi

) 0.71**

(0.01)

0.42**

(0.01)

0.71**

(0.01)

0.42**

(0.01)

0.71**

(0.01)

0.42**

(0.01)

Importer's income ln(Yj) 0.79**

(0.01)

0.31**

(0.01)

0.79**

(0.01)

0.31**

(0.01)

0.79**

(0.01)

0.31**

(0.01)

Relative land/labor ln(FEij) 0.18**

(0.01)

0.00

(0.00)

0.18**

(0.01)

0.00

(0.00)

0.18**

(0.01)

0.00

(0.00)

Distance ln(DTij) -0.84**

(0.02)

-0.38**

(0.02)

-0.84**

(0.02)

-0.39**

(0.02)

-0.84**

(0.02)

-0.38**

(0.02)

Common border CBij

0.77**

(0.08)

-0.08

(0.12)

0.77**

(0.08)

-0.08

(0.12)

0.78**

(0.08)

-0.08

(0.12)

Landlockedness LLij

-0.42**

(0.04)

0.05*

(0.02)

-0.42**

(0.04)

0.05*

(0.02)

-0.42**

(0.04)

0.05*

(0.02)

Language similarity LSij

0.13**

(0.02)

0.13**

(0.02)

0.13**

(0.02)

Colonial heritage CHij

1.79**

(0.09)

5.86**

(0.06)

1.79**

(0.09)

5.85**

(0.06)

1.79**

(0.09)

5.84**

(0.06)

Mutual RTA membership MAij

0.79**

(0.24)

0.12

(0.32)

0.61**

(0.05)

0.52**

(0.10)

Asymmetrical RTA membership AAij

0.19

(0.24)

-0.42

(0.30)

-0.56**

(0.05)

-0.52**

(0.10)

Constant C 16.08**

(0.29)

2.51**

(0.33)

16.25**

(0.18)

2.10**

(0.15)

16.87**

(0.17)

2.61**

(0.16)

No. of observations 32,572 32,572 32,572 32,572 32,572 32,572

Censored observations 6,641 6,641 6,641 6,641 6,641 6,641

Log likelihood -70,770 -70,770 -70,772 -70,772 -70,777 -70,777

Wald-statistic 30,454 30,454 30,494 30,494 30,398 30,398

rho ρμ 0.06 0.06 0.06 0.06 0.07 0.07

sigma σ 2.35 2.35 2.35 2.35 2.35 2.35

lambda λ 0.15 0.15 0.15 0.15 0.16 0.16

Notes: The dependent variable is the natural log of agricultural bilateral trade (lnXijt) from country i to country j in year t. RTA = reciprocal 

trade agreement. MA = mutual-agreement index. AA = Asymmetric-agreement index. All regressions are estimated using 5-year panel data 

from 1975 to 2005. Coeffi cient estimates for the fi xed time effects are not reported for brevity. Standard errors are in parentheses. They are 

calculated using White’s heteroskedastic robust standard errors. ** denotes the null hypothesis is rejected at the 0.01 level.

Source: USDA, Economic Research Service.
15

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0.07 and 0.20 percent. However, contiguity was found not to affect the decision to trade in the selection equations. 

The empirical results show that “cultural distances” matter. Language similarity and colonial heritage have the expected positive sign and are signifi cant 

at the 1-percent level in the agricultural sector. The ability of a signifi cant 

proportion of the population in both countries to communicate in the same 

language increases trade relative to other countries between 0.6 and 0.9 

percent, on average. Possession of a colonial heritage also affects the decision 

to trade. Given an affi rmative decision to trade, the colonial linkage augments 

bilateral trade in agriculture between 3 and 5 percent. 

The benchmark and sample-selection models generated trade policy parameters that are similar in magnitude and statistical signifi cance for each of 

the three specifi cations. The models that include both MA and AA variables 

provided statistical evidence that RTAs expand trade between member countries but no evidence that these agreements contract trade from nonmembers. 

However, given the high correlation between the two trade-policy variables, 

multicollinearity causes diffi culty in identifying the separate effects of MA

and AA. We, therefore, ran separate equations, one excluding the mutualagreement and the other excluding the asymmetric-agreement variables. 

Dropping one of the trade policy variables generated parameter estimates of 

the anticipated correct signs that were statistically signifi cant at the 0.01 level. 

More specifi cally, the MA coeffi cients fell from 0.82 (0.79) in the MA and 

AA specifi cation to 0.66 (0.61) in the MA-only benchmark (sample-selection) 

model. In addition, the AA coeffi cients became statistically signifi cant in 

the two TD-only models, equaling -0.61 in the benchmark and -0.56 in the 

sample-selection models. 

The long-run increase in RTA-induced trade between countries mutually 

belonging to the same agreements was found, on average, to outpace the 

fall in trade characterized by asymmetric membership. Results from the 

MA-only models show that, on average, mutual RTA membership enhances 

partner trade in agriculture between 93 and 84 percent for the benchmark 

and Heckman models, respectively.21 Similarly, estimates from the AA-only 

models indicate that asymmetrical RTA membership lowers bilateral trade 

between 46 and 43 percent when the importer is a member of an RTA to 

which the exporter does not belong.

Findings from the generalized models

The MA and AA coeffi cients were not statistically signifi cant in the contemporaneous generalized gravity model when both trade-policy variables were 

included in the estimating equation (table 4, column 1). However, upon 

purging the equations of severe multicollinearity via the removal of either the 

MA or AA variable, the parameter estimates for both trade-policy variables 

became statistically signifi cant at the 0.01 level and were of the correct sign 

(table 4, column 2 & 3). Interestingly, the 0.29 coeffi cient for MA and the 

-0.30 coeffi cient for AA are less than half the size of corresponding estimates 

in tables 2 and 3. The lower parameter estimates for the trade-policy variables indicate that the longrun percentage increase (decrease) in agricultural 

trade due to common (asymmetric) RTA membership is, on average, 34 (26) 

21The percentage change in trade 

attributable to landlockedness in the 

benchmark equation is (eβ5 - 1) x 100.
16

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percent. The smaller RTA impacts generated by the generalized model are 

due to more comprehensive control of both observed and unobserved heterogeneity than in either the benchmark or Heckman models.22

Table 5 and 6 show the parameter estimates from our RTA phase-in gravity 

models for total agricultural trade. We calculate the sum of the contemporaneous and lag coeffi cients of MA and AA occurring over 10 years to gauge the 

cumulative impact of RTAs on partner trade as these agreements mature. The 

percentage change in trade expansion and trade contraction are reported as 

“total MA effect” and “total AA effect” when the sum of the parameter estimates MAt

 + MAt-5 + MAt-10 and AAt + AAt-5 + AAt-10 were determined to be 

signifi cantly different from zero via Wald test statistics, respectively. 

To examine whether RTAs may have had an impact on various partner 

combinations, we divided our global sample of observed trade fl ows into 

high-income (HIC), low-income (LIC), and all (ALL) exporter/importer 

groupings. We then ran the dummy-intensive gravity model on the following 

eight subsamples: ALL imports from ALL, HIC imports from ALL, ALL 

imports from HIC, HIC imports from HIC, LIC imports from HIC, LIC 

imports from ALL, ALL imports from LIC, LIC imports from LIC, and HIC 

imports from LIC.

The sum of the generated MA parameter estimates from our global sample 

of 19,225 agricultural trade fl ows equals 0.72 (table 5, column 1). This 

sum is similar to the 10-year cumulative MA estimates of 0.76 and 0.81, 

denoting trade expansion for total merchandise trade estimated by Baier and 

Bergstrand (2007) and for agricultural trade calculated by Grant and Lambert 

(2008), respectively.23 Our estimate indicates that the longrun cumulative 

22These empirical fi ndings are 

consistent with results elsewhere. 

Magee (2008); Eicher and Henn 

(2009); and Baier and Bergstrand 

(2007) found that the inclusion of 

country-pair fi xed effects in gravity 

equations lowered RTA parameter 

estimates.

23Neither of these studies addressed 

the issue of RTA-induced trade 

contraction. 

Table 4

Generalized gravity model

Variables

Coeffi cients

Symbols MA and AA MA only AA only

Mutual RTA membership MAij

0.09

(0.15)

0.29**

(0.05)

Asymmetrical RTA membership AAij

-0.22

(0.16)

-0.30**

(0.05)

Constant C 14.11**

(0.17)

12.85**

(0.42)

13.48**

(0.38)

Adjusted R2 0.84 0.84 0.84

F-statistic 19.04 19.04 19.04

Root MSE 1.28 1.28 1.28

No. of observations 26,114 26,114 26,114

Notes: The dependent variable is the natural log bilateral trade (lnXijt) from country i to country j in year t. RTA = reciprocal trade agreement. 

MA = mutual-agreement index. AA = Asymmetric-agreement index. All regressions are estimated using 5-year panel from 1975 to 2005 and 

include exporter-by-time, importer-by-time, and exporter-to-importer bilateral fi xed effects omitted in the table for brevity. Robust standard errors 

are in parentheses. ** denotes the null hypothesis is rejected at the 0.01 level. 

Source: USDA, Economic Research Service.
17

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impact of mutual membership in RTAs increases bilateral agricultural trade 

105 percent, on average, beyond what would have occurred in the absence of 

these agreements when allowing for 10 years of phase-in effects.

Inspection of the empirical results from the various subsamples reveals that 

much of the agricultural trade expansion identifi ed in the global sample 

stemmed from mutual RTA membership between countries in the lowincome grouping. The payoff to agricultural LIC exporters belonging to the 

same RTA as their LIC partner was particularly pronounced, increasing 

1.5-fold, on average (table 5, column 8). This fi nding suggests that RTAs may 

be a particularly effective policy instrument, serving as a catalyst to more 

open agricultural markets in the developing world. 

Interestingly, there was no discernable increase in bilateral agricultural trade 

at mean values due to mutual RTA membership by either HIC exporters 

supplying affi liate LIC markets or by LIC exporters supplying affi liate HIC 

markets (columns 5 and 9). However, trade increased, on average, for HIC 

agricultural exporters supplying HIC markets when partners were members 

Table 5

Agricultural trade expansion derived from generalized gravity equations with RTA phase-in effects

12345678 9

ALL 

imports 

from ALL

HIC 

imports 

from ALL

ALL 

imports 

from HIC

HIC 

imports 

from HIC

LIC 

imports 

from HIC

LIC 

imports 

from ALL

ALL 

imports 

from LIC

LIC 

imports 

from LIC

HIC 

imports 

from LIC

MAijt

0.18**

(0.05)

0.07

(0.07)

0.03

(0.07)

0.17*

(0.07)

-0.06

(0.14)

0.28**

(0.10)

0.35**

(0.10)

0.63**

(0.17)

0.08

(0.15)

MAijt-5

0.24**

(0.06)

0.23**

(0.07)

0.21**

(0.07)

0.32**

(0.07)

0.03

(0.20)

0.19

(0.13)

0.07

(0.13)

0.02

(0.21)

-0.10

(0.21)

MAijt-10

0.29**

(0.07)

0.14

(0.07)

0.10

(0.07)

0.05

(0.06)

-0.21

(0.22)

0.13

(0.15)

0.21

(0.17)

0.26

(0.22)

-0.04

(0.33)

Constant 13.85**

(0.22)

15.49**

(0.07)

16.12**

(0.20)

17.86**

(0.30)

14.44**

(0.05)

13.18**

(0.39)

12.99**

(0.36)

12.86**

(0.15)

14.46**

(0.15)

MAijt sum

0.72**

(0.08)

0.44**

(0.09)

0.34**

(0.09)

0.53**

(0.09)

-0.24

(0.29)

0.61**

(0.17)

0.63**

(0.17)

0.90**

(0.23)

-0.06

(0.40)

Total MA effect 1.05 0.55 0.40 0.70 0.84 0.88 1.46

Adjusted R2 0.86 0.90 0.90 0.94 0.85 0.81 0.82 0.76 0.86

F-statistic 14.51 16.59 19.35 31.69 11.04 9.44 7.67 5.95 7.36

Root MSE 1.18 0.94 0.91 0.54 1.05 1.32 1.35 1.53 1.10

No. of observations 19,225 8,076 8,263 2,994 5,269 11,149 10,962 5,880 5,082

Notes: The dependent variable is the natural log of agricultural bilateral trade (lnXijt) from country i to country j in year t. RTA = reciprocal trade 

agreement. MA = mutual-agreement index. AA = asymmetric-agreement index. HIC = high-income countries. LIC = low-income countries. 

ALL = both high-income and low-income countries. All regressions are estimated using 5-year panel data from 1975 to 2005 and include 

exporter-by-time, importer-by-time, and exporter-to-importer bilateral fi xed effects omitted in the table for brevity. The “total MA effect” measures 

the percentage change in bilateral trade attributable to mutual membership in an RTA. It is calculated when the MAijt sum is signifi cantly 

different than zero. Standard errors are in parentheses. They are calculated using White’s heteroskedastic robust standard errors. * and ** 

denote the null hypothesis is rejected at the 0.05 and 0.01 level, respectively.

Source: USDA, Economic Research Service.
18

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of the same RTA (column 4). This trade increase is 70 percent in the long 

run.

The rise in RTA-member agricultural exports to RTA-member partners came 

at the expense of trade with other agricultural suppliers. In the global sample, 

agricultural sales fell 49 percent, on average, for exporters supplying import 

partners affi liated with RTAs to which the exporters did not belong (table 6, 

column 1). When comparing subsample results (columns 2-9), agricultural 

trade contraction was the least, falling 24 percent in the long run, for an HIC 

supplier exporting to a country in the set of ALL importers (column 3).24 24Similarly, agricultural trade 

creation was also the least for HICs 

exporting to the set of all importers, 

rising 40 percent.

Table 6

Agricultural trade contraction derived from generalized gravity equations with RTA phase-in effects

12345678 9

ALL 

imports 

from ALL

HIC 

imports 

from ALL

ALL 

imports 

from HIC

HIC 

imports 

from HIC

LIC 

imports 

from HIC

LIC 

imports 

from ALL

ALL 

imports 

from LIC

LIC 

imports 

from LIC

HIC 

imports 

from LIC

AAijt

-0.15**

(0.05)

-0.04

(0.07)

0.02

(0.07)

-0.16*

(0.08)

0.19

(0.15)

-0.23*

(0.10)

-0.30**

(0.10)

-0.59**

(0.17)

0.03

(0.15)

AAijt-5

-0.26**

(0.06)

-0.24**

(0.08)

-0.27**

(0.07)

-0.35**

(0.07)

-0.14

(0.20)

-0.23

(0.13)

-0.06

(0.13)

-0.03

(0.21)

0.09

(0.21)

AAijt-10

-0.26**

(0.07)

-0.14

(0.08)

-0.04

(0.07)

-0.03

(0.07)

0.45*

(0.22)

-0.04

(0.15)

-0.23

(0.16)

-0.23

(0.21)

-0.05

(0.31)

Constant 14.79**

(0.18)

16.46**

(0.10)

15.51**

(0.30)

18.26**

(0.36)

13.90**

(0.26)

13.59**

(0.31)

13.78**

(0.29)

13.60**

(0.30)

14.52**

(0.36)

AAijt sum

-0.67**

(0.08)

-0.42**

(0.09)

-0.28**

(0.10)

-0.54**

(0.09)

0.50

(0.27)

-0.50**

(0.16)

-0.58**

(0.17)

-0.85**

(0.23)

0.07

(0.35)

Total AA effect -0.49 -0.34 -0.24 -0.42 -0.39 -0.44 -0.57

Adjusted R2 0.86 0.90 0.90 0.94 0.85 0.81 0.82 0.76 0.86

F-statistic 14.46 16.54 19.35 32.02 11.10 9.43 7.66 5.95 7.34

Root MSE 1.18 0.94 0.91 0.54 1.05 1.32 1.35 1.53 1.10

No. of observations 19,225 8,076 8,263 2,994 5,269 11,149 10,962 5,880 5,082

Notes: The dependent variable is the natural log of agricultural bilateral trade (lnXijt) from country i to country j in year t. RTA = reciprocal trade 

agreement. MA = mutual-agreement index. AA = asymmetric-agreement index. HIC = high-income countries. LIC = low-income countries. 

ALL = both high-income and low-income countries. All regressions are estimated using 5-year panel data from 1975 to 2005 and include 

exporter-by-time, importer-by-time, and exporter-to-importer bilateral fi xed effects omitted in the table for brevity. The “total AA effect” measures 

the percentage change in bilateral trade attributable to mutual membership in an RTA. It is calculated when the AAijt sum is signifi cantly 

different than zero. Standard errors are in parentheses. They are calculated using White’s heteroskedastic robust standard errors. * and ** 

denote the null hypothesis is rejected at the 0.05 and 0.01 level, respectively.

Source: USDA, Economic Research Service.
19

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Model Tradeoffs

RTAs are viewed by some analysts as a vehicle for government policymakers 

to use to circumvent domestic regulations in foreign countries by virtue 

of their ability to get “behind the border” and remove domestic barriers 

in foreign countries that inhibit partner trade. Lawrence (1996) posits, for 

instance, a link between the formation of RTAs and antitrust rules, product 

standards, corporate governance, tax codes, and internal shipping regulations. 

Yet such phenomena are not included in gravity equations because they are 

diffi cult, if not impossible, to quantify. 

The absence of factors driving trade, such as domestic rules and regulations, in our benchmark and sample-selection models may yield biased and 

inconsistent coeffi cient estimates attributable to omitted variables. Errorsin-variable bias arises when variables omitted in applied models are correlated with both the dependent variable and one or more of the explanatory 

variables. 

The fi rst generalized model we estimate includes year, exporter-by-time, 

importer-by-time, and exporter-to-importer fi xed effects. Year dummies 

control for numerous factors, including infl ation common to all countries and 

the general increase in trade taking place due to globalization. The countryby-time fi xed effects pick up domestic policies and country-specifi c macroeconomic shocks characterizing exporters and importers, as well as what 

Anderson and van Wincoop (2004) refer to as “multilateral resistances” that 

affect each trading partner. The exporter-to-importer fi xed effects control for 

unobserved heterogeneity, such as unique institutional linkages and political 

arrangements characterizing each country pair.

The empirical results show that gravity models that do not comprehensively 

account for heterogeneity, via the inclusion of appropriate fi xed effects, 

produce upwardly biased RTA coeffi cients. Note, for example, parameter 

estimates for the statistically signifi cant RTA variables denoting MA and AA 

generated from the contemporaneous generalized gravity model are substantially smaller (less than one-half) than corresponding coeffi cients in either of 

the two conventional models.

The second generalized model we estimate is similar to the fi rst. It includes 

the same set of fi xed effects but also accounts for RTA lag effects. Empirical 

results indicate that the trade impacts of RTAs grow as producers and 

consumers adjust to policy-induced changes in the structure of markets and as 

the implementing provisions of these agreements are phased in over a period 

of 10 years. 

The shortcoming of the two generalized models is that the intensive use of 

fi xed effects sweeps away specifi c variables that trade theory identifi es as 

driving cross-border trade. Neither of the generalized models, for example, 

can accommodate the relative resource endowment variable. Thus, no tests 

can be performed to determine if the exporter/importer-to-land/labor ratio is 

statistically signifi cant. By contrast, both our benchmark and sample-selection models provide empirical evidence that relative factor endowment is an 

important driver of trade in agriculture, just as theory suggests.
20

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Finally, we address concerns expressed in the literature about the possibility 

of bias in parameter estimates obtained from log-linear gravity models. The 

dependent variable in log-linear models is not really bilateral trade, but bilateral trade contingent on a trading relationship because the log of zero is not 

defi ned. Our empirical results show that dropping missing and/or unreported 

trade, as is commonly done, generates modestly biased estimates for some 

independent variables, including that of MA and AA. Interestingly, the coeffi cients generated by the OLS models were virtually identical and of the same 

level of statistical signifi cance as those derived from the MLE models for the 

other explanatory variables (e.g., relative factor endowments).
21

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Summary of Results

In this study, ERS examined the impact of reciprocal trade agreements on 

bilateral trade expansion and trade contraction in the world agricultural 

marketplace. We used a generic dummy variable to identify the infl uence on 

partner trade of mutual RTA membership. We innovated by developing and 

deploying a similarly constructed dummy variable, but one that is capable of 

detecting the infl uence of these agreements on trade between RTA member 

countries and their nonmember partners. 

Four types of gravity equations were estimated: a benchmark model, a 

Heckman sample-selection model, a generalized model focused on contemporaneous impacts, and a generalized model that accommodates RTA phasein effects. Model results provide empirical evidence that RTAs augment 

trade among and between countries mutually belonging to a common RTA, 

on average. We also fi nd evidence that this increase in trade comes at the 

expense of other suppliers. Imports of agricultural goods by countries that 

belong to RTAs typically fall from exporters who do not share a common 

RTA membership with their trading partner. Interestingly, results in each 

of the four types of models show that the percentage increase in bilateral 

trade attributable to mutual RTA membership is greater than the percentage 

decrease in partner trade due to asymmetric membership. 

Results from the benchmark models indicate that joint RTA membership, 

on average, boosts agricultural trade 93 percent in the long run, while the 

decrease in bilateral trade due to asymmetric membership is 46 percent. The 

Heckman sample-selection models depict somewhat lower longrun RTA 

impacts on bilateral trade. These models, which, unlike the OLS models, 

account for the absence of partner trade, show that membership in a common 

RTA generates 84 percent more agricultural trade between partner countries. 

Results also show that exports by countries supplying agricultural products 

to importers belonging to RTAs to which the exporter is not a member fall by 

43 percent. 

Our fi rst generalized model focuses exclusively on the contemporaneous 

effect of RTAs. It generates much smaller RTA impacts than either the benchmark or Heckman models. This is due to the generalized model’s comprehensive control of both observed and unobserved heterogeneity. Empirical 

results from this generalized model show that mutual RTA membership 

increases bilateral trade by 34 percent in the long run, on average. The model 

also shows that asymmetric membership decreases agricultural trade by 26 

percent for countries importing from export suppliers not affi liated with an 

RTA to which the importer is a member. 

Our second generalized model accounts not only for the contemporaneous 

impact of RTAs but also for their lagged effects. In our view, this model 

generates the most accurate estimates of RTA-induced trade expansion and 

trade contraction. It allows for implementation of the free-trade provisions 

of RTAs to be phased in over a period of years. It also allows for the time 

often required for market participants to adjust their behavior to RTA-induced 

changes in market structure. 
22

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The generalized model with phase-in effects estimates the 10-year cumulative increase in agricultural exports to RTA partners to be 105 percent in the 

long run (on average), or triple the contemporaneous impact. The cumulative 

decrease in trade for an exporter supplying agricultural goods to an import 

partner affi liated with an RTA to which the exporter does not belong is estimated to be 49 percent, almost double the contemporaneous impact of 26 

percent. These fi ndings demonstrate that the trade impacts of RTAs grow as 

producers and consumers adjust to policy-induced changes in the structure of 

markets.

Subsample estimations using the generalized gravity model with RTA phasein effects revealed that much of the agricultural trade expansion identifi ed in 

the global sample stemmed from mutual RTA membership between countries 

in the low-income grouping. The payoff was particularly pronounced when 

both partners were members of the same RTA, increasing 1.5-fold over the 

long run. This fi nding suggests that even though many policies in low-income 

countries continue to protect agriculture, RTAs are relatively effective instruments in removing impediments to bilateral trade. It also indicates that RTAs 

may open markets that were previously closed or nearly closed within the 

developing world. Even a small increase in agricultural trade induced by the 

formation of an RTA between two low-income countries generates a large 

percentage change in trade when the previous level of trade between them 

was low.

Interestingly, there was no discernable increase in agricultural trade due to 

mutual RTA membership by either high-income country exporters supplying 

affi liate low-income country markets or by low-income country exporters 

supplying affi liate high-income country markets, on average. Many developing countries, nevertheless, place a high priority on forging trade agreements with high-income countries rather than with low-income countries.

Policymakers may wish to think strategically when selecting partner countries with whom to form trade agreements. For example, a country is less 

likely to experience the adverse effects of import trade diversion when 

it chooses to form a trade alliance with countries whose exports are cost 

competitive with other foreign sources of supply. Similarly, a country is more 

likely to gain from export expansion by forging agreements with countries 

having high tariffs. The volume of cross-border trade is surely to grow with 

such countries as import levies are negotiated downward. 
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Appendix: Economic Trade Theory and 

Advances in Applied Analyses

In the abstract world of neoclassical economics, relative price differentials 

provide incentives for cross-border trade that result in price convergence. 

However, given trade impediments such as transportation and other transaction costs in the real world, trade and domestic price differentials can persist 

if transaction costs equal differences in production costs. To further empirical 

understanding about the forces underpinning bilateral trade fl ows, Tinbergen 

(1962) and Pöyhonen (1963) pioneered estimation of gravity equations. The 

basic model can be expressed as follows: 

Vij = f(Yi , Yj , Dij) (1)

where Vij, the value of trade between countries i and j, is a positive function 

of Yi

 and Yj, the income (i.e., market size) of i and j, and a negative function 

of Dij, the distance separating the two trading partners signifying transaction 

costs of commercial activity. 

Many variations of the basic gravity model have been used in the literature to 

examine the factors hypothesized to drive product specialization and trade. 

Modifi ed equations often include variables denoting specifi c supply conditions at the origin (e.g., factor endowments, technology), additional demand 

conditions at the destination (e.g., per capita income), and/or numerous 

economic forces that either assist or resist the movement of bilateral trade 

(e.g., colonial linkages, trade agreements). 

Applied gravity analyses fell out of favor for a number of years due to data 

and statistical problems as well as to concerns about the absence of clear 

linkages to economic trade theory. Recent contributions in the theoretical and 

applied literature have, however, enhanced credibility and sparked a revival in 

gravity-based research.

A number of studies have strengthened microeconomic foundations. 

Deardorff (1998) addresses whether gravity models can work in the neoclassical world. He shows that the gravity equations are able to accommodate 

both the perfectly competitive Heckscher-Ohlin model and the monopolisticcompetitive model of Dixit-Stiglitz (1977). Feenstra et al. (2001) develop a 

national (Armington) product and a monopolistic competition model, both 

of which include transaction costs. They conclude that a wider range of theories than previously recognized is consistent with the gravity-type equation. 

Evenett and Keller (2002) demonstrate that the gravity framework can be 

used to test for increasing-returns-to-scale and relative-factor-endowment 

explanations of trade under conditions of perfect and imperfect specialization. 

Eaton and Kortum (2002) derive a gravity model from the Ricardian theory 

of international trade. A recent contribution to this literature is the work of 

Anderson and van Wincoop (2003, 2004). They developed an analytical 

framework that establishes linkages between trade theory, in which p rices 

play a central equilibrating role, and the generalized gravity model. 

Anderson and van Wincoop (AvW) manipulate the constant-elasticity-ofsubstitution (CES) expenditure system to derive an operational model based 
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upon trade costs. Market-clearing conditions are imposed to solve for generalequilibrium prices, prices that embody bilateral resistances confronting both 

the exporter and the importer with all of their trading partners. The most 

important insight obtained from their gravity model is that bilateral trade 

depends not only on the bilateral drivers, such as distance, characterizing 

the joint partnership of i and j, but also on multilateral drivers confronting 

exporter i and importer j in their other markets. 

The generalized gravity equation that emerges from AvW’s framework is 

consistent with economic theory:

ln( ) ln( ) ln( ) ln( ) (1 ) ln( ) ln( ) ln( ) (2) ij i j w ) ln( ) ln( ) ln( ) (1 ) ) ln( ) ln( ) ln( ) ln( ) ln( ) ln( ) (1 ) ln( ) ln( ) ln( ) (1 ) ln( ) ln( ) ln( ) ln( ) ⎡ ⎤ l( ) l( ) l( ) l( ) l( ) l( ) l( ) l( ⎣ ⎦) ij i j ln( ) ln( ) ln( ln( ) ln( ) ( ) ( ( ) ) ln( ) ln( ) ln( ) ln(

where Xij is the value of exports from i to j; Yi, Yj, and Yw are the outputs of 

country i, j, and the world (w), respectively; σ is the elasticity of substitution 

between the countries’ goods; TIij represents trade impediments; Pi captures 

“outward multilateral resistances” that depict the average trade resistance 

between origin i and its importing partner; Pj embodies “inward multilateral 

resistances” that represent destination j’s average trade resistance with its 

supplying partners; and the θs denote income shares. 

Fixed-effects statistical models can account for unobservable omitted variables (Feenstra, 2003). Given that the fi xed-effects models are computationally easier to estimate than customized nonlinear least squares (NLS) models, 

most applied researchers have adopted the least squares dummy variables 

(LSDV) approach to estimating generalized gravity equations. The prototype 

model of the LSDV-type is as follows:24

1

 ln(X ) ln( ) ln( ) ln( ) (3)

M

ij i j i j m ij ij 1 2 ) ln( ) ln( ) ln( ) m

β ln( ) m

m ij ( ij i j 1 2 ln( ) ln( ) l( ) l( ) () l( ) l( =

ln( ln( ) 1 2 ) ln( ) ) ln( ) ln( 2 ∑

where the fi xed effects (γi) and (γj) control for multilateral prices, each m TIij

represents a proxy vector denoting bilateral trade costs and εij refers to the 

disturbance term.25

Recent developments in the applied literature have advanced gravity analyses 

by addressing statistical issues that had led to model misspecifi cation and 

incorrect interpretation of empirical results in the early years. Mátyás (1997) 

and Egger and Pfaffermayr (2003) have shown that proper use of fi xed effects 

can correct for omitted variables. Mátyás maintains that gravity models that 

test the signifi cance of trading blocs are misspecifi ed unless they are specifi ed as a triple-index model that accounts for exporter, importer, and time 

fi xed effects. Egger and Pfaffermayr assert that proper specifi cation of the 

gravity equation includes, in addition to Mátyás’s three indexes, bilateral 

fi xed effects. Baier and Bergstrand (2007) present a case for using countryby-time and country-pair fi xed effects in a theoretically motivated gravity 

equation. Baldwin (2006) recommends ignoring gravity results that do not 

comprehensively control for such heterogeneity.

24The term – ln(Yw) is common 

across all countries and is therefore 

captured through a constant in the 

regression model. The term ln(Yi) – 

ln(Pi

) is constant across all exporters 

for a given importer. It is captured by 

the exporter dummy, (δi). The term 

ln(Yi) – ln(Pi) is constant across all 

importers for a given exporter. It is 

captured through the importer dummy, 

(δj).

25The “trade costs” for exogenous 

factor m is ) ρβ σ m m β / (1 ) , where is 

the substitution elasticity.