The Variational Method of Moments

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" summary

Proposes the variational method of moments (VMM): a minimax formulation that replaces K test functions with a rich RKHS or neural-net class and an optimal-weighting penalty to recover identification, asymptotic normality and semiparametric efficiency for finite-dimensional θ; two-stage VMM yields consistent, asymptotically linear estimates and a minimax-on-minimax procedure that consistently estimates the asymptotic variance for valid confidence intervals. Implements kernel VMM and neural VMM (optimized with O-ADAM), shows lower MSE than spline/sieve IV in experiments and improving coverage with larger n.

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" chapters (14)

1. 0:00Intro
2. 1:03Endogeneity
3. 2:45IV Model
4. 8:29Reduction to Marginal Moment Problem
5. 12:28Sieve approaches
6. 15:06Minimax approaches
7. 19:11Variational Reformulation of OWGMM
8. 21:38Variational Method of Moments
9. 24:11VMM Variants
10. 26:12Implementing VMM
11. 33:09Semiparametric Efficiency
12. 36:17Kernel VMM Inference
13. 39:59Beyond efficiency
14. 47:36Experiments

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