Dynamic Random Utility

Abstract

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 (Ut) of utilities. We show first that even when (Ut) is arbitrary, dynamic random utility imposes new testable across‐period restrictions on behavior, 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 period‐t choices reveal information about Ut, which 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 imposing natural Bayesian rationality axioms restricts the form of randomness that (Ut) 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 allow 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.

Random Utility, Repeated Choice, and Consumption Dependence

“…Related Literature. Our paper is most closely related to Lu and Saito (2020) and Frick et al (2019). Lu and Saito (2020) studies the individual interpretation of stochastic choice when the agent's utility potentially takes into account both today's consumption as well as the agent's continuation value.…”

“…A second difficulty that may arise, even in the case of a myopic agent, is that the agent's preference tomorrow may be a random function of not only their preference today but of their choice today as well. Borrowing the language of Frick et al (2019), this phenomenon is called consumption dependence. In the case of consumption dependence, the agent's stationary distribution over preferences may depend on the set of alternatives available to them.…”

“…In their setting, they find that dynamic sophistication leads to biased estimation if and only if the agent's utility function over today's consumption c and their continuation value v does not take the form U(c, v) = (1 −β)u(c) + βv where u is a random expected utility function and β ∈ (0, 1] is a random discount factor. Frick et al (2019) proposes the dynamic random expected utility model in order to axiomatically study choice data that is apparently history dependent. One of their main goals is to characterize patterns of history dependence which are spurious.…”

“…In an earlier version of their paper, they extend their model to explicitly allow for consumption dependence and characterize which forms of history dependence can arise due to consumption dependence. Our paper is concerned with how consumption dependence, as studied in Frick et al (2019), may lead to troubles when aggregating the repeated decisions of a single agent, a similar problem to the one studied in Lu and Saito (2020).…”

“…Falmagne (1978), Barberá and Pattanaik (1986), McFadden andRichter (1990), andFiorini (2004) offer axiomatic characterization of the random utility model. Gul and Pesendorfer (2006) introduces the random expected utility model which serves as the basis for many of the papers, including Frick et al (2019) and Lu and Saito (2020), studying random utility in dynamic settings. To our knowledge, Fudenberg and Strzalecki (2015) is the first to study the axioms of a random utility model in a dynamic setting.…”