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Benford’s law and the FSD distribution of economic behavioral micro data

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  • Villas-Boas, Sofia B.
  • Fu, Qiuzi
  • Judge, George

Abstract

In this paper, we focus on the first significant digit (FSD) distribution of European micro income data and use information theoretic-entropy based methods to investigate the degree to which Benford’s FSD law is consistent with the nature of these economic behavioral systems. We demonstrate that Benford’s law is not an empirical phenomenon that occurs only in important distributions in physical statistics, but that it also arises in self-organizing dynamic economic behavioral systems. The empirical likelihood member of the minimum divergence-entropy family, is used to recover country based income FSD probability density functions and to demonstrate the implications of using a Benford prior reference distribution in economic behavioral system information recovery.

Suggested Citation

  • Villas-Boas, Sofia B. & Fu, Qiuzi & Judge, George, 2017. "Benford’s law and the FSD distribution of economic behavioral micro data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 711-719.
    • Handle: RePEc:eee:phsmap:v:486:y:2017:i:c:p:711-719
    DOI: 10.1016/j.physa.2017.05.093
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    References listed on IDEAS

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    1. Shao, Lijing & Ma, Bo-Qiang, 2010. "The significant digit law in statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3109-3116.
    2. Grendar, Marian & Judge, George & Schechter, Laura, 2007. "An empirical non-parametric likelihood family of data-based Benford-like distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 429-438.
    3. Pietronero, L. & Tosatti, E. & Tosatti, V. & Vespignani, A., 2001. "Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(1), pages 297-304.
    4. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
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    Cited by:

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    2. Katherine M. Anderson & Kevin Dayaratna & Drew Gonshorowski & Steven J. Miller, 2022. "A New Benford Test for Clustered Data with Applications to American Elections," Stats, MDPI, vol. 5(3), pages 1-15, August.
    3. González Fernando Antonio Ignacio, 2019. "Detecting Anomalous Data in Household Surveys: Evidence for Argentina," Journal of Social and Economic Statistics, Sciendo, vol. 8(2), pages 1-10, December.

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    More about this item

    Keywords

    Benford’s law; Information theoretic methods; Micro income data; Empirical likelihood criterion; Minimum divergence distance measures; Cross entropy;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

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