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Difference in Difference Models
What is DID
How can we estimate the effects of higher education reform in China?
Yang and Chen ()
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Problem set up
Cross-sectional and time series data
One group is ‘treated’ with intervention
Have pre-post data for group receiving intervention
Can examine time-series changes but, unsure how much of the change is due to secular changes
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time
Y
t1
t2
Ya
Yb
Yt1
Yt2
True effect = Yb-Ya
Estimated effect =Yt2-Yt1
ti
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Intervention occurs at time period t1
True effect of law
Ya – Yb
Only have data at t1 and t2
If using time series, estimate Yt1 – Yt2
Solution?
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Difference in difference models
Basic two-way fixed effects model
Cross section and time fixed effects
Use time series of untreated group to establish what would have occurred in the absence of the intervention
Key concept: can control for the fact that the intervention is more likely in some types of states
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time
Y
t1
t2
Yt1
Yt2
treatment
control
Yc1
Yc2
Treatment effect=
(Yt2-Yt1) – (Yc2-Yc1)
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Difference in Difference
Before
Change
After
Change
Difference
Group 1
(Treat)
Yt1
Yt2
ΔYt
= Yt2-Yt1
Group 2
(Control)
Yc1
Yc2
ΔYc
=Yc2-Yc1
Difference
ΔΔY
ΔYt – ΔYc
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Key Assumption
Control group identifies the time path of outcomes that would have happened in the absence of the treatment
In this example, Y falls by Yc2-Yc1 even without the intervention
Note that underlying ‘levels’ of outcomes are not important (return to this in the regression equation)
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time
Y
t1
t2
Yt1
Yt2
treatment
control
Yc1
Yc2
Treatment effect=
(Yt2-Yt1) – (Yc2-Yc1)
Treatment
Effect