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Social Indicators Research

, Volume 137, Issue 1, pp 45–60 | Cite as

Extension of JRR Method for Variance Estimation of Net Changes in Inequality Measures

  • Gianni Betti
  • Francesca Gagliardi
Article

Abstract

The linearisation approach to approximating variance of complex non-linear statistics is a well-established procedure. The basis of this approach is to reduce non-linear statistics to a linear form, justified on the basis of asymptotic properties of large populations and samples. For diverse cross-sectional measures of inequality such linearised forms are available, though the derivations involved can be complex. Replication methods based on repeated resampling of the parent sample provide an alternative approach to variance estimation of complex statistics from complex samples. These procedures can be computationally demanding but tend to be straightforward technically. Perhaps the simplest and the best established among these is the Jackknife Repeated Replication (JRR) method. Recently the JRR method has been shown to produce comparable variance for cross-sectional poverty measures (Verma and Betti in J Appl Stat 38(8):1549–1576, 2011); and it has also been extended to estimate the variance of longitudinal poverty measures for which Taylor approximation is not currently available, or at least cannot be easily derived. This paper extends the JRR methodology further to the estimation of variance of differences and averages of inequality measures. It illustrates the application of JRR methodology using data from four waves of the EU-SILC for Spain. For cross-sectional measures design effect can be decomposed into the effect of clustering and stratification, and that of weighting under both methodologies. For differences and averages of these poverty measures JRR method is applied to compute variance and three separate components of the design effect—effect of clustering and stratification, effect of weighting, and an additional effect due to correlation of different cross-sections from panel data—combining these the overall design effect can be estimated.

Keywords

Variance Linearisation Jackkinfe SILC Poverty Design effect Weighting 

References

  1. Alper, M. O., & Berger, Y. G. (2015). Variance estimation of change in poverty rates: An application to Turkish EU-SILC survey. Journal of Official Statistics, 31(2), 155–175.Google Scholar
  2. Berger, Y. G., & Priam, R. (2016). A simple variance estimator of change for rotating repeated surveys: An application to the EU-SILC household surveys. Journal of the Royal Statistical Society, Series A, 179(1), 251–272.CrossRefGoogle Scholar
  3. Berger, Y. G., & Skinner, C. J. (2003). Variance estimation of a low-income proportion. Journal of the Royal Statistical Society, Series C, 52, 457–468.CrossRefGoogle Scholar
  4. Betti, G., Gagliardi, F., Lemmi, A., & Verma, V. (2012). Sub-national indicators of poverty and deprivation in Europe: Methodology and applications. Cambridge Journal of Regions, Economy and Society, 5(1), 149–162.CrossRefGoogle Scholar
  5. Betti, G., Gagliardi, F., & Verma, V. (2016). Variance estimation for cumulative and longitudinal poverty indicators from panel data at regional level. In M. Pratesi (Ed.), Analysis of poverty data by small area estimation (pp. 129–147). Hoboken: Wiley.CrossRefGoogle Scholar
  6. Binder, D. A. (1983). On the variance of asymptotically normal estimators from complex surveys. International Statistical Review, 51, 279–292.CrossRefGoogle Scholar
  7. Binder, D. A., & Kovacevic, M. S. (1995). Estimating some measures of income inequality from survey data: An application of the estimation equation approach. Survey Methodology, 21, 137–145.Google Scholar
  8. Binder, D. A., & Patak, Z. (1994). Use of estimation functions for interval estimation from complex surveys. Journal of the American Statistical Association, 89, 1035–1043.CrossRefGoogle Scholar
  9. Demnati, A., & Rao, J. N. K. (2004). Linearization variance estimators for survey data. Survey Methodology, 30, 17–26.Google Scholar
  10. Deville, J. C. (1999). Variance estimation for complex statistics and estimators: Linearization and residual techniques. Survey Methodology, 25, 193–203.Google Scholar
  11. Elbers, C., Lanjouw, J. O., & Lanjouw, P. (2003). Micro-level estimation of poverty and inequality. Econometrica, 71(1), 355–364.CrossRefGoogle Scholar
  12. Gagliardi, F., Nandi, T. K., & Verma, V. (2006). Variance estimation of longitudinal measures of poverty. DMQ Working Paper 64, University of Siena.Google Scholar
  13. Giusti, C., Marchetti, S., Pratesi, M., & Salvati, N. (2012). Robust small area estimation and oversampling in the estimation of poverty indicators. Survey Research Methods, 6(3), 155–163.Google Scholar
  14. Goedemé, T. (2013). How much confidence can we have in EU-SILC? Complex sample design and standard error of the Europe 2020 poverty indicators. Social Indicators Research, 110, 89–110.CrossRefGoogle Scholar
  15. Graf, E., & Tillé, Y. (2014). Variance estimation using linearization for poverty and social exclusion indicators. Survey Methodology, 40(1), 61–79.Google Scholar
  16. Instituto Nacional De Estadistica (INE) (2012). Intermediate quality report, survey on income and living conditions Spain (Spanish ECV 2011).Google Scholar
  17. Kovacevic, M. S., & Yung, W. (1997). Variance estimation for measures of income inequality and polarization—an empirical study. Survey Methodology, 23(1), 41–52.Google Scholar
  18. Muennich, R., Zins, S. (2011). Variance estimation for indicators of poverty and social exclusion. Work package of the European project on Advanced Methodology for European Laeken Indicators (AMELI).Google Scholar
  19. Osier, G. (2009). Variance estimation for complex indicators of poverty and inequality using linearization techniques. Survey Research Methods, 3, 167–195.Google Scholar
  20. Piacentini, M. (2014). Measuring income inequality and poverty at the regional level in OECD countries. OECD Statistics Working Papers, 2014/03, OECD Publishing.Google Scholar
  21. Preston, I. (1995). Sampling distributions of relative poverty statistics. Applied Statistics, 44, 91–99.CrossRefGoogle Scholar
  22. Verma, V., & Betti, G. (2006). EU statistics on income and living conditions (EU-SILC): Choosing the survey structure and sample design. Statistics in Transition, 7(5), 935–970.Google Scholar
  23. Verma, V., & Betti, G. (2011). Taylor linearization sampling errors and design effects for poverty measures and other complex statistics. Journal of Applied Statistics, 38(8), 1549–1576.CrossRefGoogle Scholar
  24. Verma, V., Betti, G., & Gagliardi, F. (2010). Robustness of some EU-SILC based indicators at regional level, Eurostat methodologies and working papers. Luxembourg: Publications Office of the European Union.Google Scholar
  25. Verma, V., Betti, G., & Ghellini, G. (2007). Cross-sectional and longitudinal weighting in a rotational household panel: applications to EU-SILC. Statistics in Transition, 8(1), 5–50.Google Scholar
  26. Zheng, B. (2001). Statistical inference for poverty measures with relative poverty lines. Journal of Econometrics, 101, 337–356.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.University of SienaSienaItaly
  2. 2.University of PisaPisaItaly

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