Specification Analysis of
Linear and Structural Quantile Regression Models
(with Juan Carlos Escanciano)
14
December 2009
Abstract
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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 demand
for wholesale fish at the former Fulton Fish Market in Lower Manhattan. |
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KEYWORDS: Quantile regression, instrumental
variables, structural models |
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