Final exam more material Flashcards
Under which assumptions are usual SE valid? And under which assumptions are Robust SE valid?
1) SE: MLR1 - MLR5
2) Robust SE: MLR1 - MLR4
Why would we run the squared residuals on the explanatory variables?
This is done to test for heteroskedasticity using the BP-test.
-> If the coefficients are significant it means that the error variance depends on the explanatory variables (heteroskedasticity)
What is the idea of linear hypothesis test?
The explanatory variables are not jointly significant. We test for that joint hypothesis
-> Test for heteroskedasticity
State a set of assumptions under which the OLS estimator is unbiased
MLR1 (linear in parameters)
MLR3 (no perfect collinearity)
MLR4 (zero conditional mean)
We said that OLS is consistent when, among other things, weak dependence holds. A random walk
is a counterexample to that. Write down the formula for a simple random walk without covariates.
Yt = Yt-1 + et
Explain how you would test in the present situation for serial correlation (of order 1). What is the
null hypothesis, the alternative, the test statistic (in general, there is no output related to this test),
and the critical value at the 5% level (in this particular situation here; if the degrees of freedom are
in-between two values in the table, then use the bigger one)?
(1) Regress the residuals on their lagged values
Ût = p(rho)Ût-1 + et
(2)
H0: p = 0
H1: p = not 0
(3)
t-statistic
Suppose there is serial correlation. What is the effect of this on the estimates?
The estimator is not efficient
Explain, step by step, how you could transform the data to un-do the effect of serial correlation.
Subtract from each variable p(rho) times its lagged value
State the conditions under which the instruments are valid
1) Exogeneity: no direct correlation with the error term
2) Relevance: must have a causal relationship with DV
Why can’t we test exogeneity condition?
Because the error term is unobservable
