James M. Robins and Larry Wasserman
However, we shall show that SGS's asymptotics implicitly assume that probability of there being ``no unmeasured common causes'' of X and Y\ is positive and not small relative to sample size. We prove that, under an asymptotics for which the probability of ``no unmeasured common causes'' is small relative to sample size, causal relationships are non-identifiable from the data alone, even when we assume distributions are faithful to the causal graph. We argue that, in observational epidemiologic, econometric, and social scientific studies, a formal asymptotic analysis that models the probability of ``no unmeasured common causes'' as small relative to sample size accurately reflects the beliefs of practicing professionals. We argue that these beliefs derive both from experience and from the fact that the world contains so many potential unmeasured common causes (i.e., confounders) that it is a priori highly unlikely that not a single one actually causes both X and Y. We conclude that, in observational studies, small causal effects can never be either reliably ruled in or ruled out; furthermore, one should not make the leap from even relatively large empirical associations to causation without substantive subject-matter-specific background information.