Mann Iterations with Power Means

Ahmad Naimzada and Gian Italo Bischi

No 106, Working Papers from University of Milano-Bicocca, Department of Economics

Abstract: In 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.

Keywords: Forward-looking models; Learning; Mann Iterations; Nonautonomous difference equations (search for similar items in EconPapers)
JEL-codes: A (search for similar items in EconPapers)
Pages: 15 pages
Date: 2007, Revised 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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