IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v38y2011i8p1549-1576.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2010.515674
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2010.515674?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chattopadhyay, Amit K. & Mallick, Sushanta K., 2007. "Income distribution dependence of poverty measure: A theoretical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 241-252.
    2. Zheng, Buhong, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.
    3. Yitzhaki, Shlomo, 1991. "Calculating Jackknife Variance Estimators for Parameters of the Gini Method," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(2), pages 235-239, April.
    4. Yves G. Berger & Chris J. Skinner, 2003. "Variance estimation for a low income proportion," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 457-468, October.
    5. Ian Preston, 1995. "Sampling Distributions of Relative Poverty Statistics," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(1), pages 91-99, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tim Goedemé, 2013. "How much Confidence can we have in EU-SILC? Complex Sample Designs and the Standard Error of the Europe 2020 Poverty Indicators," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 110(1), pages 89-110, January.
    2. 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.
    3. Tim Goedemé & Karel Van den Bosch & Lina Salanauskaite & Gerlinde Verbist, 2013. "Testing the Statistical Significance of Microsimulation Results: Often Easier than You Think. A Technical Note," ImPRovE Working Papers 13/10, Herman Deleeck Centre for Social Policy, University of Antwerp.
    4. Tim Goedemé & Diego Collado, 2016. "The EU Convergence Machine at Work. To the Benefit of the EU's Poorest Citizens?," Journal of Common Market Studies, Wiley Blackwell, vol. 54(5), pages 1142-1158, September.
    5. Channing Arndt & Kenneth R. Simler, 2007. "Consistent poverty comparisons and inference," Agricultural Economics, International Association of Agricultural Economists, vol. 37(2‐3), pages 133-139, September.
    6. Kenneth R. Simler & Channing Arndt, 2007. "Poverty Comparisons With Absolute Poverty Lines Estimated From Survey Data," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(2), pages 275-294, June.
    7. Michal Brzezinski, 2011. "Variance Estimation for Richness Measures," LWS Working papers 11, LIS Cross-National Data Center in Luxembourg.
    8. Tim Goedemé & Lorena Zardo Trindade & Frank Vandenbroucke, 2017. "A Pan-European Perspective on Low-Income Dynamics in the EU," Working Papers 1703, Herman Deleeck Centre for Social Policy, University of Antwerp.
    9. Buhong Zheng, 2004. "Poverty comparisons with dependent samples," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 19(3), pages 419-428.
    10. Shan Luo & Gengsheng Qin, 2017. "New non-parametric inferences for low-income proportions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 599-626, June.
    11. Yves G. Berger & Chris J. Skinner, 2003. "Variance estimation for a low income proportion," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(4), pages 457-468, October.
    12. Brennan S. Thompson, 2013. "Empirical Likelihood-Based Inference for Poverty Measures with Relative Poverty Lines," Econometric Reviews, Taylor & Francis Journals, vol. 32(4), pages 513-523, December.
    13. Goedemé, Tim & Decerf, Benoit & Van den Bosch, Karel, 2020. "A new poverty indicator for Europe: the extended headcount ratio," INET Oxford Working Papers 2020-26, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
    14. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    15. Karoly, Lynn & Schröder, Carsten, 2015. "Fast methods for jackknifing inequality indices," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 37(1), pages 125-138.
    16. Wei Zou & Xiaopei Cheng & Zengzeng Fan & Wenxi Yin, 2023. "Multidimensional Relative Poverty in China: Identification and Decomposition," Sustainability, MDPI, vol. 15(6), pages 1-27, March.
    17. Barham, Bradford & Boucher, Stephen, 1998. "Migration, remittances, and inequality: estimating the net effects of migration on income distribution," Journal of Development Economics, Elsevier, vol. 55(2), pages 307-331, April.
    18. Li, Jiaxin & Wang, Zihan & Cheng, Xin & Shuai, Jing & Shuai, Chuanmin & Liu, Jing, 2020. "Has solar PV achieved the national poverty alleviation goals? Empirical evidence from the performances of 52 villages in rural China," Energy, Elsevier, vol. 201(C).
    19. Joachim Frick & Jan Goebel, 2008. "Regional Income Stratification in Unified Germany Using a Gini Decomposition Approach," Regional Studies, Taylor & Francis Journals, vol. 42(4), pages 555-577.
    20. Carsten Schröder & Yolanda Golan & Shlomo Yitzhaki, 2014. "Inequality and the time structure of earnings: evidence from Germany," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(3), pages 393-409, September.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:japsta:v:38:y:2011:i:8:p:1549-1576. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.