[George Ford]

I remain confused about the data. You say "To clear things up - I do mean common timing in the way Jeff interpreted it. Such that the one treated unit is untreated for a number of periods and then becomes treated for the rest of the time periods."

Jeff's interpretation was that you had one treated unit and a single treatment period. My interpretation was that you had one treated unit with several treatment periods.

Jeff's idea works with his interpretation (both actually), but SC can handle my interpretation.

To be clear: How many pre-treatment and post-treatment periods do you have?

[Zhehui Luo]

Unfortunately, the validity of SC requires many post-treatment periods -- otherwise the inference is not valid. I've proposed a different approach based on the representation of DiD as a cross-sectional regression. You average the pre-treatment periods and subtract, for each unit (treated or otherwise), from the average of the post-treatment period. In this case, the single time period. Now you have a single cross section, and you can regress the differenced variable on a constant and the treatment dummy. If you believe the classical linear model assumptions hold for this cross-sectional equation, you can use the usual t statistic. With a single treated unit, this is identical to "outlier" analysis, which makes sense: you are testing whether the treated unit is an outlier compare with the controls. The coefficient on the treatment dummy is the Studentized residual from outlier analysis. I discuss this in Section 9.5 of my introductory econometrics book. In case it is useful, I'm attaching slides from a workshop I've taught. In Section 5, I show how to collapse the data and do the simple OLS regression. With 21 control units, you could even include some covariates. I have the Stata code, too, but it's pretty simple.

Minor typo? Should be: The t-statistic on the treatment dummy is the Studentized residual from outlier analysis. Or the coefficient on the treatment dummy is the raw residual from outlier analysis.

[Jeff Wooldridge]

Correct Zhehui! Thanks for catching that.