The Power Asymmetry in Fuzzy Regression Discontinuity Designs

In a fuzzy regression discontinuity (RD) design, the probability of treatment jumps when a running variable (R) passes a threshold (R0). Fuzzy RD estimates are obtained via a procedure analogous to two-stage least squares (2SLS), where an indicator I(R > R0) plays the role of the instrument. Recently, Keane and Neal (2023, 2024) showed that 2SLS t-tests suffer from a “power asymmetry”: 2SLS standard errors are spuriously small (large) when the 2SLS estimate is close to (far from) the OLS estimate. Here, we show that a similar problem arises in Fuzzy RD. Hence, if the endogeneity bias is positive, the Fuzzy RD t-test has little power to detect true negative effects, and inflated power to find false positives. The problem persists even if the instrument is very strong. To avoid this problem one should rely exclusively on the intent-to-treat (ITT) regression to assess significance of the treatment effect.