GMM Quantile Regression
88 Pages Posted: 13 Aug 2019 Last revised: 27 Nov 2020
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: Suggested Citation