GMM with many moment conditions

Chirok Han, Peter C.B. Phillips

Research output: Contribution to journalArticlepeer-review

86 Citations (Scopus)


This paper provides a first order asymptotic theory for generalized method of moments (GMM) estimators when the number of moment conditions is allowed to increase with the sample size and the moment conditions may be weak. Examples in which these asymptotics are relevant include instrumental variable (IV) estimation with many (possibly weak or uninformed) instruments and some panel data models that cover moderate time spans and have correspondingly large numbers of instruments. Under certain regularity conditions, the GMM estimators are shown to converge in probability but not necessarily to the true parameter, and conditions for consistent GMM estimation are given. A general framework for the GMM limit distribution theory is developed based on epiconvergence methods. Some illustrations are provided, including consistent GMM estimation of a panel model with time varying individual effects, consistent limited information maximum likelihood estimation as a continuously updated GMM estimator, and consistent IV structural estimation using large numbers of weak or irrelevant instruments. Some simulations are reported.

Original languageEnglish
Pages (from-to)147-192
Number of pages46
Issue number1
Publication statusPublished - 2006 Jan
Externally publishedYes


  • Epiconvergence
  • GMM
  • IV
  • Irrelevant instruments
  • LIML estimation
  • Large numbers of instruments
  • Panel models
  • Pseudo true value
  • Signal
  • Signal variability
  • Weak instrumentation

ASJC Scopus subject areas

  • Economics and Econometrics


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