Identifying the discount factor in dynamic discrete choice models

Empirical research often cites observed choice responses to variation that shifts expected discounted future utilities, but not current utilities, as an intuitive source of information on time preferences. We study the identification of dynamic discrete choice models under such economically motivated exclusion restrictions on primitive utilities. We show that each exclusion restriction leads to an easily interpretable moment condition with the discount factor as the only unknown parameter. The identified set of discount factors that solves this condition is finite, but not necessarily a singleton. Consequently, in contrast to common intuition, an exclusion restriction does not in general give point identification. Finally, we show that exclusion restrictions have nontrivial empirical content: The implied moment conditions impose restrictions on choices that are absent from the unconstrained model.