CAUSALITY. Models, Reasoning, and Inference 1 CAMBRIDGE UNIVERSITY PRESS. Judea Pearl. University of California, Los Angeles

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1 CAUSALITY Models, Reasoning, and Inference Judea Pearl University of California, Los Angeles 1 CAMBRIDGE UNIVERSITY PRESS

2 Preface page xiii 1 Introduction to Probabilities, Graphs, and Causal Models Introduction to Probability Theory Why Probabilities? Basic Concepts in Probability Theory Combining Predictive and Diagnostic Supports Random Variables and Expectations Conditional Independence and Graphoids Graphs and Probabilities Graphical Notation and Terminology Bayesian Networks The d-separation Criterion Inference with Bayesian Networks Causal Bayesian Networks Causal Networks as Oracles for Interventions Causal Relationships and Their Stability Functional Causal Models Structural Equations Probabilistic Predictions in Causal Models Interventions and Causal Effects in Functional Models Counterfactuals in Functional Models Causal versus Statistical Terminology 38 2 A Theory of Inferred Causation Introduction The Causal Modeling Framework Model Preference (Occam's Razor) Stable Distributions Recovering DAG Structures Recovering Latent Structures Local Criteria for Causal Relations 54 VII

3 2.8 Nontemporal Causation and Statistical Time Conclusions On Minimality, Markov, and Stability 61 Causal Diagrams and the Identification of Causal Effects Introduction Intervention in Markovian Models Graphs as Models of Interventions Interventions as Variables Computing the Effect of Interventions Identification of Causal Quantities Controlling Confounding Bias The Back-Door Criterion The Front-Door Criterion Example: Smoking and the Genotype Theory A Calculus of Intervention Preliminary Notation Inference Rules Symbolic Derivation of Causal Effects: An Example Causal Inference by Surrogate Experiments Graphical Tests of Identifiability Identifying Models Nonidentifying Models Discussion Qualifications and Extensions Diagrams as a Mathematical Language Translation from Graphs to Potential Outcomes Relations to Robins's G-Estimation 102 Actions, Plans, and Direct Effects Introduction Actions, Acts, and Probabilities Actions in Decision Analysis Actions and Counterfactuals Conditional Actions and Stochastic Policies When Is the Effect of an Action Identifiable? Graphical Conditions for Identification Remarks on Efficiency Deriving a Closed-Form Expression for Control Queries Summary The Identification of Plans Motivation Plan Identification: Notation and Assumptions Plan Identification: A General Criterion Plan Identification: A Procedure 124

4 4.5 Direct Effects and Their Identification Direct versus Total Effects Direct Effects, Definition, and Identification Example: Sex Discrimination in College Admission Average Direct Effects 130 Causality and Structural Models in Social Science and Economics Introduction Causality in Search of a Language SEM: How its Meaning Became Obscured Graphs as a Mathematical Language Graphs and Model Testing The Testable Implications of Structural Models Testing the Testable Model Equivalence Graphs and Identifiability Parameter Identification in Linear Models Comparison to Nonparametric Identification Causal Effects: The Interventional Interpretation of Structural Equation Models Some Conceptual Underpinnings What Do Structural Parameters Really Mean? Interpretation of Effect Decomposition Exogeneity, Superexogeneity, and Other Frills Conclusion 170 Simpson's Paradox, Confounding, and Collapsibility Simpson's Paradox: An Anatomy A Tale of a Non-Paradox A Tale of Statistical Agony Causality versus Exchangeability A Paradox Resolved (Or: What Kind of Machine Is Man?) Why There Is No Statistical Test for Confounding, Why Many Think There Is, and Why They Are Almost Right Introduction Causal and Associational Definitions How the Associational Criterion Fails Failing Sufficiency via Marginality Failing Sufficiency via Closed-World Assumptions Failing Necessity via Barren Proxies Failing Necessity via Incidental Cancellations Stable versus Incidental Unbiasedness Motivation Formal Definitions Operational Test for Stable No-Confounding 192

5 x 6.5 Confounding, Collapsibility, and Exchangeability Confounding and Collapsibility Counfounding versus Confounders Exchangeability versus Structural Analysis of Confounding Conclusions The Logic of Structure-Based Counterfactuals Structural Model Semantics Definitions: Causal Models, Actions, and Counterfactuals Evaluating Counterfactuals: Deterministic Analysis Evaluating Counterfactuals: Probabilistic Analysis The Twin Network Method Applications and Interpretation of Structural Models Policy Analysis in Linear Econometric Models: An Example The Empirical Content of Counterfactuals Causal Explanations, Utterances, and Their Interpretation From Mechanisms to Actions to Causation Simon's Causal Ordering Axiomatic Characterization The Axioms of Structural Counterfactuals Causal Effects from Counterfactual Logic: An Example Axioms of Causal Relevance Structural and Similarity-Based Counterfactuals Relations to Lewis's Counterfactuals Axiomatic Comparison Imaging versus Conditioning Relations to the Neyman-Rubin Framework Exogeneity Revisited: Counterfactual and Graphical Definitions Structural versus Probabilistic Causality The Reliance on Temporal Ordering The Perils of Circularity The Closed-World Assumption Singular versus General Causes Summary Imperfect Experiments: Bounding Effects and Counterfactuals Introduction Imperfect and Indirect Experiments Noncompliance and Intent to Treat Bounding Causal Effects Problem Formulation The Evolution of Potential-Response Variables Linear Programming Formulation 266

6 xi The Natural Bounds Effect of Treatment on the Treated Example: The Effect of Cholestyramine Counterfactuals and Legal Responsibility A Test for Instruments Causal Inference from Finite Samples Gibbs Sampling The Effects of Sample Size and Prior Distribution Causal Effects from Clinical Data with Imperfect Compliance Bayesian Estimate of Single-Event Causation 280 8:6 Conclusion Probability of Causation: Interpretation and Identification Introduction Necessary and Sufficient Causes: Conditions of Identification Definitions, Notation, and Basic Relationships Bounds and Basic Relationships under Exogeneity Identifiability under Monotonicity and Exogeneity Identifiability under Monotonicity and Nonexogeneity Examples and Applications Example 1: Betting against a Fair Coin Example 2: The Firing Squad Example 3: The Effect of Radiation on Leukemia Example 4: Legal Responsibility from Experimental and Nonexperimental Data Summary of Results Identification in Nonmonotonic Models Conclusions The Actual Cause Introduction: The Insufficiency of Necessary Causation Singular Causes Revisited Preemption and the Role of Structural Information Overdetermination and Quasi-Dependence Mackie's INUS Condition Production, Dependence, and Sustenance Causal Beams and Sustenance-Based Causation Causal Beams: Definitions and Implications Examples: From Disjunction to General Formulas Beams, Preemption, and the Probability of Single-Event Causation Path-Switching Causation Temporal Preemption Conclusions 327

7 xii Epilogue The Art and Science of Cause and Effect A public lecture delivered November 1996 as part of the UCLA Faculty Research Lectureship Program 331 Bibliography 359 Name Index 375 Subject Index 379