GMM and econometrics teaching

My last post discussed the impact of GMM on econometrics theory. I would also add that the ideas behind GMM could also have an impact on econometrics teaching. The explanation is a bit technical.

In most econometrics courses, the teaching roughly follows the path that econometrics took during its discovery. So least squares is taught first, then variations on least squares, then more complex testing, then maximum likelihood estimation, and so on. Least squares is intuitively relatively appealing, so the students have an easy entry to the course. However, at some point, around the entry of two stage least squares or instrumental variables, the student has to shift from the intuitive graphical representation of least squares to the abstract representation of orthogonality. The effect is a little jarring, like cycling along at a fair rate, then peddling backwards and going down a side street some hundred metres back. If the student hasn't got the idea by then, they will struggle with the derivations of recent tests on bias in residuals, which often use orthogonality twice or more in their testing procedure.

Since GMM theory establishes the general applicability of orthogonality, it seems like a reasonable idea to introduce the whole econometrics theory with a discussion of it. Of course least squares' derivation can be retained, but it should act as a support for orthogonality in the introduction rather than being the centre of attention. The whole idea of orthogonality can be given a graphical representation for each of the types of estimator - it is only right angles in a suitable space after all, and even the founding paper of GMM could be portrayed in a child's cartoon, albeit a seriously dull one. Then the main sections of conventional analysis of each of the estimators and tests could occur.