Bayesian inference in dynamic discrete choice models

In this dissertation, I develop methods for Bayesian inference in dynamic discrete choice models (DDCMs.) Chapter 1 proposes a reliable method for Bayesian estimation of DDCMs with serially correlated unobserved state variables. Inference in these models involves computing high-dimensional integrals that are present in the solution to the dynamic program (DP) and in the likelihood function. First, the chapter shows that Markov chain Monte Carlo (MCMC) methods can handle the problem of multidimensional integration in the likelihood, which was previously considered infeasible for DDCMs with serially correlated unobservables. Second, the chapter presents an efficient algorithm for solving the DP suitable for use in conjunction with the MCMC estimation procedure. The algorithm utilizing random grids and nearest neighbor approximations iterates the Bellman equation only once for each parameter draw. The chapter evaluates the method's performance on two different DDCMs using real and artificial datasets. The experiments demonstrate that ignoring serial correlation in unobservables of DDCMs can lead to serious misspecification errors. Experiments on dynamic multinomial logit models, for which analytical integration is also possible, show that the estimation accuracy of the proposed method is good.

Chapter 2 presents a proof of the complete (and thus a.s.) uniform convergence of the DP solution approximations proposed in Chapter 1 to the true values under mild assumptions on the primitives of DDCMs. It also establishes the complete convergence of the corresponding approximated posterior expectations.

Chapter 3 proposes a method for inference in DDCMs that combines MCMC and artificial neural networks (ANN.) MCMC is intended to handle high dimensional integration in the likelihood function of richly specified DDCMs. ANNs approximate the DP solution as a function of the parameters and state variables beforehand of the estimation procedure to reduce the computational burden. Potential applications of the proposed methodology include inference in DDCMs with random coefficients, serially correlated unbservables, and dependent observations. The chapter discusses MCMC estimation of DDCMs, provides relevant background on ANNs, and derives a theoretical justification of the method. Experiments suggest that application of ANNs in the MCMC estimation of DDCMs is a promising approach.