- The Early History of Rational and Implicit Expectations
- History of Political Economy
- Duke University Press
- Volume 33, Number 4, Winter 2001
- pp. 773-813
- Article
- View Citation
- Additional Information

*History of Political Economy* 33.4 (2001) 773-813

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## The Early History of Rational and Implicit Expectations

### Warren Young and William Darity Jr.

During the 1950s, three alternate models of endogenous expectations formation were developed: adaptive, rational, and implicit. While the first two are well known, the history of implicit expectations has not been dealt with, nor has the early history of rational expectations itself. The objects of this paper are, therefore, to survey the early development of these approaches, the reactions to them during the period of their dissemination, and their initial utilization. In the first section of the paper, we focus on the recollections of those who developed the models—John Muth and Edwin Mills—and those who were intimately involved in their development, including Herbert Simon, Marc Nerlove, Michael Lovell, and others. The recollections were collected by means of identical questions put to these personalities and supplementary questions based upon their initial replies, as will be seen below. In the second section, we will present the recollections of those who attended the December 1959 meeting of the Econometric Society where Muth and Mills presented papers outlining their alternative models. Again, identical questions were **[End Page 773]** put to those who participated at the meeting. In the third section, we provide the recollections of those who used the alternative approaches in a microeconometric testing program, such as Nerlove, and those who applied one or other of the models on the theoretical level in a general equilibrium model, such as Roy Radner and T. Negishi, and also those who initially used Muth's approach in a macroeconomic framework, such as Edwin Phelps and Robert Lucas. Before proceeding, however, a brief description of the three approaches—adaptive, implicit, and rational expectations—is called for.

Lovell (1986, 111) provided concise and lucid descriptions of the alternate approaches to expectations “developed in the 1950's.” The “adaptive approach” developed by Nerlove (1954), among others, emanated from J. R. Hicks's (1939) notion of the “elasticity of expectations.” In its simplest form, this approach can be set out as follows:

P = A_{t - 1} + l(P_{t - 1} - A_{t - 1}) , |

where *P* is the predicted value, *A* is the actual value, (*P* - *A*) is the forecast “error,” and l is the weight attached to the forecast error. According to Lovell (1986, 112), by hypothesizing “reasonable stochastic properties,” it seemed “reasonable … to hypothesize that expectations” were unbiased, that is, that there was a zero expected value of the error in the forecast (e) such that

e = P - A . |

Two alternatives were then proposed to the adaptive approach, by Mills (1957a, 1957b, 1959a) and Muth (1959a, 1959b, 1961). In his seminal studies of inventory behavior, Mills (1957a, 1957b) presented his notion of implicit expectations. This was based upon the conjecture that there was no correlation between the prediction error and the actual realization. On the basis of this “restriction,” as Lovell (1986, 112) put it, “the basic assumption of the regression model is satisfied with the anticipated variable selected as the dependent variable.” This can be represented as follows:

P = a_{0}+ a_{1}A + e, |

where a_{0} = 0, a_{1} = 1, and *E* (e) = 0, that is, the expected value of the “error term” is zero. Based upon this argument, the actual realization was used by Mills as a proxy “for the unobserved anticipated level of sales” in his study of inventory behavior (Mills 1957b; Lovell 1986, 112). **[End Page 774]**

Muth, for his part, developed a hypothesis just the opposite of Mills's implicit expectations approach. Muth's rational expectations hypothesis “required that the forecast error be distributed independently of the anticipated value” (Muth 1961; Lovell 1986, 112). This can be represented as

A = b_{0}+ b_{1} P + e, |

where *b*_{0} = 1, *b*_{1} = 1 and *E* (e) = 0. In this case, *P* must be uncorrelated with e, so that e, must be correlated with *A*, and thus the variance of *P* is smaller than that of *A*. As Lovell (1986, 112) noted, “All this...

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