IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v234y2023i1p301-326.html
   My bibliography  Save this article

Identification of unobserved distribution factors and preferences in the collective household model

Author

Listed:
  • Hubner, Stefan

Abstract

This paper develops a non-parametric collective random utility model with a continuous choice of consumption and sharing. We allow for a heterogeneous population by introducing unobserved distribution factors and preferences that are non-separable in the stochastic household choice system. We provide necessary and sufficient conditions for invertibility with respect to the vector of unobserved heterogeneity. Further, we show non-parametric identification of each individual’s idiosyncratic preferences and Pareto weights from the distribution of observed choices. Based on this result we develop a non-parametric two-step estimation procedure and estimate individual counterfactuals in a collective labour supply model for households with children using the LISS panel.

Suggested Citation

  • Hubner, Stefan, 2023. "Identification of unobserved distribution factors and preferences in the collective household model," Journal of Econometrics, Elsevier, vol. 234(1), pages 301-326.
    • Handle: RePEc:eee:econom:v:234:y:2023:i:1:p:301-326
    DOI: 10.1016/j.jeconom.2022.01.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407622000173
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2022.01.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    2. J. P. Florens & J. J. Heckman & C. Meghir & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models With Continuous, Endogenous Treatment and Heterogeneous Effects," Econometrica, Econometric Society, vol. 76(5), pages 1191-1206, September.
    3. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    4. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    5. Martin Browning & Pierre-André Chiappori & Arthur Lewbel, 2013. "Estimating Consumption Economies of Scale, Adult Equivalence Scales, and Household Bargaining Power," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1267-1303.
    6. Walter Beckert & Richard Blundell, 2008. "Heterogeneity and the Non-Parametric Analysis of Consumer Choice: Conditions for Invertibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(4), pages 1069-1080.
    7. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    8. Laurens Cherchye & Bram De Rock & Arthur Lewbel & Frederic Vermeulen, 2015. "Sharing Rule Identification for General Collective Consumption Models," Econometrica, Econometric Society, vol. 83(5), pages 2001-2041, September.
    9. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    10. repec:hal:spmain:info:hdl:2441/4kovgv3hs883bok2tvdkibejb6 is not listed on IDEAS
    11. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers 60/17, Institute for Fiscal Studies.
    12. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
    13. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    14. Duncan Thomas, 1990. "Intra-Household Resource Allocation: An Inferential Approach," Journal of Human Resources, University of Wisconsin Press, vol. 25(4), pages 635-664.
    15. P.-A. Chiappori & I. Ekeland, 2009. "The Microeconomics of Efficient Group Behavior: Identification," Econometrica, Econometric Society, vol. 77(3), pages 763-799, May.
    16. Chiappori, Pierre-André & Komunjer, Ivana & Kristensen, Dennis, 2015. "Nonparametric identification and estimation of transformation models," Journal of Econometrics, Elsevier, vol. 188(1), pages 22-39.
    17. 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 1067-1096, December.
    18. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    19. Geoffrey R. Dunbar & Arthur Lewbel & Krishna Pendakur, 2021. "Identification of Random Resource Shares in Collective Households Without Preference Similarity Restrictions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 402-421, March.
    20. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    21. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    22. Richard Blundell & Pierre-Andre Chiappori & Thierry Magnac & Costas Meghir, 2007. "Collective Labour Supply: Heterogeneity and Non-Participation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 417-445.
    23. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2012. "Married with Children: A Collective Labor Supply Model with Detailed Time Use and Intrahousehold Expenditure Information," American Economic Review, American Economic Association, vol. 102(7), pages 3377-3405, December.
    24. 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.
    25. C. Lanier Benkard & Steven Berry, 2006. "On the Nonparametric Identification of Nonlinear Simultaneous Equations Models: Comment on Brown (1983) and Roehrig (1988)," Econometrica, Econometric Society, vol. 74(5), pages 1429-1440, September.
    26. Pierre-André Chiappori & Olivier Donni & Ivana Komunjer, 2012. "Learning from a Piece of Pie," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(1), pages 162-195.
    27. Fortin, Bernard & Lacroix, Guy, 1997. "A Test of the Unitary and Collective Models of Household Labour Supply," Economic Journal, Royal Economic Society, vol. 107(443), pages 933-955, July.
    28. Richard Blundell & Antoine Bozio & Guy Laroque, 2013. "Extensive and Intensive Margins of Labour Supply: Work and Working Hours in the US, the UK and France," Fiscal Studies, Institute for Fiscal Studies, vol. 34(1), pages 1-29, March.
    29. Donald J. Brown & Rosa L. Matzkin, 1998. "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand," Cowles Foundation Discussion Papers 1175, Cowles Foundation for Research in Economics, Yale University.
    30. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    31. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015. "Vector quantile regression: an optimal transport approach," CeMMAP working papers 58/15, Institute for Fiscal Studies.
    32. Martin Browning & Mette Gørtz, 2012. "Spending Time and Money within the Household," Scandinavian Journal of Economics, Wiley Blackwell, vol. 114(3), pages 681-704, September.
    33. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, September.
    34. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, September.
    35. Pierre‐André Chiappori & Ju Hyun Kim, 2017. "A note on identifying heterogeneous sharing rules," Quantitative Economics, Econometric Society, vol. 8(1), pages 201-218, March.
    36. 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 438-471, February.
    37. Deaton,Angus & Muellbauer,John, 1980. "Economics and Consumer Behavior," Cambridge Books, Cambridge University Press, number 9780521296762, September.
    38. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    39. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, September.
    40. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    41. Browning,Martin & Chiappori,Pierre-André & Weiss,Yoram, 2014. "Economics of the Family," Cambridge Books, Cambridge University Press, number 9780521795395.
    42. Stefan Hoderlein & Jörg Stoye, 2014. "Revealed Preferences in a Heterogeneous Population," The Review of Economics and Statistics, MIT Press, vol. 96(2), pages 197-213, May.
    43. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    44. Allen, Roy, 2022. "Injectivity and the law of demand," Economics Letters, Elsevier, vol. 215(C).
    45. Richard Blundell & Pierre-André Chiappori & Costas Meghir, 2005. "Collective Labor Supply with Children," Journal of Political Economy, University of Chicago Press, vol. 113(6), pages 1277-1306, December.
    46. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
    47. Stefan Hoderlein & Enno Mammen, 2009. "Identification and estimation of local average derivatives in non-separable models without monotonicity," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 1-25, March.
    48. Chiappori, Pierre-Andre, 1988. "Rational Household Labor Supply," Econometrica, Econometric Society, vol. 56(1), pages 63-90, January.
    49. 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.
    50. Richard Blundell & Rosa L. Matzkin, 2014. "Control functions in nonseparable simultaneous equations models," Quantitative Economics, Econometric Society, vol. 5, pages 271-295, July.
    51. 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.
    52. Chiappori, Pierre-Andre, 1992. "Collective Labor Supply and Welfare," Journal of Political Economy, University of Chicago Press, vol. 100(3), pages 437-467, June.
    53. Stefan Hubner, 2020. "It's complicated: A Non-parametric Test of Preference Stability between Singles and Couples," Bristol Economics Discussion Papers 20/735, School of Economics, University of Bristol, UK.
    54. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2011. "The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 176-198.
    55. repec:hal:spmain:info:hdl:2441/4c5431jp6o888pdrcs0fuirl40 is not listed on IDEAS
    56. Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2016. "Vector Quantile Regression: An Optimal Transport Approach," SciencePo Working papers hal-03567920, HAL.
    57. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-829, July.
    58. Stefan Hoderlein & Jörg Stoye, 2015. "Testing stochastic rationality and predicting stochastic demand: the case of two goods," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 313-328, October.
    59. 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.
    60. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
    61. Alexander Torgovitsky, 2015. "Identification of Nonseparable Models Using Instruments With Small Support," Econometrica, Econometric Society, vol. 83(3), pages 1185-1197, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    2. Cherchye, Laurens & Cosaert, Sam & De Rock, Bram & Kerstens, Pieter Jan & Vermeulen, Frederic, 2018. "Individual welfare analysis for collective households," Journal of Public Economics, Elsevier, vol. 166(C), pages 98-114.
    3. Donni, Olivier & Molina, José Alberto, 2018. "Household Collective Models: Three Decades of Theoretical Contributions and Empirical Evidence," IZA Discussion Papers 11915, Institute of Labor Economics (IZA).
    4. Laurens CHERCHYE & Thomas DEMUYNCK & Bram DE ROCK, 2010. "Noncooperative household consumption with caring," Working Papers of Department of Economics, Leuven ces10.34, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    5. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2017. "Household Consumption When the Marriage Is Stable," American Economic Review, American Economic Association, vol. 107(6), pages 1507-1534, June.
    6. 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.
    7. Lewbel, Arthur & Lin, Xirong, 2022. "Identification of semiparametric model coefficients, with an application to collective households," Journal of Econometrics, Elsevier, vol. 226(2), pages 205-223.
    8. Botosaru, Irene & Muris, Chris & Pendakur, Krishna, 2023. "Identification of time-varying transformation models with fixed effects, with an application to unobserved heterogeneity in resource shares," Journal of Econometrics, Elsevier, vol. 232(2), pages 576-597.
    9. Cherchye, Laurens & Chiappori, Pierre-André & De Rock, Bram & Ringdal, Charlotte & Vermeulen, Frederic, 2021. "Feed the Children," IZA Discussion Papers 14687, Institute of Labor Economics (IZA).
    10. Irene Botosaru & Chris Muris & Krishna Pendakur, 2020. "Intertemporal Collective Household Models: Identification in Short Panels with Unobserved Heterogeneity in Resource Shares," Department of Economics Working Papers 2020-09, McMaster University.
    11. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers 60/17, Institute for Fiscal Studies.
    12. Calvi, Rossella & Penglase, Jacob & Tommasi, Denni & Wolf, Alexander, 2023. "The more the poorer? Resource sharing and scale economies in large families," Journal of Development Economics, Elsevier, vol. 160(C).
    13. Laurens Cherchye & Bram De Rock & Arthur Lewbel & Frederic Vermeulen, 2015. "Sharing Rule Identification for General Collective Consumption Models," Econometrica, Econometric Society, vol. 83(5), pages 2001-2041, September.
    14. José L. Casco, 2024. "Intra-household resource shares under poverty transfers: evidence from Ecuador," Review of Economics of the Household, Springer, vol. 22(3), pages 1243-1274, September.
    15. Denni Tommasi, 2016. "Household Responses to cash Transfers," Working Papers ECARES ECARES 2016-20, ULB -- Universite Libre de Bruxelles.
    16. Denni Tommasi & Alexander Wolf, 2016. "Overcoming Weak Identification in the Estimation of Household Resource Shares," Working Papers ECARES ECARES 2016-12, ULB -- Universite Libre de Bruxelles.
    17. Brown, Caitlin & Calvi, Rossella & Penglase, Jacob, 2021. "Sharing the pie: An analysis of undernutrition and individual consumption in Bangladesh," Journal of Public Economics, Elsevier, vol. 200(C).
    18. Dieter Saelens, 2022. "Unitary or collective households? A nonparametric rationality and separability test using detailed data on consumption expenditures and time use," Empirical Economics, Springer, vol. 62(2), pages 637-677, February.
    19. Sam Cosaert & Thomas Demuynck, 2018. "Nonparametric Welfare and Demand Analysis with Unobserved Individual Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 100(2), pages 349-361, May.
    20. Lucia Mangiavacchi & Luca Piccoli, 2022. "Gender Inequalities Among Adults and Children: Exposure to Migration and the Evolution of Social Norms in Albania," Journal of Family and Economic Issues, Springer, vol. 43(3), pages 546-564, September.

    More about this item

    Keywords

    Identification; Nonparametric; Collective household model; Random utility; Unobserved heterogeneity; Invertibility; Individual counterfactuals;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • D13 - Microeconomics - - Household Behavior - - - Household Production and Intrahouse Allocation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:234:y:2023:i:1:p:301-326. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.