On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls
大量时期与大量对照单位下合成控制估计量的性质
We consider the asymptotic properties of the synthetic control (SC) estimator when both the number of pretreatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which the SC unit asymptotically recovers the factor structure of the treated unit, even when the pretreatment fit is imperfect. This happens when there are weights diluted among an increasing number of control units such that a weighted average…