# Muth’s Rational Expectations Hypothesis, That '…The Subjective Probability Distributions Are Distributed Around an Objective Probability Distribution, for a given Information Set…' is an Oxymoron. It Can Be Corrected by Amending It to Read '…The Subjective Probability Distributions Are Distributed Around a Subjective Consensus Probability Distribution, for a given Information Set…'

26 Pages Posted: 29 May 2019

Date Written: May 5, 2019

### Abstract

Jeremy Bentham’s Maximization of Utility model, set out in chapter three and pages 186-187 of the Principles of Morals and Legislation, where all decision makers knew the exact, precise probabilities and precise, exact consequences of their actions, was combined by him with a redefinition of the term "rational" to mean ONLY the successful optimization of utility over time. Bentham thus conflated the term rational, which meant planning, preparing, reasoning, thinking and introspection, with the concept of successful utility maximization over time. He also failed to state whether his probabilities were subjective or objective. The maximizing utility approach was then combined by him in his later writings with a pendulum-oscillation model. The economy would always self adjust so that the result would be a full employment of all resources equilibrium, so long as the government did not interfere with the private sector economy in any way, "was quite", and "stayed out of the sunshine" of business. Bentham also assumed that there were no external, exogenous shocks from drought, famine, natural disasters, civil war, revolution, or war. However, if such random events took place, their impact would naturally dissipate gradually over time, so that the pendulum, representing the change over time in the macro economy, would always approach the natural equilibrium state of full employment.

Bentham incorporated economic growth and technological advance over time into his theory through his concept of forced savings, whereby bankers would loan businessmen the funds that would enable them to bid away resources from the production of consumer goods, in order to produce more advanced investment goods, which would then shift the Production Possibilities Curve outward over time.

Bentham’s literary theory is the same as the mathematical rational expectations hypothesis if it is combined with real business cycles and dynamic stochastic general equilibrium theory.The only differences between the two theories is how they were expressed - one in literary form and the other in mathematical form.

Muth’s 1961 definition of rational expectations in Econometrica that "…the subjective probability distributions are distributed around a true objective probability distribution, for a given information set…", can be viewed as an attempt by him to provide Bentham's model of rational, utility maximizing producers and consumers with a modern mathematical and statistical foundation.

However, Muth's definition, that the subjective probabilities (distributions) of such decision makers are distributed around the one true, right, correct objective distribution, for a given information set, is an oxymoron that fails to take into account that there is no subjective probability theory (Bayesian) that accepts the concept of objective probability (Frequentist), while there is no objective probability theory (Frequentist) that accepts the concept of subjective probability (Bayesian). Both the logical and subjective approaches to probability are strident reactions against the frequentist attack on the subjectivity of classical probability and the concepts of initial, a priori probability and inverse probability. Frequentists argue that there is no such thing as an initial or an a priori probability and that inverse probability, in the words of Ronald Fisher, is just wrong. Subjectivists, like Bruno de Finetti, argue that there is no such thing as objective probability.

Muth does not cite any sources in his 1961 paper that dealt with the Bayesian (subjective) or Frequentist (objective) distinctions. It is, therefore, impossible to be able to identify what his definitions of subjective and objective probability actually were. It is impossible for subjective probability estimates to be distributed around anything but a consensus subjective probability distribution of experts based on an application of Savage's Principle of Stable Estimation, combined with applications of Proper Scoring Rules to prevent dishonesty in the reporting of claims made about forecasting accuracy vis-à-vis other competing forecasting approaches.

**Keywords:** rational expectations, Bentham, Muth, Keynes, Rescher, subjective probability, objective probability

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

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