Quantile-Regression Inference With Adaptive Control of Size Articles uri icon

publication date

  • July 2019

start page

  • 1382

end page

  • 1393


  • 527


  • 114

International Standard Serial Number (ISSN)

  • 0162-1459

Electronic International Standard Serial Number (EISSN)

  • 1537-274X


  • Regression quantiles have asymptotic variances that depend on the conditional densities of the response variable given regressors. This article 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


  • Economics


  • asymptotic variance; conditional density estimation; regression quantile; standard error