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

  • Holger Dette
  • Stefan Hoderlein

    ()

    (Institute for Fiscal Studies and Boston College)

  • Natalie Neumeyer

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.

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File URL: http://cemmap.ifs.org.uk/wps/cwp1411.pdf
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP14/11.

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Date of creation: May 2011
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Handle: RePEc:ifs:cemmap:14/11
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  1. Rosa L. Matzkin, 1999. "Nonparametric Estimation of Nonadditive Random Functions," Working Papers 38, Universidad de San Andres, Departamento de Economia, revised Sep 2001.
  2. Wolak, Frank A, 1991. "The Local Nature of Hypothesis Tests Involving Inequality Constraints in Nonlinear Models," Econometrica, Econometric Society, vol. 59(4), pages 981-95, July.
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  5. Stefan Hoderlein, 2009. "How Many Consumers are Rational?," Boston College Working Papers in Economics 748, Boston College Department of Economics.
  6. Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(04), pages 614-632, August.
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  8. Marc Hallin & Davy Paindaveine & Miroslav Šiman, 2010. "Multivariate quantiles and multiple-output regression quantiles: From L1 optimization to halfspace depth," ULB Institutional Repository 2013/127979, ULB -- Universite Libre de Bruxelles.
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  10. Pendakur, K., 1999. "Taking Prices Seriously in the Measurement of Inequality," Discussion Papers dp99-7, Department of Economics, Simon Fraser University.
  11. Holger Dette & Jens Wagener & Stanislav Volgushev, 2011. "Comparing Conditional Quantile Curves," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(1), pages 63-88, 03.
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  13. Haag, Berthold R. & Hoderlein, Stefan & Pendakur, Krishna, 2009. "Testing and imposing Slutsky symmetry in nonparametric demand systems," Journal of Econometrics, Elsevier, vol. 153(1), pages 33-50, November.
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  17. Kihlstrom, Richard E & Mas-Colell, Andreu & Sonnenschein, Hugo, 1976. "The Demand Theory of the Weak Axiom of Revealed Preference," Econometrica, Econometric Society, vol. 44(5), pages 971-78, September.
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