Since Bartik (1991), it has become popular in empirical studies to estimate regressions in which the variable of interest is a shift-share  , such as when a regional labor market outcome is regressed on a weighted average of observed sectoral shocks, using the regional sector shares as weights. 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. We derive novel confidence intervals that correctly account for the potential correlation in the regression residuals  .
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 .
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Since Bartik (1991), it has become popular in empirical studies to estimate regressions in which the variable of interest is a
We study inference in
A
regression designs
D
labor market
D
the
R
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
We conduct a placebo exercise in which we estimate
R
randomly generated placebo
a shift-share regressor constructed with randomly generated
R
in
across
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commuting zones, we find that a
Commuting Zones. Tests based on commonly used standard errors with
R
\% level significance test based on standard errors clustered at the state level rejects
\% nominal significance level reject
R
45
55
R
interventions. We derive novel confidence intervals that correctly account for the potential
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
A
. We show that our methods yield substantially wider confidence intervals in popular applications of shift-share regression designs