Shift-Share Designs: Theory and Inference
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.
We thank Kirill Borusyak, Peter Egger, Gordon Hanson, Bo Honoré, and seminar participants at Carleton University, Princeton University, Yale University, the Globalization & Inequality BFI conference, IDB, GTDW, Unil, EESP-FGV, PUCRio, and the Princeton-IES conference for very useful comments. We thank Juan Manuel Castro Vincenzi for excellent research assistance. We thank David Autor, David Dorn and Gordon Hanson for sharing their code and data. All errors are our own. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.
Rodrigo Adão & Michal Kolesár & Eduardo Morales, 2019. "Shift-Share Designs: Theory and Inference*," The Quarterly Journal of Economics, vol 134(4), pages 1949-2010.