TERM 2 LECTURE NOTES PANEL DATA Flashcards
in a linear panel model what does xit show?
i is the particular observation
t is the time period
What is panel data?
When the same individual is observed at different points in time.
What is balanced panels?
The same number of time periods for each observations.
What does a linear panel equation normally look like and what are the different aspects?
What does at capture?
-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
What is a pooled OLS model?
No individual heterogeneity
What are the different types of panel data estimation models?
- pooled OLS
- Different slopes + different intercepts
-Fixed effects / within groups estimator
-GLE / random effects
-1st difference estimator
What are the assumptions in panel models?
What is the Different slopes + different intercepts model?
-Fully heterogenous and allow everything to model through each person
What is the fixed effects model?
- yit = Bxit + ai +epsilonit
same slope coefficient but let ai vary = intercept
-you are subtracting the x specific mean and y specific mean
What is the random effects model?
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.
Why is it better to use linear panel models?
As it does not yield biased coefficient estimates.
What is the OLS estimate for pooled panel mean and variance
What is the OLS estimate for changing slope mean and variance
What is the evaluation of this?
No a good model as you need high level of t and small number of observations
How do you conduct the fixed effects / within groups
Regress yit = ai + vit
regress xit = ai + wit
save residuals on both of these
vhatit = delta1 . whatit + uit
What is better the random effects estimator or fixed effects?
How can you estimate this?
if individual hetergeneity is not correlated with error term random effects is better
Hausman test
What is the hausman test?
How do you estimate a dynamic model in panel?
What is the relationship between the fixed effect model and the 1st difference
If Fixed Effect model has time = 2 then it is the same at the first difference model.
How do you do the 1st difference panel model
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
Which model is better between fixed effect and first difference?
- Depends on which one has a more well behaved error term
What is the Hausman test for panel data?
How do you create the test statistic?
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
Why can’t you use fixed effects for dynamic panel models?
As the lagged dependent variable is correlated to error term
causes OLS to be inconsistent
What is the correct way to estimate the dynamic panel models?
-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
