By Paul Davidson, America’s foremost post-Keynesian economist. Davidson is currently the Holly Professor of Excellence, Emeritus at the University of Tennessee in Knoxville. In 1978 Davidson and Sydney Weintraub founded the Journal for Post-Keynesian Economics. Davidson is the author of numerous books, the most recent of which is an introduction to a post-Keynesian perspective on the recent crisis entitled ‘The Keynes Solution: The Path to Global Prosperity’.
Introduction by Philip Pilkington
In a recent interview I asked the US’s leading post-Keynesian economist and founder of the Journal of Post-Keynesian Economics, Paul Davidson to discuss what is known as the ‘ergodic axiom’ in economics. This is a particularly important axiom as it allows mainstream economists (including left-wing Keynesians like Paul Krugman and Joseph Stiglitz) to claim that they can essentially know the future in a very tangible way. It does this by assuming that the future can be known by examining the past.
Without this axiom the whole edifice of mainstream theory rests on very shaky grounds. Yet, it should be clear to anyone that given that the theory is supposed to explain human behaviour it is unlikely that the future will correlate with the past because people and institutions tend to change and evolve over a given period of time.
Yes, often past behaviour will help us understand future behaviour – apply this in a simple psychological way to anyone you know and you will find it to be true – however, it should be quite clear that all future behaviour cannot be wholly explained by past behaviour. Clearly it should be quite obvious that the same should apply when we consider large aggregates of individuals and yet mainstream economics steadfastly refuses to accept this.
What follows is an particularly succinct overview of these ideas and a summary of their importance that Professor Davidson has kindly written for us. He also lays out the alternative view that the future is not determined by probabilistic risk but is instead subject to an absolute unknowability or uncertainty as laid out in the work of John Maynard Keynes and the implications of this.
This is a hugely important debate in that it essentially touches on what a good economic theory would allow for in terms of government policy. The ergodic axiom is possibly one of the key reasons that many economists show a remarkable anxiety when it comes to any human action undertaken outside of their models.
– — Philip Pilkington
I. DECISION MAKING IN ECONOMICS
The economy is a process in historical time. Time is a device that prevents everything from happening at once. The production of commodities takes time; and the consumption of goods, especially durables, takes considerable time. Economics is the study of how households and firms make decision choices regarding production and consumption when the outcome (pay-off) of today’s decision occurs at a significantly later date.
Any study of the behavior of economic decision-makers, therefore, requires the analyst to make some assumption regarding what today’s decision-makers ‘know’ about future outcomes.
There are two different concepts of the uncertain knowledge regarding the future outcomes of decisions made today. The mainstream concept regarding knowledge about the future and the Keynes General Theory concept. The ability of economists to explain the importance of the role of money, liquidity, and the existence of persistent unemployment in a market economy depends on which concept of knowledge about the future economists use as the basis of their economic analysis.
Because economists are split into two major theoretical camps about what decision-makers know about the future, these groups provide differing explanations of economic problems and their policy solutions. Understanding the differences in these two concepts of knowledge of future outcomes is essential to understanding the philosophical differences between economists on the role for government and economic policies in the economic system.
As explained below, mainstream economics assumes that households and entrepreneurs are optimal decision makers, that is, they choose the decision today that optimizes their utility, income and profits over time.
II. THE ABSENCE OF UNCERTAINTY IN 19TH CENTURY CLASSICAL ECONOMICS
Ricardo (1817), the father of 19th century classical economics, assumed a world of perfect certainty. All households and businesses were assumed to possess a full and correct knowledge of a presumed programmed external economic reality that governed all past, present, and future economic outcomes. The external economic environment was assumed immutable in the sense that it was not susceptible to change induced by human action. The path of the economy, like the path of the planets under Newton’s celestial mechanics, was determined by timeless natural laws. Economic decision makers had complete knowledge of these laws. Households and firms never made errors in their spending choices. They always spend everything they earned on things with the highest ‘known’ future pay-off in terms of utility for households and profits for businesses. Accordingly, there could never be a lack of demand for the products of industry or for workers who wanted to work. Classical economics justified a laissez-faire philosophy for the economic system. No government action could provide a higher pay-off than the decisions individuals made with complete information about the future in free markets.
III. UNCERTAINTY IN TODAY’S ORTHODOX ECONOMICS
In the early 20th century, classical economists tended to substitute the notion of probabilistic risk premiums and “certainty equivalents” for the perfect knowledge assumption of earlier classical theory. Risk premiums was said to provide “uncertainty” allowances where the latter referred to the difference between the estimated value of a future event, held with an objective (frequency distribution) probability of less than unity and the value of a perfectly certain (p = 1) event that evokes the same behavior.
By the 1970s this classical risk analysis had evolved into what mainstream economists call the New Classical Theory of ‘rational expectations’ where individuals make decisions based on their subjective probability distributions regarding future events where the subjective probabilities are presumed to be equal to immutable objective probability distributions that govern future outcomes [Lucas, 1972]. Today all mainstream economists interpret uncertainty in economics as synonymous with objective probability distributions [Lucas and Sargent, 1981; Machina 1987] that govern future events but are completely known to all persons today.
This device of labelling statistically reliable estimates of probabilistic risk regarding future outcomes as uncertainty permits mainstream economists to preserve intact most of the laissez faire efficient market analysis that had been developed under the earlier perfect certainty assumption. While rejecting the perfect certainty model, mainstream economists still accept, as a universal truth, the existence of a predetermined external economic reality (similar to Newton’s celestial mechanics which, for example, permits the astronomer to accurately predict the next solar eclipse) that can be fully described by unchanging objective conditional probability functions that are fully known by the decision makers in one’s model… Unlike the perfect certainty model, however, conflating the concept of uncertainty with the probabilitistic risk permits individual decision makers to make an occasional erroneous choice (in the short run) just as a single sample means can differ from the true universe value. In the long run, the assumption that people with rational expectations already “know” the objective probabilities assures correct choices on average for those “fittest” decision makers who survived in the Darwinian world of free markets. In other words, free markets lead to optimal solutions at least in the long run
In mainstream economics, economic data are typically viewed as part of time series realization generated by an ergodic stochastic processes. In fact, Nobel Prize winner Paul Samuelson (1969) has made the acceptance of the ergodic axiom the sine qua non of the scientific method in economics. What is this ergodic axiom that Samuelson insists is necessary for economics to be a science?
IV. UNCERTAINTY AND ERGODIC STOCHASTIC PROCESSES
Logically, to make statistically reliable probabilistic forecasts about future economic events, today’s decision-makers should obtain and analyze sample data from the future. Since that is impossible, the assumption of ergodic stochastic economic processes permits the analyst to assert that the outcome at any future date is the statistical shadow of past and current market data.
A realization of a stochastic process is a sample value of a multidimensional variable over a period of time, i.e., a single time series. A stochastic process makes a universe of such time series. Time statistics refer to statistical averages (e.g., the mean, standard deviation) calculated from a single fixed realization over an indefinite time space. Space statistics, on the other hand, refer to a fixed point of time and are formed over the universe of realizations (i.e. they are statistics obtained from cross-sectional data).
Statistical theory asserts that if the stochastic process is ergodic then for an infinite realization, the time statistics and the space statistics will coincide. For finite realizations of ergodic processes, time and space statistics coincide except for random errors; they will tend to converge (with the probability of unity) as the number of observations increase. Consequently, if ergodicity is assumed, statistics calculated from past time series or cross-sectional data are statistically reliable estimates of the statistics probabilities that will occur at any future date.
In simple language, the ergodic presumption assures that economic outcomes on any specific future date can be reliably predicted by a statistical probability analysis of existing market data. By assumption, New Classical economic theory imposes the condition that economic relationships are timeless or ahistoric ‘natural’ laws. The historical dates when observations are collected do not affect the estimates of the statistical time and space averages. Accordingly, the mainstream presumption (utilized by both New Classical economists and New Keynesian economists) that decision-makers possess rational expectations imply that people in one’s model process information embedded in past and present market data to form statistical averages (or decision weights) that reliably forecast the future. Or as 2011 Nobel Prize winner Thomas Sargent [1993, p. 3], one of the leaders of the rational expectations school, states “rational expectations models impute much more knowledge to the agents within the model (who use the equilibrium probability distributions)… than is possessed by an econometrician, who faces estimation and inference problems that the agents in the model have somehow solved”.
By using probabilistic distributions calculated from past market data, rational expectations theory assumes that, on average, the actions fostered by these expectations are precisely those that would be forthcoming in a perfectly certain world – at least in the long run.
In recent years, partly in reaction to the rational expectations hypothesis, some mainstream economists have raised questions regarding the use of such stochastic concepts to define uncertainty. For example, Nobel Prize winner R. M. Solow (1985, p. 328) has stated “economics is a social science….much of what we observe cannot be treated as the realization of a stationary stochastic process without straining credulity”. Since stationary is a necessary but not sufficient condition for ergodicity, Solow’s statement implies that only the very gullible would ever believe that most important macroeconomic processes are ergodic.
V. DISTINGUISHING BETWEEN UNCERTAINTY AND PROBABILISTIC RISK
Beginning with Knight’s  seminal work, some economists have drawn a distinction between “true” uncertainty and probabilistic risk, where the latter is calculable based on past frequency distributions and is, therefore, conceptually insurable, while uncertainty is neither calculable nor insurable.
John Maynard Keynes (1936) launched a revolution in economics. Keynes explicitly developed an alternative “general theory” to classical theory. Keynes argued that the difference between probabilistic risk and uncertainty had important implications for understanding (a) the operations of a market economy and (b) the role of government in influencing market outcomes through deliberate legislative policies.
In Keynes’s (1936) analysis, whenever the full consequences of today’s economic decisions occur many days in the future, uncertainty would prevail and economic behavior could not be described as an “outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities”.
Unlike today’s orthodox economists, Keynes did not write in the idiom of stochastic processes in developing his concept of uncertainty. Keynes (1937) simply described uncertainty as occurring when there is no scientific basis to form any calculable probability. Nevertheless, in criticizing Tinbergen’s use of econometric analysis, Keynes (1939) argued that Tinbergen’s ‘method’ was not applicable to economic data because “the economic environment is not homogeneous over a period of time”, a criticism that is equivalent to stating economic time series are not stationary.
With the development of ergodic theory and stochastic process analysis since Keynes wrote, it is possible to interpret Keynes’s uncertainty concept in terms of this statistical lexicon. Keynes’s theory required decision-makers to recognize that in the market system in which they operate, in some but not necessarily all economic dimensions, the future is uncertain and cannot be reliably predicted on the basis of any statistical analysis of past evidence. The absence of ergodic conditions, therefore, is a sufficient condition for Keynes’s concept of uncertainty. In a nonergodic environment, even if agents have the capacity to obtain and statistically process past and current market data, these observations do not, and cannot, provide a statistically reliable basis for forecasting the probability distributions, if any, that will govern outcomes at any specific date in the future. According to Keynes (1937), “About these [future] matters there is no scientific basis to form any calculable probability whatever. We simply do not know.”
Keynes’s uncertainty concept implies that the future is transmutable or creative in the sense that future economic outcomes may be permanently changed in nature and substance by today’s actions of individuals, groups (e.g., unions, cartels) and/or governments, often in ways not even perceived by the creators of change. (It is also possible that changes that are not predetermined can occur even without any deliberate human economic action.). [George Soros’s concept of ‘reflexivity’ asserts future market outcomes are determined by market participants’ actions today.]
This nonergodic view of modelling the future out comes as being determined by peoples’ actions rather than a timeless probability distribution has been described by Nobel Prize winner Sir John Hicks (1977) as a situation where people in the model “do not know what is going to happen and know that they do not what is going to happen. As in history!” Hicks (1979) declared that “I am bold enough to conclude from these considerations that the usefulness of ‘statistical’ or ‘stochastic’ methods in economics is a good deal less than is now conventionally supposed.”
Accordingly, mainstream macroeconomics is logically inconsistent with Keynes’ macroeconomic general theory explaining employment, interest, and money. The result has been a continuing debate between the followers of Keynes and mainstream theorists over the relevant policy prescriptions for solving the macroeconomic problems of the real world.
The first postulate of mainstream economics is the presumption that there exists a finite set of acts and outcomes and that each agent can make a complete and transitive preference ordering of all possible alternative choices. Decision making by agents who know the statistically reliable future can characterize the decision process as “Look before you leap”. This “Look before you leap” analysis, however, is not a general theory of decision making for it does not explicitly deal with uncertainty per se. As the statistical theorist Leonard Savage recognized “a person may not know [all] the consequences of the acts open to him in each state of the world. He might be … ignorant” and hence might want to leave his options open; a decision that Savage characterizes as “You can cross that bridge when you come to it”. Savage admits the latter is often a more accurate description of the human economic predicament. When a decision maker is ‘ignorant’ and wants to wait before making a decision, we can classify the situation as one involving Keynes’ uncertainty concept and therefore the mainstream ergodic axiom is violated.
As Savage puts it, mainstream economics “attack[s] relatively simple problems of decision by artificially confining attention to so small a world that the `Look before you leap’ principle can be applied”, i.e., where Keynes’ uncertainty concept is not relevant. Savage warns that mainstream theory is “practical [only] in suitably limited domains… At the same time, the behavior of people is often at variance with the theory. The departure is sometimes flagrant … the `Look before you leap’ principle is preposterous if carried to extremes”. Yet when today’s mainstream economic theorists talk about efficient free markets they treat uncertainty in economics as synonymous with a probability measure The behavior they describe flagrantly departs from the behavior that determines employment in a money-using market economy.
If, as Savage recognizes, in some areas of economic activity the ability of humans to form a complete preference ordering regarding all potential consequences of all actions is not possible, then mainstream theory cannot provide a useful explanation of the behavior of decision-makers in these areas. It is here that Keynes’ uncertainty concept becomes paramount
In the classical (ergodic) theory, where all outcomes are conceptually calculable, there is never a need to keep options open. People will therefore spend all they earn on the products of industry (Say’s Law) and there can never be a lack of effective demand to prevent the system from reaching full employment.
On the other hand, when households and firms “know that they do not know” the future and therefore cannot order all future consequences associated with any possible choice today, they may wish to defer forever making “look before they leap” decisions. When people believe the future is uncertain in the sense of Keynes, they prefer to leave their options open, i.e., to cross that bridge when, and if, they come to it.
Whenever households and business managers believe they cannot predict the future with any degree of a priori or statistically reliable probability, then the axiomatic foundation of mainstream economic theory is violated. Hicks (1979) has associates this transgression of mainstream axiomatic ergodic basis with Keynes’ long-term ‘liquidity’ concept. For Keynes, it is the existence of an uncertain future that makes a long-run demand for liquidity (money and other liquid assets traded in well organized markets where prices movements are ‘orderly’) a ubiquitous fact of life. The ability to save one’s income in the form of money and other liquid assets permits households and firms to keep their options open by not having to spend all of their earned income on the products of industry, even in the long-run.
As long as income-earning decision-makers have this option of demanding liquidity rather than the products of industry, then a laissez-faire market system cannot assure that peoples’ total market demand for goods and services will be sufficient to make it profitable for firms to fully employ all who want to work.
The notion of a demand for long-term liquidity can only be justified in a world of Keynes’ (nonergodic) uncertainty. This desire for long-term liquidity is incompatible with mainstream’s optimal decision makers in an ergodic environment. Only the Keynes concept of uncertainty in economics provides a logical, statistical explanation of the phenomenon of persistent unemployment that occurs in the market economies in the world we inhabit. Only the Keynes uncertainty concept can justify a role for governmental policies to assure full employment when questions of liquidity are important.
Davidson, P. (1991) “Is Probability Theory Relevant For Uncertainty? A Post Keynesian Perspective”, Journal of Economic Perspectives, 5. (Distinguishes between economic decisions where ergodic circumstances might prevail, and situations where nonergodic circumstances are likely. The former are called routine decisions, the latter are crucial decisions.)
Hicks, J. R. (1977), Economic Perspectives, Oxford University Press, Oxford.(Argues for economic models where agents ‘know’ that they cannot reliably predict the future.)
Hicks, J. R (1979), Causality in Economics, Basic Books, New York. (Argues that economics is embedded in time in a way that the physical sciences are not. Consequently stochastic theory is not applicable to most dynamic economic problems.)
Keynes, J. M. (1936), The General Theory of Employment, Interest and Money Harcourt, New York. (The basis for the ‘Keynesian Revolution’ where the existence of uncertainty explains why market economies have no endogenous forces that assure full employment.)
Keynes, J. M. (1937), “The General Theory of Employment” Quarterly Journal of Economics, 52. (A further extension of what Keynes means by ‘uncertainty’ and why uncertainty is the root cause of unemployment in market economies.)
Keynes, J. M. (1939), “Professor Tinbergen’s Method”, The Economic Journal, 47. (Keynes attacks the statistical method of regression analysis as not applicable to economic time series data.)
Knight, F. N. (1921), Risk, Uncertainty, and Profit, Houghton Mifflin, New York. (Distinguished between probabilistic risk and uncertainty.)
Lucas, R. E., (1972) “Expectations and the Neutrality of money”, Journal of Economic Theory,4. (The article that initiated the rational expectations analysis in macroeconomics.)
Lucas R. E., and Sargent, T. J. (1981), Rational Expectations and Econometric Practices, Minneapolis, University of Minnesota Press. (Develops the relationship between the rational expectations hypothesis and the axioms underlying econometric analysis for macroeconomic analysis.)
Machina, M. J. “Choice Under Uncertainty; Problems Solved and Unsolved”, Journal of Economic Perspectives, 1. (Attempts to shore up the theory of choice under uncertainty on “solid axiomatic foundations” of probabilistic risk in the face of the famous St. Petersburg paradox and other challenges to expected utility theory).
Ricardo, D. (1817), On the Principles of Political Economy and Taxation. (The first economist to formulate the axiom of perfect certainty in economics.)
Savage, L. (1954), The Foundations of Statistics Wiley, New York.(Develops the Expected Utility Theory of economics for making decision with complete subjective probabilistic information.)
Sargent, T. J. (1993), Bounded Rationality in Macroeconomics, Oxford, Clarendon Press. (A founder of the rational expectations school who now argues that rational expectations are not applicable to situations where people find themselves in new, i.e., nonergodic, situations.)
Solow, R. M. (1985), “Economic History and Economics”, American Economic Review Papers and Proceedings, 75.