My email is cugarte@berkeley.edu

Economic models usually endow agents with (well-behaved) differentiable utilities. However, the behavioral implications of such an assumption are unclear. We study conditions under which consumer choices can be rationalized by a differentiable utility, which we call smooth rationalization. The main consequence of assuming a differentiable utility is that choices that are revealed indifferent to each other must have the same marginal rate of substitution. To include this requirement, we propose a modification of the original data set using the revealed indifference relation and show that rationalizing the modified data set is equivalent to smooth rationalization. The same reasoning applies when differentiability is required for a strictly concave utility. We also show that the existence of second- and higher-order derivatives, which are used in comparative statics, cannot be tested. We test smooth rationalization into several experimental data sets. Our results suggest that, in most cases, assuming differentiability is not costly from an empirical standpoint.

We study the problem of recovering preferences from choices that are inconsistent with the Generalized Axiom of Revealed Preferences (GARP). The underlying model is that the failure of GARP arises because the agent imperfectly implements her preferences. Existing methods to recover preferences rely on intuitive motivations but lack desirable statistical properties. Instead, we propose the first statistically consistent estimator. The main assumption is that revealed preferences, the classical tool used to analyze choices, are more likely to be correct than incorrect. Therefore, they are a trustworthy source of information. The set of possible estimators for finite data is characterized by the directly revealed preferences that are interpreted as incorrect. Besides consistency, our estimator also satisfies partial efficiency, which is a standard requirement in the literature. We apply our estimator to laboratory data and compare it with that derived from the Varian index. Our estimator presents a stronger correlation between accuracy and its measure of distance from GARP. It is also significantly faster and more feasible to implement for subjects with many inconsistencies. Finally, we extend our method to a vast class of choice problems, beyond the classical consumer setting.

Economic research usually endows consumers with a single-valued demand function. When choices are rationalizable, this assumption can be tested by the Strong Axiom of Revealed Preferences, SARP, as if they fail such a test, the demand is set-valued. We extend this test to non-rationalizable choices using partial efficiency, the most popular method to recover preferences. Under partial efficiency, a single-valued demand cannot be tested; furthermore, it can always be chosen to be infinitely differentiable. Hence, the existence of a single-valued, infinitely differentiable demand is falsified if, and only if, choices are rationalizable but fail SARP, which we do not observe in laboratory data. From an empirical standpoint, our results suggest that assuming a differentiable demand does not carry a cost.