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Taylor linearization sampling errors and design effects for poverty measures and other complex statistics

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  • Vijay Verma
  • Gianni Betti

Abstract

A systematic procedure for the derivation of linearized variables for the estimation of sampling errors of complex nonlinear statistics involved in the analysis of poverty and income inequality is developed. The linearized variable extends the use of standard variance estimation formulae, developed for linear statistics such as sample aggregates, to nonlinear statistics. The context is that of cross-sectional samples of complex design and reasonably large size, as typically used in population-based surveys. Results of application of the procedure to a wide range of poverty and inequality measures are presented. A standardized software for the purpose has been developed and can be provided to interested users on request. Procedures are provided for the estimation of the design effect and its decomposition into the contribution of unequal sample weights and of other design complexities such as clustering and stratification. The consequence of treating a complex statistic as a simple ratio in estimating its sampling error is also quantified. The second theme of the paper is to compare the linearization approach with an alternative approach based on the concept of replication, namely the Jackknife repeated replication (JRR) method. The basis and application of the JRR method is described, the exposition paralleling that of the linearization method but in somewhat less detail. Based on data from an actual national survey, estimates of standard errors and design effects from the two methods are analysed and compared. The numerical results confirm that the two alternative approaches generally give very similar results, though notable differences can exist for certain statistics. Relative advantages and limitations of the approaches are identified.

Suggested Citation

  • Vijay Verma & Gianni Betti, 2011. "Taylor linearization sampling errors and design effects for poverty measures and other complex statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(8), pages 1549-1576, August.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:8:p:1549-1576
    DOI: 10.1080/02664763.2010.515674
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    Cited by:

    1. Stephen P. Jenkins & Philippe Van Kerm, 2016. "Assessing Individual Income Growth," Economica, London School of Economics and Political Science, vol. 83(332), pages 679-703, October.
    2. Gianni Betti & Vasco Molini & Dan Pavelesku, 2023. "Using poverty maps to improve the design of household surveys: the evidence from Tunisia," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(5), pages 1641-1657, December.
    3. Margherita Casini & Simone Bastianoni & Francesca Gagliardi & Massimo Gigliotti & Angelo Riccaboni & Gianni Betti, 2019. "Sustainable Development Goals Indicators: A Methodological Proposal for a Multidimensional Fuzzy Index in the Mediterranean Area," Sustainability, MDPI, vol. 11(4), pages 1-25, February.
    4. Berger Yves G. & Munoz Juan F., 2015. "On Estimating Quantiles Using Auxiliary Information," Journal of Official Statistics, Sciendo, vol. 31(1), pages 101-119, March.
    5. Betti Gianni, 2014. "The effect of equivalence scales on poverty at Oblast level in Ukraine," Экономика региона, CyberLeninka;Федеральное государственное бюджетное учреждение науки «Институт экономики Уральского отделения Российской академии наук», issue 2, pages 78-88.
    6. Ilaria Benedetti & Federico Crescenzi & Tiziana Laureti, 2020. "Measuring Uncertainty for Poverty Indicators at Regional Level: The Case of Mediterranean Countries," Sustainability, MDPI, vol. 12(19), pages 1-19, October.
    7. Michal Brzezinski, 2011. "Variance Estimation for Richness Measures," LWS Working papers 11, LIS Cross-National Data Center in Luxembourg.
    8. Gianni Betti & Francesca Gagliardi, 2018. "Extension of JRR Method for Variance Estimation of Net Changes in Inequality Measures," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 137(1), pages 45-60, May.
    9. Yuyin Shi & Bing Liu & Gengsheng Qin, 2020. "Influence function-based empirical likelihood and generalized confidence intervals for the Lorenz curve," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 427-446, September.
    10. Federico Crescenzi & Gianni Betti & Francesca Gagliardi, 2015. "Comparing small area techniques for estimating poverty measures," Department of Economics University of Siena 721, Department of Economics, University of Siena.
    11. Brzezinski, Michal, 2013. "Asymptotic and bootstrap inference for top income shares," Economics Letters, Elsevier, vol. 120(1), pages 10-13.
    12. Pu, Christy & Lee, Miaw-Chwen & Hsieh, Tsung-Che, 2023. "Income-related inequality in out-of-pocket health-care expenditures under Taiwan's national health insurance system: An international comparable estimation based on A System of Health Accounts," Social Science & Medicine, Elsevier, vol. 326(C).
    13. Ilaria Benedetti & Gianni Betti & Federico Crescenzi, 2020. "Measuring Child Poverty and Its Uncertainty: A Case Study of 33 European Countries," Sustainability, MDPI, vol. 12(19), pages 1-12, October.
    14. Federico Crescenzi & Gianni Betti & Francesca Gagliardi, 2016. "Comparing Small Area Techniques for Estimating Poverty Measures: the Case Study of Austria and Spain," Economy of region, Centre for Economic Security, Institute of Economics of Ural Branch of Russian Academy of Sciences, vol. 1(2), pages 396-404.
    15. Gianni Betti, 2017. "What impact has the economic crisis had on quality of life in Europe? A multidimensional and fuzzy approach," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(1), pages 351-364, January.
    16. Gianni Betti & Rossella Soldi & Ilija Talev, 2016. "Fuzzy Multidimensional Indicators of Quality of Life: The Empirical Case of Macedonia," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 127(1), pages 39-53, May.
    17. Dioggban Jakperik & Romanus Otieno Odhiambo & George Otieno Orwa, 2019. "Inference on poverty indicators for Ghana," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(1), pages 1-4.
    18. Asma Zedini & Besma Belhadj, 2015. "A New Approach to Unidimensional Poverty Analysis: Application to the Tunisian Case," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 465-476, September.
    19. Gianni Betti & Francesca Gagliardi & Achille Lemmi & Vijay Verma, 2015. "Comparative measures of multidimensional deprivation in the European Union," Empirical Economics, Springer, vol. 49(3), pages 1071-1100, November.
    20. Verma, Vijay & Lemmi, Achille & Betti, Gianni & Gagliardi, Francesca & Piacentini, Mario, 2017. "How precise are poverty measures estimated at the regional level?," Regional Science and Urban Economics, Elsevier, vol. 66(C), pages 175-184.
    21. Benedetti, Ilaria & Crescenzi, Federico, 2023. "The role of income poverty and inequality indicators at regional level: An evaluation for Italy and Germany," Socio-Economic Planning Sciences, Elsevier, vol. 87(PA).
    22. Oguz Alper Melike & Berger Yves G., 2015. "Variance Estimation of Change in Poverty Rates: an Application to the Turkish EU-SILC Survey," Journal of Official Statistics, Sciendo, vol. 31(2), pages 155-175, June.
    23. Michal Brzezinski, 2014. "Statistical inference for richness measures," Applied Economics, Taylor & Francis Journals, vol. 46(14), pages 1599-1608, May.
    24. Vincenzo Salvucci & Gianni Betti & Francesca Gagliardi, 2012. "Multidimensional and Fuzzy Measures of Poverty and Inequality at National and Regional Level in Mozambique," Department of Economics University of Siena 649, Department of Economics, University of Siena.
    25. Marcel de Toledo Vieira & Maria de Fátima Salgueiro & Peter W. F. Smith, 2016. "Investigating impacts of complex sampling on latent growth curve modelling," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1310-1321, July.

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