Semiparametric identification and heterogeneity in discrete choice dynamic programming models

Empirical discrete choice dynamic programming models have become important empirical tools. A question that arises in estimation and interpretation of the results from these specifications is which combination of data and assumptions are needed to overcome problems of heterogeneity, selection, and omited variables bias. This paper addresses this question by considering nonparametric identification of a version of the model that allows for quite general forms of unobservable and information structures. I show that the model can be identified under conditions similar to a static polychotomous choice model. Using a stochastic version of an ‘identification of infinity’ argument, utility can be identified up to a monotonic transformation of the observables under strong support conditions and two types of exclusion restriction. The first type is similar to a standard static exclusion restriction: a variable that influences the first period decision, but does not enter the second period decision directly. The second type requires a variable that does not affect the utility of the first option directly, but is known during the first period, and has predictive power on the choice during the second. I also provide two specifications under which the full error structure can be identified. This requires the additional assumption of stochastic innovations in the observables. I then use the model to estimate schooling decisions in which students deciding whether to drop out of high school account for the option value of attending college.