10 Panel data

Question 1

advantages of panel data

Answer 1

• better control over omitted variables
• more observations
• many research questions typically involve a time component

Question 2

unobserved heterogeneity embodied in Zi

Answer 2

…

Question 3

panel data with more than 2 time periods

Answer 3

Yit =β0 + β1Xit + β2Zi + uit

Equation can be interpreted as model with n specific intercepts (one for each state)
Yit =β1Xit + αi + uit, with αi =β0 + β2Zi

αi , i = 1, …, n are called entity fixed effects
αi models impact of omitted time-invariant variables on Yit

Use dummy variables to quantify αi

Question 4

entity demeaned variable

Answer 4

̃(Yit) = Yit − avg(Yi)

Question 5

LSDV

Answer 5

Least Squares Dummy Variables

Question 6

fixed effects regression model

Answer 6

Yit = β1Xit + αi + λt + uit

statistical assumptions are:

• E(uit|Xi1,…,XiT,αi,λt)=0
• (Xi 1 , …, XiT , Yi 1 , …, YiT ) are i.i.d. over the cross-section - large outliers are unlikely
• no perfect multicollinearity
• cov(uit, uis | Xi1, .., Xit, αi, λt) = 0 for t != s

Question 7

(panel data regression)

What if error terms are correlated over time?

Answer 7

HAC-standard errors (clustered standard errors)

• robust to arbitrary correlation within clusters (entities)
• robust to heteroskedasticity
• assume no correlation across entities