*By Paul Davidson*

*INET published a paper, written by John Kay, that deals with the relationship between economics and the world we live in. The Map Is Not the Territory: An Essay on the State of Economics spells out methodological critiques of economic theory in general, and of DSGE models and rational expectations in particular.*

*INET forwarded Kay’s paper to a handful economists and invited them to respond. Paul **Davidson responds here, taking issue with the “classical” axioms, in particular with what he calls the "ergodic axiom": the notion that the future is predetermined by the past and present state of affairs, that past and knowable probability distributions govern future events. He praises rigor, consistency, and the deductive approach, but says the classical axioms are inapplicable to the world we live in: “The financial crisis of 2007-2009 should have been sufficient empirical evidence to indicate that the axiomatic basis of the mainstream theory needs to be replaced.”*

John Kay has written two excellent Financial Times articles and a summary paper for the INET website. In these articles Kay attempts to explain why mainstream economic theory does not provide a “science” approach to learning about the economic world in which we live. Kay indicates that the claim by mainstream economists’ (e.g., Lucas, Cochrane) for rigor, consistency, and mathematics in economics has created the basis for the low reputation of economists – especially since the financial crash of 2008 was not foreseen by their theory.

John Kay’s argument suggests that the love of rigor and mathematics and the use of computer models has encouraged the use of efficient market theory. Whether they declare themselves Monetarists, Rational Expectation theorists, Neoclassical Synthesis [Old] Keynesians or New Keynesians, the backbone of their theories is the efficient market analysis where the future can be known.

To stimulate discussion of Kay’s articles, I wish to address two aspects of Kay’s writings that I think should be clarified. The first involves content where what is missing from the Kay articles is the explicit discussion of the difference between a nonergodic stochastic process and an ergodic stochastic process for “knowing” the future. The second, and related aspect , (2) involves Kay blaming the messenger (the use of the deductive axiomatic logical analysis and mathematics by mainstream economists) for the message of the Lucas mainstream theory. The message that Kay rejects is that markets are efficient and that the Ricardian equivalence theorem makes fiscal stimulus policies useless– at least in the long run. But as Kay notes “Ricardian equivalence requires that households have a great deal of information about future budgetary options”. The message is wrong because in the real world, not only do households not have much information about the future, but neither do budgetary policy makers. The erroneous message based on the assumption of people having significantly reliable knowledge about the future is the result of accepting bad axioms as the basis for their classical theory. It is not the fault of using the deductive method and mathematics per se.

### The ergodic axiom

First, let’s take up the ergodic- nonergodic stochastic process distinction. Paul Samuelson [1969] 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.^{[1]} 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 [1981] 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., Lucas, Cochrane, Sargent, 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. What is this ergodic axiom? For a technical explanation of the difference between ergodic and nonergodic stochastic processes, the reader should read Davidson (2009).^{[2]} 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. 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 misread the future and thereby mess up the beauty of the efficient market system.

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 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. In an ergodic world, all future events are already predetermined and beyond change by human action today.

John Kay’s Financial Times articles, however, indicated that the future of the economic system is "created" by peoples current reactions to politics, other people’s reactions, policy decisions government debates, etc. This implies that economics is a nonergodic stochastic system. Actions by people and governments today can create future economic events. In a nonergodic system past probability calculations whether based on time series or cross sectional data cannot provide statistical significant estimates of future probabilities.

### Keynes’ uncertainty, Soros’ reflexivity, and the ergodic axiom

In his The General Theory, John Maynard Keynes stated that classical economists

“resemble Euclidean Geometers in a non Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight – as the only remedy for the unfortunate collisions which are occurring. 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 today in economics."

^{[3]}

In this analogy comparing Euclidean geometry in a non-Euclidean world to classical theory in our world of experience, Keynes was alluding to the fact that in the classical analysis the future is presumed to be known and therefore free markets are efficient since they produce full employment (the equivalent of the “parallel lines”). Yet significant and persistent unemployment (the “unfortunate collisions”) occur in the real world. Accordingly, classical economists rebuking the lines in the real world for not keeping straight is equivalent to blaming the workers for their unemployment problem because workers would not accept lower wages.

In creating a “non Euclidean” economic theory to explain why these unemployment “collisions” occur in the world of experience, Keynes uses the logical deductive method but he had to deny (“throw over”) the relevance of several classical axioms for understanding the real world. The classical ergodic axiom which assumes that the future is known and can be calculated as the statistical shadow of the past was one of the most important classical assertions that Keynes rejected.^{[4]}

Keynes’s general theory is a deductive method of analysis. Keynes’s concept of uncertainty about the economic future requires the economic system to be generated by a nonergodic process. At the time of his writing The General Theory, Keynes did not know of the ergodic stochastic theory that was being developed by the Moscow School of Probability in the 1930s. Nevertheless in his criticism of Tinbergen’s [econometric] method , Keynes [1939]^{[5]} wrote that Tinbergen’s method is not valid for any economic forecasting because economic data “are not homogeneous” over time. Non homogeneity is a sufficient condition for nonergodicity.

George Soros has explained why he believes the efficient market theory is not applicable to real world financial markets. In an article entitled “The Crisis and What To Do About It” that appeared in the December 4, 2008 issue of the New York Review of Books Soros wrote: “we must abandon the prevailing [efficient market] theory of market behavior”. Instead Soros insists that we should recognize that there is a connection “between market prices and the underlying reality [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’s insistence on applying the ergodic axiom to economics because 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 can affect and alter the future path the market takes. Soros’s concept of reflexivity, therefore, is the equivalent of Keynes’s throwing over of the ergodic axiom.

Kay mentions Taleb’s Black Swan concept in his writings. It should be noted that Knight’s vision of uncertainty and Taleb’s Black Swan concept are both based on the ergodic presumption for the economy. Taleb’s Black Swan is an already predetermined outcome but the Black Swan event is so far out in the tail of the ergodic probability distribution that its occurrence is so rare that it is never likely to be observed– except in the long run when we will all be dead. Similarly Knight’s applied his uncertainty concept to an event that is “in a high degree unique"^{[6]} and hence so far out in the distribution as to be observed perhaps only once in several lifetimes.

For Keynes, as well as for Soros, the belief that intelligent people “know” that they cannot know the future is an essential element in understanding the operation of our economic world. 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, however, that for these important decisions, making a mistake about the future can be very costly and therefore sometimes putting off a commitment today in order to remain liquid maybe the most judicious decision possible.

Our modern capitalist society has attempted to create an arrangement that will provide people with some control over their uncertain economic destinies. In capitalist economies the use of money and legally binding money contracts to organize production, sales and purchases of goods and services permits individuals to have some control over their future cash inflows and outflows and therefore some control of their monetary economic future. It also provides other parties (business firms) to engage in money sales contracts with the legal promise of current and future cash inflows sufficient to meet the business firms’ costs of production and generate a profit.

Households and business entrepreneurs willingly enter into money contracts because each party thinks it is in their best self interest to fulfill the terms of the contractual agreement. If, because of some unforeseen event, either party to a contract finds itself unable or unwilling to meet its contractual commitments, then the judicial branch of the government will enforce the contract and require the defaulting party to either meet its contractual obligations or pay a sum of money sufficient to reimburse the other party for damages and losses incurred. Thus, as the biographer of Keynes, Lord Robert Skidelsky has noted, for Keynes “injustice is a matter of uncertainty, justice a matter of contractual predictability”. In other words, by entering into contractual arrangements people assure themselves a measure of predictability in terms of their contractual cash inflows and outflows, even in a world of uncertainty.

Money is that thing that government decides will settle all legal contractual obligations. An individual is said to be liquid if he/she can meet all contractual obligations as they come due. For business firms and households the maintenance of one’s liquid status is of prime importance if bankruptcy is to be avoided. In our world, bankruptcy is the economic equivalent to a walk to the gallows. Maintaining one’s liquidity permits a person or business firm to avoid the gallows of bankruptcy. Thus, liquidity is at the center of the operations of our monetary economy and therefore financial markets that are well organized and orderly permit decision makers to maintain liquidity in case some unforeseen future event should make it otherwise impossible to meet a future money contractual obligation unless they can readily sell a liquid asset for money in an orderly market.

### Blaming the messenger for the mainstream message

If the future is nonergodic, then what Kay says is apropos about mainstream economic theory creating a completely artificial world remote from reality-since the theory requires the ergodic axiom. But mainstream economists are not wrong in the need for rigor in economic theorizing. Kay seems to state that Lucas and others arguments for rigor and consistency creates the useless economic models that make mainstream economists look so poorly. As Kay states “Rigour means that the only valid claims are logical deductions from specified assumptions [i.e., axioms]. Consistency is therefore an invitation to ideology, rigour an invitation to mathematics” Kay therefore argues that “this curious combination of ideology and mathematics is the hallmark of what is often called ‘freshwater economics’… Consistency and rigour are features of a deductive approach, which draws conclusions from a group of axioms – and whose empirical relevance depends entirely on the validity of the axioms”.

Instead of checking on the validity of the axioms of both efficient market theorists and Old and New Keynesians, Kay complains that such logical deductions describe only “complete artificial worlds” while ignoring an induction approach which is “based on experience and careful observation”

Unfortunately, I believe that Kay’s analogy here is not a correct one. What Kay should be objecting to is the underlying classical axioms that are completely inapplicable to the real world. The question that Kay needs to explore further is how do we humans gain knowledge of the world in which we live?

Since biblical times humans have tried to understand the world about them and what caused things that humans observed to happen. In general the human mind believes that there must be a cause for any event we observe.

For most of the history of mankind, it was believed that the design of God or the Gods was the cause of anything that happened in the world of experience. Beginning in the 17^{th} century, however, philosophers believed that explanations of events that one observed could be developed on the basis of reasoning of the mind rather than religious belief. This was the beginning of the intellectual movement historians call The Enlightenment or The Age of Reason where order and regularity was seen to come from the human analysis of observed phenomena. The power of reason was not in the possession of truth, but in the acquisition of truth.

Any understanding of the world as humans perceive always be the creation of the human mind. Reasoning involves the mind creating a deductive theory to explain what people observe happening about them (using inductive views). For example, Sir Isaac Newton saw an apple fall from the bough of a tree to the ground. Newton explained why the apple always falls to the ground by the theory of gravity.

A theory is the way humans describe real world observations on the basis of a model that starts with a few axioms. An axiom is an assumption accepted as a universal truth that does not need to be proved. From this axiomatic foundation, the theorist uses the laws of logic to deduce conclusions that explains what we observe in the world of experience. All theories are generally accepted in some tentative fashion. Theories are not ever conclusively established and can be replaced when events are observed that are deviations from the current existing theory. Thus, the financial crisis of 2007-2009 should have been sufficient empirical evidence to indicate that the axiomatic basis of the mainstream theory needs to be replaced.

Economic theory is an analytical device where the economic theorist builds a model by starting with some axioms that he/she accepts as a self evident truth. The tools of logical deduction are then used to reach one or more conclusions. These conclusions are then presented to the public as the explanation of economic events that are occurring in the world of experience. The theory can then be used to suggest the cure for any real world economic problems.

Accordingly, it is perfectly acceptable to have rigour and even math in economic models – as both Marshall and Keynes had. But the axioms underlying the model must be thoroughly examined to see if they are applicable to the real world. What Kay is objecting to is not rigor, but to the imposition of axioms, such as the ergodic axiom, that have no relationship to the world we live in.

Keynes’s general theory is rigorous and consistent – and once one recognizes that the future is uncertain in terms of a nonergodic stochastic process, then one can understand that to self-interest of each individual is to protect themselves from an uncertain future where bankruptcy can occur if one cannot meet one’s money contractual obligations in a capitalist system.

Thus money contracts (inflows and outflows) are used by individuals to protect themselves from adverse unmanageable net cash flows. The purpose of liquid assets^{[7]} traded on organized and orderly financial markets is to provide a security blanket against one’s inability to meet a contractual obligation outflow.

Thus when the market for mortgage backed derivatives that were advertised to be “as good as cash” i.e., perfectly liquid (and triple A rated) collapsed, the loss of so much liquidity caused panic (a reflexivity response) in other markets for assets that had been previously thought to be very liquid. Asset holders in many markets tried to make “fast exits” and the result was a financial collapse and crisis.

In sum, Keynes’s liquidity theory of the operation of financial markets is a rigorous, logically deductive system that appears to be applicable to the real world in which we live and should replace the artificial world model of Lucas and other mainstream economists.

[1] P. A. Samuelson,[1969] “Classical and Neoclassical Theory” in Monetary Theory, edited by R.W. Clower (Penguin Books,, London) p.12.

[2] P. Davidson (2009), The Keynes Solution: The Path To Global Economic Prosperity (Macmillan/Palgrave, New York).

[3] J. M. Keynes (1936), The General Theory of Employment, interest, and Money, Macmillan, London, p. 16.

[4] The other classical axioms Keynes threw over were (1) the neutrality of money axiom as it related to questions of inflation, and (2) the gross substitution axiom as it related to the zero substitution between liquid assets and real producible durables. See Davidson [2009].

[5] J. M. Keynes [1939],”Professor Tinbergen’s Method” Economic Journal, 49, reprinted in The Collected Writings of John Maynard Keynes vol. 14, edited by D. Moggridge [Macmillan, London, 1973].

[6] F. Knight, (1921), Risk, Uncertainty and Profit (Houghton Mifflin, New York) p.233

[7] Keynes has an entire chapter in the GENERAL THEORY entitled “The Essential Properties of Interest and Money” in which he specifically indicates that all liquid assets have certain essential mathematical properties, namely (1) the elasticity of production is zero and (2) the elasticity of substitution between liquid assets and durable producible goods is zero. Keynes specified these elasticity properties by induction via his knowledge of financial markets.

*This post was originally published at INET blog and has been re-published here with the express permission of the author.*

*Paul Davidson** is the Editor of Journal of Post Keynesian Economics affiliated with the University of Tennessee-Knoxville.*