Averaging Estimation for Instrumental Variables Quantile Regression

Abstract

Abstract This paper proposes two averaging estimation methods to improve the finite‐sample efficiency of the instrumental variables quantile regression (IVQR) estimator. I propose using the usual quantile regression for averaging to take advantage of cases when endogeneity is not too strong. I also propose using two‐stage least squares to take advantage of cases when heterogeneity is not too strong. The first averaging method is to apply a recent proposal for GMM averaging to the IVQR model based on this proposed intuition. My implementation involves many computational considerations and builds on recent developments in the quantile literature. The second averaging method is a new bootstrap model averaging method that directly averages among IVQR, quantile regression, and two‐stage least squares estimators. More specifically, I find the optimal weights from bootstrapped samples and then apply the bootstrap‐optimal weights to the original sample. The bootstrap method is simpler to compute and generally performs better in simulations, but uniform dominance results have not been formally proved. Simulation results demonstrate that in the multiple‐regressors/instruments case, both the GMM averaging and bootstrap estimators have uniformly smaller risk than the IVQR estimator across data‐generating processes with a variety of combinations of different endogeneity levels and heterogeneity levels.