🔎 What Was Examined

Shift-share regression designs—where a regional outcome is regressed on a weighted average of sectoral shocks using regional sector shares as weights—are evaluated for valid inference. A placebo exercise constructs a shift-share regressor from randomly generated sectoral shocks and estimates its effect on actual labor market outcomes across U.S. commuting zones.

📊 Placebo Test and Surprising Result

• Tests that rely on commonly used standard errors and a 5% nominal significance level reject the null hypothesis of no effect in up to 55% of placebo samples.
• The placebo thus reveals substantial overrejection relative to the nominal rate.

🧭 What Explains the Overrejection

A stylized economic model links the overrejection to correlation in regression residuals: regions with similar sectoral shares tend to have correlated residuals regardless of geographic proximity. That correlation structure violates assumptions underlying standard inference methods and produces biased rejection rates.

🛠️ New Inference Methods Developed

• Novel inference procedures are derived that remain valid under arbitrary cross-regional correlation in the regression residuals.
• These methods explicitly allow for residual correlation driven by similarity in sectoral shares rather than by geographic clustering.

📈 Practical Implications

• Applying the new methods to popular shift-share applications shows that confidence intervals can become substantially wider in practice.
• The results imply that conventional standard errors used in shift-share designs may understate uncertainty and overstate the precision of estimated effects.

💡 Bottom Line

Shift-share regressions are vulnerable to overrejection because of residual correlation tied to sectoral-share similarity. Inference procedures that accommodate arbitrary cross-regional residual correlation provide more reliable uncertainty quantification and often produce noticeably wider confidence intervals.