John Muth

John Fraser Muth (1930 – October 23 2005 in Key West, Florida) was an American economist. He is known as "the father of the rational expectations revolution in economics", primarily due to his article "Rational Expectations and the Theory of Price Movements" from 1961.

Muth earned his Ph.D. in mathematical economics from Carnegie Mellon University, and was in 1954 the first recipient of the Alexander Henderson Award. He was affiliated with Carnegie Mellon as a research associate from 1956 until 1959, as an assistant professor from 1959 to 1962, and as an associate professor without tenure from 1962 to 1964.

Muth asserted that expectations "are essentially the same as the predictions of the relevant economic theory." Although he formulated the rational expectations principle in the context of microeconomics it has subsequently become associated with macroeconomics and the work of Robert Lucas, Jr., Finn E. Kydland, Edward C. Prescott, Neil Wallace, Thomas J. Sargent, and others.

Holt, Modigliani, Muth, and Simon (1960)

Two divergent approaches to economic modelling, which have later become cornerstones of modelling of economic systems, originated at the Graduate School of Industrial Administration (GSIA) at Carnegie Mellon in the late 1950s and early 1960s. At the same time as John Muth was developing the concept of rational expectations, Herbert A. Simon had been refining his ideas on bounded rationality, emphasizing people's limited computational abilities.

Together with their two collagues at GSIA Charles C. Holt and Franco Modigliani, Muth and Simon collaborated on a book on problems of production scheduling and inventory management for the firm. Their goal was to derive tractable, operational rules that could easily be applied in practice. Rather than a coincidence that the two apparently contradictory approaches to economic modelling were developed at GSIA at the same time, it is more likely that fruitful interaction in the quest to answer a common set of problems led the two researchers to two different solutions.

In an earlier work, Herb Simon had shown that with quadratic costs and under a certain set of assumptions about the probability distributions, optimal decision rules for production and inventories would be linear functions of the variables describing the state. In his model, firms only needed to take into account the "expected value" and ignore all higher moments of the probabiliy distribution of future sales. This result, known as "certainty equivalence" drastically reduces the computational burden on a representative decision maker.

Simon's result that decision makers only focus on "expected values" of stochastic variables was very sensitive to the assumed structure of the problem, hence indirectly on the formulation of expectations. This lack of a general theory of expectations was an unsatisfactory state of affairs and proved to be key in Muth's approach to solve the problem which has often been termed intereaction between expectations and reality". In his article from 1961, Muth writes: "To make dynamic economic models complete, various expectational formulas have been used. There is, however, little evidence to suggest that the presumed relations bear a resemblance to the way the economy works."

Muth (1960)

Phillip Cagan, Milton Friedman and others used the "ad hoc" updating rule which they labeled adaptive expectations to forecast the hidden state "y*" (eg, permanent income). In his 1960 paper Muth answered the question for what stochastic process for "y" will adaptive expectations as postulated by Cagan and Friedman be the optimal forecast of "y*". Muth's approach to find recursive optimal linear forecast of a “hidden” state vector, "x", given an “observer”, "y" is very similar to the Kalman filter, presented by Rudolf Kalman in his paper from the same year.

In his paper "Optimal Properties of Exponentially Weighted Forecasts", which was published in the "Journal of the American Statistical Association" in 1960, Muth rationalized Friedman’s adaptive expectations model for permanent income. He did this by reverse engineering a stochastic process for income for which Cagan’s expectation formula equals a mathematical expectation of future values conditioned on the infinite history of past incomes. Among Muth’s insights was that the stochastic process being forecast should dictate both the distributed lag and the conditioning variables that people use to forecast the future.

Muth (1961)

In contrast to Simon, Muth puts forward his hypothesis: "I should like to suggest that expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory. At the risk of confusing this purely descriptive hypothesis with a pronouncement as to what firms ought to do, we call such expectations "rational"."

t.b.a.

Legacy

It has hard to point to one substantial area of economic research into dynamic problems which has "not" changed as a result of the publication of Muth's works at GSIA. Almost paradoxically, the only viable alternative to Muth's hypothesis is the research agenda put forward by Herb Simon and his concept of "bounded rationality".

Quote|Muth's role in the history of economics is unusual. Like Hermann Heinrich Gossen, he became famous for one idea, he provided the analytical key to developments that, in the jargon of scientific journalism, were described as revolutionary, and he was virtually ignored by his immediate contemporaries. However, whereas Gossen had no influence on those developments, his key results being independently rediscovered by Jevons and Walras, the rational expectations economics of the 1970s and 1980s was a direct outgrowth of Muth's seminal idea. In fact, Muth's contribution is one of the relatively few instances in which there is no indication that the history of economics would have taken about the same course in its absence. It was a novel and ingenious idea, it was not "in the air," and no multiple discovery has yet come to light.| cite book
last = Niehans
first = Jürg
title = A History of Economic Theory
publisher = The Johns Hopkins University Press
year = 1990
isbn = 0801838347 Page 509.

Major works

*Charles C. Holt, Franco Modigliani, John F. Muth, and Herbert A. Simon (1960). "Planning Production, Inventories, and Work Force".
*John F. Muth. (1960). "Optimal Properties of Exponentially Weighted Forecasts", "JASA"
*John F. Muth. (1961). "Rational Expectations and the Theory of Price Movements", "Econometrica" 29, pp. 315-335.