TERM 2 LECTURE NOTES PANEL DATA

Question 1

in a linear panel model what does xit show?

Answer 1

i is the particular observation
t is the time period

Question 2

What is panel data?

Answer 2

When the same individual is observed at different points in time.

Question 3

What is balanced panels?

Answer 3

The same number of time periods for each observations.

Question 4

What does a linear panel equation normally look like and what are the different aspects?

What does at capture?

Answer 4

-yit = at + Bxit + ai + epsilont

at varies with time
ai varies with individual (individual heteregoneity

something that varies along all people in time

Something that varies per person

Question 5

What is a pooled OLS model?

Answer 5

No individual heterogeneity

Question 6

What are the different types of panel data estimation models?

Answer 6

• pooled OLS
• Different slopes + different intercepts
  -Fixed effects / within groups estimator
  -GLE / random effects
  -1st difference estimator

Question 7

What are the assumptions in panel models?

Question 8

What is the Different slopes + different intercepts model?

Answer 8

-Fully heterogenous and allow everything to model through each person

Question 9

What is the fixed effects model?

Answer 9

• yit = Bxit + ai +epsilonit
  same slope coefficient but let ai vary = intercept

-you are subtracting the x specific mean and y specific mean

Question 10

What is the random effects model?

Answer 10

Must be done under specific assumptions that:
mean of ai is 0
variance of ai is constant
and that ai is uncorellated with error term

Do a transformation using lamda

RE is efficient as you are not estimating like fixed effects.

if ai is correlated with error term random effects yields inconsistent error terms.

Question 11

Why is it better to use linear panel models?

Answer 11

As it does not yield biased coefficient estimates.

Question 12

What is the OLS estimate for pooled panel mean and variance

Question 13

What is the OLS estimate for changing slope mean and variance

What is the evaluation of this?

Answer 13

No a good model as you need high level of t and small number of observations

Question 14

How do you conduct the fixed effects / within groups

Answer 14

Regress yit = ai + vit

regress xit = ai + wit
save residuals on both of these

vhatit = delta1 . whatit + uit

Question 15

What is better the random effects estimator or fixed effects?

How can you estimate this?

Answer 15

if individual hetergeneity is not correlated with error term random effects is better

Hausman test

Question 16

What is the hausman test?

Question 17

How do you estimate a dynamic model in panel?

Question 18

What is the relationship between the fixed effect model and the 1st difference

Answer 18

If Fixed Effect model has time = 2 then it is the same at the first difference model.

Question 19

How do you do the 1st difference panel model

Answer 19

Do the model for
yit = bit + ai + eit
yit-1 = bit-1 + ai + eit-1

Then subtract from each other
change yit = change bit + change eit

Do OLS estimate of this which is
sum of T . sum of i change y . change x / sum of t and j . change X^2

Question 20

Which model is better between fixed effect and first difference?

Answer 20

• Depends on which one has a more well behaved error term

Question 21

What is the Hausman test for panel data?

How do you create the test statistic?

Answer 21

H0: Cov(ai, xit) = 0 R.E is consistent and efficient

H1: Cov(ai, xit) is not equaled to 0 is inconsistent

In both cases fixed effect is consistent but inefficient.

H = (bFe- bRe)^2 / V(bFe) - V(bRe)
under H0 this should approach 0
under H1 this should approach infinity

distributed as chi squared 1

v(bFe) > bRe as FE is inefficient

Question 22

Why can’t you use fixed effects for dynamic panel models?

Answer 22

As the lagged dependent variable is correlated to error term

causes OLS to be inconsistent

Question 23

What is the correct way to estimate the dynamic panel models?

Answer 23

-Change it into change in yit

-Then with this equation estimate it using IV on lags of y

As the variance will not be correlated during to the limited memory of the model