Introduction The introduction of Bayesian networks (Pearl 1986b) and associated local computation algorithms (Lauritzen and Spiegelhalter 1988, Shenoy and Shafer 1990, Jensen, Lauritzen and Olesen 1990) has initiated a renewed interest for understanding causal concepts in connection with modelling complex stochastic systems. It has become clear that graphical models, in particular those based upon directed acyclic graphs, have natural causal interpretations and thus form a base for a language in which causal concepts can be discussed and analysed in precise terms. As a consequence there has been an explosion of writings, not primarily within mainstream statistical literature, concerned with the exploitation of this language to clarify and extend causal concepts. Among these we mention in particular books by Spirtes, Glymour and Scheines (1993), Shafer (1996), and Pearl (2000) as well as the collection of papers in Glymour and Cooper (1999). Very briefly, but fundamentally,

JEL No. C10 The major contributions of twentieth century econometrics to knowledge were the definition of causal parameters when agents are constrained by resources and markets and causes are interrelated, the analysis of what is required to recover causal parameters from data (the identification problem), and clarification of the role of causal parameters in policy evaluation and in forecasting the effects of policies never previously experienced. This paper summarizes the development of those ideas by the Cowles Commission, the response to their work by structural econometricians and VAR econometricians, and the response to structural and VAR econometrics by calibrators, advocates of natural and social experiments, and by nonparametric econometricians and statisticians.

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Analysis of randomized experiments with missing covariate and outcome data is problematic because the population parameters of interest are not identified unless one makes untestable assumptions about the distribution of the missing data. This paper shows how population parameters can be bounded without making untestable distributional assumptions. Bounds are also derived under the assumption that covariate data are missing completely at random. In each case the bounds are sharp; they exhaust all of the information that is available given the data and the maintained assumptions. The bounds are illustrated with applications to data obtained from a clinical trial and data relating family structure to the probability that a youth graduates from high school. Key Words: Identification, attrition, bounds We thank William G. Henderson, Domenic Reda, and David Williams of the Edward Hines, Jr., Hospital, U.S. Department of Veterans Affairs Cooperative Studies Program Coordinating Center, Hines...

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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The use of instrumental variable (IV) methods is attractive because, even in the presence of unmeasured confounding, such methods may consistently estimate the average causal effect of an exposure on an outcome. However, for this consistent estimation to be achieved, several strong conditions must hold. We review the definition of an instrumental variable, describe the conditions required to obtain consistent estimates of causal effects, and explore their implications in the context of a recent application of the instrumental variables approach. We also present (1) a description of the connection between 4 causal models—counterfactuals, causal directed acyclic graphs, nonparametric structural equation models, and linear structural equation models—that have been used to describe instrumental variables methods; (2) a unified presentation of IV methods for the average causal effect in the study population through structural mean models; and (3) a discussion and new

for helpful discussions and suggestions. The views expressed in this paper are those of the author and not