🤖 AI Summary
This paper addresses the heterogeneity and nonlinearity of treatment effects in share-shift designs. We propose an identification framework that, under exogenous treatment shares, constructs a triangular model and incorporates a control function to correct for endogeneity, enabling systematic identification of four target parameters: (i) observable heterogeneity, (ii) a comprehensive heterogeneity measure, (iii) counterfactual policy allocation mechanisms, and (iv) their employment effects. Relative to conventional linear instrumental-variable approaches, our method uncovers pronounced heterogeneity and nonlinearity in the impact of Chinese import shocks on U.S. manufacturing employment—avoiding aggregation bias inherent in average-effect estimates. The proposed heterogeneity measure is both interpretable and policy-comparable. Empirical results demonstrate that the method substantially improves causal inference precision, overcoming a fundamental limitation of classical instruments in modeling structural heterogeneity.
📝 Abstract
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.