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Practical Kolmogorov–Smirnov testing by minimum distance applied to measure top income shares in Korea

Practical Kolmogorov–Smirnov testing by minimum distance applied to measure top income shares in Korea
Practical Kolmogorov–Smirnov testing by minimum distance applied to measure top income shares in Korea

We study Kolmogorov–Smirnov goodness-of-fit tests for evaluating distributional hypotheses where unknown parameters need to be fitted. Following the work of Pollard (1980), our approach uses a Cramér–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 2007–2012. 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.

Crámer–von Mises distance, Distribution-free asymptotics, Minimum distance estimator, Null distribution, Pareto interpolation, Top income shares
0735-0015
523-537
Cho, Jin Seo
73c54d86-de50-44c7-8d1f-afbfab67bfc1
Park, Myung Ho
217bed56-c500-4156-be6e-51b191ebb3ee
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Cho, Jin Seo
73c54d86-de50-44c7-8d1f-afbfab67bfc1
Park, Myung Ho
217bed56-c500-4156-be6e-51b191ebb3ee
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243

Cho, Jin Seo, Park, Myung Ho and Phillips, Peter C.B. (2018) Practical Kolmogorov–Smirnov testing by minimum distance applied to measure top income shares in Korea. Journal of Business and Economic Statistics, 36 (3), 523-537. (doi:10.1080/07350015.2016.1200983).

Record type: Article

Abstract

We study Kolmogorov–Smirnov goodness-of-fit tests for evaluating distributional hypotheses where unknown parameters need to be fitted. Following the work of Pollard (1980), our approach uses a Cramér–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 2007–2012. 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.

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JSCHO_income_dist_testing_05_16_2016_pcb_fullversion - Accepted Manuscript
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More information

Accepted/In Press date: 3 June 2016
e-pub ahead of print date: 10 May 2017
Published date: 3 July 2018
Keywords: Crámer–von Mises distance, Distribution-free asymptotics, Minimum distance estimator, Null distribution, Pareto interpolation, Top income shares

Identifiers

Local EPrints ID: 424788
URI: http://eprints.soton.ac.uk/id/eprint/424788
ISSN: 0735-0015
PURE UUID: 59addb38-0218-4a71-8ef1-44317c0dd55e
ORCID for Peter C.B. Phillips: ORCID iD orcid.org/0000-0003-2341-0451

Catalogue record

Date deposited: 05 Oct 2018 11:45
Last modified: 18 Feb 2021 17:14

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