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

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  • Holger Dette
  • Stefan Hoderlein

    ()
    (Institute for Fiscal Studies and Boston College)

  • Natalie Neumeyer

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.

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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. 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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  16. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, 07.
  17. Robert Serfling, 2002. "Quantile functions for multivariate analysis: approaches and applications," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 56(2), pages 214-232.
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Cited by:
  1. Jerry Hausman & Whitney Newey, 2013. "Individual heterogeneity and average welfare," CeMMAP working papers CWP34/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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