In this paper I attempt to reconcile the apparent deﬁniteness of econometric practice with the vagueness of subjective probabilities assumed in Knightian decision theory. I argue that some standard uses of classical inference are Knightian in spirit, even though the formal justiﬁcation of classical methods uses the frequentist notion of probability. Classical conﬁdence regions may be viewed as deﬁning sets of posterior means corresponding to a standardized set of prior distributions. Tests of the null hypothesis that a parameter equals a particular value may be viewed as determining whether it is rational, from a Knightian point of view, to act as if the null hypothesis were true. This interpretation of the tests seems to correspond fairly well to practice and to the informal story told by classical statisticians. Hence, one could argue that to this extent classical statisticians act unconsciously as Knightian decision makers. If one accepts this argument, then it is of interest to know what level of uncertainty aversion corresponds to the popular 5% signiﬁcance level.
Bewley, Truman F., "Knightian Decision Theory and Econometric Inference" (1988). Cowles Foundation Discussion Papers. 1111.