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Abstract: This review presents empirical researchers with recent advances 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, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects ” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret, ” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiosis analysis that uses the strong features of both.

We consider probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., noncollapsibility), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjustment will reduce, increase, or leave unchanged the degree of bias in an association of two variables when that association is taken to represent a causal effect of one variable on the other. We then consider situations in which adjustment may partially remove or introduce a potential source of bias in estimating causal effects, and some additional special cases useful for case-control studies, cohort studies with loss, and trials with noncompliance (nonadherence).

This paper aims to acquaint researchers in the quantitative social and behavior sciences with recent advances in causal inference which provide a systematic methodology for defining, estimating, testing, and defending causal claims in experimental and observational studies. These advances are illustrated using a general theory of causation based on nonparametric structural equation models (SEM) – a natural generalization of those used by econometricians and social scientists in the 1950-60s, which provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret,” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper clarifies the role of propensity score matching in causal analysis, defines the relationships between the structural and potential-outcome frameworks, and develops symbiotic tools that use the strong features of both.

Abstract: This review presents empirical researcherswith recent advances 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, the conditional nature of all causal and counterfactual claims, and the methods that have been developed for the assessment of such claims. These advances are illustrated using a general theory of causation based on the Structural Causal Model (SCM) described in Pearl (2000a), which subsumes and unifies other approaches to causation, and provides a coherent mathematical foundation for the analysis of causes and counterfactuals. In particular, the paper surveys the development of mathematical tools for inferring (from a combination of data and assumptions) answers to three types of causal queries: (1) queries about the effects of potential interventions, (also called “causal effects ” or “policy evaluation”) (2) queries about probabilities of counterfactuals, (including assessment of “regret, ” “attribution” or “causes of effects”) and (3) queries about direct and indirect effects (also known as “mediation”). Finally, the paper defines the formal and conceptual relationships between the structural and potential-outcome frameworks and presents tools for a symbiotic analysis that uses the strong features of both.

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Recent advances in causal reasoning have given rise to a computation model that emulates the process by which humans generate, evaluate and distinguish counterfactual sentences. Though compatible with the “possible world ” account, this model enjoys the advantages of representational economy, algorithmic simplicity and conceptual clarity. Using this model, the paper demonstrates the processing of counterfactual sentences on a classical example due to Ernst Adam. It then gives a panoramic view of several applications where counterfactual reasoning has benefited problem areas in the empirical sciences. 1

We review probabilistic and graphical rules for detecting situations in which a dependence of one variable on another is altered by adjusting for a third variable (i.e., non-collapsibility or noninvariance under adjustment), whether that dependence is causal or purely predictive. We focus on distinguishing situations in which adjustment will reduce, increase, or leave unchanged the degree of bias in an association that is taken to represent a causal effect of one variable on the other. We then consider situations in which adjustment may partially remove or introduce a bias in estimating causal effects, and some additional special cases useful for case-control studies, cohort studies with loss, and trials with non-compliance (non-adherence). Key words: Bias; causality; causal models; collapsibility; compliance; confounding; graphical models; instrumental variables; mediation analysis; odds ratio. 1

We ask whether it is possible to determine, from statistical averages alone, whether a population under study consists of several subpopulations, unknown to the investigator, each responding differently to a given treatment? We show that such determination is feasible in three cases: (1) randomized trials with binary treatments, (2) models where treatment effects can be identified by adjustment for covariates, and (3) models in which treatment effects can be identified by mediating instruments. In each of these cases we provide an explicit condition which, if observed empirically, proves that treatment-effect is not uniform, but varies across individuals. 1