A regularized approach to the synthetic control method: an empirical evaluation

The synthetic control method (SCM) estimates the treatment effect for a single treated unit by constructing a counterfactual outcome as a weighted average of the outcomes from untreated donor units. SCM requires that the estimated weights be greater than zero and sum to one. However, these constraints can be suboptimal if the treated unit's time series exhibits consistently higher or lower values or variance, or opposite trends relative to the donor units. To address this limitation, we systematically evaluate a regularized version of SCM (RSCM), allowing weights to take on any value. Simulation results show that SCM and RSCM perform equally well when outcomes of the treated unit are located inside the outcome set of donor units. However, when treated unit outcomes are at the boundary, RSCM outperforms SCM. Finally, placebo tests in two empirical applications confirm that RSCM accurately predicts employment levels for different labour market sectors.