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We study the interrelations between (conditional) independence and causal relations in settable systems. We provide definitions in terms of functional dependence for direct, indirect, and total causality as well as for (indirect) causality via and exclusive of a set of variables. We then provide necessary and sufficient causal and stochastic conditions for (conditional) dependence among random vectors of interest in settable systems. Immediate corollaries ensure the validity of Reichenbach’s principle of common cause and its informative extension, the conditional Reichenbach principle of common cause. We relate our results to notions of d-separation and D-separation in the artificial intelligence literature.

This paper reviews recent advances in the foundations of causal inference and introduces a systematic methodology for defining, estimating and testing causal claims in experimental and observational studies. It is based on non-parametric structural equation models (SEM) – a natural generalization of those used by econometricians and social scientists in the 1950-60s, 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 the effects of potential interventions (also called “causal effects” or “policy evaluation”), as well as direct and indirect effects (also known as “mediation”), in both linear and non-linear systems. Finally, the paper clarifies the role of propensity score matching in causal analysis, defines the relationships between the structural and

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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.

With the passage of No Child Left Behind (NCLB), attention has focused on the need for evidenced-based educational research, particularly educational policies and interventions that rest on what NCLB refers to as ”scientifically based research”. In practice, this focus on scientifically based educational research has translated into a preference for research

In this paper we will argue that quasi-experiments can be equated to theoretical randomized experiments based on the extent of statistical control for confounding factors accounted for by measures such as a pre-test. That is, we use theoretical randomization as a baseline for evaluating the effective control of any study instead of using a single randomized empirical study as a gold standard against which to compare others. Ultimately, we will report that the quasi-experiment in Hong and Raudenbush (2005) used to infer an effect of kindergarten retention on reading achievement crosses the threshold for equivalence with a theoretical randomized study. We then develop a general formula and guidelines for equating quasi-experiments and randomized experiments based on the degree of statistical control achieved. In the discussion we emphasize the validity of causal inferences from quasi-experiments. 2

excellent research assistance. This paper was prepared for the festschrift volume in honor Minorities are generally subject to higher rates of policing, such as automobile or pedestrian stops, than whites. For instance, Ridgeway (2007) reports that 87 percent of stops of the New York police department in 2006 were nonwhite, and 51 percent of these were black. These differentials are often referred to as racial profiling. Racial profiling has

1 Exogeneity and Causal Language In communicating with colleagues in econometrics, I am often asked how concepts based on classical econometric models fit into modern vocabulary of causal reasoning. One of the issues that is brought up in such discussions is the notion of exogeneity, which seems to have played a major role in 1 the history of econometric thought and which received a formal, albeit problematic treatment in the classical paper of Engel, Hendry and Richard (EHR) (Engle et al., 1983). Since EHR’s paper is quoted in almost every advanced textbook in econometrics, it is natural to ask whether the EHR concept of exogeneity, especially its causal version called “super-exogeneity, ” corresponds to an analogous concept in the modern language of causal inference, particularly the language of causal diagrams, do-calculus, structural models, potential outcomes, and counterfactual logic (Pearl, 2009). The answer, of course, is

Nancy Cartwright’s recent book Hunting Causes and Using Them comes to causality in an interesting stage of its stormy, century-old courtship with economics. A survey article by Hoover (2004, ‘Lost causes’) counts the frequency of causal terminology in econometrics articles and asks, ‘Where