Efficient GMM estimation with singular system of moment conditions
- Resource Type
- article
- Authors
- Zhiguo Xiao
- Source
- Statistical Theory and Related Fields, Vol 4, Iss 2, Pp 172-178 (2020)
- Subject
- singular moment condition models
generalised method of moments
reflexive generalised inverses
imposing random noises
Probabilities. Mathematical statistics
QA273-280
- Language
- English
- ISSN
- 2475-4269
2475-4277
24754269
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.