Shift-Share Designs: Theory and Inference

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.

Relaxing the Exclusion Restriction in Shift-Share Instrumental Variable Estimation

“…Recent methodological literature discusses ways in which the exclusion restriction in shiftshare estimation might be fulfilled (Borusyak, Hull, and Jaravel, 2018;Goldsmith-Pinkham, Sorkin, and Swift, 2018), ways in which it might be violated (Jaeger, Ruist, and Stuhler, 2018), diagnostics to analyze which instruments are prone to lead to a large bias of the estimator (Goldsmith-Pinkham, Sorkin, and Swift, 2018) and improved inference (Adão, Kolesár, and Morales, 2018). I contribute to this literature by applying newly developed methods to substantially relax the exclusion restriction, requiring that only a majority or a plurality of products needs to be valid.…”

“…In the following, I use the proposed methods in a Monte Carlo exercise to show that the methods outperform the standard shift-share estimator. I then reestimate the effect of Chinese import competition on employment with Autor, Dorn, and Hanson's (2013) data and of immigration on native labor market outcomes as in Adão, Kolesár, and Morales (2018). I first reproduce the original estimates by using the standard shift-share IV which uses all shift-share products, irrespectively of their validity.…”

Losing by Less? Import Competition, Unemployment Insurance Generosity, and Crime

“…It would take a 74% increase in our standard errors to fail to reject at the 10% significance level. These numbers are at or above the upper end of what Adão, Kolesár, and Morales (2018) illustrate is likely to happen when they explore alternative standard error corrections.…”

“…For instance, Goldsmith-Pinkham, Sorkin, and Swift (2018), Borusyak, Hull, and Jaravel (2018), and Adão, Kolesár, and Morales (2018) all have applications to the Autor, Dorn, and Hanson (2013) instrument used above. For instance, Goldsmith-Pinkham, Sorkin, and Swift (2018), Borusyak, Hull, and Jaravel (2018), and Adão, Kolesár, and Morales (2018) all have applications to the Autor, Dorn, and Hanson (2013) instrument used above.…”

“…Before proceeding to our main robustness checks, it is worth noting that a relatively recent literature has emerged on the econometrics of shift-share instruments that draw on regional employment patterns as the basis of their instrument. For instance, Goldsmith-Pinkham, Sorkin, and Swift (2018), Borusyak, Hull, and Jaravel (2018), and Adão, Kolesár, and Morales (2018) all have applications to the Autor, Dorn, and Hanson (2013) instrument used above. One of the central takeaways from these papers is that clustering standard errors at the state level may not be sufficient.…”