Skip to main content
SpringerLink
Log in

Confidence Interval Estimation for Inequality Indices of the Gini Family

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

In this paper we present some nonparametric bootstrap methods to constructdistribution-free confidence intervals for inequality indices belonging to theGini family. These methods have a coverage accuracy better than that obtainedwith the asymptotic distribution of their natural estimators, typically thestandard normal. The coverage performances of these methods are evaluated forthe index R by Gini with a Monte Carlo experiment on samples simulated fromthe Dagum income model (Type I), which is usually used to describe the incomedistribution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Beran, R.J. (1987). Prepivoting to reduce level error of confidence sets. Biometrika, 74, 457-468.

    Google Scholar 

  • Dagum, C. (1977). A new model of personal income distribution: specification and estimation. Economie Appliquée, 30, 413-436.

    Google Scholar 

  • Dagum, C. (1990). On the relationship between income inequality measures and social welfare functions. Journal of Econometrics, 48, 91-102.

    Google Scholar 

  • Dagum, C. and Lemmi, A. (eds.) (1995). Researches on Income Inequality. In D.J. Slotjee (ed.), Income Distribution, Social Welfare, Inequality and Poverty, Vol. VI, Jai Press, Greenwich.

  • David, H.A. (1981). Order Statistics. Wiley, New York.

    Google Scholar 

  • Davison, A.C. and Hinkley, D.V. (1997). Bootstrap Methods and their Applications. Cambridge University Press, Cambridge.

    Google Scholar 

  • Efron, B. (1979). Bootstrap methods: another look at the jackknife. The Annals of Statistics 7, 1-26.

    Google Scholar 

  • Efron, B. (1987). Better bootstrap confidence intervals (with discussion). Journal of the American Statistical Association, 82, 171-200.

    Google Scholar 

  • Efron, B. and Tibshirani, R.J. (1993). An Introduction to the Bootstrap. Chapman & Hall, New York.

    Google Scholar 

  • Fattorini, L. and Lemmi, A. (1979). Proposta di un modello alternativo per l'analisi della distribuzione del reddito. In Atti delle Giornate di Lavoro AIRO, Bologna, pp. 89-117.

  • Giorgi, G.M. and Provasi, C. (1995). An experimental analysis to verify some properties of inequality indices of the Gini family. In P. Barbini, C. Dagum, A. Lemmi and C. Provasi (eds.), Quantitative Methods for Applied Sciences, Nuova Immagine, Siena, pp. 254-285.

    Google Scholar 

  • Kahaner, D., Moler, C. and Nash, S. (1988). Numerical Methods and Software. Prentice Hall.

  • Kakwani, N.C. (1990). Large sample distribution of several inequality measures: with application to Cote d'Ivoire. In R.A.L. Carter, J. Dutta and A. Ullah (eds.), Contribution to Econometric: Theory and Application, Springer-Verlag, New York, pp. 50-81.

    Google Scholar 

  • Nygård, F. and Sandström, A. (1981). Measuring Income Inequality. Almqvist & Wiksell International, Stockholm.

    Google Scholar 

  • Nygård, F. and Sandström, A. (1989). Income inequality measures based on sample survey. Journal of Econometrics, 42, 81-95.

    Google Scholar 

  • Palmitesta, P., Provasi, C. and Spera, C. (1999). Approximated distributions of sampling inequality indices. Computational Economics, 13, 211-226.

    Google Scholar 

  • Salem, A.B.Z. and Mount, T.D. (1974). A convenient descriptive model of income distribution: the gamma density. Econometrica, 42, 1115-1127.

    Google Scholar 

  • Schmittlein, D.C. (1983). Some sampling properties of a model for income distribution. Journal of Business & Economic Statistics, 1, 147-153.

    Google Scholar 

  • Sendler, W. (1979). On statistical inference in concentration measurement. Metrika, 26, 109-122.

    Google Scholar 

  • Shao, J. and Tu, D. (1995). The Jackknife and Bootstrap. Springer-Verlag, New York.

    Google Scholar 

  • Shorack, G.R. (1972). Functions of order statistics. Ann. Math. Statist., 43, 412-427.

    Google Scholar 

  • Singh, S.K. and Maddala, G.S. (1976). A function for size distribution of incomes. Econometrica, 5, 963-970.

    Google Scholar 

  • Vinod, H.D. (1993). Bootstrap methods: applications in econometrics. In G.S. Maddala, C.R. Rao and H.D. Vinod (eds.), Econometrics, North-Holland, Amsterdam, pp. 629-662.

    Google Scholar 

  • Vinod, H.D. (1995). Double bootstrap for shrinkage estimators. Journal of Econometrics, 68, 287-302.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Quantitative Methods, University of Siena, P.zza S. Francesco 8, 53100, Siena, Italy

    Paola Palmitesta & Cosimo Spera

  2. Department of Statistical Sciences, University of Padova, Via S. Francesco 33, 35121, Padova, Italy

    Corrado Provasi

Authors
  1. Paola Palmitesta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Corrado Provasi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cosimo Spera
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Palmitesta, P., Provasi, C. & Spera, C. Confidence Interval Estimation for Inequality Indices of the Gini Family. Computational Economics 16, 137–147 (2000). https://doi.org/10.1023/A:1008761721593

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008761721593

Search

Navigation