Estimation and Inference on Nonlinear and Heterogeneous Effects

While multiple regression offers transparency, interpretability, and desirable theoretical properties, the method’s simplicity precludes the discovery of complex heterogeneities in the data. We introduce the Method of Direct Estimation and Inference, which embraces these potential complexities, is interpretable, has desirable theoretical guarantees, and, unlike some existing methods, returns appropriate uncertainty estimates. The proposed method uses a machine learning regression methodology to estimate the observation-level partial effect, or “slope,” of a treatment variable on an outcome and allows this value to vary with background covariates. Importantly, we introduce a robust approach to uncertainty estimates. Specifically, we combine a split sample and conformal strategy to fit a confidence band around the partial effect curve that will contain the true partial effect curve at some controlled proportion of the data, say 90% or 95%, even in the presence of model misspecification. Simulation evidence and an application illustrate the method’s performance.