Publication Type

Journal Article

Version

submittedVersion

Publication Date

11-2025

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 Cramér–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 -statistic. In case these conditions are invalid we propose another test called the -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

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

252

First Page

1

Last Page

19

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2025.106110

Publisher

Elsevier

Copyright Owner and License

Authors

Additional URL

https://doi.org/10.1016/j.jeconom.2025.106110

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