wooldridge theory
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7/27/2019 Wooldridge theory
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Economics 20 - Prof. Anderson 1
Panel Data Methods
yit= b0 + b1xit1 + . . . bkxitk+ uit
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Economics 20 - Prof. Anderson 2
A True Panel vs.
A Pooled Cross Section
Often loosely use the term panel data to
refer to any data set that has both a cross-
sectional dimension and a time-seriesdimension
More precisely its only data following the
same cross-section units over timeOtherwise its a pooled cross-section
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Economics 20 - Prof. Anderson 3
Pooled Cross Sections
We may want to pool cross sections just to
get bigger sample sizes
We may want to pool cross sections toinvestigate the effect of time
We may want to pool cross sections to
investigate whether relationships havechanged over time
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Economics 20 - Prof. Anderson 4
Difference-in-Differences
Say random assignment to treatment andcontrol groups, like in a medical experiment
One can then simply compare the change inoutcomes across the treatment and controlgroups to estimate the treatment effect
For time 1,2, groups A, B (y2,B
y2,A
) -(y1,By1,A), or equivalently (y2,By1,B) -(y2,Ay1,A), is the difference-in-differences
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Economics 20 - Prof. Anderson 5
Difference-in-Differences (cont)
A regression framework using time and
treatment dummy variables can calculate
this difference-in-difference as wellConsider the model:yit= b0 + b1treatmentit
+ b2afterit+ b3treatmentit*afterit+ uit
The estimated b3 will be the difference-in-differences in the group means
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Economics 20 - Prof. Anderson 6
Difference-in-Differences (cont)
When dont truly have random assignment,the regression form becomes very useful
Additionalxs can be added to theregression to control for differences acrossthe treatment and control groups
Sometimes referred to as a naturalexperiment especially when a policychange is being analyzed
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Economics 20 - Prof. Anderson 7
Two-Period Panel Data
Its possible to use a panel just like pooled
cross-sections, but can do more than that
Panel data can be used to address somekinds of omitted variable bias
If can think of the omitted variables as
being fixed over time, then can model ashaving a composite error
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Economics 20 - Prof. Anderson 8
Unobserved Fixed Effects
Suppose the population model isyit= b0 +d0d2t+ b1xit1++ bkxitk+ ai + uit
Here we have added a time-constantcomponent to the error, uit= ai + uit
Ifaiis correlated with thexs, OLS will bebiased, since we a
i
is part of the error term
With panel data, we can difference-out theunobserved fixed effect
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First-differences
We can subtract one period from the other,
to obtain Dyi = d0 + b1Dxi1++ bkDxik+
DuiThis model has no correlation between the
xs and the error term, so no bias
Need to be careful about organization ofthe data to be sure compute correct change
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Differencing w/ Multiple Periods
Can extend this method to more periods
Simply difference adjacent periods
So if 3 periods, then subtract period 1 from
period 2, period 2 from period 3 and have 2
observations per individual
Simply estimate by OLS, assuming the Duitare uncorrelated over time
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