Semiparametric Estimation of a Dynamic Game of Incomplete Information

Recently, empirical industrial organization economists have proposed estimators for dynamic games of incomplete information. In these models, agents choose from a finite number actions and maximize expected discounted utility in a Markov perfect equilibrium. Previous econometric methods estimate the probability distribution of agents’ actions in a first stage. In a second step, a finite vector of parameters of the period return function are estimated. In this paper, we develop semiparametric estimators for dynamic games allowing for continuous state varaibles and a nonparametric first stage. The estimates of the structural parameters are T consistent (where T is the sample size) and asymptotically normal even though the first stage is estimated nonparametrically. We also propose sufficient conditions for identification of the model. ∗We would like to thank the National Science Foundation and the Sloan Foundation for generous research support. We would also like to thank John Krainer for detailed comments on an earlier draft.