Hi Sander

I would say yes and no to your modelling question. Some things will not change, like the basic structure of the national accounts. But other parts, as you describe, do not fit well into any traditional macroeconomic modelling structures. The closest thing that exists is the agent-based approaches that grew out of the Santa Fe Institute and similar research efforts. A lot of research is being carried out currently in this area but by nature it tends to be more micro in approach.

Hector

I suppose you already know that a specific brand of post-Keynesians of the Paul Davidson type beleives that the macro economy is non-ergodic. If you watch one of Paul's recent videos on Ytube he explained it by saying that we cannot project the future from past data modelled in a statistical or econometric fashion. Besides Paul's numerous works on Keynesian economics, he has had the blessing of Sir John Hicks on his side and therefore, should be taken seriously.

@Hector: Agent-based macroeconomics is a recent development I am somewhat involved in. But it is uncertain whether this will be able to provide any answers to such deep questions... only time will tell. The Santa Fe institute... yes, but where are they now? It seems all the action in ABMacro is happening in Europe at the moment.

@Lall: Indeed, I respect the post-Keynesians a lot. Could you please provide a reference to Sir Hicks' contention that the economy would be non-ergodic? I know the Stockholm School of the 1930s (Erik Lundberg, Erik Lindahl) also had similar ideas about sequential dynamics in economies, but I do not know exactly whether they also were discussing the notion of non-ergodicity. If anyone would have knowledge on this, I would be interested.

Dear Sander

I attach a file with three pages from Davidson 2007 book. Hicks letter to him in footnote 13 also attached verify the point. Hope it helps.

Hi Sander,

This might sound like quite an abstract response but I hope it is useful...

The question of ergodicity can be asked about open systems in general. Really, the problem is how one can define the phase space for such nonautonomous systems, since any time dependent trajectory will diverge from its origin. The way to stop this is to simply add more dimensions to the system that account for the time-dependence, so that its trajectory is "wrapped" in phase space. However, when you do this the system starts to look complex and stochastic so while it may be ergodic, it is no longer very useful.

Alternatively one can conduct stroboscopic analysis, either by taking a slice of time and constructing the attractor for different initial conditions or, if the time-dependence is periodic, from a single trajectory at a point in the phase of the oscillation. This provides a more useful representation of the system (for example, making it easier to define its dimension) but it is no longer ergodic as each point of the trajectory in time essentially corresponds to a different attractor with different statistics.

So I would say that the economy can be modelled by an ergodic system but it may be more useful to consider it as a time-dependent non-ergodic system.

I will completely confess that some of the more technical aspects of ergodic theory are completely over my head but I interpret the spirit of the question to be about the long-run behavior of the economy over time. If we approach this from the history of economic thought, I would argue that in the past there is some support for the view that the economy is something of an ergodic process. Jevons, for example, argued that there was something of a 20-year cycle in the economy that was linked to sunspots (not entirely whacky given the importance of agriculture in the past). Kondratiev had his waves of economic activity. Former Federal Reserve Governor Larry Meyer gave a speech arguing that productivity growth evolved in waves or at least long periods of alternating high and low growth.(http://www.federalreserve.gov/boarddocs/speeches/2001/20010606/default.htm). I am not sure the statistical methods for ergodic processes would be helpful in modeling the cycle but the spirit behind the question has fascinated economists for a long time.

Sander, for an economy, a system, to be ergodic it would have to be closed, low dimensional and not evolving. This might be interesting as a mathematical and statistical problem and, of course, it would be possible to model. Non-ergodic systems, as you mention, are open and generate new information all the time. A Darwinian evolutionary process is perhaps the most well known of these kinds of systems; but economic systems in which learning and adaptation are the source of dynamic behavior also fall in that category. I believe it is correct to say that John Holland's motivation for modeling adaptive behavior was to find a way to model these kinds of systems. His GA is perhaps his most well known contribution, but he also developed something called a learning classifier system. An LCS might be thought of as a GA with a memory; basically it is an evolutionary computational approach to searching a large, complex space. Holland, Arthur and others used the approach in the early 1990s on economic problems. We have been using LCSs recently in multi-agent simulations of a fishing economy (Wilson, et al. Costly information ... JEBO July 2013 attached). This work has led me to believe the key to understanding non-ergodic economic systems, i.e., systems that are continually generating new information, is to treat information as a scarce, even if peculiar, resource. The attached paper describes a non-ergodic model of a small complex system. So, my answer to your question, is yes it is possible to model non-ergodic systems.

@Lall: Thank you for the copy of Davidson's book and Hicks's letter. It put me on the track of "The ergodic axiom: Davidson versus Stiglitz and Lucas" (link attached).

If I summarize the discussion so far:

- proponent of the Ergodic Axiom are: Stiglitz, Lucas

- opponents of the Ergodic Axiom are: Keynes, Hicks, Davidson

The Non-Ergodic Axiom would state that:

- past data cannot be used to predict the future behaviour of a system

- quantifiable models of non-ergodic systems are difficult (?)

- this does NOT mean that economics is not a science: evolutionary theory is a scientific theory, even if it deals with newness, open system, and non-ergodicity.

http://rwer.wordpress.com/2012/03/28/the-ergodic-axiom-davidson-versus-stiglitz-and-lucas/

@James: If you allow me to summarize it in this fashion:

"A Darwinian evolutionary process is non-ergodic" and "Economic systems with learning, adaptation and innovation are open systems"

You could think of the space of all possible DNA combinations, and define an evolutionary process as a giant GA over this space. Mathematically, the space is finite and closed. It just takes a very, very long time to traverse it, and to collect time averages, to ascertain whether or not this process is then ergodic or non-ergodic.

(We remain with the problem of genotypic determinism, that is, does the genotype uniquely determine the phenotype...)

Similarly for economic processes of innovation: you could think of the space of all possible inventions, even if it would be quite large.

The problem is not that we cannot formulate this mathematically. The problem is more fundamental: ergodicity is an asymptotic concept. The time averages have to be taken over the entire phase space, then let time tend to infinity, and then compare that to ensemble averages. Even if the phase space is well-defined and finite, testing for ergodicity is problematic, due to this "let time tend to infinity"-clause in the definition of ergodicity. If you cannot test it, it is not a scientific hypothesis, a la Popper.

I must confess to a tendency to side with Keynes that "in the long run we are all dead " and to subscribe to Marshall's advice to scrap formalism and replace it with words once the results are in sight. That been said, pure ergodicity requires the asymptotic conditions covered explicitly or implicitly in the previous threads.And that the economy is a multiscaled system makes it hard to extend the results from one scale to another (i.e. spanning scale breaks) by the use of a single method that is premised on ergodicity. Another issue that seems to support non-ergodicity characterizations of the economy is the notion of reflexivity that throws a wrench into any permanent effort rooted on the assumption of ergodicity. That models used to study economic phenomenon may eventually take on a life and interest of their own (i.e. metadata), apart from their role as analytical instruments, continue to baffle and confound pundits. In light of such premises, GA & CA seem to offer at least some hope because of their recursive nature ( addresses scale breaks), and their generative, projective nature that allows us to escape the gravitational pull of past data and reach for what is possible (i. e. scenarios), and alternative universes. At least the lessons from deterministic chaos and complexity science would have sensitized us to such  possibilities. The utility of GA & CA models is such that at the asymptotic limit (stated in t iterations), the  hitherto  non- ergodic system would begin to collapse back to what resembles an ergodic system, or an emergent fitness landscape would have presented itself; suggesting a tractable approach to its solution witin the bounds of a set of parameters. Hence GA & CA assist in parsing the phase space of systems.They are not to be treated as pure substitutes for conventional methods based on ergodic assumptions.

 I wonder if almost all non-mainstream economists were fooled by Paul Davidson. Uncertainty as a concept different from risk is important, but this kind of distinction goes back to the famous Knight's 1921 book  Risk, Uncertainty, and Profit.  Davidson discovered that Paul Samuelson has once used the term "ergodic hypothesis" of one of his old days assumption and fabricated it as the the sine qua non for the scientific method in economics.

Let me cite Davidson's own words:

• First, let us 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.    (Cited in The ergodic axiom: Davidson versus Stiglitz and Lucas https://rwer.wordpress.com/2012/03/28/the-ergodic-axiom-davidson-versus-stiglitz-and-lucas/ )

Davison cited Samuelson (1969). It is a reprint of Samueslons (1968) paper in The Canadian Journal of Economics 1(1) 1-15. The main part of the paper is a recollection of  his young days. He wrote

• Mine is the great advantage of having once been a jackass. From 2 January 1932 until an indeterminate date in 1937, 1 was a classical monetary theorist.  (p.1)

Samuelson explains the hypotheses  of those classical monetary theorists and that he had abandoned since circa 1937. Even in this paper, Samuelson did not write 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."

Samuelson wrote:

• Finally, there was an even more interesting third assumption implicit and explicit in the classical mind. It was a belief in unique long-run equilibrium independent of initial conditions. I shall call it the "ergodic hypothesis" by analogy to the use of this term in statistical mechanics. (pp.11-12)
• Technically speaking, we theorists hoped not to introduce hysteresis phenomena into our model, as the Bible does when it says "We pass this way only once" and, in so saying, takes the subject out of the realm of science into the realm of genuine history. (p.12) (emphasis is mine)

But it is necessary to note that this hypothesis was the old one Samuelson once believed but did not adhere to when he wrote the paper. It was Paul Davidson who fabricated "ergodic axiom" and postulated it as the sine qua non for the scientific method in economics. 

We must be free from this widely accepted, but completely misleading characterization of economics. Ergodic hypothesis may be useful to criticize Dynamical Stochastic General Equilibrium models, but not a good criterion to classify strands of existing economics.

See also the footnotes 16,  p.34 in my paper Microfoundations of Evolutionary Economics

https://www.researchgate.net/publication/301766363_Microfoundations_of_Evolutionary_Economics

Working Paper Microfoundations of Evolutionary Economics

Dear Professor Yoshinori Shiozawa,

Yes.You are 100 % correct on both issues concerning Samuelson and Keynes.Keynes's definition of uncertainty  in the GT has nothing to do with Davidson's bogus claims about  ergodicity or non ergodicity.Keynes's definition of uncertainty is that it is a function of his" weight of the evidence" variable,w, that he  introduced to the readers of his A treatise on Probability (1921)in chapter 6 and analyzed in chapter 26 of that book.The best confirmation of this  is to read the Keynes -Townshend exchanges in Volume 29 of the CWJMK in 1937 and1938..

You are also correct that Davidson has fabricated his false claims about Paul Samuelson.You might want to take a look at my two SSRN working papers. I like your paper.

Unfortunately, you are also correct that Davidson has completely mislead all heterodox economists with his flim flam.

Either Tiago Camarinha Lopes or Charles Grimshaw recommended my post on December 15, 2016 (three post above). I must thank him for reminding me that I posted it almost six years ago.

I am a Sraffian and in a broad sense a Post Keynesian, of the last of which Paul Davison counts as one of the founders. It is sad to say that one of Davidson's main contention originated from a kind of fraud. However, I believe it is much better that Davidson's misleading terminology is detected by some objectors to Post Keynesian economics. Post Keynesian economics does not draw on Davidson's misleading ideas.

I think that economies are much more non-ergodic, but economics is, of course, moe ergodic than non-erodic. In many economic models, erodicity is highly exaggerated. Examples: representative agents and firms, maximization of utility and profit, aggregate production functions etc.

صحيح

Ergodicity economics is an approach to economic theory which emphasizes the ergodicity question, namely whether expectation values of stochastic processes are equal to their time averages. This yields alternative solutions to classic problems in economics. In essence, ergodicity economics explores what aspects of economics can be informed by avoiding implicit assumptions of ergodicity. It insists on a physical justification when expectation values are used. In ergodicity economics, expectation values are replaced, where necessary, by averages that account for the ergodicity or non-ergodicity of the observables involved.

Chuck, you should stop adding contributions (that do not fit to the question raised and the discussion) which are merely copied or extracted from wikipedia (in order to collect recommendations or disturb the discussion?)

the ergodicity assumption has come under scrutiny in recent years. Critics argue that many economic systems do not exhibit ergodic behaviour. Instead, they exhibit path dependence, non-stationarity, and heterogeneity. In such cases, the behaviour of the system as a whole cannot be accurately represented by the behaviour of an average individual.

For instance, the occurrence of financial bubbles and crashes demonstrates non-ergodic behaviour. In a bubble, asset prices rise rapidly based on speculative behaviour and positive feedback loops, leading to an unsustainable increase in valuations. Eventually, the bubble bursts, resulting in a significant price correction or crash.

During a bubble, the behaviour of the market as a whole is influenced by factors such as herd behaviour, irrational exuberance, and market sentiment. These factors are not captured by traditional models that assume rationality and efficient markets. The dynamics of bubbles and crashes are path-dependent, meaning that historical events and initial conditions can have a lasting impact on the behaviour of the market.

Furthermore, the impact of a market crash or financial crisis can be non-ergodic as well. The consequences of such events are often not distributed uniformly across market participants or assets. Some individuals or sectors may experience significant losses, while others may benefit or remain relatively unaffected.

The presence of non-ergodic behaviour in financial markets challenges the assumptions made in traditional economic models. To better capture the dynamics of financial markets, researchers have developed models that incorporate elements of behavioural finance, investor sentiment, and heterogeneous agents. These approaches recognize that individual behaviours and market dynamics can deviate from the assumptions of rationality and efficiency, leading to non-ergodic outcomes.

Non-ergodicity has significant implications for economic modelling. When a system is non-ergodic, the long-term statistical properties observed in the data may not be representative of the behaviour of individual agents or the system as a whole. This challenges the traditional assumptions and simplifications made in economic models.

To address non-ergodicity, economists have developed alternative modelling approaches. These approaches often consider the heterogeneity of agents, path-dependent dynamics, and the importance of initial conditions and historical events. Agent-based modelling, complexity economics, and behavioural economics are some of the frameworks that aim to capture non-ergodic behaviour by incorporating these elements into economic models.

I want to read more about non-ergodic behavior in other sciences like hydrology and water security and the impact of the ergodic type of planning when facing water crises.