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.
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).
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 Kálmán 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.
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.