Preparations for Lecture 26, December 6

Lecture Note 8, Generalized Method of Moments, Box 2 and section 3, p. 12 and 16-19 (5 pages).

Supplementary readings: Verbeek, Introduction to Modern Econometrics, section 5.8, Generalized Method of Moments.

Section 3 covers the GMM estimator in the case of a linear model with endogenous variables. Using a set of instruments, we can estimate the model's parameters by GMM. Importantly, as the model is linear, we can derive an analytical expression for the MM estimator (if we have exact identification) and the GMM estimator (if we have over-identification). In particular, note how a general expression for the GMM estimator is derived for some weight matrix, and how this expression simplifies as we make different assumptions about the sample moments.

Box 1 explains pseudo-maximum likelihood estimation (which we also considered in Topic 4 on ARCH models). Importantly, despite that a maximum likelihood estimator is based on the wrong likelihood estimator, it is consistent as long as the unconditional expectation of the scores are zero. If this is the case, the unconditional expectation of the scores provides a set of valid moment conditions, which we know from the theory on GMM is sufficient for the estimator to be consistent.

Lecture Note 8, Generalized Method of Moments.