Causal Inference Notes

My study notes on causal inference and causal machine learning, arranged as a reading path. Each chapter builds on the previous ones, but every note can be read on its own.

1. Start here

Overviews and reading lists to get oriented.

• A Review of Causal Inference Methods — twelve methods, from DiD, IV and RD to causal forests and DML, compared side by side.
• Learning Resource: Causal Inference — videos, courses and reading lists on theory, R, Python, DiD and synthetic control.
• Learning Resource: Causal Machine Learning with DoubleML — an introduction to double machine learning, with learning resources.

2. Selection on observables

Unconfoundedness: weighting, outcome modeling, and combining the two.

• Notes on Propensity Score Methods — the propensity score for dimension reduction, stratification, weighting and balance (Ding 2024).
• Adjust Censoring and Confounding Bias by IP Weighting — inverse probability weights for confounding and right censoring in survival data.
• Intuition for Doubly Robust Estimator — why combining a propensity model and an outcome model protects against misspecification.
• Balancing Weights for Causal Inference — choosing weights to balance covariates directly.
• AIPW vs. Residual-on-Residual Regression — the nonparametric AIPW estimator versus the partially linear residual-on-residual estimator.

3. Debiased machine learning and semiparametric theory

Why ML nuisance estimates can still give valid inference.

• Notes on Semiparametric Models — tangent spaces, nuisance tangent spaces and efficient estimation.
• From Donsker Classes to Neyman Orthogonality — how orthogonality and cross-fitting replace Donsker conditions.
• Orthogonal vs Non-orthogonal Learning — a simulation comparing naive and Neyman-orthogonal estimators.
• Big Picture of Debiased Machine Learning — DML as a generic recipe: a plug-in estimator plus a correction term.
• A Road Map of Nonparametric Efficiency in Causal Inference — efficiency bounds, the efficient influence function and its link to the Riesz representer (Kennedy 2023).
• What is the Critical Radius in Riesz Regression? — the complexity measure behind Riesz representer rates.
• Calibrate Your Nuisances — calibrating nuisance estimates for doubly robust inference.

4. Unobserved confounding

When unconfoundedness fails: instruments, discontinuities, and sensitivity.

• Notes on Instrumental Variables — from the linear constant-effect model to LATE.
• Notes on IV Free Methods — latent instruments and Gaussian copula approaches.
• Notes on Control Function Method — correcting endogeneity by modeling the first stage.
• Regression Discontinuity — identification when treatment is assigned by a cutoff, so there is no overlap.
• Hausman-Taylor Estimator Notes — an R example for panel data with time-invariant regressors and endogeneity.
• Bounding OVB in Causal ML — sensitivity analysis for omitted-variable bias.

5. Panel data, DiD and synthetic control

Using time to build counterfactuals.

• Callaway & Sant’Anna (2021): Staggered Adoption DiD — group-time ATTs under staggered treatment timing.
• Notes on DML for DiD — a unified debiased-ML approach to difference-in-differences.
• Notes on Synthetic Control — weighting donor units to reproduce the treated unit.
• The Augmented Synthetic Control Method — bias correction when the synthetic control does not fit well.
• Matrix Completion for Causal Panel Data — imputing untreated outcomes with low-rank structure (Athey et al. 2021).
• Notes on Interactive Fixed Effects — factor models for unobserved time-varying confounding (Bai 2009).
• Same Root, Different Leaves — horizontal vs. vertical regression in panel data.
• Triply Robust Panel Estimators — combining unit weights, time weights and outcome models.
• Synthetic Controls for Experimental Design — choosing which units to treat (Abadie and Zhao 2025).
• Conformal Inference for Counterfactual and Synthetic Controls — inference with a single treated unit as a residual-based test.

6. Heterogeneity, survival and experiments

Beyond the average effect.

• A Walkthrough of How Causal Forest Works — estimating heterogeneous treatment effects, following the grf tutorial.
• Notes on Causal Survival Forest — causal forests for right-censored outcomes (Cui et al. 2023).
• Doubly Robust Censoring Unbiased Transformation — combining Buckley–James and IPCW into one doubly robust transformation (Rubin and van der Laan 2007).
• The Experimental Selection Correction Estimator — combining experimental and observational data to remove bias (Athey, Chetty and Imbens).

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