DID双重差分回归教学课件

1、1Difference in Difference Models第1页，共20页。What is DIDHow can we estimate the effects of higher education reform in China?Yang and Chen (2009)2第2页，共20页。3Problem set upCross-sectional and time series dataOne group is treated with interventionHave pre-post data for group receiving interventionCan examin

2、e time-series changes but, unsure how much of the change is due to secular changes第3页，共20页。4timeYt1t2YaYbYt1Yt2True effect = Yb-YaEstimated effect =Yt2-Yt1ti第4页，共20页。5Intervention occurs at time period t1True effect of lawYa YbOnly have data at t1 and t2If using time series, estimate Yt1 Yt2Solution

3、?第5页，共20页。6Difference in difference modelsBasic two-way fixed effects modelCross section and time fixed effectsUse time series of untreated group to establish what would have occurred in the absence of the interventionKey concept: can control for the fact that the intervention is more likely in some

4、 types of states第6页，共20页。7timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatment effect=(Yt2-Yt1) (Yc2-Yc1)第7页，共20页。8Difference in DifferenceBeforeChangeAfterChangeDifferenceGroup 1(Treat)Yt1Yt2Yt = Yt2-Yt1Group 2(Control)Yc1Yc2Yc=Yc2-Yc1DifferenceYYt Yc第8页，共20页。9Key AssumptionControl group identifies the t

5、ime path of outcomes that would have happened in the absence of the treatmentIn this example, Y falls by Yc2-Yc1 even without the interventionNote that underlying levels of outcomes are not important (return to this in the regression equation)第9页，共20页。10timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatment

6、 effect=(Yt2-Yt1) (Yc2-Yc1)TreatmentEffect第10页，共20页。11In 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 effectIn this example, suppose inter

7、vention occurs in area with faster falling Y第11页，共20页。12timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2True treatment effectEstimated treatmentTrueTreatmentEffect第12页，共20页。13Basic Econometric ModelData varies by state (i)time (t)Outcome is YitOnly two periodsIntervention will occur in a group of observations

8、(e.g. states, firms, etc.)第13页，共20页。14Three key variablesTit =1 if obs i belongs in the state that will eventually be treatedAit =1 in the periods when treatment occursTitAit - interaction term, treatment states after the interventionYit = 0 + 1Tit + 2Ait + 3TitAit + it第14页，共20页。15Yit = 0 + 1Tit + 2

9、Ait + 3TitAit + itBeforeChangeAfterChangeDifferenceGroup 1(Treat)0+ 10+ 1+ 2+ 3Yt = 2+ 3Group 2(Control)00+ 2Yc= 2DifferenceY = 3第15页，共20页。16More general modelData varies by state (i)time (t)Outcome is YitMany periodsIntervention will occur in a group of states but at a variety of times第16页，共20页。17u

10、i is a state effectvt is a complete set of year (time) effectsAnalysis of covariance modelYit = 0 + 3 TitAit + ui + t + it第17页，共20页。18What is nice about the modelSuppose interventions are not random but systematicOccur in states with higher or lower average YOccur in time periods with different YsTh

11、is is captured by the inclusion of the state/time effects allows covariance between ui and TitAitt and TitAit第18页，共20页。19Group effects Capture differences across groups that are constant over timeYear effectsCapture differences over time that are common to all groups第19页，共20页。20Questions to ask?What parameter is identified by the quasi-experiment? Is this an economically meaningfu