On the Power of Heteroskedasticity Tests in Regression: A Monte Carlo Simulation Study

Abstract

An important assumption for the classical linear regression model (CLRM) is homoskedasticity, which assumes that variances of the error vector of the regression model are constant. But if the variances are varying (not constant), this means that the problem of heteroskedasticity is present, and as a result there are some consequences to it, such as the Gauss-Markov theorem not being applied, the ordinary least squares (OLS) estimators no longer being BLUE (Best Linear Unbiased Estimator), the regression predictions being inefficient too, and the standard for the least squares estimator being wrong. Several diagnostic tests have been developed to detect the heteroskedasticity problem. The most common ones include Breusch-Pagan test, White test, and Goldfeld-Quandt test. In this paper we focus on four tests for heteroskedasticity, namely Goldfeld-Quandt (GQ), Glesjer, White, and ARCH tests. We explain each test and indicate the difference between each test. After that we used the Monte Carlo simulation study to apply and compare the performance between the four tests in three types of heteroskedasticity to determine which test has the best performance. The Monte Carlo simulation study has been conducted to evaluate these tests. Several scenarios of simulations were used, such as different sample sizes, different values of the coefficient of variation of the variance of the error, and others. The simulation results were close to each other, but for the first type of heteroskedasticity, the Goldfeld-Quandt test has the best performance and most power. While for the second and third types of heteroskedasticity, the Goldfeld-Quandt and ARCH tests have power close to each other.