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From Heavy-Tailed Micro to Macro: on the characterization of firm-level heterogeneity and its aggregation properties

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  • Dewitte, Ruben

Abstract

This paper emphasizes the importance of two sufficient statistics to characterize firm-level heterogeneity in the workhorse heterogeneous firms trade model: the Cumulative Distribution Function (CDF) and the mean of firm-level sales. Contradicting the strong focus on the CDF, a close fit to average sales proves to be critical for model performance. Moreover, this average varies largely across finite sample draws due to sales being heavy-tailed, providing evidence that individual firms can influence the aggregate economy. As a result, modeled aggregate trade elasticities and Gains From Trade are unlikely to materialize: they are biased in finite samples and underlying characterizations of firm-level heterogeneity are rejected by the data.

Suggested Citation

  • Dewitte, Ruben, 2020. "From Heavy-Tailed Micro to Macro: on the characterization of firm-level heterogeneity and its aggregation properties," MPRA Paper 103170, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:103170
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    File URL: https://mpra.ub.uni-muenchen.de/103170/1/MPRA_paper_103170.pdf
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    References listed on IDEAS

    as
    1. Peter J. Klenow & Sergii Meleshchuk & Martha Denisse Pierola & Andres Rodriguez-Clare, 2018. "The Intensive Margin in Trade," IMF Working Papers 2018/259, International Monetary Fund.
    2. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9j4i07 is not listed on IDEAS
    3. Erick Sager & Olga A. Timoshenko, 2019. "The double EMG distribution and trade elasticities," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 52(4), pages 1523-1557, November.
    4. di Giovanni, Julian & Levchenko, Andrei A. & Rancière, Romain, 2011. "Power laws in firm size and openness to trade: Measurement and implications," Journal of International Economics, Elsevier, vol. 85(1), pages 42-52, September.
    5. Vasco M. Carvalho & Basile Grassi, 2019. "Large Firm Dynamics and the Business Cycle," American Economic Review, American Economic Association, vol. 109(4), pages 1375-1425, April.
    6. 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.
    7. Keith Head & Thierry Mayer & Mathias Thoenig, 2014. "Welfare and Trade without Pareto," American Economic Review, American Economic Association, vol. 104(5), pages 310-316, May.
    8. Luckstead, Jeff & Devadoss, Stephen, 2017. "Pareto tails and lognormal body of US cities size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 573-578.
    9. Andrew B. Bernard & J. Bradford Jensen & Stephen J. Redding & Peter K. Schott, 2012. "The Empirics of Firm Heterogeneity and International Trade," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 283-313, July.
    10. Marc J. Melitz & Stephen J. Redding, 2015. "New Trade Models, New Welfare Implications," American Economic Review, American Economic Association, vol. 105(3), pages 1105-1146, March.
    11. Lucian Cernat, 2016. "Toward “Trade Policy Analysis 2.0”: From National Comparative Advantage to Firm-Level Trade Data," ADB Institute Series on Development Economics, in: Ganeshan Wignaraja (ed.), Production Networks and Enterprises in East Asia, edition 1, chapter 0, pages 21-31, Springer.
    12. Peter Neary & Monika MrázováMathieu Parenti, 2015. "Technology, Demand, And The Size Distribution Of Firms," Economics Series Working Papers 774, University of Oxford, Department of Economics.
    13. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    14. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    15. Marco Bee & Stefano Schiavo, 2018. "Powerless: gains from trade when firm productivity is not Pareto distributed," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 154(1), pages 15-45, February.
    16. Erick Sager & Olga A. Timoshenko, 2019. "The double EMG distribution and trade elasticities," Canadian Journal of Economics, Canadian Economics Association, vol. 52(4), pages 1523-1557, November.
    17. Jonathan Eaton & Samuel Kortum & Francis Kramarz, 2011. "An Anatomy of International Trade: Evidence From French Firms," Econometrica, Econometric Society, vol. 79(5), pages 1453-1498, September.
    18. Ruben Dewitte & Michel Dumont & Glenn Rayp & Peter Willemé, 2022. "Unobserved heterogeneity in the productivity distribution and gains from trade," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(3), pages 1566-1597, August.
    19. Andrew Atkeson & Ariel Tomás Burstein, 2010. "Innovation, Firm Dynamics, and International Trade," Journal of Political Economy, University of Chicago Press, vol. 118(3), pages 433-484, June.
    20. Hall, Peter & Yao, Qiwei, 2003. "Inference in ARCH and GARCH models with heavy-tailed errors," LSE Research Online Documents on Economics 5875, London School of Economics and Political Science, LSE Library.
    21. Taleb, Nassim Nicholas, 2019. "How much data do you need? An operational, pre-asymptotic metric for fat-tailedness," International Journal of Forecasting, Elsevier, vol. 35(2), pages 677-686.
    22. 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.
    23. repec:hal:spmain:info:hdl:2441/nki2gcedn93280ns6fslbhdnm is not listed on IDEAS
    24. Costas Arkolakis, 2016. "A Unified Theory of Firm Selection and Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 89-155.
    25. Cornea-Madeira, Adriana & Davidson, Russell, 2015. "A Parametric Bootstrap For Heavy-Tailed Distributions," Econometric Theory, Cambridge University Press, vol. 31(3), pages 449-470, June.
    26. Gabaix, Xavier & Ibragimov, Rustam, 2011. "Rank − 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 24-39.
    27. Costinot, Arnaud & Rodríguez-Clare, Andrés, 2014. "Trade Theory with Numbers: Quantifying the Consequences of Globalization," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 197-261, Elsevier.
    28. Peter Hall & Qiwei Yao, 2003. "Inference in Arch and Garch Models with Heavy--Tailed Errors," Econometrica, Econometric Society, vol. 71(1), pages 285-317, January.
    29. Igor Fedotenkov, 2014. "A note on the bootstrap method for testing the existence of finite moments," Statistica, Department of Statistics, University of Bologna, vol. 74(4), pages 447-453.
    30. Julian di Giovanni & Andrei A. Levchenko, 2012. "Country Size, International Trade, and Aggregate Fluctuations in Granular Economies," Journal of Political Economy, University of Chicago Press, vol. 120(6), pages 1083-1132.
    31. Abu Bakar, S.A. & Hamzah, N.A. & Maghsoudi, M. & Nadarajah, S., 2015. "Modeling loss data using composite models," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 146-154.
    32. Nigai, Sergey, 2017. "A tale of two tails: Productivity distribution and the gains from trade," Journal of International Economics, Elsevier, vol. 104(C), pages 44-62.
    33. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
    34. 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.
    35. Russell Davidson, 2012. "Statistical inference in the presence of heavy tails," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 31-53, February.
    36. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    37. Ioannides, Yannis & Skouras, Spyros, 2013. "US city size distribution: Robustly Pareto, but only in the tail," Journal of Urban Economics, Elsevier, vol. 73(1), pages 18-29.
    38. Igor Fedotenkov, 2013. "A bootstrap method to test for the existence of finite moments," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 25(2), pages 315-322, June.
    39. repec:hal:spmain:info:hdl:2441/5fjm1f1p0v93k9png4qo8ltnrf is not listed on IDEAS
    40. repec:hal:spmain:info:hdl:2441/2j87pv5ou185f980qgrpf9net0 is not listed on IDEAS
    41. 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.
    42. repec:hal:spmain:info:hdl:2441/6apm7lruv088iagm4rv2c33jtg is not listed on IDEAS
    43. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1103-1144.
    44. Gopinath, G. & Helpman, . & Rogoff, K. (ed.), 2014. "Handbook of International Economics," Handbook of International Economics, Elsevier, edition 1, volume 4, number 4.
    45. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," Post-Print hal-03579844, HAL.
    46. Jonathan Eaton & Samuel S. Kortum & Sebastian Sotelo, 2012. "International Trade: Linking Micro and Macro," NBER Working Papers 17864, National Bureau of Economic Research, Inc.
    47. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p2m9j4i07 is not listed on IDEAS
    48. Giuseppe Cavaliere & Iliyan Georgiev & A. M. Robert Taylor, 2013. "Wild Bootstrap of the Sample Mean in the Infinite Variance Case," Econometric Reviews, Taylor & Francis Journals, vol. 32(2), pages 204-219, February.
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    Cited by:

    1. Ruben Dewitte & Michel Dumont & Glenn Rayp & Peter Willemé, 2022. "Unobserved heterogeneity in the productivity distribution and gains from trade," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(3), pages 1566-1597, August.

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    More about this item

    Keywords

    Average productivity; firm size distribution; heavy-tailed Distributions; granularity; gains from trade;
    All these keywords.

    JEL classification:

    • F11 - International Economics - - Trade - - - Neoclassical Models of Trade
    • F12 - International Economics - - Trade - - - Models of Trade with Imperfect Competition and Scale Economies; Fragmentation
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

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