Semiparametric Estimation of Dynamic Discrete Choice Models

Abstract

ABSTRACT. We consider the estimation of dynamic discrete 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 Bellman-like recursive representation for the unknown quantile function of the utility shocks. Our estimators are straightforward to compute; some are simple and require no iteration, and resemble classic estimators from the literature on semiparametric regression and average derivative estimation. Monte Carlo simulations demonstrate that our estimator performs well in small samples. To highlight features of this estimator, we estimate a structural model of dynamic labor supply for New York City taxicab drivers.

Joint analysis of the discount factor and payoff parameters in dynamic discrete choice models

“…Q is typically assumed known in most empirical applications. Conditions for the identification of Q exist when is a continuous variable using a large support type argument; for example, see Aguirregabiria and Suzuki (, Proposition 1), Buchholz, Shum, and Xu (, Lemma 4), and Chen (, Theorem 4). Our results do not depend on any continuity assumption to achieve identification as we take to be a discrete random variable.…”