An RCM Approach to Causal Inference with Two-level Data and Unobserved Social Contextual Heterogeneity: An application for the decomposition analysis of the gender income gap and the gender gap in positional rank in Japan

This article introduces a new RCM method based on the inverse probability of treatment weighting for the analysis of two-level data of individuals and their social contexts when we expect unobserved contextual effects on the treatment and outcome. The method is an alternative to the use of fixed effects for social contexts in the estimation of propensity score when the fixed effects cannot be included in the estimation of propensity score due to small sample sizes for a non-negligible number of social contexts. The method is based on a novel ignorability assumption that may hold in many cases and permits the elimination of confounding unobserved contextual effects under such a situation. An application of the new method to the decomposition analysis of inequality by combining it with the DiNardo-Fortin-Lemieux method focuses on the decomposition of the gender income gap and gender gap in positional rank among white-collar regular employees in Japan when their employers are the social contexts. The application provides findings that are consistent with the hypotheses that women tend to remain employed in firms for which their relative income and relative opportunity of being promoted to supervisory positions compared with men are better than in other firms, and that the gender gap is consequently reduced among those who remain employed.