B1837
Title: Penalized synthetic controls on truncated data with multiple treated and control units
Authors: Bikram Karmakar - University of Florida (United States) [presenting]
Gourab Mukherjee - University of Southern California (United States)
Wreetabrata Kar - Purdue University (United States)
Abstract: In causal inference from a panel dataset with a treated unit and multiple control units, the synthetic control (SC) method fits the pre-treatment observations of the treated unit using the pre-treatment observations of a convex combination of the control units, called the synthetic control (SC) unit. Then, the SC unit's post-treatment outcome estimates the target unit's counterfactual post-treatment outcome. Most applications of the SC method in the literature have used aggregated units, e.g., states, where observations average over latent patterns in the finer units data and retain the common factors. In aggregated data, weights in the SC methods attempt to equate the factor loading of the target unit to the weighted average of the loadings of the control units. However, for finer-grained data, when there are local structures, a prior study notes that there might be significant interpolation bias when using the SC method. A new method is proposed for causal inference from fine-grained panel data: a novel penalized SC method that accommodates the latent structures inherent in the data. Under a truncated flexible additive mixture model, it is shown that the SC method has uncontrolled maximal risk without the proposed penalty; by contrast, the proposed penalized method provides efficient estimates. Finally, using the proposed method, the effects of the passage of a medical marijuana law are studied on direct payments to opioid-prescribing physicians by opioid manufacturers.
