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Model-Based Estimation of Small Area Dissimilarity Indexes: An Application to Sex Occupational Segregation in Spain

Author

Listed:
  • María Bugallo

    (Miguel Hernández University of Elche)

  • Domingo Morales

    (Miguel Hernández University of Elche)

  • María Dolores Esteban

    (Miguel Hernández University of Elche)

  • Maria Chiara Pagliarella

    (Universita degli Studi di Cassino e del Lazio Meridionale)

Abstract

This paper introduces a new statistical methodology for estimating Duncan dissimilarity indexes of occupational segregation by sex in administrative areas and time periods. Given that direct estimators of the proportion of men (or women) in the group of employed people for each occupational sector are not accurate enough in the considered estimation domains, we fit to them a three-fold Fay–Herriot model with random effects at three hierarchical levels. Based on the fitted area-level model, empirical best predictors of the cited proportions and Duncan segregation indexes are derived. A parametric bootstrap algorithm is implemented to estimate the mean squared error. Some simulation studies are included to show how the proposed predictors have a good balance between bias and mean squared error. Data from the Spanish Labour Force Survey are used to illustrate the performance of the new statistical methodology and to give some light about the current state of sex occupational segregation by province in Spain. Research claims that there is a sex gap that persists despite advances in the inclusion of women in the labour market in recent years and that is related to the unequal sharing of family responsabilities and the stigmas still present in modern societies.

Suggested Citation

  • María Bugallo & Domingo Morales & María Dolores Esteban & Maria Chiara Pagliarella, 2024. "Model-Based Estimation of Small Area Dissimilarity Indexes: An Application to Sex Occupational Segregation in Spain," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 174(2), pages 473-501, September.
    • Handle: RePEc:spr:soinre:v:174:y:2024:i:2:d:10.1007_s11205-024-03393-w
    DOI: 10.1007/s11205-024-03393-w
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    References listed on IDEAS

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    1. Marchetti, Stefano & Tzavidis, Nikos & Pratesi, Monica, 2012. "Non-parametric bootstrap mean squared error estimation for M-quantile estimators of small area averages, quantiles and poverty indicators," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2889-2902.
    2. Branko Milanovic & Paola Salardi, 2016. "The Evolution of Gender and Racial Occupational Segregation Across Formal and Non-Formal Labor Markets in Brazil, 1987 to 2006," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62, pages 68-89, August.
    3. Jan Pablo Burgard & Joscha Krause & Domingo Morales, 2022. "A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 204-234, March.
    4. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "$$\ell _2$$ ℓ 2 -penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 459-489, May.
    5. Marhuenda, Yolanda & Molina, Isabel & Morales, Domingo, 2013. "Small area estimation with spatio-temporal Fay–Herriot models," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 308-325.
    6. Nikos Tzavidis & Nicola Salvati & Monica Pratesi & Ray Chambers, 2008. "M-quantile models with application to poverty mapping," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 393-411, July.
    7. Miguel Boubeta & María José Lombardía & Domingo Morales, 2016. "Empirical best prediction under area-level Poisson mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 548-569, September.
    8. Boubeta, Miguel & Lombardía, María José & Morales, Domingo, 2017. "Poisson mixed models for studying the poverty in small areas," Computational Statistics & Data Analysis, Elsevier, vol. 107(C), pages 32-47.
    9. Das, Smita & Kotikula, Aphichoke, 2019. "Gender-Based Employment Segregation: Understanding Causes and Policy Interventions," Jobs Group Papers, Notes, and Guides 30947812, The World Bank.
    10. Yolanda Marhuenda & Isabel Molina & Domingo Morales & J. N. K. Rao, 2017. "Poverty mapping in small areas under a twofold nested error regression model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1111-1136, October.
    11. Esther López-Vizcaíno & María José Lombardía & Domingo Morales, 2015. "Small area estimation of labour force indicators under a multinomial model with correlated time and area effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 535-565, June.
    12. María Dolores Esteban & María José Lombardía & Esther López‐Vizcaíno & Domingo Morales & Agustín Pérez, 2022. "Empirical best prediction of small area bivariate parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1699-1727, December.
    13. Tomáš Hobza & Domingo Morales & Laureano Santamaría, 2018. "Small area estimation of poverty proportions under unit-level temporal binomial-logit mixed models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 270-294, June.
    14. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    15. Roberto Benavent & Domingo Morales, 2021. "Small area estimation under a temporal bivariate area-level linear mixed model with independent time effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 195-222, March.
    16. Domingo Morales & Joscha Krause & Jan Pablo Burgard, 2022. "On the Use of Aggregate Survey Data for Estimating Regional Major Depressive Disorder Prevalence," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 344-368, March.
    17. González-Manteiga, W. & Lombardi­a, M.J. & Molina, I. & Morales, D. & Santamari­a, L., 2008. "Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5242-5252, August.
    18. Esteban, M.D. & Morales, D. & Pérez, A. & Santamaría, L., 2012. "Small area estimation of poverty proportions under area-level time models," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2840-2855.
    19. Song Cai & J.N.K. Rao, 2022. "Selection of Auxiliary Variables for Three-Fold Linking Models in Small Area Estimation: A Simple and Effective Method," Stats, MDPI, vol. 5(1), pages 1-11, February.
    20. Ray Chambers & Nicola Salvati & Nikos Tzavidis, 2016. "Semiparametric small area estimation for binary outcomes with application to unemployment estimation for local authorities in the UK," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(2), pages 453-479, February.
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