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Firm Heterogeneity, Home Market Effect, and Gravity Equation in an Oligopoly

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Abstract

Developing a two-country oligopoly model with firm heterogeneity, this paper examines the relationship among market size, the Home Market Effect, and the gravity equation. We show that in the long-run with free entry, the Home Market Effect holds, namely, more firms locate in the large-sized country. This leads the large-sized country to be a net exporter of the oligopoly good. In the short-run with restricted entry, the Home Market Effect no longer holds and the large-sized country becomes a net importer of the oligopoly good. These results suggest that the theoretical predictions of Feenstra et al. (Can J Econ 34(2):430–447, 2001) survive firm heterogeneity.

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Data Availibility

The unpublished appendix is available upon request from the author.

Notes

  1. A variety of surveys on trade and firm heterogeneity are available. See, for example, Bernard et al. (2007, 2012, 2018), Melitz and Redding (2014), and Bonfiglioli et al. (2022).

  2. Gabaix (2011) and Di Giovanni and Levchenko (2012) define granularity as the phenomenon that idiosyncratic shocks to large firms generate nontrivial aggregate shocks. Table 1 of Gaubert and Itskhoki (2021, p. 880) shows that ‘a 10 percentage point greater top three sales share in the domestic market is associated with a 9% (log points) increase in aggregate sectoral exports.’

  3. For example, see Head and Mayer (2014), Feenstra (2016), and Yotov et al. (2016) for a comprehensive review of gravity equations.

  4. Head and Spencer (2017) show that the share of oligopoly models in the trade literature has declined over the last forty years.

  5. The introductory section in Breinlich et al. (2023) provides a comprehensive survey on gravity equations in an oligopoly model.

  6. The main purpose of Atkeson and Burstein (2008) is to show the deviations of prices from purchasing power parity, and that of Edmond et al. (2015) is to quantify gains from trade.

  7. The reader familiar with Melitz (2003) and Melitz and Ottaviano (2008) can skip this subsection.

  8. Note that the firm must pay the entry cost f even if it shuts down.

  9. Throughout this paper, we ignore the integer constraint. While several predecessors propose to incorporate this constraint, we assume away it for analytical convenience. We provide further comments in the concluding section.

  10. Although \(n_E\) and \(n_E^*\) are a continuous variable, we continue to use the terminology ‘number’ to avoid unnecessary confusion.

  11. As Section 4 discusses, if the utility function is quadratic, the same conclusion holds only if Home and Foreign have a sufficiently close market size.

  12. Do not confuse \(N^H\) and \(N^F\) with \(n^H+n^F\) and \(n^{H*}+n^{F*}\), namely, the number of varieties each country’s consumers enjoy.

  13. We leave technical details in the unpublished appendix.

  14. The same is true of the monopolistic competition model of Melitz and Ottaviano (2008).

  15. We will sometimes use terminologies ‘large’ (resp. ‘small’) firms and ‘oligopolistic’ (resp. ‘monopolistically competitive’) firms interchangeably.

  16. This subsection and the associated appendix owe to the referee’s suggestion.

References

  • Alfaro M, Warzynski F (2021) Trade liberalization with granular firms. Econ Model 105(C)

  • Amiti M, Itskhoki O, Konings J (2014) Importers, exporters and exchange rate disconnect. Am Econ Rev 104:1942–1978

    Article  Google Scholar 

  • Atkeson A, Burstein A (2008) Pricing-to-market, trade costs, and international relative prices. Am Econ Rev 98(5):1998–2031

    Article  Google Scholar 

  • Baldwin J, Gu W (2009) The impact of trade on plant scale, production-run length and diversification. In: Dunne T, Jensen JB, Roberts MJ (eds) Producer dynamics: new evidence from micro data. University of Chicago Press, Chicago, pp 557–592

    Chapter  Google Scholar 

  • Baldwin R, Forslid R, Martin P, Ottaviano GIP (2003) Economic geography and public policy. Princeton University Press, Princeton

    Google Scholar 

  • Bekkers E, Francois J (2013) Trade and industrial structure with large firms and heterogeneity. Eur Econ Rev 60:69–90

    Article  Google Scholar 

  • Bernard AB, Jensen JB (1995) Exporters, jobs, and wages in U.S. manufacturing: 1976–1987. Brookings Papers on Economic Activity 26:67–119

    Article  Google Scholar 

  • Bernard AB, Jensen JB, Redding SJ, Schott PK (2007) Firms in international trade. J Econ Perspect 21(3):105–130

    Article  Google Scholar 

  • Bernard AB, Jensen JB, Redding SJ, Schott PK (2012) The empirics of firm heterogeneity and international trade. Annu Rev Econom 4(1):283–313

    Article  Google Scholar 

  • Bernard AB, Jensen JB, Redding SJ, Schott PK (2018) Global firms. J ECON LIT 56(2):565–619

    Article  Google Scholar 

  • Bonfiglioli A, Crino R, Gancia G (2022) International trade with heterogeneous firms: theory and evidence. Oxford Research Encyclopedia of Economics and Finance

  • Brander JA (1981) Intra-industry trade in identical commodities. J Int Econ 11(1):1–14

    Article  Google Scholar 

  • Brander JA, Krugman PR (1983) A ‘reciprocal dumping’ model of international trade. J Int Econ 15(3–4):313–321

    Article  Google Scholar 

  • Breinlich H, Fadinger H, Nocke V, Schutz N (2023) ‘Gravity with granularity. CEP Discussion Papers dp1752, Centre for Economic Performance, LSE

  • Di Giovanni J, Levchenko A (2012) Country size, international trade, and aggregate fluctuations in granular economies. J Political Econ 120:1083–1132

    Article  Google Scholar 

  • Edmond C, Midrigan V, Xu DY (2015) Competition, markups, and the gains from international trade. Am Econ Rev 105(10):3183–3221

    Article  Google Scholar 

  • Feenstra RC (2016) Advanced international trade: theory and evidence, 2nd edn. Princeton University Press, Princeton

    Google Scholar 

  • Feenstra RC, Markusen JR, Rose AK (2001) Using the gravity equation to differentiate among alternative theories of trade. Can J Econ 34(2):430–447

    Article  Google Scholar 

  • Freund C, Pierola MD (2015) Export superstars. Rev Econ Stat 97(5):1023–1032

    Article  Google Scholar 

  • Gabaix X (2011) The granular origins of aggregate fluctuations. Econometrica 79:733–772

    Article  Google Scholar 

  • Gaubert C, Itskhoki O (2021) Granular comparative advantage. J Political Econ 129(3):871–939

    Article  Google Scholar 

  • Graziano AG (2020) Trade policy and industrial concentration, Ph.D. Dissertation, University of Maryland

  • Graziano AG (2022) International trade, industrial concentration, and welfare. Mimeo

  • Head K, Mayer T (2014) Gravity equations: workhorse, toolkit, and cookbook. In: Gopinath G, Helpman E, Rogoff K (eds) Handbook of international economics, vol 4. Elsevier, Amsterdam, pp 131–195

    Google Scholar 

  • Head K, Spencer BJ (2017) Oligopoly in international trade: rise, fall and resurgence. Can J Econ 50(5):1414–1444

    Article  Google Scholar 

  • Heid B, Stähler F (2024) Structural gravity and the gains from trade under imperfect competition: quantifying the effects of the European single market. Econ Model 131:106604

    Article  Google Scholar 

  • Impullitti G, Licandro O, Rendahl P (2022) Technology, market structure and the gains from trade. J Int Econ 135:103557

    Article  Google Scholar 

  • Krugman PR (1980) Scale economies, product differentiation, and the pattern of trade. Am Econ Rev 70(5):950–959

    Google Scholar 

  • Long NV, Raff H, Stähler F (2011) Innovation and trade with heterogeneous firms. J Int Econ 84(2):149–159

    Article  Google Scholar 

  • Mayer T, Ottaviano GIP (2008) The happy few: the internationalisation of European firms. Intereconomics 43(3):135–148

    Article  Google Scholar 

  • Melitz MJ (2003) The impact of trade on intra-industry Reallocations and aggregate industry productivity. Econometrica 71(6):1695–1725

    Article  Google Scholar 

  • Melitz MJ, Ottaviano GIP (2008) Market size, trade, and productivity. Rev Econ Stud 75(1):295–316

    Article  Google Scholar 

  • Melitz MJ, Redding SJ (2014) Heterogeneous firms and trade. In: Gopinath G, Helpman E, Rogoff K (eds) Handbook of international economics, vol 4. Elsevier, Amsterdam, pp 1–54

    Google Scholar 

  • Neary JP (2010) Two and a half theories of trade. World Econ 33(1):1–19

    Article  Google Scholar 

  • Parenti M (2018) Large and small firms in a global market: David vs. Goliath. J Int Econ 110(C): 103-118

  • Shimomura K, Thisse J (2012) Competition among the big and the small. RAND J Economics 43(2):329–347

    Article  Google Scholar 

  • Yotov YV, Piermartini R, Monteiro JA, Larch M (2016) An advanced guide to trade policy analysis: the structural gravity model. World Trade Organization

  • Zhou H (2010) Oligopolistic competition, firm heterogeneity, and the impact of international trade. East Econ J 36:107–119

    Article  Google Scholar 

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Acknowledgements

I thank an anonymous referee and the editor for useful comments and suggestions. Any remaining error is my own.

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  1. School of Economics, Kwansei Gakuin University, Uegahara 1-1-155, Nishinomiya, Hyogo, 662-8501, Japan

    Kenji Fujiwara

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Correspondence to Kenji Fujiwara.

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I thank an anonymous referee for useful comments and suggestions. Any remaining error is my own.

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Fujiwara, K. Firm Heterogeneity, Home Market Effect, and Gravity Equation in an Oligopoly. Open Econ Rev (2024). https://doi.org/10.1007/s11079-024-09760-x

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