The ergodic axiom: Davidson versus Stiglitz and Lucas
Contemporary neoclassical economists proceed under the assumption that as concerns the economy there exists a predetermined reality that can be fully described by “unchanging objective conditional probability functions”. This is called the ”ergodic axiom”, and its current supporters include Joseph . Stiglitz and Robert Lucas. In the anti-scientism spirit of Keynes, Paul Davidson has long campaigned against the use of the ergodic axiom, but never so tellingly as in his most recent paper, Is economics a science? Should economics be rigorous? It appears in the current issue of the Real-World Economics. Here is one section from this paper.
The ergodic axiom
First, let us take up the ergodic – nonergodic stochastic process distinction. Paul Samuelson  has written that if economists hope to move economics from “the realm of history” into “the realm of science” they must impose the “ergodic hypothesis” on their theory. In other words Nobel Prize Winner Paul Samuelson has made the ergodic axiom the sine qua non for the scientific method in economics. Lucas and Sargent  have also claimed the principle behind the ergodic axiom is the only scientific method of doing economics.
Following Samuelson’s lead, most economists (e.g., Cochrane, Stiglitz, Mankiw, M. Friedman, Scholes, etc) and economic textbook writers either implicitly or explicitly have assumed that observable economic events are generated by an ergodic stochastic process.
But not Keynes! Keynes [1936, p. 16] suggested the way to understand why classical economic theory (e,g., efficient market theory) is not relevant to the world of experience, when he noted that old economic thinkers were “like Euclidean geometers in a non-Euclidean world who discover that apparent parallel line collide, rebuke these lines for not keeping straight. Yet, in truth there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required to-day in economics”. Keynes developed a theory that is more general than classical and mainstream economic theory because it is based on fewer restrictive fundamental axioms. The fewer the number of underlying axioms, the more general the theory. The most important classical axiom Keynes eliminated in his general theory is the ergodic axiom.
This ergodic axiom assumes the economic future is already predetermined . The economy is governed by an existing ergodic stochastic process. One merely has to calculate probability distributions regarding future prices and output to draw significant and reliable statistical inferences [information] about the future. Once self-interested decision makers have reliable information about the future, their actions on free markets will optimally allocate resources into those activities that will have the highest possible future returns thereby assuring global prosperity.
In order to draw any statistical (probabilistic risk) inferences regarding any universe, however, one should draw a sample from that universe. Since drawing a sample from the future economic universe is impossible, the ergodic axiom presumes that the economic future is governed by an already existing unchanging ergodic stochastic process. Consequently, a sample drawn from the past is equivalent to a sample drawn from the future. In other words, calculating the probability distribution from past statistical data sample is presumed to be the same as calculating the risks from a sample drawn from the future. This ergodic axiom is an essential foundation for all the complex risk management computer models developed by the “quants” on Wall Street. If the economy is nonergodic, however, then these computer models are weapons of math destruction [For deterministic models, the “ordering axiom” plays the same role as the ergodic axiom in stochastic models.]
For a technical explanation of the difference between ergodic and nonergodic stochastic processes one should read my book, The Keynes Solution: The Path To Global Economic Prosperity [Davidson (2009)] . For our discussion here we merely need note that, in essence, the ergodic axiom imposes the condition that the future is already predetermined by existing parameters (market fundamentals). Consequently the future can be reliably forecasted by analyzing past and current market data to obtain the probability distribution governing future events. In other words, if future events are assumed to be generated by an ergodic stochastic process (to use the language of mathematical statisticians), then the future is predetermined and can be discovered today by the proper statistical probability analysis of past and today’s data regarding market “fundamentals”. If the system is nonergodic, calculated past and current probability distributions do not provide any statistically reliable estimates regarding the probability of future events.
New Keynesians such as Stiglitz accept the ergodic axiom as the basis of the economic system but then add additional ad hoc assumptions to try to tame this presumed knowledge of the future approach to better reflect what they believe is reality. Stiglitz, for example, in his asymmetric information theory assumes that some market participants cannot make the proper statistical calculations because they do not perceive the correct information about the future. In other words, Stiglitz imposes the asymmetric information condition that there are some decision makers who act while lacking the correct information about the (presumed to exist today) probability distribution of future events. Consequently these decision makers (speculative fools?) misread the future and thereby mess up the beauty of the efficient market system.
Nobel prize winner Robert Lucas [1981, p. 287] has boasted that the mainstream theory axioms are “artificial, abstract, patently unreal”. Like Nobel Laureate Samuelson, Lucas insists such unreal assumptions are the only scientific method of doing economics. Lucas insists that “Progress in economic thinking means getting better and better abstract, analogue models, not better verbal observations about the real world” [Lucas, 1981, p. 276]. The rationale underlying this argument is that these unrealistic assumptions make the problem more tractable and, with the aid of a computer, the analyst can then predict the future. Never mind that the prediction might be disastrously wrong.
In the introduction to his book Against The Gods, a treatise that deals with the questions of relevance of risk management techniques on Wall Street, Peter L. Bernstein [ 1996, p. 6] writes:
“The story that I have to tell is marked all the way through by a persistent tension between those who assert that the best decisions are based on quantification and numbers, determined by the [statistical] patterns of the past, and those who based their decisions on more subjective degrees of belief about the uncertain future. This is a controversy that has never been resolved . . . to what degree should we rely on the patterns of the past to tell us what the future will be like?”
One would hope that the empirical evidence of the collapse of those “masters of the economic universe “ that have dominate Wall Street machinations for the last three decades has at least created doubt regarding the applicability of the ergodic axiom to our economic world. Even Alan Greenspan in testimony before Congress in October 2008 seems to be having second thoughts although he still has not completely changed his tune. Keynes’s ideas and Soros’s reflexivity concept support Bernstein’s latter group.
Samuelson, Lucas and others adopted the ergodic axiom because they want economics to be in the same class as the “hard sciences” such as physics or astronomy. For example the science of astronomy is based on the presumption of an ergodic stochastic process that governs the movement of all the heavenly bodies from the moment of the “Big Bang” to the day the universe ends. Accordingly probability analysis using past measurements of the movements of heavenly bodies permit astronomers to predict future solar eclipses within a few seconds of when they actually occur. Nothing Congress, the President of the United States, the United Nations, or environmentalists can do will alter the predetermined dates and time for future eclipses. For example, Congress cannot pass a law outlawing solar eclipses in order to provide more sunshine and thereby enhance crop production. In an ergodic world, all future events are already predetermined and beyond change by human action today. The future movement of the heavenly bodies can be known by anyone who has measured past movements and projected these movements into the future. There are no speculative fools, who suffering from asymmetric information, think Mars is going to crash into the earth.
George Soros has explained why the efficient market theory is not applicable to real world financial markets with a slightly different terminology than Keynes but conceptually in the same way. Soros (2008) wrote: “we must abandon the prevailing [efficient market] theory of market. behavior. ” Soros states that there is a direct connection “between market prices and the underlying realty [that] I [Soros] call reflexivity”.
What is this reflexivity? In a letter to the Editor published in the March 15-21, 1997 issue of The Economist Soros objects to Paul Samuelson insistence on requiring the ergodic axiom to make economics a science. Soros argues the ergodic hypothesis does not permit “the reflexive interaction between participants’ thinking and the actual state of affairs” that characterizes real world financial markets. In other words, the way people think about the market today can affect and alter the future path the market takes; the future is not predetermined. Soros’s concept of reflexivity, therefore, is the equivalent of Keynes’s rejection of the ergodic axiom. Reflexivity means peoples thoughts and actions create the future, while mainstream economists presume the future has already been predetermined and can be discovered by analyzing today’s market fundamentals.
. P. A. Samuelson, “Classical and Neoclassical Theory” in Monetary Theory, edited by R.W. Clower (Penguin Books,, London) p.12.
. Keynes [1936, p. 3] stated that the classical economics fundamental axioms are applicable to a “special case….[that] happen[s] not to be those of the economic society in which we live with the result that its teaching is misleading and disastrous if we attempt to apply it to fact of experience”. This “special case” statement is even more applicable today, given the economic austerity discussions in Washington, the UK, Euroland, etc, and the export-led growth , i.e., mercantilist, policies pursued by nations such as China who are still enjoying an “economic miracle” in an otherwise depressed global economy.
. Two other axioms that Keynes rejected are 1. Money is neutral (at least in the long run) so that changes in the quantity of money do not affect real outcomes, and 2. Gross substitution is ubiquitous and therefore liquid assets are good substitutes for real capital goods. (See Davidson , 2009).
. Consequently, government action today can only delay, but not change the long run optimal solution already predetermined by free markets.
. This is equivalent to thinking that drawing the sample of heights from a pygmy tribe in Africa is equivalent to drawing a sample of Swedish citizens’ height.
. In place of the rejected ergodic axiom Keynes argued that when crucial economic decisions had to be made, decision makers could not merely assume that the future can be reduced to quantifiable risks calculated from already existing market data. Instead they depended on “animal spirits” since most animals do not know how to calculate the moments around the mean!
For decisions that involved potential large spending outflows or possible large income inflows that span a significant length of time, people “know” that they do not know what the future will be. They do know that for these important decisions, making a mistake about the future can be very costly and therefore sometimes putting off a commitment by maintaining liquidity today may be the most judicious decision possible.
You can read Davidson’s whole paper: Is economics a science? Should economics be rigorous?