Essays on Dynamic Discrete Choice Models

<p dir="ltr">In the first chapter, “A Structural Approach to Opioid Misuse: Health, Labor, Policies, and Misperception of Opioid Misuse Risk,” I highlight the heterogeneous opioid misuse opioid behavior in health and employment statuses and the role of misperception of the risk of opioid misuse in evaluating policy interventions to reduce opioid misuse. Three aggregate changes that characterize the opioid epidemic during 2015-2019 are considered: the increased probability of death from opioid misuse, the expansion of state-level policies on opioid prescribing, and the fluctuating illegally traded opioid prices. A dynamic model of opioid misuse and labor decisions with two-dimensional latent health with a stochastic misperception of the risk of misusing opioids is developed, where the misperception bias induces agents to discount the probability of dying from opioid misuse more than the rational agent. The model estimates show that separation from the labor market is just as important as poor health conditions in determining opioid misuse. Moreover, I find that people who experience a misperception of opioid misuse risk significantly discount the probability of death from opioid misuse. The decomposition exercise using the 2015 population as a benchmark shows that the observed secular trend in the decrease in opioid misuse rate is almost entirely attributed to the increased statistical probability of death from opioid use. State-level policies on opioid prescribing decrease the opioid misuse rate for the population who are not displaced from the labor market or in good physical and mental health, but its effect is offset by those who are separated from the labor market or people in poor health. Although I find reasonable signs for the price elasticity in illegally traded opioid misuse across health and labor statuses, I find no effect of opioid price changes on opioid misuse rates. Lastly, I find that shutting down the misperception of the risk of opioid misuse can significantly decrease opioid misuse, shedding light on a new channel to decrease opioid misuse.</p><p dir="ltr">In the second chapter, "Identification and Estimation of Dynamic Discrete Choice Models with a Terminal State," I show that setting the terminal value to zero in a dynamic discrete choice model is not an innocuous assumption. I apply the observational equivalence theorem from Arcidiacono and Miller (2020) to this class of models to show the terminal value appears nonlinearly in the choice-specific conditional value function. I then provide a simple numerical example to illustrate how the utility parameter estimates can be biased even with the correct specification for the flow utility if the terminal value is set to zero. This exercise thus suggests that econometricians should leave the value of the terminal state to be estimated along with the flow utility of our choice, especially since we often make a strong parametric assumption on the flow utility than what is necessary for identification. Alternatively, a researcher may modify the flow utility to take the role of the value of the terminal state. </p><p dir="ltr">In the third chapter, "Estimation of Dynamic Discrete Choice Models with Subjective Beliefs under Finite Dependence Property," I propose a novel estimation strategy for estimating a dynamic discrete choice model whose transition probabilities exhibit 1-period finite dependence and the economic agents' perceived transition probabilities deviate from rational expectations. Estimating dynamic discrete choice models where the perceived transition probabilities differ from rational expectations is challenging because the transition probabilities are now a function of structural parameters that need to be estimated along with utility parameters. I extend the two-step estimation strategy in Arcidiacono and Miller (2011) to overcome this challenge by iterating between finding the finite dependence paths for the conditional value function contrasts and estimating the structural parameters given the set of conditional value function differences. By deploying a parsimonious infinite horizon dynamic discrete choice model with a terminal state with stochastic perception bias, I show numerically that the method works well.</p>