Generalized Indirect Inference for Discrete Choice Models

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. In particular, the method uses an auxiliary model---typically a linear probability model---to summarize the statistical properties of the observed and simulated data. The method then chooses the structural parameters so that the coefficients of the auxiliary model in the simulated data match as closely as possible those in the observed data. The main difficulty in implementing indirect inference in discrete choice models is that the objective surface is a step function, rendering useless gradient-based optimization methods. To overcome this obstacle, this paper shows how to smooth the objective surface. The key idea is to use a smooth 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. 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