DID双重差分回归

1、1Difference in Difference ModelsWhat is DID How can we estimate the effects of higher education reform in China? Yang and Chen (2009)23Problem 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-serie

2、s changes but, unsure how much of the change is due to secular changes4timeYt1t2YaYbYt1Yt2True effect = Yb-YaEstimated effect =Yt2-Yt1ti5 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 Solution?6Difference in differen

3、ce 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 Key concept: can control for the fact that the intervention is more likely in some types of states7timeYt1t2Yt1

4、Yt2treatmentcontrolYc1Yc2Treatment effect=(Yt2-Yt1) (Yc2-Yc1)8Difference in DifferenceBeforeChangeAfterChangeDifferenceGroup 1(Treat)Yt1Yt2Yt = Yt2-Yt1Group 2(Control)Yc1Yc2Yc=Yc2-Yc1DifferenceYYt Yc9Key Assumption Control group identifies the time path of outcomes that would have happened in the ab

5、sence 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)10timeYt1t2Yt1Yt2treatmentcontrolYc1Yc2Treatment effect=(Yt2-Yt1) (Yc2-Yc1)TreatmentEffect11 In contrast, what

6、 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 Y12timeYt1t2Yt1Yt2treatment

7、controlYc1Yc2True treatment effectEstimated treatmentTrueTreatmentEffect13Basic Econometric Model Data varies by state (i) time (t) Outcome is Yit Only two periods Intervention will occur in a group of observations (e.g. states, firms, etc.)14 Three key variables Tit =1 if obs i belongs in the state

8、 that will eventually be treated Ait =1 in the periods when treatment occurs TitAit - interaction term, treatment states after the intervention Yit = 0 + 1Tit + 2Ait + 3TitAit + it15Yit = 0 + 1Tit + 2Ait + 3TitAit + itBeforeChangeAfterChangeDifferenceGroup 1(Treat)0+ 10+ 1+ 2+ 3Yt = 2+ 3Group 2(Cont

9、rol)00+ 2Yc= 2DifferenceY = 316More general model 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 times17 ui is a state effect vt is a complete set of year (time) effects Analysis of covariance model Yit = 0 + 3 TitAit +

10、ui + t + it18What 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 Ys This is captured by the inclusion of the state/time effects allows covariance between ui and TitAit t and TitAit19 Group effects Capture differences across groups that are constant over time Year effects Capture differences over time that are common to all groups20Questions to ask? What parameter is identified by the quasi-experiment? Is this an economically meaningf