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

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Listed:
  • 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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    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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