John Muth

Holt, Modigliani, Muth, and Simon (1960)

Two divergent approaches to economic modeling, which have later become cornerstones of modeling 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 colleagues 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 modeling 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 probability 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 interaction 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* (e.g., 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.

Muth's notion was that the professors [of economics], even if correct in their model of man, could do no better in predicting than could the hog farmer or steelmaker or insurance company. The notion is one of intellectual modesty. [] The common sense is "rationality": therefore Muth called the argument "rational expectations".

Legacy

It is 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.

Of course we knew about [rational expectations]. Muth was a colleague of ours [in the early 1960s]. We just didn't think it was important. The hypothesis was more or less buried during the '60s. Arrow used it in his paper on learning-by-doing in the '60s. Prescott and I used it in that paper of ours on investment. People were aware of it, but I didn't understand then how fundamental a difference it made econometrically. I didn't realize that if you took it seriously you had to rethink the whole question of testing and estimation. I guess no one else did either, except for Muth.

It must be quite an experience to write papers that radical and have people just pat you on the head and say 'That's interesting,' and nothing happens.

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.

Major works