Predicting gender employment discrepancies: A multivariate Fay-Herriot model for transformed proportions

Exposure indices measure the degree of contact between two groups and are used to quantify occupational discrepancies between genders in a set of occupational sectors. This paper presents a novel methodology for predicting area-level proportions of employed men and women across various occupation sectors, along with estimating exposure indexes. The challenge arises from the compositional nature of the direct estimators of proportions, which tend to be imprecise when sample sizes are small. To overcome this problem, we propose to use a compositional multivariate Fay–Herriot model. By applying log-ratio transformations to the direct estimators of proportions, we can effectively capture the underlying structure and dependencies within the data. Small area estimators for proportions and exposure indexes are derived from the fitted model, and their corresponding root-mean-squared errors are estimated using parametric bootstrap techniques. To demonstrate the applicability of our approach, we conduct a case study using data from quarters 3 and 4 of the Spanish Labour Force Survey of 2022. The primary objective is to investigate the state of gender occupational segregation in Spanish provinces, thereby providing valuable insights into this socioeconomic phenomenon.