Identification of Intertemporal Preferences in History-Dependent Dynamic Discrete Choice Models

We study the identification of intertemporal preferences in a stationary dynamic discrete decision model. We propose a new approach which focuses on problems which are intrinsically dynamic: either there is endogenous variation in the choice set, or preferences depend directly on the history. History dependence links the choices of the decision-maker across periods in a more fundamental sense standard dynamic discrete choice models typically assume. We consider both exponential discounting as well as the quasi-hyperbolic discounting models of time preferences. We show that if the utility function or the choice set depends on the current states as well as the past choices and/or states, then time preferences are non-parametrically point-identified separately from the utility function under mild conditions on the data and we may also recover the instantaneous utility function without imposing any normalization on the utility across states