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Practical Kolmogorov-Smirnov Testing by Minimum Distance Applied to Measure Top Income Shares in Korea

Author

Listed:
  • JIN SEO CHO

    (Yonsei University)

  • MYUNG-HO PARK

    (Korea Institute of Public Finance)

  • PETER C.B. PHILLIPS

    (Yale University, University of Auckland Singapore Management University & University of Southampton)

Abstract

We study Kolmogorov-Smirnov goodness of fit tests for evaluating distributional hypotheses where unknown parameters need to be fitted. Following work of Pollard (1980), our approach uses a Cram¢¥ervon 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 estimating the upper 0.1% or higher income shares, the conventional assumption of a Pareto tail distribution cannot be rejected. But the Pareto tail hypothesis is rejected for estimating the top 1.0% or 0.5% income shares at the 5% significance level. A Supplement containing proofs and data descriptions is available online. Key Words: Distribution-free asymptotics, null distribution, minimum distance estimator, Cr¢¥amer-von Mises distance, top income shares, Pareto interpolation.

Suggested Citation

  • Jin Seo Cho & Myung-Ho Park & Peter C.B. Phillips, 2016. "Practical Kolmogorov-Smirnov Testing by Minimum Distance Applied to Measure Top Income Shares in Korea," Working papers 2016rwp-88, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2016rwp-88
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    1. repec:hit:hitjcm:v:56:y:2015:i:1:p:1-19 is not listed on IDEAS
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    Cited by:

    1. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    2. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    3. Jin Seo Cho & Myung-Ho Park & Peter C.B. Phillips, 2016. "Supplement to ¡°Practical Kolmogorov-Smirnov Testing by Minimum Distance Applied to Measure Top Income Shares in Korea¡±," Working papers 2016rwp-88a, Yonsei University, Yonsei Economics Research Institute.

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    More about this item

    Keywords

    distribution-free asymptotics; null distribution; minimum distance estimator; cr¢¥amer-von mises distance; top income shares; pareto interpolation.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • E01 - Macroeconomics and Monetary Economics - - General - - - Measurement and Data on National Income and Product Accounts and Wealth; Environmental Accounts
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration

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