  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.
