Generalized method of moments — generalizes the founding example of → Partially specified models

Partially specified models are introduced through a single worked example: a linear regression y = + v where only E[v|x] = 0 is assumed about the noise, with no distributional form specified, which the paper shows is already enough to identify w* under distributional shift (concrete-problems, §"Partially specified models: method of moments, unsupervised risk estimation, causal identification, and limited-information maximum likelihood.", p. 17). The generalized method of moments is presented as both the historical motivation for this insight and its general form: an econometric framework for identifying parameters from a set of moment conditions like E[v|x]=0, without specifying the full data-generating distribution (concrete-problems, same section, p. 18). Where the worked example is a single illustrative moment condition, GMM is the machinery for combining many such conditions and proving identification and consistency for the resulting estimator, which is what lets partial specification scale past toy cases.