Rginal Cost Functions with Incomplete Knowledge of Strategic Behavior

In this paper I develop a new approach for identi…cation and estimation of the parameters of an oligopoly model, without relying on a potentially unveri…able equilibrium assumption. Rather, I consider inference on model parameters when the researcher does not know precisely what decision rule …rms use, but is willing to consider a set of possibilities. In contrast to traditional approaches in the literature, the proposed methodology allows …rm behavior to vary ‡exibly across observations, in a manner consistent with many Nash Equilibria. I derive identi…cation results for both homogeneous product and di¤erentiated product markets. Due to the ‡exibility a¤orded to …rm behavior, the parameters of …rms’marginal cost functions may only be set identi…ed rather than point identi…ed. The restrictions of the model are, however, still informative. I …nd that the size of the identi…ed 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 I implement the methodology of Rosen (2005) to construct asymptotically valid con…dence regions for the partially identi…ed marginal cost parameters. The application illustrates how I thank Allan Collard-Wexler, Joel Horowitz, Nir Jaimovich, Mike Mazzeo, Bill Rogerson, Itai Sher, Andrew Sweeting, Mike Whinston, and Fan Zhang for comments and suggestions on this paper. I am especially grateful to Chuck Manski, Aviv Nevo, Rob Porter, and Elie Tamer for continued discussion and feedback. Furthermore, I thank Rob Porter for supplying me with data on the Joint Executive Committee. I have bene…tted from the comments of seminar participants at LSE, Sloan, UCL, UC Irvine, the 2005 Econometric Society World Congress and the 2006 Southern Economic Association Meetings. Financial support from the Robert Eisner Memorial Fellowship and the Center for the Study of Industrial Organization are gratefully acknowledged. All errors are my own. yMailing address: Department of Economics, University College London, Gower Street, London WC1E 6BT, United Kingdom. Email: [email protected].