Working Paper: NBER ID: w24944
Authors: Rodrigo Adao; Michal Kolesar; Eduardo Morales
Abstract: We study inference in shift-share regression designs, such as when a regional outcome is regressed on a weighted average of observed 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 that our methods yield substantially wider confidence intervals in popular applications of shift-share regression designs.
Keywords: Shift-share regression; Inference; Labor market outcomes; Economic shocks
JEL Codes: C13; C26; F16; F22
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| traditional standard error formulas (C46) | overrejection problem (D64) |
| correlation of regression residuals across regions with similar sectoral shares (C21) | overrejection problem (D64) |
| novel inference methods (C59) | wider confidence intervals (C46) |
| wider confidence intervals (C46) | more reliable inference in empirical applications (C20) |
| sector-level shocks are randomly assigned (L00) | valid confidence intervals (C46) |
| correlated residuals and shares (C29) | correct identification of causal effects (C32) |