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A simple and efficient test for the Pareto law

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  • Francisco Goerlich

Abstract

This note presents a simple and locally optimal test statistic for the Pareto law. The test is based on the Lagrange multiplier principle and can be computed easily once the maximum likelihood estimator of the scale parameter of the Pareto density has been obtained. A Monte Carlo exercise shows the good small sample properties of the test under the null of the Pareto law and also its power against some sensible and interesting alternatives. In addition, the proposed test is compared to a goodness of fit test which is powerful against more or less all alternatives. Eventually, a simple application to urban economics is performed. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Francisco Goerlich, 2013. "A simple and efficient test for the Pareto law," Empirical Economics, Springer, vol. 45(3), pages 1367-1381, December.
    • Handle: RePEc:spr:empeco:v:45:y:2013:i:3:p:1367-1381
    DOI: 10.1007/s00181-012-0654-5
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    1. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    2. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    3. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    4. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378, Elsevier.
    5. Moshe Levy & Sorin Solomon, 1996. "Power Laws Are Logarithmic Boltzmann Laws," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 595-601.
    6. Rosen, Kenneth T. & Resnick, Mitchel, 1980. "The size distribution of cities: An examination of the Pareto law and primacy," Journal of Urban Economics, Elsevier, vol. 8(2), pages 165-186, September.
    7. Yoshihiko Nishiyama & Susumu Osada & Yasuhiro Sato, 2008. "OLS ESTIMATION AND THE t TEST REVISITED IN RANK‐SIZE RULE REGRESSION," Journal of Regional Science, Wiley Blackwell, vol. 48(4), pages 691-716, October.
    8. Fan, C Cindy & Casetti, Emilio, 1994. "The Spatial and Temporal Dynamics of U.S. Regional Income Inequality, 1950-1989," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 28(2), pages 177-196.
    9. Urzua, Carlos M., 2000. "A simple and efficient test for Zipf's law," Economics Letters, Elsevier, vol. 66(3), pages 257-260, March.
    10. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    11. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    12. J. V. Henderson & J. F. Thisse (ed.), 2004. "Handbook of Regional and Urban Economics," Handbook of Regional and Urban Economics, Elsevier, edition 1, volume 4, number 4.
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    1. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.

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    More about this item

    Keywords

    LM test; Pareto law; Statistical distributions; C01; C12; D31;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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