Revealed Preferences in Theory and Experiments

This dissertation investigates the empirical content of one of the most basic assumptions in economics: the existence of a preference relation that describes the agent’s decision- making process. As preferences cannot be observed, only choices can be, the relation between preferences and choices, i.e., the study of revealed preferences, is a fundamental question in social sciences. This dissertation broadens our knowledge about revealed preferences by studying two topics: when are choices consistent with a utility function that satisfy some (widely assumed) characteristics, and how can we analyze choices that are not perfectly consistent with any preference relation./nChapter 1 studies when choices that satisfy the Generalized Axiom of Revealed Preferences (GARP) can be described using a strictly concave and differentiable utility function. Strict concavity and differentiability are commonly assumed. They assure that an agent’s behavior presents regularities that make it tractable for analysis. This chapter provides the first necessary and sufficient conditions on demand data for the existence of a strictly concave and differentiable utility. An empirical analysis of laboratory data suggests that such property is substantially more common than what would have been concluded using previously existing methods./nChapters 2 and 3 study the problem of learning about a consumer’s preferences when her choices are an imperfect implementation of such preferences, i.e., when the observed choices fail GARP. Chapter 2 focuses on recovering preferences using partial efficiency, the most widespread tool in the literature. Specifically, it studies whether we can falsify that the agent’s utility function generates a (single-valued) differentiable demand function. A differentiable demand function presents several advantages from an analytical standpoint and is usually assumed in theoretical and empirical work. If an agent’s choices are not a perfect implementation of her preferences, then a differentiable demand function cannot be falsified. Hence such utility can be falsified only if the observed choices satisfy the Generalized Axiom of Revealed Preferences but fail its strong version. An empirical implementation of this test on laboratory data finds that we cannot falsify the existence of a utility function generating a differentiable demand for any subject. Therefore assuming such demand does not provide an empirical cost./nChapter 3 presents a new method to learn about an agent’s preferences when her choices are an imperfect implementation of such preferences. Previous methods rely on intuitive motivations but lack basic statistical properties; in particular, they do not assure the recovery of the agent’s underlying preference. This chapter presents the first method that asymptotically recovers the agent’s preference relation, i.e., that is statistically consistent, under imperfect implementation. Empirical analysis shows that this method presents a higher correlation (when compared with existing alternatives) between its measure of decision-making quality and its out-of-sample accuracy. This result suggests that the question about which preferences we measure distance from choices is not innocuous. The last part of this chapter shows the generality of the proposed method by showing that its properties also apply in a vast class of choice environments beyond the classical consumer problem.

Advisor: Kariv, Shachar