Primary Submission Category: Difference in Differences, Synthetic Control, Methods for Panel and Longitudinal Data
Cluster-robust inference with a single treated cluster using the t-test
Authors: Xinran Li, Chun Pong Lau,
Presenting Author: Xinran Li*
We consider the situation where treatment is assigned at the cluster level and unobserved dependencies exist among units within each cluster. This situation often occurs in difference-in-differences estimation, where a single treated cluster is compared to a finite number of control clusters. We assume the availability of asymptotically Gaussian cluster-level estimators, albeit with asymptotic variances that are unknown and challenging to estimate due to dependencies within clusters. Inference for treatment effects in this context is equivalent to a two-sample testing problem, where (i) one group comprises a single observation while the other includes a finite number of observations with a common mean, and (ii) all observations follow independent Gaussian distributions with potentially heteroskedastic and unknown variances. We propose exact t-tests tailored to this problem, incorporating constraints on relative heterogeneity of variances across groups. We illustrate the advantage of the proposed method through both simulations and empirical applications.