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 is to bring to the attention of investigators several basic limitations of the associational criterion. We will show that the associational criterion does not ensure unbiased e#ect estimates, nor does it follow from the requirement of unbiasedness. After demonstrating, by examples, the absence of logical connections between the statistical and the causal notions of confounding, we will de#ne a stronger notion of unbiasedness, called stable unbiasedness, relative to which a modi#ed statistical criterion will be shown necessary and su#cient. The necessary part will then yield a practical test for stable unbiasedness which, remarkably, does not require knowledge of all potential confounders in a problem. Finally,wewill argue that the prevailing practice of substituting statistical criteria for the e#ect-based de#nition of confounding is not entirely misguided, because stable unbiasedness is in fact what investigators have been and should be aiming to achieve, and stable unbiasedness is what statistical criteria can test.

According to common judicial standard, judgment in favor of plaintiff should be made if and only if it is "more probable than not" that the defendant's action was the cause for the plaintiff's damage (or death). This paper provides formal semantics, based on structural models of counterfactuals, for the probability that event x was a necessary or sufficient cause (or both) of another event y. The paper then explicates conditions under which the probability of necessary (or sufficient) causation can be learned from statistical data, and shows how data from both experimental and nonexperimental studies can be combined to yield information that neither study alone can provide. Finally,weshow that necessity and sufficiency are two independent aspects of causation, and that both should be invoked in the construction of causal explanations for specific scenarios.

There is hardly a concept in econometrics that is more enigmatic and controvertial than that of exogeneity. This report---an edited excerpt from (Pearl 2000)---claims that exogeneity is a rather simple concept, readily definable in terms of standard econometric models, and that the confusion stems primarily from improper usage of statistical vocabulary in a structural framework. 1 Introduction Economics textbooks invariably warn readers that the distinction between exogenous and endogenous variables is, on the one hand, "most important for model building" (Darnell 1994, p. 127) and, on the other hand, "a subtle and sometimes controversial complication" (Greene 1997, p. 712). Economics students would naturally expect the concepts and tools of causal modeling (e.g., (Pearl 2000)) to shed some light on the subject, and rightly so. This paper offers a simple definition of exogeneity that captures the important nuances appearing in the literature and that is both palatable and precise...