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Unformatted text preview: Generalized Indirect Inference for Discrete Choice Models Michael Keane and Anthony A. Smith, Jr. * PRELIMINARY AND INCOMPLETE November 2003 (first version: June 2003) Abstract This paper develops and implements a practical simulation-based method for estimat- ing dynamic discrete choice models. The method, which can accommodate lagged dependent variables, serially correlated errors, unobserved variables, and many alter- natives, builds on the ideas of indirect inference. In particular, the method uses a descriptive statistical (or auxiliary) modeltypically a linear probability modelto 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 objec- tive 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 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. * Both authors are in the Department of Economics at Yale University. We thank seminar par- ticipants at the Board of Governors of the Federal Reserve Bank, Carnegie Mellon University, University of Rochester, University of Texas at Austin, University of Virginia, Yale University, and the 2003 Annual Meetings of the Society for Economic Dynamics for helpful comments. 1 Introduction Many economic models have the feature that it is simple to simulate data from the model (given knowledge of the model parameters), but that estimation of the model is extremely difficult. Models with discrete outcomes or mixed discrete/continuous outcomes commonly fall into this category. A leading example is the multinomial probit model, in which an agent chooses from amongst several discrete alternatives the one with highest utility. Simulation of data from this model is trivial: the agents simply construct the utility of each alternative (algebraic operations) and then choose the alternative that gives highest utility. But esti- mation of the model, via either maximum likelihood (ML) of method of moments (MOM), is exceedingly difficult. This difficulty arises because, from the perspective of the econome- trician, the probability that an agent chooses a particular alternative is a high dimensional integral over stochastic factorsunobserved by the econometricianthat affect the utilities that the agent assigns to each alternative. These probability expressions must be evaluatedthat the agent assigns to each alternative....
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