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Identification and estimation of firms' marginal cost functions with incomplete knowledge of strategic behavior

  • Adam Rosen

    ()

    (Institute for Fiscal Studies and University College London)

In this paper I develop a new approach for identification and estimation of the parameters of an oligopoly model, without relying on a potentially unverifiable equilibrium assumption. Rather, I consider inference on model parameters when the researcher does not know precisely what decision rule firms use, but is willing to consider a set of possibilities. In contrast to traditional approaches in the literature, the proposed methodology allows firm behavior to vary flexibly across observations, in a manner consistent with many Nash Equilibria. I derive identification results for both homogeneous product and differentiated product markets. Due to the flexibility afforded to firm behavior, the arameters of firms' marginal cost functions may only be set identified rather than point identified. The restrictions of the model are, however, still informative. I find that the size of the identified set for marginal cost parameters depends on the elasticity of market demand, the set of decision rules considered, and the functional form assumptions imposed. I formulate how to compute consistent set estimates for marginal cost parameters and demonstrate the proposed methodology with price and quantity data on the Joint Executive Committee, a 19th century railway cartel. To perform statistical inference implement the methodology of Rosen (2005) to construct asymptotically valid confidence regions for the partially identified marginal cost parameters. The application illustrates how the precision of estimated marginal costs depends on the elasticity of market demand as well as the extent to which firm behavior is allowed to vary.

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File URL: http://cemmap.ifs.org.uk/wps/cwp0703.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP03/07.

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Length: 43 pp.
Date of creation: Feb 2007
Date of revision:
Handle: RePEc:ifs:cemmap:03/07
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  1. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
  2. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, 06.
  3. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  4. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
  5. Alberto Salvo, 2004. "Inferring conduct under the threat of entry: the case of the Brazilian cement industry," LSE Research Online Documents on Economics 6728, London School of Economics and Political Science, LSE Library.
  6. Green, Edward J & Porter, Robert H, 1984. "Noncooperative Collusion under Imperfect Price Information," Econometrica, Econometric Society, vol. 52(1), pages 87-100, January.
  7. Graddy, K., 1993. "Testing for Imperfect Competition at the Fulton Fish Market," Papers 137, Princeton, Department of Economics - Financial Research Center.
  8. Glenn Ellison, 1994. "Theories of Cartel Stability and the Joint Executive Committee," RAND Journal of Economics, The RAND Corporation, vol. 25(1), pages 37-57, Spring.
  9. Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Cosslett, Stephen R. & Lee, Lung-Fei, 1985. "Serial correlation in latent discrete variable models," Journal of Econometrics, Elsevier, vol. 27(1), pages 79-97, January.
  11. Bresnahan, Timothy F., 1982. "The oligopoly solution concept is identified," Economics Letters, Elsevier, vol. 10(1-2), pages 87-92.
  12. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June.
  13. Gasmi, Farid & Laffont, Jean-Jacques & Vuong, Quang, 1992. "Econometric Analysis of Collusive Behavior in a Soft Drink Market," IDEI Working Papers 16, Institut d'Économie Industrielle (IDEI), Toulouse.
  14. Berry, Steven & Briggs, Hugh, 1988. "A non-parametric test of a first-order Markov process for regimes in a non-cooperatively collusive industry," Economics Letters, Elsevier, vol. 27(1), pages 73-77.
  15. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, 09.
  16. Andrew Sweeting, 2005. "Coordination Games, Multiple Equilibria and the Timing of Radio Commercials," 2005 Meeting Papers 490, Society for Economic Dynamics.
  17. E. Tamer & V. Chernozhukov & H. Hong, 2004. "Parameter Set Inference in a Class of Econometric Models," Econometric Society 2004 North American Winter Meetings 382, Econometric Society.
  18. Philip Haile, 2000. "Inference with an Incomplete Model of English Auctions," Econometric Society World Congress 2000 Contributed Papers 1546, Econometric Society.
  19. Corts, Kenneth S., 1998. "Conduct parameters and the measurement of market power," Journal of Econometrics, Elsevier, vol. 88(2), pages 227-250, November.
  20. Nevo, Aviv, 1998. "Identification of the oligopoly solution concept in a differentiated-products industry," Economics Letters, Elsevier, vol. 59(3), pages 391-395, June.
  21. David Genesove & Wallace P. Mullin, 1998. "Testing Static Oligopoly Models: Conduct and Cost in the Sugar Industry, 1890-1914," RAND Journal of Economics, The RAND Corporation, vol. 29(2), pages 355-377, Summer.
  22. Rosse, James N, 1970. "Estimating Cost Function Parameters without Using Cost Data: Illustrated Methodology," Econometrica, Econometric Society, vol. 38(2), pages 256-75, March.
  23. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
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