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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 Cram'er-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," Working papers 2024rwp-232, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2024rwp-232
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    References listed on IDEAS

    as
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    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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