Flashcards in Second half Deck (16)

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1

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

###
Null of homoskedasticity:

H0: E(ui^2|xi)=σ^2

2

## what is the alternative Breusch-Pagan test

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

3

## 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)

4

## which has fatter tails out of logit and probit

### logit has fatter tails

5

## 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,

6

## 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

7

## how do you work out the conditional log-likelihood function

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

8

## 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)

9

## what do you need to remember for Breusch Pagan stat

###
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

10

## why is ols good under homoskedasticity

### because it gives equal weight to observations

11

## 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

12

## 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

13

## 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

14

## alternative for f test / Breusch-Pagan test

###
H0: β=0 for all β,

H1: βj≠0, for at least one value of j

15

## 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

16