Essays on estimating dynamic discrete choice models: methods and applications

Abstract

Estimating dynamic discrete choice models (DDCM) is a common task in many disciplines, including various fields of economics. In a typical DDCM a forwardlooking decision-maker chooses from a finite set of actions in each time period by maximizing the expected sum of current and discounted future values of an objective function. The parameters that determine the objective function are called structural parameters. For example, consider the problem of a senior teacher deciding the timing of retirement. The retirement decision is in uenced by the current and future salaries, unobserved random factors, and pension rules. The teacher's objective function is the expected utility from the ow of salary or pension benefit. The structural parameters that shape the teacher's utility depict the teacher's preference and are independent of the environment (such as the pension rules.) Because the structural parameters are invariant to changes in environment, estimation of structural parameters is especially useful for simulating new policies that have not been employed in the past. A DDCM is often presented as a dynamic programming (DP) problem. Solving the DP model involves solving the Bellman equation. Even with a limited set of state variables solving the Bellman equation can be time consuming. Conventional structural estimation requires repeatedly solving the Bellman equation. High computational cost limits applications of structural discrete choice models in policy analysis. The proposed research seeks improving computational efficiency for dynamic binary choice models (DBCM), through deep neural networks (DNN). The thesis consists of three chapters. Chapter 1 proposes and implements a new method that uses DNN-aided learning to solve DP models during the process of estimation. We compare the new algorithm with several existing algorithms for estimating infinite horizon DBCM. The comparison of algorithm performance is made in the context of estimating three variants of Rust's (1987) optimal engine replacement model, the benchmark model in the literature of structural estimation. We find that without sacrificing much accuracy, the new approach substantially cuts computational time of the conventional approach (in Rust (1987)), is comparable to the ones developed by Imai et al. (2009), Norets (2009) and Norets (2012), and has the potential to outperform others when the model is more complex than the Rust model. The reduction in computational costs also allows us investigate the shape of likelihood function more intensively, and we find that the benchmark Rust model with serially correlated error may be unidentified. Chapter 2 focuses on structural estimation of DBCM in finite horizons. We consider teachers' optimal retirement problem. First, we show that the solutions to two similar models, DP and the option value model by Stock and Wise (1990) (SW), can both be presented by thresholds of preference errors. Second, we modify the three-step procedure of Norets (2012) to a simulated sample of teachers. We achieve reduction in computational time of the conventional nested algorithm by around 20-fold for DP and 5-fold for SW, without significant loss of accuracy. Lastly, the accuracy of the DNN aided algorithm is high enough to distinguish DP from SW as data generating model. Chapter 3 applies the DNN-aided structural estimation to analyze the effect of Illinois teacher pension rules. We first estimate structural parameters using data on Illinois teacher retirement. The structural estimation accounts for the dependence of sample distribution on previous pension policies. Then, as an out-of-sample test, we use the estimated structural parameters to simulate teacher's response to a historical pension enhancement, the "22 upgrade". The estimated structural model produces good in- and out-of sample fit and is useful for policy simulations.