treatment group that could be the result of trends. ∙ With repeated cross sections, let A be the control group and B the treatment group. Write
y 0 1dB 0d2 1d2 dB u,
where y is the outcome of interest. The dummy dB captures possible differences between the treatment and control groups prior to the policy change. The dummy d2 captures aggregate factors that would cause changes in y even in the absense of a policy change. The coefficient of interest is 1. ∙ The difference-in-differences estimate is
1 ȳB,2 − ȳB,1 − ȳA,2 − ȳA,1.
Inference based on even moderate sample sizes in each of the four groups is straightforward, and is easily made robust to different group/time period