Is there some literature about two-year difference-in-differences (DiD) models? Suppose a policy was implemented in 1982, but not strictly enforced among all people. Can I still estimate a DiD model using the data only from 2012 to 2016?
Is there some literature about two-year difference-in-difference (DiD) models?
The traditional two-group/two-period DiD design was quite popular 25 years ago, though it's less common today to find evaluations where entities are observed in only one time period pre- and post-shock. DiD methods hinge on the graphical exhibition of common group trends before program exposure. You cannot possibly demonstrate this, visually or statistically, with less than three pre-treatment time periods. Serial observations pre- and post-treatment is not necessary, but is very much preferred. In my opinion, your study is likely to be met with skepticism if you do not observe individuals for a sufficient number of time periods before your treatment of interest.
Suppose a policy was implemented in 1982, but not strictly enforced among all people. Can I still estimate a DiD model using the data only from 2012 to 2016?
Unless I misunderstood your question, the immediate policy adoption year is 1982. If you were to restrict your time series to the years from 2012 to 2016, then by definition, you're only observing entities in the post-policy phase. This assumes the policy has persisted until 2016. Unless the policy was rescinded and reintroduced in the interval you referenced, then you cannot possibly conduct a DiD evaluation. Assessing treated and untreated entities post-policy is a posttest-only evaluation. A posttest-only design is not considered a DiD evaluation; you must observe entities pre- and post-shock.
But suppose, for example, a completely new policy is introduced in between the years you referenced (e.g., 2014). Before its introduction, all individuals are untreated. Once it is instituted, only a subset of individuals will be eligible. The individuals affected by the policy comprise your treatment group, while all non-affected persons comprise your control group. At a basic level, the 'classical' DiD approach requires you to observe a treatment group and a control group at least one year before and at least one year after your policy. If you do not observe any pre-event data, then you must model the effect of the policy in a different way.