Decomposition of Gender or Racial Inequality with Endogenous Intervening Covariates: An extension of the DiNardo-Fortin-Lemieux method

This paper first clarifies that, unlike propensity-score weighting in Rubin's causal model where confounding covariates can be endogenous, propensity-score weighting in the DiNardo-Fortin-Lemieux (DFL) decomposition analysis may generate biased estimates for the decomposition of inequality into"direct"and"indirect"components when intervening variables are endogenous. The paper also clarifies that the Blinder-Oaxaca method confounds the modeling of two distinct counterfactual situations: one where the covariate effects of the first group become equal to those of the second group, and the other where the covariate distribution of the second group becomes equal to that of the first group. The paper shows that the DFL method requires a distinct condition to provide an unbiased decomposition of inequality that remains under each counterfactual situation. The paper then introduces a combination of the DFL method with Heckman's two-step method as a way of testing and eliminating bias in the DFL estimate when some intervening covariates are endogenous. The paper also intends to bring gender and race back into the center of statistical causal analysis. An application focuses on the decomposition of gender inequality in earned income among white-collar regular employees in Japan.