Mann Iterations with Power Means
AbstractIn this paper we analyze a recurrence , where is a weighted power mean of ,…., . Such an iteration scheme has been proposed to model a class of non-linear forward-looking economic models ( the state today is affected by tomorrow’ s expectation ) under bounded rationality; the agents employ a recursive learning rule to update beliefs using weighted power means of the past states. A proposition on the convergence of the dynamical system with memory, proven with a general weighted power mean, generalizes some results given in the literature, where only the arithmetic mean is considered. A power weighted mean with exponentially decreasing weights decreasing is proposed to simulate a fading memory. In this case the iteration scheme with memory is reduced to an equivalent two-dimensional autonomous map whose possible kinds of asymptotic behaviors are the same as those of a one-dimensional map. By this general technique it is proved, for a function f which maps a compact interval into itself, that the presence of a long memory has a stabilizing effect, in the sense that with a sufficiently strong memory convergence to a steady state is obtained even for an otherwise oscillating, or chaotic, dynamical system. In the appendix is considered an economic example from an overlapping generation models which leads to a harmonic mean.
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Bibliographic InfoPaper provided by University of Milano-Bicocca, Department of Economics in its series Working Papers with number 106.
Length: 15 pages
Date of creation: 2007
Date of revision: 2007
Forward-looking models; Learning; Mann Iterations; Nonautonomous difference equations;
Find related papers by JEL classification:
- A - General Economics and Teaching
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-01-23 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Benassy, Jean-Pascal & Blad, Michael C., 1989. "On learning and rational expectations in an overlapping generations model," Journal of Economic Dynamics and Control, Elsevier, vol. 13(3), pages 379-400, July.
- Balasko, Yves & Royer, Daniel, 1996. "Stability of Competitive Equilibrium with Respect to Recursive and Learning Processes," Journal of Economic Theory, Elsevier, vol. 68(2), pages 319-348, February.
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