Pictures

Question 1

What is the estimate for αhat in this equation: yt=αyt-1+ut

Answer 1

Question 2

what is the weighted least squares model

Answer 2

E(ui^2|xi)=σ^2h(xi)

Question 3

Equation for F test based on R^2

Answer 3

Question 4

Equation for Logit

Answer 4

Question 5

Equation for probit model

Answer 5

φ(.) is the standard normal cumulative distribution function

Question 6

what is the densitiy of the logit

Answer 6

Question 7

what is the marginal effects of the Logit

Answer 7

Question 8

what is the marginal effects of the Probit

Answer 8

Question 9

what is the probability P(X=x) for a Bernoulli distribution

Answer 9

Question 10

what is the little tricks that help you derive the OLS estimator

Answer 10

Question 11

what are the conditions for Pooled OLS to be consistent and normally distributed in large samples

Answer 11

Question 12

what are the conditions for random effects GLS to be consistent and normally distributed in large samples

Answer 12

Question 13

what are the conditions for Fixed Effects OLS to be consistent and normally distributed in large samples

Answer 13

Question 14

what are the conditions for FIirst Differenced OLS to be consistent and normally distributed in large samples

Answer 14

Question 15

what is the random effects GLS conditional variances with strong exogeneity assumption E(ui|Xi)=0

Answer 15

Question 16

What is the estimator for the variance of βRE given conditional homoskedasticity and no serial correlation of uit, E(uituis|Xi)=0

Answer 16

Question 17

what is the between estimator

Answer 17

Question 18

What is the fixed effects OLS equation that takes into account endogeneity

Answer 18

Question 19

What is the further assumption on Fixed Effects OLS to make it efficient

Answer 19

That the uit are further conditionally homoskedastic and not serially correlated. uiui’ because its a matrix

Question 21

what is the setting for the first differenced OLS

Answer 21

Question 22

What is the process of first differenced OLS

Answer 22

Question 23

Given this equation what is the condition for the OLS estimator for β to be consistent and normally distributed in large samples

Answer 23

Question 24

Given this equation, assuming there is feedback from ui,t-1 to xit, show that the FD OLS model is biased and inconsistent

Answer 24

Question 25

How is the endogeneity problem of the fixed effects OLS solved

Answer 25

First differenced model is a good starting point. Then use xi,t-j as an instrument as it satisfies the exogeneity condition as it is not correlated with (uit-ui,t-1) and is clearly correlated with the endogenous variable (xit-xi,t-1) as x responds to past realised shocks

Question 26

what is the density of the standard logistic distribution

Answer 26

Question 27

what is the density of the standard normal distribution function (probit)

Answer 27

Question 28

what are the marginal effects of the logit model

Answer 28

Question 29

what is the marginal effect of the probit model

Answer 29

Question 30

what is the maximum likelihood estimation for the probit model

Answer 30

Maximum likelihood for the probit: the conditional distribution yi | xi is Bernoulli

Question 31

what is βhat in matrix form

Answer 31

Question 32

how do you work out the conditional log-likelihood function (with picture)

Answer 32

write down the conditional density, then take logs

Question 33

what is the derivative of the logistic function

Answer 33

Question 34

what is the derivatives of logL wrt beta for logit

Answer 34

derivation ex lec 6

Question 35

what is the derivative of the logL wrt beta for probit

Answer 35

Question 36

what is the conditional log-likelihood function

Answer 36

Question 37

what is the density of a random variable

Answer 37

the derivative of its sumulative distribution function

Question 38

what is the derivative of LogL wrt beta for the probit model

Answer 38

Question 39

what is the AR(1) correlogram for equation yt=ρyt-1+et

Answer 39

Question 40

is AR(1) weakly dependent

Answer 40

AR(1) is weakly stationary and automatically satisfies weak dependence because Var=

Question 41

equation for an f test

Answer 41

Question 42

what is the White robust variance estimator

Answer 42

Question 43

equation for the average marginal effect of probit

Answer 43

Question 44

what is the marginal effects of probit at means

Answer 44

Question 45

average marginal effect of probit when binary variable

Answer 45

Question 46

what is the hausman test

Answer 46

Question 47

what is the covariance in an AR(1) process

Answer 47

Question 48

how do you get to the covariance for an AR(1) process

Answer 48

substitute for ytyt-1 then ytyt-2, but don't substitute the whole equation in

Question 49

what is the variance covariance matrix of an AR(1) process

Answer 49

E(εtεt-j)=

Question 50

what is the variance covariance matrix for heteroskedasticity

Answer 50