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 crossregional correlation in the regression residuals. We show that our methods yield substantially wider confidence intervals in popular applications of shift-share regression designs.

Globalization, robotization, and electoral outcomes: Evidence from spatial regressions for Italy

“…Do voters' decisions map any differences across LLMAs that are correlated with variations in the local economic structure but not with the shocks of interest? To address these questions and to shed light on the mechanisms driving the results, we use state‐of‐the‐art methodologies developed to analyze the identification approach based on a shift–share IV (Adão et al, 2018; Borusyak et al, 2018; Goldsmith‐Pinkham et al, 2020).…”

“…This approach is widely used in the literature that studies labor market developments and voting patterns on the basis of the differentiated regional exposure to common shocks. Recent technical advances make it possible to investigate the validity of such design and to refine the interpretation of the findings associated with it (Adão et al, 2018; Borusyak et al, 2018; Goldsmith‐Pinkham et al, 2020). By employing such state‐of‐the‐art techniques, in Section 4.3 we shall discuss the plausibility of the identification strategy and exploit the Rotemberg decomposition of the shift–share IV to interpret the results.…”

“…Furthermore, by employing state‐of‐the‐art methodologies developed to analyze the sources and the validity of the identification based on shift–share instrumental variables (IVs; Adão, Kolesár, & Morales, 2018; Borusyak, Hull, & Jaravel, 2018; Goldsmith‐Pinkham, Sorkin, & Swift, 2020), we provide evidence on the plausibility of the identification strategy for assessing the impact of Chinese import competition on the local electoral outcomes. The analysis supports the validity of the shift–share IV approach in both periods and it makes it possible to appreciate that, in the second time span, the impact of the China shock is differentiated across industries as certain sectors benefited from the expansion of Chinese exports to other advanced countries, while others suffered from the direct competition.…”

Spatial skill concentration agglomeration economies

“…The use of shift‐share or Bartik instruments in economics is widespread and growing. A manifestation of the current interest in the subject are the contributions on the validity, exogeneity, and asymptotic properties of shift‐share instruments by Adão et al (2019), Borusyak et al (2018), and Goldsmith‐Pinkham et al (2018). Using Bartik‐style instruments is particularly appealing in the present case because the calculation of the skill concentration measures is already based on the shift‐share logic.…”

“…Shift‐share instruments have been popular in economics since Bartik (1991) and Altonji and Card (1991). The properties and validity of this type of instrument are thoroughly reviewed by Adão, Kolesár, and Morales (2019), Borusyak, Hull, and Jaravel (2018) and Goldsmith‐Pinkham, Sorkin, and Swift (2018). In the present case, the endogenous variable, that is the local concentration of skills can be calculated by summing the share of individuals employed in occupation in municipality times their skill value across occupations.…”