  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 mod- els.
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.
