Specification analysis of linear quantile models

This paper introduces a nonparametric test for the correct specification of a linear conditional quantile function over a continuum of quantile levels. These tests may be applied to assess the validity of post-estimation inferences regarding the effect of conditioning variables on the distribution of outcomes. We show that the use of an orthogonal projection on the tangent space of nuisance parameters at each quantile index both improves power and facilitates the simulation of critical values via the application of a simple multiplier bootstrap procedure. Monte Carlo evidence and an application to the empirical analysis of age–earnings curves are included.