{"schemaVersion":2,"id":"gmm","title":"Generalized Method of Moments (GMM)","totalStages":33,"modules":[{"id":"gmm-moments","title":"1 · Moment conditions","summary":"GMM turns 'what we know about the population' into equations the data must satisfy, then minimizes how far the sample violates them.","stageCount":8,"stages":[{"id":"gmm-moments-01","index":0,"moduleId":"gmm-moments","moduleIndex":0,"type":"read","title":"From assumptions to equations","skillIds":["gmm.moment-conditions"],"estimatedMinutes":6,"difficulty":"advanced","points":5},{"id":"gmm-moments-02","index":1,"moduleId":"gmm-moments","moduleIndex":1,"type":"read","title":"When you have more equations than unknowns","skillIds":["gmm.gmm-identification"],"estimatedMinutes":6,"difficulty":"advanced","points":5},{"id":"gmm-moments-03","index":2,"moduleId":"gmm-moments","moduleIndex":2,"type":"code","title":"Hand-roll GMM for a mean","skillIds":["gmm.moment-conditions"],"estimatedMinutes":10,"difficulty":"advanced","points":10},{"id":"gmm-moments-04","index":3,"moduleId":"gmm-moments","moduleIndex":3,"type":"interactive","title":"Watch the GMM objective J(μ)","skillIds":["gmm.gmm-identification"],"estimatedMinutes":8,"difficulty":"advanced","points":10},{"id":"gmm-moments-05","index":4,"moduleId":"gmm-moments","moduleIndex":4,"type":"quiz","title":"Check: counting moments","skillIds":["gmm.moment-conditions"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-moments-06","index":5,"moduleId":"gmm-moments","moduleIndex":5,"type":"quiz","title":"Check: what is a moment condition?","skillIds":["gmm.gmm-identification"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-moments-07","index":6,"moduleId":"gmm-moments","moduleIndex":6,"type":"fillblank","title":"Counting the surplus","skillIds":["gmm.moment-conditions"],"estimatedMinutes":4,"difficulty":"advanced","points":15},{"id":"gmm-moments-08","index":7,"moduleId":"gmm-moments","moduleIndex":7,"type":"numeric","title":"How many over-identifying restrictions?","skillIds":["gmm.gmm-identification"],"estimatedMinutes":5,"difficulty":"advanced","points":20}]},{"id":"gmm-iv","title":"2 · IV as GMM","summary":"Instrumental variables is GMM with the moment 'instruments are uncorrelated with the error.' We derive the IV/2SLS estimator from that single idea.","stageCount":8,"stages":[{"id":"gmm-iv-01","index":8,"moduleId":"gmm-iv","moduleIndex":0,"type":"read","title":"The instrument moment condition","skillIds":["gmm.gmm-criterion"],"estimatedMinutes":6,"difficulty":"advanced","points":5},{"id":"gmm-iv-02","index":9,"moduleId":"gmm-iv","moduleIndex":1,"type":"read","title":"Solving the just-identified case","skillIds":["gmm.iv-as-gmm"],"estimatedMinutes":6,"difficulty":"advanced","points":5},{"id":"gmm-iv-03","index":10,"moduleId":"gmm-iv","moduleIndex":2,"type":"code","title":"Endogeneity bias, then the IV fix","skillIds":["gmm.gmm-criterion"],"estimatedMinutes":10,"difficulty":"advanced","points":10},{"id":"gmm-iv-04","index":11,"moduleId":"gmm-iv","moduleIndex":3,"type":"code","title":"Same answer from statsmodels (the production tool)","skillIds":["gmm.iv-as-gmm"],"estimatedMinutes":10,"difficulty":"advanced","points":10},{"id":"gmm-iv-05","index":12,"moduleId":"gmm-iv","moduleIndex":4,"type":"interactive","title":"Instrument strength vs. precision","skillIds":["gmm.gmm-criterion"],"estimatedMinutes":8,"difficulty":"advanced","points":10},{"id":"gmm-iv-06","index":13,"moduleId":"gmm-iv","moduleIndex":5,"type":"quiz","title":"Check: which moment defines IV?","skillIds":["gmm.iv-as-gmm"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-iv-07","index":14,"moduleId":"gmm-iv","moduleIndex":6,"type":"quiz","title":"Check: just-identified weighting","skillIds":["gmm.gmm-criterion"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-iv-08","index":15,"moduleId":"gmm-iv","moduleIndex":7,"type":"fillblank","title":"Just-identified GMM has another name","skillIds":["gmm.iv-as-gmm"],"estimatedMinutes":4,"difficulty":"advanced","points":15}]},{"id":"gmm-overid","title":"3 · Over-identification & the J-test","summary":"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.","stageCount":9,"stages":[{"id":"gmm-overid-01","index":16,"moduleId":"gmm-overid","moduleIndex":0,"type":"read","title":"More instruments than you need","skillIds":["gmm.efficient-weighting"],"estimatedMinutes":6,"difficulty":"advanced","points":5},{"id":"gmm-overid-02","index":17,"moduleId":"gmm-overid","moduleIndex":1,"type":"read","title":"Hansen's J-statistic","skillIds":["gmm.j-test"],"estimatedMinutes":6,"difficulty":"advanced","points":5},{"id":"gmm-overid-03","index":18,"moduleId":"gmm-overid","moduleIndex":2,"type":"code","title":"Compute the J-statistic by hand","skillIds":["gmm.efficient-weighting"],"estimatedMinutes":10,"difficulty":"advanced","points":10},{"id":"gmm-overid-04","index":19,"moduleId":"gmm-overid","moduleIndex":3,"type":"code","title":"statsmodels reports jval for you","skillIds":["gmm.j-test"],"estimatedMinutes":10,"difficulty":"advanced","points":10},{"id":"gmm-overid-05","index":20,"moduleId":"gmm-overid","moduleIndex":4,"type":"interactive","title":"Push an instrument out of validity","skillIds":["gmm.efficient-weighting"],"estimatedMinutes":8,"difficulty":"advanced","points":10},{"id":"gmm-overid-06","index":21,"moduleId":"gmm-overid","moduleIndex":5,"type":"quiz","title":"Check: degrees of freedom","skillIds":["gmm.j-test"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-overid-07","index":22,"moduleId":"gmm-overid","moduleIndex":6,"type":"quiz","title":"Check: interpreting a small p-value","skillIds":["gmm.efficient-weighting"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-overid-08","index":23,"moduleId":"gmm-overid","moduleIndex":7,"type":"truefalse","title":"Does passing the J-test prove validity?","skillIds":["gmm.j-test"],"estimatedMinutes":3,"difficulty":"advanced","points":10},{"id":"gmm-overid-09","index":24,"moduleId":"gmm-overid","moduleIndex":8,"type":"multi","title":"What over-identification actually buys","skillIds":["gmm.efficient-weighting"],"estimatedMinutes":5,"difficulty":"advanced","points":20}]},{"id":"gmm-efficient","title":"4 · Efficient (two-step) GMM","summary":"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.","stageCount":8,"stages":[{"id":"gmm-efficient-01","index":25,"moduleId":"gmm-efficient","moduleIndex":0,"type":"read","title":"The optimal weighting matrix","skillIds":["gmm.gmm-variance"],"estimatedMinutes":6,"difficulty":"advanced","points":5},{"id":"gmm-efficient-02","index":26,"moduleId":"gmm-efficient","moduleIndex":1,"type":"read","title":"The chicken-and-egg, solved in two steps","skillIds":["gmm.gmm-variance"],"estimatedMinutes":6,"difficulty":"advanced","points":5},{"id":"gmm-efficient-03","index":27,"moduleId":"gmm-efficient","moduleIndex":2,"type":"code","title":"One-step vs two-step: the efficiency gain","skillIds":["gmm.gmm-variance"],"estimatedMinutes":10,"difficulty":"advanced","points":10},{"id":"gmm-efficient-04","index":28,"moduleId":"gmm-efficient","moduleIndex":3,"type":"interactive","title":"Number of (valid) instruments → efficiency","skillIds":["gmm.gmm-variance"],"estimatedMinutes":8,"difficulty":"advanced","points":10},{"id":"gmm-efficient-05","index":29,"moduleId":"gmm-efficient","moduleIndex":4,"type":"quiz","title":"Check: the efficient weighting matrix","skillIds":["gmm.gmm-variance"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-efficient-06","index":30,"moduleId":"gmm-efficient","moduleIndex":5,"type":"quiz","title":"Check: why two steps?","skillIds":["gmm.gmm-variance"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-efficient-07","index":31,"moduleId":"gmm-efficient","moduleIndex":6,"type":"quiz","title":"Check: a hidden bonus","skillIds":["gmm.gmm-variance"],"estimatedMinutes":5,"difficulty":"advanced","points":15},{"id":"gmm-efficient-08","index":32,"moduleId":"gmm-efficient","moduleIndex":7,"type":"truefalse","title":"Is more instruments always better?","skillIds":["gmm.gmm-variance"],"estimatedMinutes":3,"difficulty":"advanced","points":10}]}]}