This paper develops and implements a practical simulation-based method for estimating dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many alternatives, builds on the ideas of indirect inference. The main difficulty in implementing indirect inference in discrete choice models is that the objective surface is a step function, rendering gradientbased optimization methods useless. To overcome this obstacle, this paper shows how to smooth the objective surface. The key idea is to use a smoothed function of the latent utilities as the dependent variable in the auxiliary model. As the smoothing parameter goes to zero, this function delivers the discrete choice implied by the latent utilities, thereby guaranteeing consistency. We establish conditions on the smoothing such that our estimator enjoys the same limiting distribution as the indirect inference estimator, while at the same time ensuring that the smoothing facilitates the convergence of gradient-based optimization methods. A set of Monte Carlo experiments shows that the method is fast, robust, and nearly as efficient as maximum likelihood when the auxiliary model is sufficiently rich.

This paper presents uniform convergence rates for kernel regression estimators, in the setting of a structural nonlinear cointegrating regression model. We generalise the existing literature in three ways. First, the domain to which these rates apply is much wider than has been previously considered, and can be chosen so as to contain as large a fraction of the sample as desired in the limit. Second, our results allow the regression disturbance to be serially correlated, and cross-correlated with the regressor; previous work on this problem (of obtaining uniform rates) having been confined entirely to the setting of an exogenous regressor. Third, we permit the bandwidth to be data-dependent, requiring only that it satisfy certain weak asymptotic shrinkage conditions. Our assumptions on the regressor process are consistent with a very broad range of departures from the standard unit root autoregressive model, allowing the regressor to be fractionally integrated, and to have an infinite variance (and even infinite lower-order moments).

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