Panel treatment effects measurement: Factor or linear projection modelling?

Abstract

We discuss methods of measuring the treatment effects of a unit through the use of other units in panel data by either the factor-based (FB) approach or the linear projection (LP) approach under different sample configurations of cross-sectional dimension $N$ and time series dimension $T$. We show that the LP approach in general yields smaller mean square prediction error than the FB approach when either both $N$ and $T$ are large or $N$ fixed and $T\to \infty$ or $T$ fixed and $N$ large. The Monte Carlo simulation and empirical example are also conducted to consider their finite sample performances.