An Afriat Theorem for the Collective Model of Household Consumption

We provide a nonparametric 'revealed preference' characterization of rational household behavior in terms of the collective consumption model, while accounting for general (possibly non-convex) individual preferences. We establish a Collective Axiom of Revealed Preference (CARP), which provides a necessary and sufficient condition for data consistency with collective rationality. Our main result takes the form of a 'collective' version of the Afriat Theorem for rational behavior in terms of the unitary model. This theorem has some interesting implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.collective model, consumption, Pareto efficiency, revealed preferences, Afriat theorem, Collective Axiom of Revealed Preferences

An Afriat Theorem for the Collective Model of Household Consumption

We provide a nonparametric 'revealed preference' characterization of rational household behavior in terms of the collective consumption model, while accounting for general (possibly non-convex) individual preferences. We establish a Collective Axiom of Revealed Preference (CARP), which provides a necessary and su¢ cient condition for data consistency with collective rationality. Our main result takes the form of a 'collective' version of the Afriat Theorem for rational behavior in terms of the unitary model. This theorem has some interesting implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.Collective model;consumption;Pareto efficiency;revealed preferences;Afriat theorem;Collective Axiom of Revealed Preferences

An afriat theorem for the collective model of household consumption.

We provide a nonparametric ‘revealed preference’ characterization of rational household behavior in terms of the collective consumption model, while accounting for general (possibly non-convex) individual preferences. We establish a Collective Axiom of Revealed Preference (CARP), which provides a necessary and sufficient condition for data consistency with collective rationality. Our main result takes the form of a ‘collective’ version of the Afriat Theorem for rational behavior in terms of the unitary model. This theorem has some interesting implications. With only a finite set of observations, the nature of consumption externalities (positive or negative) in the intra-household allocation process is non-testable. The same non-testability conclusion holds for privateness (with or without externalities) or publicness of consumption. By contrast, concavity of individual utility functions (representing convex preferences) turns out to be testable. In addition, monotonicity is testable for the model that assumes all household consumption is public.

Private versus public consumption within groups : testing the nature of goods from aggregate data

We study the testability implications of public versus private consumption. The distinguishing feature of our approach is that we start from a revealed preference characterization of collectively rational behavior. Remarkably, we find that assumptions regarding the public or private nature of specific goods do have testability implications, even if one only observes the aggregate group consumption. In fact, these testability implications apply as soon as the analysis includes three goods and four obervations. This stands in sharp contrast with existing results that start from a differential characterization of collectively rational behavior. In our opinion, our revealed preference approach obtains stronger testability conclusions because it focuses on a global characterization of collective rationality, whereas the differential approach starts from a local characterization.Collective model, revealed preferences, public goods, private goods, consumption externalities.

On the rationalizability of observed consumers’ choices when preferences depend on budget sets and (potentially) on anything else

We prove that defining consumers’ preferences over budget sets is both necessary and sufficient to make every fully informative and finite set of observed consumption choices rationalizable by a collection of preferences which are transitive, complete, and monotone with respect to own consumption. Our finding has two important theoretical consequences. First, assuming that preferences depend on budget sets is illegitimate under the scientific commitments of revealed preference theory. Second, as long as consumers’ preferences are not defined over budget sets, we can assume that preferences depend on observable objects other than own consumption without compromising the logical possibility to reject the model against observation. We however point out that, despite this logical possibility, in practice it can be almost impossible to reject a model where preferences are defined over objects that depend on budget sets. As an example of this we show that if preferences are defined over consumption choices of other individuals then rationalization fails only in cases of negligible practical interest.Revealed Preferences, Budget Sets, Rational Preferences, Rationalizability

The Housing Problem and Revealed Preference Theory: Duality and an application

This paper exhibits a duality between the theory of revealed preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat’s theorem can be interpreted as a second welfare theorem in the housing problem. Using this duality, the revealed preference problem is connected to an optimal assignment problem, and a geometrical characterization of the rationalizability of experiment data is given. This allows in turn to give new indices of rationalizability of the data and to define weaker notions of rationalizability, in the spirit of Afriat’s efficiency index

Degrees of cooperation in household consumption models: a revealed preference analysis

We develop a revealed preference approach to analyze non-unitary consumption models with intrahousehold allocations deviating from the cooperative (or Pareto efficient) solution. At a theoretical level, we establish revealed preference conditions of household consumption models with varying degrees of cooperation. Using these conditions, we show independence (or non-nestedness) of the different (cooperative-noncooperative) models. At a practical level, we show that our characterization implies testable conditions for a whole spectrum of cooperative-noncooperative models that can be verified by means of mixed integer programming (MIP) methods. This MIP formulation is particularly attractive in view of empirical analysis. An application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the empirical relevance of consumption models that account for limited intrahousehold cooperation.household consumption, intrahousehold cooperation, revealed preferences, Generalized Axiom of Revealed Preference (GARP), mixed integer programming (MIP).

Degrees of Cooperation in Household Consumption Models: A Revealed Preference Analysis

We develop a revealed preference approach to analyze non-unitary con- sumption models with intrahousehold allocations deviating from the cooper- ative (or Pareto e¢ cient) solution. At a theoretical level, we establish re- vealed preference conditions of household consumption models with varying degrees of cooperation. Using these conditions, we show independence (or non-nestedness) of the di¤erent (cooperative-noncooperative) models. At a practical level, we show that our characterization implies testable conditions for a whole spectrum of cooperative-noncooperative models that can be verified by means of mixed integer programming (MIP) methods. This MIP formula- tion is particularly attractive in view of empirical analysis. An application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demon- strates the empirical relevance of consumption models that account for limited intrahousehold cooperation.household consumption;intrahousehold cooperation;revealed preferences;Generalized Axiom of Revealed Preference (GARP);mixed in- teger programming (MIP).

Degrees of cooperation in household consumption models: a revealed preference analysis.

We develop a revealed preference approach to analyze non-unitary consumption models with intrahousehold allocations deviating from the cooperative (or Pareto eff cient) solution. At a theoretical level, we establish revealed preference conditions of household consumption models with varying degrees of cooperation. Using these conditions, we show independence (or non-nestedness) of the different (cooperative-noncooperative) models. At a practical level, we show that our characterization implies testable conditions for a whole spectrum of cooperative-noncooperative models that can be verified by means of mixed integer programming (MIP) methods. This MIP formulation is particularly attractive in view of empirical analysis. An application to data drawn from the Russia Longitudinal Monitoring Survey (RLMS) demonstrates the empirical relevance of consumption models that account for limited intrahousehold cooperation.