I am running into a tricky issue with the execution of the synthetic control method for my data. For reference, my outcome data has an odd temporal gap (uniformly, across all units, no data is avaliable for 1993). However, temporal coverage is sufficient barring this one-year gap. Unfortunatley, across various units, the treatment occurs near 1993. This means that this temporal gap creates an artifical year of missing data in the pre- or post-treatment period. My question is, does this pose a serious threat to the feasability of the synthetic control method for my project?
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You can define a new time variable that does not have that gap, and then proceed as usual after dropping the 1993 rows from the analysis. When plotting your results, you can return to normal time and insert breaks in the time plots at 1993. This will be a bit tricky if you want to report a cumulative effect for the post-treatment period, but maybe you can keep it flat for that year.
As a robustness check, you can try to interpolate the 1993 data with an average of 1992 and 1994. If that mixes treated 1994 and untreated 1992 for units treated in 1993, you can impute using a weighted average. So if treatment happened on December 31st of 1993, then use a 364/365 weight on 1992 to reflect that most of the year was untreated. Ideally, the results would be similar to what you get above. I think other types of modern imputation would be computationally prohibitive.
This assumes there was nothing special about 1993, so the data is missing at random. You will have to use your domain expertise to convince yourself and your audience of that.
