Estimating Dynamic Models of Imperfect Competition

We describe a two-step algorithm for estimating dynamic games where the agents are assumed to play a Markov Perfect equilibrium. In the first step, the policy functions and the law of motion for the state variables are estimated. In the second step, the remaining structural parameters are estimated using the optimality conditions for equilibrium. For non-identified models, we describe a bounds approach to the second step estimation. For identified models, the second step estimator is a simple maximum likelihood estimator that is similar to a probit model. We discuss how the approach applies to dynamic discrete choice models and a class of dynamic oligopoly models with lumpy investment policies.