Semiparametric Identification of the Discount Factor and Payoff Function in Dynamic Discrete Choice Models
Prof. Katsumi Shimotsu
Professor,
University of Tokyo
We study the identification of the discount factor and payoff function in standard stationary infinite-horizon dynamic discrete choice models. In single-agent models with an exclusion restriction, we show that the discount factor is identified up to a finite set, with its cardinality bounded by that of the state space. We demonstrate that commonly imposed nonparametric assumptions on per-period payoffs – such as homogeneity, monotonicity, concavity, and zero cross-differences – provide identifying restrictions on the discount factor through equality and inequality constraints. In dynamic game models, we show that standard nonparametric assumptions – such as irrelevance of other firms’ lagged actions, exchangeability of other firms’ actions, and independence of entry cost from other firms’ actions – enable identification of the firm-specific discount factors. Our results highlight how commonly used nonparametric and semiparametric modeling assumptions in economic analysis help identify the discount factor and payoff functions.