Difference In Difference

Fixed Effects Model for Panel Data

DiD analysis is a way of observing and doing statistics on natural experiments. It’s called difference-in-difference because we’re comparing the differences in the change between the control and treatment groups. The model is:

$$Y_{it}={\beta }_0+{\beta }_1\text{isTreated}+{\beta }_2\text{isAfter}+{\beta }_3\text{isTreated}\times \text{isAfter}+{ϵ}_{it}$$

where $\text{isTreated}$ and $\text{isAfter}$ each is a dummy variable. The regression will look something like this: $(a)$ illustrated when there is no difference-in-difference. $(b)$ illustrates when there is a difference-in-difference. ${\beta }_3$, the coefficient that measures additional effect when there is treatment and is after treatment is the important coefficient.