1 · Moment conditions
GMM turns 'what we know about the population' into equations the data must satisfy, then minimizes how far the sample violates them.
Generalized Method of Moments (GMM)
Moment conditions as a unifying estimator, IV-GMM, over-identification, efficiency.
Course overview
Learn Generalized Method of Moments (GMM) interactively
This free course uses real Python and statsmodels in your browser. Work through the modules below with explanations, executable examples, interactive controls, and questions.
2 · IV as GMM
Instrumental variables is GMM with the moment 'instruments are uncorrelated with the error.' We derive the IV/2SLS estimator from that single idea.
3 · Over-identification & the J-test
Extra instruments give extra moment conditions. They can't all be satisfied at once — and that leftover disagreement becomes a test of whether your instruments are valid.
4 · Efficient (two-step) GMM
Among all weighting matrices, the inverse of the moment covariance gives the smallest variance. Two-step GMM estimates it from a first pass and re-optimizes.