A Uniform Confidence Band for the Marginal Treatment Effect Function

This paper presents a method for constructing uniform confidence bands for the marginal treatment effect (MTE) function. The shape of the MTE function provides insight into how the unobserved propensity to receive treatment relates 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. 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 application based on the rural electrification program is included.