IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v71y2013i2p97-104.html
   My bibliography  Save this article

The relationship between the absolute deviation from a quantile and Gini’s mean difference

Author

Listed:
  • Shlomo Yitzhaki
  • Peter Lambert

Abstract

We investigate the relationship between Gini’s mean difference (GMD), the mean absolute deviation, the least absolute deviation and the absolute deviation from a quantile. The latter can all be interpreted as equivalents either to the GMD of a transformed distribution or to a between-group GMD measure, according to the particular partition of the data. They all possess properties of the GMD but each omits the intra-group variability—and they give rise to different regression techniques. We argue that the analyst using one of these techniques should justify the omission of the intra-group variability from the analysis. Copyright Sapienza Università di Roma 2013

Suggested Citation

  • Shlomo Yitzhaki & Peter Lambert, 2013. "The relationship between the absolute deviation from a quantile and Gini’s mean difference," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 97-104, September.
    • Handle: RePEc:spr:metron:v:71:y:2013:i:2:p:97-104
    DOI: 10.1007/s40300-013-0015-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s40300-013-0015-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s40300-013-0015-y?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. Peter J. Lambert & Andre' Decoster, 2005. "The Gini coefficient reveals more," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 373-400.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731.
    3. Liang Peng, 2003. "Least absolute deviations estimation for ARCH and GARCH models," Biometrika, Biometrika Trust, vol. 90(4), pages 967-975, December.
    4. Frick, Joachim R. & Goebel, Jan & Schechtman, Edna & Wagner, Gert G. & Yitzhaki, Shlomo, 2006. "Using Analysis of Gini (ANOGI) for Detecting Whether Two Subsamples Represent the Same Universe: The German Socio-Economic Panel Study (SOEP) Experience," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 34(4), pages 427-468.
    5. Frick, Joachim R. & Goebel, Jan & Schechtman, Edna & Wagner, Gert G. & Yitzhaki, Shlomo, 2004. "Using Analysis of Gini (ANoGi) for Detecting Whether Two Sub-Samples Represent the Same Universe: The SOEP Experience," IZA Discussion Papers 1049, Institute of Labor Economics (IZA).
    6. Schechtman, E. & Yitzhaki, S., 1999. "On the proper bounds of the Gini correlation," Economics Letters, Elsevier, vol. 63(2), pages 133-138, May.
    7. Edna Schechtman & Shlomo Yitzhaki & Taina Pudalov, 2011. "Gini’s multiple regressions: two approaches and their interaction," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 67-99.
    8. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    9. Yitzhaki, Shlomo, 2002. "Do we need a separate poverty measurement?," European Journal of Political Economy, Elsevier, vol. 18(1), pages 61-85, March.
    10. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    11. Yusif Simaan, 1997. "Estimation Risk in Portfolio Selection: The Mean Variance Model Versus the Mean Absolute Deviation Model," Management Science, INFORMS, vol. 43(10), pages 1437-1446, October.
    12. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    13. Pakes, Ariel, 1982. "On the Asymptotic Bias of Wald-Type Estimators of a Straight Line When Both Variables Are Subject to Error," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 23(2), pages 491-497, June.
    14. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    15. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Téa Ouraga, 2019. "A note on Gini Principal Component Analysis," Economics Bulletin, AccessEcon, vol. 39(2), pages 1076-1083.
    2. Iddo Eliazar & Giovanni M. Giorgi, 2020. "From Gini to Bonferroni to Tsallis: an inequality-indices trek," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 119-153, August.
    3. Shlomo Yitzhaki & Peter Lambert, 2014. "Is higher variance necessarily bad for investment?," Review of Quantitative Finance and Accounting, Springer, vol. 43(4), pages 855-860, November.
    4. Ndene Ka & Stephane Mussard, 2015. "l1 Regressions: Gini Estimators for Fixed Effects Panel Data," Cahiers de recherche 15-02, Departement d'économique de l'École de gestion à l'Université de Sherbrooke.
    5. Ndéné Ka & Stéphane Mussard, 2016. "ℓ 1 regressions: Gini estimators for fixed effects panel data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1436-1446, June.
    6. Ndéné Ka & Stéphane Mussard, 2015. "Book Review of The Gini Methodology: A Primer on a Statistical Methodology," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 13(2), pages 321-324, June.

    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. Edna Schechtman & Shlomo Yitzhaki & Taina Pudalov, 2011. "Gini’s multiple regressions: two approaches and their interaction," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 67-99.
    2. Giovanni Bonaccolto & Massimiliano Caporin & Sandra Paterlini, 2018. "Asset allocation strategies based on penalized quantile regression," Computational Management Science, Springer, vol. 15(1), pages 1-32, January.
    3. Javier Alejo, 2013. "Relación de Kuznets en América Latina. Explorando más allá de la media condicional," Económica, Departamento de Economía, Facultad de Ciencias Económicas, Universidad Nacional de La Plata, vol. 59, pages 3-55, January-D.
    4. Wagner Piazza Gaglianone & Luiz Renato Lima & Oliver Linton & Daniel R. Smith, 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 150-160, January.
    5. Halkos, George E., 2011. "Nonparametric modelling of biodiversity: Determinants of threatened species," Journal of Policy Modeling, Elsevier, vol. 33(4), pages 618-635, July.
    6. Halkos, George, 2010. "Modelling biodiversity," MPRA Paper 39075, University Library of Munich, Germany.
    7. Thomas Q. Pedersen, 2015. "Predictable Return Distributions," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(2), pages 114-132, March.
    8. Krüger, Steffen & Rösch, Daniel, 2017. "Downturn LGD modeling using quantile regression," Journal of Banking & Finance, Elsevier, vol. 79(C), pages 42-56.
    9. Zhu, Min, 2013. "Return distribution predictability and its implications for portfolio selection," International Review of Economics & Finance, Elsevier, vol. 27(C), pages 209-223.
    10. Marcel, Bräutigam & Marie, Kratz, 2018. "On the Dependence between Quantiles and Dispersion Estimators," ESSEC Working Papers WP1807, ESSEC Research Center, ESSEC Business School.
    11. Lu, Xun & Su, Liangjun, 2015. "Jackknife model averaging for quantile regressions," Journal of Econometrics, Elsevier, vol. 188(1), pages 40-58.
    12. repec:wyi:journl:002112 is not listed on IDEAS
    13. Fan, Rui & Lee, Ji Hyung, 2019. "Predictive quantile regressions under persistence and conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(1), pages 261-280.
    14. Gaglianone, Wagner Piazza & Guillén, Osmani Teixeira de Carvalho & Figueiredo, Francisco Marcos Rodrigues, 2018. "Estimating inflation persistence by quantile autoregression with quantile-specific unit roots," Economic Modelling, Elsevier, vol. 73(C), pages 407-430.
    15. Paolo Liberati & Shlomo Yitzhaki, 2012. "GDP and beyond: an implementation of welfare considerations to the distribution of earnings in Italy," Departmental Working Papers of Economics - University 'Roma Tre' 0146, Department of Economics - University Roma Tre.
    16. Huber, Martin & Melly, Blaise, 2011. "Quantile Regression in the Presence of Sample Selection," Economics Working Paper Series 1109, University of St. Gallen, School of Economics and Political Science.
    17. Yang, Lu & Tian, Shuairu & Yang, Wei & Xu, Mingli & Hamori, Shigeyuki, 2018. "Dependence structures between Chinese stock markets and the international financial market: Evidence from a wavelet-based quantile regression approach," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 116-137.
    18. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    19. Narula, Subhash C. & Wellington, John F. & Lewis, Stephen A., 2012. "Valuating residential real estate using parametric programming," European Journal of Operational Research, Elsevier, vol. 217(1), pages 120-128.
    20. Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
    21. M. Grazia Pittau & Shlomo Yitzhaki & Roberto Zelli, 2011. "The make-up of a regression coefficient: An application to gender," DSS Empirical Economics and Econometrics Working Papers Series 2011/3, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.

    More about this item

    Keywords

    GMD; LAD; MAD; QUAD; C2; C10; C58;
    All these keywords.

    JEL classification:

    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

    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:spr:metron:v:71:y:2013:i:2:p:97-104. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.