Testing Heteroskedasticity Under Measurement Error

2026-05-19

AI Summary

This study addresses the challenge of testing for heteroskedasticity in regression models when explanatory variables are contaminated by measurement error. Building upon the integrated conditional moment (ICM) framework, the authors construct a test statistic based on a deconvolution residual-marked empirical process. Asymptotic theory is established under both known and unknown measurement error distributions, and multiplier bootstrap procedures are developed to approximate critical values. This work provides the first robust heteroskedasticity test in the presence of measurement error, effectively accounting for estimation effects and accommodating both ordinary smooth and supersmooth error distributions. Monte Carlo simulations and empirical applications to corn yield and household budget share data demonstrate that the proposed method performs well in finite samples and offers substantial practical utility.

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.

Problem

• heteroskedasticity
• measurement error
• regression models
• deconvolution
• empirical process

Innovation

• heteroskedasticity testing
• measurement error
• deconvolution
• multiplier bootstrap
• integrated conditional moment