Abstract Is the Pareto optimality of matching mechanisms robust to the introduction of boundedly rational behavior? To address this question I define a restrictive and a permissive notion of Pareto optimality and consider the large set of hierarchical exchange mechanisms which contains serial dictatorship as well as Gales top trading cycles. Fix a housing problems with boundedly rational agents and a hierarchical exchange mechanism. Consider the set of matchings that arise under all possible assignments of agents to initial endowments in this mechanism. I show that this set is nested between the sets of Pareto optima according to the restrictive and the permissive notion. These containment relations are generally strict, even when deviations from rationality are minimal. In a similar vein, minimal deviations from rationality suffice for the set of outcomes of Gale's top trading cycles for all possible initial endowments to differ from the set of outcomes of serial dictatorship for all possible orders of agents as dictators.

In this paper, we introduce a new measure of how close a set of choices are to satisfying the observable implications of rational choice, and apply it to a large balanced panel of household level consumption data. We use this method to answer three related questions: (i) "How close are individual consumption choices to satisfying the model of utility maximization? " (ii) "Are there di¤erences in rationality between di¤erent demographic groups? " (iii) "Can choices be aggregated across individuals under the assumption of homogeneous preferences? " Crucially, in answering these questions, we take into account the power of budget sets faced by each household to expose failures of rationality. To summarize our results we …nd that: (i) while observed violations of rationality are small in absolute terms, our households are only moderately more rational than the benchmark of random choice; (ii) there are signi…cant di¤erences in the rationality of di¤erent groups, with multi-head households more rational than single head households, and the youngest households more rational than middle age households; (iii) the assumption of homogenous preferences is strongly rejected: choice data that is aggregated across households exhibits high levels of irrationality.

We introduce a new measure of how close a set of choices are to satisfying the observable implications of rationality and apply it to a large balanced panel of household level consump-tion data. This new measure, the Minimum Cost Index, is the minimum cost of breaking all revealed preference cycles found in choices from budget sets. Unlike existing measures of rationality, it responds to both the number and severity of revealed preference violations.

We bring revealed preference theory to bear on the problem of re-covering approximate parametric preferences from consistent and in-consistent consumer choices. The paper investigates two measures for the incompatibility between the revealed preference relation implied by choices and the ranking induced by the proposed parametric preferences. We provide a novel characterization of several well-known inconsistency indices through these incompatibility measures. This allows a researcher to analyze both consistent and inconsistent choices, by decomposing an incompatibility measure into inconsistency and misspecification indices. We are grateful to the editor Ali Hortaçsu and anonymous referees for insightful com-ments and suggestions that significantly improved this work. We thank Jose Apesteguia,