Overidentification in Shift-Share Designs

TL;DR

This paper examines the testability of identifying restrictions in shift-share (Bartik) instruments for causal inference, proposing robust overidentification tests and analyzing their implications in short panel data settings.

Contribution

It introduces overidentification tests for shift-share instruments that are valid in high-dimensional, heteroskedastic, and clustered data regimes, and clarifies their importance in short panel analyses.

Findings

Proposes overidentification tests valid in high-dimensional settings.

Shows limitations of long panel strategies in short panel contexts.

Highlights empirical relevance using US labor market data.

Abstract

This paper studies the testability of identifying restrictions commonly employed to assign a causal interpretation to two stage least squares (TSLS) estimators based on Bartik instruments. For homogeneous effects models applied to short panels, our analysis yields testable implications previously noted in the literature for the two major available identification strategies. We propose overidentification tests for these restrictions that remain valid in high dimensional regimes and are robust to heteroskedasticity and clustering. We further show that homogeneous effect models in short panels, and their corresponding overidentification tests, are of central importance by establishing that: (i) In heterogenous effects models, interpreting TSLS as a positively weighted average of treatment effects can impose implausible assumptions on the distribution of the data; and (ii) Alternative identifying strategies relying on long panels can prove uninformative in short panel applications. We highlight the empirical relevance of our results by examining the viability of Bartik instruments for identifying the effect of rising Chinese import competition on US local labor markets.