# J. Muth’s 1961, Econometrica Article Conception of Probability Was Inconsistent and Incoherent: There Is No Such Thing as a Hybrid Subjective-Objective Theory of Probability

19 Pages Posted: 15 Oct 2018

Date Written: September 23, 2018

### Abstract

J. Muth published a paper in 1961 in Econometrica that was incoherent and inconsistent because it was based on a hybrid amalgamation of directly conflicting Subjective and Objective theories of probability. Muth’s hybrid amalgamation did not exist before 1961, in 1961, or after 1961. Muth jumps back and forth in his article by combining subjective and objective (relative-limiting frequency) interpretations of probability that are distinct and do not have any overlapping parts that intersect.

Muth uses expected utility without citing Von Neumann’s (and Morgenstern’s) theory of risk. Von Neumann, an adherent of Keynes’s logical theory of probability between 1936 and 1942, and Morgenstern used objective limiting frequencies to explicate risk since their exposition was limited to risk. Under uncertainty, Von Neumann and Morgenstern used a safety first approach based on Max-Min techniques. However, subjective probabilities require the use of Subjective Expected Utility a la F Ramsey, L J Savage and B. de Finetti. There are no citations in Muth’s references /citations to any book/article written by either/or any academic expert in either subjective and/or objective theories of probability. How the subjective or objective probabilities are supposed to converge to the true objective probability is never explained. If one is using subjective probabilities, then reference to Savages principle of stable estimation is required. On the other hand, if one is using objective probabilities, a discussion of limits is needed as the number of observations becomes large over time.

Currently, there is no extant theory of probability that shows how subjective probabilities converge to objective probabilities over time as the subjective theory of probability states that objective probabilities do not exist and could never exist. Similarly, adherents of objective probability do not accept the concept of subjective probability.

**Keywords:** Muth, Types of Probability, Subjective, Objective, Rational Expectations

**JEL Classification:** B10, B12, B14, B16, B20, B22

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