Difference in Differences

Difference in differences (sometimes 'differences-in-differences', 'DID', or 'DD') is a quasi-experimental technique used in econometrics that measures the effect of a treatment at a given period in time. It is often used to measure the change induced by a particular treatment or event, though it may be subject to certain biases (mean reversion bias, etc.). In contrast to a within-subjects estimate of the treatment effect (that measures the difference in an outcome after and before treatment) or a between-subjects estimate of the treatment effect (that measures the difference in an outcome between the treatment and control groups), the DID estimator represents the difference between the pre-post, within-subjects differences of the treatment and control groups.

The basic premise of DID is to examine the effect of some sort of treatment by comparing the treatment group after treatment both to the treatment group before treatment and to some other control group. Naively, you might consider simply looking at the treatment group before and after treatment to try to deduce the effect of the treatment. However, a lot of other things were surely going on at exactly the same time as the treatment. DID uses a control group to subtract out other changes at the same time, assuming that these other changes were identical between the treatment and control groups. (The Achilles' heel of DID is when something else changes between the two groups at the same time as the treatment.) For it to be an accurate estimation, we must also assume that the composition of the two groups remains the same over the course of the treatment. Also we need to consider the possible serial correlation issues.