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Samuelson and Davidson on ergodicity: A reformulation
Authors:Miguel Carrión Álvarez  Dirk Ehnts
Abstract:The concept of ergodicity in economics seems to have the qualities of a shibboleth—a word or saying used by adherents of a party, sect, or belief, and usually regarded by others as empty of real meaning. It is in use by both neoclassical economics—after Samuelson (1965 Samuelson, P. A. “Proof That Properly Anticipated Prices Fluctuate Randomly.” Industrial Management Review, 1965, 6 (2), 4149.[Web of Science ®] [Google Scholar], p. 43), who used the term in his paper on what later became a foundation of the efficient market hypothesis—and post Keynesian economics—after Davidson, who picked up the term in order to highlight methodological differences. Considering the origin of the concept in statistical physics and its use in the topology of dynamical systems, which most economists are not conversant with, the importance ascribed to ergodicity in economic debate seems mystifying. We deconstruct the meaning of the term in the major contributions of Samuelson and Davidson. We suggest an alternative to (non)ergodicity to discuss the nature of randomness in the real world. While neoclassical theory assumes stochastic randomness, post Keynesians assume nonstochastic randomness, a term developed by the mathematician Kolmogorov (1986 Kolmogorov, A.N. “On the Logical Foundations of Probability Theory.” In K. Ito, and J.V. Prokhorov (eds.), Probability and Mathematical Statistics, Moscow, 1986, pp. 467471. [Google Scholar], p. 467). We argue that even in an ergodic world there is a problem with the idea that stochastic randomness can be dealt with by the financial system.
Keywords:Efficient market hypothesis  ergodicity  Paul Davidson  Paul Samuelson  stochastic
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