Nash bargained consumption decisions: a revealed preference analysis.

We present a revealed preference analysis of the testable implications of the Nash bargaining solution. Our specific focus is on a two-player game involving consumption decisions. We consider a setting in which the empirical analyst has information on both the threat points bundles and the bargaining outcomes. We first establish a revealed preference characterization of the Nash bargaining solution. This characterization implies conditions that are both necessary and sufficient for consistency of observed consumption behavior with the Nash bargaining model. However, these conditions turn out to be nonlinear in unknowns and therefore difficult to verify. Given this, we subsequently present necessary conditions and sufficient conditions that are linear (and thus easily testable). We illustrate the practical usefulness of these conditions by means of an application to experimental data. Such an experimental setting implies a most powerful analysis of the empirical goodness of the Nash bargaining model for describing consumption decisions. To our knowledge, this provides a first empirical test of the Nash bargaining model on consumption data. Finally, we consider the possibility that threat point bundles are not observed. This obtains testable conditions for the Nash bargaining model that can be used in non-experimental (e.g. household consumption) settings, which often do not contain information on individual consumption bundles in threat points.

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.

Economic well-being and poverty among the elderly: an analysis based on a collective consumption model

We apply the collective consumption model of Browning, Chiappori and Lewbel (2006) to analyse economic well-being and poverty among the elderly. The model focuses on individual preferences, a consumption technology that captures the economies of scale of living in a couple, and a sharing rule that governs the intra-household allocation of resources. The model is applied to a time series of Dutch consumption expenditure surveys. Our empirical results indicate substantial economies of scale and a wife’s share that is increasing in total expenditures. We further calculated poverty rates by means of the collective consumption model. Collective poverty rates of widows and widowers turn out to be slightly lower than traditional ones based on a standard equivalence scale. Poverty among women (men) in elderly couples, however, seems to be heavily underestimated (overestimated) by the traditional approach. Finally, we analysed the impact of becoming a widow(er). Based on cross-sectional evidence, we find that the drop (increase) in material well-being following the husband’s death is substantial for women in high (low) expenditure couples. For men, the picture is reversed.collective model, intra-household allocation, indi¤erence scales, economies of scale, poverty.

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).

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

Economic Well-Being and Poverty among the Elderly: An Analysis Based on a Collective Consumption Model

We apply the collective consumption model of Browning, Chiappori and Lewbel (2006) to analyse economic well-being and poverty among the elderly. The model focuses on individual preferences, a consumption technology that captures the economies of scale of living in a couple, and a sharing rule that governs the intra-household allocation of resources. The model is applied to a time series of Dutch consumption expenditure surveys. Our empirical results indicate substantial economies of scale and a wife’s share that is increasing in total expenditures. We further calculated poverty rates by means of the collective consumption model. Collective poverty rates of widows and widowers turn out to be slightly lower than traditional ones based on a standard equivalence scale. Poverty among women (men) in elderly couples, however, seems to be heavily underestimated (overestimated) by the traditional approach. Finally, we analysed the impact of becoming a widow(er). Based on cross-sectional evidence, we find that the drop (increase) in material well-being following the husband’s death is substantial for women in high (low) expenditure couples. For men, the picture is reversed.collective model, intra-household allocation, indifference scales, economies of scale, poverty

The Anosov relation for the Nielsen numbers of maps of infra-nilmanifolds.

In 1985 toonde D. Anosov aan dat voor elke continue afbeelding&nbs p;f:M->M op een nilvariëteit M geldt dat N(f)=|L(f)| . Het Nielsen getal N(f) en het Lefschetz getal L(f) zijn twee aan f geassocieerde getallen die informatie geven over h et aantal vaste punten van f (i.e. x in M: f(x)=x) . Als voor een gegeven f geldt dat deze twee getallen op teken na gelijk zijn, dan zeggen we dat f voldoet aan de Ano sov relatie. In mijn thesis heb ik dit resultaat op twee manieren veralgemeend. Een eerste, voor de hand liggend, manier is om aan te tonen dat d it resultaat ook geldt voor andere klassen van variëteiten. Ik heb dit g edaan voor drie klassen van infra-nilvariëteiten en deze klassen zijn al len gedefinieerd op basis van de geassocieerde holonomiegroep. Ten eerst e toonde ik aan dat elke continue afbeelding van een infra-nilvariëteit met holonomiegroep van oneven orde aan de Anosov relatie voldoet. Hetzel fde resultaat is geldig als we werken met platte, oriënteerbare, veralge meende Hantzsche-Wendt variëteiten. Tot slot toonde ik aan dat de Anosov relatie ook geldt voor continue afbee ldingen op infra-nilvariëteiten met cyclische holonomiegroep, mits een specifieke voorwaarde op de generator van de holono miegroep voldaan is. Een tweede manier om het resultaat van Anosov te veralgemenen, is werken met klassen van afbeeldingen in plaats van alle continue afbeeldingen o p een gegeven variëteit te beschouwen. Deze aanpak gebruikte ik om de An osov diffeomorfismen op infra-nilvariëteiten te onderzoeken en ik stelde vast dat deze eigenschap weinig invloed heeft op de geldigheid va n de Anosov relatie. Echter, voor nergens expanderende afbeeldingen op i nfra-nilvariëteiten toonde ik aan dat de Anosov relatie altijd voldaan i s. Tot slot voor expanderende afbeeldingen f op infra-nilvari ëteiten M leidde ik het volgende: f vold oet aan de Anosov relatie als en slechts als M oriënteer baar is. In een laatste deel onderzocht ik wat deze resultaten ons zeggen met bet rekking tot de Anosov relatie voor afbeeldingen op infra-nilvariëteiten met als dimensie hoogstens 4. Zo toonde ik aan dat reeds veel infra-nilv ariëteiten behandeld worden door onze resultaten en ontdekte ik enkele o nderzoeksvragen voor de toekomst.

The revealed preference approach to collective consumption behavior: testing, recovery and welfare analysis.

We extend the nonparametric ‘revealed preference’ methodology for analyzing collective consumption behavior (with consumption externalities and public consumption), to render it useful for empirical applications that deal with welfare-related questions. First, we provide a nonparametric necessary and sufficient condition for collectively rational group behavior that incorporates the possibility of assignable quantity information. This characterizes collective rationality in terms of feasible personalized prices, personalized quantities and income shares (representing the underlying sharing rule). Subsequently, we present nonparametric testing tools for data consistency with special cases of the collective model, which impose specific structure on the preferences of the group members (in terms of consumption externalities and public consumption); and we show that these testing tools in turn allow for nonparametrically recovering (bounds on) feasible personalized prices, personalized quantities and income shares that underlie observed (collectively rational) group behavior. In addition, we present formally similar testing and recovery tools for the general collective consumption model, which imposes minimal a priori structure. Interestingly, the proposed testing and recovery methodology can be implemented through integer programming (IP and MILP), which is attractive for practical applications. Finally, while we argue that assignable quantity information generally entails more powerful recovery results, we also demonstrate that precise nonparametric recovery (i.e. tight bounds) can be obtained even if no assignable quantity information is available.Business; Economics; Efficiency; Management; Research; Research in economics; University; University-research; Preference; Consumption; Behavior; Welfare;

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.

Testable implications of general equilibrium models: an integer programming approach.

Focusing on the testable implications on the equilibrium manifold, we show that the rationalizability problem is NP-complete. Subsequently, we present an integer programming (IP) approach to characterizing general equilibrium models. This approach avoids the use of the Tarski-Seidenberg algorithm for quantifier elimination that is commonly used in the literature. The IP approach naturally applies to settings with any number of observations, which is attractive for empirical applications. In addition, it can easily be adjusted to analyze the testable implications of alternative general equilibrium models (that include, e.g., public goods, externalities and/or production). Further, we show that the IP framework can easily address recoverability questions (pertaining to the structural model that underlies the observed equilibrium behavior), and account for empirical issues when bringing the IP methodology to the data (such as goodness-of-fit and power). Finally, we show how to develop easy-to-implement heuristics that give a quick (but possibly inconclusive) answer to whether or not the data satisfy the general equilibrium models.General equilibrium; Equilibrium manifold; Exchange economies; Production economies; NP-completeness; Nonparametric restrictions; GARP; integer programming;