Difference in differences is a method of evaluating non-experimental effects. It consists of comparing two groups of individuals (those receiving the treatment and those excluded from it, the control group) in at least two time periods, before and after the introduction of the policy.

The untestable assumption on which the method is based, and which in some cases is not plausible, is that the factors differentiating beneficiaries and excluded individuals, net of certain observable characteristics that can be identified and isolated, remain constant over time.

By exploiting this assumption, the method makes it possible to eliminate selection bias and estimate the effect of the policy.

In this case, the counterfactual value is obtained by adding the difference between the final and initial values for the control group to the initial value of the result variable for the treated group.

The effect of the policy is then calculated as the difference between the final value of the result variable for the treated group and the counterfactual.

Hence the name of the method.

For public policies characterised by rigid and known administrative rules that reliably determine exposure to the treatment, a marked discontinuity is created between those admitted to the treatment and those who are not. This holds even if the values of the observable characteristic used for selection are very similar for the two groups of individuals.

The threshold value, and the resulting selection process, can for example refer to income (exemption from healthcare co-payments, allowances), to age (Young People's Guarantee), to the score obtained in a selection test.

The discontinuity that is created around the threshold can be exploited to identify the effect of the policy by comparing the results for marginal individuals, i.e. those situated just below (excluded) or just above (admitted) the threshold. The similarity between the individuals around the threshold enables a random selection (randomisation) in which the effect of the treatment is not subject to self-selection bias.

The estimate thus obtained of the effect is, however, local, in other words valid only for those situated around the threshold (the marginal individuals) and is, therefore, difficult to generalise. Internal validity is obtained by sacrificing external validity.

This limitation to exploiting the threshold discontinuity can in part be mitigated by using all the available observations (so not just those relating to the individuals around the threshold) with the help of regression. This is how the Regression Discontinuity Design approach is obtained.