  Many estimators of dynamic discrete choice models with persistent unobserved
heterogeneity have desirable statistical properties but are computationally
intensive. In this paper we propose a method to quicken estimation for a broad
class of dynamic discrete choice problems by exploiting semiparametric index
restrictions. Specifically, we propose an estimator for models whose reduced
form parameters are invertible functions of one or more linear indices (Ahn,
Ichimura, Powell and Ruud 2018), a property we term index invertibility. We
establish that index invertibility implies a set of equality constraints on the
model parameters. Our proposed estimator uses the equality constraints to
decrease the dimension of the optimization problem, thereby generating
computational gains. Our main result shows that the proposed estimator is
asymptotically equivalent to the unconstrained, computationally heavy
estimator. In addition, we provide a series of results on the number of
independent index restrictions on the model parameters, providing theoretical
guidance on the extent of computational gains. Finally, we demonstrate the
advantages of our approach via Monte Carlo simulations.
