Measuring Treatment Effects with Big N Panels

This paper considers the problem of estimating treatment effects when there is a large number of potential control units. The paper introduces to the economics literature the idea of polytope volume minimization as a method of estimating a factor model when observed outcomes are assumed to be a convex combination of the unobserved factor values. The paper shows that this method is particularly well-suited to the case where there are a large number of cross-sectional units. The paper presents identification results for both exact and approximate factor models which are new to the literature. It presents simulations that compare standard methods such as difference-in-difference and synthetic controls to the proposed approach. The estimator is used to estimate the effect of reunification on German growth rates.