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An alternative to explicitly modelling the heteroskedasticity is using a resampling method such as the wild bootstrap. Given that the studentized bootstrap, which standardizes the resampled statistic by its standard error, yields an asymptotic refinement, [13] heteroskedasticity-robust standard errors remain nevertheless useful.
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.
An alternative to the White test is the Breusch–Pagan test, where the Breusch-Pagan test is designed to detect only linear forms of heteroskedasticity. Under certain conditions and a modification of one of the tests, they can be found to be algebraically equivalent.
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.
The disturbance in matrix A is homoscedastic; this is the simple case where OLS is the best linear unbiased estimator. The disturbances in matrices B and C are heteroscedastic. In matrix B, the variance is time-varying, increasing steadily across time; in matrix C, the variance depends on the value of . The disturbance in matrix D is ...
When the observational errors are uncorrelated and the weight matrix, W=Ω −1, is diagonal, these may be written as ^ =. If the errors are correlated, the resulting estimator is the BLUE if the weight matrix is equal to the inverse of the variance-covariance matrix of the observations.
The Heckman correction is a two-step M-estimator where the covariance matrix generated by OLS estimation of the second stage is inconsistent. [7] Correct standard errors and other statistics can be generated from an asymptotic approximation or by resampling, such as through a bootstrap .
If the test statistic has a p-value below an appropriate threshold (e.g. p < 0.05) then the null hypothesis of homoskedasticity is rejected and heteroskedasticity assumed. 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 ...