DID双重差分回归课件
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cha重差分回归
3
Y
Yt1 Ya Yb Yt2
True effect = Yb-Ya Estimated effect =Yt2-Yt1
t1
ti
t2
time
DID双重差分回归
4
• Intervention occurs at time period t1 • True effect of law
• Tit =1 if obs i belongs in the state that will eventually be treated • Ait =1 in the periods when treatment occurs • TitAit -- interaction term, treatment states after the intervention
DID双重差分回归
9
Y Yc1
Yc2 Yt1
Yt2
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
control Treatment Effect
treatment
t1
t2
time
DID双重差分回归
10
• In contrast, what is key is that the time trends in the absence of the intervention are the same in both groups
• What assumptions must be true in order for the model to provide and unbiased estimate of β3?
• Do the authors provide any evidence supporting these assumptions?
DID双重差分回归
20
此课件下载可自行编辑修改，供参考！ 感谢您的支持，我们努力做得更好！
DID双重差分回归
• Year effects
• Capture differences over time that are common to all groups
DID双重差分回归
19
Questions to ask?
• What parameter is identified by the quasi-experiment? Is this an economically meaningful parameter?
2
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
• Many periods • Intervention will occur in a group of states but at a variety of times
DID双重差分回归
16
• ui is a state effect • vt is a complete set of year (time) effects • Analysis of covariance model
DID双重差分回归
6
Y
Yc1 Yt1
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
Yc2
Yt2
control
treatment
t1
t2
time
DID双重差分回归
7
Difference in Difference
Before Change
Group 1 Yt1 (Treat)
Group 2 β0 (Control)
Difference
β0+ β1+ β2+ β3 ΔYt = β2+ β3
β0+ β2
ΔYc = β2
ΔΔY = β3
DID双重差分回归
15
More general model
• Data varies by
• state (i) • time (t) • Outcome is Yit
• 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)
• Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
DID双重差分回归
14
Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
Before After Change Change
Difference
Group 1 β0+ β1 (Treat)
• Yit = β0 + β3 TitAit + ui + λt + εit
DID双重差分回归
17
What is nice about the model
• Suppose interventions are not random but systematic
• Occur in states with higher or lower average Y • Occur in time periods with different Y’s
Difference in Difference Models
DID双重差分回归
1
What is DID
• How can we estimate the effects of higher education reform in China?
• Yang and Chen (2009)
DID双重差分回归
• 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
Group 2 Yc1 (Control)
Difference
After Change Yt2
Yc2
Difference
ΔYt = Yt2-Yt1 ΔYc =Yc2-Yc1 ΔΔY ΔYt – ΔYc
DID双重差分回归
8
Key Assumption
• Control group identifies the time path of outcomes that would have happened in the absence of the treatment
• 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
• This is captured by the inclusion of the state/time effects – allows covariance between
• ui and TitAit • λt and TitAit
DID双重差分回归
18
• Group effects
• Capture differences across groups that are constant over time
• state (i) • time (t) • Outcome is Yit
• Only two periods • Intervention will occur in a group of observations (e.g. states, firms,
etc.)
DID双重差分回归
13
• Three key variables
DID双重差分回归
11
Y
Yc1 Yt1
Yc2
Yt2
Estimated treatment
True treatment effect
control
treatment
True Treatment Effect
t1
t2
time
DID双重差分回归
12
Basic Econometric Model
• Data varies by
• Ya – Yb
• Only have data at t1 and t2
• If using time series, estimate Yt1 – Yt2
• Solution?
DID双重差分回归
5
Difference in difference models
• Basic two-way fixed effects model
3
Y
Yt1 Ya Yb Yt2
True effect = Yb-Ya Estimated effect =Yt2-Yt1
t1
ti
t2
time
DID双重差分回归
4
• Intervention occurs at time period t1 • True effect of law
• Tit =1 if obs i belongs in the state that will eventually be treated • Ait =1 in the periods when treatment occurs • TitAit -- interaction term, treatment states after the intervention
DID双重差分回归
9
Y Yc1
Yc2 Yt1
Yt2
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
control Treatment Effect
treatment
t1
t2
time
DID双重差分回归
10
• In contrast, what is key is that the time trends in the absence of the intervention are the same in both groups
• What assumptions must be true in order for the model to provide and unbiased estimate of β3?
• Do the authors provide any evidence supporting these assumptions?
DID双重差分回归
20
此课件下载可自行编辑修改，供参考！ 感谢您的支持，我们努力做得更好！
DID双重差分回归
• Year effects
• Capture differences over time that are common to all groups
DID双重差分回归
19
Questions to ask?
• What parameter is identified by the quasi-experiment? Is this an economically meaningful parameter?
2
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
• Many periods • Intervention will occur in a group of states but at a variety of times
DID双重差分回归
16
• ui is a state effect • vt is a complete set of year (time) effects • Analysis of covariance model
DID双重差分回归
6
Y
Yc1 Yt1
Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
Yc2
Yt2
control
treatment
t1
t2
time
DID双重差分回归
7
Difference in Difference
Before Change
Group 1 Yt1 (Treat)
Group 2 β0 (Control)
Difference
β0+ β1+ β2+ β3 ΔYt = β2+ β3
β0+ β2
ΔYc = β2
ΔΔY = β3
DID双重差分回归
15
More general model
• Data varies by
• state (i) • time (t) • Outcome is Yit
• 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)
• Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
DID双重差分回归
14
Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
Before After Change Change
Difference
Group 1 β0+ β1 (Treat)
• Yit = β0 + β3 TitAit + ui + λt + εit
DID双重差分回归
17
What is nice about the model
• Suppose interventions are not random but systematic
• Occur in states with higher or lower average Y • Occur in time periods with different Y’s
Difference in Difference Models
DID双重差分回归
1
What is DID
• How can we estimate the effects of higher education reform in China?
• Yang and Chen (2009)
DID双重差分回归
• 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
Group 2 Yc1 (Control)
Difference
After Change Yt2
Yc2
Difference
ΔYt = Yt2-Yt1 ΔYc =Yc2-Yc1 ΔΔY ΔYt – ΔYc
DID双重差分回归
8
Key Assumption
• Control group identifies the time path of outcomes that would have happened in the absence of the treatment
• 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
• This is captured by the inclusion of the state/time effects – allows covariance between
• ui and TitAit • λt and TitAit
DID双重差分回归
18
• Group effects
• Capture differences across groups that are constant over time
• state (i) • time (t) • Outcome is Yit
• Only two periods • Intervention will occur in a group of observations (e.g. states, firms,
etc.)
DID双重差分回归
13
• Three key variables
DID双重差分回归
11
Y
Yc1 Yt1
Yc2
Yt2
Estimated treatment
True treatment effect
control
treatment
True Treatment Effect
t1
t2
time
DID双重差分回归
12
Basic Econometric Model
• Data varies by
• Ya – Yb
• Only have data at t1 and t2
• If using time series, estimate Yt1 – Yt2
• Solution?
DID双重差分回归
5
Difference in difference models
• Basic two-way fixed effects model