Uniform Confidence Band for Marginal Treatment Effect Function

TL;DR

This paper introduces a computationally simple method for constructing uniform confidence bands for the marginal treatment effect function, aiding interpretation of treatment effects and unobserved heterogeneity.

Contribution

It develops a Gaussian approximation-based approach for confidence bands that requires minimal data, applicable to both new and published studies.

Findings

Bands achieve correct coverage probabilities

Bands are less conservative than Gumbel-based methods

Method performs well in Monte Carlo simulations

Abstract

This paper presents a method for constructing uniform confidence bands for the marginal treatment effect (MTE) function. The shape of the MTE function offers insight into how the unobserved propensity to receive treatment is related to the treatment effect. Our approach visualizes the statistical uncertainty of an estimated function, facilitating inferences about the function's shape. The proposed method is computationally inexpensive and requires only minimal information: sample size, standard errors, kernel function, and bandwidth. This minimal data requirement enables applications to both new analyses and published results without access to original data. We derive a Gaussian approximation for a local quadratic estimator and consider the approximation of the distribution of its supremum in polynomial order. Monte Carlo simulations demonstrate that our bands provide the desired coverage and are less conservative than those based on the Gumbel approximation. An empirical illustration regarding the returns to education is included.