In the regression discontinuity design, it is common practice to asses the credibility of the design by testing whether the means of baseline covariates do not change at the cuto ff (or threshold) of the running variable. This practice is partly motivated by the stronger implication derived by Lee (2008), who showed that under certain conditions the distribution of baseline covariates in the RDD must be continuous at the cuto ff. We propose a permutation test based on the so-called induced ordered statistics for the null hypothesis of continuity of the distribution of baseline covariates at the cutoff ; and introduce a novel asymptotic framework to analyze its properties. The asymptotic framework is intended to approximate a small sample phenomenon: even though the total number n of observations may be large, the number of eff ective observations local to the cuto ff is often small. Thus, while traditional asymptotics in RDD require a growing number of observations local to the cuto ff as n → ∞ , our framework keeps the number q of observations local to the cutoff fixed as n → ∞. The new test is easy to implement, asymptotically valid under weak conditions, exhibits finite sample validity under stronger conditions than those needed for its asymptotic validity, and has favorable power properties relative to tests based on means. In a simulation study, we find that the new test controls size remarkably well across designs. We then use our test to evaluate the validity of the design in Lee (2008), a well-known application of the RDD to study incumbency advantage.
Approximate permutation tests and induced order statistics in the regression discontinuity design
19 August 2016
Working Paper (CWP33/16)