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Numerous studies use regression discontinuity design (RDD) for panel data byassuming that the treatment effects are homogeneous across allindividuals/groups and pooling the data together. It is unclear how to test forthe significance of treatment effects when the treatments vary acrossindividuals/groups and the error terms may exhibit complicated dependencestructures. This paper examines the estimation and inference of multipletreatment effects when the errors are not independent and identicallydistributed, and the treatment effects vary across individuals/groups. Wederive a simple analytical expression for approximating the variance-covariancestructure of the treatment effect estimators under general dependenceconditions and propose two test statistics, one is to test for the overallsignificance of the treatment effect and the other for the homogeneity of thetreatment effects. We find that in the Gaussian approximations to the teststatistics, the dependence structures in the data can be safely ignored due tothe localized nature of the statistics. This has the important implication thatthe simulated critical values can be easily obtained. Simulations demonstrateour tests have superb size control and reasonable power performance in finitesamples regardless of the presence of strong cross-section dependence or/andweak serial dependence in the data. We apply our tests to two datasets and findsignificant overall treatment effects in each case.

Tests for Many Treatment Effects in Regression Discontinuity Panel Data Models