Consider this example:[1] state A passes a bill offering tax deduction to employers providing health insurance. Let us also consider that in the year after the bill passed (year 2) the percentage of firms offering health insurance increased by 30% compared to the year before the bill was passed (year 1). To estimate the impact of the bill on the percentage of firms offering health insurance, we could simply do a before and after analysis and conclude that the bill increased insurance offerings by 30%. The problem is that there could be a trend over time for more employers to offer insurance. It is impossible to identify if the tax deductibility or the time trend caused this increase in firm offering.

One way to identify the impact of the bill is to run a DID regression. If there is a state B that did not change the way it treated employer provided health insurance, we could use this as a control group to compare the changes between A and B between the two years.

via Difference in differences – Wikipedia, the free encyclopedia.