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Testing multivariate economic restrictions using quantiles: the example of Slutsky negative semidefiniteness

Author

Listed:
  • Holger Dette

    (Institute for Fiscal Studies)

  • Stefan Hoderlein

    () (Institute for Fiscal Studies and Boston College)

  • Natalie Neumeyer

    (Institute for Fiscal Studies)

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 the 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 individual data, and show that rationality is an acceptable description of actual individual behavior.

Suggested Citation

  • Holger Dette & Stefan Hoderlein & Natalie Neumeyer, 2011. "Testing multivariate economic restrictions using quantiles: the example of Slutsky negative semidefiniteness," CeMMAP working papers CWP14/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:14/11
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    File URL: http://cemmap.ifs.org.uk/wps/cwp1411.pdf
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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 Jul 2017.
    2. repec:eee:jetheo:v:172:y:2017:i:c:p:163-201 is not listed on IDEAS
    3. 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.
    4. Blomquist, Sören & Kumar, Anil & Liang, Che-Yuan & Newey, Whitney K., 2014. "Individual Heterogeneity, Nonlinear Budget Sets, and Taxable Income," Working Paper Series, Center for Fiscal Studies 2014:1, Uppsala University, Department of Economics.
    5. Yuichi Kitamura & Jorg Stoye, 2016. "Nonparametric Analysis of Random Utility Models," Papers 1606.04819, arXiv.org, revised Dec 2017.
    6. Arman Bidarbakht Nia, 2017. "A generalization to QUAIDS," Empirical Economics, Springer, pages 393-410.
    7. David M. Kaplan & Longhao Zhuo, 2015. "Bayesian and frequentist nonlinear inequality tests," Working Papers 1709, Department of Economics, University of Missouri, revised Apr 2017.
    8. 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.
    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. 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.
    11. 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.

    More about this item

    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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