Testing Heteroskedasticity Under Measurement Error

TL;DR

This paper introduces a new statistical test for detecting heteroskedasticity in regression models affected by measurement error, utilizing deconvolution and bootstrap methods for improved accuracy.

Contribution

It develops a novel heteroskedasticity test based on deconvolved residuals, addressing measurement error and unknown error distributions with bootstrap techniques.

Findings

Test performs well in simulations and empirical studies.

Method effectively handles known and unknown measurement error distributions.

Bootstrap methods provide reliable critical values.

Abstract

In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test statistics based on a deconvolved residual-marked empirical process and establish their asymptotic properties in both ordinary smooth and supersmooth cases, assuming the measurement error distribution is known. The issue of an unknown measurement error distribution is addressed by employing estimators of the measurement error characteristic function based on repeated measurements. Furthermore, depending on whether the measurement error distribution is known or not, to obtain critical values from the case-dependent limiting null distributions, we propose two computationally attractive multiplier bootstrap methods where the "parameter estimation effect" is successfully addressed. Finally, simulation results and empirical studies about corn yields and household budget shares confirm the favorable properties of the proposed tests.