IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v146y2011i5p1965-1994.html
   My bibliography  Save this article

Industry dynamics: Foundations for models with an infinite number of firms

Author

Listed:
  • Weintraub, Gabriel Y.
  • Benkard, C. Lanier
  • Van Roy, Benjamin

Abstract

This paper explores the connection between three important threads of economic research offering different approaches to studying the dynamics of an industry with heterogeneous firms. Finite models of the form pioneered by Ericson and Pakes (1995) capture the dynamics of a finite number of heterogeneous firms as they compete in an industry, and are typically analyzed using the concept of Markov perfect equilibrium (MPE). Infinite models of the form pioneered by Hopenhayn (1992), on the other hand, consider an infinite number of infinitesimal firms, and are typically analyzed using the concept of stationary equilibrium (SE). A third approach uses oblivious equilibrium (OE), which maintains the simplifying benefits of an infinite model but within the more realistic setting of a finite model. The paper relates these three approaches. The main result of the paper provides conditions under which SE of infinite models approximate MPE of finite models arbitrarily well in asymptotically large markets. Our conditions require that the distribution of firm states in SE obeys a certain âlight-tailâ condition. In a second set of results, we show that the set of OE of a finite model approaches the set of SE of the infinite model in large markets under a similar light-tail condition.

Suggested Citation

  • Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2011. "Industry dynamics: Foundations for models with an infinite number of firms," Journal of Economic Theory, Elsevier, vol. 146(5), pages 1965-1994, September.
  • Handle: RePEc:eee:jetheo:v:146:y:2011:i:5:p:1965-1994
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053111000731
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Doraszelski, Ulrich & Pakes, Ariel, 2007. "A Framework for Applied Dynamic Analysis in IO," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 30, pages 1887-1966, Elsevier.
    2. Jones, Larry E., 1987. "The efficiency of monopolistically competitive equilibria in large economies: Commodity differentiation with gross substitutes," Journal of Economic Theory, Elsevier, vol. 41(2), pages 356-391, April.
    3. 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.
    4. Boyan Jovanovic, 1987. "Micro Shocks and Aggregate Risk," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 102(2), pages 395-409.
    5. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    6. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2008. "Markov Perfect Industry Dynamics With Many Firms," Econometrica, Econometric Society, vol. 76(6), pages 1375-1411, November.
    7. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    8. Novshek, William, 1985. "Perfectly competitive markets as the limits of cournot markets," Journal of Economic Theory, Elsevier, vol. 35(1), pages 72-82, February.
    9. Beth Allen & Martin Hellwig, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 175-204.
    10. 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.
    11. Dixit, Avinash K & Stiglitz, Joseph E, 1977. "Monopolistic Competition and Optimum Product Diversity," American Economic Review, American Economic Association, vol. 67(3), pages 297-308, June.
    12. Yi Daniel Xu, 2008. "A Structural Empirical Model of R&D, Firm Heterogeneity , and Industry Evolution," 2008 Meeting Papers 744, Society for Economic Dynamics.
    13. Roberts, Donald John & Postlewaite, Andrew, 1976. "The Incentives for Price-Taking Behavior in Large Exchange Economies," Econometrica, Econometric Society, vol. 44(1), pages 115-127, January.
    14. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    15. 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.
    16. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    17. Hopenhayn, Hugo & Rogerson, Richard, 1993. "Job Turnover and Policy Evaluation: A General Equilibrium Analysis," Journal of Political Economy, University of Chicago Press, vol. 101(5), pages 915-938, October.
    18. Hopenhayn, Hugo A, 1992. "Entry, Exit, and Firm Dynamics in Long Run Equilibrium," Econometrica, Econometric Society, vol. 60(5), pages 1127-1150, September.
    19. Mas-Colell, Andreu, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part I: Mixed strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 153-170, June.
    20. Novshek, William & Sonnenschein, Hugo, 1978. "Cournot and Walras equilibrium," Journal of Economic Theory, Elsevier, vol. 19(2), pages 223-266, December.
    21. Allen, Beth & Hellwig, Martin, 1986. "Price-Setting Firms and the Oligopolistic Foundations of Perfect Competition," American Economic Review, American Economic Association, vol. 76(2), pages 387-392, May.
    22. Besanko, David & Perry, Martin K & Spady, Richard H, 1990. "The Logit Model of Monopolistic Competition: Brand Diversity," Journal of Industrial Economics, Wiley Blackwell, vol. 38(4), pages 397-415, June.
    23. Matthew F. Mitchell, 2000. "The Scope and Organization of Production: Firm Dynamics Over the Learning Curve," RAND Journal of Economics, The RAND Corporation, vol. 31(1), pages 180-205, Spring.
    24. Novshek, William & Sonnenschein, Hugo, 1983. "Walrasian equilibria as limits of noncooperative equilibria. Part II: Pure strategies," Journal of Economic Theory, Elsevier, vol. 30(1), pages 171-187, June.
    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. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    2. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
    3. Haoyang Cao & Jodi Dianetti & Giorgio Ferrari, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Papers 2105.07213, arXiv.org.
    4. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2021. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Dynamic Games and Applications, Springer, vol. 11(3), pages 463-490, September.
    5. Kikuchi, Tomoo & Nishimura, Kazuo & Stachurski, John, 2018. "Span of control, transaction costs and the structure of production chains," Theoretical Economics, Econometric Society, vol. 13(2), May.
    6. Krishnamurthy Iyer & Ramesh Johari & Mukund Sundararajan, 2014. "Mean Field Equilibria of Dynamic Auctions with Learning," Management Science, INFORMS, vol. 60(12), pages 2949-2970, December.
    7. Cao, Haoyang & Dianetti, Jodi & Ferrari, Giorgio, 2021. "Stationary Discounted and Ergodic Mean Field Games of Singular Control," Center for Mathematical Economics Working Papers 650, Center for Mathematical Economics, Bielefeld University.
    8. Sachin Adlakha & Ramesh Johari, 2013. "Mean Field Equilibrium in Dynamic Games with Strategic Complementarities," Operations Research, INFORMS, vol. 61(4), pages 971-989, August.
    9. Piotr Więcek & Eitan Altman, 2015. "Stationary Anonymous Sequential Games with Undiscounted Rewards," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 686-710, August.
    10. Jian Yang, 2017. "A link between sequential semi-anonymous nonatomic games and their large finite counterparts," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 383-433, May.
    11. Jian Yang, 2021. "Analysis of Markovian Competitive Situations Using Nonatomic Games," Dynamic Games and Applications, Springer, vol. 11(1), pages 184-216, March.
    12. Jian Yang, 2015. "A Link between Sequential Semi-anonymous Nonatomic Games and their Large Finite Counterparts," Papers 1510.06809, arXiv.org, revised Jun 2016.
    13. Jian Yang, 2015. "Analysis of Markovian Competitive Situations using Nonatomic Games," Papers 1510.06813, arXiv.org, revised Apr 2017.
    14. Ren'e Aid & Matteo Basei & Giorgio Ferrari, 2023. "A Stationary Mean-Field Equilibrium Model of Irreversible Investment in a Two-Regime Economy," Papers 2305.00541, arXiv.org.

    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. Weintraub, Gabriel Y. & Benkard, C. Lanier & Van Roy, Benjamin, 2007. "Markov Perfect Industry Dynamics with Many Firms," Research Papers 1919r, Stanford University, Graduate School of Business.
    2. Adlakha, Sachin & Johari, Ramesh & Weintraub, Gabriel Y., 2015. "Equilibria of dynamic games with many players: Existence, approximation, and market structure," Journal of Economic Theory, Elsevier, vol. 156(C), pages 269-316.
    3. Gabriel Y. Weintraub & C. Lanier Benkard & Benjamin Van Roy, 2010. "Computational Methods for Oblivious Equilibrium," Operations Research, INFORMS, vol. 58(4-part-2), pages 1247-1265, August.
    4. Erzo G.J. Luttmer, 2010. "Models of Growth and Firm Heterogeneity," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 547-576, September.
    5. Vivek Farias & Bar Ifrach & Gabriel Weintraub, 2012. "A Framework for Dynamic Oligopoly in Concentrated Industries," 2012 Meeting Papers 505, Society for Economic Dynamics.
    6. C. Lanier Benkard & Benjamin Van Roy & Gabriel Y. Weintraub, 2005. "Markov perfect industry dynamics with many firms," Working Paper Series 2005-23, Federal Reserve Bank of San Francisco.
    7. Gabriel Weintraub & C. Lanier Benkard & Ben Van Roy, 2005. "Markov Perfect Industry Dynamics with Many Firms," NBER Working Papers 11900, National Bureau of Economic Research, Inc.
    8. Gualdi, Stanislao & Mandel, Antoine, 2016. "On the emergence of scale-free production networks," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 61-77.
    9. A. Kerem Co?ar & Nezih Guner & James Tybout, 2016. "Firm Dynamics, Job Turnover, and Wage Distributions in an Open Economy," American Economic Review, American Economic Association, vol. 106(3), pages 625-663, March.
    10. Roman Fossati, 2011. "Outsourcing versus Vertical Integration: A Dynamic Model of Industry Equilibrium," 2011 Meeting Papers 1421, Society for Economic Dynamics.
    11. 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.
    12. Light, Bar & Weintraub, Gabriel, 2018. "Mean Field Equilibrium: Uniqueness, Existence, and Comparative Statics," Research Papers 3731, Stanford University, Graduate School of Business.
    13. Acemoglu, Daron & Cao, Dan, 2015. "Innovation by entrants and incumbents," Journal of Economic Theory, Elsevier, vol. 157(C), pages 255-294.
    14. Andrew B. Bernard & Stephen J. Redding & Peter K. Schott, 2011. "Multiproduct Firms and Trade Liberalization," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(3), pages 1271-1318.
    15. Yoshifumi Konishi & Nori Tarui, 2015. "Emissions Trading, Firm Heterogeneity, and Intra-industry Reallocations in the Long Run," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 2(1), pages 1-42.
    16. GABLER, Alain & POSCHKE, Markus, 2011. "Growth through Experimentation," Cahiers de recherche 11-2011, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    17. Cristiana Benedetti Fasil, 2009. "Product and Process Innovation in a Growth Model of Firm Selection," Economics Working Papers ECO2009/30, European University Institute.
    18. Vincent Sterk & Petr Sedláček & Benjamin Pugsley, 2021. "The Nature of Firm Growth," American Economic Review, American Economic Association, vol. 111(2), pages 547-579, February.
    19. Şeker, Murat, 2012. "A structural model of firm and industry evolution: Evidence from Chile," Journal of Economic Dynamics and Control, Elsevier, vol. 36(6), pages 891-913.
    20. Satyajit Chatterjee & Esteban Rossi‐Hansberg, 2012. "Spinoffs And The Market For Ideas," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(1), pages 53-93, February.

    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:eee:jetheo:v:146:y:2011:i:5:p:1965-1994. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.