Skip to main content
SpringerLink
Log in

Enlarging the collective model of household behavior: A revealed preference analysis

  • Research Article
  • Published:
Economic Theory Aims and scope Submit manuscript

Abstract

We use a comprehensive model of strategic household behavior in which the spouses’ expenditure on each public good is decomposed into autonomous spending and coordinated spending à la Lindahl. We obtain a continuum of semi-cooperative regimes parameterized by the relative weights put on autonomous spending, by each spouse and for each public good, nesting full cooperative and noncooperative regimes as limit cases. Testing is approached through revealed preference analysis, by looking for rationalizability of observed data sets, with the price of each public good lying between the maximum and the sum of the hypothesized marginal willingness to pay of the two spouses. Once rationalized, an observed data set always allows to identify the sharing rule, except when both spouses contribute in full autonomy to some public good (a situation of local income pooling).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. d’Aspremont and Dos Santos Ferreira (2014).

  2. See Ulph (2006), Lundberg and Pollak (1993) and Chen and Woolley (2001). For a survey, see Donni (2007).

  3. In earlier models the disagreement point was taken to be divorce (Manser and Brown 1980; McElroy and Horney 1981).

  4. See Lechene and Preston (2005, 2011) and Browning et al. (2010).

  5. Income pooling is already present in unitary models (Samuelson 1956, and Becker 1974) as well as in divorce threat bargaining models (Manser and Brown 1980; McElroy and Horney 1981)

  6. For references, see Browning and Chiappori (1998) and Vermeulen (2002).

  7. Each individual is assumed to have a (personal) Bergson–Samuelson Social Welfare Function (SWF) through which she/he “cares” about the utility of each member in her/his household. This is in contrast with Samuelson (1956) consensus model where all members care and have the same SWF and with Becker (1974) where only one member (say the husband) cares. By varying the degree of intrahousehold caring for each individual member, Cherchye et al. (2015) also obtain a continuum of household consumption models between the fully cooperative model and the fully noncooperative model without caring.

  8. Cherchye et al. (2015) have already shown that the sharing rule is identifiable for fully cooperative-rationalized data sets and not for noncooperative-rationalized data sets. Sharing rule identifiability also fails in models with caring, except when full cooperation is rationalized (Cherchye et al. 2015).

  9. Suppose \(g_{k}^{B}=0\) and \(g_{k}^{A}>0\). Since \( Q_{k}^{A}=g_{k}^{A}+g_{k}^{B} \), \(\left( \left( Q_{k}^{A}-g_{k}^{A}\right) /Q_{k}^{A}\right) P_{k}=0\). This cannot be optimal as \(U^{B}\left( q^{B},Q^{B}\right) \) would increase if \(g_{k}^{B}\) (and \(Q_{k}^{B}\)) is increased (for free).

  10. The initial marriage agreement could be viewed as the result of a preliminary stage where each spouse J chooses strategically the degrees of autonomy \(\theta _{k}^{J}\) for all k. This creates a moral hazard problem for the Lindahl mechanism since \(\theta \) identically zero may not be the equilibrium strategy of the first-stage game, although some other arrangement, with positive \(\theta \), may well be implementable. If there is incomplete information, efficiency may be even more difficult to reach (see Gori and Villanacci 2011).

  11. As stated in d’Aspremont and Dos Santos Ferreira (2014, Proposition 2), the outcome of any \(\theta \)-equilibrium with separate spheres ( i.e., with \(g_{k}^{A}g_{k}^{B}=0\) for any public good k) coincides, even for \(\left( \theta ^{A},\theta ^{B}\right) \ne \left( 1,1\right) \), with the outcome of an equilibrium of the game with voluntary contributions to public goods.

  12. One possible way of tackling this problem would be to use the exclusivity assumption suggested by Chiappori and Ekeland (2009), “whereby each member is the exclusive consumer of at least one good.”

  13. Of course, rationalizability of any kind may also fail, as it can be easily shown using Example 1 in Cherchye et al. (2007).

  14. For an application to the sharing rule recovery in the collective model along these lines, see Cherchye et al. (2011).

  15. We have used Gusek software, which combines the SCIntilla based Text Editor (SciTE) plus the linear/integer programming solver GNU Linear Programming Kit (GLPK).

References

  • Becker, G.: A theory of social interactions. J. Polit. Econ. 82, 1063–1093 (1974)

    Article  Google Scholar 

  • Browning, M., Chiappori, P.-A.: Efficient intra-household allocations: a general characterisation and empirical tests. Econometrica 66, 1241–1278 (1998)

    Article  Google Scholar 

  • Browning, M., Chiappori, P.-A., Lechene, V.: Distributional effects in household models: separate spheres and income pooling. Econ. J. 120, 786–799 (2010)

    Article  Google Scholar 

  • Chen, Z., Woolley, F.: A Cournot-Nash model of family decision making. Econ. J. 111, 722–748 (2001)

    Article  Google Scholar 

  • Cherchye, L., Cosaertz, S., Demuynck, T., De Rock, B.: Noncooperative household consumption with caring, KU Leuven, Center for Economic Studies DPS15.29 (2015)

  • Cherchye, L., Demuynck, T., De Rock, B.: Revealed preference analysis of non-cooperative household consumption. Econ. J. 121, 1073–1096 (2011)

    Article  Google Scholar 

  • Cherchye, L., De Rock, B., Vermeulen, F.: The collective model of household consumption: a nonparametric characterization. Econometrica 75, 553–574 (2007)

    Article  Google Scholar 

  • Chiappori, P.-A.: Rational household labor supply. Econometrica 56, 63–90 (1988)

    Article  Google Scholar 

  • Chiappori, P.-A.: Collective labor supply and welfare. J. Polit. Econ. 100, 437–46 (1992)

    Article  Google Scholar 

  • Chiappori, P.-A., Ekeland, I.: The microeconomics of efficient group behavior: identification. Econometrica 77, 763–799 (2009)

    Article  Google Scholar 

  • d’Aspremont, C., Dos Santos Ferreira, R.: Household behavior and individual autonomy: an extended Lindahl mechanism. Econ. Theory 55, 643–664 (2014). https://doi.org/10.1007/s00199-013-0763-1

    Article  Google Scholar 

  • Donni, O.: Contribution 6.154.9. Household Behavior and Family Economics, in Mathematical models in Economics, vol. 1, The Encyclopedia of Life Support Systems (EOLSS) (2007)

  • Gori, M., Villanacci, A.: A bargaining model in general equilibrium. Econ. Theory 46, 327–375 (2011). https://doi.org/10.1007/s00199-009-0515-4

    Article  Google Scholar 

  • Hurwicz, L.: Outcome functions yielding Walrasian and Lindahl allocations at Nash equilibrium points. Rev. Econ. Stud. 46, 217–225 (1979)

    Article  Google Scholar 

  • Lechene, V., Preston, I.: Household Nash equilibrium with voluntarily contributed public goods. Econ Series WP 226, Oxford, (2005)

  • Lechene, V., Preston, I.: Noncooperative household demand. J. Econ. Theory 146, 504–527 (2011)

    Article  Google Scholar 

  • Lundberg, S., Pollak, R.A.: Separate spheres bargaining and the marriage market. J. Polit. Econ. 101, 988–1010 (1993)

    Article  Google Scholar 

  • Manser, M., Brown, M.: Marriage and household decision-making: a bargaining analysis. Intern. Econ. Rev. 21, 31–44 (1980)

    Article  Google Scholar 

  • McElroy, M.B., Horney, M.J.: Nash-bargained household decisions: toward a generalization of the theory of demand. Intern. Econ. Rev. 22, 333–349 (1981)

    Article  Google Scholar 

  • Samuelson, P.A.: Social indifference curves. Q. J. Econ. 70, 1–22 (1956)

    Article  Google Scholar 

  • Ulph, D.: A general non-cooperative Nash model of household consumption behavior. University of Bristol, Economics Discussion Paper 88/205, 1988. French translation: Un modèle non-coopératif de consommation des m énages. L’Actualité économique 82, 53–85 (2006)

  • Varian, H.: The nonparametric approach to demand analysis. Econometrica 50, 945–973 (1982)

    Article  Google Scholar 

  • Vermeulen, F.: Collective household models: principles and main results’. J. Econ. Surv. 16, 533–564 (2002)

    Article  Google Scholar 

  • Walker, M.: A simple incentive compatible scheme for attaining Lindahl allocations. Econometrica 49, 65–71 (1981)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CORE, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Claude d’Aspremont

  2. BETA, Université de Strasbourg, Strasbourg, 67085, France

    Rodolphe Dos Santos Ferreira

  3. Católica Lisbon School of Business and Economics, Lisbon, Portugal

    Rodolphe Dos Santos Ferreira

Authors
  1. Claude d’Aspremont
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rodolphe Dos Santos Ferreira
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Claude d’Aspremont.

Additional information

CORE is affiliated to ECORES.

This work was supported by the ANR FamPol project, grant ANR-14-FRAL-0007 of the French Agence Nationale de la Recherche.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

d’Aspremont, C., Dos Santos Ferreira, R. Enlarging the collective model of household behavior: A revealed preference analysis. Econ Theory 68, 1–19 (2019). https://doi.org/10.1007/s00199-018-1110-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00199-018-1110-3

Keywords

JEL Classification

Search

Navigation