IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01457398.html
   My bibliography  Save this paper

Statistical Methods for Distributional Analysis

Author

Listed:
  • Frank A. Cowell

    (STICERD - LSE - London School of Economics and Political Science)

  • Emmanuel Flachaire

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

Abstract

This Chapter is about the techniques, formal and informal, that are commonly used to give quantitative answers in the field of distributional analysis - covering subjects including inequality, poverty and the modelling of income distributions. It deals with parametric and non-parametric approaches and the way in which imperfections in data may be handled in practice.

Suggested Citation

  • Frank A. Cowell & Emmanuel Flachaire, 2015. "Statistical Methods for Distributional Analysis," Post-Print hal-01457398, HAL.
    • Handle: RePEc:hal:journl:hal-01457398
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    2. Russell Davidson & Jean-Yves Duclos, 1997. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, Econometric Society, vol. 65(6), pages 1453-1466, November.
    3. DiNardo, John & Fortin, Nicole M & Lemieux, Thomas, 1996. "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach," Econometrica, Econometric Society, vol. 64(5), pages 1001-1044, September.
    4. Facundo Alvaredo & Emmanuel Saez, 2009. "Income and Wealth Concentration in Spain from a Historical and Fiscal Perspective," Journal of the European Economic Association, MIT Press, vol. 7(5), pages 1140-1167, September.
    5. John Dagsvik & Zhiyang Jia & Bjørn Vatne & Weizhen Zhu, 2013. "Is the Pareto–Lévy law a good representation of income distributions?," Empirical Economics, Springer, vol. 44(2), pages 719-737, April.
    6. Jianqing Fan & Tsz Ho Yim, 2004. "A crossvalidation method for estimating conditional densities," Biometrika, Biometrika Trust, vol. 91(4), pages 819-834, December.
    7. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    8. Bishop, John A. & Chakraborti, S. & Thistle, Paul D., 1988. "Large sample tests for absolute Lorenz dominance," Economics Letters, Elsevier, vol. 26(3), pages 291-294.
    9. Bishop, John A & Formby, John P & Thistle, Paul D, 1992. "Convergence of the South and Non-South Income Distributions, 1969-1979," American Economic Review, American Economic Association, vol. 82(1), pages 262-272, March.
    10. Russell Davidson, 2012. "Statistical inference in the presence of heavy tails," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 31-53, February.
    11. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    12. Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
    13. Cowell, Frank A & Victoria-Feser, Maria-Pia, 1996. "Robustness Properties of Inequality Measures," Econometrica, Econometric Society, vol. 64(1), pages 77-101, January.
    14. Frank A. Cowell & Maria-Pia Victoria-Feser, 2002. "Welfare Rankings in the Presence of Contaminated Data," Econometrica, Econometric Society, vol. 70(3), pages 1221-1233, May.
    15. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    16. Russell Davidson, 2009. "Testing for Restricted Stochastic Dominance: Some Further Results," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 1(1), pages 34-59, September.
    17. Richard V. Burkhauser & Shuaizhang Feng & Stephen P. Jenkins, 2009. "Using The P90/P10 Index To Measure U.S. Inequality Trends With Current Population Survey Data: A View From Inside The Census Bureau Vaults," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(1), pages 166-185, March.
    18. Cowell, Frank A., 1991. "Grouping bounds for inequality measures under alternative informational assumptions," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 1-14.
    19. Wen‐Hao Chen & Jean‐Yves Duclos, 2011. "Testing for poverty dominance: an application to Canada," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 44(3), pages 781-803, August.
    20. Frank A. Cowell & Russell Davidson & Emmanuel Flachaire, 2015. "Goodness of Fit: An Axiomatic Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 54-67, January.
    21. Garry F. Barrett & Stephen G. Donald & Debopam Bhattacharya, 2014. "Consistent Nonparametric Tests for Lorenz Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(1), pages 1-13, January.
    22. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    23. Stephen G. Donald & David A. Green & Harry J. Paarsch, 2000. "Differences in Wage Distributions Between Canada and the United States: An Application of a Flexible Estimator of Distribution Functions in the Presence of Covariates," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(4), pages 609-633.
    24. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
    25. Davidson, Russell, 2009. "Reliable inference for the Gini index," Journal of Econometrics, Elsevier, vol. 150(1), pages 30-40, May.
    26. Cowell, F.A., 2000. "Measurement of inequality," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 2, pages 87-166, Elsevier.
    27. François Bourguignon & Christian Morrisson, 2002. "Inequality Among World Citizens: 1820-1992," American Economic Review, American Economic Association, vol. 92(4), pages 727-744, September.
    28. Frank Cowell & Carlo Fiorio, 2011. "Inequality decompositions—a reconciliation," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 509-528, December.
    29. Cowell, Frank A. & Flachaire, Emmanuel, 2007. "Income distribution and inequality measurement: The problem of extreme values," Journal of Econometrics, Elsevier, vol. 141(2), pages 1044-1072, December.
    30. C. M. Beach & S. F. Kaliski, 1986. "Lorenz Curve Inference with Sample Weights: An Application to the Distribution of Unemployment Experience," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 35(1), pages 38-45, March.
    31. Beach, Charles M & Richmond, James, 1985. "Joint Confidence Intervals for Income Shares and Lorenz Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 439-450, June.
    32. Russell Davidson, 2010. "Innis Lecture: Inference on income distributions," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 43(4), pages 1122-1148, November.
    33. Butler, Richard J. & McDonald, James B., 1989. "Using incomplete moments to measure inequality," Journal of Econometrics, Elsevier, vol. 42(1), pages 109-119, September.
    34. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    35. 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.
    36. Bishop, John A & Formby, John P & Smith, W James, 1991. "Lorenz Dominance and Welfare: Changes in the U.S. Distribution of Income, 1967-1986," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 134-139, February.
    37. Cowell, Frank A. & Victoria-Feser, Maria-Pia, 2006. "Distributional Dominance With Trimmed Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 291-300, July.
    38. Martin Biewen & Stephen P. Jenkins, 2006. "Variance Estimation for Generalized Entropy and Atkinson Inequality Indices: the Complex Survey Data Case," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(3), pages 371-383, June.
    39. Russell Davidson, 2010. "Inference on Income Distributions," Working Papers halshs-00541164, HAL.
    40. Barrett, Garry F. & Donald, Stephen G., 2009. "Statistical Inference with Generalized Gini Indices of Inequality, Poverty, and Welfare," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 1-17.
    41. A.B. Atkinson & F. Bourguignon (ed.), 2000. "Handbook of Income Distribution," Handbook of Income Distribution, Elsevier, edition 1, volume 1, number 1.
    42. David H. Autor & Lawrence F. Katz & Melissa S. Kearney, 2008. "Trends in U.S. Wage Inequality: Revising the Revisionists," The Review of Economics and Statistics, MIT Press, vol. 90(2), pages 300-323, May.
    43. Burkhauser, Richard V. & Feng, Shuaizhang & Larrimore, Jeff, 2010. "Improving imputations of top incomes in the public-use current population survey by using both cell-means and variances," Economics Letters, Elsevier, vol. 108(1), pages 69-72, July.
    44. Bhattacharya, Debopam, 2007. "Inference on inequality from household survey data," Journal of Econometrics, Elsevier, vol. 137(2), pages 674-707, April.
    45. Cowell, Frank A. & Victoria-Feser, Maria-Pia, 1996. "Poverty measurement with contaminated data: A robust approach," European Economic Review, Elsevier, vol. 40(9), pages 1761-1771, December.
    46. Frank A. Cowell, 2008. "Income Distribution and Inequality," Chapters, in: John B. Davis & Wilfred Dolfsma (ed.), The Elgar Companion to Social Economics, chapter 13, Edward Elgar Publishing.
    47. 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.
    48. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    49. Frank Cowell & Emmanuel Flachaire & Sanghamitra Bandyopadhyay, 2013. "Reference distributions and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(4), pages 421-437, December.
    50. Frank Cowell & Maria-Pia Victoria-Feser, 2003. "Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(3), pages 191-219, December.
    51. Bishop, John A & Formby, John P & Zheng, Buhong, 1997. "Statistical Inference and the Sen Index of Poverty," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 381-387, May.
    52. Richard V. Burkhauser & Amy D. Crews & Mary C. Daly, 1997. "A new look at the distributional effects of economic growth during the 1980s: a comparative study of the United States and Germany," Economic Review, Federal Reserve Bank of San Francisco, pages 18-31.
    53. Stephen G. Donald & Yu‐Chin Hsu & Garry F. Barrett, 2012. "Incorporating covariates in the measurement of welfare and inequality: methods and applications," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 1-30, February.
    54. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September.
    55. Robert F. Bordley & James B. McDonald & Anand Mantrala, 1997. "Something New, Something Old: Parametric Models for the Size of Distribution of Income," Journal of Income Distribution, Ad libros publications inc., vol. 6(1), pages 5-5, June.
    56. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    57. Frank Cowell & Maria-Pia Victoria-Feser, 2007. "Robust stochastic dominance: A semi-parametric approach," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(1), pages 21-37, April.
    58. repec:bla:econom:v:58:y:1991:i:232:p:461-77 is not listed on IDEAS
    59. Richard V. Burkhauser & Shuaizhang Feng & Stephen P. Jenkins, 2009. "Using The P90/P10 Index To Measure U.S. Inequality Trends With Current Population Survey Data: A View From Inside The Census Bureau Vaults," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 55(1), pages 166-185, March.
    60. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
    61. Ahamada, Ibrahim & Flachaire, Emmanuel, 2010. "Non-Parametric Econometrics," OUP Catalogue, Oxford University Press, number 9780199578009.
    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. Russell Davidson, 2010. "Innis Lecture: Inference on income distributions," Canadian Journal of Economics, Canadian Economics Association, vol. 43(4), pages 1122-1148, November.
    2. Stephen P. Jenkins & Richard V. Burkhauser & Shuaizhang Feng & Jeff Larrimore, 2011. "Measuring inequality using censored data: a multiple‐imputation approach to estimation and inference," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 174(1), pages 63-81, January.
    3. Stéphane Guerrier & Samuel Orso & Maria-Pia Victoria-Feser, 2018. "Parametric Inference for Index Functionals," Econometrics, MDPI, vol. 6(2), pages 1-11, April.
    4. Francesco Andreoli, 2018. "Robust Inference for Inverse Stochastic Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 146-159, January.
    5. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2020. "Bayesian assessment of Lorenz and stochastic dominance," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 767-799, May.
    6. David Lander & David Gunawan & William E. Griffiths & Duangkamon Chotikapanich, 2016. "Bayesian Assessment of Lorenz and Stochastic Dominance Using a Mixture of Gamma Densities," Department of Economics - Working Papers Series 2023, The University of Melbourne.
    7. Rothe, Christoph, 2010. "Nonparametric estimation of distributional policy effects," Journal of Econometrics, Elsevier, vol. 155(1), pages 56-70, March.
    8. Stephen G. Donald & Yu‐Chin Hsu & Garry F. Barrett, 2012. "Incorporating covariates in the measurement of welfare and inequality: methods and applications," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 1-30, February.
    9. Frank A. Cowell & Philippe Kerm, 2015. "Wealth Inequality: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(4), pages 671-710, September.
    10. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    11. Wen-Hao Chen & Jean-Yves Duclos, 2011. "Testing for poverty dominance: an application to Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 44(3), pages 781-803, August.
    12. Frank Cowell & Maria-Pia Victoria-Feser, 2003. "Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(3), pages 191-219, December.
    13. Richard Burkhauser & Shuaizhang Feng & Stephen Jenkins & Jeff Larrimore, 2011. "Estimating trends in US income inequality using the Current Population Survey: the importance of controlling for censoring," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 393-415, September.
    14. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    15. Stengos, Thanasis & Thompson, Brennan S., 2012. "Testing for bivariate stochastic dominance using inequality restrictions," Economics Letters, Elsevier, vol. 115(1), pages 60-62.
    16. Jean-Marie Dufour & Emmanuel Flachaire & Lynda Khalaf, 2019. "Permutation Tests for Comparing Inequality Measures," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 457-470, July.
    17. Judith Clarke & Nilanjana Roy, 2012. "On statistical inference for inequality measures calculated from complex survey data," Empirical Economics, Springer, vol. 43(2), pages 499-524, October.
    18. Christopher J. Bennett, 2013. "Inference For Dominance Relations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(4), pages 1309-1328, November.
    19. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    20. Vladimir Hlasny & Paolo Verme, 2022. "The Impact of Top Incomes Biases on the Measurement of Inequality in the United States," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(4), pages 749-788, August.

    More about this item

    Keywords

    Economie quantitative;

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

    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:hal:journl:hal-01457398. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.