Comparison of performances of heteroskedasticity tests under measurement error

Abstract

While measurement error has an impact on the unbiasedness of the ordinary least squares (OLS) estimator, the heteroskedastic error term causes inefficient OLS estimators and biased variance estimates. Although the econometric literature has answers to these two fundamental concerns, such as applying measurement error correction methods and heteroskedasticity-robust standard errors, they do not directly address testing heteroskedasticity. This paper investigates the power of the most commonly used heteroskedasticity tests in the presence of error-in-variables. Monte Carlo simulations under different heteroscedasticity forms and sample sizes show that since measurement error inflates the variance of the explanatory variable and the response variable, heteroskedasticity tests lose their power in detecting heteroskedasticity. Simulations also show that the Glejser test is the most powerful one while the White test is weak, and the other tests lie in between them.

Keywords

• Heteroskedasticity
• measurement error
• classical linear regression model
• errors in variables

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