Causal Inference
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.
Core components
- Potential outcomes framework (Rubin Causal Model)
- Structural causal models and do-calculus (Pearl)
- Distinction between observation P(Y|X) and intervention P(Y|do(X))
- Counterfactual reasoning
- Confounding and back-door criterion
- Front-door criterion
- Causal graphs (DAGs with causal interpretation)
- Randomized controlled trials as gold standard
- Quasi-experimental methods (instrumental variables, regression discontinuity, difference-in-differences, propensity scores)
- Mediation analysis
- Causal discovery from observational data
- Connection to Bayesian networks
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
- The fundamental problem of causal inference (counterfactuals are unobserved) means that all causal claims from observational data require strong identifying assumptions that are often unverifiable
- tension between Rubin's potential outcomes and Pearl's structural causal models has produced substantial methodological debate (largely productive but sometimes generating confusion)
- causal discovery from observational data alone is often impossible without strong assumptions
- commercial 'causal AI' platforms vary in fidelity to underlying methodology
- the framework's mathematical sophistication can mask substantial subjectivity in DAG specification or assumption choice
- integration with machine learning is genuinely productive but requires substantial methodological care
- cross-cultural and cross-context generalization of causal estimates is a genuine challenge (transportability questions)
- the framework's success has produced 'causal' as buzzword in many applications where the methodology isn't actually being applied rigorously
- tension between observational and experimental approaches continues despite formal equivalences.
Lineage
- Child of
- Bayesian Networks
- Siblings
- Bayesian Networks, Bayesian Inference, Regression Analysis
- Derived from
- Bayesian Networks