How can a treatment reverse in a staggered difference-in-difference setting?

Question

I saw a discussion from Thomas Bilach here and I cannot comment in this post because I do not have enough 50 reputations and I also cannot start a chat with him. So, I am wondering right at the first few sentences:

When creating the time dummies, what is the value for the control group? Always 0?

Yes.

The timing of the intervention isn't standardized. In fact, the onset of treatment is staggered over time. That is, some entities start early, while others start late. Some treatments may even reverse. In this setting, the "generalized" difference-in-differences estimator must be used.

I am wondering what does "some treatments may even reverse" mean and is there an example helping me to understand it? And why does he use the word "generalized" here, what will we use if we are not using "generalized" DiD?

Answer 1

By "reverse" I mean some treatments may be withdrawn. The canonical example in economics is the work by Acemoglu and colleagues (2019) which investigates the effects of democracy on economic growth (peruse the un-gated copy of their work here). The authors follow 175 countries over 50 years. The transition to democracy isn't standardized. Some countries transitioned early, while others transitioned much later. Some countries experienced a permanent democratic transition, while others had a more transient experience. Some even switched in and out of a democratic style of governance multiple times. This is what I meant when I used the term "reversal" in my response. In settings with a dichotomous treatment variable, this amounts to a dummy switching 'on' and 'off' over time within a subset of treated countries. The epochs where a country 'transitions out' may be referred to as a period of treatment reversal.

In my own research, I've investigated law enforcement interventions that were intermittent. By "intermittent" I mean strategies implemented multiple times over many years. If the intervention is only 'in effect' for a few months every year, then treatment is pulsating 'on' and 'off' over time. In this setting, a "reversal" is when the intervention is withdrawn or terminated. In my own experience, government interventions can be quite costly, so they aren't always 'in effect' in perpetuity. Researchers may want model the periods where treatment is withdrawn to investigate whether effects decay beyond conclusion of the intervention.

And lastly, I may use the term "generalized" estimator because it is a generalization of the "classical" estimator. The "classical" estimator is typically used when the timing of a policy/law (i.e., treatment) is standardized. By "standardized" I mean the units in the treatment group become exposed to the treatment at the same time. In other words, their "post-treatment" epochs are very well-defined. Once we depart from the "classical" setting and the roll of some policy/law isn't uniform across treated entities, then you should probably consider the "generalized" estimator.

The following paper by Wing and colleagues (2018) offers a gentle introduction to difference-in-differences methods and their practical applications.