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

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  • Dette, Holger
  • Hoderlein, Stefan
  • Neumeyer, Natalie

Abstract

This paper is concerned with testing a core economic restriction, negative semidefiniteness of the Slutsky matrix. We consider a system of nonseparable structural equations with infinite dimensional unobservables, and 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 use quantiles of linear combinations of the dependent variable, develop a new empirical process based test that applies kernel quantile estimators, and investigate its finite and large sample behavior. Finally, we apply all concepts to Canadian microdata.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:191:y:2016:i:1:p:129-144
    DOI: 10.1016/j.jeconom.2015.07.004
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    More about this item

    Keywords

    Nonparametric testing; Heterogeneity; Integrability; Nonseparable models; Consumer demand; Quantile regression;
    All these keywords.

    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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