Essays on Structural Dynamic Discrete Models

Abstract

In the dynamic discrete choice model of Rust (1987), any economic variable relevant to decision-making and correlated across time must be observed by the econometrician. This can be an inconvenient restriction. In the first chapter of this thesis, "Hidden Rust Models", I introduce a class of models allowing for unobserved dynamics in a dynamic discrete choice context. Hidden Rust models can be thought of as partially observed classical Rust models. There is an unobserved component to the discrete Markovian state variable. The unobserved random utility shocks (the "epsilons") remain independent and identically distributed across time. This makes the estimation of hidden Rust models fast and convenient. By contrast, the popular alternative models with autoregressive random utility shocks (AR(1) epsilons) is much harder to estimate. The chapter focuses on the practical estimation of hidden Rust models and illustrates their use in a model of dynamic financial incentives inspired by Duflo et al. (2012).

A hidden Rust model can be seen as a partially observed Markov chain whose transition matrix is constrained by economic theory. There are two types of constraints: (1) conditional independences and structural zero transition probabilities (2) compatibility with a lower-dimensional utility parameter in accordance with the economic model of decision-making. Many lessons from chapter 1 carry over to any economic model fitting this description. Those structural dynamic discrete models are what brings together the three chapters of this thesis.

In the second chapter, "Algebraic models have a generic and stable identification structure", I study the issue of identification for models whose identification equation can be written as a system of polynomial equations, "algebraic models" for short. Structural dynamic discrete models are a foremost example of algebraic models. I show that algebraic models have a generic identification structure and that dynamic algebraic models have a stable identification structure.

In the last chapter of this thesis, "Times-series asymptotics for structural dynamic discrete models", I prove that structural dynamic discrete models have good statisical asymptotic properties under a set of assumptions geared at hidden Rust models in particular, and I comment on extensions to more general models.