Specification Analysis of Structural Quantile Regression Models

This paper introduces a broad family of tests for the hypothesis of linearity in parameters of functions that are identified by conditional quantile restrictions involving instrumental variables. These tests are tantamount to assessments of lack of fit for quantile regression models involving endogenous conditioning variables, and may be applied to assess the validity of post-estimation inferences regarding the counterfactual effect of endogenous treatments 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 improves power performance and facilitates the simulation of critical values via the application of simple multiplier-type bootstrap procedures. Monte Carlo evidence is included, along with an application to an empirical analysis of the structure of demand for a particular subsegment of the market for anti-bacterial drugs in India.