At three separate recent non-American conferences, I heard three separate European econometricians refer to generalized method of moments (GMM) as a "strange American estimator." Needless to say, that raised my eyebrows. One doesn't hear that phrase too often in, say, Stanford or Chicago or Cambridge (Massachusetts, that is).
Although I am American, I have some sympathy for the European view (if I may be so bold as to assert that my sample of size three has indeed uncovered a "view"). I may even have significantly more sympathy than do most Americans. But ultimately my feelings are mixed.
On the one hand, it seems clear that frequentist statisticians dismissed method-of-moments and minimum chi-squared (their term for GMM) ages ago as inefficient relative to MLE, and that Bayesian statisticians never dismissed them because they never paid them any attention in the first place. Instead, both communities have always thoroughly and intentionally focused on the likelihood -- frequentists on the location of its max and its curvature in an epsilon-neighborhood of the max, and Bayesians on its entire shape.
Surely this historical background is what drives the European view. And against that background, I too am always a bit perplexed by the GMM phenomenon, as distilled for example in Hayashi's classic econometrics text, which reads in significant part as something of a prayer book for the GMM congregation. (Never mind that my friend and former-colleague Hayashi is Japanese; his econometrics training and style are thoroughly American.)
That is, I must admit that, in part, I too am rather skeptical. Somehow my community just never got the religion. My belief is probably restrained significantly by the fact that my interest centers on dynamic predictive econometric modeling, which is often best done in reduced-form (see No Hesitations, June 12, 2013). Hence one of the grand sources of GMM moment conditions -- orthogonality between instruments and disturbances in estimating causal effects -- is, for me, typically neither here nor there.
On the other hand, my sympathy for the European view is far from complete. For example, some important classes of economic models produce moment restrictions but not full likelihoods. Despite the GMM crowd's repeating that mantra ad nauseum, it's as true now as ever. But if the story of GMM's appeal ended with its usefulness when a model fails to produce a likelihood, I'd be underwhelmed. Maybe I'd even move to Europe.
What then do I find so additionally impressive about GMM? Stay tuned for the next post.