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Aggregation and the gravity equation

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  • Stephen J. Redding
  • David E. Weinstein

Abstract

One of the most successful empirical relationships in international trade is the gravity equation, which relates bilateral trade flows between an origin and destination to bilateral trade frictions, origin characteristics, and destination characteristics. A key decision for researchers in estimating this relationship is the level of aggregation, since the gravity equation is log linear, whereas aggregation involves summing the level rather than the log level of trade flows. In this paper, we derive an exact Jensen's inequality correction term for the gravity equation in a nested constant elasticity of substitution (CES) import demand system, such that a log-linear gravity equation holds exactly for each nest of this demand system. We use this result to decompose the effect of distance on bilateral trade in the aggregate gravity equation into the contribution of a number of different terms from sectoral gravity equations. We show that changes in sectoral composition make a quantitatively relevant contribution towards the aggregate effect of distance, particularly for more disaggregated definitions of sectors.

Suggested Citation

  • Stephen J. Redding & David E. Weinstein, 2019. "Aggregation and the gravity equation," CEP Discussion Papers dp1595, Centre for Economic Performance, LSE.
    • Handle: RePEc:cep:cepdps:dp1595
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    1. Stephan Heblich & Stephen J Redding & Daniel M Sturm, 2020. "The Making of the Modern Metropolis: Evidence from London," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(4), pages 2059-2133.
    2. Martin, Philippe & Rey, Helene, 2004. "Financial super-markets: size matters for asset trade," Journal of International Economics, Elsevier, vol. 64(2), pages 335-361, December.
    3. Bas, Maria & Mayer, Thierry & Thoenig, Mathias, 2017. "From micro to macro: Demand, supply, and heterogeneity in the trade elasticity," Journal of International Economics, Elsevier, vol. 108(C), pages 1-19.
    4. Krugman, Paul, 1980. "Scale Economies, Product Differentiation, and the Pattern of Trade," American Economic Review, American Economic Association, vol. 70(5), pages 950-959, December.
    5. Nelson Lind & Natalia Ramondo, 2023. "Trade with Correlation," American Economic Review, American Economic Association, vol. 113(2), pages 317-353, February.
    6. Gabriel M. Ahlfeldt & Stephen J. Redding & Daniel M. Sturm & Nikolaus Wolf, 2015. "The Economics of Density: Evidence From the Berlin Wall," Econometrica, Econometric Society, vol. 83, pages 2127-2189, November.
    7. Davis, Donald R. & Weinstein, David E., 1999. "Economic geography and regional production structure: An empirical investigation," European Economic Review, Elsevier, vol. 43(2), pages 379-407, February.
    8. Alan V. Deardorff, 2011. "Determinants of Bilateral Trade: Does Gravity Work in a Neoclassical World?," World Scientific Book Chapters, in: Robert M Stern (ed.), Comparative Advantage, Growth, And The Gains From Trade And Globalization A Festschrift in Honor of Alan V Deardorff, chapter 24, pages 267-293, World Scientific Publishing Co. Pte. Ltd..
    9. Combes, Pierre-Philippe & Lafourcade, Miren & Mayer, Thierry, 2005. "The trade-creating effects of business and social networks: evidence from France," Journal of International Economics, Elsevier, vol. 66(1), pages 1-29, May.
    10. Ferdinando Monte & Stephen J. Redding & Esteban Rossi-Hansberg, 2018. "Commuting, Migration, and Local Employment Elasticities," American Economic Review, American Economic Association, vol. 108(12), pages 3855-3890, December.
    11. Redding, Stephen & Venables, Anthony J., 2004. "Economic geography and international inequality," Journal of International Economics, Elsevier, vol. 62(1), pages 53-82, January.
    12. Costas Arkolakis & Svetlana Demidova & Peter J. Klenow & Andres Rodriguez-Clare, 2008. "Endogenous Variety and the Gains from Trade," American Economic Review, American Economic Association, vol. 98(2), pages 444-450, May.
    13. Costas Arkolakis & Arnaud Costinot & Andres Rodriguez-Clare, 2012. "New Trade Models, Same Old Gains?," American Economic Review, American Economic Association, vol. 102(1), pages 94-130, February.
    14. Robert C. Feenstra & James R. Markusen & Andrew K. Rose, 2001. "Using the gravity equation to differentiate among alternative theories of trade," Canadian Journal of Economics, Canadian Economics Association, vol. 34(2), pages 430-447, May.
    15. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(2), pages 441-487.
    16. repec:hal:spmain:info:hdl:2441/nki2gcedn93280ns6fslbhdnm is not listed on IDEAS
    17. James E. Anderson, 2011. "The Gravity Model," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 133-160, September.
    18. James E. Anderson & Eric van Wincoop, 2003. "Gravity with Gravitas: A Solution to the Border Puzzle," American Economic Review, American Economic Association, vol. 93(1), pages 170-192, March.
    19. Natalia Ramondo & Andrés Rodríguez-Clare & Milagro Saborío-Rodríguez, 2016. "Trade, Domestic Frictions, and Scale Effects," American Economic Review, American Economic Association, vol. 106(10), pages 3159-3184, October.
    20. Arnaud Costinot & Dave Donaldson & Ivana Komunjer, 2012. "What Goods Do Countries Trade? A Quantitative Exploration of Ricardo's Ideas," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 581-608.
    21. Berthelon, Matias & Freund, Caroline, 2008. "On the conservation of distance in international trade," Journal of International Economics, Elsevier, vol. 75(2), pages 310-320, July.
    22. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September.
    23. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, vol. 98(4), pages 1707-1721, September.
    24. Keith Head & John Ries, 2001. "Increasing Returns versus National Product Differentiation as an Explanation for the Pattern of U.S.-Canada Trade," American Economic Review, American Economic Association, vol. 91(4), pages 858-876, September.
    25. J. M. C. Santos Silva & Silvana Tenreyro, 2006. "The Log of Gravity," The Review of Economics and Statistics, MIT Press, vol. 88(4), pages 641-658, November.
    26. Combes, Pierre-Philippe & Lafourcade, Miren & Mayer, Thierry, 2005. "The trade-creating effects of business and social networks: evidence from France," Journal of International Economics, Elsevier, vol. 66(1), pages 1-29, May.
    27. repec:hal:spmain:info:hdl:2441/2j87pv5ou185f980qgrpf9net0 is not listed on IDEAS
    28. Marc J. Melitz, 2003. "The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity," Econometrica, Econometric Society, vol. 71(6), pages 1695-1725, November.
    29. repec:hal:spmain:info:hdl:2441/6apm7lruv088iagm4rv2c33jtg is not listed on IDEAS
    30. Gopinath, G. & Helpman, . & Rogoff, K. (ed.), 2014. "Handbook of International Economics," Handbook of International Economics, Elsevier, edition 1, volume 4, number 4.
    31. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," Post-Print hal-03579844, HAL.
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    Cited by:

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    3. Peter R. Herman, 2022. "A pragmatic approach to estimating nondiscriminatory non‐tariff trade costs," Review of International Economics, Wiley Blackwell, vol. 30(4), pages 1258-1287, September.
    4. Jareb, Colin & Nigai, Sergey, 2022. "Gravity models and the Law of Large Numbers," Economics Letters, Elsevier, vol. 221(C).
    5. Vandenbussche, Hylke & Aw-Roberts, Bee Yan & Lee, Yi, 2019. "The Importance of Consumer Taste in Trade," CEPR Discussion Papers 13614, C.E.P.R. Discussion Papers.
    6. Ingo Borchert & Mario Larch & Serge Shikher & Yoto V. Yotov, 2022. "Disaggregated gravity: Benchmark estimates and stylized facts from a new database," Review of International Economics, Wiley Blackwell, vol. 30(1), pages 113-136, February.
    7. Lionel Fontagné & Houssein Guimbard & Gianluca Orefice, 2020. "Product-Level Trade Elasticities: Worth Weighting For," Working Papers DT/2020/08, DIAL (Développement, Institutions et Mondialisation).
    8. Zheng, Han, 2022. "Heterogeneous Internal Trade Cost and Its Implications in Trade," Discussion paper series HIAS-E-117, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    9. Gabriel E. Kreindler & Yuhei Miyauchi, 2019. "Measuring Commuting and Economic Activity inside Cities with Cell Phone Records," Boston University - Department of Economics - Working Papers Series WP2020-006, Boston University - Department of Economics, revised Apr 2020.

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    More about this item

    Keywords

    gravity equation; trade; aggregation;
    All these keywords.

    JEL classification:

    • F10 - International Economics - - Trade - - - General
    • F14 - International Economics - - Trade - - - Empirical Studies of Trade
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation

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