Review Articles

Efficient GMM estimation with singular system of moment conditions

Zhiguo Xiao

Department of Statistics, School of Management, Fudan University, Shanghai, People's Republic of China

Pages 172-178 | Received 21 Apr. 2019, Accepted 05 Aug. 2019, Published online: 23 Aug. 2019,
  • Abstract
  • Full Article
  • References
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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.


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