The New Palgrave Dictionary of Economics

Living Edition
| Editors: Matias Vernengo, Esteban Perez Caldentey, Barkley J. Rosser Jr

Adaptive Expectations

  • Michael Parkin
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The adaptive expectations hypothesis may be stated most succinctly in the form of the equation:

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The adaptive expectations hypothesis may be stated most succinctly in the form of the equation:
$$ {E}_t{x}_{t+1}=\sum_{i=0}^{\infty}\lambda {\left(1-\lambda \right)}^i{x}_{t- i;} 0<\lambda <1 $$
where E denotes an expectation, x is the variable whose expectation is being calculated and t indexes time. What this says is that the expectation formed at the present time, E t of some variable, x, at the next future date, t + 1, may be viewed as a weighted average of all previous values of the variable, x t i, where the weights, λ(1 – λ)i, decline geometrically. The weight attaching to the most recent, or current, observation is λ. The above equation can be manipulated readily to deliver:
$$ {E}_t{x}_{t+1}={E}_{t-1}{x}_t+\lambda \left({x}_t-{E}_{t-1}{x}_t\right). $$

What this equation says is that, viewed from time t, the expected value of the variable, x at t + 1, is equal to the value which, at time t −1 was expected for t, plus an adjustment for the extent to which the variable turned out to be different at t from the value which, viewed from date t −1, had been expected. The change in the expectation is simply the fraction λ multiplied by the most recently observed forecast error. In this formulation, the adaptive expectations hypothesis is sometimes called the error learning hypothesis (see Mincer 1969, pp. 83–90).

The adaptive expectations hypothesis was first used, though not by name, in the work of Irving Fisher (1911). The hypothesis received its major impetus, however, as a result of Phillip Cagan’s (1956) work on hyperinflations. The hypothesis was used extensively in the late 1950s and 1960s in a variety of applications. L.M. Koyck (1954) used the hypothesis, though not in name, to study investment behaviour. Milton Friedman (1957), used it as a way of generating permanent income in his study of the consumption function. Marc Nerlove (1958) used it in his analysis of the dynamics of supply in the agricultural sector. Work on inflation and macroeconomics in the 1960s was dominated by the use of this hypothesis. The most comprehensive survey of that work is provided by David Laidler and Michael Parkin (1975).

The adaptive expectations (or error learning) hypothesis became popular and was barely challenged from the middle-1950s through the late-1960s. It was not entirely unchallenged but it remained the only extensively-used proposition concerning the formation of expectations of inflation and a large number of other variables for something close to two decades. In the 1970s the hypothesis fell into disfavour and the rational expectations hypothesis became dominant.

The adaptive expectations hypothesis became and remained popular for so long for three reasons. First, in its error learning form it had the appearance of being an application of classical statistical inference. It looked like classical updating of an expectation based on new information.

Second, the adaptive expectations hypothesis was empirically easy to employ. Koyck (1954) showed how a simple transformation of an equation with an unobservable expectation variable in it could be rendered observable by performing what became a famous transformation bearing Koyck’s name. If some variable, y, is determined by the expected future value of x, that is:
$$ {y}_t=\alpha +\beta {E}_t{x}_{t+1} $$
where α and β are constants, then we can obtain an estimate of α and β by using a regression model in which Eq. 1 [or equivalently (2)] is used to eliminate the unobservable expected future value of x. To do this, substitute (1) into (3). Then write down an equation identical to (3) but for one period earlier. Multiply that second equation by 1 − λ and subtract the result from (3) (Koyck 1954, p. 22), to give:
$$ {y}_t=\alpha \lambda +\beta \lambda {x}_t+\left(1-\lambda \right){y}_{t-1} $$

An equation like this may be used to estimate not only the desired values of α and β but also the value of λ, the coefficient of expectations adjustment. Thus, economists seemed to have a very powerful way of modelling situations in which unobservable expectational variables were important and of discovering speeds of response both of expectations to past events and of current events to expectations of future events.

Third, the adaptive expectations hypothesis seemed to work. That is, when equations like (4) were estimated in the wide variety of situations in which the hypothesis was applied (see above), ‘sensible’ parameter values for α, ß, λ were obtained and, in general, a high degree of explanatory power resulted.

If the adaptive expectations hypothesis was so intuitively appealing, easy to employ, and successful, why was it eventually abandoned? There are three key reasons. First, the interpretation of the hypothesis as an application of classical inference came to be questioned, notably by John Muth (1960). Muth pointed out that the adaptive expectations hypothesis would only be optimal in the sense of delivering unbiased and minimum mean square error forecasts for a variable whose first difference was a first-order moving average process. Since this is likely to be a limited class of variables, the general validity of interpreting the adaptive expectations hypothesis as being consistent with classical inference came to be questioned. Second, in the area of macroeconomics, the adaptive expectations hypothesis was seen to be logically inconsistent with what came to be called the ‘natural rate hypothesis’ (Lucas 1972). The latter hypothesis, that unemployment and other real variables are ultimately determined by real forces and not influenced by anticipations of inflation (at least not to a first-order) is so deeply entrenched in economics that the logical clash of the two hypotheses had to result in the modification of adaptive expectations (see Friedman 1968; Phelps 1970). Third, and as almost always happens in scientific developments, a new, rational expectations alternative to adaptive expectations became available. The new theory had all the intuitive appeal of the old and, eventually, became equally tractable in empirical studies and began to show signs of success.

See Also


  1. Cagan, P. 1956. The monetary dynamics of hyper-inflation. In Studies in the quantity theory of money, ed. Milton Friedman. Chicago: University of Chicago Press.Google Scholar
  2. Fisher, I. 1911. The purchasing power of money. New York: Macmillan. (latest edition, A.M. Kelley, New York, 1963).Google Scholar
  3. Friedman, M. 1957. A theory of the consumption function. Princeton: Princeton University Press.Google Scholar
  4. Friedman, M. 1968. The role of monetary policy. American Economic Review 58 (March): 1–17.Google Scholar
  5. Koyck, L.M. 1954. Distributed lags and investment analysis. Amsterdam: North-Holland.Google Scholar
  6. Laidler, D., and M. Parkin. 1975. Inflation: A survey. Economic Journal 85 (December): 741–809.Google Scholar
  7. Lucas, R.E. Jr. 1972. Econometric testing of the natural rate hypothesis. In The econometrics of price determination, ed. Otto Eckstein. Washington, DC: Board of Governors of the Federal Reserve System.Google Scholar
  8. Mincer, J. 1969. Economic forecasts and expectations. New York: National Bureau of Economic Research.Google Scholar
  9. Muth, J.F. 1960. Optimal properties of exponentially weighted forecasts. Journal of the American Statistical Association 55: 299–306.CrossRefGoogle Scholar
  10. Nerlove, M. 1958. The dynamics of supply: Estimation of farmers’ response to price. Baltimore: Johns Hopkins Press.Google Scholar
  11. Phelps, E.S. 1970. Microeconomic foundations of employment and inflation theory. New York: Norton.Google Scholar

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Authors and Affiliations

  • Michael Parkin
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  1. 1.