Nonlinear Treatment Effects in Shift-Share Designs

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.