IDEAS home Printed from https://ideas.repec.org/a/kap/jecinq/v16y2018i4d10.1007_s10888-018-9377-y.html
   My bibliography  Save this article

Information theoretic approaches to income density estimation with an application to the U.S. income data

Author

Listed:
  • Sung Y. Park

    (Chung-Ang University)

  • Anil K. Bera

    (University of Illinois)

Abstract

The size distribution of income is the basis of income inequality measures which in turn are needed for evaluation of social welfare. Therefore, proper specification of the income density function is of special importance. In this paper, using information theoretic approach, first, we provide a maximum entropy (ME) characterization of some well-known income distributions. Then, we suggest a class of flexible parametric densities which satisfy certain economic constraints and stylized facts of personal income data such as the weak Pareto law and a decline of the income-share elasticities. Our empirical results using the U.S. family income data show that the ME principle provides economically meaningful and a very parsimonious and, at the same time, flexible specification of the income density function.

Suggested Citation

  • Sung Y. Park & Anil K. Bera, 2018. "Information theoretic approaches to income density estimation with an application to the U.S. income data," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 16(4), pages 461-486, December.
    • Handle: RePEc:kap:jecinq:v:16:y:2018:i:4:d:10.1007_s10888-018-9377-y
    DOI: 10.1007/s10888-018-9377-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10888-018-9377-y
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10888-018-9377-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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Park, Sung Y. & Bera, Anil K., 2009. "Maximum entropy autoregressive conditional heteroskedasticity model," Journal of Econometrics, Elsevier, vol. 150(2), pages 219-230, June.
    2. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2010. "A model of personal income distribution with application to Italian data," Empirical Economics, Springer, vol. 39(2), pages 559-591, October.
    3. Richard Burkhauser & Shuaizhang Feng & Stephen Jenkins & Jeff Larrimore, 2009. "Recent Trends in Top Income Shares in the USA: Reconciling Estimates from March CPS and IRS Tax Return Data," Working Papers 09-26, Center for Economic Studies, U.S. Census Bureau.
    4. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    5. Dhaene, Geert & Hoorelbeke, Dirk, 2004. "The information matrix test with bootstrap-based covariance matrix estimation," Economics Letters, Elsevier, vol. 82(3), pages 341-347, March.
    6. Majumder, Amita & Chakravarty, Satya Ranjan, 1990. "Distribution of Personal Income: Development of a New Model and Its Application to U.S. Income Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 189-196, April-Jun.
    7. Salem, A B Z & Mount, T D, 1974. "A Convenient Descriptive Model of Income Distribution: The Gamma Density," Econometrica, Econometric Society, vol. 42(6), pages 1115-1127, November.
    8. Ransom, Michael R. & Cramer, Jan S., 1983. "Income distribution functions with disturbances," European Economic Review, Elsevier, vol. 22(3), pages 363-372.
    9. Wu, Ximing & Perloff, Jeffrey M., 2007. "GMM estimation of a maximum entropy distribution with interval data," Journal of Econometrics, Elsevier, vol. 138(2), pages 532-546, June.
    10. Kloek, Teun & van Dijk, Herman K., 1978. "Efficient estimation of income distribution parameters," Journal of Econometrics, Elsevier, vol. 8(1), pages 61-74, August.
    11. Camelia Minoiu & Sanjay Reddy, 2014. "Kernel density estimation on grouped data: the case of poverty assessment," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(2), pages 163-189, June.
    12. Jhun, Myoungshic & Jeong, Hyeong-Chul, 2000. "Applications of bootstrap methods for categorical data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 35(1), pages 83-91, November.
    13. Wu, Ximing, 2003. "Calculation of maximum entropy densities with application to income distribution," Journal of Econometrics, Elsevier, vol. 115(2), pages 347-354, August.
    14. Samuel Dastrup & Rachel Hartshorn & James McDonald, 2007. "The impact of taxes and transfer payments on the distribution of income: A parametric comparison," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 353-369, December.
    15. 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.
    16. Feng, Shuaizhang & Burkhauser, Richard V. & Butler, J.S., 2006. "Levels and Long-Term Trends in Earnings Inequality: Overcoming Current Population Survey Censoring Problems Using the GB2 Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 57-62, January.
    17. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    18. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    19. McDonald, James B & Mantrala, Anand, 1995. "The Distribution of Personal Income: Revisited," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 201-204, April-Jun.
    20. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    21. McDonald, James B & Ransom, Michael R, 1979. "Functional Forms, Estimation Techniques and the Distribution of Income," Econometrica, Econometric Society, vol. 47(6), pages 1513-1525, November.
    22. Richard V. Burkhauser & Shuaizhang Feng & Stephen P. Jenkins & Jeff Larrimore, 2012. "Recent Trends in Top Income Shares in the United States: Reconciling Estimates from March CPS and IRS Tax Return Data," The Review of Economics and Statistics, MIT Press, vol. 94(2), pages 371-388, May.
    23. Dorothée Boccanfuso & Bernard Decaluwé & Luc Savard, 2008. "Poverty, income distribution and CGE micro-simulation modeling: Does the functional form of distribution matter?," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 6(2), pages 149-184, June.
    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. Vladimir Hlasny, 2021. "Parametric representation of the top of income distributions: Options, historical evidence, and model selection," Journal of Economic Surveys, Wiley Blackwell, vol. 35(4), pages 1217-1256, September.
    2. Kazuhiko Kakamu & Haruhisa Nishino, 2016. "Bayesian Estimation Of Beta-Type Distribution Parameters Based On Grouped Data," Discussion Papers 2016-08, Kobe University, Graduate School of Business Administration.
    3. Kazuhiko Kakamu & Haruhisa Nishino, 2019. "Bayesian Estimation of Beta-type Distribution Parameters Based on Grouped Data," Computational Economics, Springer;Society for Computational Economics, vol. 54(2), pages 625-645, August.
    4. Michał Brzeziński, 2013. "Parametric Modelling of Income Distribution in Central and Eastern Europe," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 5(3), pages 207-230, September.
    5. Christophe Muller, 2001. "The Properties of the Watts Poverty Index under Lognormality," Economics Bulletin, AccessEcon, vol. 9(1), pages 1-9.
    6. Vanesa Jorda & José María Sarabia & Markus Jäntti, 2021. "Inequality measurement with grouped data: Parametric and non‐parametric methods," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 964-984, July.
    7. Boccanfuso, Dorothée & Richard, Patrick & Savard, Luc, 2013. "Parametric and nonparametric income distribution estimators in CGE micro-simulation modeling," Economic Modelling, Elsevier, vol. 35(C), pages 892-899.
    8. 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.
    9. Feng Zhu, 2005. "A nonparametric analysis of the shape dynamics of the US personal income distribution: 1962-2000," BIS Working Papers 184, Bank for International Settlements.
    10. Dorothée Boccanfuso & Bernard Decaluwé & Luc Savard, 2003. "Poverty, Income Distribution and CGE Modeling: Does the Functional Form of Distribution Matter?," Cahiers de recherche 0332, CIRPEE.
    11. Guanghua Wan, 2012. "Towards Greater Equality in China: The Economic Growth Dividend," Working Papers 2012/33, Maastricht School of Management.
    12. Vanesa Jorda & Jos Mar a Sarabia & Markus J ntti, 2020. "Estimation of Income Inequality from Grouped Data," LIS Working papers 804, LIS Cross-National Data Center in Luxembourg.
    13. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2010. "A model of personal income distribution with application to Italian data," Empirical Economics, Springer, vol. 39(2), pages 559-591, October.
    14. 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.
    15. Jordá, Vanesa & Niño-Zarazúa, Miguel, 2019. "Global inequality: How large is the effect of top incomes?," World Development, Elsevier, vol. 123(C), pages 1-1.
    16. Kazuhiko Kakamu, 2016. "Simulation Studies Comparing Dagum and Singh–Maddala Income Distributions," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 593-605, December.
    17. Christian Kleiber, 2008. "A Guide to the Dagum Distributions," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 6, pages 97-117, Springer.
    18. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July.
    19. Walter, Paul & Weimer, Katja, 2018. "Estimating poverty and inequality indicators using interval censored income data from the German microcensus," Discussion Papers 2018/10, Free University Berlin, School of Business & Economics.
    20. Singh, Vijay P., 2018. "Systems of frequency distributions for water and environmental engineering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 50-74.

    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:kap:jecinq:v:16:y:2018:i:4:d:10.1007_s10888-018-9377-y. 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.