Semiparametric estimation of dynamic discrete choice models

We consider the estimation of dynamic binary choice models in a semiparametric setting, in which the per-period utility functions are known up to a finite number of parameters, but the distribution of utility shocks is left unspecified. This semiparametric setup differs from most of the existing identification and estimation literature for dynamic discrete choice models. To show identification we derive and exploit a new recursive representation for the unknown quantile function of the utility shocks. Our estimators are straightforward to compute, and resemble classic closed-form estimators from the literature on semiparametric regression and average derivative estimation. Monte Carlo simulations demonstrate that our estimator performs well in small samples.