[On-going] Appendix
A. Estimation Algorithms for SDID
B. Placebo Variance Estimation
Arkhangelsky et al. (2021) propose three variance estimation methods to construct asymptotically valid confidence intervals based on their theoretical framework. However, both the bootstrap and jackknife approaches are tailored for settings with a large number of treated units and may yield unreliable results when the number of treated units is small—as in our case, where N_tr = 1.
Therefore, we adopt the third method—placebo variance estimator. This method evaluates the variability of the synthetic control estimator by systematically replacing the treated unit with control units and assessing the distribution of placebo effects. Specifically, Algorithm 2 implements this approach by generating placebo predictions using only unexposed units to estimate the variance V^tau, which is then used to construct confidence intervals as specified in Equation (5).
