Difference in differences in reverse

Abstract

In the usual difference in differences (DD), there is a control group that is never treated and a treatment group that is treated at some time point. However, there are DD cases where the control group is always treated (instead of always untreated), which we call 'DD in reverse (DDR)'. This paper examines how the usual DD identification and estimation procedures change for DDR. As it turns out, DDR estimation can be performed in the same way as DD estimation. In contrast, the identification procedure is quite different, because DDR essentially identifies pre-treatment-period effects, whereas DD identifies post-treatment-period effects. An empirical illustration of the effects of a work-hour limit law on actual work hours and wages is provided, where the law is applied to large firms first and then small firms 1 year later in South Korea so that in the second year, the large firms constitute the always-treated control group and the small firms constitute the treatment group. We find that the law raised South Korean workers' well-being, as their work hours decreased while their real weekly wage increased.