Increasing Marginal Costs, Firm Heterogeneity, and the Gains from “Deep” International Trade Agreements

Bergstrand, Jeffrey H. and Cray, Stephen R. and Gervais, Antoine (2022): Increasing Marginal Costs, Firm Heterogeneity, and the Gains from “Deep” International Trade Agreements.

Abstract

Two parameters are central to several modern quantitative models of bilateral international trade flows: the elasticity of substitution in consumption (σ) and the inverse index of heterogeneity of firms’ productivities (θ). However, structural parameter estimation applications using the seminal Feenstra econometric methodology typically focus on estimates of only σ and a bilateral export supply elasticity – which we will term γ. Separately, modern trade agreements are increasingly “deep,” meaning they reduce fixed trade costs alongside variable trade costs (such as tariffs). Although Melitz models of international trade recognize both trade costs theoretically, very little is known quantitatively about their relative impacts on trade and welfare. In this paper, we offer three contributions. First, in the spirit of Arkolakis (2010), we extend the canonical Melitz model of trade to allow for increasing marginal market-penetration costs, alongside fixed marketing costs, to show theoretically the importance of accounting for increasing marginal costs (via γ) – in the presence of firm heterogeneity – in understanding the relative impacts on trade, extensive margins, intensive margins, and welfare of reducing fixed trade costs and variable trade costs. Second, we provide a microeconomic foundation for estimating all three parameters using the Feenstra econometric methodology alongside a gravity equation. Third, we demonstrate the importance of increasing marginal costs using two counterfactual exercises. One illustrative quantitative implication for U.S. trade policy is that, under (empirically rejected) constant marginal costs, fixed trade costs would have to be reduced by 57 percent for a welfare-equivalent reduction in variable trade costs of 3 percent; by contrast, under (empirically supported) increasing marginal costs, fixed trade costs would have to be reduced by only 14 percent.

• Item Type: MPRA Paper
• Language: English
• Keywords: International trade, deep trade agreements, Melitz models, increasing marginal costs, gravity equations
• Subjects: F - International Economics > F1 - Trade

References

Alvarez, F. and R. Lucas (2007). General equilibrium analysis of the eaton-kortum model of international trade. Journal of Monetary Economics 54(6), 1726–1768. Anderson, J. (1979). A theoretical foundation for the gravity equation. American Economic Review 69(1), 106–116. Anderson, J. (2011). The gravity model. Annual Review of Economics 3, 133–160. Anderson, J. and E. van Wincoop (2003). Gravity with gravitas: A solution to the border puzzle. American Economic Review 93(1), 170–192. Anderson, J. and E. van Wincoop (2004). Trade costs. Journal of Economic Literature 42 (3), 691–751. Arkolakis, C. (2010). Market penetration costs and the new consumers margin in international trade. Journal of Political Economy 118(6), 1151–1199. Arkolakis, C., A. Costinot, and A. Rodriguez-Clare (2012). New trade models, same old gains? American Economic Review 102(1), 94–130. Arkolakis, C., S. Ganapati, and M.-A. Muendler (2021). The extensive margin of exporting products: A firm-level analysis. American Economic Journal: Macroeconomics 13(4), 182–245. Bagwell, K. (2007). The economic analysis of advertising. In M. Armstrong and R. Porter (Eds.), Handbook of Industrial Organization, pp. 1701–1844. Amsterdam, Netherlands: North Holland. Baier, S. and J. Bergstrand (2007). Do free trade agreements actually increase members’ international trade? Journal of International Economics 71(1), 72–95. Baier, S., J. Bergstrand, and M. Clance (2018). Heterogeneous effects of economic integration agreements. Journal of Development Economics 135, 587–608. Baier, S., J. Bergstrand, P. Egger, and P. McLaughlin (2008). Do economic integration agreements actually work? issues in understanding the causes and consequences of the growth of regionalism. The World Economy 31(4), 461–497. Baier, S., J. Bergstrand, and M. Feng (2014). Economic integration agreements and the margins of international trade. Journal of International Economics 93(2), 339–350. 48 Baier, S., A. Kerr, and Y. Yotov (2017). Gravity, distance, and international trade. In W. Wesley and B. Blonigen (Eds.), Handbook of International Trade and Transportation. Edward Elgar Publishing. Baier, S. and N. Regmi (2020). Using machine learning to capture heterogeneity in trade agreements and its effect on trade flows. Working Paper. Balisteri, E., R. Hillberry, and T. Rutherford (2011). Structural estimation and solution of in- ternational trade models with heterogeneous firms. Journal of International Economics 83, 95–108. Bartelme, D., A. Costinot, D. Donaldson, and A. Rodriguez-Clare (2019). The textbook case for industrial policy: Theory meets data. Working Paper. Berden, K., J. Francois, S. Tamminen, M. Thelle, and P. Wymenga (2010). Non-Tariff Measures in EU-US Trade and Investment. The Netherlands: ECORYS. Bergstrand, J. (1985). The gravity equation in international trade: Some microeconomic foundations and empirical evidence. Review of Economics and Statistics 67(3). Bernard, A., S. Redding, and P. Schott (2011). Multiproduct firms and trade liberalization. Quarterly Journal of Economics 126, 1271–1318. Breinlich, H., V. Corradi, N. Rocha, M. Ruta, J. Silva, and T. Zylkin (2021). Machine learning in international trade research: Evaluating the impact of trade agreements. Working Paper. Broda, C., N. Limao, and D. Weinstein (2008). Optinmal tariffs and market power: The evidence. American Economic Review 98(5), 2032–2065. Broda, C. and D. Weinstein (2006). Globalization and the gains from variety. Quarterly Journal of Economics 121(2), 541–585. Chaney, T. (2008). Distorted gravity: The intensive and extensive margins of international trade. American Economic Review 98(4), 1707–1721. Costinot, A. and A. Rodriguez-Clare (2014). Trade theory with numbers. In G. Gopinath, E. Helpman, and K. Rogoff (Eds.), Handbook of Interantional Economics, Volume 4. Amsterdam: Elsevier. Crowley, M., L. Han, and T. Prayer (2020). The value of deep trade agreements in the presence of pricing-to-market. Working Paper. 49

Dai, M., M. Muitra, and M. Yu (2016). Unexceptional exporter performance in China? The role of processing trade. Journal of Development Economics 121, 177–189. Dixon, P., M. Jerie, and M. Rimmer (2016). Modern trade theory for CGE modelling: The Armington, Krugman and Melitz models. Journal of Global Economic Analysis 1(1), 1–110. Eaton, J. and S. Kortum (2002). Technology, geography and trade. Econometrica 70(5). Eaton, J., S. Kortum, and F. Kramarz (2011). An anatomy of international trade: Evidence from french firms. Econometrica 79(5), 1453–1498. Fajgelbaum, P. D., O. K. Goldberg, P. J. Kennedy, and A. K. Khandelwal (2020). The return of protectionism. Quarterly Journal of Economics 135(1), 1–55. Farrokhi, F. and A. Soderbery (2020). Trade elasticities in general equilibrium. Working Paper. Feenstra, R. (1994). New product varieties and the measurement of international prices. American Economic Review 84(1), 157–177. Feenstra, R. (2010). Product Variety and the Gains from International Trade. Cambridge, MA: MIT Press. Feenstra, R. (2016). Advanced International Trade: Theory and Evidence, Second Edition. Princeton, New Jersey: Princeton University Press. Feenstra, R. and J. Romalis (2014). International prices and endogenous quality. Quarterly Journal of Economics 129(2), 477–527. Feenstra, R. C., , P. Luck, M. Obstfeld, and K. N. Russ (2018). In search of the Armington elasticity. Review of Economics and Statistics 100(1), 135–150. Feenstra, R. C. and D. E. Weinstein (2017). Globalization, markups, and U.S. welfare. Journal of Political Economy 125(4), 1040–1074. Flach, L. and F. Unger (2022). Quality and gravity in international trade. Journal of International Economics 137. Fontagne, L., N. Rocha, M. Ruta, and G. Santoni (2022). The economic impact of deep trade agreements. CESifo Working Paper (9529). Goldberg, P. K. and N. Pavcnik (2016). The effects of trade policy. In K. Bagwell and R. Staiger (Eds.), The Handbook of Commercial Policy. Elsevier, Amsterdam, Volume 1, pp. 161–206. Elsevier. 50

Grossman, G., P. McCalman, and R. Staiger (2021). The new economics of trade agreements: From trade liberalization to regulatory convergence? Econometrica 89(1). Head, K. and T. Mayer (2014). Gravity equations: Workhorse, toolkit, and cookbook. In G. Gopinath, E. Helpman, and K. Rogoff (Eds.), Handbook of Interantional Economics, Volume 4. Amsterdam: Elsevier. Hillberry, R. and D. Hummels (2013). Trade elasticity parameters for a computable general equilibrium model. In P. B. Dixon and D. W. Jorgenson (Eds.), Handbook of Computable General Equiilibrium Modeling, pp. 1213–1269. Amsterdam: Elsevier. Hofmann, C., A. Osnago, and M. Ruta (2017). Horizontal depth: A new database on the content of preferential trade agreements. World Bank Working Paper 7981. Horn, H., P. Mavroidis, and A. Sapir (2010). Beyond the wto? an anatomy of eu and us preferential trade agreements. The World Economy 33(11), 1565–1588. Hottman, C., S. Redding, and D. Weinstein (2016). Quantifying the sources of firm hetero- geneity. Quarterly Journal of Economics 131(3), 1291–1364. Jones, J. P. (1995). New Proof Tat Advertising Triggers Sales. New York, NY: Lexington. Kohl, T., S. Brakman, and H. Garretsen (2016). Do trade agreements stimulate international trade differently? evidence from 296 trade agreements. The World Economy 39 (1), 97–131. Krugman, P. (1980). Scale economies, product differentiation, and the pattern of trade. American Economic Review 70(5), 950–959. Kucheryavyy, K., G. Lyn, and A. Rodriguez-Clare (2019). Grounded by gravity: A well- behaved trade model with industry-level economies of scale. unpublished manuscript. Lashkaripour, A. and V. Lugovskyy (2019). Scale economies and the structure of trade and industrial policy. unpublished manuscript. Lu, D. (2010). Exceptional exporter performance? Evidence from Chinese manufacturing firms. Job Market Paper. Mas-Colell, A., M. Whinston, and J. Green (1995). Microeconomic Theory. Oxford University Press. Mattoo, A., N. Rocha, and M. Ruta (2020). The evolution of deep trade agreements. In A. Mattoo and N. Rocha (Eds.), Handbook of Deep Trade Agreements. World Bank. 51

Melitz, M. (2003). The impact of trade on intra-industry reallocations and aggregate industry productivity. Econometrica 71(6), 1695–1725. Norberg, H. (2015). TTIP is not your father’s free trade agreement: It has potential to benefit all. CATO Online Forum. Ossa, R. (2016). Quantitative models of commerical policy. In K. Bagwell and R. Staiger (Eds.), Handbook of Commercial Policy, Volume 1A, pp. 207–259. Amsterdam, The Netherlands: Elsevier. Redding, S. (2011). Theories of heterogeneous firms. Annual Review of Economics 3. Saunders, J. (1987). The specification of aggregate market models. European Journal of Marketing 21, 5–47. Simonovska, J. and J. Waugh (1980). The shape of the advertising response function. Journal of Advertising Research 20, 767–784. Soderbery, A. (2015). Estimating import supply and demand elasticities: Analysis and implications. Journal of International Economics 96, 1–17. Soderbery, A. (2018). Trade elasticities, heterogeneity, and optimal tariffs. Journal of International Economics 114, 44–62. Sutton, J. (1991). Sunk Costs and Market Structure. Cambridge, MA: MIT Press. Trefler, D. (1993). Trade liberalization and the theory of endogeneous protection: An econometric study of u.s. import policy. Journal of Political Economy 101(1), 138–160. U.S. Intl. Trade Commission (2019). U.S.-Mexico-Canada Trade Agreement: Likely Impact on the U.S. Economy and on Specific Industry. Washington, DC: USITC. Vannoorenberghe, G. (2012). Firm-level volatility and exports. Journal of International Economics 86(1), 57–67. WorldBank (2020). Doing Business. Washington, DC: World Bank. Zhai, F. (2008). Armington meets Melitz: Introducing firm heterogeneity in a global CGE model of trade. Journal of Economic Integration 23(3), 575–604.