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Adaptive Expectations

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

$${E_t}{x_{t + 1}} = {\sum\limits_{i = 0}^\infty {\lambda \left( {1 - \lambda } \right)} ^i}{x_{t - i}};\,\,0< \lambda< 1$$

whereE denotes an expectation,x is the variable whose expectation is being calculated andt 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 isλ The above equation can be manipulated readily to deliver:

$${E_t}{x_{t + 1}} = {E_{t - 1}}{x_t} + \lambda \left( {{x_t} - {E_{t - 1}}{x_t}} \right)$$

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© 2008 Palgrave Macmillan, a division of Macmillan Publishers Limited

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Parkin, M. (2008). Adaptive Expectations. In: Durlauf, S.N., Blume, L.E. (eds) The New Palgrave Dictionary of Economics. Palgrave Macmillan, London.

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