Abstract
This thesis contains three independent chapters on dynamic discrete choice models (DDCMs).
The first chapter begins with an introduction to DDCMs, detailing some of the main estimators in the literature. Then, it provides numerical results for when such models entail a finite mixture specification, comparing three estimators, one of which is a modified version of the EM algorithm adapted to DDCMs by \cite{arcidiacono2011conditional}. The maximum likelihood in their algorithm's M-step is replaced here with GLS/OLS estimators in order to simplify computation. Such numerical study provides small sample evidence on the performance of linear and nonlinear two-step estimators under unobserved heterogeneity.
The second chapter constructs and estimates a dynamic discrete choice structural model of the decision of employers to invest in further training of their workers, considering the resultant economic cost and impact on productivity and wages. In doing so, I intend to provide the literature on firm training, which dates back to \cite{becker1964}, with a means to conduct counterfactual analysis and policy evaluation. Using an unbalanced panel on retail trade containing data on 1220 German establishments, I estimate the economic cost and long-run value of training, and show how productivity and wage levels affect the employer's decision to train. The findings indicate that establishments with non-extreme values of productivity and wages, and a large number of employees are the ones most likely to train. In addition, they show that having trained previously acts as an incentive for current training because the estimated cost of keeping training is lower than that of starting to train.
The third chapter, like the first one, explores unobserved heterogeneity, however now expressed continuously. It is an extension of the work by \cite{chesher2002taste}, who present an approximation to logit models with taste variation. Here, the same approach is derived for DDCMs, resulting in a maximum likelihood estimator and an iterated least squares estimator being proposed, which deliver estimates with reduced bias relative to an estimation that ignores the existence of heterogeneity. Moreover, advantages over current parametric and nonparametric methods are that no distributional assumptions for the heterogeneity must be made and no grids must be chosen. Finally, the maximum likelihood estimator solves the dynamic programming problem (DPP) without any unobserved heterogeneity considered, such that the DPP is solved only once at each evaluation of the likelihood. Meanwhile, a typical nonparametric approach would require the DPP to be solved at each point of a selected grid for each likelihood evaluation. This can potentially cause computational time and convergence issues, which are here avoided.