Instrumental Variable Regression with Varying-Intensity Repeated Treatments

Abstract

Instrumental variable models with repeated endogenous treatments are popular in empirical research using pooled cross-sectional or short panel datasets. This paper proposes a novel semi-parametric approach that explicitly considers treatment effect dynamics by allowing for 1) path-dependency in the contemporaneous treatment effect and 2) a direct carryover effect from last period's treatment. We show that if either of these new features is present, the textbook two-stage least-squares estimator is generally invalid. We apply the proposed semi-parametric estimation and inference approach to revisit the work of Acemoglu et al. (2016). Using industry-level data, we find that the magnitude of contemporaneous impact of increased Chinese import competition on US manufacturing employment depends on an industry's past import exposure. In particular, industries with larger trade shocks in the 1990s tend to experience stronger impacts from contemporaneous trade shocks in the 2000s.

Keywords: repeated treatment, endogeneity, external instrument, treatment effect dynamics, path-dependent contemporaneous effect