Before revision:  In this paper, we discuss inference in these regressions. We show that standard economic models imply that the regression residuals are likely to be correlated across regions with similar sector shares, independently of their geographic location. These correlations are ignored by inference procedures commonly used in these regressions, which can lead to severe undercoverage. In regressions studying the effect of randomly generated placebo sectoral shocks on actual labor market outcomes in U.S. commuting zones, we find that a 5 \% level significance test based on standard errors clustered at the state level rejects the null of no effect in up to 45 \% of the placebo interventions.
After revision:  We conduct a placebo exercise in which we estimate the effect of randomly generated placebo sectoral shocks on actual labor market outcomes in U.S. commuting zones, we find that a 5 \% level significance test based on standard errors clustered at the state level rejects the null of no effect in up to 45 \% of the placebo interventions.