# The Rational Expectations Hypothesis Can Never, Ever Be Shown to Be True (False), Correct (Incorrect), Right (Wrong) or Proven (Not Proven): Ignoring Haavelmo’s Warning about Confusing Deduction (Mathematics, Logic) with Induction (Probability, Statistics, Econometrics) Leads to Oxymorons Such As 'Objectively True Probability Assessments'

34 Pages Posted: 10 Jul 2019

Date Written: July 7, 2019

### Abstract

Advocates and opponents of the rational expectations hypothesis have both confused statistics with mathematics (logic). Only in mathematics can I prove something to be true, false, correct, incorrect, right or wrong. The best one can do in statistics is, by the use of proper scoring rules, establish that one forecaster (model) is better, more accurate or reliable relative to another forecaster (model). A best forecast can never, ever be a true forecast.

Definitions of what the rational expectations hypothesis is are confused, ambiguous, hazy, unclear, and foggy. Practically none of the definitions involve a correct use of statistics and probability. The one technical definition, given by R.Muth in 1961 in an article in Econometrica, is an intellectual mess due to Muth’s own misunderstandings of what statistics and probability meant when the terms subjective theory of probability and objective theory of probability are used. Subjective theories of probability involve degree of belief. Objective theories of probability involve empirical, relative frequencies based on the direct observation of outcomes in a very large number of repeated experiments carried out under identical conditions. An estimate of a subjective probability can never be an estimate of an objective probability. Muth’s definition was that “…for a given information set, the subjective probabilities (distributions) were distributed around a unique, objective probability distribution.” This definition is simply impossible and would be rejected by all of the existing theories of probability (limiting (relative) frequency, subjective, logical, propensity, classical).

The Rational expectations hypothesis appears to mean no more than the claim that all producers and consumers, who are rational, make use of all available information so that they all have a complete information set. However, this definition is not substantially different from the very similar definition used by Jeremy Bentham in his disputes with Adam Smith over the nature of probability in 1787 in his revised The Principles of Moral and Legislation. Bentham argued that all men love money at all times, that all men calculate, especially outcomes involving pecuniary concerns, and that all the calculated probabilities were linear, exact, definite and precise,as were all of the outcomes, so that all rational people could calculate their Maximal Utility. Smith, on the other hand, argued that probability was inexact, imprecise and non linear, as risk was not proportional to returns. Keynes’s views on decision making and probability are very similar to Adam Smith’s views.

**Keywords:** rational expectations, BEST estimator, true expectations, a true objective probability, Lucas, Haavelmo, systems of statistical equations versus systems of mathematical equations

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

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