Preparations for Lecture 25, December 5

Lecture Note 8, Generalized Method of Moments, section 3.1.1-3.1.2 and 4.4, p. 17-19 and 28-32 (8 pages).

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

Section 4.4 explains how to estimate the parameters of the consumption CAPM model by GMM. Note that this model is non-linear and does not have a standard "linear regression form" with a dependent variable that is a linear function of a set of explanatory variables and an error term. Instead, we simply use the fact that the model implies a set of "conditional moment conditions," which imply a set of population moment conditions that we can use to estimate the model's parameters by GMM. In particular, pay attention to how the moment conditions are derived within the model.

Section 3.1.1 and 3.1.2 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.

Lecture Note 8, Generalized Method of Moments.