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1、1,Difference in Difference Models,What is DID,How can we estimate the effects of higher education reform in China?Yang and Chen(2009),2,3,Problem set up,Cross-sectional and time series dataOne group is treated with interventionHave pre-post data for group receiving interventionCan examine time-serie
2、s changes but,unsure how much of the change is due to secular changes,4,time,Y,t1,t2,Ya,Yb,Yt1,Yt2,True effect=Yb-Ya,Estimated effect=Yt2-Yt1,ti,5,Intervention occurs at time period t1True effect of lawYa YbOnly have data at t1 and t2If using time series,estimate Yt1 Yt2Solution?,6,Difference in dif
3、ference models,Basic 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 types of states,7,time,Y,t1
4、,t2,Yt1,Yt2,treatment,control,Yc1,Yc2,Treatment effect=(Yt2-Yt1)(Yc2-Yc1),8,Difference in Difference,9,Key Assumption,Control group identifies the time 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 u
5、nderlying levels of outcomes are not important(return to this in the regression equation),10,time,Y,t1,t2,Yt1,Yt2,treatment,control,Yc1,Yc2,Treatment effect=(Yt2-Yt1)(Yc2-Yc1),TreatmentEffect,11,In contrast,what is key is that the time trends in the absence of the intervention are the same in both g
6、roups If the intervention occurs in an area with a different trend,will under/over state the treatment effectIn this example,suppose intervention occurs in area with faster falling Y,12,time,Y,t1,t2,Yt1,Yt2,treatment,control,Yc1,Yc2,True treatment effect,Estimated treatment,TrueTreatmentEffect,13,Ba
7、sic Econometric Model,Data varies by state(i)time(t)Outcome is YitOnly two periodsIntervention will occur in a group of observations(e.g.states,firms,etc.),14,Three key variablesTit=1 if obs i belongs in the state that will eventually be treatedAit=1 in the periods when treatment occursTitAit-intera
8、ction term,treatment states after the interventionYit=0+1Tit+2Ait+3TitAit+it,15,Yit=0+1Tit+2Ait+3TitAit+it,16,More general model,Data varies by state(i)time(t)Outcome is YitMany periodsIntervention will occur in a group of states but at a variety of times,17,ui is a state effectvt is a complete set
9、of year(time)effectsAnalysis of covariance modelYit=0+3 TitAit+ui+t+it,18,What is nice about the model,Suppose interventions are not random but systematicOccur in states with higher or lower average YOccur in time periods with different YsThis is captured by the inclusion of the state/time effects a
10、llows covariance between ui and TitAitt and TitAit,19,Group effects Capture differences across groups that are constant over timeYear effectsCapture differences over time that are common to all groups,20,Questions to ask?,What parameter is identified by the quasi-experiment?Is this an economically meaningful parameter?What assumptions must be true in order for the model to provide and unbiased estimate of 3?Do the authors provide any evidence supporting these assumptions?,
