A1650
Title: Optimal estimation for regression discontinuity design with binary outcomes
Authors: Takuya Ishihara - Tohoku University (Japan)
Kohei Yata - University of Wisconsin-Madison (United States)
Masayuki Sawada - Hitotsubashi University (Japan) [presenting]
Abstract: A finite-sample optimal estimator is developed for regression discontinuity design when outcomes are bounded, including binary outcomes as the leading case. The estimator achieves minimax mean squared error among linear shrinkage estimators with nonnegative weights when the regression function lies in a Lipschitz class. Although the original minimax problem involves an iterative nonconvex optimization problem, the estimator is obtained by solving a convex optimization problem. A key advantage of the proposed estimator is that the Lipschitz constant is its only tuning parameter. A uniformly valid inference procedure is also proposed without a large-sample approximation. In a simulation exercise for small samples, the estimator exhibits smaller mean squared errors and shorter confidence intervals than those of conventional large-sample techniques. In an empirical multi-cutoff design in which the sample size for each cutoff is small, the method yields informative confidence intervals, in contrast to the leading large-sample approach.
