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GMM Estimation with Brownian Kernels Applied to Income Inequality Measurement

Author

Listed:
  • Jin Seo Cho

    (Yonsei University)

  • Peter C. B. Phillips

    (Yale University)

Abstract
In GMM estimation, it is well known that if the moment dimension grows with the sample size, the asymptotics of GMM differ from the standard finite dimensional case. The present work examines the asymptotic properties of infinite dimensional GMM estimation when the weight matrix is formed by inverting Brownian motion or Brownian bridge covariance kernels. These kernels arise in econometric work such as minimum Cramer-von Mises distance estimation when testing distributional specification. The properties of GMM estimation are studied under different environments where the moment conditions converge to a smooth Gaussian or non-differentiable Gaussian process. Conditions are also developed for testing the validity of the moment conditions by means of a suitably constructed J-statistic. In case these conditions are invalid we propose another test called the U-test. As an empirical application of these infinite dimensional GMM procedures the evolution of cohort labor income inequality indices is studied using the Continuous Work History Sample database. The findings show that labor income inequality indices are maximized at early career years, implying that economic policies to reduce income inequality should be more effective when designed for workers at an early stage in their career cycles.

Suggested Citation

  • Jin Seo Cho & Peter C. B. Phillips, 2024. "GMM Estimation with Brownian Kernels Applied to Income Inequality Measurement," Cowles Foundation Discussion Papers 2411, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2411
    as

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    File URL: https://cowles.yale.edu/sites/default/files/2024-10/d2411.pdf
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    References listed on IDEAS

    as
    1. Eisenbarth, Anthony & Chen, Zhou Fu, 2022. "The evolution of wage inequality within local U.S. labor markets," Journal for Labour Market Research, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 56, pages 1-2.
    2. Carrasco, Marine, 2012. "A regularization approach to the many instruments problem," Journal of Econometrics, Elsevier, vol. 170(2), pages 383-398.
    3. Jin Seo Cho & Myung-Ho Park & Peter C. B. Phillips, 2018. "Practical Kolmogorov–Smirnov Testing by Minimum Distance Applied to Measure Top Income Shares in Korea," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 523-537, July.
    4. Simon Kuznets & Elizabeth Jenks, 1953. "Shares of Upper Income Groups in Income and Savings (1953)," NBER Books, National Bureau of Economic Research, Inc, number kuzn53-1.
    5. Chiaki Moriguchi & Emmanuel Saez, 2008. "The Evolution of Income Concentration in Japan, 1886-2005: Evidence from Income Tax Statistics," The Review of Economics and Statistics, MIT Press, vol. 90(4), pages 713-734, November.
    6. Simon Kuznets & Elizabeth Jenks, 1953. "Shares of Upper Income Groups in Savings," NBER Chapters, in: Shares of Upper Income Groups in Income and Savings (1953), pages 171-218, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • O15 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Economic Development: Human Resources; Human Development; Income Distribution; Migration
    • P36 - Political Economy and Comparative Economic Systems - - Socialist Institutions and Their Transitions - - - Consumer Economics; Health; Education and Training; Welfare, Income, Wealth, and Poverty

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