With Øystein Daljord and Fedor Iskhakov, I am studying the identification of time preferences from dynamic discrete choice data.

The recent literature often cites Fang and Wang (2015) for analyzing the identification of time preferences in dynamic discrete choice under exclusion restrictions (e.g. Yao et al., 2012; Lee, 2013; Ching et al., 2013; Norets and Tang, 2014; Dubé et al., 2014; Gordon and Sun, 2015; Bajari et al., 2016; Chan, 2017; Gayle et al., 2018). Fang and Wang's Proposition 2 claims generic identification of a dynamic discrete choice model with hyperbolic discounting. This claim uses a definition of "generic" that does not preclude the possibility that a generically identified model is nowhere identified. To illustrate this point, we provide two simple examples of models that are generically identified in Fang and Wang's sense, but that are, respectively, everywhere and nowhere identified. We conclude that Proposition 2 is void: It has no implications for identification of the dynamic discrete choice model. We show that its proof is incorrect and incomplete and suggest alternative approaches to identification.

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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.

We derive conditions for identification of sophisticated, quasi-hyperbolic time preferences in a finite horizon, dynamic discrete choice model under a set of exclusion restrictions that are commonly used to identify time-consistent preferences. Identification is reduced to characterizing of the zero set of two bivariate polynomial moment conditions. The number of discount function parameters in the identified set is bounded by known features of the data distribution. We show that though the discount function parameters are formally identified, it is hard to precisely estimate each parameter separately. We argue that the standard approach to identify time-consistent preferences does not well capture preference-reversals, which is the defining feature of time-inconsistent preferences.