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

Author

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  • Adam Rosen

    (Institute for Fiscal Studies and Duke University)

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.

Suggested Citation

  • Adam Rosen, 2007. "Identification and estimation of firms' marginal cost functions with incomplete knowledge of strategic behavior," CeMMAP working papers CWP03/07, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:03/07
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    File URL: http://cemmap.ifs.org.uk/wps/cwp0703.pdf
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    References listed on IDEAS

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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, March.
    2. Laura Coroneo & Valentina Corradi & Paulo Santos Monteiro, 2018. "Testing for optimal monetary policy via moment inequalities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(6), pages 780-796, September.
    3. Joris Pinkse & Margaret E. Slade, 2010. "The Future Of Spatial Econometrics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 103-117, February.
    4. 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.
    5. Hahn, Jinyong & Ridder, Geert & Snider, Connan, 2013. "Partial identification and mergers," Economics Letters, Elsevier, vol. 118(1), pages 126-129.

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