The Mathematics of Causal Relations

This paper introduces empirical researchers to recent a d v ances in causal inference and stresses the paradigmatic shifts that must be undertaken in moving from traditional statistical analysis to causal analysis of multivariate data. Special emphasis is placed on the assumptions that underly all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. In particular, the paper advocates a formalism based on nonparametric structural equations Pearl, 2000a] which p r o vides both a mathematical foundation for the analysis of counterfactuals and a conceptually transparent language for expressing causal knowledge. This framework gives rise to a friendly calculus of causation that uniies the graphical, potential outcome (Neyman-Rubin) and structural equation approaches and resolves long-standing problems in several of the sciences. These include questions of confounding, causal eeect estimation, policy analysis, legal responsibility, direct and indirect eects, instrumental variables, surrogate designs, and the integration of data from experimental and observational studies.

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