GMM Estimation with Brownian Kernels Applied to Income Inequality Measurement

Jin Seo Cho () and Peter Phillips

No 2024rwp-232, Working papers from Yonsei University, Yonsei Economics Research Institute

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.

Keywords: Infinite-dimensional GMM estimation; Brownian motion kernel; Brownian bridge kernel; Gaussian process; Infinite-dimensional MCMD estimation; Labor income inequality. (search for similar items in EconPapers)
JEL-codes: C13 C18 C32 C55 D31 O15 P36 (search for similar items in EconPapers)
Pages: 46pages
Date: 2024-10
New Economics Papers: this item is included in nep-ecm and nep-ets
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Working Paper: GMM Estimation with Brownian Kernels Applied to Income Inequality Measurement (2024)
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