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• W4241773093 abstract "‘Rational Expectations’ is an equilibrium concept that can be applied to dynamic economic models that have elements of ‘self reference’, that is, models in which the endogenous variables are influenced by the expectations about future values of those variables held by the agents in the model. The concept was introduced and applied by John F. Muth (1960, 1961) in two articles that interpreted some econometric distributed lag models. Muth used explicitly stochastic dynamic models, and brought to bear an extensive knowledge of classical linear prediction theory to interpret distributed lags in terms of economic parameters. For Muth, an econometric model with rational expectations possesses the defining property that the forecasts made by agents within the model are no worse than the forecasts that can be made by the economist who has the model. Muth’s first concrete application of rational expectations was to find restrictions on a stochastic process for income that would render Milton Friedman’s (1957) geometric distributed lag formula for permanent income an optimal predictor for income. Muth showed that if the first difference of income is a first order moving average process, then Friedman’s formula is optimal for forecasting income over any horizon. The independence of this formula from the horizon makes precise the sense in which Friedman’s formula extracts from past income an estimator of ‘permanent’ income. In working backwards from Friedman’s formula to a process for income in this way, Muth touched Lucas’s Critique (1976). Given any distributed lag for forecasting income, one can work backwards as Muth did and discover a stochastic process for income that makes that distributed lag an optimal predictor for income over some horizon. Solving a few such problems in the fashion of Muth quickly reveals the dependence of a distributed lag associated with forecasting the future on the form of the stochastic process that is being forecast. In 1963 Peter Whittle published a book that conveniently summarized and made more accessible to economists the classical linear prediction theory that Muth had used. That book reports and repeatedly applies the Wiener–Kolmogorov formula for the optimal j-step ahead predictor of a covariance stationary stochastic process xt with moving average representation $$ {x}_t=c(L);{upepsilon}_t $$ . The Wiener–Kolmogorov formula displays the dependence of the optimal distributed lag for predicting future x on the form of c(L). That dependence underlies Lucas’s critique of econometric policy evaluation procedures that were common when Lucas composed his critique in 1973. Those procedures had assumed that distributed lags in behavioural relations would remain invariant with respect to alterations in government policy rules, alterations which took the form of changes in c(L) for government policy instruments. Although the formulas in Whittle’s book were used extensively by Nerlove (1967) to work out additional examples along the lines of Muth’s, it was not until the writing of Lucas’s Critique in 1973 and its publication in 1976 that the implications for econometric practice of Muth’s ideas and the prediction formulas in Whittle began to be widely appreciated." @default.
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• W4241773093 date "1987-01-01" @default.
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• W4241773093 title "Rational Expectations" @default.
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• W4241773093 doi "https://doi.org/10.1057/978-1-349-95121-5_1684-1" @default.
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