Theory

The mathematical foundations, in two tracks. This is the section to read slowly. The Estimation and Inference sections tell you how to run the methods; this section is the why, the derivations and the guarantees.

Theory

  • The FLM Framework is the influence-function theory, worked through linear and logit: the enriched structural model, why naive plug-in inference fails, the influence-function correction and where it comes from, the three regimes for the expected Hessian, and the formal convergence and normality guarantees.

  • RieszNet and Automatic Debiasing is the Riesz-representer theory: the debiasing term, the mixed-bias (double-robustness) property, the Riesz loss that learns the representer without an analytic formula, targeted regularization, and the bridge showing that the FLM correction and the RieszNet correction are the same object.

The core insight

Machine learning and economic structure are complements, not substitutes.

  • ML alone fits data well but extrapolates nonsensically and cannot answer causal questions.

  • Structure alone provides interpretability but misses heterogeneity.

  • Combined, ML learns the heterogeneity patterns \(\theta(X)\) while the structure keeps the economics, and the target, valid.

β€œThe central idea is that machine learning methods and economic structure are complements, not substitutes. Machine learning methods alone predict well, but extrapolate nonsensically. Economic structure alone can produce robust inference, but may miss important heterogeneity that is visible in the data.” (Farrell, Liang, Misra, 2021)

The papers are collected, annotated, on the References page.