Lectures on causal inference

A twelve-chapter graduate textbook, written from scratch. The series builds sequentially from the Neyman-Rubin potential-outcomes framework to modern machine-learning-augmented causal inference. Each chapter contains: intended learning outcomes, a suggested 3-lecture plan, formal theorems with proofs, numbered equations, Python code with numpy / scikit-learn / statsmodels / econml / dowhy / pgmpy, synthetic worked examples, and graded exercises.

Target reader: strong first-year PhD student in statistics, economics, or machine learning.

Part I, Foundations

• Chapter 1 · Potential outcomes and causal estimands. Neyman-Rubin framework, ATE/ATT/CATE, the fundamental problem, Neyman’s 1923 variance formula, Fisher’s randomization test, SUTVA.
• Chapter 2 · Identification. Strong ignorability, g-formula proof, the Rosenbaum-Rubin propensity-score theorem, identification vs. estimation, sensitivity analysis with $\Gamma$-bounds and E-values.
• Chapter 3 · DAGs and the do-calculus. d-separation, backdoor and frontdoor criteria, Pearl’s three rules, Shpitser-Pearl identification algorithm.

Part II, Classical estimation

• Chapter 4 · Randomized experiments. Design choices, Neyman allocation, CUPED variance reduction with identity proof, cluster-randomized inference.
• Chapter 5 · Regression adjustment and weighting. Outcome regression, IPW, AIPW with double-robustness proof, matching.
• Chapter 6 · Instrumental variables. 2SLS, the Imbens-Angrist LATE theorem with full proof, weak-instrument diagnostics, control functions.

Part III, Panel data and staggered designs

• Chapter 7 · Difference-in-differences. Parallel trends, Goodman-Bacon decomposition, Callaway-Sant’Anna, the heterogeneous-effects revolution.
• Chapter 8 · Regression discontinuity. Sharp and fuzzy RD, local linear regression, CCT bias correction, McCrary density test.
• Chapter 9 · Synthetic control. Abadie-Diamond-Hainmueller, placebo inference, generalized SCM, synthetic DiD (Arkhangelsky et al. 2021).

Part IV, Modern ML-augmented causal inference

• Chapter 10 · Double machine learning. Neyman orthogonality, cross-fitting, rate conditions. The bridge between classical identification and modern ML estimation.
• Chapter 11 · Causal forests. Honest-split trees, Wager-Athey consistency theorem, generalized random forests, policy learning.
• Chapter 12 · Bayesian causal inference. Rubin’s Bayesian potential outcomes, BART (Hill 2011), Bayesian Causal Forests (Hahn-Murray-Carvalho 2020), Bayesian sensitivity analysis.

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