What happens if an irrelevant x is included in the regression model? correct answers As estimators (betas) are unbiased, the estimate of the coefficient will generally be around 0.
This inclusion has an undesirable effect on the variance of the other estimators.
What happens if a relevant varia...
Econometrics Exam Review || A+ Verified Solutions.
What happens if an irrelevant x is included in the regression model? correct answers As
estimators (betas) are unbiased, the estimate of the coefficient will generally be around 0.
This inclusion has an undesirable effect on the variance of the other estimators.
What happens if a relevant variable is omitted? correct answers The estimators (betas) will be
biased (over or under-estimated).
Omitted variable bias!
What is the difference between the Breusch-Pagan test and the White-test? correct answers The
Breusch-Pagan test detects any linear form of heteroskedasticity whereas the White-test allows
for non-linearity by using squares and cross-products of all x's.
Does the presence of heteroskedasticity affect the size of the OLS estimates? correct answers
Generally, it doesn't. The OLS estimators remain unbiased if we do not assume homoskedasticity
(however they are not BLUE). However, MLR5 (constant variance of the error term u) is needed
for using the formula of the variance of OLS estimators, which is needed to make inferences
about the population.
Why use weighted least squares (WLS) estimation? correct answers WLS is used when the form
of heteroskedasticity is known. It produces more efficient estimates than OLS.
The basic idea is to transform the model into one that has homoskedastic errors, called WLS.
The weighted model regains heteroskedasticity.
Briefly explain what the BP-test (Breusch-Pagan) is used for and how is works. correct answers
The BP-test is used to identify heteroskedasticity of the error term.
To perform the test, run the standard regression and save its squared residuals. Then regress
those residuals on all the independent variables. Finally, perform an F-test using the R^2 of the
last regression. There, we test if the coefficients of the last regression are all 0, which would
indicate homoskedasticity.
What is the White-test used for and how does it work? correct answers The White-test is used to
identify heteroskedasticity.
It is very similar to the BP-test with the exception that is regresses the squared residuals of the
original regression on the fitted values and square of fitted values of the original regression.
An, F-test is then performed to test if all coefficients are 0, which would indicate
homoskedasticity.
Why do economists still prefer to use OLS regression standard errors rather than robust standard
errors? correct answers Because the t-stats follow an exact t-distribution under CLM
assumptions. Heteroskedastic errors are only valid asymptotically (MLR1-6).
What is are two possibilities to deal with heteroskedasticity? correct answers 1. You can use
robust standard errors after estimation by OLS.
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