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Flashcards in Second half Deck (16)
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what is the null for the Breusch-Pagan test for heteroskedasticity

Null of homoskedasticity:
H0: E(ui^2|xi)=σ^2


what is the alternative Breusch-Pagan test

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


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

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)


which has fatter tails out of logit and probit

logit has fatter tails


what is the pseudo R^2 for logit and probit

R^2 = 1 - logL(βhat)/logL0(β0hat),
logL0(β0hat) is value of log likelihood w/ just a constant,


what is the test for multiple hypothesis in logit

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


how do you work out the conditional log-likelihood function

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


consequence of heteroskedasticity for OLS

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)


what do you need to remember for Breusch Pagan stat

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


why is ols good under homoskedasticity

because it gives equal weight to observations


what does the weighted least squares do

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


difference between feasible gls and wls

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


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

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


alternative for f test / Breusch-Pagan test

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


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

AR(1) don't substitute both for the equation,
MA(1) do substitute both equations


criticism of estimating marginal effects at the means

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