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Benford’s Law and Naturally Occurring Prices in Certain ebaY Auctions

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Abstract

We show that certain the winning bids for certain ebaY auctions obey Benford’s Law. One implication of this is that it is unlikely that these bids are subject to collusion among bidders, or “shilling” on the part of sellers. Parenthetically, we also show that numbers from the naturally occurring Fibonacci and Lucas sequences also obey Benford’s Law.

Suggested Citation

  • David E. Giles, 2005. "Benford’s Law and Naturally Occurring Prices in Certain ebaY Auctions," Econometrics Working Papers 0505, Department of Economics, University of Victoria.
  • Handle: RePEc:vic:vicewp:0505
    Note: ISSN 1485-6441
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    File URL: http://www.uvic.ca/socialsciences/economics/assets/docs/econometrics/ewp0505.pdf
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    References listed on IDEAS

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    1. 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.
    2. De Ceuster, Marc J. K. & Dhaene, Geert & Schatteman, Tom, 1998. "On the hypothesis of psychological barriers in stock markets and Benford's Law," Journal of Empirical Finance, Elsevier, vol. 5(3), pages 263-279, September.
    3. Giles, David E., 2005. "Testing for a Santa Claus effect in growth cycles," Economics Letters, Elsevier, vol. 87(3), pages 421-426, June.
    4. Canessa, Enrique, 2003. "Theory of analogous force on number sets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 44-52.
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    Cited by:

    1. Bauer Johannes & Groß Jochen, 2011. "Difficulties Detecting Fraud? The Use of Benford’s Law on Regression Tables," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(5-6), pages 733-748, October.
    2. T. Mir, 2016. "The leading digit distribution of the worldwide illicit financial flows," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 271-281, January.
    3. T. A. Mir, 2016. "The leading digit distribution of the worldwide illicit financial flows," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 271-281, January.
    4. David E. A. Giles, 2006. "The Exact Asymptotic Distribution Function of Watson's UN-Squared for Testing Goodness-of-Fit With Circular Discrete Data," Econometrics Working Papers 0607, Department of Economics, University of Victoria.
    5. Holz, Carsten A., 2014. "The quality of China's GDP statistics," China Economic Review, Elsevier, vol. 30(C), pages 309-338.
    6. Alexis Stenfors, 2017. "Bid-Ask Spread Determination in the FX Swap Market: Competition, Collusion or a Convention?," Working Papers in Economics & Finance 2017-03, University of Portsmouth, Portsmouth Business School, Economics and Finance Subject Group.
    7. Lee, Joanne & Cho, Wendy K. Tam & Judge, George G, 2009. "Stigler's approach to recovering the distribution of first significant digits in natural data sets," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt9745m98d, Department of Agricultural & Resource Economics, UC Berkeley.
    8. Bormashenko, Ed. & Shulzinger, E. & Whyman, G. & Bormashenko, Ye., 2016. "Benford’s law, its applicability and breakdown in the IR spectra of polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 524-529.
    9. Whyman, G. & Ohtori, N. & Shulzinger, E. & Bormashenko, Ed., 2016. "Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 595-601.
    10. Rosa Abrantes-Metz & Sofia Villas-Boas & George Judge, 2011. "Tracking the Libor rate," Applied Economics Letters, Taylor & Francis Journals, vol. 18(10), pages 893-899.
    11. Kundt, Thorben, 2014. "Applying “Benford’s law” to the Crosswise Model: Findings from an online survey on tax evasion," Working Paper 148/2014, Helmut Schmidt University, Hamburg.
    12. Paul Hofmarcher & Kurt Hornik, 2013. "First Significant Digits and the Credit Derivative Market During the Financial Crisis," Contemporary Economics, University of Finance and Management in Warsaw, vol. 7(2), June.
    13. Karl-Heinz Tödter, 2009. "Benford's Law as an Indicator of Fraud in Economics," German Economic Review, Verein für Socialpolitik, vol. 10, pages 339-351, August.
    14. Mir, T.A., 2012. "The law of the leading digits and the world religions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 792-798.
    15. David E. Giles, 2012. "Exact Asymptotic Goodness-of-Fit Testing For Discrete Circular Data, With Applications," Econometrics Working Papers 1201, Department of Economics, University of Victoria.
    16. Kalaichelvan, Mohandass & Lim Kai Jie, Shawn, 2012. "A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford’s Law," MPRA Paper 40960, University Library of Munich, Germany.
    17. Lee, Joanne & Judge, George G, 2008. "Identifying falsified clinical data," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt8x00h1c1, Department of Agricultural & Resource Economics, UC Berkeley.
    18. Mir, T.A., 2014. "The Benford law behavior of the religious activity data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 1-9.

    More about this item

    Keywords

    Benford’s Law; auction prices; football; Kuiper test; Watson test;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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