双重差分模型幻灯片 - difference in differences models
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Baidu Nhomakorabea
16
ui is a state effect vt is a complete set of year (time) effects Analysis of covariance model Yit = β0 + β3 TitAit + ui + λt + εit
17
WHAT IS NICE ABOUT THE MODEL
Difference ∆Yt = Yt2-Yt1 ∆Yc =Yc2-Yc1 ∆(∆Y)= ∆Yt – ∆Yc
7
Y Treatment effect= (Yt2-Yt1) – (Yc2-Yc1) Yc1 Yt1
Yc2
Yt2
control treatment t1 t2
time
8
KEY ASSUMPTION
Suppose interventions are not random but systematic
Occur in states with higher or lower average Y Occur in time periods with different Y’s
This is captured by the inclusion of the state/time effects – allows covariance between
Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
14
YIT = Β0 + Β1TIT + Β2AIT + Β3TITAIT + ΕIT
Before Change Group 1 (Treat) Group 2 (Control) Difference β0 + β1 β0 After Change Difference
11
Y
Estimated treatment Yc1 Yt1 Yc2
True treatment effect
control
Yt2 treatment t1 t2
True Treatment Effect
time
12
BASIC ECONOMETRIC MODEL:基准模型 基准模型
Data varies by
5
THREE DIFFERENT PRESENTATIONS
Tabular Graphical Regression equation
6
DIFFERENCE IN DIFFERENCES
Before Change Group 1 (Treat) Group 2 (Control) Difference Yt1 Yc1 After Change Yt2 Yc2
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)
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
DIFFERENCE IN DIFFERENCE MODELS
Maybe the most popular identification strategy in applied work today Attempts to mimic random assignment with comparison” treatment and “comparison sample comparison Application of two-way fixed effects model
2
Y True effect = Yb-Ya Estimated effect = Yt2-Yt1 Yt1 Ya Yb Yt2
t1
ti
t2
time
3
Intervention occurs at time period t1 True effect of law
Ya – Yb
Only have data at t1 and t2
state (i) time (t) Outcome is Yit
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 Ait =1 in the periods when treatment occurs TitAit -- interaction term, treatment states after the intervention
β0+ β1+ β2+ β3 ∆Yt = β2 + β3 β0 + β2 ∆Yc = β2 ∆(∆Y )= β3
15
MORE GENERAL MODEL：扩展的一般模型
Data varies by
state (i) time (t) Outcome is Yit
Many periods Intervention will occur in a group of states but at a variety of times
If using time series, estimate Yt1 – Yt2
Solution?
4
DIFFERENCE IN DIFFERENCE MODELS
Basic two-way fixed effects model
Cross section and time fixed effects
9
Y Yc1 Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
Yc2 Yt1
control Yt2 treatment t1 t2 Treatment Effect
time
10
In contrast, what is key is that the time trends in the absence of the intervention are the same in both groups 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
ui and TitAit λt and TitAit
18
1
PROBLEM SET UP
CrossCross-sectional and time series data: pooled crosscross-sectional data One group is ‘treated’ with intervention preHave pre-post data for group receiving intervention timeCan examine time-series changes but, unsure how much of the change is due to secular changes
16
ui is a state effect vt is a complete set of year (time) effects Analysis of covariance model Yit = β0 + β3 TitAit + ui + λt + εit
17
WHAT IS NICE ABOUT THE MODEL
Difference ∆Yt = Yt2-Yt1 ∆Yc =Yc2-Yc1 ∆(∆Y)= ∆Yt – ∆Yc
7
Y Treatment effect= (Yt2-Yt1) – (Yc2-Yc1) Yc1 Yt1
Yc2
Yt2
control treatment t1 t2
time
8
KEY ASSUMPTION
Suppose interventions are not random but systematic
Occur in states with higher or lower average Y Occur in time periods with different Y’s
This is captured by the inclusion of the state/time effects – allows covariance between
Yit = β0 + β1Tit + β2Ait + β3TitAit + εit
14
YIT = Β0 + Β1TIT + Β2AIT + Β3TITAIT + ΕIT
Before Change Group 1 (Treat) Group 2 (Control) Difference β0 + β1 β0 After Change Difference
11
Y
Estimated treatment Yc1 Yt1 Yc2
True treatment effect
control
Yt2 treatment t1 t2
True Treatment Effect
time
12
BASIC ECONOMETRIC MODEL:基准模型 基准模型
Data varies by
5
THREE DIFFERENT PRESENTATIONS
Tabular Graphical Regression equation
6
DIFFERENCE IN DIFFERENCES
Before Change Group 1 (Treat) Group 2 (Control) Difference Yt1 Yc1 After Change Yt2 Yc2
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)
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
DIFFERENCE IN DIFFERENCE MODELS
Maybe the most popular identification strategy in applied work today Attempts to mimic random assignment with comparison” treatment and “comparison sample comparison Application of two-way fixed effects model
2
Y True effect = Yb-Ya Estimated effect = Yt2-Yt1 Yt1 Ya Yb Yt2
t1
ti
t2
time
3
Intervention occurs at time period t1 True effect of law
Ya – Yb
Only have data at t1 and t2
state (i) time (t) Outcome is Yit
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 Ait =1 in the periods when treatment occurs TitAit -- interaction term, treatment states after the intervention
β0+ β1+ β2+ β3 ∆Yt = β2 + β3 β0 + β2 ∆Yc = β2 ∆(∆Y )= β3
15
MORE GENERAL MODEL：扩展的一般模型
Data varies by
state (i) time (t) Outcome is Yit
Many periods Intervention will occur in a group of states but at a variety of times
If using time series, estimate Yt1 – Yt2
Solution?
4
DIFFERENCE IN DIFFERENCE MODELS
Basic two-way fixed effects model
Cross section and time fixed effects
9
Y Yc1 Treatment effect= (Yt2-Yt1) – (Yc2-Yc1)
Yc2 Yt1
control Yt2 treatment t1 t2 Treatment Effect
time
10
In contrast, what is key is that the time trends in the absence of the intervention are the same in both groups 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
ui and TitAit λt and TitAit
18
1
PROBLEM SET UP
CrossCross-sectional and time series data: pooled crosscross-sectional data One group is ‘treated’ with intervention preHave pre-post data for group receiving intervention timeCan examine time-series changes but, unsure how much of the change is due to secular changes