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Efficient GMM estimation with singular system of moment conditions

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  • Zhiguo Xiao

Abstract

Standard generalised method of moments (GMM) estimation was developed for nonsingular system of moment conditions. However, many important economic models are characterised by singular system of moment conditions. This paper shows that efficient GMM estimation of such models can be achieved by using the reflexive generalised inverses, in particular the Moore–Penrose generalised inverse, of the variance matrix of the sample moment conditions as the weighting matrix. We provide a consistent estimator of the optimal weighting matrix and establish its consistency. Potential issues of using generalised inverse and some remedies are also discussed.

Suggested Citation

  • Zhiguo Xiao, 2020. "Efficient GMM estimation with singular system of moment conditions," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 4(2), pages 172-178, July.
    • Handle: RePEc:taf:tstfxx:v:4:y:2020:i:2:p:172-178
    DOI: 10.1080/24754269.2019.1653159
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    Cited by:

    1. Jonathan Gillard & Emily O’Riordan & Anatoly Zhigljavsky, 2023. "Polynomial whitening for high-dimensional data," Computational Statistics, Springer, vol. 38(3), pages 1427-1461, September.

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