Double difference regression allows to assess whether the impact is statistically significant. Moreover, it allows to take into account the influence of additional periodic or structural factors.
According to the European Commission’s methodological document, it is reasonable to develop the following regression model:
Yi,t = a + b1*Ti + b2*Pt + b3*Ti*Pt + ԑi,t
Yi,t is the outcome of the person i (e.g. the number of days worked by the person / the fact of being employed at least a certain number of days per year (1 or 0) / person’s income) in the period t;
Ti is a variable with two possible values: 1, if a person participated in the intervention, and 0, if a person did not participate in the intervention;
Pt is a variable with two possible values: 0 reflects the period before the intervention, and 1 reflects the period after the intervention;
Ti*Pt is the outcome of the two aforementioned variables which acquires value 1 only when the outcome of the person who participated in the intervention, in the period after the intervention, is taken into account;
ԑi,t is an error of the regression;
a, b1, b2, b3 are parameters of the regression that are under evaluation:
parameter a reflects the average outcome (e.g. income) of the persons who did not participate in the intervention, in the period before receiving the assistance;
parameter b1 reflects the initial difference between the treatment and control groups;
parameter b2 reflects the difference of the outcomes (e.g. income) of the persons who did not participate in the intervention between periods;
parameter b3 reflects an impact estimate.
At the same time, the significance of the parameters is evaluated. For example, in the cases where the parameter reflecting the impact estimate turns out to be statistically insignificant, it is important to refrain from strong statements regarding definite impact of the assistance. For developing such regression models, econometric packages, for example, free software R (https://www.r-project.org/
), are employed.