Inter-Industry and Inter-Region Differentials: Mechanics and Interpretation

In their seminal study on inter-industry wage differentials, Krueger and Summers (1988) expressed estimated industry differences as deviations from a hypothetical employment-share weighted mean. Virtually the whole labor literature has followed their approach, yet most studies avoid calculating the exact standard errors of these differences. This note relates this problem to the general literature on dummy variables and their interpretation. It is demonstrated that the implementation of exact estimates only involves simple matrix operations making any approximative procedure difficult to justify. Disregarding this conclusion will in practice, even with large samples, lead to substantially overstated standard errors of the estimated differentials and to the understatement of their overall variability.