Alternative Semi‐parametric Likelihood Approaches to Generalised Method of Moments Estimation

Abstract

Since Hansen's (1982) seminal paper, the generalised method of moments (GMM) has become an increasingly important method for estimation and inference in econometrics. This paper examines alternative semi‐parametric quasi‐likelihood approaches. Essentially, these methods embed sample versions of the moment conditions used in GMM in a non‐parametric quasi‐likelihood function by use of additional parameters associated with these moment conditions. Specification and misspecification tests may be defined which are similar in nature to the classical tests and are first‐order equivalent to the corresponding GMM statistics. The structure of the semi‐parametric quasi‐maximum likelihood estimator is explored for models estimated by instrumental variables.