Bayesian Estimation of a Dynamic Game with Endogenous, Partially Observed, Serially Correlated State

We consider dynamic games that can have state variables that are partially observed, serially correlated, endogenous, and heterogeneous. We propose a Bayesian method that uses a particle filter to compute an unbiased estimate of the likelihood within a Metropolis chain. Unbiasedness guarantees that the stationary density of the chain is the exact posterior, not an approximation. The number of particles required is easily determined. The regularity conditions are weak. Results are verified by simulation from two dynamic oligopolistic games with endogenous state. One is an entry game with feedback to costs based on past entry and the other a model of an industry with a large number of heterogeneous firms that compete on product quality.