We analyze heterogenous, nonlinear treatment effects in shift-share designs with exogenous shares. We employ a triangular model and correct for treatment endogeneity using a control function. Our tools identify four target parameters. Two of them capture the observable heterogeneity of treatment effects, while one summarizes this heterogeneity in a single measure. The last parameter analyzes counterfactual, policy-relevant treatment assignment mechanisms. We propose flexible parametric estimators for these parameters and apply them to reevaluate the impact of Chinese imports on U.S. manufacturing employment. Our results highlight substantial treatment effect heterogeneity, which is not captured by commonly used shift-share tools.

翻译：本文研究了具有外生份额的份额转移设计中异质且非线性的处理效应。我们采用三角模型，并利用控制函数校正处理的内生性问题。所提出的工具识别了四个目标参数：其中两个参数捕捉处理效应的可观测异质性，另一个参数将这种异质性汇总为单一度量指标，最后一个参数则用于分析反事实且具有政策相关性的处理分配机制。我们为这些参数提出了灵活的参数估计方法，并将其应用于重新评估中国进口对美国制造业就业的影响。研究结果揭示了显著的处理效应异质性，而常用的份额转移工具未能捕捉到这一特征。