(Stata16): Heteroskedasticity and Robust Standard Errors

‪@CrunchEconometrix‬ This video explains how to correct heteroscedasticity with robust standard errors. Coined from the Greek word hetero (which means different or unequal), and skedastic (which means spread or scatter). So, homoskedasticity means equal spread, and heteroskedasticity, on the other hand, means unequal spread. The measure of spread is the variance, hence, heteroskedasticity deals with unequal variances. Heteroskedasticity or heteroscedasticity is the same. Only be consistent. Yes! The longest word in the econometrics dictionary with 18 words. One of the assumptions of ordinary least squares (OLS) is that the model must be homoskedastic. Needed to justify the usual t tests, F tests, and confidence intervals for OLS estimation of the linear regression model, even in large samples. In general, heteroskedasticity is more likely to occur in cross-sectional analysis. This does not imply that heteroskedasticity in time series models is impossible. What are the causes of heteroskedasticity? (1) Poor data sampling method may lead to heteroskedasticity particularly when collecting primary data. (2) Wrong data transformation. For instance, over-differencing a variable may lead to heteroskedasticity. (3) Wrong model specification. Related to the functional form: log-log, log-level, and level-level models. (4) The presence of outliers can lead to your model becoming heteroskedastic. Bogus figures that stands out. Very obvious to the prying eyes. (5) Skewness of one or more regressors (closely related to outliers being evident in the data). Consequences of heteroskedasticity: (1) OLS estimators, β ̂_OLS are still linear, unbiased and consistent. Hence the regression estimates remain unbiased and consistent. (2) But the estimators, β ̂_OLS are inefficient (that is, not having minimum variance) in the class of minimum variance estimators. (3) Therefore, OLS is no longer BLUE (Best Linear Unbiased Estimator). (4) Such that regression predictors (estimates) are also inefficient, though consistent. (5) Implies that the regression estimates cannot be used to construct confidence intervals, or used for inferences. (6) Affects the variances (and standard errors) of the estimated β ̂_S. (7) OLS method under-estimates the variances (and standard errors). (8) Yields low standard errors (9) Leads to higher than expected values of t and F statistics. (10) Yields statistically significant coefficients. (11) Rejection of the null hypothesis too often (12) Causes Type I error. (13) Both the t and the F statistics are no longer reliable any more for hypothesis testing. Some heteroskedasticity tests are: Breusch-Pagan LM Test; Glesjer LM Test; Harvey-Godfrey LM Test; Park LM Test; Goldfeld-Quandt Test; White’s Test; Engle’s ARCH Test; and Koenker-Basset Test. Heteroskedasticity can be resolved by: (1) Functional Forms; (2) Generalised (Weighted) Least Squares (GLS/WLS); and (3) White’s Robust-Standard Errors. How to detect heteroskedasticity? The truth is that there is no hard and fast rule for detecting heteroskedasticity. Therefore, more often than not, heteroskedasticity may be a case of educated guesswork, prior empirical experiences or mere speculation. However, informal and formal approaches can be used in detecting the presence of heteroskedasticity such as: Informal approach: Plotting the residuals from the regression against the estimated dependent variable
Formal approach: Perform econometric tests. There are several tests of heteroskedasticity, each based on certain assumptions. The interested reader may want to consult the references listed at the end of the video.

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References and Readings: Asteriou and Hall (2016) Applied Econometrics, 3ed; Wooldridge, J. M. (1995). Econometric Analysis of Cross Section and Panel Data. London, England: The MIT Press, Cambridge, Massachusetts; Baltagi, B.H. (1995) Econometric Analysis of Panel Data. New York, NY: John Wiley and Sons; Hsiao, C. (1986) Analysis of Panel Data, Econometric Society Monographs No. 11. Cambridge, United Kingdom: Cambridge University Press; Gujarati and Porter (2009) Basic Econometrics, International Edition; John, F. (1997) Applied Regression Analysis, Linear Models, and Related Methods, Sage Publications, California, p. 306; Mankiw, GN. (1990) “A Quick Refresher Course in Macroeconomics,” Journal of Economic Literature, Vol. XXVIII, p. 1648

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