Staggered policy with boundary discontinuity design

[juliana pinto]

Dear Statalists, Please, could anyone help me?
I have a panel data set from 2001-2020, municipality level (I have 3 states with and the data is per municipalities of each state). In 2007, a policy was implemented just in one state. This state has boundaries with the other two states. Therefore, I believe I could use boundary discontinuity design. However, the policy is staggered throughout the years, that's, its adoption didn't occur instantaneously after 2007.
I thought I could use then difference in discontinuity.
Do you know the command I could use to create this analysis of study event using boundary discontinuity with a staggered policy and or/ this geographic difference in discontinuity?

Many thanks in advance!
Cheers.

[Fei Wang]

A simple solution is to conduct a DiD analysis for municipalities near boundaries only, as long as you have a sufficiently large number of boundary municipalities. Not sure about what you meant by "its adoption didn't occur instantaneously after 2007". Was the policy enforced weakly for all municipalities in the treated state and then turned stronger, OR enforced in part of the municipalities and then extended to other municipalities of the treated state? Model specifications differ in the two cases. I assume the former one. Then you define p1 and p2, dummies indicating weakly and strongly enforced periods, respectively. And define d = 1 for municipalities in the treated state and 0 for those in other two states. Further define a dummy b indicating municipalities near boundaries. A simple DiD setting would be

xtset municipalityID year
xtreg y c.d#c.p1 c.d#c.p2 i.year if b == 1, fe vce(cl municipalityID)

This setting may be generalized in various directions, like adding covariates, and adjusting the range of municipalities for study.

[juliana pinto]

Hi Prof. Fei, Many thanks for answering.
The policy started in 2007, but the farms located in the municipalities had to adapt their infrastructure to comply with the policy. Thus, it could not happen immediately in 2007. The farms had to invest and started changing and adhering to the policy through the years. So, some farms complied with the policy before others throughout the period.
Does the same equation apply to this scenario?
thank you.

[Fei Wang]

I think what you described in #3 matches what I did in #2. But in #2, I assume two periods: p1 for adaptation period and p2 for fully enforced period. If you don't have clear cutoffs of timing for the implementation of the policy, I would suggest starting with a comprehensive set of interactions after year 2007, something like

xtset municipalityID year
xtreg y c.d#c.(y07 y08 y09 y10 y11 y12 y13 y14 y15 y16 y17 y18 y19 y20) i.year if b == 1, fe vce(cl municipalityID)

where "y#" is a dummy for a specific year #. From these results, you would be able to see how policy effects evolve by year and then refine your model specification accordingly.

[juliana pinto]

Many thanks Prof. Fei!
Please, can I ask what are c and c1?
Cheers,

[Fei Wang]

"c." is a factor-variable operator telling Stata to keep the original forms of variables in the interactions. You may refer to -help fvvarlist- for more details. "cl" is an abbreviation of "cluster" (so it's "cl" not "c1"), which asks Stata to cluster standard errors at the level of municipality.

[juliana pinto]

Many thanks Prof. Fei!! Cheers!