Goodness-of-Fit Tests based on Series Estimators in Nonparametric Instrumental Regression

TL;DR

This paper introduces new series estimator-based goodness-of-fit tests for nonparametric instrumental regression, capable of testing model specifications, exogeneity, and showing strong theoretical properties including consistency and asymptotic distributions.

Contribution

It develops novel test statistics based on series estimators for nonparametric instrumental regression, with comprehensive theoretical analysis and finite sample evaluation.

Findings

Tests are consistent against all alternatives.

Asymptotic distributions are derived under correct and local alternatives.

Monte Carlo simulations demonstrate good finite sample performance.

Abstract

This paper proposes several tests of restricted specification in nonparametric instrumental regression. Based on series estimators, test statistics are established that allow for tests of the general model against a parametric or nonparametric specification as well as a test of exogeneity of the vector of regressors. The tests' asymptotic distributions under correct specification are derived and their consistency against any alternative model is shown. Under a sequence of local alternative hypotheses, the asymptotic distributions of the tests is derived. Moreover, uniform consistency is established over a class of alternatives whose distance to the null hypothesis shrinks appropriately as the sample size increases. A Monte Carlo study examines finite sample performance of the test statistics.