Decomposition of Inequality By an Extension of the Dinardo-Fortin-Lemieux Method: An Application to an Analysis of Gender Inequality in the Proportion of Managers in Japan

As a method for analyzing how inequality in one dimension is explained by inequalities in other dimensions, this paper introduces a method for the decomposition of a group difference in the outcome into several components, explained by differences in the covariate values among groups and a component unexplained by them. The method is an extension of the decomposition method introduced by DiNardo, Fortin and Lemieux (DFL) based on propensity-score weighting.  An application of this method focuses on the amount by which gender inequality in the proportion of managers is explained by sex differences in human-capital variables. The regression-based Blinder-Oaxaca (BO) method cannot be employed for a decomposition of the difference in proportion because the linear probability model cannot be specified as a regression model. Unlike the BO method, the DFL method can be applied to decompose a difference in proportion, but the latter does not permit a simple further decomposition of the explained component into elements explained by each covariate. The method introduced in this paper enables alternative sequential decompositions to assess the contribution of each variable to the explained component.

     Suppose we denote by C, birth cohorts, by E, the educational attainment, and by D, the employment duration, and the causal order, C→E→D. The decomposition of gender inequality in the proportion of managers by the forward order of equating the conditional distributions of C, E, and D between sexes leads to a sequential application of the DFL method and identifies the effects of C, E, and D including each variable’s indirect effects through causally posterior variables. The decomposition by the backward order of D, E, and C to assess the unique contribution of each covariate’s effect on gender inequality requires an extension of the DFL method, however. This paper demonstrates the usefulness of this extension.