Semiparametric Estimation of Dynamic Discrete Choice Models

Abstract

We consider the estimation of dynamic discrete choice models in a semiparametric setting, in which the per-period utility functions are known up to a finite number of parameters, but the distribution of utility shocks is left unspecified. This semiparametric setup differs from most of the existing identification and estimation literature for dynamic discrete choice models. To show identification we derive and exploit a new Bellman-like recursive representation for the unknown quantile function of the utility shocks. Our estimators are straightforward to compute; some are simple and require no iteration, and resemble classic estimators from the literature on semiparametric regression and average derivative estimation. Monte Carlo simulations demonstrate that our estimator performs well in small samples. To highlight features of this estimator, we estimate a structural model of dynamic labor supply for New York City taxicab drivers.

A Dynamic Discrete Choice Model of Reverse Mortgage Borrower Behavior

“…For example Taber (2000) considered the case where the distribution of errors is instead left unspecified, under certain exclusion restrictions. In more recent work, Buchholz et al (2016) build on Srisuma and Linton (2012)'s framework for continuous-state models to develop a single-index representation and a corresponding closed-form semiparametric estimator for dynamic binary choice models with linear utility functions and unspecified error distributions. Komarova et al (2018) also consider models with linear payoffs, but with a focus on identification of the discount factor, payoff coefficients, and switching cost parameters when the distribution of errors is known.…”

Partial Identification and Inference for Dynamic Models and Counterfactuals

“…(Unknown β and G.) Although we assume a known discount factor, it is straightforward to extend our analysis by either making use of the contributions by Magnac and Thesmar (2002) and Abbring and Daljord (2019) to identify β, or by indexing Π I by β and taking the identified set for π as the union of the sets Π I (β)'s for all admissible discount factors. Similarly, Blevins (2014), Chen (2017), and Buchholz, Shum, and Xu (2019) consider identification of G under different model assumptions. One can combine their assumptions to identify G and Π I simultaneously, or take the union of the sets Π I (G)…”

Joint analysis of the discount factor and payoff parameters in dynamic discrete choice models

“…Q is typically assumed known in most empirical applications. Conditions for the identification of Q exist when is a continuous variable using a large support type argument; for example, see Aguirregabiria and Suzuki (, Proposition 1), Buchholz, Shum, and Xu (, Lemma 4), and Chen (, Theorem 4). Our results do not depend on any continuity assumption to achieve identification as we take to be a discrete random variable.…”