week 2 part 4 Flashcards
What does the assumption of constant variability claim? (homoscedasticity).
That the variance of the error term is the same for all observations, meaning there is no heteroscedasticity.
What is the problem with changing variability?
The OLS estimates are still unbiased. However, we can no longer rely on the estimated standard errors for OLS, which makes it impossible to rely on common t- or F-tests since they are based on the estimated standard errors.
How can we detect changing variability?
Use residual plots to see if variability increases or decreases over the values of xj
What does the Assumption of no correlated observations claim? (no autocorrelation).
That there should be no serial correlation.
What should we use to correct the standard errors when we have changing variability?
Use the OLS coefficient estimates and correct the standard errors with White’s robust standard errors. These allow us to perform valid t-tests.
What should you do if you have correlated observations?
You can still use the OLS estimators but not the standard errors. You need to correct them with the Newey west robust standard errors method.
Why can´t you use the normal standard errors when you have correlated observations?
They are often distorted downwards, giving a better picture of the model than it actually is. It can also lead to t and F-tests indicating that the explanatory variables are individually and jointly significant, which may not always be true.
How can we detect correlated observations?
If we plot the residuals sequentially over time, we can see correlated patterns around the horizontal axis.
What does the Assumption of no correlation between the standard error and the explanatory variables (no endogeneity) claim?
That the error term must not be correlated with the explanatory variables.
When is there often endogenity?
If important explanatory variables are omitted, as they are then included in the error term.
What does endogenity lead to?
Unreliable coefficient estimates and makes linear regression models incapable of establishing causality.
What should you do if you detect endogenity?
Include all relevant explanatory variables in the regression model.
What can´t we do if the error term is not normally distributed?
Make interval estimates or hypothesis tests unless we have very large samples.
