Considerations in Extending Shift‐Share Analysis: Note

One of the limitations to the widespread use of the Esteban‐Marquillas shift‐share extension has been the Stokes (1974) proof of the lack of regional additivity of the Esteban‐Marquillas competitive components. Since the Arcelus extension (1984) of the traditional shift‐share decomposition is a continuation of the logical framework by Esteban‐Marquillas (1972), the Stokes criticism would at first appear to have equal relevance to this new work. This note demonstrates that the relationship between the rate of growth of the larger region and the rates of growth of its constituent subregions is ignored in the Stokes criticism and in the subsequent critique by Beaudry and Martin (1979). By explicitly incorporating the relationship between the rate of growth of the larger region and the rates of growth of the constituent subregions, we also demonstrate that the recent shift‐share extensions by Esteban‐Marquillas and Arcelus share with the classical shift‐share decomposition the desirable additive properties under regional disaggregation of the data.