Repeated Choice: A Theory of Stochastic Intertemporal Preferences
We provide a repeated-choice foundation for stochastic choice. We obtain necessary and sufficient conditions under which an agent's observed stochastic choice can be represented as a limit frequency of optimal choices over time. In our model, the agent repeatedly chooses today's consumption and tomorrow's continuation menu, aware that future preferences will evolve according to a subjective ergodic utility process. Using our model, we demonstrate how not taking into account the intertemporal structure of the problem may lead an analyst to biased estimates of risk preferences. Estimation of preferences can be performed by the analyst without explicitly modeling continuation problems (i.e. stochastic choice is independent of continuation menus) if and only ifthe utility process takes on the standard additive and separable form. Applications include dynamic discrete choice models when agents have non-trivial intertemporal preferences, such as Epstein-Zin preferences. We provide a numerical example which shows the significance of biases caused by ignoring the agent's Epstein-Zin preferences.