Real Example
Consider one of the more famous DID studies, the Card and Krueger article on minimum wage in New Jersey (NJ), published in 1994.
Card and Krueger are looking at the effect of an April 1, 1992 increase in NJ's minimum wage from $4.25 to $5.05. They collect data on fast food employment before (February) and after (November) the change. In NJ, average employment per restaurant rises from 20.44 FTEs (or full-time equivalents) before the wage change to 21.03 FTEs after the wage change. Naively, you might interpret this to mean that the minimum wage change caused a 0.59 FTE increase in employment per store. But lots of other things changed. For one thing, we're in a different season; do fast food restaurants face more demand in winter than in spring? For another thing, the macroeconomic conditions may have changed more broadly. Perhaps unemployment is shrinking across the board. Perhaps employment would have gone up by even more in the absence of the minimum wage increase.
Card and Krueger needed a control group. They turn to fast food restaurants in Pennsylvania, a state that faces very similar macroeconomic conditions. They expect that major changes in the fast food environment in NJ are probably also occurring in PA. In PA, FTE employment actually fell from April to November, from 23.33 to 21.17.
If you think fast food restaurants in PA are identical to fast food restaurants in NJ, then you expect NJ restaurants to see a similar −2.16 FTE change in employment. Instead, we see a +0.59 change. So employment in NJ rose by 2.76 FTEs more than we would expect just based on what was happening in PA.
That is, we take the difference between Period 1 and Period 2 separately for the treatment and control groups (+0.59 and −2.16). Then we calculate the difference between those two differences (0.59 − (−2.16)) to get the DID estimate.
We know one major difference between NJ and PA at the time: the change in the minimum wage. The DID method thus implies that the minimum wage increase appears to have led to a 2.76 increase in FTEs per fast food restaurant. (This is probably not going to convince you that raising the minimum wage raises employment, but at the very least it strongly implies that a minimum wage hike cannot DECREASE fast-food employment by all that much.)
The Card and Krueger paper goes into quite a bit more detail, of course, including several other specifications of the same basic concept; reading it is a good tutorial on the method.
Read more about this topic: Difference In Differences
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