Journal Article

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


Holger Dette, Stefan Hoderlein, Natalie Neumeyer

Published Date

1 March 2016


Journal Article

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.

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