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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.

This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl (1999) by presenting sharp bounds based on combined experimental and nonexperimental data under no process assumptions, as well as under the mild assumptions of exogeneity (no confounding) and monotonicity (no prevention). These results delineate more precisely the basic assumptions that must be made before statistical measures such as the excess-risk-ratio could be used for assessing attributional quantities such as the probability of causation. 1

This paper aims at assisting empirical researchers benefit from recent advances in causal inference. The paper 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. These emphases are illustrated through a brief survey of recent results, including the control of confounding, the assessment of causal effects, the interpretation of counterfactuals, and a symbiosis between counterfactual and graphical methods of analysis.

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Directed Acyclic Graphs (DAG's) and Error Correction Models (ECM's) are employed to analyze questions of price discovery between spatially separated commodity markets and the transportation market linking them together. Results from our analysis suggest these markets are highly interconnected but it is the inland commodity market that is strongly influenced by both the transportation and commodity export markets. However, the commodity markets affect the volatility of the transportation market over longer horizons. Our results suggest that transportation rates are critical in the price discovery process lending support for the recent development of exchange traded barge rate futures contracts.

Although probabilistic knowledge representations and probabilistic reasoning have by now secured their position in artificial intelligence, it is not uncommon to encounter misunderstanding of their foundations and lack of appreciation for their strengths. This paper describes five properties of probabilistic knowledge representations that are particularly useful in intelligent systems research. (1) Directed probabilistic graphs capture essential qualitative properties of a domain, along with its causal structure. (2) Concepts such as relevance and conflicting evidence have a natural, formally sound meaning in probabilistic models. (3) Probabilistic schemes support sound reasoning at a variety of levels ranging from purely quantitative to purely qualitative levels. (4) The role of probability theory in reasoning under uncertainty can be compared to the role of first order logic in reasoning under certainty. Probabilistic knowledge representations provide insight into the foundations of logic-based schemes, showing their difficulties in highly uncertain domains. Finally, (5) probabilistic knowledge representations support automatic generation of understandable explanations of inference for the sake of user interfaces to intelligent systems.

This paper provides a conceptual introduction to causal inference, aimed to assist health services researchers benefit from recent advances in this area. The paper 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 underlie all causal inferences, the languages used in formulating those assumptions, and the conditional nature of causal claims inferred from nonexperimental studies. These emphases are illustrated through a brief survey of recent results, including the control of confounding, corrections for noncompliance, and a symbiosis between counterfactual and graphical methods of analysis.

The paper considers the use of directed acyclic graphs (DAGs), and their construction from observational data with PC-algorithm TETRAD II, in providing over-identifying restrictions on the innovations from a vector autoregression. Results from Sims ’ 1986 model of the US economy are replicated and compared using these data-driven techniques. The directed graph results show Sims ’ six-variable VAR is not rich enough to provide an unambiguous ordering at usual levels of statistical significance. A significance level in the neighborhood of 30 % is required to find a clear structural ordering. Although the DAG results are in agreement with Sims ’ theory-based model for unemployment, differences are noted for the other five variables: income, money supply, price level, interest rates, and investment. Overall the DAG results are broadly consistent with a monetarist view with adaptive expectations and no hyperinflation.

This paper deals with the problem of identifying direct causal effects in recursive linear structural equation models. The paper establishes a sufficient criterion for identifying individual causal effects and provides a procedure computing identified causal effects in terms of observed covariance matrix.