Causal inference with a single-treated case using the synthetic control method

Abstract

This paper studies causal inference with a single-treated case using the synthetic control method (SCM) with both empirical data and Monte Carlo Simulations. SCM identifies the causal effects of a single-treated case by constructing a synthetic control, a weighted average of controls, that resembles a treated unit on observables and pre-treatment outcomes. As an empirical illustration, we examine the effects of the Great Hanshin Earthquake on poverty in Hyogo prefecture. Several years after the earthquake, poverty (measured as proportions of welfare recipients) increased in Hyogo prefecture, and it continues to be higher than in counterfactual groups 15 years after the quake. We then compare performances between SCM and a Difference-in-Differences (DD) estimator. Results from Monte Carlo Simulations indicate that when unit-specific time trends are assumed to be absent, SCM and DD perform similarly. However, when such trends are assumed to be present, biases produced by DD are greater than those produced by SCM. This suggests that SCM is suitable for identifying causal effects with a single-treated case when there are unobserved time trends.