Statistical power for the comparative regression discontinuity design with a nonequivalent comparison group

Area of Science:

• Econometrics
• Policy Evaluation
• Social Sciences

Background:

• The sharp regression discontinuity design (RD) is widely used for causal inference but suffers from multicollinearity, reducing efficiency.
• Adding untreated comparison data to RD creates a comparative regression discontinuity design (CRD), improving upon basic RD.

Purpose of the Study:

• To evaluate the statistical power and efficiency of CRD, particularly CRD with a comparison group (CRD-CG), relative to basic RD and randomized control trials.
• To demonstrate the practical benefits of CRD-CG, including reduced sensitivity to cutoff location and fewer required treated units.

Main Methods:

• Theoretical development of CRD-CG power under linear functional forms.
• Numerical predictions comparing RD, CRD-CG, and randomized control trials.
• Empirical testing using data from the National Head Start Impact study.

Main Results:

• CRD-CG demonstrates greater statistical power than basic RD.
• CRD-CG is less sensitive to the assignment variable's cutoff location and distribution.
• Fewer treated units are needed in CRD-CG, potentially leading to cost savings.

Conclusions:

• CRD-CG offers significant advantages in power and efficiency over basic RD.
• Empirical results align with theoretical predictions, supporting CRD-CG's superiority.
• CRD should be considered the preferred design for many applications currently using basic RD.