Difference in Difference Regression

The difference-in-difference (DID) technique is a quasi-experimental design that makes use of longitudinal data from treatment and control groups to obtain an appropriate counterfactual to estimate a causal effect. DID is typically used to estimate the effect of a specific intervention or treatment by comparing the changes in outcomes over time between a population that is enrolled in a program (the intervention group) and a population that is not (the control group).

It is called the ‘controlled before-and-after study’ in some social sciences.

DID is used in observational settings. DID requires data from pre-/post-intervention, such as cohort or panel data (individual level data over time) or repeated cross-sectional data (individual or group level).

Difference-in-Difference estimation, graphical explanation (See Pic Above)

Regression Model

DID is usually implemented as an interaction term between time and treatment group dummy variables in a regression model. (See Pic Below)

Y= β0 + β1*[Time] + β2*[Intervention] + β3*[Time*Intervention] + β4*[Covariates] + ε