Topic 9: Heteroskedasticity Flashcards
Under what conditions can we dispense with the normality of the error term and still perform valid statistical analysis?
If the other MLR assumptions hold and we have a large sample size.
What is the formula for the estimate of a heteroskedastic robust variance of beta^1 in the MLR?
Var(beta^1) = [sum (r^ij)^2 * (u^ij)^2]
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[sum (r^ij)^2]^2
What is a formula for betaj in the linear probability model where the dependent variable is binary in terms of change based on the model: y = beta0 + beta1x1 +beta2x2 + u?
betaj = deltaP ( y=1 | x1, x2)
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delta x1
How does heteroskedasticity affect each the bias, consistency, and variance of OLS estimators?
The OLS estimator will be unbiased and consistent, but the estimator of the variance of the OLS estimator, and thus standard errors, will be wrong/inconsistent.
Are heteroskedasticity robust standard errors valid only in the case of a large sample size?
Yes, and if the sample size is large and the error term homoskedastic the robust standard errors are still valid.
Are robust standard errors always larger than usual standard errors?
No, they can be larger or smaller.
IS OLS for heteroskedastic error terms BLUE?
No, but they are unbiased and consistent, just not efficient.
Stata: How do you create dummy variables for categorical or ordinal variables without creating a new variable for each?
use “i.varname” and stata will create dummy variables for each, leaving out the first as the base group, so each coefficient is relative to the base group.
What is the Breusch-Pagan test used for?
The B-P test is used for testing the heteroskedasticity of the variance of the error term.
How does one perform the B-P test?
The null hypothesis is homoskedasticity. Estimate your regression by OLS. Save the residuals, uhati, regress uhati^2 on x1….xk. Look at the p-value for F, the overall significance of the regression. Small reject the null, large fail to reject the null.
How does one perform the White special test?
The null hypothesis is homoskedasticity. Estimate your regression by OLS. Save the residuals, uhati, save the fitted values (predict yhat, xb), generate squared values for each. Regress uhati^2 on yhat and yhat2. Look at the p-value for F, the overall significance of the regression. Small reject the null, large fail to reject the null.
What do we use the White special test for?
It is a test for homoskedasticity that can provide evidence of correlation between the fitted values and the residuals by using linear combinations of the fitted values.
What is the difference between the B-P test and White test?
The White test includes linear combinations of the original variables and the B-P test does not. The B-P test is intended for larger sample sizes. White is intended to test for forms of heteroskedasticity that invalidate test stats in linear combinations of the x’s.
If your tests have small p values, do we reject the null hypothesis that the standard errors are homoskedastic? If so what do we do?
Yes. We should use robust standard errors, by using the “,robust” post-estimation command.
How does heteroskedasticity robust procedures help the econometrician?
They are valid in large sample sizes whether or not the errors have a constant variance (under homo or heteroskedasticity, under the later produces consistent standard errors), allowing one to perform statistical analysis without the homoskedasticity assumption.
