Repeated Choice: A Theory of Stochastic Intertemporal Preferences

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Abstract: We provide a repeated choice foundation for models of stochastic choice. An agent chooses from a menu repeatedly over time generating a time series of choices. We study the limit frequency of these choices and characterize when they are generated by a subjective ergodic utility process. All parameters of the model can be fully identified from binary choices. When the agent satisfies Independence of Continuation Menus (ICM), inference can be performed without modeling repetition and continuation problems explicitly. On the other hand, if ICM is violated, then ignoring continuation menus will lead to biased estimates and inferences. We show that ICM holds if and only if the utility process is standard, i.e. additively separable across time. Moreover, it is equivalent to indifference to the timing of resolution of uncertainty and a repeated version of the classic independence axiom. Applications include elicitation of risk-aversion under stochastic Epstein-Zin preferences and estimation under dynamic discrete-choice models.