双重差分模型幻灯片differenceindifferencesmodels.pptVIP

Difference in Difference Models Bill Evans Spring 2008 Difference in difference models Maybe the most popular identification strategy in applied work today Attempts to mimic random assignment with treatment and “comparison” sample Application of two-way fixed effects model 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 change is due to secular changes 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? Difference in difference 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 states Three different presentations Tabular Graphical Regression equation Difference in Difference Key Assumption 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) 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 Basic 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.) 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 a