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Sharing rule identification for general collective consumption models

  • Laurens CHERCHYE
  • Bram DE ROCK
  • Arthur LEWBEL
  • Frederic VERMEULEN

We propose a method to identify bounds (i.e. set identification) on the sharing rule for a general collective household consumption model. Unlike the effects of distribution factors, it is well known that the level of the sharing rule cannot be uniquely identified without strong assumptions on preferences across households of different compositions. Our new results show that, though not point identified without these assumptions, bounds on the sharing rule can still be obtained. We get these bounds by applying revealed preference restrictions implied by the collective model to the household’s continuous aggregate demand functions. We obtain informative bounds even if nothing is known about whether each good is public, private, or assignable within the household, though having such information tightens the bounds. An empirical application demonstrates the practical usefulness of our method.

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Paper provided by Katholieke Universiteit Leuven, Centrum voor Economische Studiën in its series Center for Economic Studies - Discussion papers with number ces12.05.

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Date of creation: May 2012
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Handle: RePEc:ete:ceswps:ces12.05
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  1. Browning, M. & Chiappori, P.A., 1994. "Efficient Intra-Household allocations: A General Characterization and Empirical Tests," DELTA Working Papers 94-16, DELTA (Ecole normale supérieure).
  2. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2012. "Married with Children: A Collective Labor Supply Model with Detailed Time Use and Intrahousehold Expenditure Information," ULB Institutional Repository 2013/131705, ULB -- Universite Libre de Bruxelles.
  3. Browning, M. & Bourguignon, F. & Chiappori, P.A. & Lechene, V., 1992. "Incomes and Outcomes: A structural Model of Intra-Household Allocation," DELTA Working Papers 92-23, DELTA (Ecole normale supérieure).
  4. repec:sfu:sfudps:dp12-11 is not listed on IDEAS
  5. Bargain, Olivier & Donni, Olivier, 2009. "The Measurement of Child Costs: A Rothbarth-Type Method Consistent with Scale Economies," IZA Discussion Papers 4654, Institute for the Study of Labor (IZA).
  6. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A nonparametric characterization," ULB Institutional Repository 2013/98559, ULB -- Universite Libre de Bruxelles.
  7. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 176-198.
  8. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  9. Richard Blundell & Pierre-Andre Chiappori & Thierry Magnac & Costas Meghir, 2007. "Collective Labour Supply: Heterogeneity and Non-Participation," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 417-445.
  10. Lewbel, Arthur & Pendakur, Krishna, 2008. "Estimation of collective household models with Engel curves," Journal of Econometrics, Elsevier, vol. 147(2), pages 350-358, December.
  11. Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  12. Richard Blundell & Martin Browning & Ian Crawford, 2005. "Best nonparametric bounds on demand responses," IFS Working Papers W05/20, Institute for Fiscal Studies.
  13. Pierre-Andre Chiappori & Bernard Fortin & Guy Lacroix, 2002. "Marriage Market, Divorce Legislation, and Household Labor Supply," Journal of Political Economy, University of Chicago Press, vol. 110(1), pages 37-72, February.
  14. Richard Blundell & Pierre-Andr� Chiappori & Costas Meghir, 2005. "Collective Labor Supply with Children," Journal of Political Economy, University of Chicago Press, vol. 113(6), pages 1277-1306, December.
  15. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2010. "An Afriat theorem for the collective model of household consumption," ULB Institutional Repository 2013/131711, ULB -- Universite Libre de Bruxelles.
  16. repec:ner:tilbur:urn:nbn:nl:ui:12-3857700 is not listed on IDEAS
  17. Geoffrey Dunbar & Arthur Lewbel & Krishna Pendakur, 2010. "Children's Resources in Collective Households: Identification, Estimation and an Application to Child Poverty in Malawi," Boston College Working Papers in Economics 758, Boston College Department of Economics, revised 31 Jan 2012.
  18. P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, 05.
  19. Blundell, Richard & Kristensen, Dennis & Matzkin, Rosa, 2014. "Bounding quantile demand functions using revealed preference inequalities," Journal of Econometrics, Elsevier, vol. 179(2), pages 112-127.
  20. BARGAIN Olivier & DONNI Olivier, 2010. "The Measurement of Child Costs: A Rothbarth-Type Method Consistent with Scale Economies and Parents’ Bargaining," LISER Working Paper Series 2010-30, LISER.
  21. Martin Browning & Pierre-Andrée Chiappori & Arthur Lewbel, 2004. "Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power," Boston College Working Papers in Economics 588, Boston College Department of Economics, revised 01 Sep 2010.
  22. Bossert, Walter, 1993. "Continuous Choice Functions and the Strong Axiom of Revealed Preference," Economic Theory, Springer, vol. 3(2), pages 379-85, April.
  23. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2012. "Economic well-being and poverty among the elderly: an analysis based on a collective consumption model," ULB Institutional Repository 2013/131702, ULB -- Universite Libre de Bruxelles.
  24. Chiappori, P.A. & Ekeland, I., 2006. "The micro economics of group behavior: General characterization," Journal of Economic Theory, Elsevier, vol. 130(1), pages 1-26, September.
  25. Jeremy Lise & Shannon Seitz, 2004. "Consumption Inequality and Intra-Household Allocations," Working Papers 1019, Queen's University, Department of Economics.
  26. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-67, June.
  27. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
  28. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, 09.
  29. Menon, Martina & Pendakur, Krishna & Perali, Federico, 2012. "On the expenditure-dependence of children’s resource shares," Economics Letters, Elsevier, vol. 117(3), pages 739-742.
  30. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The revealed preference approach to collective consumption behavior: nonparametric testing and sharing rule recovery," ULB Institutional Repository 2013/98560, ULB -- Universite Libre de Bruxelles.
  31. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  32. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-46, July-Aug..
  33. Marjorie B. McElroy, 1990. "The Empirical Content of Nash-Bargained Household Behavior," Journal of Human Resources, University of Wisconsin Press, vol. 25(4), pages 559-583.
  34. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
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