Causal Machine Learning

Reference for semiparametric ML estimators: DML with cross-fitting, generalized random forests, debiased regularization, and nuisance function approximation. Covers Neyman-orthogonal moment conditions, sample splitting, plug-in bias correction, and heterogeneous treatment effects.

When to Use This Skill

Use when the user is:

• Estimating treatment effects with high-dimensional controls (p large relative to n)
• Interested in heterogeneous treatment effects (CATE) as a primary estimand
• Applying ML for flexible nuisance function estimation within a causal framework
• Implementing cross-fitting, sample splitting, or Neyman-orthogonal estimators
• Using econml, DoubleML, or grf packages

Skip when:

• Sample is small (n < 500 — ML nuisance models need data)
• A well-specified parametric model is available and defensible
• The task is standard IV/DiD/RDD without high-dimensional controls (use causal-inference skill)
• Structural modeling is needed (use structural-modeling skill)
• The task needs formal identification proof (use identification-proofs skill)

Where to Start

• Choosing a method? Jump to Method Selection Guide
• ATE with many controls? See references/dml.md
• Heterogeneous treatment effects? See references/grf-meta-learners.md
• Variable selection for controls? See references/high-dim-cross-fitting.md
• Reporting HTE results? See references/hte-inference.md
• Connecting to traditional methods? See references/connections-traditional.md

Causal ML vs Traditional Methods

| Dimension | Traditional (IV, DiD, RDD) | Causal ML | |-----------|--------------------------|-----------| | Functional form | Parametric | Nonparametric / semi-parametric | | High-dimensional controls | Problematic | Native support | | Heterogeneous effects | Secondary (subgroup analysis) | Primary estimand (CATE) | | Sample requirements | Moderate N | ML nuisance needs large N | | Identification | Explicit (IV, DiD, RCT) | Same assumptions — ML is estimation, not identification |

Critical point: Causal ML does not relax identification assumptions. If you need a valid instrument, parallel trends, or no unmeasured confounding, those must still hold.

Double Machine Learning (DML)

DML (Chernozhukov et al. 2018) fixes regularization bias in naive ML-in-regression. Partial out controls X from both Y and D using separate ML nuisance models, then regress residuals. Two properties: Neyman orthogonality (moment condition locally insensitive to nuisance error) and cross-fitting (prevents overfitting bias).

PLR (Partially Linear Regression): $Y = \theta D + g(X) + \varepsilon$. Workhorse for continuous or binary D with ATE under selection on observables. IRM (Interactive Regression Model): relaxes additive separability for binary D with heterogeneous effects.

Full implementation (Python/R code, cross-fitting from scratch, diagnostics) in references/dml.md.

Causal Forests

Causal forests (Wager-Athey 2018; Athey-Tibshirani-Wager 2019) estimate CATE $\tau(x) = EY(1)-Y(0)|X=x]$ using honest forests (structure learned on one subsample, effects estimated on another). Use when CATE is the primary estimand and n $\geq$ 2,000. Always run the calibration test before reporting heterogeneity.

R (grf) and Python (econml) implementations, ATE/ATT extraction, BLP projections in references/grf-meta-learners.md.

Meta-Learners

Decompose CATE estimation into supervised learning sub-problems. DR-Learner (Kennedy 2023): best properties when both nuisance models are well-specified. T-Learner: simplest baseline. X-Learner: designed for imbalanced treatment. For applied work: DR-Learner primary, T-Learner benchmark. Large disagreement signals nuisance model problems.

All implementations in references/grf-meta-learners.md.

High-Dimensional Controls

PDS-LASSO (Belloni-Chernozhukov-Hansen 2014): separate LASSOes of Y on X and D on X, union of selected variables, then OLS. Works at moderate n (~200 with sparse confounders). See references/high-dim-cross-fitting.md.

HTE Inference

Before reporting CATE, test for genuine heterogeneity using BLP calibration test. Do not report heterogeneous effects if calibration test fails (p > 0.10). See references/hte-inference.md.

Method Selection Guide

Decision Heuristic

1. n < 500? → Use standard methods (causal-inference skill)
2. High-dim controls (p > 20), want ATE? → PDS-LASSO or DML-PLR; binary D → DML-IRM
3. CATE is primary estimand? → Causal Forest (large n) or DR-Learner (doubly robust)
4. Endogenous treatment with instrument? → DML-PLIV
5. Treatment is rare/imbalanced? → X-Learner
6. Quick benchmark? → Always compute T-Learner as baseline

Full Method Comparison

| Method | Estimand | Python | R | Min n | Key diagnostic | |--------|----------|--------|---|-------|----------------| | DML-PLR | ATE | doubleml, econml | DoubleML | ~500 | Nuisance R², residual balance | | DML-IRM | ATE (binary D) | doubleml, econml | DoubleML | ~500 | Propensity AUC, trim threshold | | DML-PLIV | LATE | doubleml, econml | DoubleML | ~1,000 | Effective F-stat | | Causal Forest | CATE(x) | econml | grf | ~2,000 | Calibration test, ATE match | | DR-Learner | CATE(x) | econml.dr | manual/grf | ~1,000 | Propensity calibration | | PDS-LASSO | ATE (high-dim X) | sklearn + manual | hdm | ~200 | Union size, penalty sensitivity | | X-Learner | CATE (imbalanced D) | econml | manual | ~1,000 | Compare to DR-Learner |

Limitations to State Explicitly

• ML needs data: Causal forests need n $\geq$ 2,000; DML needs n $\geq$ 500. Below these, use parametric methods.
• Identification is not relaxed: ML is better nuisance estimation, not weaker assumptions.
• CATE inference is hard: Individual-level CIs are conservative; policy targeting requires care.
• Publication: DML and causal forests are mainstream in top applied micro journals. Compare to traditional estimators.

Connections to Traditional Methods

Causal ML nests traditional estimators: DML with linear nuisance = OLS (Frisch-Waugh), DML + IV = PLIV, causal forests + instrument = heterogeneous LATE (grf::instrumental_forest), post-LASSO + many instruments = sparse instrument selection then 2SLS. Details in references/connections-traditional.md.

Integration with Plugin

Agents: econometric-reviewer (post-estimation review, table/code consistency), identification-critic (IV/PLIV assumptions), numerical-auditor (convergence, seeding, Monte Carlo validation).

Cross-references: empirical-playbook skill → sensitivity-analysis.md (specification curve over ML choices), empirical-playbook skill → diagnostic-battery.md (nuisance R², overlap, calibration), numerical-auditor agent (synthetic data with known CATE).

Relationship to causal-inference skill: Use causal-inference to establish identification; use causal-ml for implementation with high-dimensional controls or when heterogeneity is primary. Complements, not substitutes.

Reference Files

• references/dml.md — Full DML implementation: PLR, IRM, PLIV with econml/DoubleML, cross-fitting, diagnostics
• references/grf-meta-learners.md — Causal forests (grf/econml), DR/T/S/X-Learner, calibration tests
• references/high-dim-cross-fitting.md — PDS-LASSO, Belloni-Chernozhukov-Hansen, cross-fitting protocols
• references/hte-inference.md — Calibration tests, individual CATE CIs, BLP projections, subgroup analysis
• references/connections-traditional.md — DML-OLS equivalence, PLIV, instrumental forests, post-LASSO