Quantile-Regression Inference With Adaptive Control of Size

TL;DR

This paper introduces a new variance estimator for regression quantiles that improves the accuracy of Wald-type tests and confidence regions, ensuring better size control and power in large samples.

Contribution

It develops an adaptive variance estimation method for regression quantiles that enhances the performance of inference procedures compared to traditional approaches.

Findings

The new estimator improves size control of Wald tests across various scenarios.

Monte Carlo simulations show increased power in testing heterogeneity of quantile effects.

Empirical example demonstrates practical applicability of the method.

Abstract

Regression quantiles have asymptotic variances that depend on the conditional densities of the response variable given regressors. This paper develops a new estimate of the asymptotic variance of regression quantiles that leads any resulting Wald-type test or confidence region to behave as well in large samples as its infeasible counterpart in which the true conditional response densities are embedded. We give explicit guidance on implementing the new variance estimator to control adaptively the size of any resulting Wald-type test. Monte Carlo evidence indicates the potential of our approach to deliver powerful tests of heterogeneity of quantile treatment effects in covariates with good size performance over different quantile levels, data-generating processes and sample sizes. We also include an empirical example. Supplementary material is available online.