The estimator of the group by the time period interaction in a study in which the subjects in two different groups are observed in two different time periods.
Normally one of the groups is the control group and the other group is provided the treatment in the second period but not in the first period. The differences-in-differences estimator of the causal effect of treatment is simply difference in the period means for the second group minus the difference in the period means for the first group. The differences-in-differences estimator is striking because it can be seen as resulting from sweeping out both subject-specific intercepts and the period-specific intercepts from a model comprising such terms. It is the standard approach to the program evaluation in the study of economics.