Replication Data for: 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 (MDEI) that 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.尽管多元回归具备透明度、可解释性与优良的理论性质，但该方法的简单性使其无法发掘数据中存在的复杂异质性。本文提出直接估计与推断法（Method of Direct Estimation and Inference，MDEI），该方法可适配数据中的潜在复杂异质性，同时具备可解释性与优良的理论保障，且与部分现有方法不同，其能够生成恰当的不确定性估计。本文所提方法采用机器学习回归方法，对处理变量在结果变量上的观测层面偏效应（即"斜率"）进行估计，并允许该偏效应值随背景协变量发生变化。尤为重要的是，本文提出了一种针对不确定性估计的稳健方法：具体而言，我们结合拆分样本与保形策略，为偏效应曲线拟合置信带，该置信带可在指定受控数据占比（如90%或95%）下覆盖真实偏效应曲线，即便在存在模型设定偏误的场景下亦能实现这一目标。仿真实验与实际应用案例验证了该方法的性能表现。