Under dynamic random utility, an agent (or population of agents) solves a dynamic decision problem subject to evolving private information. We analyze the fully general and non-parametric model, axiomatically characterizing the implied dynamic stochastic choice behavior. A key new feature relative to static or i.i.d. versions of the model is that when private information displays serial correlation, choices appear history dependent: different sequences of past choices reflect different private information of the agent, and hence typically lead to different distributions of current choices. Our axiomatization imposes discipline on the form of history dependence that can arise under arbitrary serial correlation. Dynamic stochastic choice data lets us distinguish central models that coincide in static domains, in particular private information in the form of utility shocks vs. learning, and to study inherently dynamic phenomena such as choice persistence. We relate our model to specifications of utility shocks widely used in empirical work, highlighting new modeling tradeoffs in the dynamic discrete choice literature. Finally, we extend our characterization to allow past consumption to directly affect the agent’s utility process, accommodating models of habit formation and experimentation.
We provide an axiomatic analysis of dynamic random utility, characterizing the stochastic choice behavior of agents who solve dynamic decision problems by maximizing some stochastic process (U_t) of utilities. We show first that even when (U_t) is arbitrary, dynamic random utility imposes new testable restrictions on how behavior across periods is related, over and above period-by-period analogs of the static random utility axioms: An important feature of dynamic random utility is that behavior may appear history dependent, because past choices reveal information about agents’ past utilities and (U_t) may be serially correlated; however, our key new axioms highlight that the model entails specific limits on the form of history dependence that can arise. Second, we show that when agents’ choices today influence their menu tomorrow (e.g., in consumption-savings or stopping problems), imposing natural Bayesian rationality axioms restricts the form of randomness that (U_t) can display. By contrast, a specification of utility shocks that is widely used in empirical work violates these restrictions, leading to behavior that may display a negative option value and can produce biased parameter estimates. Finally, dynamic stochastic choice data allows us to characterize important special cases of random utility—in particular, learning and taste persistence—that on static domains are indistinguishable from the general model.
We propose nonparametric definitions of absolute and comparative naivete. These definitions leverage ex-ante choice of menu to identify predictions of future behavior and ex-post (random) choices from menus to identify actual behavior. The main advantage of our definitions is their independence from any assumed functional form for the utility function representing behavior. An individual is sophisticated if she is indifferent between choosing from a menu ex-post or committing to the actual distribution of choices from that menu ex-ante. She is naive if she prefers the flexibility in the menu, reflecting a mistaken belief that she will act more virtuously than she actually will. We propose two definitions of comparative naivete and explore the restrictions implied by our definitions for several prominent models of time inconsistency. Finally, we discuss the implications of general naivete for welfare and the design of commitment devices.
We propose nonparametric definitions of absolute and comparative naivete. These definitions leverage ex-ante choice of menu to identify predictions of future behavior and ex-post (random) choices from menus to identify actual behavior. The main advantage of our definitions is their independence from any assumed functional form for the utility function representing behavior. An individual is sophisticated if she is indifferent ex-ante between retaining the option to choose from a menu ex-post or committing to her actual distribution of choices from that menu. She is naive if she prefers the flexibility in the menu, reflecting a mistaken belief that she will act more virtuously than she actually will. We propose two definitions of comparative naivete and explore the restrictions implied by our definitions for several prominent models of time inconsistency.