Randomly evolving tastes and delayed commitment

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Abstract

We consider a decision maker with randomly evolving tastes who faces dynamic decision situations that involve intertemporal tradeoffs, such as those in consumption savings problems. We axiomatize a recursive representation of choice that features uncertain consumption utilities, which evolve according to a subjective Markov process. The parameters of the representation, which are the subjective Markov process governing the evolution of utilities, and the discount factor, are uniquely identified from behavior. We relate the correlation of tastes over time and the desire to delay commitment to future consumption.

Introduction

While taste is often modeled as a stable trait of the individual decision maker, tastes do evolve over time in many instances. For example, risk aversion tends to change over time (see Bekaert et al., 2010 and the references therein.) Accounting for evolving tastes, or taste shocks, is important in dynamic models of choice in macroeconomics and applied microeconomics, where data is usually noisy. The literature makes various assumptions about such taste shocks, including serial correlation. However, Magnac and Thesmar (2002) find that dynamic models with serially correlated (unobservable) taste shocks cannot be identified based on discrete choice data alone.

We consider a decision maker who perceives a particular type of Markov process that governs the evolution of his tastes, that is, his current taste is a sufficient statistic for his current beliefs over future tastes. We then analyze initial preferences over Infinite Horizon Consumption Problems as introduced in Gul and Pesendorfer (2004) (henceforth GP) where, in every period, choice is between lotteries over current consumption and a continuation choice problem for the next period. Theorem 1 fully characterizes the behavioral implications of our model for this dynamic choice data and shows that it is the appropriate data for full identification.

Consider, then, the dynamic behavior of a forward looking decision maker, who is aware that his tastes may change, and who embraces the future changes in tastes, in the sense that he evaluates future consumption based on his expectation of future consumption tastes. On the one hand, if tastes evolve randomly, then he prefers not to commit to consumption choice in advance. On the other hand, if tastes are correlated between subsequent periods, then the reluctance to commit will be reduced as the time of consumption draws nearer. That is, the decision maker prefers to delay necessary commitment.1

Importantly, however, the Markovian structure of the process that governs the evolution of tastes means that he is willing to commit to a continuation problem for the next period, contingent on the current taste. While this taste is not observable by the analyst, we argue that this willingness to commit should also hold contingent on current consumption choice from a large enough menu. Our key novel axiom, Choice Contingent Continuation Strategic Rationality (Choice Contingent CSR), formalizes this notion.

Krishna and Sadowski (2014) (henceforth KS) model a decision maker in a dynamic environment who chooses over acts on an objective space of states of the world, and who has stable but noisy state-contingent tastes. A common special case of their model and ours features a stable and state independent underlying taste that is perturbed by iid noise (or transient taste shocks). Axiom N.1 relaxes their notion of unconditional Continuation Strategic Rationality.

Our other axioms, while many, are quite standard. Our static Axioms S.1–S.4, in particular, are well studied in the menu choice literature, and are independent of whether the problem is static or dynamic. Most of our dynamic Axioms D.1–D.4 are discussed in KS. Those dynamic axioms are necessary for any model of dynamic preferences that is recursive, stationary, and Markovian. In addition, we impose a structural condition, Persistent Preference for Flexibility (Axiom N.2,) that ensures that the subjective states in the representation are neither transient nor absorbing.

According to Theorem 1, the Markov process that governs the evolution of tastes over time in our representation is uniquely identified from first period preferences, as is the only other preference parameter, the discount factor. To further explore the tight connection between observable behavior and the correlation of consumption tastes over time, note that for correlated tastes, knowledge of the taste at one point will reduce an individual’s uncertainty about future tastes. In that case, the individual’s aversion to commit to a consumption choice should decrease between one period and the next, more so the more correlated tastes are over time. For example, an investor will be less averse to commit to a more or less risky portfolio (say by accepting a penalty for reallocating his funds) given his current risk aversion, if his risk aversion is strongly correlated over time. This is independent of ex-ante uncertainty about the level of risk aversion. Theorem 2 provides comparative statics that formalize this intuition.

Section snippets

A model of randomly evolving tastes

This section provides our representation result. Section 2.1 describes the environment, Section 2.2 has the behavioral axioms, Section 2.3 contains the representation result and Section 2.4 provides intuition for the proof of the representation result.

Correlated tastes and delayed commitment

Tastes in our model are correlated over time. Thus, DM’s knowledge of his taste at one point in time might reduce his uncertainty about future tastes. This implies that DM’s willingness to commit to future consumption upon learning his current taste will depend on the degree to which his tastes are correlated over time. We now formalize this intuition as a basis for comparing decision makers.13

Related literature

Rather than passively learning about the taste, as in our model, a decision maker might actively contemplate his taste, where such contemplation is costly. Ergin and Sarver (2010) provide a model of costly contemplation in the context with only one instance of consumption choice, as first analyzed by Dekel et al. (2001). A related model in a dynamic context is provided by Dillenberger et al. (2020), where the decision maker tries to learn about the verifiable state of the world, rather than his

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Cited by (0)

We would like to thank Haluk Ergin, Wolfgang Pesendorfer, Todd Sarver, and Norio Takeoka, as well as the editor and referees, for helpful comments and suggestions, and Vivek Bhattarcharya, Matt Horne, and Justin Valasek for valuable research assistance.

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