Testing for Essential Heterogeneity in the Marginal Treatment Effects Model

We propose a test for essential heterogeneity in the marginal treatment effects model without imposing additive separability. On the observed support of the propensity score, no essential heterogeneity implies that the conditional mean of the outcome is affine in the propensity score, and this affine restriction is the sharp testable implication of the null. We implement the test using a projected Gaussian-process statistic that is Neyman-orthogonal to the first-step estimation error, so the multiplier bootstrap avoids re-estimating nuisance parameters. Monte Carlo experiments show accurate size control and good power, and, unlike the fixed-scale integrated conditional moment benchmark, the data-driven median rule retains power as the conditioning set grows in dimension. In an application to the Ugandan ELA programme, the omnibus statistic rejects the null of no essential heterogeneity for aspirations at the midline follow-up.