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Firm Size Distribution under Horizontal and Vertical Innovation

Author

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  • Pedro Mazeda Gil
  • Fernanda Figueiredo
Abstract
This paper studies the firm size distribution arising from an endogenous growth model of quality ladders with expanding variety. The probability distribution function of a given cohort of firms is a Poisson distribution that converges asymptotically to a normal of log size. However, due to firm entry propelled by horizontal R&D, the total distribution – i.e., when the entire population of firms is considered – is a mixture of overlapping Poisson distributions which is systematically right skewed and exhibits a fatter upper tail than the normal distribution of log size. Our theoretical results qualitatively match the empirical evidence found both for the cohort and the total distribution, and which has been presented as a challenge for theory to explain. Moreover, by obtaining a total distribution with a gradually falling variance over a long time span, the model is able to address complementary empirical evidence that points to a total distribution subtly evolving over time.

Suggested Citation

  • Pedro Mazeda Gil & Fernanda Figueiredo, 2011. "Firm Size Distribution under Horizontal and Vertical Innovation," DEGIT Conference Papers c016_065, DEGIT, Dynamics, Economic Growth, and International Trade.
    • Handle: RePEc:deg:conpap:c016_065
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    1. de Wit, Gerrit, 2005. "Firm size distributions: An overview of steady-state distributions resulting from firm dynamics models," International Journal of Industrial Organization, Elsevier, vol. 23(5-6), pages 423-450, June.
    2. 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.
    3. Poschke, Markus, 2009. "Employment protection, firm selection, and growth," Journal of Monetary Economics, Elsevier, vol. 56(8), pages 1074-1085, November.
    4. Rui Castro & Gian Clementi, 2009. "The economic effects of improving investor rights in Portugal," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 8(2), pages 59-97, August.
    5. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    6. Jones, Charles I & Williams, John C, 2000. "Too Much of a Good Thing? The Economics of Investment in R&D," Journal of Economic Growth, Springer, vol. 5(1), pages 65-85, March.
    7. Evans, Geroge W & Honkapohja, Seppo & Romer, Paul, 1998. "Growth Cycles," American Economic Review, American Economic Association, vol. 88(3), pages 495-515, June.
    8. Peretto, Pietro F, 1998. "Technological Change and Population Growth," Journal of Economic Growth, Springer, vol. 3(4), pages 283-311, December.
    9. Gil, Pedro Mazeda & Brito, Paulo & Afonso, Oscar, 2013. "Growth And Firm Dynamics With Horizontal And Vertical R&D," Macroeconomic Dynamics, Cambridge University Press, vol. 17(7), pages 1438-1466, October.
    10. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
    11. Kim P. Huynh & David T. Jacho‐Chávez, 2010. "Firm size distributions through the lens of functional principal components analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(7), pages 1211-1214, November/.
    12. Thompson, Peter, 2001. "The Microeconomics of an R&D-Based Model of Endogenous Growth," Journal of Economic Growth, Springer, vol. 6(4), pages 263-283, December.
    13. 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.
    14. Paul S. Segerstrom, 2007. "Intel Economics," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(1), pages 247-280, February.
    15. 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.
    16. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
    17. Segerstrom, Paul S, 2000. "The Long-Run Growth Effects of R&D Subsidies," Journal of Economic Growth, Springer, vol. 5(3), pages 277-305, September.
    18. Francisco L. Rivera-Batiz & Luis A. Rivera-Batiz, 2018. "Economic Integration and Endogenous Growth," World Scientific Book Chapters, in: Francisco L Rivera-Batiz & Luis A Rivera-Batiz (ed.), International Trade, Capital Flows and Economic Development, chapter 1, pages 3-32, World Scientific Publishing Co. Pte. Ltd..
    19. Alain Gabler & Omar Licandro, 2007. "Endogenous Growth through Selection and Imitation," Economics Working Papers ECO2007/26, European University Institute.
    20. McCloughan, Patrick, 1995. "Simulation of Concentration Development from Modified Gibrat Growth-Entry-Exit Processes," Journal of Industrial Economics, Wiley Blackwell, vol. 43(4), pages 405-433, December.
    21. 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.
    22. Holger Strulik, 2007. "Too Much of a Good Thing? The Quantitative Economics of R&D‐driven Growth Revisited," Scandinavian Journal of Economics, Wiley Blackwell, vol. 109(2), pages 369-386, June.
    23. Klepper, Steven, 1996. "Entry, Exit, Growth, and Innovation over the Product Life Cycle," American Economic Review, American Economic Association, vol. 86(3), pages 562-583, June.
    24. 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.
    25. Gallegati, M. & Palestrini, A., 2010. "The complex behavior of firms' size dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 75(1), pages 69-76, July.
    26. Etro, Federico, 2008. "Growth leaders," Journal of Macroeconomics, Elsevier, vol. 30(3), pages 1148-1172, September.
    27. Steven Klepper & Peter Thompson, 2006. "Submarkets and the evolution of market structure," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 861-886, December.
    28. Patrizio Pagano & Fabiano Schivardi, 2003. "Firm Size Distribution and Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 105(2), pages 255-274, June.
    29. Steven Klepper & Peter Thompson, 2006. "Submarkets and the evolution of market structure," RAND Journal of Economics, The RAND Corporation, vol. 37(4), pages 861-886, December.
    30. 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.
    31. Philippe Aghion & Christopher Harris & Peter Howitt & John Vickers, 2001. "Competition, Imitation and Growth with Step-by-Step Innovation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 467-492.
    32. Mansfield, Edwin, 1986. "The R&D Tax Credit and Other Technology Policy Issues," American Economic Review, American Economic Association, vol. 76(2), pages 190-194, May.
    33. Luís Cabral, 2007. "Small firms in Portugal: a selective survey of stylized facts, economic analysis, and policy implications," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 6(1), pages 65-88, April.
    34. David B. Audretsch, 1995. "Innovation and Industry Evolution," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011468, April.
    35. Geroski, P. A., 1995. "What do we know about entry?," International Journal of Industrial Organization, Elsevier, vol. 13(4), pages 421-440, December.
    36. Boyan Jovanovic, 1993. "The Diversification of Production," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 24(1 Microec), pages 197-247.
    37. Christopher Laincz, 2009. "R&D subsidies in a model of growth with dynamic market structure," Journal of Evolutionary Economics, Springer, vol. 19(5), pages 643-673, October.
    38. Gaffeo, Edoardo & Gallegati, Mauro & Palestrini, Antonio, 2003. "On the size distribution of firms: additional evidence from the G7 countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 117-123.
    39. Chris Freeman & Luc Soete, 1997. "The Economics of Industrial Innovation, 3rd Edition," MIT Press Books, The MIT Press, edition 3, volume 1, number 0262061953, April.
    40. Peter Howitt, 1999. "Steady Endogenous Growth with Population and R & D Inputs Growing," Journal of Political Economy, University of Chicago Press, vol. 107(4), pages 715-730, August.
    41. G. Bottazzi & E. Cefis & G. Dosi & A. Secchi, 2007. "Invariances and Diversities in the Patterns of Industrial Evolution: Some Evidence from Italian Manufacturing Industries," Small Business Economics, Springer, vol. 29(1), pages 137-159, June.
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    Cited by:

    1. Świadek Arkadiusz & Szopik-Depczyńska Katarzyna, 2014. "Changes In Innovation Activity In Regional Industrial System In The Context Of Size Of Enterprises In West Pomeranian Province," Folia Oeconomica Stetinensia, Sciendo, vol. 14(2), pages 225-238, December.
    2. Zakaria Babutsidze, 2016. "Innovation, competition and firm size distribution on fragmented markets," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 143-169, March.
    3. 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.
    4. Pedro Mazeda Gil & Gustavo Iglésias,, 2018. "Endogenous Growth and Real Effects of Monetary Policy: R&D and Physical Capital Complementarities in a Cash-in-Advance Economy," CEF.UP Working Papers 1802, Universidade do Porto, Faculdade de Economia do Porto.
    5. Arkadiusz Świadek, 2014. "Wpływ wielkości przedsiębiorstw na innowacyjność systemu przemysłowego w Polsce," Gospodarka Narodowa. The Polish Journal of Economics, Warsaw School of Economics, issue 1, pages 121-139.
    6. Pedro Mazeda Gil & Gustavo Iglésias, 2020. "Endogenous Growth and Real Effects of Monetary Policy: R&D and Physical Capital Complementarities," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 52(5), pages 1147-1197, August.
    7. Christian Cordes & Tong-Yaa Su & Pontus Strimling, 2019. "A critical human group size and firm size distributions in industries," Journal of Bioeconomics, Springer, vol. 21(2), pages 123-144, July.

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    More about this item

    Keywords

    Firm size distribution; Skewness; Heavy tails; Endogenous growth; Horizontal and vertical R&D;
    All these keywords.

    JEL classification:

    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
    • O38 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Government Policy
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

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