Generalized Difference in Difference

[Md Shoeb]

I understand that this topic has been repeatedly discussed in the forum and I have went through numerous post but I couldn't find the answer to my problem hence I am posting.

I have panel data from 2008 to 2021 consisting of two sets of banks, government owned and private owned. The government owned banks receive capital infusion from the government so they are the treatment group and the privately owned banks are my control group. My outcome variables are systemic risk and moral hazard. But here's the problem - Different government owned bank get infused in different years. Infusion happen every year from 2009 to 2021 but for different government banks (some get infused while others do not in treatment group every year). In this setting a classical DID setup isn't applicable from what I read in statalist and some research papers. Would a generalized difference in difference would be applicable in this setup ? if yes the model would be sytemic risk = a + bank fixed effects + year fixed effects + B1 interaction term + error term. Now my question is how should this interaction/did term be defined ?

[Jared Greathouse]

Don't worry about defining it, see this by FernandoRios or this estimator. You can also use didmultiple_gt.


For a very general review, see this paper.

[Øyvind Snilsberg]

the did term should be equal to 1 when treated banks are treated, and 0 otherwise,

* Example generated by -dataex-. For more info, type help dataex
clear
input float bank str10 treated float(time did)
1 "never"   2010 0
1 "never"   2011 0
1 "never"   2012 0
1 "never"   2013 0
2 "in 2011" 2010 0
2 "in 2011" 2011 1
2 "in 2011" 2012 1
2 "in 2011" 2013 1
3 "in 2013" 2010 0
3 "in 2013" 2011 0
3 "in 2013" 2012 0
3 "in 2013" 2013 1
end

[Md Shoeb]

Thank you Jared I will definitely look into this as it seems the results might be incorrect with GDID. Thank you Øyvind now it is very clear to me how the did term is defined. I am assuming the interpretation will be same in this case as in the classical did setup ? If possible can you please explain the logic behind the generalized DID variable? Or can you suggest some papers I can refer to ?

[Øyvind Snilsberg]

It depends. In the 2x2 DiDset-up, the beta coefficient from the generalized DiD/two-way fixed effects (TWFE) model equals the usual DiD estimate. When treated units are treated at different times, however, the TWFE estimator is not an easily interpretable parameter; it’s a weighted average of all possible 2x2 DiD estimators in the data, a variance-weighted average of cross-group treatment effects. Even more, if the treatment effect vary across time, a portion of some of these 2x2 estimates are subtracted from the global DiD estimate. This can lead to substantial bias in the estimate, which is what the estimators that Jared refers to aim to address.