GMM quantile regression

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 when it diverges to infinity jointly with the sample size. As an alternative to GMM, we also propose a minimum distance estimator over a given subset of quantiles. Moreover, we 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. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper develops generalized method of moments (GMM) estimation and inference procedures for quantile regression models. The proposed GMM estimator allows simultaneous estimation across multiple quantiles, leading to efficiency gains compared to standard methods. As an alternative, a minimum distance estimator over a given subset of quantiles is also proposed. The paper also provides specification tests for the imposed restrictions, and the estimators and tests are simple to implement in practice. Numerical evidence from Monte Carlo simulations is used to evaluate the finite sample properties of the methods. Finally, the methods are applied to estimate the effects of smoking on birthweight of live infants at the extreme bottom of the conditional distribution.