Quantile Regression Random Effects

51 Pages Posted: 14 Mar 2016 Last revised: 24 Jan 2017

See all articles by Antonio F. Galvao

Antonio F. Galvao

Michigan State University

Alexandre Poirier

Georgetown University - Department of Economics

Date Written: January 20, 2017

Abstract

This paper develops a random effects model for quantile regression (QR). We establish identification of the QR coefficients, and develop practical estimation and inference procedures. We employ a simple pooled QR estimator to estimate the coefficients of interest, and derive its statistical properties. The random effects induce cluster dependence hence we use a cluster-robust variance-covariance matrix estimator for inference, and establish its uniform consistency over the set of quantiles. We also develop a new test procedure for uniform testing of linear hypotheses in QR models. This procedure is a modified Wald test applied on a growing number of quantiles such that, asymptotically, the test is uniform over the quantiles. We show this procedure can be applied to test the random effects hypothesis in QR panel data models. Two significant differences between our model and fixed-effects QR models are that effects of time-invariant regressors can be estimated, and that the time-series dimension can be small and finite. We provide Monte Carlo simulations to evaluate the finite sample performance of the estimation and inference procedures. Finally, we apply the proposed methods to study the roles of education and ability in wage determination. We document strong heterogeneity in returns to education along the conditional distribution of earnings.

Keywords: Quantile Regression, Panel Data, Random Effects, Hypothesis Testing

JEL Classification: C12, C13, C23

Suggested Citation

Galvao, Antonio F. and Poirier, Alexandre, Quantile Regression Random Effects (January 20, 2017). Available at SSRN: https://ssrn.com/abstract=2746894 or http://dx.doi.org/10.2139/ssrn.2746894

Antonio F. Galvao (Contact Author)

Michigan State University ( email )

486 W. Circle Drive 110 Marshall-Adams Hall
East Lansing, MI 48824
United States

Alexandre Poirier

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States

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