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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 (Citation1965, 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 (Citation1986, 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.
Notes
1Source is http://plato.stanford.edu/entries/statphys-Boltzmann/#2. The text refers to Ehrenfest and Ehrenfest (1912), which should be Citation1911.
2The content of this section is broadly based on chapters 7–9 of Emch and Liu (2002), to which we refer the reader for additional details. See Horst (Citation2008) for a shorter text written for economists.
3Davidson (2015b) notes 1898 as the year the term was coined. The Merriam-Webster dictionary claims its first known use dates from 1926, without further indications.
4The existence of thermodynamic equilibrium is an empirical matter, codified as the Zeroth law of thermodynamics, which has humorously been summarized as “temperature is a good thing.” Postulates of physical theories, such as the Zeroth law, are accepted without logical proof on the basis of a sufficient amount of suggestive evidence.
5Indistinguishability in principle but not in practice is behind classic statistical physics “paradoxes” such as Maxwell’s demon and the Gibbs mixing entropy.
6The Stanford Encyclopedia on Philosophy article on “Interpretations of Probability” (available at http://plato.stanford.edu/entries/probability-interpret/) attributes the term principle of indifference to Keynes (Citation1921, ch. 4), who credits the principle “widely adopted … under the title of The Principle of Non-Sufficient Reason” to James Bernoulli and devotes an entire chapter (ibid., ch. 30) to “Laplace’s Method.”
7This is the origin of the classical paradoxes encompassed under the category of “geometric probability.” See Solomon (Citation1978).
8Page writes: “So far as I know, these are the longest finite times that have so far been explicitly calculated by any physicist.”
9It is possible for the probability function in the model to contain just a single price with a probability of 100 percent. There is nothing ergodic about this, of course.
10This text has been reprinted in the Clower (Citation1969) volume.
11This has inspired us to start this article with the quote from Lewis Carroll’s Through the Looking-Glass.
12See Samuelson (Citation1968, pp. 1, 2, 5) as the source of the following quotes.
13This is not a statement of the ergodic axiom. “Actuarial certainty” probably means an enumeration of all possible outcomes.
14In his latest, Davidson (Citation2015b) points to Samuelson (1969, p. 112). However, the page is the beginning of an article by M.L. Burstein on the quantity theory of money and mentions neither Samuelson nor ergodicity.
15The literature we chose was presented to support our view that economics has mostly ignored the ergodic versus nonergodic categories.
16An alternative interpretation could be sloppiness of language. However, other authors repeat that claim. Fazzari (2009, p. 15) writes: “the world these days seems fundamentally uncertain and nonergodic.”
17O’Donnell (2015) criticizes the ergodic theory put forward by Paul Davidson along twelve issues. We agree with the critique and support the human abilities and characteristics (HAC) approach. Davidson (Citation2015b) has replied to O’Donnell (2015), with Rosser (2015) examining both positions.
18O’Donnell (Citation2013) distinguishes probabilistic and nonprobabilistic uncertainty. With the latter, probabilities are not known. O’Donnell uses the term “irreducible uncertainty” to highlight the human limitations to reduce the uncertainty.
19The parameter characterizing this behavior is called a Lyapunov exponent.
20Thus, stationarity is neither exclusively ergodic nor nonergodic. We disagree with Dunn (Citation2012, p. 435) who writes, “the fact that most macroeconomic time series are non-stationary provides empirical evidence for this [nonergodic] view.”
21Davidson (2007, p. 31) writes: “If one conceives of the economy as a stochastic (probability) process, then the future outcome of any current decision is determined via a probability distribution.” It is utterly confusing to have something “determined” by a stochastic process.
22Not using a stochastic frame when it would be possible can be rational, as Gigerenzer claims. Kahneman (Citation2011, p. 416) seems to agree with this view.
23We are at a loss to understand what Davidson means by “predetermined,” “stable,” and “conservative”— these terms have precise meanings in physics and mathematics, but not necessarily in economics. Again, to speak of something “predetermined” in a stochastic world is a misuse of language.
24See the discussion of Brownian motion above.
25Soros called the manipulative function the participating function before changing terms in Soros (Citation2008).
26Soros uses the correspondence theory of truth to make his point, as Carrión Álvarez and Ehnts point out (Citation2012, p. 3).
27The bail-out of American Insurance Group (AIG) ex-post validated insurance contracts that did obviously not protect the book of the insurer. Stein (Citation2012, 99) writes that, losses in 2007 totaled $11.5 billion, twice the aggregate net income produced by this division from 1994 to 2006.’