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Journal Article

A Convenient Descriptive Model of Income Distribution: The Gamma Density

A. B. Z. Salem and T. D. Mount
Econometrica
Vol. 42, No. 6 (Nov., 1974), pp. 1115-1127
Published by: The Econometric Society
DOI: 10.2307/1914221
Stable URL: http://www.jstor.org/stable/1914221
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Convenient Descriptive Model of Income Distribution: The Gamma Density
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Abstract

The distribution of personal income is approximated by a two-parameter gamma density function (Pearson Type III). The two parameters may be considered as indicators of scale and of inequality, respectively. Maximum likelihood estimates of the parameters are derived from a random sample using graphical techniques, and a likelihood ratio test for the hypothesis that the inequality parameter is the same for different distributions is presented. The derivation of both the estimates and the test statistic requires computing the arithmetic and geometric means from the sample. An empirical application, including a comparison of the gamma and lognormal distributions to demonstrate the better fit of the gamma, is made to personal income data in the United States for the years 1960 to 1969. Using the gamma density, inequality is shown to decrease when unemployment or inflation decreases, or when the real national product increases.

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