Panel data

Question 1

what is panel data

Answer 1

a panel data set contains repeated observations over time for individuals, firms, countries etc

Question 2

what is heterogeneity

Answer 2

the quality or state of being diverse in character or content

Question 3

what is the main advantage of panel data

Answer 3

we are able to allow for certain forms of unobserved individual heterogeneity that is constant over time which cannot be done with cross-sectional or time-series

Question 4

what is the panel data equation

Answer 4

yit = xit’β + vit,
=xit’β + αi + uit,
α are unobserved constant individual effects,
uit idiosyncratic shock

Question 5

how does Pooled OLS and Random Effects GLS deal with panel data

Answer 5

Pooled OLS and Random Effects GLS are biased and inconsistent if the unobserved fixed individual components αi are correlated with the explanatory variables xit

Question 6

why are Fixed-Effects OLS and First-Differenced OLS better with panel data

Answer 6

they are also consistent when there is correlation between the αi and the xit.
They solve the endogeneity without need for instrumental variables

Question 7

what does the pooled OLS do

Answer 7

simply treats the panel as a very large cross-section with nT observations

Question 8

what are the four estimators for panel data

Answer 8

pooled OLS,
random effects GLS,
Fixed effects OLS,
First differenced OLS

Question 9

what is the main condition for pooled OLS

Answer 9

E(vi|Xi)=0,
this means E(α|Xi)=0 and E(uit|xit)=0,
for pooled to be consistent there cannot be correlation between the unobserved fixed component αi and xit

Question 10

for pooled OLS with vit=αi+uit what is the variance

Answer 10

E(vitvis)≠0 for s≠t,
if E(uituis)=0 for s≠t then,
E(vitvis)=E(αi^2)=σσ^2 (second σ is subscript),
standard errors that don’t take the serial correlation of vit into account will be wrong (try derive from E(vitvis) in notes)

Question 11

do you need cluster robust standard errors for pooled OLS

Answer 11

yes, standard errors don’t take the serial correlation of vit into account will be wrong,
need cluster rob se unless σσ^2=0 (2nd σ subscript)

Question 12

what is the main assumption of the random effects GLS

Answer 12

E(vi|Xi)=0,
E(αi|Xi)=0 and xit strictly exogenous,
E(uit|xis)=0

Question 13

how is the random effects GLS better than pooled OLS

Answer 13

improves efficiency of pooled ols by taking clusters into account

Question 14

what is process of random effects gls

Answer 14

takes stylised model, assumes complete homoskedasticity, get a variance covariance matrix and plug into GLS estimator (like WLS in that it divides)

Question 15

what are the assumptions for the consistency and efficiency of random effects GLS (equations)

Answer 15

E(vi|Xi)=0
E(αi|Xi)=0
E(ui|Xi)=0
E(vivi’|Xi)=Ω

Question 16

what is the case in a random effects GLS when var=Ω

Answer 16

when var=Ω the estimator is efficient

Question 17

what is the case in random effects GLS when var≠Ω

Answer 17

if not, as long as strict exogeneity the estimator is still consistent and normal but no longer efficient

Question 18

what are the assumptions in words for the efficiency of random effects GLS

Answer 18

strict exogeneity,
no correlation between α and x (E(αi|Xi)=0),
specific variance covariance structure = Ω

Question 19

what is the main thing that the fixed effects OLS allows for

Answer 19

correlation between αi and the regressors,
E(αi|Xi)≠0,
it is a positive function of x

Question 20

how does fixed effects solve the endogeneity problem of alpha

Answer 20

by estimating the model including n individual intercepts, or a constant and n-1 dummies

Question 21

what is still assumed for the fixed effects OLS even though it allows for correlation between α and x

Answer 21

FE OLS estimator is consistent, allowing for general, unspecified correlations between α and x, under the assumption of strict exogeneity of the regressors,
E(uit|xis)=0

Question 22

does the full model with n intercepts need to estimated for fixed effects OLS

Answer 22

no,

the estimator just takes into account distances of variables from their means

Question 23

describe fixed effects ols in a nice sentence

Answer 23

we simply regress the dependent variable in deviations from the individual specific means on the regressors in deviations of their respective individual specific means

Question 24

what is one disadvantage of fixed effects ols compared to first differenced OLS

Answer 24

fixed effects OLS needs strict exogeneity so requires no correlation between xit and any of the idiosyncratic shocks uis,
so, this excludes feedback ie inputs xit do not respond to shocks in the past,
E(xituit)=0

Question 25

what is an assumption of fixed effects OLS in order for it to be efficient

Answer 25

If strong exogeneity holds, E(ui|Xi)=0 and the ui are further conditionally homoskedastic and not serially correlated,
E(uiui’|Xi)=σu^2IT,
fixed effects is the efficient estimator when allowing for general correlations between α and x

Question 26

how does first differenced OLS solve the α issue

Answer 26

taking first differences over time for an individual eliminates αi

Question 27

what are the consequences of first difference OLS to do with exogeneity

Answer 27

is a weaker assumption than strong exogeneity,
cannot have ut-1 affecting xt but can have ut-2 affecting xt,
first differenced so loss of n-1 degrees of freedom

Question 28

do you have to do clustering or robust standard errors for first differenced

Answer 28

yes have to do clustering and robust standard errors,
robust allows for general serial correlation patterns and general forms of heteroskedasticity of the variances and covariances

Question 29

how are common time effects taken care of in the panel data estimators

Answer 29

common time effects can be taken care of by time specific coefficients, inclusion of time dummies:
yit=xit’β+λt+αi+ui

Question 30

what do clustered standard errors do

Answer 30

account for heteroskedasticity across clusters of observations (states, schools or individuals), used when each unit observed across time, allows for correlations between observations

Question 31

which estimators need cluster robust standard errors

Answer 31

pooled ols and first differenced ols always,

RE gls and fe ols do if you want to allow for heteroskedasticity as they both assume homo