A concise guide to Difference-in-Differences methods for economists with applications to taxation, regulation, and environment

Difference-in-Differences (DiD) is a useful statistical technique employed to estimate the effects that exogenous events can have on the outcome of some response variables. The latter are obtained from a random sample of treated units (i.e. units exposed to the event) ideally drawn from an infinite population. The comparable random sample/s of untreated units serve as control comparison group/s. The event is termed “treatment†, but it could be equally termed “causal factor†to emphasise that with DiD we are not estimating a mere statistical association among phenomena. With DiD we try to evaluate whether a precise causal link between causes and effects –defined according to a model based on a proper identification of the relationship among variables– is actually consistent with the data, and to estimate how intensive and statistically robust the causal-effect link actually is. This Guide will present the DiD techniques starting from the very basic methods used to estimate the Average Treatment Effect upon Treated (ATET) originally developed for the 2–period and 2–group case and covers many of the issues that have recently emerged in the multi units and multi period context. Particular attention will be devoted to the correct definition of the identification process of the causal-effect relationship in the multi period case, namely to the parallel trend and to the no anticipation assumption. Some space will be devoted to the developments associated to the techniques employed with either treatment homogeneity or treatment heterogeneity. Also, extensions of the DiD estimators accounting for complex data structures are discussed. The Guide includes a brief presentation of some policy-oriented applications of DiD. Areas covered are income taxation, migration, regulation and environment management.