Minimum Distance Testing and Top Income Shares in Korea

Jin Seo Cho (), Myung-Ho Park and Peter Phillips
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Myung-Ho Park: Korea Institute of Public Finance

No 2007, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We study Kolmogorov-Smirnov goodness of fit tests for evaluating distributional hypotheses where unknown parameters need to be fitted. Following work of Pollard (1979), our approach uses a Cram�r-von Mises minimum distance estimator for parameter estimation. The asymptotic null distribution of the resulting test statistic is represented by invariance principle arguments as a functional of a Brownian bridge in a simple regression format for which asymptotic critical values are readily delivered by simulations. Asymptotic power is examined under fixed and local alternatives and finite sample performance of the test is evaluated in simulations. The test is applied to measure top income shares using Korean income tax return data over 2007 to 2012. When the data relate to the upper 0.1% or higher tail of the income distribution, the conventional assumption of a Pareto tail distribution cannot be rejected. But the Pareto tail hypothesis is rejected for the top 1.0% or 0.5% incomes at the 5% significance level.

Keywords: Brownian bridge; Cram�r-von Mises statistic; Distribution-free asymptotics; Null distribution; Minimum distance estimator; Empirical distribution; goodness-of-fit test; Cr�mer-von Mises distance; Top income shares; Pareto interpolation (search for similar items in EconPapers)
JEL-codes: C12 C13 D31 E01 O15 (search for similar items in EconPapers)
Pages: 48 pages
Date: 2015-06
New Economics Papers: this item is included in nep-ecm and nep-mac
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