Identification and semiparametric estimation of a finite horizon dynamic discrete choice model with a terminating action

Abstract

We study identi…cation and estimation of …nite-horizon dynamic discrete choice models with a terminal action. We …rst demonstrate a new set of conditions for the identi…cation of agents' time preferences. Then we prove conditions under which the per-period utilities are identi…ed for all actions in the agent's choice-set, without having to normalize the utility for one of the actions. Finally, we develop a computationally tractable semiparametric estimator. The estimator uses a two-step approach that does not use either backward induction or forward simulation. Our methodology can be implemented using standard statistical packages without the need to write specialized computational routines, as it involves linear (or nonlinear) projections only. Monte Carlo studies demonstrate the superior performance of our estimator compared with existing two-step estimation methods.Monte Carlo studies further demonstrate that the ability to identify the per-period utilities for all actions is crucial for counterfactual predictions. As an empirical illustration, we apply the estimator to the optimal default behavior of subprime mortgage borrowers, and the results show that the ability to identify the discount factor, rather than assuming an arbitrary number as typically done in the literature, is also crucial for obtaining correct counterfactual predictions. These …ndings highlight the empirical relevance of key identi…cation results of the paper.

Linear IV Regression Estimators for Structural Dynamic Discrete Choice Models

“…A terminal action ends the decision making process. Examples of terminal actions include a worker retiring (Rust and Phelan, 1997), a mortgage owner defaulting (Bajari, Chu, Nekipelov, and Park, 2016), and a household adopting a PV system (De Groote and Verboven, 2019). For both renewal and terminal actions, (6) simplifies to…”

Partial Identification and Inference for Dynamic Models and Counterfactuals

“…Rust (1994) showed that DDC models are not identified nonparametrically, and Magnac and Thesmar (2002) characterized the degree of underidentification. Important advances that followed include (but are not limited to) Heckman and Navarro (2007), Pesendorfer and Schmidt-Dengler (2008), Blevins (2014), Bajari, Chu, Nekipelov, and Park (2016), and Abbring and Daljord (2019). In terms of estimation, Rust (1987) introduced the nested fixed point maximum likelihood estimator in his seminal contribution, and Hotz and Miller (1993) pioneered a computationally convenient two-step estimator that was then further analyzed by a host of important studies (Hotz, Miller, Sanders, and Smith, 1994;Aguirregabiria andMira, 2002, 2007;Bajari, Benkard, and Levin, 2007;Pakes, Ostrovsky, and Berry, 2007;Pesendorfer and Schmidt-Dengler, 2008).…”

Partial Identification and Inference for Dynamic Models and Counterfactuals

“…Rust (1994) showed that DDC models are not identified nonparametrically, and Magnac and Thesmar (2002) characterized the degree of underidentification. Important advances that followed include (but are not limited to) Heckman and Navarro (2007), Pesendorfer and Schmidt-Dengler (2008), Blevins (2014), Bajari, Chu, Nekipelov, and Park (2016), and Abbring and Daljord (2019). In terms of estimation, Rust (1987) introduced the nested fixed point maximum likelihood estimator in his seminal contribution, and Hotz and Miller (1993) pioneered a computationally convenient two-step estimator that was then further analyzed by a host of important studies (Hotz, Miller, Sanders, and Smith, 1994;Aguirregabiria andMira, 2002, 2007;Bajari, Benkard, and Levin, 2007;Pakes, Ostrovsky, and Berry, 2007;Pesendorfer and Schmidt-Dengler, 2008).…”