Hello Statalist,
My question is partly about econometrics and partly about whether there is a paper (and perhaps an accompanying statistical package) that addresses this issue. Frequently, triple differences exploits differences in policy implementation by unit, time, and some within-unit group difference in qualification for the policy. How does one proceed when the treated and untreated group definitions within each treated unit differ somewhat?
My case offers a more concrete example: My dependent variable measures outcomes at the state-month-[age of affected person] level. I have a policy that turns on for some states and not others. Each treated state has an age cutoff for the policy to affect that person, but the age cutoff is not uniform (e.g., one requires age<12, and another requires age<15).
The best I could think of was to drop all the "sometimes treated" age groups and compare the "always treated" ages (<12 in my example) to the "never treated" ages (15+ in my example). It's clean, but it drops data. In principle, it seems like there should be a way to keep all the data and only make the “proper” comparisons, but in practice I cannot answer the following:
1. How would one construct such an estimator? (The “control group” in untreated states would change based on the specific treatment state's age cutoff, I think)
2. What new assumptions one would have to make for identification?
3. Most terrifyingly for a non-econometrician, how would one construct the confidence interval?
Like I said, maybe there is a paper / package I just haven't found. Thanks for your help!
Best wishes,
Alex Henke
My question is partly about econometrics and partly about whether there is a paper (and perhaps an accompanying statistical package) that addresses this issue. Frequently, triple differences exploits differences in policy implementation by unit, time, and some within-unit group difference in qualification for the policy. How does one proceed when the treated and untreated group definitions within each treated unit differ somewhat?
My case offers a more concrete example: My dependent variable measures outcomes at the state-month-[age of affected person] level. I have a policy that turns on for some states and not others. Each treated state has an age cutoff for the policy to affect that person, but the age cutoff is not uniform (e.g., one requires age<12, and another requires age<15).
The best I could think of was to drop all the "sometimes treated" age groups and compare the "always treated" ages (<12 in my example) to the "never treated" ages (15+ in my example). It's clean, but it drops data. In principle, it seems like there should be a way to keep all the data and only make the “proper” comparisons, but in practice I cannot answer the following:
1. How would one construct such an estimator? (The “control group” in untreated states would change based on the specific treatment state's age cutoff, I think)
2. What new assumptions one would have to make for identification?
3. Most terrifyingly for a non-econometrician, how would one construct the confidence interval?
Like I said, maybe there is a paper / package I just haven't found. Thanks for your help!
Best wishes,
Alex Henke
Comment