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Hierarchical Bayes multivariate estimation of poverty rates based on increasing thresholds for small domains

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  • Fabrizi, Enrico
  • Ferrante, Maria Rosaria
  • Pacei, Silvia
  • Trivisano, Carlo

Abstract

A model-based small area method for calculating estimates of poverty rates based on different thresholds for subsets of the Italian population is proposed. The subsets are obtained by cross-classifying by household type and administrative region. The suggested estimators satisfy the following coherence properties: (i) within a given area, rates associated with increasing thresholds are monotonically increasing; (ii) interval estimators have lower and upper bounds within the interval (0, 1); (iii) when a large domain-specific sample is available the small area estimate is close to the one obtained using standard design-based methods; (iv) estimates of poverty rates should also be produced for domains for which there is no sample or when no poor households are included in the sample. A hierarchical Bayesian approach to estimation is adopted. Posterior distributions are approximated by means of MCMC computation methods. Empirical analysis is based on data from the 2005 wave of the EU-SILC survey.

Suggested Citation

  • Fabrizi, Enrico & Ferrante, Maria Rosaria & Pacei, Silvia & Trivisano, Carlo, 2011. "Hierarchical Bayes multivariate estimation of poverty rates based on increasing thresholds for small domains," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1736-1747, April.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:4:p:1736-1747
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    References listed on IDEAS

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    1. Chris Elbers & Jean O. Lanjouw & Peter Lanjouw, 2003. "Micro--Level Estimation of Poverty and Inequality," Econometrica, Econometric Society, vol. 71(1), pages 355-364, January.
    2. Sharon L. Lohr & J. N. K. Rao, 2009. "Jackknife estimation of mean squared error of small area predictors in nonlinear mixed models," Biometrika, Biometrika Trust, vol. 96(2), pages 457-468.
    3. Isabel Molina & Ayoub Saei & M. José Lombardía, 2007. "Small area estimates of labour force participation under a multinomial logit mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(4), pages 975-1000, October.
    4. Longford, Nicholas T., 2010. "Small area estimation with spatial similarity," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1151-1166, April.
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    Cited by:

    1. Bilton, Penny & Jones, Geoff & Ganesh, Siva & Haslett, Steve, 2017. "Classification trees for poverty mapping," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 53-66.
    2. Maria Rosaria Ferrante & Silvia Pacei, 2017. "Small domain estimation of business statistics by using multivariate skew normal models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1057-1088, October.
    3. 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.
    4. Fabrizi, Enrico & Trivisano, Carlo, 2016. "Small area estimation of the Gini concentration coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 223-234.
    5. Tsvetana Spasova, 2019. "Regional Income Distribution in the European Union: A Parametric Approach," Research on Economic Inequality, in: What Drives Inequality?, volume 27, pages 1-18, Emerald Group Publishing Limited.
    6. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    7. Enrico Fabrizi & Maria Rosaria Ferrante & Carlo Trivisano, 2020. "A functional approach to small area estimation of the relative median poverty gap," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1273-1291, June.
    8. Souza Debora F. & Moura Fernando A. S., 2016. "Multivariate Beta Regression with Application in Small Area Estimation," Journal of Official Statistics, Sciendo, vol. 32(3), pages 747-768, September.
    9. Enrico Fabrizi & Maria Ferrante & Carlo Trivisano, 2013. "Small area estimation of labor productivity for the Italian manufacturing SME cross-classified by region, industry and size," ERSA conference papers ersa13p894, European Regional Science Association.

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