Comparison of performances of heteroskedasticity tests under measurement error

Year 2025, Volume: 74 Issue: 2, 333 - 345, 19.06.2025

Selin Alıca , Şenay Açıkgöz , Rukiye Dağalp , Şahika Gökmen

https://doi.org/10.31801/cfsuasmas.1632865

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

References

• Adamec, V., Power of heteroskedasticity tests in presence of various types of skedastic function and sample size, AIP Conference Proceedings, (2017), 1863, 100002.
• Ali, M. M., Giaccotto, C., A study of several new and existing tests for heteroscedasticity in the general linear model, Journal of Econometrics, 26(3) (1984), 355-373.
• Bickel, P. J., Using residuals robustly I: Tests for heteroskedasticity, nonlinearity, Annals of Statistics, (1978), 6: 266-269.
• Breusch, T. S., Pagan, A. R., A simple test for heteroskedasticity and random coefficient variation, Econometrica, 47(5) (1979), 1287–94.
• Carroll, R. J., Ruppert, D., Stefanski, L. A., Crainiceanu, C. M., Measurement error in nonlinear models, USA, Chapman and Hall/CRC, 2006.
• Dufour, J. M., Khalaf, L., Monte Carlo test methods in Econometrics, in Companion to Theoretical Econometrics, (Ed. Badi Baltagi) Chapter 23, 494-519, Blackwell, Oxford, U.K, 2001.
• Dufour, J. M., Khalaf, L., Bernard, J. T. and Genest, I., Simulation-based finite-sample tests for heteroskedasticity and arch effects, Journal of Econometrics, 122(2) (2004), 317-47.
• Duncan, O. D., Introduction to Structural Equation Models, New York: Academic Press, 1975.
• Glejser, H., A new test for heteroskedasticity. Journal of the American Statistical Association, 64(325) (1969), 316-23.
• Gokmen, S., Dagalp, R. and Kilickaplan, S., Multicollinearity in measurement error models, Communication in Statistics: Theory and Methods, 51(2) (2022), 474-485.
• Goldfeld, S. M., Quandt, R. E., Nonlinear methods in Econometrics, Amsterdam, North Holland, (1972).
• Goldfeld, S. M., Quandt, R. E., Some tests for homoscedasticity, Journal of the American Statistical Association, 60(310) (1965), 539-47.
• Griffiths, W. and Surekha, K., A Monte Carlo evaluation of the power of some tests for heteroscedasticity, Journal of Econometrics, 31(2) (1986), 219-31.
• Gujarati, D., Basic Econometrics, 4th Edition, The McGraw-Hill Co, 2004.
• Harrison, M. J., McCabe, B. P. M., A test for heteroscedasticity based on ordinary least squares residuals, Journal of the American Statistical Association, 74(365) (1979), 30-36.
• Harvey, A. C., Estimating regression models with multiplicative heteroskedasticity, Econometrica, 44 (1976), 461-466.
• Harvey, A.C., Phillips, G. D. A., A comparison of the power of some tests for heteroskedasticity in the general linear model, Journal of Econometrics, 2 (1974), 307-316.
• Hedayat, A. S., Robson, D. S., A study of orthogonal arrays for asymmetric factorial designs, Annals of Mathematical Statistics, 41(6) (1970), 1655-1670.
• Johnston, J., Econometric methods, 2nd Edition, New York, McGraw-Hill, 1972.
• Lyon, J. D., and Tsai, C. L., A comparison of tests for heteroscedasticity, The Statistician, 45(3) (1996), 337-49.
• Park, R. E., Estimation with heteroscedastic error terms, Econometrica, 34(4) (1966), 888.
• Pesaran, M. H., Taylor, L. W., Diagnostics for IV regressions, Oxford Bulletin of Economics and Statistics, 61(4) (1999), 507-523.
• Szroeter, J., A class of parametric tests for heteroskedastic regression models, Econometrica, 46 (1978), 1311-1327.
• Uyanto, S., Monte Carlo power comparison of seven most commonly used heteroscedasticity tests, Communications in Statistics - Simulation and Computation, 48(4) (2019), 817-38.
• Wallentin, B., Agren, A., Test of heteroscedasticity in a regression model in the presence of measurement errors, Economics Letters, 76(2) (2002), 205-211.
• White, H., A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica, 48(4) (1980), 817-38.
• Won, E. Y. T., Incomplete corrections for regressor unreliabilities, Sociological Methods and Research, 10 (1982), 271-284.
• Wooldridge, J. M., Solutions: Asymptotic Properties of Tests for Heteroskedasticity under Measurement Error, Econometric Theory, 12(2) (1996), 402-403.
• Wooldridge, J. M., Introductory Econometrics: A Modern Approach, 2nd Edition, South-Western Publishing Co, 2004.
• Zeileis, A., Econometric computing with HC and HAC covariance matrix estimators, Journal of Statistical Software, 11(10) (2004), 1-17.