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Reducing bias and increasing precision by adding either a pretest measure of the study outcome or a nonequivalent comparison group to the basic regression discontinuity design

This paper raises three questions about CRD designs: first, to what extent do CRD-Pre and CRD-CG reduce bias and increase precision compared to RD? Second, which is better for reducing bias and increasing precision - CRD-Pre or CRD-CG? Third, to what extent are CRD-Pre and CRD-CG as good as the RCT in producing unbiased and precise estimates? To answer these questions, we will first estimate the usual RCT ATE as well as RCT local effects at and above the cutoff. These local effects also serve as benchmarks to compare with RD, CRD-Pre and CRD-CG. Second, we will check if the parallel assumption is met. Our hypothesis is that if the parallel assumption is met, CRD will produce unbiased causal estimates. When it is not met, the estimation of treatment effect is likely to suffer from bias. Third, to compare RD, CRD designs with RCT benchmarks, we propose our own criterion to define how similar the two estimates need to be in order to consider as though they are similar. Fourth, within the limit of our definition of accuracy, we will compare RD, CRD-Pre and CRD-CG estimates with RCT benchmarks to check the accuracy and precision of the estimates, both at and away from the cutoff. We will separate the results when the CRD parallel assumption is met and when it is not. Lastly, we will compare CRD designs with RD, CRD-Pre with CRD-CG, and CRD designs with RCT to study whether CRD designs improve RD, which CRD design has smaller bias and greater precision, and the performance of CRD designs relative to RCT. (author abstract)
Resource Type:
Reports & Papers
United States

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