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Heteroskedasticity-consistent standard errors that differ from classical standard errors may indicate model misspecification. Substituting heteroskedasticity-consistent standard errors does not resolve this misspecification, which may lead to bias in the coefficients. In most situations, the problem should be found and fixed. [5]
Heteroscedasticity-consistent standard errors (HCSE), while still biased, improve upon OLS estimates. [2] HCSE is a consistent estimator of standard errors in regression models with heteroscedasticity. This method corrects for heteroscedasticity without altering the values of the coefficients.
White test is a statistical test that establishes whether the variance of the errors in a regression model is constant: that is for homoskedasticity. This test, and an estimator for heteroscedasticity-consistent standard errors, were proposed by Halbert White in 1980. [1]
Plot with random data showing heteroscedasticity: The variance of the y-values of the dots increases with increasing values of x. In statistics , a sequence of random variables is homoscedastic ( / ˌ h oʊ m oʊ s k ə ˈ d æ s t ɪ k / ) if all its random variables have the same finite variance ; this is also known as homogeneity of variance.
In Stata, the command newey produces Newey–West standard errors for coefficients estimated by OLS regression. [13] In MATLAB, the command hac in the Econometrics toolbox produces the Newey–West estimator (among others). [14] In Python, the statsmodels [15] module includes functions for the covariance matrix using Newey–West.
Analogous to how Huber-White standard errors are consistent in the presence of heteroscedasticity and Newey–West standard errors are consistent in the presence of accurately-modeled autocorrelation, clustered standard errors are consistent in the presence of cluster-based sampling or treatment assignment.
If the Breusch–Pagan test shows that there is conditional heteroskedasticity, one could either use weighted least squares (if the source of heteroskedasticity is known) or use heteroscedasticity-consistent standard errors.
Step 3: Select the equation with the highest R 2 and lowest standard errors to represent heteroscedasticity. Step 4: Perform a t-test on the equation selected from step 3 on γ 1. If γ 1 is statistically significant, reject the null hypothesis of homoscedasticity.