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

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  • Adam Rosen

    ()
    (Institute for Fiscal Studies and University College London)

Abstract

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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Bibliographic Info

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. Rosse, James N, 1970. "Estimating Cost Function Parameters without Using Cost Data: Illustrated Methodology," Econometrica, Econometric Society, vol. 38(2), pages 256-75, March.
  2. Green, Edward J. & Porter, Robert H., 1982. "Noncooperative Collusion Under Imperfect Price Information," Working Papers 367, California Institute of Technology, Division of the Humanities and Social Sciences.
  3. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
  4. 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.
  5. Ariel Pakes & Michael Ostrovsky & Steve Berry, 2004. "Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Examples)," Harvard Institute of Economic Research Working Papers 2036, Harvard - Institute of Economic Research.
  6. J. Levin & P. Bajari, 2004. "Estimating Dynamic Models of Imperfect Competition," 2004 Meeting Papers 579, Society for Economic Dynamics.
  7. Haile,P.A. & Tamer,E.T., 2000. "Inference with an incomplete model of English auctions," Working papers 18, Wisconsin Madison - Social Systems.
  8. 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.
  9. 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.
  10. Graddy, K., 1993. "Testing for Imperfect Competition at the Fulton Fish Market," Papers 137, Princeton, Department of Economics - Financial Research Center.
  11. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
  12. 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.
  13. Elie Tamer & Federico Ciliberto, 2004. "Market Structure and Multiple Equilibria in Airline Markets," Econometric Society 2004 North American Winter Meetings 517, Econometric Society.
  14. Gasmi, F & Laffont, J J & Vuong, Q, 1992. "Econometric Analysis of Collusive Behavior in a Soft-Drink Market," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 1(2), pages 277-311, Summer.
  15. Nevo, Aviv, 1998. "Identification of the oligopoly solution concept in a differentiated-products industry," Economics Letters, Elsevier, vol. 59(3), pages 391-395, June.
  16. 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.
  17. Bresnahan, Timothy F., 1982. "The oligopoly solution concept is identified," Economics Letters, Elsevier, vol. 10(1-2), pages 87-92.
  18. Andrew Sweeting, 2005. "Coordination Games, Multiple Equilibria and the Timing of Radio Commercials," 2005 Meeting Papers 490, Society for Economic Dynamics.
  19. 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.
  20. 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.
  21. 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.
  22. Corts, Kenneth S., 1998. "Conduct parameters and the measurement of market power," Journal of Econometrics, Elsevier, vol. 88(2), pages 227-250, November.
  23. 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.
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Citations

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Cited by:
  1. Céline Bonnet & Pierre Dubois, 2010. "Inference on vertical contracts between manufacturers and retailers allowing for nonlinear pricing and resale price maintenance," RAND Journal of Economics, RAND Corporation, vol. 41(1), pages 139-164.
  2. Hahn, Jinyong & Ridder, Geert & Snider, Connan, 2013. "Partial identification and mergers," Economics Letters, Elsevier, vol. 118(1), pages 126-129.
  3. 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.
  4. Coroneo, Laura & Corradi, Valentina & Santos Monteiro, Paulo, 2012. "Testing for optimal monetary policy via moment inequalities," The Warwick Economics Research Paper Series (TWERPS) 985, University of Warwick, Department of Economics.

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