CLRM Flashcards
assumptions, diagnostics, violations
what are the five assumption underlying the CLRM?
- error mean is zero
- error variance is sigma²
- covariance of errors is zero
- covariance of an error and an explanatory variable is zero
- errors are normally distributed
What does BLUE stand for?
Best Linear Unbiased Estimator
What does consistency imply?
it implies that the estimator is the probability limit of the true value
as the sample size increases, the sampling distribution of alpha and beta become increasingly concentrated around the true values
What does ubiasedness imply?
on average the estimated values will be equal to the true values. Proving it requires cov(error, x) = 0
what does efficiency imply?
the distance from the estimate to the true value of beta is minimized
what is the requirement so that we can test if the mean of the residuals is zero?
there needs to be a constant term in the regression
when dealing with heteroscedasticity, you can apply GLS which differs in two cases:
1) for infeasible heteroscedasticity (given). In reality we usually don’t know the true form of the heteroscedasticity, which makes this form of GLS infeasible.
2) feasible heteroscedasticity: estimates the model coefficients by applying the OLs estimator to the data scaled by the estimated inverse of the variance of the OLS residuals (via Weighted Least Squares)
To detect heteroscedasticity, we apply…
the GQ test: splitting the sample into two parts, estimating variances and comparing them. the H0 is that the variances of both subsamples are equal. If H0 is rejected, it means that heteroscedasticity is present
GLS is used for…
adjusting a regression model if heteroscedasticity is present ( residual variance is not constant). This method accounts for changing error variances, which ultimately leads to more efficient estimates compared to OLS
WLS ( Weighted Least Squares) is used for…
if the heteroscedasticity is feasible (the form/cause is known) you can assign weights to each observation based on the inverse of the variance of the OLS residuals
What do you do in case heteroscedasticity is infeasible?
The residual variance is approximated based on certain assumptions. Then you can implement GLS
When do you use GLS and when WLS?
WLS : for feasible heteroscedasticity
GLS: for infeasible heteroscedasticity
Cov (ui, uj)=0 means
that there is no predictability of the errors, they are linearly independent from each other
If there is predictability over time patterns in residuals, that means that the residuals are
autocorrelated AC
Autocorrelation between residuals means
that residuals in a regression model are correlated with their own past values
positive AC: positive/negative errors follow positive/negative errors
negative AC: reversal; positive follows negative an vice versa (Over time!!!)
no pattern: what we want! as no AC means cov is zero
