problems with using did_imputation for repeated cross-section data

[Yupei Ma]

I am using did_imputation by Borusyak, Jaravel, and Spiess (2021) in Stata 17.

I am confused about the command for cross-section data. I want to investigate the effect of policy A on outcome y. Policy A was adopted at the county level from 2014 to 2010. Each period I have a different sample of individuals in each county. I thought the command would be the following:

did_imputation y county year E_county, fe(county year) cluster(county)

where y is the outcome at the individual level, county is the county id, year is the time variable, and E_county is the year where the policy was adopted in the corresponding county.

However, when I read did_imputation's documentation, I find the following statement:

21) Repeated cross-sections:
When in each period you have a different sample of individiuals i in the same groups (e.g. regions), replace individual FEs with group FEs and consider
clustering at the regional level:
. did_imputation Y i t Ei, fe(region t) cluster(region) ...

Note the main parameters still include i, and not region, as the unit identifier.

It says I still need to include i (not region) as the main parameter. What does this mean? I am not sure how i and E_i are defined since each individual only appears in the sample one time. I would really appreciate it if you could shed some light on it. Thank you very much!

Best,
Yupei