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Causality refers to the relationship between events where one set of events (the effects) is a direct consequence of another set of events (the causes). Causal inference is the process by which one can use data to make claims about causal relationships. Since inferring causal relationships is one of the central tasks of science, it is a topic that has been heavily debated in philosophy, statistics, and the scientific disciplines. This entry reviews the models of causation and tools for causal inference most prominent in the social sciences, including regularity approaches, associated with David Hume, and counterfactual models, associated with Jerzy Splawa-Neyman, Donald Rubin, and David Lewis, among many others. One of the most notable developments in the study of causation is the increasing unification of disparate methods around a common conceptual and mathematical language that treats causality in counterfactual terms—that is, the Neyman-Rubin model. This entry discusses how counterfactual models highlight the deep challenges involved in making the move from correlation to causation, particularly in the social sciences, where controlled experiments are relatively rare.

Regularity Models of Causation

Until the advent of counterfactual models, causation was primarily defined in terms of observable phenomena. It was the philosopher Hume in the 18th century who began the modern tradition of regularity models of causation by defining causation in terms of repeated “conjunctions” of events. In An Enquiry Into Human Understanding (1751), Hume argued that the labeling of two particular events as being causally related rested on an untestable metaphysical assumption. Consequently, Hume (1739) argued that causality could be adequately defined only in terms of empirical regularities involving classes of events. He asked, “How could we know that a flame caused heat?”—only by calling “to mind their constant conjunction in all past instances. Without further ceremony, we call the one cause and the other effect and infer the existence of one from that of the other” (Treatise of Human Nature, Book 1, Pt. 3, sec. 6). In the Enquiry, Hume argued that three empirical phenomena were necessary for inferring causality: (1) contiguity (the cause and effect must be contiguous in time and space), (2) succession (the cause must be prior to the effect), and (3) constant conjunction (there must be a constant union between the cause and effect). Under this framework, causation was defined purely in terms of empirical criteria, rather than unobservable assumptions. In other words, Hume's definition of causation and his mode of inference were one and the same.

John Stuart Mill, who shared the regularity view of causation with David Hume, elaborated basic tools for causal inference that were highly influential in the social sciences. For Mill, the goal of science was the discovery of regular empirical laws. To that end, Mill proposed in his 1843 A System of Logic, a series of rules or “canons” for inductive inference. These rules entailed a series of research designs that examined whether there existed covariation between a hypothesized cause and its effect, time precedence of the cause, and no plausible alternative explanation of the effect under study. Mill argued that these research designs were effective only when combined with a manipulation in an experiment. Recognizing that manipulation was unrealistic in many areas of the social sciences, Mill expressed skepticism about the possibility of causal inference for questions not amenable to experiments.

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