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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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Han, X., & Cheng, Y. (2023) · Environmental and Resource Economics · doi:10.1007/s10640-023-00783-5 · Cited by 29
“Helpman et al. (2008) developed a two-stage procedure consisting of both the selection of trade partners and trade-flow equations to incorporate the zero trade flows; Santos Silva and Tenreyro (2006) proposed estimating the gravity models in multiplicative form by using the Poisson…”
MethodHeterogeneous effects of bilateral investment treaties
Falvey, R., & Foster‐McGregor, N. (2017) · Review of World Economics · doi:10.1007/s10290-017-0287-z · Cited by 24
“Helpman et al. (2008) for example propose a modified Heckman selection type model, while Santos and Tenreyro (2006) suggest using a Pseudo Poisson Maximum Likelihood model.”
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Sorgho, Z., & Larue, B. (2017) · Journal of Agricultural & Food Industrial Organization · doi:10.1515/jafio-2017-0010 · Cited by 24
“The model is estimated with the Helpman, Melitz, and Rubinstein (2008) two-stage approach (HMR).”
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“The theoretical foundation is based on seminal papers from several scholars such as Anderson (1979); Anderson and van Wincoop (2003); the neo-classical Heckscher-Ohlin framework (Bergstrand, 1985); the classical Ricardian framework of Eaton and Kortum (2002); entry of heterogeneous firms, selection into markets (Helpm…”
BackgroundExploring the Links between Bilateral and Regional Trade Agreements and Merchandise Trade
Barbalet, F., Greenville, J., Crook, W., Gretton, P., & Breunig, R. V. (2015) · Asia & the Pacific Policy Studies · doi:10.1002/app5.101 · Cited by 24
“Helpman et al. (2008) showed that studies that discard bilateral trade links for which no trade occurs are likely to derive biased results as a consequence.”
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A Causal Interpretation of Extensive and Intensive Margin Effects in Generalized Tobit Models
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“For instance, firm entry regulation measures such as the number of procedures should primarily be a fixed cost and not affect variable trading costs (Helpman, Melitz and Rubinstein, 2008).”
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Where Do Firms Export, How Much and Why?
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European Wines Exports Towards Emerging Markets. The Role of Geographical Identity
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Homeward bound FDI: Are migrants a bridge over troubled finance?
Cuadros, A., Martín-Montaner, J. A., & Paniagua, J. (2016) · Economic Modelling · doi:10.1016/j.econmod.2016.05.021 · Cited by 24
“The model closely follows standard trade and FDI setups like those described by Melitz (2003), Helpman et al. (2008), Manova (2013), and Crinò and Ogliari (2015).”
BackgroundMethodThe Gravity of Water: Water Trade Frictions in California
Regnacq, C., Dinar, A., & Hanak, E. (2016) · American Journal of Agricultural Economics · doi:10.1093/ajae/aaw051 · Cited by 24
“Again, some recent work in the field of international trade introduced a fixed component to the estimation of the gravity equation (Helpman, Melitz, and Rubinstein 2008; Chaney 2008; Arkolakis 2010; Allen 2014).”
Deepening and Widening of Production Networks in ASEAN
Obashi, A., & Kimura, F. (2017) · Asian Economic Papers · doi:10.1162/asep_a_00479 · Cited by 24
Aid for trade and international transactions in goods and services
Hoekman, B. M., & Shingal, A. (2019) · Review of International Economics · doi:10.1111/roie.12452 · Cited by 23
“…see Novak-Lehmann et al. 2013; Pettersson and Johansson, 2013).14 14We also attempted the two-step Heckman following the estimation strategy in Helpman et al. (2008) to account for any sample selection bias using the (log) cost of trading from the World Bank’s Doing Business Indicators as an…”
Financial frictions and trade intermediation: Theory and evidence
Chan, J. M. L. (2018) · European Economic Review · doi:10.1016/j.euroecorev.2018.04.002 · Cited by 24
Do firm–bank relationships affect firms’ internationalization?
Bonis, R. D., Ferri, G., & Rotondi, Z. (2015) · International Economics · doi:10.1016/j.inteco.2014.11.001 · Cited by 24
How Much do Agreements Matter for Services Trade?Preprint
Shingal, A. (2010) · SSRN Electronic Journal · doi:10.2139/ssrn.1586839 · Cited by 24
Economic development, growth, institutions and geographyPreprint
Bhupatiraju, S., & Verspagen, B. (2013) · RePEc: Research Papers in Economics · Cited by 24
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Vigani, M., Raimondi, V., & Olper, A. (2010) · SSRN Electronic Journal · doi:10.2139/ssrn.1571202 · Cited by 24
“…PPML approach produces biased results when used in the presence of a large fraction of zero trade flow, a situation consistent with recent trade models with firms’ heterogeneity (Melitz 2003; Helpman et al. 2008) and very frequently working at a disaggregated product level as in our application.”
MethodResultRipple effects in regional value chains: Evidence from an episode of the US–China trade war
Hayakawa, K., Pyun, J. H., Yamashita, N., & Yang, C. (2023) · World Economy · doi:10.1111/twec.13444 · Cited by 23
International competition in the first wave of globalization: new evidence on the margins of trade
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Why Is Agricultural Trade within ECOWAS So High?
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Cultural distance and international trade in services: A disaggregate view
Harms, P., & Shuvalova, D. (2020) · Economic Systems · doi:10.1016/j.ecosys.2020.100786 · Cited by 22
“…to predict better when the selection equation contains at least one variable excluded from the behavioral equation (Heckman, 1976), we follow Helpman et al. (2008) and choose the religion dummy as an excluded regressor, since we expect it to mainly influence the decision about trade (fixed…”
BackgroundTourism, insularity, and remoteness: A gravity-based approach
Dropsy, V., Montet, C., & Poirine, B. (2019) · Tourism Economics · doi:10.1177/1354816619855233 · Cited by 23
“…model of trade predicts that highincome countries will mostly trade with each other, the gravity equation fits well this type of intraindustry trade (see Anderson, 1979; Bergstrand, 1985; Deardorff, 1998; Helpman et al., 2008; and for a textbook treatment, Feenstra and Taylor, 2014: Ch. 6).”
BackgroundAre EU standards detrimental to Africa’s exports?
Kareem, F. O., & Martínez‐Zarzoso, I. (2020) · Journal of Policy Modeling · doi:10.1016/j.jpolmod.2020.04.006 · Cited by 23
Dutt, P. (2020) · European Economic Review · doi:10.1016/j.euroecorev.2020.103507 · Cited by 23
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Veeramani, C., & Saini, G. K. (2011) · Cited by 23
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Nabeshima, K., & Obashi, A. (2020) · Journal of the Japanese and International Economies · doi:10.1016/j.jjie.2020.101120 · Cited by 22
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“Since there are substantially higher marginal costs for approaching new customers in old markets (Arkolakis, 2010), and there are also fixed costs to be paid for exploring new markets (Helpman et al., 2008), all these higher costs might translate into higher prices.”
BackgroundState productivity growth in agriculture: catching-up and the business cycle
Ball, V. E., San-Juan-Mesonada, C., & Ulloa, C. A. (2013) · Journal of Productivity Analysis · doi:10.1007/s11123-013-0352-0 · Cited by 22
“A particular case in which this can happen is when we only consider export markets where we observe zero trade flows between specific pairs of countries (see Helpman, Melitz, and Rubinstein, 2008).”
BackgroundParticipation in export and Chinese firms’ capacity utilization
Tian, X.-L. (2016) · Journal of International Trade & Economic Development · doi:10.1080/09638199.2015.1128473 · Cited by 22
Dissecting the Trade Effects of Europe’s Economic Integration Agreements
Soete, S., & Hove, J. V. (2017) · Journal of Economic Integration · doi:10.11130/jei.2017.32.1.193 · Cited by 21
Intellectual property rights and the margins of international trade
Foster‐McGregor, N. (2012) · Journal of International Trade & Economic Development · doi:10.1080/09638199.2012.664556 · Cited by 21
“The approach of Helpman et al. (2008) has been criticised due to its heavy reliance on assumptions of normality and homoscedasticity (see Santos-Silva and Tenreyro 2006), while Martinez Zarzoso et al. (2007) find that the Poisson method proposed by Santos-Silva and Tenreyro (2006) suffers from a…”
BackgroundMethodInfluentialBuono, I. (2010) · SSRN Electronic Journal · doi:10.2139/ssrn.1523213 · Cited by 22
Product Space Analysis of the Exports of Brazil
Cruz, J. D. L., & Riker, D. A. (2012) · Cited by 21
New nonlinear estimators of the gravity equation
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Impacts of the belt and road initiative on China’s bilateral trade
Jing, W., & Tian, X. (2022) · Journal of the Asia Pacific Economy · doi:10.1080/13547860.2022.2042110 · Cited by 21
“Helpman, Melitz, and Rubinstein (2008) revealed the importance of considering the two trade margins (see also Eaton, Kortum, and Kramarz 2004; Volpe Martincus et al. 2010).”
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Gil‐Pareja, S., Llorca‐Vivero, R., & Martínez‐Serrano, J. A. (2015) · Open Economies Review · doi:10.1007/s11079-015-9385-5 · Cited by 23
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How different aid flows affect different trade flows: Evidence from Africa and its largest donors
Savin, I. V., Marson, M., & Sutormina, M. I. (2020) · Structural Change and Economic Dynamics · doi:10.1016/j.strueco.2020.08.004 · Cited by 21
Goldberg, P. K. (2015) · Edward Elgar Publishing eBooks · doi:10.4337/9781784716424 · Cited by 22
Chi, T., & Kilduff, P. D. F. (2010) · Journal of Fashion Marketing and Management · doi:10.1108/13612021011061915 · Cited by 21
The Emergence of Iran in the World Car Industry: An Estimation of its Export Potential
Abedini, J., & Péridy, N. (2009) · World Economy · doi:10.1111/j.1467-9701.2008.01153.x · Cited by 21
OECD imports: diversification of suppliers and quality search
Cadot, O., Carrère, C., & Strauss‐Kahn, V. (2013) · Review of World Economics · doi:10.1007/s10290-013-0172-3 · Cited by 23
Corporate taxes and intra-firm trade
Egger, P. H., & Seidel, T. (2013) · European Economic Review · doi:10.1016/j.euroecorev.2013.07.007 · Cited by 21
“…volume of bilateral intra-firm 14Notice that such an assumption is often considered to be innocuous in structural empirical work (see, for example, Helpman et al., 2008). imports at the sector level (classified according to the NAICS industry classification) are provided by the Bureau of Economic…”
BackgroundTrade Booms, Trade Busts, and Trade Costs
Jacks, D. S., Meissner, C. M., & Novy, D. (2009) · Journal of International Economics · doi:10.1016/j.jinteco.2010.10.008 · Cited by 123
“Helpman et al. (2008), and the heterogeneous firms model by Melitz and Ottaviano (2008) with a linear, non-CES demand structure.”
BackgroundThe Effect of Product Standards on Agricultural Exports from Developing Countries
Ferro, E., Wilson, J. S., & Otsuki, T. (2013) · World Bank, Washington, DC eBooks · doi:10.1596/1813-9450-6518 · Cited by 21
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InfluentialGravity trade model with firm heterogeneity and horizontal foreign direct investment
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“10 An alternative to the PPML estimation would be to follow Helpman et al. (2008), who propose using a form of sample selection estimation to solve the problem of zero trade flows being dropped.”
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“This concept was applied to the international economy by Tinbergen (1962) and further developed, among others, by Anderson (1979), Bergstrand (1985), Anderson and van Wincoop (2003) and Helpman et al. (2008).”
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5 Choosing the Best Model in the Presence of Zero Trade: A Fish Product Analysis
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“However with large datasets, the full maximum likelihood approach is computationally burdensome, and in that case, the Heckman two-step estimation might be considered as the best procedure (Helpman et al., 2008; Wooldridge, 2002).”
MethodMeasuring fixed costs for firms’ use of a free trade agreement: Threshold regression approach
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Evolution of Machinery Production Networks: Linkage of North America with East Asia
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The Effects of NAFTA/CUSFTA on Agricultural Trade Flows: An Empirical Investigation
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The Economics of Language Policy
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Schulze, C., Pamp, O., & Thurner, P. W. (2017) · International Studies Quarterly · doi:10.1093/isq/sqx031 · Cited by 19
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“8This feature of the data is particularly important in view of the prediction derived by Antràs and Helpman (2008), who show that, in a PRT world, the quality of contracting institutions governing investments by the HQ has the opposite effect on firm integration compared to contracting institutions…”
BackgroundMethodInfluentialHome country bias in international emissions trading: Evidence from the EU ETS
Hintermann, B., & Ludwig, M. (2022) · Resource and Energy Economics · doi:10.1016/j.reseneeco.2022.101336 · Cited by 19
“(16)The decomposition of trade flows into extensive and intensive margins builds on the seminal work of Helpman et al. (2008).”
BackgroundDo regional trade agreements affect agri‐food trade? Evidence from a meta‐analysis
Afesorgbor, S. K., Fiankor, D. D., & Demena, B. A. (2023) · Applied Economic Perspectives and Policy · doi:10.1002/aepp.13410 · Cited by 20
Is environmental efficiency trade inducing or trade hindering?
Doganay, S. M., Sayek, S., & Taşkın, F. (2014) · Energy Economics · doi:10.1016/j.eneco.2014.04.004 · Cited by 19
Import sourcing of Chinese cities: Order versus randomness
Head, K. C., Jing, R., & Ries, J. (2017) · Journal of International Economics · doi:10.1016/j.jinteco.2017.01.003 · Cited by 19
“In contrast to the hierarchy model where we retained the multiplicative functional forms of Helpman et al. (2008), analytical tractability in the random sourcing model is helped by assuming additive transport costs.”
BackgroundMethodResultInfluentialOffshoring and Home Country R&D
Karpaty, P., & Tingvall, P. G. (2014) · World Economy · doi:10.1111/twec.12226 · Cited by 19
“(B) Following Helpman et al. (2008) we include higher order terms of z to control for firm heterogeneity where z is defined as 1 ˆ ˆˆ ( ) ,z p n p is the predicted probability of positive R&D and n is Mill’s ratio.”
InfluentialRailroads and the Raj: The Economic Impact of Transportation Infrastructure.
Donaldson, D. (2008) · Cited by 19
Trade to aid: EU's temporary tariff waivers for flood-hit Pakistan
Cheong, J., Kwak, D. W., & Yuan, H. (2016) · Journal of Development Economics · doi:10.1016/j.jdeveco.2016.10.005 · Cited by 19
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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