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Heterogeneity and the Non-Parametric Analysis of Consumer Choice: Conditions for Invertibility

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  • Walter Beckert
  • Richard Blundell

Abstract

This paper considers structural non-parametric random utility models for continuous choice variables with unobserved heterogeneity. We provide sufficient conditions on random preferences to yield reduced-form systems of non-parametric stochastic demand functions that allow global invertibility between demands and non-separable unobserved heterogeneity. Invertibility is essential for global identification of structural consumer demand models, for the existence of well-specified probability models of choice and for the non-parametric analysis of revealed stochastic preference. We distinguish between new classes of models in which heterogeneity is separable and non-separable in the marginal rates of substitution, respectively. Copyright 2008, Wiley-Blackwell.

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  • 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.
    • Handle: RePEc:oup:restud:v:75:y:2008:i:4:p:1069-1080
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    File URL: http://hdl.handle.net/10.1111/j.1467-937X.2008.00500.x
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    References listed on IDEAS

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    1. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
    2. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    3. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    4. 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.
    5. Daniel McFadden, 2005. "Revealed stochastic preference: a synthesis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 245-264, August.
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    Cited by:

    1. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    2. Romuald Meango, 2023. "Using Probabilistic Stated Preference Analyses to Understand Actual Choices," Papers 2307.13966, arXiv.org.
    3. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    4. Sher, Itai & Kim, Kyoo il, 2014. "Identifying combinatorial valuations from aggregate demand," Journal of Economic Theory, Elsevier, vol. 153(C), pages 428-458.
    5. 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.
    6. Cherchye, Laurens & Demuynck, Thomas & Rock, Bram De, 2019. "Bounding counterfactual demand with unobserved heterogeneity and endogenous expenditures," Journal of Econometrics, Elsevier, vol. 211(2), pages 483-506.
    7. Roy Allen, 2019. "Injectivity and the Law of Demand," Papers 1908.05714, arXiv.org.
    8. Ian Crawford & Matthew Polisson, 2015. "Demand Analysis with Partially Observed Prices," Discussion Papers in Economics 15/12, Division of Economics, School of Business, University of Leicester, revised Dec 2016.
    9. Christopher Dobronyi & Christian Gouri'eroux, 2020. "Consumer Theory with Non-Parametric Taste Uncertainty and Individual Heterogeneity," Papers 2010.13937, arXiv.org, revised Jan 2021.
    10. 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.
    11. Andreas Chai & Christian Kiedaisch & Nicholas Rohde, 2021. "The saturation of household spending diversity and emergent properties of representative households," DeFiPP Working Papers 2104, University of Namur, Development Finance and Public Policies.
    12. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers CWP60/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. 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.
    14. Allen, Roy, 2022. "Injectivity and the law of demand," Economics Letters, Elsevier, vol. 215(C).
    15. Andreas Chai & Christian Kiedaisch & Nicholas Rohde, 2017. "The saturation of spending diversity and the truth about Mr Brown and Mrs Jones," Discussion Papers in Economics economics:201701, Griffith University, Department of Accounting, Finance and Economics.
    16. Walter Beckert, 2007. "Specification and Identification of Stochastic Demand Models," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 669-683.
    17. 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.
    18. Andreas Chai & Nicholas Rohde & Jacques Silber, 2015. "Measuring The Diversity Of Household Spending Patterns," Journal of Economic Surveys, Wiley Blackwell, vol. 29(3), pages 423-440, July.
    19. NAKABAYASHI Jun & HIROSE Yohsuke, 2016. "Structural Estimation of the Scoring Auction Model," Discussion papers 16008, Research Institute of Economy, Trade and Industry (RIETI).

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • D1 - Microeconomics - - Household Behavior

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