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Estimating Trade Flows: Trading Partners and Trading Volumes *
Open accessAbstract
We develop a simple model of international trade with heterogeneous firms that is consistent with a number of stylized features of the data. In particular, the model predicts positive as well as zero trade flows across pairs of countries, and it allows the number of exporting firms to vary across destination countries. As a result, the impact of trade frictions on trade flows can be decomposed into the intensive and extensive margins, where the former refers to the trade volume per exporter and the latter refers to the number of exporters. This model yields a generalized gravity equation that accounts for the self-selection of firms into export markets and their impact on trade volumes. We then develop a two-stage estimation procedure that uses an equation for selection into trade partners in the first stage and a trade flow equation in the second. We implement this procedure parametrically, semiparametrically, and nonparametrically, showing that in all three cases the estimated effects of trade frictions are similar. Importantly, our method provides estimates of the intensive and extensive margins of trade. We show that traditional estimates are biased and that most of the bias is due not to selection but rather due to the omission of the extensive margin. Moreover, the effect of the number of exporting firms varies across country pairs according to their characteristics. This variation is large and particularly so for trade between developed and less developed countries and between pairs of less developed countries.
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“Endogeneity has been a major obstacle in gravity models.”
From Estimating the effects of trade agreements: Lessons from 60 years of methods and data (2024) · cites this paper as Helpman et al., 2008
In the citing paper
“the profession has struggled to address this issue using standard techniques (e.g., instrumental variable (IV) treatment) due to the fact that very often what determines the probability to sign a trade agreement also affects the volume of trade flows (Egger et al., 2008;Egger et al., 2011;Helpman et al., 2008;Jochmans & Verardi, 2022).”
From Estimating the effects of trade agreements: Lessons from 60 years of methods and data (2024) · cites this paper as Helpman et al., 2008
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“Theoretical foundations for estimating gravity equations were enhanced in Anderson 180 SAJGBR 2,2 and van Wincoop (2003, 2004), and more recently, in Helpman et al. (2008).”
BackgroundMedin, H. (2018) · World Economy · doi:10.1111/twec.12756 · Cited by 31
The composition of trade flows and the aggregate effects of trade barriers
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“This paper is primarily related to the very large literature which uses quantitative trade models to determine the effects of trade barriers on aggregate variables, especially aggregate income and welfare, including Eaton and Kortum (2002); Anderson and van Wincoop (2003); Alvarez and Lucas (2007); and Helpman et al.…”
Margins of Multinational Labor Substitution
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“7Gravity regressions have become very popular in analyzing trade flows (Anderson and van Wincoop, 2003; Helpman et al., 2008) primarily because they can be derived from an equilibrium model with optimizing firms.”
BackgroundRandom-Coefficients Logit Demand Estimation with Zero-Valued Market Shares
Dubé, J., Hortaçsu, A., & Joo, J. (2021) · Marketing Science · doi:10.1287/mksc.2020.1280 · Cited by 30
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Does Corruption Hinder Trade for the New EU Members?
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“Building on the work of Helpman et al. (2008) and Dutt and Traca (2010), we use a common religion index and a measure of remoteness as instruments, along with lagged values, in an attempt to overcome this problem.”
MethodTalking trade: language barriers in intra-Canadian commerce
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The determinants of large-scale land investments in Africa
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A Meta-Analysis of Estimates of the Impact of Technical Barriers to TradePreprint
Li, Y., & Beghin, J. C. (2010) · SSRN Electronic Journal · doi:10.2139/ssrn.1511827 · Cited by 30
The Design of International Trade Agreements: Introducing a New DatabasePreprint
Dür, A., Baccini, L., Elsig, M., & Milewicz, K. (2012) · SSRN Electronic Journal · doi:10.2139/ssrn.2141141 · Cited by 32
Firm Heterogeneity and Aggregate WelfarePreprint
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“More specifically, for the Heckman selection model a two-step procedure is performed, with the initial application of a Probit model followed by an OLS, based on the results of the previous procedure [66].”
MethodNigeria’s cocoa exports: a gravity model approach
Abdullahi, N. M., Shahriar, S., Kea, S., Abdullahi, A. M., Zhang, Q., & Huo, X. (2021) · Ciência Rural · doi:10.1590/0103-8478cr20201043 · Cited by 30
Graham, B. S. (2020) · Handbook of econometrics · doi:10.1016/bs.hoe.2020.05.001 · Cited by 32
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“As pointed out by Hanson and Xiang (2011) for the case of movies, and Helpman et al. (2008) more generally, it is difficult to distinguish between measures that affect variable costs and fixed entry costs.”
BackgroundTrade, Migration and Integration – Evidence and Policy Implications
Hatzigeorgiou, A., & Lodefalk, M. (2014) · World Economy · doi:10.1111/twec.12236 · Cited by 29
Exports and International Logistics*
Behar, A., Manners, P., & Nelson, B. D. (2012) · Oxford Bulletin of Economics and Statistics · doi:10.1111/j.1468-0084.2012.00715.x · Cited by 29
Assessing the Impact of SPS Regulations on U.S. Fresh Fruit and Vegetable Exports
Grant, J. H., Peterson, E., & Ramniceanu, R. (2015) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.197381 · Cited by 30
Institutions and gravity model: the role of political economy and corporate governance
Bilgin, M. H., Gözgör, G., & Lau, C. K. M. (2016) · Eurasian economic review : · doi:10.1007/s40821-016-0069-x · Cited by 29
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Camarero, M., Gómez-Herrera, E., & Tamarit, C. R. (2018) · Open Economies Review · doi:10.1007/s11079-018-9479-y · Cited by 29
Cross-border circulation of films and cultural diversity in the EU
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“Some examples in the literature have opted for common language, common religion (Helpman et al. 2008), governance indicators of regulatory quality or the historical frequency of trade.”
Home-biased gravity: The role of migrant tastes in international trade
Zhang, P. (2020) · World Development · doi:10.1016/j.worlddev.2019.104863 · Cited by 29
“First, it introduces consumer preference heterogeneity into gravity models, which is additional to the gravity with firm heterogeneity (Chaney, 2008; Helpman et al., 2008), the non-homothetic gravity with consumer income heterogeneity (Fajgelbaum and Khandelwal, 2016), and the gravity with consumer geography heterogen…”
BackgroundProductivity and Firm Selection: Quantifying the 'New' Gains from TradePreprint
Corcos, G., Gatto, M. D., Mion, G., & Ottaviano, G. I. P. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1941819 · Cited by 29
CEECs Integration into Regional and Global Production NetworksPreprint
Martínez‐Zarzoso, I., Voicu, A. M., & Vidovic, M. (2011) · SSRN Electronic Journal · doi:10.2139/ssrn.1850623 · Cited by 29
“A possible explanation of the discrepancy with respect to results in Table 3 is that the Helpman et al. (2008) method distinguishes between trade margins whereas the Baldwin and Taglioni (2006) method considers only the effect on total trade.”
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Entrepreneurship policy and globalization
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Food safety regulations and fish trade: Evidence from European Union-Africa trade relations
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Trade Gains from Legal Rulings in the WTO Dispute Settlement System
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“In our estimation model, all missing observations are replaced with zeros, such as ln(1 + real imports), assuming that all non-reported information for trade values at the HS 6-digit sectoral level is zero (Helpman et al., 2008).”
Sustaining International Trade with China: Does ACFTA Improve ASEAN Export Efficiency?
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“Additionally, Helpman, Melitz, and Rubinstein [39] suggest that zero trade is a practical result when an exporting country is below necessary productive levels to serve a foreign market.”
BackgroundPamp, O., Lebacher, M., Thurner, P. W., & Ziegler, E. (2021) · European Journal of Political Economy · doi:10.1016/j.ejpoleco.2021.102033 · Cited by 28
The multilayer architecture of the global input-output network and its properties
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“Nevertheless, similarly to what has recently been found for the World Trade network (e.g., see Felbermayr & Kohler, 2006; Helpman et al., 2008; De Benedictis & Tajoli, 2011), intensive margin effects play a more important role in explaining the evolution of the global input-output network.”
InfluentialLatin American Agri-Food Exports, 1994–2019: A Gravity Model Approach
Ayuda, M., Belloc, I., & Pinilla, V. (2022) · Mathematics · doi:10.3390/math10030333 · Cited by 30
“[48] propose a theoretically founded two-step selection process where exporters must absorb certain fixed costs in order to enter a market.”
BackgroundMethodInfluentialDoes Distance Matter? The Influence of ICT on Bilateral Trade Flows
Demirkan, H., Goul, M., Kauffman, R. J., Weber, D. M., & Carey, W. P. (2009) · Journal of the Association for Information Systems · Cited by 28
The economic analysis of multinationals and foreign direct investment: A review
Latorre, M. C. (2009) · RePEc: Research Papers in Economics · Cited by 28
Cultural proximity: A source of trade flow resilience?
Carrère, C., & Masood, M. (2018) · World Economy · doi:10.1111/twec.12646 · Cited by 28
Exaggerated death of distance: Revisiting distance effects on regional price dispersions
Kano, K., Kano, T., & Takechi, K. (2013) · Journal of International Economics · doi:10.1016/j.jinteco.2013.02.002 · Cited by 28
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BackgroundMethodInfluentialInternational Trade and Aggregate Fluctuations in Granular EconomiesPreprint
di Giovanni, J., & Levchenko, A. A. (2009) · RePEc: Research Papers in Economics · Cited by 28
Foreign Languages and TradePreprint
Fidrmuc, J., & Fidrmuc, J. (2014) · SSRN Electronic Journal · doi:10.2139/ssrn.2411407 · Cited by 28
Hayakawa, K., Ito, T., & Kimura, F. (2016) · Review of Development Economics · doi:10.1111/rode.12208 · Cited by 27
“One variation is to separate differentiated products from non-differentiated products following the definition provided by Rauch (1999). It is an empirical question whether tariff reduction and NTB removal may affect differently compared with nondifferentiated products.”
BackgroundEstimating export equations: a survey of the literature
Bayar, G. (2017) · Empirical Economics · doi:10.1007/s00181-016-1220-3 · Cited by 27
Lin, J. H., & Lincoln, W. F. (2017) · Journal of International Economics · doi:10.1016/j.jinteco.2017.05.008 · Cited by 27
Compensation modes of border effects in cross‐border regions
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“…process of firms selection,whereby the least productive segment is forced out of themarket, as demonstrated by convincing empirical evidence (Helpman et al., 2008;Melitz &Ottaviano, 2008).4 At aggregate level, borders have been taken indirectly into account in the regional growth spillovers…”
BackgroundEXPORT DIVERSIFICATION AND EXPORT PERFORMANCE BY DESTINATION COUNTRY
del Rosal, I. (2018) · Bulletin of Economic Research · doi:10.1111/boer.12181 · Cited by 27
Institutional quality and the duration of agri‐food trade flows
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The Importance of Business Travel for Trade: Evidence from the Liberalization of the Soviet Airspace
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Estimating gravity equation models in the presence of sample selection and heteroscedasticity
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“The new trade theory, pioneered by Melitz (2003) and developed by several others such as Chaney (2008) and HMR, attributes the absence of trade to firms’ selection behaviour: zero trade flow is observed when no firm in the potential exporting country finds it profitable to bear the fixed costs of trade and sell to the…”
BackgroundMethodInfluentialThe Determinants of Cross-Border Lending in the Euro Zone
Heuchemer, S., Kleimeier, S., & Sander, H. (2009) · Comparative Economic Studies · doi:10.1057/ces.2009.9 · Cited by 27
“heterogeneous firms with firm-level differentials (see eg Melitz, 2003; Helpman et al., 2008).”
Wieck, C., Schlueter, S. W., & Britz, W. (2012) · World Economy · doi:10.1111/j.1467-9701.2012.01461.x · Cited by 27
“Helpman et al. (2008) argue that the excluded variable has to be uncorrelated with the trade flow equation’s error terms and that the excluded variable should influence trade only through fixed trade costs because variable trade costs impact the extent of the volume of trade, thus variable trade costs are not uncorrel…”
InfluentialDistance and Border Effects in International Trade: A Comparison of Estimation Methods
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“While Helpman et al. (2008) use a Heckman-type selection model that is derived from theory and accounts for firm heterogeneity, alternatives such as Zero Inflated models deliver biased results.”
BackgroundMethodInfluentialDoes quality differentiation matter in exporters' pricing behaviour? Comparing China and India
Mallick, S., & Marqués, H. (2016) · China Economic Review · doi:10.1016/j.chieco.2016.06.001 · Cited by 27
Analysis of China’s Importance in “Belt and Road Initiative” Trade Based on a Gravity Model
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“However, these methods still have some shortcomings: they are (1) not robust to heteroskedasticity (NLS) and give (2) less weight to observations with large conditional means (GPML) [24].”
MethodNoisy information, distance and law of one price dynamics across US cities
Crucini, M. J., Shintani, M., & Tsuruga, T. (2015) · Journal of Monetary Economics · doi:10.1016/j.jmoneco.2015.06.003 · Cited by 27
Standards, reputation, and trade: evidence from US horticultural import refusals
Jouanjean, M.-A. (2012) · World Trade Review · doi:10.1017/s1474745612000274 · Cited by 34
“The Melitz (2003) model and its extension by Helpman et al. (2008) and Chaney (2008) is now widely accepted.”
InfluentialEffects of Urban Growth Controls on Intercity Commuting
Ogura, L. M. (2010) · Urban Studies · doi:10.1177/0042098009356126 · Cited by 27
“Linders and de Groot (2006) and Helpman et al. (2008) apply this method to estimate trade flows.”
MethodTrade performances and technology in the enlarged European Union
Antimiani, A., & Costantini, V. (2013) · Journal of Economic Studies · doi:10.1108/01443581311283961 · Cited by 27
“We have also adopted a two stage procedure as suggested by Helpman et al. (2008) by considering a first stage probit selection equation in order to reduce bias coming from zero values in export flows.”
MethodGondwe, G. (2021) · Journal of African Trade · doi:10.2991/jat.k.210311.001 · Cited by 26
Gil‐Pareja, S., Llorca‐Vivero, R., & Paniagua, J. (2013) · Applied Economics Letters · doi:10.1080/13504851.2013.802082 · Cited by 26
“Additionally, we perform a robustness check using the two-stage estimation method proposed by Helpman et al. (2008, HMR hereafter) for the invested quantities.”
MethodHanousek, J., & Evžen Kočenda, A. (2014) · Economic Systems · doi:10.1016/j.ecosys.2014.06.001 · Cited by 26
“Finally, the differences in the impact of the trade directions is also in accord with asymmetric trade flows among countries as shown in Helpman et al. (2008).”
InfluentialThe surprising instability of export specializations
Daruich, D., Easterly, W. R., & Ariell Reshef, Y. (2018) · Journal of Development Economics · doi:10.1016/j.jdeveco.2018.10.009 · Cited by 26
What goes around comes around: Export-enhancing effects of import-tariff reductions
Hayakawa, K., Ishikawa, J., & Tarui, N. (2020) · Journal of International Economics · doi:10.1016/j.jinteco.2020.103362 · Cited by 26
Does aid for trade diversify sub-Saharan Africa’s exports at the intensive and extensive margins?
Nathoo, R. K., Salim, R. A., Ancharaz, V. D., & Kabir, M. (2021) · Applied Economics · doi:10.1080/00036846.2021.1940084 · Cited by 26
“Recent heterogeneous-firm trade theories (Chaney 2008; Helpman, Melitz, and Rubinstein 2008; Melitz 2003) highlight the role of trade costs in influencing trade at both the intensive and extensive margins.”
BackgroundFuture Prospects of the Gravity Model of Trade: A Bibliometric Review (1993–2021)
Jadhav, S., & Ghosh, I. (2023) · Foreign Trade Review · doi:10.1177/00157325221140154 · Cited by 29
“…1985), GMoT based on standard trade theories (Deardorff, 1998), general equilibrium GMoT (Anderson & van Wincoop, 2003; Baier & Bergstrand, 2007), GMoT based on firm heterogeneity (Helpman et al., 2008), and GMoT at disaggregate level under general equilibrium settings (Anderson & Yotov, 2010).”
MethodPreferential trade agreements and the structure of international trade
Foster‐McGregor, N., & Stehrer, R. (2011) · Review of World Economics · doi:10.1007/s10290-011-0093-y · Cited by 25
“It would also be possible to adopt the approaches of Helpman et al (2008) and Santos and Tenreyro (2006) mentioned in footnote 14 to consider the issue of zero values of the IIT index. positive, with a value around one, as expected, and we obtain small, negative (but significant) coefficients on…”
BackgroundMethodInternational productivity gaps and the export status of firms: Evidence from France and Japan
Bellone, F., Kiyota, K., Matsuura, T., Musso, P., & Nesta, L. J. (2014) · European Economic Review · doi:10.1016/j.euroecorev.2014.01.017 · Cited by 26
“The mechanism is particularly consistent with the models that explicitly feature country-speci c trade costs such as Helpman, Melitz, and Rubinstein (2008) or the models that feature rm heterogeneity, comparative advantage and country-speci c trade costs all together such as the Bernard, Redding,…”
MethodThere will be exports and licensing: The effects of patent rights and innovation on firm sales
Briggs, K., & Park, W. G. (2013) · Journal of International Trade & Economic Development · doi:10.1080/09638199.2013.843199 · Cited by 26
“Anderson and van Wincoop (2003) and Helpman, Melitz, and Rubinstein (2008) argue that domestic factors can shape the home environment that influences the export decision.”
BackgroundTrade and Sectoral Productivity
Fadinger, H., & Fleiss, P. (2011) · The Economic Journal · doi:10.1111/j.1468-0297.2011.02434.x · Cited by 26
“When estimating this more general model with a two-step procedure as suggested by Helpman, Melitz and Rubinstein [2008] we continue to obtain quite similar results for our sectoral productivity estimates (columns labeled ”Heckman” & ”Heterogeneous Firms”).”
ResultMigration and globalization: what’s in it for developing countries?
Hillel Rapoport, C. (2016) · International Journal of Manpower · doi:10.1108/ijm-08-2015-0116 · Cited by 26
Export and Innovation in Small and Medium Enterprises: The Role of Concentrated Bank Borrowing
Mancusi, M. L., Vezzulli, A., Frazzoni, S., Rotondi, Z., & Sobrero, M. (2017) · Economica · doi:10.1111/ecca.12252 · Cited by 26
Supply‐chain trade and labor market outcomes: The case of the 2004 European Union enlargement
Kaplan, L. C., Kohl, T., & Martínez‐Zarzoso, I. (2017) · Review of International Economics · doi:10.1111/roie.12339 · Cited by 25
Backward participation in global value chains and exchange rate driven adjustments of Swiss exports
Fauceglia, D., Lassmann, A., Shingal, A., & Wermelinger, M. (2018) · Review of World Economics · doi:10.1007/s10290-018-0310-z · Cited by 26
Multi-destination firms and the impact of exchange-rate risk on trade
Héricourt, J., & Nedoncelle, C. (2018) · Journal of Comparative Economics · doi:10.1016/j.jce.2018.07.016 · Cited by 26
Oil and Petroleum Product Armington Elasticities: A New-Geography-of-Trade Approach to Estimation
Balistreri, E. J., Al-Qahtani, A., & Dahl, C. (2010) · The Energy Journal · doi:10.5547/issn0195-6574-ej-vol31-no3-9 · Cited by 27
“, Helpman et al. (2008)], but these are based on a love-of-variety aggregator.”
The role of the extensive margin in export of Turkey: A comparative analysis
Aldan, A., & Çulha, O. Y. (2016) · Central Bank Review · doi:10.1016/j.cbrev.2016.05.002 · Cited by 26
“We now turn to the extensive margin analysis based on Hummels and Klenow (2005). Again, we first start with the analysis based on products.”
BackgroundMethodModelling Inter-Regional Freight Demand with Input–Output, Gravity and SCGE Methodologies
Ivanova, O. (2013) · Elsevier eBooks · doi:10.1016/b978-0-12-410400-6.00002-1 · Cited by 26
Bangladesh trade potential: a dynamic gravity approach
Rahman, M. M., & Ara, L. A. (2010) · Journal of International Trade Law and Policy · doi:10.1108/14770021011054296 · Cited by 26
“, 2008), international borders (Anderson and Wincoop, 2003; Gorodnichenko and Tesar, 2009), and methodological issues (Egger, 2002; Baldwin and Taglioni, 2006; Silva and Tenreyro, 2006; Helpman et al., 2008).”
BackgroundTrade, Wages, and ProductivityPreprint
Behrens, K., Mion, G., Murata, Y., & Suedekum, J. (2008) · SSRN Electronic Journal · doi:10.2139/ssrn.1268282 · Cited by 28
“Several recent contributions have derived gravity equations with heterogeneous firms (e.g., Chaney, 2008; Helpman et al., 2008; Melitz and Ottaviano, 2008).”
InfluentialEstimation of Nonlinear Panel Models with Multiple Unobserved Effects
Chen, M., & Chen, M. (2016) · Warwick Research Archive Portal (University of Warwick) · doi:10.22004/ag.econ.269326 · Cited by 26
“See Helpman et al. (2008) for additional details.”
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von Uexküll, E. (2012) · RePEc: Research Papers in Economics · Cited by 26
Bekkers, E., & Rojas‐Romagosa, H. (2018) · World Economy · doi:10.1111/twec.12670 · Cited by 25
“(2013) and Egger, Francois, Manchin, and Nelson (2015) use a trade-weighted sectoral average tariff based on the applied most-favourable nation (MFN) tariff rates, using different sources: WTO, CEPII and UNCTAD. The main difference is that Francois, Manchin, Norberg et al. (2013) use 2007 data (to be compatible with t…”
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Effects of Islamic religiosity on bilateral trust in trade: The case of Turkish exports
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Lateef, M., Tong, G., & Riaz, M. U. (2018) · Chinese Economy · doi:10.1080/10971475.2018.1481008 · Cited by 25
Assessing the implications of regional preferential market access for meat commodities
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China and the Manufacturing Terms-of-Trade of African Exporters
Villoria, N. B. (2009) · Journal of African Economies · doi:10.1093/jae/ejp004 · Cited by 25
When institutions matter: a gravity model for Chinese meat imports
Hasiner, E., & Yu, X. (2018) · International Journal of Emerging Markets · doi:10.1108/ijoem-11-2016-0290 · Cited by 25
Movements of People for Movements of Goods?
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Why do within firm-product export prices differ across markets?Preprint
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Metadata
- Authors
- Helpman, E., Melitz, M., & Rubinstein, Y.
- Affiliations
- Canadian Institute for Advanced Research (CA)
- National Bureau of Economic Research (US)
- Venue
- Quarterly Journal of Economics
- Publisher
- Oxford University Press (OUP)
- Published
- 2008-05
- Volume
- 123
- Issue
- 2
- Pages
- 441-487
- ISSN
- 0033-5533 (ISSN-L)
- 1531-4650
- OpenAlex
- W3122837923
- Cited by
- 2,436
- References
- 41
- Citations by year
- 2026: 99 · 2025: 93 · 2024: 104 · 2023: 91 · 2022: 111 · 2021: 115 · 2020: 114 · 2019: 105 · 2018: 126 · 2017: 132 · 2016: 157 · 2015: 200 · 2014: 204 · 2013: 196 · 2012: 174
- FWCI
- 286.17
- Type
- journal article
- Language
- en
- Open access
- green
- nrs.harvard.edu
- Licence
- cc-by
- Locations
- The Quarterly Journal of Economics (publishedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
- RePEc: Research Papers in Economics (submittedVersion)
- London School of Economics and Political Science Theses Online (London School of Economics and Political Science) (submittedVersion)
- Topics
- Social Sciences › Economics, Econometrics and Finance › General Economics, Econometrics and Finance › Global trade and economics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Economic and Technological Innovation
- Social Sciences › Business, Management and Accounting › Strategy and Management › Global Trade and Competitiveness
- Keywords
- international trade, trade flows, gravity model, trade friction, heterogeneous firms, intensive margin, extensive margin, exporters, two-stage estimation, selection bias, developed and developing countries
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