Quasi-Experimental Shift-Share Research Designs

TL;DR

This paper introduces a new econometric framework for shift-share IV regressions, emphasizing the quasi-random assignment of shocks and allowing endogenous exposure shares, with practical applications to trade impact studies.

Contribution

It develops a novel theoretical approach for SSIV regressions that accounts for endogenous shares and links identification to shock-level orthogonality, enhancing causal inference.

Findings

Framework clarifies conditions for SSIV consistency

Application to US trade data shows robust estimates

Provides practical insights for empirical research

Abstract

Many studies use shift-share (or ``Bartik'') instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shift-share instrument and an unobserved residual can be represented as the orthogonality between the underlying shocks and a shock-level unobservable. SSIV regression coefficients can similarly be obtained from an equivalent shock-level regression, motivating shock-level conditions for their consistency. We discuss and illustrate several practical insights of this framework in the setting of Autor et al. (2013), estimating the effect of Chinese import competition on manufacturing employment across U.S. commuting zones.