IDEAS home Printed from
   My bibliography  Save this paper

The income distribution with coarse data


  • Reza Daniels


How do you estimate poverty, inequality and earnings when the income variable consists of a combination of point-identified, interval-identified, and missing observations? This paper proposes a unifying theoretical approach to the problem of deriving point estimates when such data are present. The methodology is based on the idea of coarse data, which includes as special cases data that are censored within some predefined interval and data that are missing. A key part of the framework is to establish whether inference based on a likelihood that ignores the coarsening mechanism is equivalent to inference based on a likelihood that properly accounts for it. Results demonstrate that while the interval data are not coarsened at random (CAR), the missing data are CAR for the sample of employed economically active individuals in South Africa using the Labour Force Survey (2000 September). This requires an imputation algorithm that correctly accounts for these types of coarsening, as both univariate and multivariate parameters are affected by the choice of imputation method. It is recommended that researchers apply this framework to all analyses of the income distribution based on household survey data.

Suggested Citation

  • Reza Daniels, 2008. "The income distribution with coarse data," Working Papers 82, Economic Research Southern Africa.
  • Handle: RePEc:rza:wpaper:82

    Download full text from publisher

    File URL:
    Download Restriction: no


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

    Cited by:

    1. Koch, Steven & Alaba, Olufunke, 2010. "On health insurance and household decisions: A treatment effect analysis," Social Science & Medicine, Elsevier, vol. 70(2), pages 175-182, January.
    2. Aboozar Hadavand, 2017. "Misperceptions and mismeasurements: An analysis of subjective economic inequality," Working Papers 449, ECINEQ, Society for the Study of Economic Inequality.
    3. Reza C. Daniels, 2012. "Univariate Multiple Imputation for Coarse Employee Income Data," SALDRU Working Papers 88, Southern Africa Labour and Development Research Unit, University of Cape Town.
    4. Claire Vermaak, 2012. "Tracking poverty with coarse data: evidence from South Africa," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 10(2), pages 239-265, June.

    More about this item


    Ignorability; Coarse Data; Multiple Imputation; Earnings;

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • J30 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - General


    Access and download statistics


    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:rza:wpaper:82. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Charles Tanton). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.