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Sharing Rule Identification for General Collective Consumption Models

  • Cherchye, Laurens

    ()

    (KU Leuven)

  • De Rock, Bram

    ()

    (ECARES, Free University of Brussels)

  • Lewbel, Arthur

    ()

    (Boston College)

  • Vermeulen, Frederic

    ()

    (KU Leuven)

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 Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 6571.

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Length: 32 pages
Date of creation: May 2012
Date of revision:
Handle: RePEc:iza:izadps:dp6571
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  1. 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.
  2. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, 09.
  3. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
  4. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-67, June.
  5. Martin Browning & Pierre-André Chiappori & Arthur Lewbel, . "Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power," CAM Working Papers 2003-12, University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics, revised Dec 2003.
  6. Jeremy Lise & Shannon Seitz, 2011. "Consumption Inequality and Intra-household Allocations," Review of Economic Studies, Oxford University Press, vol. 78(1), pages 328-355.
  7. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2010. "Married with Children: A Collective Labor Supply Model with Detailed Time Use and Intrahousehold Expenditure Information," IZA Discussion Papers 5190, Institute for the Study of Labor (IZA).
  8. Pierre-André Chiappori & Bernard Fortin & Guy Lacroix, 2001. "Marriage Market, Divorce Legislation and Household Labor Supply," CIRANO Working Papers 2001s-16, CIRANO.
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  11. 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.
  12. Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2008. "Economic Well-Being and Poverty Among the Elderly : An Analysis Based on a Collective Consumption Model," Discussion Paper 2008-15, Tilburg University, Center for Economic Research.
  13. BARGAIN Olivier & DONNI Olivier, 2010. "The Measurement of Child Costs: A Rothbarth-Type Method Consistent with Scale Economies and Parents’ Bargaining," CEPS/INSTEAD Working Paper Series 2010-30, CEPS/INSTEAD.
  14. Blundell, Richard & Chiappori, Pierre-André & Magnac, Thierry & Meghir, Costas, 2005. "Collective Labour Supply: Heterogeneity and Nonparticipation," IDEI Working Papers 373, Institut d'Économie Industrielle (IDEI), Toulouse.
  15. 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.
  16. M. Browning & P. A. Chiappori, 1998. "Efficient Intra-Household Allocations: A General Characterization and Empirical Tests," Econometrica, Econometric Society, vol. 66(6), pages 1241-1278, November.
  17. 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.
  18. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
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  20. Diewert, W E, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Wiley Blackwell, vol. 40(3), pages 419-25, July.
  21. Richard Blundell & Martin Browning & Ian Crawford, 2005. "Best nonparametric bounds on demand responses," CeMMAP working papers CWP12/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  22. Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2004. "The Collective Model of Household Consumption : A Nonparametric Characterization," Discussion Paper 2004-76, Tilburg University, Center for Economic Research.
  23. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
  24. 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..
  25. Geoffrey R. Dunbar & Arthur Lewbel & Krishna Pendakur, 2013. "Children's Resources in Collective Households: Identification, Estimation, and an Application to Child Poverty in Malawi," American Economic Review, American Economic Association, vol. 103(1), pages 438-71, February.
  26. 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.
  27. Browning, Martin & Francois Bourguignon & Pierre-Andre Chiappori & Valerie Lechene, 1994. "Income and Outcomes: A Structural Model of Intrahousehold Allocation," Journal of Political Economy, University of Chicago Press, vol. 102(6), pages 1067-96, December.
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  30. Pierre-André Chiappori & Richard Blundell & Costas Meghir, 2002. "Collective labour supply with children," IFS Working Papers W02/08, Institute for Fiscal Studies.
  31. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2011. "Bounding quantile demand functions using revealed preference inequalities," CeMMAP working papers CWP21/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  32. Bossert, Walter, 1993. "Continuous Choice Functions and the Strong Axiom of Revealed Preference," Economic Theory, Springer, vol. 3(2), pages 379-85, April.
  33. Lewbel, Arthur & Pendakur, Krishna, 2008. "Estimation of collective household models with Engel curves," Journal of Econometrics, Elsevier, vol. 147(2), pages 350-358, December.
  34. Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2011. "The revealed preference approach to collective consumption behavior : Testing and sharing rule recovery," Other publications TiSEM 11c788ab-cf82-4759-a6a8-3, Tilburg University, School of Economics and Management.
  35. Olivier Bargain & Olivier Donni, 2010. "The Measurement of Child Costs: A Rothbarth-Type Method Consistent with Scale Economies," Working Papers 201001, School Of Economics, University College Dublin.
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