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Testing Multivariate Economic Restrictions Using Quantiles: The Example of Slutsky Negative Semidefiniteness

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  • Holger Dette

    () (University of Bochum)

  • Stefan Hoderlein

    (Boston College)

  • Natalie Neumeyer

    () (University of Hamburg)

Abstract

This paper is concerned with testing rationality restrictions using quantile regression methods. Specifically, we consider negative semidefiniteness of the Slutsky matrix, arguably the core restriction implied by utility maximization. We consider a heterogeneous population characterized by a system of nonseparable structural equations with infinite dimensional unobservable. To analyze this economic restriction, we employ quantile regression methods because they allow us to utilize the entire distribution of the data. Difficulties arise because the restriction involves several equations, while the quantile is a univariate concept. We establish that we may test the economic restriction by considering quantiles of linear combinations of the dependent variable. For this hypothesis we develop a new empirical process based test that applies kernel quantile estimators, and derive its large sample behavior. We investigate the performance of the test in a simulation study. Finally, we apply all concepts to Canadian microdata, and show that rationality is not rejected.

Suggested Citation

  • Holger Dette & Stefan Hoderlein & Natalie Neumeyer, 2013. "Testing Multivariate Economic Restrictions Using Quantiles: The Example of Slutsky Negative Semidefiniteness," Boston College Working Papers in Economics 836, Boston College Department of Economics.
  • Handle: RePEc:boc:bocoec:836
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Victor H. Aguiar & Nail Kashaev, 2018. "Stochastic Revealed Preferences with Measurement Error," Papers 1810.05287, arXiv.org.
    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. Soren Blomquist & Anil Kumar & Che-Yuan Liang & Whitney K. Newey, 2014. "Individual heterogeneity, nonlinear budget sets, and taxable income," CeMMAP working papers CWP21/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Alexandre Belloni & Victor Chernozhukov & Denis Chetverikov & Iv'an Fern'andez-Val, 2011. "Conditional Quantile Processes based on Series or Many Regressors," Papers 1105.6154, arXiv.org, revised Aug 2018.
    5. Bhattacharya, D., 2018. "The Empirical Content of Binary Choice Models," Cambridge Working Papers in Economics 1883, Faculty of Economics, University of Cambridge.
    6. Richard Blundell & Joel Horowitz & Matthias Parey, 2018. "Estimation of a Heterogeneous Demand Function with Berkson Errors," Papers 1811.10690, arXiv.org, revised Aug 2019.
    7. repec:eee:jetheo:v:172:y:2017:i:c:p:163-201 is not listed on IDEAS
    8. Hubner, Stefan, 2016. "Topics in nonparametric identification and estimation," Other publications TiSEM 08fce56b-3193-46e0-871b-0, Tilburg University, School of Economics and Management.
    9. David M. Kaplan & Longhao Zhuo, 2015. "Frequentist size of Bayesian inequality tests," Working Papers 1709, Department of Economics, University of Missouri, revised 26 Feb 2018.
    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. Yuichi Kitamura & Jörg Stoye, 2018. "Nonparametric Analysis of Random Utility Models," Econometrica, Econometric Society, vol. 86(6), pages 1883-1909, November.
    12. Tatiana Komarova & Javier Hidalgo, 2019. "Testing nonparametric shape restrictions," Papers 1909.01675, arXiv.org.
    13. Lee, Y-Y. & Bhattacharya, D., 2018. "Applied Welfare Analysis for Discrete Choice with Interval-data on Income," Cambridge Working Papers in Economics 1882, Faculty of Economics, University of Cambridge.
    14. David M. Kaplan & Longhao Zhuo, 2015. "Frequentist size of Bayesian inequality tests," Working Papers 1709, Department of Economics, University of Missouri, revised 26 Feb 2018.
    15. Arman Bidarbakht Nia, 2017. "A generalization to QUAIDS," Empirical Economics, Springer, vol. 52(1), pages 393-410, February.
    16. 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.
    17. 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.
    18. Richard Blundell & Joel L. Horowitz & Matthias Parey, 2018. "Estimation of a nonseparable heterogenous demand function with shape restrictions and Berkson errors," CeMMAP working papers CWP67/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    Nonparametric Testing; Heterogeneity; Integrability; Nonseparable Models; Consumer Demand; Quantile Regression;

    JEL classification:

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

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