We investigate the consequences of discreteness in the assignment variable in regression-discontinuity designs for cases where the outcome variable is itself discrete. We find that constructing confidence intervals that have the correct level of coverage in these cases is sensitive to the assumed distribution of unobserved heterogeneity. Since local linear estimators are improperly centered, a smaller variance for unobserved heterogeneity in discrete outcomes actually requires larger confidence intervals, since standard confidence intervals become narrower around a biased estimator, leading to a higher-than-nominal false positive rate. We provide a method for mapping structural assumptions regarding the distribution and variance of unobserved heterogeneity to the construction of “honest” confidence intervals that have the correct level of coverage. An application to retirement behavior reveals that the spike in retirement at age 62 in the United States can be reconciled with a wider range of values for the variance of unobserved heterogeneity (due to reservation wages or offers) than the spike at age 65.
Centre for microdata methods and practice