Specification Testing in Nonparametric Instrumental Quantile Regression

TL;DR

This paper develops a statistical test for verifying the correct specification of instrumental quantile regression models in nonseparable econometric settings, ensuring validity of inferences drawn from such models.

Contribution

It introduces a novel hypothesis testing methodology for instrumental quantile regression models, addressing issues of model misspecification and providing tools for model validation.

Findings

Test statistic is asymptotically normal under correct specification.

The test is consistent against any alternative model.

Finite sample performance is validated through Monte Carlo simulations.

Abstract

There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable variable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This paper develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly specified. Our test statistic is asymptotically normally distributed under correct specification and consistent against any alternative model. In addition, test statistics to justify the model simplification are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration is provided.