  Numerous studies use regression discontinuity design (RDD) for panel data by
assuming that the treatment effects are homogeneous across all
individuals/groups and pooling the data together. It is unclear how to test for
the significance of treatment effects when the treatments vary across
individuals/groups and the error terms may exhibit complicated dependence
structures. This paper examines the estimation and inference of multiple
treatment effects when the errors are not independent and identically
distributed, and the treatment effects vary across individuals/groups. We
derive a simple analytical expression for approximating the variance-covariance
structure of the treatment effect estimators under general dependence
conditions and propose two test statistics, one is to test for the overall
significance of the treatment effect and the other for the homogeneity of the
treatment effects. We find that in the Gaussian approximations to the test
statistics, the dependence structures in the data can be safely ignored due to
the localized nature of the statistics. This has the important implication that
the simulated critical values can be easily obtained. Simulations demonstrate
our tests have superb size control and reasonable power performance in finite
samples regardless of the presence of strong cross-section dependence or/and
weak serial dependence in the data. We apply our tests to two datasets and find
significant overall treatment effects in each case.
