Economics 20 - Prof,Anderson 1
Fixed Effects Estimation
When there is an observed fixed effect,an
alternative to first differences is fixed
effects estimation
Consider the average over time of yit =
b1xit1 +…+ bkxitk + ai + uit
The average of ai will be ai,so if you
subtract the mean,ai will be differenced out
just as when doing first differences
Economics 20 - Prof,Anderson 2
Fixed Effects Estimation (cont)
If we were to do this estimation by hand,
we’d need to be careful because we’d think
that df = NT – k,but really is N(T – 1) – k
because we used up dfs calculating means
Luckily,Stata (and most other packages)
will do fixed effects estimation for you
This method is also identical to including a
separate intercept or every individual
Economics 20 - Prof,Anderson 3
First Differences vs Fixed Effects
First Differences and Fixed Effects will be
exactly the same when T = 2
For T > 2,the two methods are different
Probably see fixed effects estimation more
often than differences – probably more
because it’s easier than that it’s better
Fixed effects easily implemented for
unbalanced panels,not just balanced panels
Economics 20 - Prof,Anderson 4
Random Effects
Start with the same basic model with a
composite error,yit = b0 + b1xit1 +,,, bkxitk
+ ai + uit
Previously we’ve assumed that ai was
correlated with the x’s,but what if it’s not?
OLS would be consistent in that case,but
composite error will be serially correlated
Economics 20 - Prof,Anderson 5
Random Effects (continued)
Need to transform the model and do GLS
to solve the problem and make correct
inferences
Idea is to do quasi-differencing with the
Economics 20 - Prof,Anderson 6
Random Effects (continued)
Need to transform the model and do GLS to solve
the problem and make correct inferences
End up with a sort of weighted average of OLS
and Fixed Effects – use quasi-demeaned data
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Economics 20 - Prof,Anderson 7
Random Effects (continued)
If ? = 1,then this is just the fixed effects
estimator
If ? = 0,then this is just the OLS estimator
So,the bigger the variance of the
unobserved effect,the closer it is to FE
The smaller the variance of the unobserved
effect,the closer it is to OLS
Stata will do Random Effects for us
Economics 20 - Prof,Anderson 8
Fixed Effects or Random?
More usual to think need fixed effects,
since think the problem is that something
unobserved is correlated with the x’s
If truly need random effects,the only
problem is the standard errors
Can just adjust the standard errors for
correlation within group
Economics 20 - Prof,Anderson 9
Other Uses of Panel Methods
It’s possible to think of models where there
is an unobserved fixed effect,even if we do
not have true panel data
A common example is where we think
there is an unobserved family effect
Can difference siblings
Can estimate family fixed effect model
Economics 20 - Prof,Anderson 10
Additional Issues
Many of the things we already know about
both cross section and time series data can
be applied with panel data
Can test and correct for serial correlation in
the errors
Can test and correct for heteroskedasticity
Can estimate standard errors robust to both