DID双重差分回归.pptVIP

* How can we estimate the effects of higher education reform in China? Yang and Chen (2009) * * 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 * time Y t1 t2 Ya Yb Yt1 Yt2 True effect = Yb-Ya Estimated effect =Yt2-Yt1 ti * 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? * 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 * time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Treatment effect= (Yt2-Yt1) – (Yc2-Yc1) * Before Change After Change Difference Group 1 (Treat) Yt1 Yt2 ΔYt = Yt2-Yt1 Group 2 (Control) Yc1 Yc2 ΔYc =Yc2-Yc1 Difference ΔΔY ΔYt – ΔYc * 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) * time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 Treatment effect= (Yt2-Yt1) – (Yc2-Yc1) Treatment Effect * 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 * time Y t1 t2 Yt1 Yt2 treatment control Yc1 Yc2 True treatment effect Estimated treatment True Treatment Effect * 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, et