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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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Salim, R. A., Kabir, M. M., & Al-Mawali, N. (2011) · Journal of Economic Integration · doi:10.11130/jei.2011.26.2.217 · Cited by 18
“Helpman et al. (2008) reveal that the influence of FTA is positive and significant in bilateral trade flow of 158 countries for 1985 in reduced and full sample, both for benchmark model and Heckman selection model.”
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“(2001), Şentürk and Erdem (2008), and Helpman et al. (2008). Moreover, the results from previous studies are not homogenous.”
ResultKareem, F. O., Martínez‐Zarzoso, I., & Brümmer, B. (2016) · RePEc: Research Papers in Economics · doi:10.22004/ag.econ.230588 · Cited by 18
“Helpman et al. (2008) argue that “by disregarding countries that do not trade with each other, these studies give up important information contained in the data” (Helpman et al. 2008 p442), and that symmetric relationship imposed by the standard gravity model biases the estimates as it is…”
InfluentialTechnology and Production Fragmentation: Domestic versus Foreign SourcingPreprint
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“What insights are generated within sections 2.2 and 2.3 that could not also be generated by the (possibly augmented) gravity model?”
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“where I MR is the inverse mills ratio (IMR) obtained from (17), and P̂R is the predicted probablity of bilateral trade corrected for the extensive margin following Helpman et al. (2008). Thus, in equation (18), bias due to self-selection of positive trade is controlled by I MRi j t and bias due to the factors that aff…”
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Lin, B., & Liu, Y. (2025) · Energy Policy · doi:10.1016/j.enpol.2025.114687 · Cited by 15
A structural quantitative analysis of services trade de-liberalization
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Jochmans, K., & Verardi, V. (2022) · Journal of Applied Econometrics · doi:10.1002/jae.2932 · Cited by 15
The impact of host country institutional quality on OFDI: Evidence from China
Zhang, Y., Li, Y., & Zhang, K. (2024) · Journal of International Trade & Economic Development · doi:10.1080/09638199.2024.2320156 · Cited by 15
“The binary margin structure of trade growth has been receiving attention from scholars since the inception of New trade theory (Helpman, Melitz, and Rubinstein 2008).”
Africa and the Clean Development Mechanism: What Determines Project Investments?
Röttgers, D., & Grote, U. (2014) · World Development · doi:10.1016/j.worlddev.2014.05.009 · Cited by 15
Honoré, B. E., & Kesina, M. (2015) · Journal of Business and Economic Statistics · doi:10.1080/07350015.2015.1123635 · Cited by 15
“This particular mixed normal distribution was chosen because it was also used in the article by Honoré and Powell (1994). The constant, c, is set to 4.”
BackgroundMethodInfluentialMarket size and entry in international trade: Product versus firm fixed costs
Steingress, W. (2019) · Review of International Economics · doi:10.1111/roie.12427 · Cited by 15
“…the relationship between market size and firm entry; for single-product firms, see the seminal paper by Campbell and Hopenhayn (2005), as well as Helpman et al. (2008), Melitz and Ottaviano (2008), Arkolakis (2010), Eaton et al. (2011); and for multi-product firms, see Arkolakis and Muendler…”
Baier, S. L., Bergstrand, J. H., & Bruno, J. P. (2019) · World Economy · doi:10.1111/twec.12870 · Cited by 15
“As noted in Helpman, Melitz, and Rubinstein (2008), or HMR, and Egger, Larch, Staub, and Winkelmann (2011), such zeros can be associated with selection bias ("selection into exporting").”
International trade, non-tariff measures and climate change: insights from Port wine exports
Macedo, A., Gouveia, S., Rebelo, J. F., Santos, J. A., & Fraga, H. (2020) · Journal of Economic Studies · doi:10.1108/jes-04-2020-0161 · Cited by 15
“The model was at first rejected for lack of theoretical foundations, but over the time both demand (Anderson, 1979; Anderson and VanWincoop, 2003; Baier and Bergstrand, 2001; Bergstrand, 1985, 1990) and supply-side (Eaton and Kortum, 2002; Chaney, 2008; Helpman et al., 2008; Melitz and Ottaviano, 2008) derivations est…”
BackgroundInfluence of food safety standards on trade: Evidence from the pistachio sector
Rabadán, A., & Triguero, Á. (2020) · Agribusiness · doi:10.1002/agr.21683 · Cited by 15
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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