The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions; otherwise, the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained. Key words: Causal inference, graph models, interventions treatment effect 1 Introduction The tools introduced in this paper are aimed at helping researchers communicate qualitative assumptions about cause-effect relationships, elucidate the ramifications of such assumptions, and derive causal inferences from a combination...

This paper considers causal inference and sample selection bias in non-experimental settings in which: (i) few units in the non-experimental comparison group are comparable to the treatment units; and (ii) selecting a subset of comparison units similar to the treatment units is difficult because units must be compared across a high-dimensional set of pretreatment characteristics. We discuss the use of propensity score matching methods, and implement them using data from the NSW experiment. Following Lalonde (1986), we pair the experimental treated units with non-experimental comparison units from the CPS and PSID, and compare the estimates of the treatment effect obtained using our methods to the benchmark results from the experiment. For both comparison groups, we show that the methods succeed in focusing attention on the small subset of the comparison units comparable to the treated units and, hence, in alleviating the bias due to systematic differences between the treated and comparison units.

tion of belief networks is given in [4]. 2 In [3], the graphs were called "causal networks," for which the authors were criticised; they have agreed to refrain from using the word "causal." In the current paper, Spiegelhalter etal. deemphasize the causal interpretation of the arcs in favor of the "irrelevance" interpretation (page 4). I think this retreat is regrettable for two reasons: first, causal associations are the primary source of judgments about irrelevance and, second, rejecting the causal interpretation of arcs prevents us from using graphical models for making legitimate predictions about the effect of actions. Such predictions are indispensable in applications such as treatment management and patient monitoring. the causal model also tells us how these probabilities would change as a result of external interventions in the system. For this reason, causal models (or "structural models" as they are often called) have been the target of relent

We are interested in estimating the average e#ect of a binary treatment on a scalar outcome. If assignment to the treatment is independent of the potential outcomes given pretreatment variables, biases associated with simple treatment-control average comparisons can be removed by adjusting for di#erences in the pre-treatmentvariables. Rosenbaum and Rubin #1983, 1984# show that adjusting solely for di#erences between treated and control units in a scalar function of the pre-treatment variables, the propensity score, also removes the entire bias associated with di#erences in pre-treatment variables. Thus it is possible to obtain unbiased estimates of the treatment e#ect without conditioning on a possibly highdimensional vector of pre-treatment variables. Although adjusting for the propensity score removes all the bias, this can come at the expense of e#ciency. We show that weighting with the inverse of a nonparametric estimate of the propensity score, rather than the true propensity scor...

It has been conspicuously hard to empirically identify clear-cut effects of Þxed exchange rates and other monetary regimes on the real economy. 1 This paucity of empirical Þndings has lead many academic economists as well as other observers to the view that radical monetary reform — such as the adoption of a

Experimental economists are leaving the reservation. They are recruiting subjects in the field rather than in the classroom, using field goods rather than induced valuations, and using field context rather than abstract terminology in instructions. We argue that there is something methodologically fundamental behind this trend. Field experiments differ from laboratory experiments in many ways. Although it is tempting to view field experiments as simply less controlled variants of laboratory experiments, we argue that to do so would be to seriously mischaracterize them. What passes for “control ” in laboratory experiments might in fact be precisely the opposite if it is artificial to the subject or context of the task. We propose six factors that can be used to determine the field context of an experiment: the nature of the subject pool, the nature of the information that the subjects bring to the task, the nature of the commodity, the nature of the task or trading rules applied, the nature

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This paper develops axioms and formal semantics for statements of the form "X is causally irrelevant to Y in context Z," which we interpret to mean "Changing X will not affect Y if we hold Z constant." The axiomization of causal irrelevance is contrasted with the axiomization of informational irrelevance, as in "Learning X will not alter our belief in Y , once we know Z." Two versions of causal irrelevance are analyzed, probabilistic and deterministic. We show that, unless stability is assumed, the probabilistic definition yields a very loose structure, that is governed by just two trivial axioms. Under the stability assumption, probabilistic causal irrelevance is isomorphic to path interception in cyclic graphs. Under the deterministic definition, causal irrelevance complies with all of the axioms of path interception in cyclic graphs, with the exception of transitivity. We compare our formalism to that of [Lewis, 1973], and offer a graphical method of proving theorems abou...

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