  We propose a one-to-many matching estimator of the average treatment effect
based on propensity scores estimated by isotonic regression. The method relies
on the monotonicity assumption on the propensity score function, which can be
justified in many applications in economics. We show that the nature of the
isotonic estimator can help us to fix many problems of existing matching
methods, including efficiency, choice of the number of matches, choice of
tuning parameters, robustness to propensity score misspecification, and
bootstrap validity. As a by-product, a uniformly consistent isotonic estimator
is developed for our proposed matching method.
