Causal Inference

framework · mathematics · formal-scientific

Pearl and Rubin's frameworks for distinguishing correlation from causation.

Causal Inference is the formal framework for drawing conclusions about causal relationships from data, addressing the foundational question of when correlation does and doesn't imply causation. Two principal frameworks have substantially shaped the modern discipline. (1) Donald Rubin's potential outcomes framework (Rubin Causal Model, articulated from the 1970s onward) defines causal effects in terms of potential outcomes — what would have happened under treatment versus control for the same unit — with the fundamental problem of causal inference being that we observe only one of these. (2) Judea Pearl's structural causal models and do-calculus (Causality 2000, second edition 2009) extends Bayesian networks (separately enriched) with causal interpretation, distinguishing observation (P(Y|X)) from intervention (P(Y|do(X))), and providing graphical criteria (back-door criterion, front-door criterion) for identifying causal effects from observational data. The two frameworks are largely equivalent (mappings exist between them) but emphasize different tools: potential outcomes is dominant in statistics and economics; structural causal models in computer science and AI. Substantial methodological developments include: randomized controlled trials as gold standard; difference-in-differences and instrumental variables in economics; propensity-score matching; regression discontinuity; mediation analysis; causal discovery (learning causal graphs from data — PC algorithm, FCI, recent deep learning approaches). The framework has had enormous impact in epidemiology (smoking-cancer establishment, COVID-19 policy), economics (development economics, labor economics — Card, Imbens, Angrist 2021 Nobel for causal inference methodology), policy analysis, and increasingly in machine learning.

Originators

Donald Rubin (potential outcomes framework, 1970s onward); Judea Pearl (structural causal models and do-calculus, 1980s onward); intellectual antecedents in Sewall Wright (path analysis, 1921), Jerzy Neyman (1923 potential outcomes precursor); subsequent foundational figures including Joshua Angrist, Guido Imbens, James Heckman high

Year / Decade

1923 (Neyman precursor); 1974 (Rubin foundational); 2000 (Pearl's Causality 1st ed); 2009 (2nd ed); 2021 (Card-Angrist-Imbens Nobel) high

Primary sources

Rubin, D.B. (1974). 'Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies', Pearl, J. (2000, 2nd ed. 2009). Causality: Models, Reasoning, and Inference, Pearl, J. & Mackenzie, D. (2018). The Book of Why (popular), Imbens, G.W. & Rubin, D.B. (2015). Causal Inference for Statistics, Social, and Biomedical Sciences high

Core components

Primary use case

Foundation of modern epidemiology (smoking-cancer, drug efficacy, public health intervention evaluation); modern empirical economics (Angrist-Pischke 'credibility revolution' methodology); policy evaluation (development economics, education economics); medical statistics and clinical research; growing application in machine learning (causal representation learning, fairness, interpretability); foundation for substantial methodological work in social and natural sciences; reference framework in modern statistics and econometrics curricula.

Common criticisms

Lineage

Child of
Bayesian Networks
Siblings
Bayesian Networks, Bayesian Inference, Regression Analysis
Derived from
Bayesian Networks