Dear All,
I have a question about how to include lagged treatment effect in a Difference-in-Differences (DD) model with multiple treatment periods.

Details:
I’m using the Medical Expenditure Panel Survey (MEPS) to estimate the effect of ACA Medicaid expansion on health care access and use for people with disabilities. In the DD model, the treatment is Medicaid expansion. The treatment group is comprised of respondents living in states that expanded Medicaid and the comparison group is made up by those living in states that did not participate in the expansion. The model is specified as follows:

Yist = β0 + β1Tst + ϒs + λt + β2Xist + β3Xst + εist

where i, s, and t index individual, state, and year respectively. Tst is the independent variable of interest, a dummy variable that equals one if the individual resides in a treatment state in year t when Medicaid expansion was in effect. Different treatment states implemented the expansion in different years, so t varies depending on the state. In Stata, I coded T as follows:

gen T=0
replace T=1 if state==”CA” & year>=2011
replace T=1 if state==”MD” & year>=2014
… and so on for the other treatment states.

I’ve been asked to include lagged treatment effects in the above model, so the right hand side of the model would look something like β0 + β1Tst + β2Tst-1 + β3Tst-2 + ϒs + λt + β4Xist + β5Xst + εist

How do I include such lags in Stata? MEPS is an overlapping panel survey with each panel only lasts for 2 years. I’m pooling 11 years to create a repeated cross-sectional dataset. I’ve read the Stata manual about tsset and the L. operator, but don’t know how to apply them to my model (or if they are the right commands I should look into). For my outcomes, I use svy:mlogit and svy:reg. Any help would be greatly appreciated!