How to designate Post Treatment period in Difference-in-differences model?

[Chul-Kyoo Jung]

Hi I just want to make a clarification about how to determine post-treatment period in DiD model.
My data starts from 1990 and ends in 2010 with unbalanced panel data.

Case A: The same treatment occurred in 2000 for some entities and 2001 for some other entities.
Case B: The treatment occurred in 2000 for the entire entities and its implementation extended to year 2001. In other words, it took 2 years to complete the treatment.

Could you tell me how to designate the POST_TREATMENT dummy variable for a simple DiD model depending on the case?

Thank you.

[Clyde Schechter]

If the treatment occurred in 2000 and 2001

What does that mean? Does it mean that treatment began in 2000, and the implementation of the treatment extended through 2001? Does it mean that some treated entities were treated in 2000 and others were treated in 2001?

And what is the structure of your data set? Specifically, do you have observations in 1999, 2000, 2001, and 2002 (plus other years before or after) for every entity in the data set?

[Chul-Kyoo Jung]

Clyde Schechter Thanks for your clarifying questions. In fact, the latter is the case: some treated entities were treated in 2000 and others were treated in 2001. My data set covers from 1990 to 2010 and I do have observation in 1999, 2000, 2001, and 2002 but not for every entity because the data is unbalanced panel data. And could you also let me know in case the treatment began in 2000 and implementation extended through 2001?

[Clyde Schechter]

Since different entities underwent treatment at different times, this is not a classical DID analysis. You must use generalized DID. This means that you do not have a variable designating treatment group vs control group, and you do not have a variable designating a pre-treatment era vs a post-treatment era. Rather for every observation you create a variable that is zero for those years before that entity received treatment (so, before 2000 for some and before 2001 for others, and for those never treated, for all years), and 1 after treatment (so from 2000 on for those who began treatment in 2000, from 2001 on for those who began treatment in 2001, and never for those who were never treated.) Let's call this variable under_treatment.

Then you estimate the treatment effect by using a two-way fixed effects model. So it will look like:

xtset panel_var year
xtreg outcome i.under_treatment i.year, fe

The coefficient of 1.under_treatment is then the generalized DID estimator of the treatment effect.

If you had a situation where treatment began for everybody in 2000 but took two years to implement, then you would be back in classical DID analysis, with a slight twist. Here I would use a trichotomous time variable: 0 before 2000, 1 in 2000 and 2001, and 2 in 2002 and thereafter. Let's call that one -era- You would need a variable that designates which entities were treated and which were not. Let's call that one group. Then the DID analysis would be:

regress outcome i.group##i.era

Note this time the absence of entity or year fixed effects. That's important: if you try to add them, you will invalidate the group#era coefficients as DID estimators of treatment effect.

Note also that as the era variable has three levels, there will be two treatment estimate effects. The coefficient of 1.group#2.era will be the one you are most interested in: it estimates the causal effect of being treated on the outcome. The coefficient of 1.group#1.era may or may not be of interest: it represents the causal effect of being in the implementation phase of treatment.

[Chul-Kyoo Jung]

Clyde Schechter Thanks so much for clarifying answers.