Generalized Indirect Inference for Discrete Choice Models

TL;DR

This paper introduces a smoothing-based simulation method for estimating complex dynamic discrete choice models, enabling gradient-based optimization and improving computational efficiency while maintaining consistency.

Contribution

It develops a novel smoothing approach for indirect inference in discrete choice models, allowing for efficient optimization and accommodating complex model features.

Findings

Method is fast and robust in Monte Carlo tests.

Nearly as efficient as maximum likelihood with rich auxiliary models.

Facilitates convergence of gradient-based optimization methods.

Abstract

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 gradient-based 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.