Shift-Share Designs: Theory and Inference

TL;DR

This paper examines the limitations of current inference methods in shift-share regressions, demonstrating overrejection issues and proposing new methods for valid inference accounting for cross-regional correlation.

Contribution

It introduces novel inference techniques that address residual correlation in shift-share designs, improving the reliability of statistical conclusions.

Findings

Standard errors often lead to overrejection of null hypotheses.

Residuals are correlated across regions with similar sectoral shares.

New methods produce wider, more accurate confidence intervals.

Abstract

We study inference in shift-share regression designs, such as when a regional outcome is regressed on a weighted average of sectoral shocks, using regional sector shares as weights. We conduct a placebo exercise in which we estimate the effect of a shift-share regressor constructed with randomly generated sectoral shocks on actual labor market outcomes across U.S. Commuting Zones. Tests based on commonly used standard errors with 5\% nominal significance level reject the null of no effect in up to 55\% of the placebo samples. We use a stylized economic model to show that this overrejection problem arises because regression residuals are correlated across regions with similar sectoral shares, independently of their geographic location. We derive novel inference methods that are valid under arbitrary cross-regional correlation in the regression residuals. We show using popular applications of shift-share designs that our methods may lead to substantially wider confidence intervals in practice.