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SEMI-PARAMETRIC LIKELIHOOD INFERENCE FOR WORST CASE DYNAMIC DISCRETE GAMES1

Zhengyuan Gao This paper considers a dynamic discrete game model with bounded rational agents. Since the appearance of bounded rationality does not lead to a consistent two-step parametric estimator, we propose an alternative two-step inference method. The first step is to control the complexity of the nonparametric approximations and estimate value and policy functions in the worst case fixed point. In the second step, given the fitted value function in the worst case, pseudo true structural parameters are consistently estimated via local Empirical Likelihood with non-smooth moment constraints. Within the local neighborhood of pseudo true parameters, the estimator is asymptotic normal and achieves the lower bound for the maximum risk. Localization renders the computational algorithm feasible and improves stability and speed.