Computing Synthetic Controls Using Bilevel Optimization

The synthetic control method (SCM) represents a notable innovation in estimating the causal effects of policy interventions and programs in a comparative case study setting. In this paper, we demonstrate that the data-driven approach to SCM requires solving a bilevel optimization problem. We show how the original SCM problem can be solved to the global optimum through the introduction of an iterative algorithm rooted in Tykhonov regularization or Karush–Kuhn–Tucker approximations.