IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/102711.html
   My bibliography  Save this paper

Unobserved Heterogeneity in the Productivity Distribution and Gains From Trade

Author

Listed:
  • Dewitte, Ruben
  • Dumont, Michel
  • Rayp, Glenn
  • Willemé, Peter

Abstract

A correct parametric approximation of the productivity distribution is essential to calculate Gains From Trade (GFT) in heterogeneous firms models. This paper argues that heterogeneity in productivity is best captured by Finite Mixture Models (FMMs). FMMs build on the existence of unobserved subpopulations in the data. As such, they are generally consistent with models of firm dynamics differing between groups of firms and allow for a very flexible distribution fit. We find FMMs to increase this fit by more than 70% compared to currently considered distributions. A GFT exercise with Portuguese data reveals that only FMMs approximate the ‘true gains’ reasonably well.

Suggested Citation

  • Dewitte, Ruben & Dumont, Michel & Rayp, Glenn & Willemé, Peter, 2020. "Unobserved Heterogeneity in the Productivity Distribution and Gains From Trade," MPRA Paper 102711, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:102711
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/102711/1/MPRA_paper_102711.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Bee Yan Aw & Mark J. Roberts & Daniel Yi Xu, 2011. "R&D Investment, Exporting, and Productivity Dynamics," American Economic Review, American Economic Association, vol. 101(4), pages 1312-1344, June.
    2. 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.
    3. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9j4i07 is not listed on IDEAS
    4. 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.
    5. Beard, T. Randolph & Caudill, Steven B. & Gropper, Daniel M., 1997. "The diffusion of production processes in the U.S. banking industry: A finite mixture approach," Journal of Banking & Finance, Elsevier, vol. 21(5), pages 721-740, May.
    6. Andrew B. Bernard & Stephen J. Redding & Peter K. Schott, 2009. "Products and Productivity," Scandinavian Journal of Economics, Wiley Blackwell, vol. 111(4), pages 681-709, December.
    7. Jan De Loecker, 2011. "Product Differentiation, Multiproduct Firms, and Estimating the Impact of Trade Liberalization on Productivity," Econometrica, Econometric Society, vol. 79(5), pages 1407-1451, September.
    8. Paolo Angelini & Andrea Generale, 2008. "On the Evolution of Firm Size Distributions," American Economic Review, American Economic Association, vol. 98(1), pages 426-438, March.
    9. 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.
    10. 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.
    11. 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.
    12. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    13. Feenstra, Robert C., 2018. "Restoring the product variety and pro-competitive gains from trade with heterogeneous firms and bounded productivity," Journal of International Economics, Elsevier, vol. 110(C), pages 16-27.
    14. Jan De Loecker, 2013. "Detecting Learning by Exporting," American Economic Journal: Microeconomics, American Economic Association, vol. 5(3), pages 1-21, August.
    15. Lorenzo Caliendo & Giordano Mion & Luca David Opromolla & Esteban Rossi-Hansberg, 2020. "Productivity and Organization in Portuguese Firms," Journal of Political Economy, University of Chicago Press, vol. 128(11), pages 4211-4257.
    16. 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.
    17. 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.
    18. Kwong, Hok Shing & Nadarajah, Saralees, 2019. "A note on “Pareto tails and lognormal body of US cities size distribution”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 55-62.
    19. 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.
    20. 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.
    21. Luís M B Cabral & José Mata, 2003. "On the Evolution of the Firm Size Distribution: Facts and Theory," American Economic Review, American Economic Association, vol. 93(4), pages 1075-1090, September.
    22. Gian Luca Clementi & Hugo A. Hopenhayn, 2006. "A Theory of Financing Constraints and Firm Dynamics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(1), pages 229-265.
    23. Rasmus Lentz & Dale T. Mortensen, 2008. "An Empirical Model of Growth Through Product Innovation," Econometrica, Econometric Society, vol. 76(6), pages 1317-1373, November.
    24. Thomas F. Cooley & Vincenzo Quadrini, 2001. "Financial Markets and Firm Dynamics," American Economic Review, American Economic Association, vol. 91(5), pages 1286-1310, December.
    25. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    26. Dias, Daniel A. & Robalo Marques, Carlos & Richmond, Christine, 2016. "Misallocation and productivity in the lead up to the Eurozone crisis," Journal of Macroeconomics, Elsevier, vol. 49(C), pages 46-70.
    27. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    28. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    29. 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.
    30. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Establishment Size Dynamics in the Aggregate Economy," American Economic Review, American Economic Association, vol. 97(5), pages 1639-1666, December.
    31. Kasahara, Hiroyuki & Rodrigue, Joel, 2008. "Does the use of imported intermediates increase productivity? Plant-level evidence," Journal of Development Economics, Elsevier, vol. 87(1), pages 106-118, August.
    32. 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.
    33. Caroline Freund & Martha Denisse Pierola, 2015. "Export Superstars," The Review of Economics and Statistics, MIT Press, vol. 97(5), pages 1023-1032, December.
    34. William J. Reed, 2002. "On the Rank‐Size Distribution for Human Settlements," Journal of Regional Science, Wiley Blackwell, vol. 42(1), pages 1-17, February.
    35. Bloom, Nicholas & Van Reenen, John, 2011. "Human Resource Management and Productivity," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 19, pages 1697-1767, Elsevier.
    36. Mihir Desai & Paul Gompers & Josh Lerner, 2003. "Institutions, Capital Constraints and Entrepreneurial Firm Dynamics: Evidence from Europe," NBER Working Papers 10165, National Bureau of Economic Research, Inc.
    37. 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.
    38. 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.
    39. Lorenzo Caliendo & Esteban Rossi-Hansberg, 2012. "The Impact of Trade on Organization and Productivity," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1393-1467.
    40. 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.
    41. repec:hal:spmain:info:hdl:2441/nki2gcedn93280ns6fslbhdnm is not listed on IDEAS
    42. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    43. 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.
    44. Amit Gandhi & Salvador Navarro & David A. Rivers, 2020. "On the Identification of Gross Output Production Functions," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 2973-3016.
    45. Fonseca, Tiago & Lima, Francisco & Pereira, Sonia C., 2018. "Understanding productivity dynamics: A task taxonomy approach," Research Policy, Elsevier, vol. 47(1), pages 289-304.
    46. Tor Jakob Klette & Samuel Kortum, 2004. "Innovating Firms and Aggregate Innovation," Journal of Political Economy, University of Chicago Press, vol. 112(5), pages 986-1018, October.
    47. 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.
    48. Greene, William, 2005. "Reconsidering heterogeneity in panel data estimators of the stochastic frontier model," Journal of Econometrics, Elsevier, vol. 126(2), pages 269-303, June.
    49. 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.
    50. 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.
    51. 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.
    52. Rui Albuquerque & Hugo A. Hopenhayn, 2004. "Optimal Lending Contracts and Firm Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(2), pages 285-315.
    53. 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.
    54. Carlos Carreira & Paulino Teixeira, 2016. "Entry and exit in severe recessions: lessons from the 2008–2013 Portuguese economic crisis," Small Business Economics, Springer, vol. 46(4), pages 591-617, April.
    55. Giulio Bottazzi & Davide Pirino & Federico Tamagni, 2015. "Zipf law and the firm size distribution: a critical discussion of popular estimators," Journal of Evolutionary Economics, Springer, vol. 25(3), pages 585-610, July.
    56. 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.
    57. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    58. Fernandes, Ana P. & Ferreira, Priscila, 2017. "Financing constraints and fixed-term employment: Evidence from the 2008-9 financial crisis," European Economic Review, Elsevier, vol. 92(C), pages 215-238.
    59. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    60. Miljkovic, Tatjana & Grün, Bettina, 2016. "Modeling loss data using mixtures of distributions," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 387-396.
    61. repec:hal:spmain:info:hdl:2441/5fjm1f1p0v93k9png4qo8ltnrf is not listed on IDEAS
    62. Paulo Bastos & Joana Silva & Eric Verhoogen, 2018. "Export Destinations and Input Prices," American Economic Review, American Economic Association, vol. 108(2), pages 353-392, February.
    63. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    64. repec:hal:spmain:info:hdl:2441/2j87pv5ou185f980qgrpf9net0 is not listed on IDEAS
    65. 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.
    66. repec:hal:spmain:info:hdl:2441/6apm7lruv088iagm4rv2c33jtg is not listed on IDEAS
    67. 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.
    68. Brooks, Wyatt & Dovis, Alessandro, 2020. "Credit market frictions and trade liberalizations," Journal of Monetary Economics, Elsevier, vol. 111(C), pages 32-47.
    69. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," SciencePo Working papers hal-03579844, HAL.
    70. Hulusi Inanoglu & Mahmoud A. El-Gamal, 2005. "Inefficiency and heterogeneity in Turkish banking: 1990-2000," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(5), pages 641-664.
    71. Luis Orea & Subal C. Kumbhakar, 2004. "Efficiency measurement using a latent class stochastic frontier model," Empirical Economics, Springer, vol. 29(1), pages 169-183, January.
    72. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p2m9j4i07 is not listed on IDEAS
    73. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Monika Mrázová & J. Peter Neary & Mathieu Parenti, 2021. "Sales and Markup Dispersion: Theory and Empirics," Econometrica, Econometric Society, vol. 89(4), pages 1753-1788, July.
    3. 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.
    4. Illenin O. Kondo & Logan T. Lewis & Andrea Stella, 2023. "Heavy tailed but not Zipf: Firm and establishment size in the United States," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 767-785, August.
    5. Halvarsson, Daniel, 2013. "Industry Differences in the Firm Size Distribution," Ratio Working Papers 214, The Ratio Institute.
    6. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2020. "Innovation and Corporate Dynamics: A Theoretical Framework," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(1), pages 1-45, March.
    7. 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.
    8. 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.
    9. Paulo Bastos & Daniel A. Dias & Olga A. Timoshenko, 2018. "Learning, prices and firm dynamics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(4), pages 1257-1311, November.
    10. 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.
    11. di Giovanni, Julian & Levchenko, Andrei A., 2013. "Firm entry, trade, and welfare in Zipf's world," Journal of International Economics, Elsevier, vol. 89(2), pages 283-296.
    12. repec:hal:spmain:info:hdl:2441/nki2gcedn93280ns6fslbhdnm is not listed on IDEAS
    13. Defever, Fabrice & Riaño, Alejandro, 2022. "Firm-destination heterogeneity and the distribution of export intensity," Economics Letters, Elsevier, vol. 219(C).
    14. Fabrice Defever & Alejandro Riano, 2017. "Twin peaks," Discussion Papers 2017-15, University of Nottingham, GEP.
    15. Till Gross & Stéphane Verani, 2012. "Financing Constraints, Firm Dynamics, and International Trade," Finance and Economics Discussion Series 2012-68, Board of Governors of the Federal Reserve System (U.S.).
    16. Flach, Lisandra & Unger, Florian, 2022. "Quality and gravity in international trade," Journal of International Economics, Elsevier, vol. 137(C).
    17. Melitz, Marc J. & Redding, Stephen J., 2014. "Heterogeneous Firms and Trade," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 1-54, Elsevier.
    18. 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.
    19. Chen Yeh, 2016. "Are firm-level idiosyncratic shocks important for U.S. aggregate volatility?," Working Papers 16-47, Center for Economic Studies, U.S. Census Bureau.
    20. Illenin O. Kondo & Logan T. Lewis & Andrea Stella, 2018. "On the U.S. Firm and Establishment Size Distributions," Finance and Economics Discussion Series 2018-075, Board of Governors of the Federal Reserve System (U.S.).
    21. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2017. "Where Gibrat meets Zipf: Scale and scope of French firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 265-275.

    More about this item

    Keywords

    Finite Mixture Model; firm size distribution; productivity distribution; 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:102711. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.