Panel Data Analysis, Josef Brüderl - Sowi
Panel Data Analysis, Josef Brüderl - Sowi
Panel Data Analysis, Josef Brüderl - Sowi
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<strong>Panel</strong> <strong>Data</strong> <strong>Analysis</strong>, <strong>Josef</strong> Brüderl 8<br />
delta(wage)<br />
-200 -100 0 100 200 300 400 500 600<br />
0 .2 .4 .6 .8 1<br />
delta(marr)<br />
Within-person change<br />
The intuition behind the FD-estimator is that it no longer uses the between-person<br />
comparison. It uses only within-person changes: If X changes, how much does Y<br />
change (within one person)? Therefore, in our example, unobserved ability<br />
differences between persons no longer bias the estimator.<br />
Fixed-Effects Estimation<br />
An alternative to differencing is the within transformation. We start from the<br />
error-components model:<br />
y it 1 x it i it .<br />
Average this equation over time for each i (between transformation):<br />
y i<br />
1 x i i i .<br />
Subtract the second equation from the first for each t (within transformation):<br />
y it − y i<br />
1 x it − x i it − i .<br />
This model can be estimated by pooled-OLS (fixed-effects (FE) estimator). The<br />
important thing is that again the i have disappeared. We no longer need the<br />
assumption that i is uncorrelated with x it . Time-constant unobserved heterogeneity<br />
is no longer a problem.<br />
What we do here is to "time-demean" the data. Again, only the within variation is<br />
left, because we subtract the between variation. But here all information is used, the<br />
within transformation is more efficient than differencing. Therefore, this estimator is<br />
also called the within estimator.<br />
Example<br />
We time-demean our data and run OLS:<br />
egen<br />
mwage mean(wage), by(id)
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