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Revealed Preferences in a Heterogeneous Population


  • Stefan Hoderlein

    (Boston College)

  • Jörg Stoye

    () (New York University)


This paper explores the empirical content of the weak axiom of revealed preference (WARP) for repeated cross-sectional data or for panel data where individuals experience preference shocks. Specifically, in a heterogeneous population, think of the fraction of consumers violating WARP as the parameter of interest. This parameter depends on the joint distribution of choices over different budget sets. Repeated cross-sections do not reveal this distribution but only its marginals. Thus, the parameter is not point identified but can be bounded. We frame this as a copula problem and use copula techniques to analyze it. The bounds, as well as some nonparametric refinements of them, correspond to intuitive behavioral assumptions in the two goods case. With three or more goods, these intuitions break down, and plausible assumptions can have counterintuitive implications. Inference on the bounds is an application of partial identification through moment inequalities. We implement our analysis with the British Family Expenditure Survey (FES) data. Upper bounds are fre- quently positive but lower bounds not significantly so, hence FES data are consistent with WARP in a heterogeneous population.

Suggested Citation

  • Stefan Hoderlein & Jörg Stoye, 2009. "Revealed Preferences in a Heterogeneous Population," Boston College Working Papers in Economics 745, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:745

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    Cited by:

    1. Sam Cosaert & Thomas Demuynck, 2015. "Revealed preference theory for finite choice sets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 169-200, May.
    2. Jerry Hausman & Whitney K. Newey, 2013. "Individual heterogeneity and average welfare," CeMMAP working papers CWP34/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram & Hjertstrand, Per, 2015. "Revealed preference tests for weak separability: An integer programming approach," Journal of Econometrics, Elsevier, vol. 186(1), pages 129-141.
    4. Yuichi Kitamura & Jorg Stoye, 2013. "Nonparametric Analysis of Random Utility Models: Testing," Cowles Foundation Discussion Papers 1902, Cowles Foundation for Research in Economics, Yale University.
    5. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2013. "Nonparametric estimation of a heterogeneous demand function under the Slutsky inequality restriction," CeMMAP working papers CWP54/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Dette, Holger & Hoderlein, Stefan & Neumeyer, Natalie, 2016. "Testing multivariate economic restrictions using quantiles: The example of Slutsky negative semidefiniteness," Journal of Econometrics, Elsevier, vol. 191(1), pages 129-144.
    7. Sokbae Lee & Kyungchul Song & Yoon-Jae Whang, 2014. "Testing For A General Class Of Functional Inequalities," KIER Working Papers 889, Kyoto University, Institute of Economic Research.
    8. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2014. "Household consumption when marriage is stable," IFS Working Papers W14/26, Institute for Fiscal Studies.
    9. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    10. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    11. Cherchye, Laurens & De Rock, Bram & Demuynck, Thomas, 0. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society.
    12. Laurens Cherchye & Sam Cosaert & Bram De Rock & Pieter Jan Kerstens & Frederic Vermeulen, 2017. "Individual Welfare Analysis for Collective Households," Working Papers ECARES ECARES 2017-44, ULB -- Universite Libre de Bruxelles.
    13. repec:spr:etbull:v:3:y:2015:i:2:d:10.1007_s40505-014-0061-5 is not listed on IDEAS
    14. 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.
    15. Arman Bidarbakht Nia, 2017. "A generalization to QUAIDS," Empirical Economics, Springer, vol. 52(1), pages 393-410, February.
    16. Jerry Hausman & Whitney K. Newey, 2014. "Individual Heterogeneity and Average Welfare," CeMMAP working papers CWP42/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    17. Laurens Cherchye & Bram De Rock & Thomas Demuynck, 2017. "Bounding Counterfactual Demand with Unobserved Heterogeneity and Endogenous Expenditures," Working Papers ECARES ECARES 2017-41, ULB -- Universite Libre de Bruxelles.
    18. Mark Dean & Daniel Martin, 2011. "Testing for Rationality with Consumption Data: Demographics and Heterogeneity," Working Papers 2011-11, Brown University, Department of Economics.

    More about this item


    Revealed Preference; Weak Axiom; Heterogeneity; Partial Identification; Moment Inequalities.;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis


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