## Why the ergodic theorem is not applicable in economics

6 May, 2015 at 15:06 | Posted in Economics | 5 CommentsAt a realistic level of analysis, Keynes’ claim that some events could have no probability ratios assigned to them can be represented as rejecting the belief that some observed economic phenomena are the outcomes of any stochastic process: probability structures do not even fleetingly exist for many economic events.

In order to apply probability theory, one must assume replicability of the experiment under the same conditions so that,

in principle, the moments of the random functions can be calculated over a large number of realizations …For macroeconomic functions it can be claimed that only a single realization exists since there is only one actual economy; hence there are no cross-sectional data which are relevant. If we do not possess, never have possessed, and conceptually never will possess an ensemble of macroeconomic worlds, then the entire concept of the definition of relevant distribution functions is questionable. It can be logically argued that the distribution function cannot be defined if all the macroinformation which can exist is only a finite part (the past and the present) of a single realization. Since a universe of such realizations must at least conceptually exist for this theory to be germane, the application of the mathematical theory of stochastic processes to macroeconomic phenomena is therefore questionable, if not in principle invalid.

To understand real world “non-routine” decisions and unforeseeable changes in behaviour, ergodic probability distributions are of no avail. In a world full of genuine uncertainty — where real historical time rules the roost — the probabilities that ruled the past are not necessarily those that will rule the future.

When we cannot accept that the observations, along the time-series available to us, are independent … we have, in strict logic, no more than one observation, all of the separate items having to be taken together. For the analysis of that the probability calculus is useless; it does not apply … 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 … We should always ask ourselves, before we apply them, whether they are appropriate to the problem in hand. Very often they are not … The probability calculus is no excuse for forgetfulness.

John Hicks,Causality in Economics, 1979:121

To simply assume that economic processes are ergodic — and *a fortiori *in any relevant sense timeless — is not a sensible way for dealing with the kind of genuine uncertainty that permeates open systems such as economies.

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Heterodoxy simply does not apply ergodicity

Comment on ‘Why the ergodic theorem is not applicable in economics’

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Imagine a rather elementary economy. Total employment is L, the wage rate is W. So total wage income is Y=WL. The household sector’s total consumption expenditures are C and equal to price P times quantity bought X, i.e. C=PX. The productivity is R, so output is O=RL. In the initial period the market is cleared X=O and the budget is balanced C=Y.*

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Now let the five elementary variables L, W, P, R, X vary at random. The respective rates of change are symmetrical around zero and a distribution function is defined so that each path meets the condition of ergodicity. Hence, by construction, each path and the whole economy is initially ergodic.

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When we run a simulation we observe a changing stock of inventory, because O-X is always different from zero, and a changing stock of money, because Y-C is always different from zero. The two stocks follow random paths.

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Next, the agents enter. The business sector sets the price in order to bring the inventory to a target value and to clear the market. Likewise the household sector adapts consumption expenditures in order to bring the stock of money to a target value and to balance the budget.

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Obviously, the economy is no longer ergodic. The reason is that agents are target oriented and interfere with pure randomness. Their behavior is formally defined by the propensity function (2015) which eliminates the initial ergodicity through directed randomness.

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Ultimately, this has nothing at all to do with uncertainty or nomological machines or rational expectations. The sheer existence of agents in a pure random system suffices to eliminate initial ergodicity.

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No heterodox economist worth his salt would ever apply ergodicity. True, orthodox economists still do but they are already irrecoverably over the cliff. Thus, it does not really matter.

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Egmont Kakarot-Handtke

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References

Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: Behavior.

SSRN Working Paper Series, 2600523: 1–17. URL

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2600523.

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* For the complete formalism see

Comment by Egmont Kakarot-Handtke— 7 May, 2015 #

And if the system isn’t ergodic (which nothing involving society are) then any thermodynamics analogy are invalid. This also makes statistics virtually useless to predict future events i society, thus mathematics(*) are useless for prediction in social science. A large part of modern social science need to be thrown out.

All improvment of models with current data is just mathematical ad hoc which does not improve the predictive ability of the model and the instances where the model works are merely pure chance.

Life is a non-ergodic state of being and equilibrium is what we call death.

(*) Mathematics and statistics can still be useful for evaluating what has happened and lend a greater understanding of what has happened or what is going on right now, but prediction is only possible for a very few instances, usually for very short periods of into the future.

Comment by Martin Kullberg— 6 May, 2015 #

Although I wouldn’t express it as colourful and imaginative as you, I basically agree. Stationarity presumes time-independent processes, and what is stationary is strictly seen actually impossible to decide within a finite samples world (as the one we happen to live in). Applying stationarity and ergodicity in the real world presupposes, at a minimum, a pre-defined time window. Without that restriction, ergodicty and stationarity are effectively non-starters for real world analyses.

Comment by Lars Syll— 6 May, 2015 #

Well my crusade against idiot savants using mathematics erronously is not restricted to economics and social science. It is a huge problem in medicin and psychology and many other disciplins. Not to mention theoretical physics, but that is a special needs program anyway.

I work with non-ergodic chemistry and non-ergodic systems every day. I have intimate experience of what goes wrong when trying to transfer knowledge from an ergodic system into a non-ergodic system.

The thermodynamics theory that economist should taka a long hard look at is Le Chatiliers principle…

Comment by Martin Kullberg— 6 May, 2015 #

Getting lost in the jargon of “time-stationary” etc obscures the most important part of this comment: economics is not thermodynamics.

If the discipline is to change, it won’t be caused by high-level sophisticated debates about the nature of ergodicity, but from easily understood arguments like: physics isn’t the only science. Darwin is the model for the study of living creatures and their societies. But biology isn’t attractive to math savants.

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But the favorite sciences of math savants are, by definition, incapable of revealing the truth about human society and the sub-field of economics.

Comment by Thornton Hall— 11 May, 2015 #