GMM Quantile Regression

88 Pages Posted: 13 Aug 2019 Last revised: 27 Nov 2020

See all articles by Sergio Firpo

Sergio Firpo

Insper

Antonio F. Galvao

Michigan State University

Cristine Campos de Xavier Pinto

University of California, Berkeley - Department of Economics

Alexandre Poirier

Georgetown University - Department of Economics

Graciela Sanroman

dECON-UDELAR

Date Written: September 2, 2020

Abstract

This paper develops generalized method of moments (GMM) estimation and inference procedures for quantile regression models. We propose a GMM estimator for simultaneous estimation across multiple quantiles. This estimator allows us to model quantile regression coefficients using flexible parametric restrictions across quantiles. The restrictions and simultaneous estimation lead to efficiency gains compared to standard methods. We establish the asymptotic properties of the GMM estimators when the number of quantiles used is fixed, and also when it diverges to infinity jointly with the sample size. As an alternative to GMM, we also propose a minimum distance (MD) estimator over a given subset of quantiles. We also provide specification tests for the imposed restrictions. The estimators and tests we propose are simple to implement in practice. Monte Carlo simulations provide numerical evidence of the finite sample properties of the methods. Finally, we apply the proposed methods to estimate the effects of smoking on birthweight of live infants at the extreme bottom of the conditional distribution.

Keywords: Quantile Regression, Generalized Method of Moments

JEL Classification: C21, C31

Suggested Citation

Firpo, Sergio and Galvao, Antonio F. and Campos de Xavier Pinto, Cristine and Poirier, Alexandre and Sanroman, Graciela, GMM Quantile Regression (September 2, 2020). Journal of Econometrics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3435264 or http://dx.doi.org/10.2139/ssrn.3435264

Sergio Firpo

Insper ( email )

R Quata 300
Sao Paulo, 04542-030
Brazil

HOME PAGE: http://https://sites.google.com/site/sergiopfirpo/

Antonio F. Galvao (Contact Author)

Michigan State University ( email )

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

Cristine Campos de Xavier Pinto

University of California, Berkeley - Department of Economics

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

Alexandre Poirier

Georgetown University - Department of Economics ( email )

Washington, DC 20057
United States

Graciela Sanroman

dECON-UDELAR ( email )

Constituyente 1502
Montevideo, Montevideo 11200
Uruguay
+598 2410 6449 (Phone)

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