Second half

Question 1

what is the null for the Breusch-Pagan test for heteroskedasticity

Answer 1

Null of homoskedasticity:

H0: E(ui^2|xi)=σ^2

Question 2

what is the alternative Breusch-Pagan test

Answer 2

E(ui^2|xi)=h(xi’δ) where h(.) is some general, unknown and unspecified function

Question 3

for GLS and WLS what is the conditional variance function given by

Answer 3

E(ui^2|xi)=σ^2(h(xi), σ^2 arbitrary, unknown constant, the (positive) function h(xi) is known (eg h(xi)=x2i^2)

Question 4

which has fatter tails out of logit and probit

Answer 4

logit has fatter tails

Question 5

what is the pseudo R^2 for logit and probit

Answer 5

R^2 = 1 - logL(βhat)/logL0(β0hat),

logL0(β0hat) is value of log likelihood w/ just a constant,

Question 6

what is the test for multiple hypothesis in logit

Answer 6

likelihood ratio test: logLu(βhat) the log-likelihood in unrestricted model and logLr(βtilda) restricted model.
LR=-2(logLr(βtilda)-logLu(βtilda))–>d χs^2

Question 7

how do you work out the conditional log-likelihood function

Answer 7

write down the conditional density (bernoulli thing), then take logs

Question 8

consequence of heteroskedasticity for OLS

Answer 8

as E(ui|xi)=0, OLS still unbiased, consistent and normally distributed in large,
OLS no longer BLUE,
robust standard errors need to be used  (homoskedastic ses wrong) (doesn't make it efficient, robust just allows for inference)

Question 9

what do you need to remember for Breusch Pagan stat

Answer 9

nR^2,
have to multiply by n and compare to χk^2 distribution where k is number of regressors testing,
R^2 gives correlation because R^2 is measure of correlation, if large then heteroskedasticity

Question 10

why is ols good under homoskedasticity

Answer 10

because it gives equal weight to observations

Question 11

what does the weighted least squares do

Answer 11

divide by square root of variance, large variance gets divided by large number and hence gets smaller weight

Question 12

difference between feasible gls and wls

Answer 12

feasible GLS is where the variance function is not known, it is approximated by specifying a function for heteroskedasticity and estimate the unknown parameters in it

Question 13

what are the main assumptions of unit root tests (DF or ADF)

Answer 13

residuals are not serially correlated,
correct model specification,
shouldn’t be structural breaks

Question 14

alternative for f test / Breusch-Pagan test

Answer 14

H0: β=0 for all β,
H1: βj≠0, for at least one value of j

Question 15

what is the difference between working out E(εtεt-s) for MA(1) and AR(1)

Answer 15

AR(1) don’t substitute both for the equation,

MA(1) do substitute both equations

Question 16

criticism of estimating marginal effects at the means

Answer 16

not useful predictively as differs when different other variables,
the individual with mean characteristics doesn’t even exist, average of exper^2 will not be the square of the average exper so can’t exist