双重差分模型幻灯片
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7
Y
Yc1 Yt1 Yc2 Yt2
t1
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
control treatment t2
time
8
Key Assumption
• Control group identifies the time path of outcomes that would have happened in the absence of the treatment
Difference in difference models
• Maybe the most popular identification strategy in applied work today
• Attempts to mimic random assignment with treatment and “comparison” sample
t1பைடு நூலகம்
ti
t2
time
3
• 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
intervention • Can examine time-series changes but,
unsure how much of the change is due to secular changes
2
Y
Yt1 Ya Yb Yt2
True effect = Yt2-Yt1 Estimated effect = Yb-Ya
• Only two periods • Intervention will occur in a group of
observations (e.g. states, firms, etc.)
13
• Three key variables
– Tit =1 if obs i belongs in the state that will eventually be treated
• 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)
• Application of two-way fixed effects model
1
Problem set up
• Cross-sectional and time series data • One group is ‘treated’ with intervention • Have pre-post data for group receiving
• Solution?
4
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
– Ait =1 in the periods when treatment occurs – TitAit -- interaction term, treatment states after
the intervention
6
Difference in Difference
Before Change
Group 1 Yt1 (Treat)
Group 2 Yc1 (Control)
Difference
After Change Yt2
Yc2
Difference
ΔYt = Yt2-Yt1 ΔYc =Yc2-Yc1 ΔΔY ΔYt – ΔYc
• Key concept: can control for the fact that the intervention is more likely in some types of states
5
Three different presentations
• Tabular • Graphical • Regression equation
• If the intervention occurs in an area with a different trend, will under/over state the treatment effect
• In this example, suppose intervention occurs in area with faster falling Y
9
Y Yc1
Yc2 Yt1
Yt2 t1
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
control Treatment Effect
treatment t2
time
10
• In contrast, what is key is that the time trends in the absence of the intervention are the same in both groups
11
Y
Yc1 Yt1
Yc2
Yt2
Estimated treatment
True treatment effect
control
treatment
True Treatment Effect
t1
t2
time
12
Basic Econometric Model
• Data varies by
– state (i) – time (t) – Outcome is Yit
Y
Yc1 Yt1 Yc2 Yt2
t1
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
control treatment t2
time
8
Key Assumption
• Control group identifies the time path of outcomes that would have happened in the absence of the treatment
Difference in difference models
• Maybe the most popular identification strategy in applied work today
• Attempts to mimic random assignment with treatment and “comparison” sample
t1பைடு நூலகம்
ti
t2
time
3
• 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
intervention • Can examine time-series changes but,
unsure how much of the change is due to secular changes
2
Y
Yt1 Ya Yb Yt2
True effect = Yt2-Yt1 Estimated effect = Yb-Ya
• Only two periods • Intervention will occur in a group of
observations (e.g. states, firms, etc.)
13
• Three key variables
– Tit =1 if obs i belongs in the state that will eventually be treated
• 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)
• Application of two-way fixed effects model
1
Problem set up
• Cross-sectional and time series data • One group is ‘treated’ with intervention • Have pre-post data for group receiving
• Solution?
4
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
– Ait =1 in the periods when treatment occurs – TitAit -- interaction term, treatment states after
the intervention
6
Difference in Difference
Before Change
Group 1 Yt1 (Treat)
Group 2 Yc1 (Control)
Difference
After Change Yt2
Yc2
Difference
ΔYt = Yt2-Yt1 ΔYc =Yc2-Yc1 ΔΔY ΔYt – ΔYc
• Key concept: can control for the fact that the intervention is more likely in some types of states
5
Three different presentations
• Tabular • Graphical • Regression equation
• If the intervention occurs in an area with a different trend, will under/over state the treatment effect
• In this example, suppose intervention occurs in area with faster falling Y
9
Y Yc1
Yc2 Yt1
Yt2 t1
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
control Treatment Effect
treatment t2
time
10
• In contrast, what is key is that the time trends in the absence of the intervention are the same in both groups
11
Y
Yc1 Yt1
Yc2
Yt2
Estimated treatment
True treatment effect
control
treatment
True Treatment Effect
t1
t2
time
12
Basic Econometric Model
• Data varies by
– state (i) – time (t) – Outcome is Yit