Wednesday, March 2, 2011

Uncertainty and Non-Ergodic Stochastic Systems

The concept of uncertainty in economic life was used by Keynes in the General Theory (1936) and also in an article defending his new theory the next year (see Keynes, “The General Theory of Employment,” Quarterly Journal of Economics 51 [1937]: 209–223).

Paul Davidson notes the nature of uncertainty in the Keynesian/Knightian sense:
“Keynes’s description of uncertainty matches technically what mathematical statisticians call a nonergodic stochastic system. In a nonergodic system, one can never expect whatever data set exists today to provide a reliable guide to future outcomes. In such a world, markets cannot be efficient” (Davidson 2002: 187).

“Keynes … rejected this view that past information from economic time-series realizations provides reliable, useful data which permit stochastic predictions of the economic future. In a world where observations are drawn from a non-ergodic stochastic environment, past data cannot provide any reliable information about future probability distributions. Agents in a non-ergodic environment ‘know’ they cannot reliably know future outcomes. In an economy operating in a non-ergodic environment, therefore – our economic world – liquidity matters, money is never neutral, and neither Say’s Law nor Walras’s Law is relevant. In such a world, Keynes’s revolutionary logical analysis is relevant” (Davidson 2006: 150).
Certain types of phenomena in our universe are what mathematicians call non-ergodic stochastic systems. The concept of radical uncertainty applies to such systems, like medium term weather events, financial markets, and economies, and other natural systems studied in physics.

In these systems, past data is not a useful tool from which one can derive an objective probability score for some specific, future state of a quantitative variable in the system. Of course, such a system can still have trends, cycles and oscillations, both in the past and future. For example, stock markets certainly have cycles of bull and bear phases, but trying to predict the specific value of some stock x, say, two years from now with an objective probability score is not possible.

But the fundamental point is that it is still possible for a powerful agency or entity to reduce uncertainty in these systems, or at least in theory in some of them. It is entirely possible that in the future – with a far more advanced human civilization – we could use technology to control local, regional or perhaps even global weather.

And even today a powerful entity like the government can intervene to reduce uncertainty in the non-ergodic stochastic system we call the economy.

Is Climate a Non-Ergodic Stochastic System?

Does the earth’s climate system have the property of non-ergodicity? This question has occurred to me more than once, but I am actually unsure of the answer.

Some quick research suggests that climate models appear to make an ergodicity assumption about climate systems:
“Thus, it is perfectly valid to consider our climate a realization of a continuous stochastic process even though the time-evolution of any particular path is governed by physical laws. In order to apply this fact to our diagnostics of the observed and simulated climate we have to assume that the climate is ergodic. That is, we have to assume that every trajectory will eventually visit all parts of phase space and that sampling in time is equivalent to sampling different paths through phase space. Without this assumption about the operation of our physical system the study of the climate would be all but impossible.

The assumption of ergodicity is well founded, at least on shorter time scales, in the atmosphere and the ocean. In both media, the laws of physics describe turbulent fluids with limited predictability (ie, small perturbations grow quickly, so two paths through phase space diverge quickly) (von Storch and Zwiers 1999: 29–30).
But then what about longer time scales? If “the laws of physics describe turbulent fluids with limited predictability” on short time scales, what sort of predictability can they provide on medium or long term time scales?

Let’s assume, for the sake of argument, that long term climate is non-ergodic, in the way that a free market economy is. Does that mean all intervention would be useless and ineffective in such a system to affect the state of it? Does it mean that we are all doomed to (in a manner of speaking) live in a “free market” climate forever?

In fact, that does not follow at all. It is probably very likely that our future technology, when it becomes sophisticated and powerful enough, will be used by humans to intervene and control climate, e.g., by preventing ice ages.


David, P. A. 2007. “Path Dependence, its Critics and the Quest for ‘Historical Economics,’” in G. M. Hodgson, The Evolution of Economic Institutions: A Critical Reader, Edward Elgar, Cheltenham. 120–144.

Davidson, P. 2002. Financial Markets, Money, and the Real World, Edward Elgar, Cheltenham.

Davidson, P. 2004. “Uncertainty and Monetary Policy,” in P. Mooslechner, H. Schuberth, and M. Sch├╝rz (eds), Economic Policy under Uncertainty: The Role of Truth and Accountability in Policy Advice, Edward Elgar, Cheltenham. 233–260.

Davidson, P. 2006. “Keynes and Money,” in P. Arestis and M. Sawyer (eds), A Handbook of Alternative Monetary Economics, Edward Elgar, Cheltenham, UK and Northampton, Mass. 139–153.

Keynes, J. M. 1937. “The General Theory of Employment,” Quarterly Journal of Economics 51 (February): 209–223.

Storch, H. von and F. W. Zwiers, 1999. Statistical Analysis in Climate Research, Cambridge University Press, Cambridge, UK and New York.


  1. >It is probably very likely that our future technology, when it becomes sophisticated and powerful enough, will be used by humans to intervene and control climate, e.g., by preventing ice ages.

    The political polarization about the global warming issue puzzles me, because the right tends to assume more of a dominator model about the environment than the left. I would expect from that model that conservatives and libertarians would in fact want man to have the technology to control Earth's climate, like an advanced civilization out of science fiction, and would therefore celebrate the accidental discovery of a means to do so through burning fossil fuels. A climate control technology belongs organically in the right's dominator agenda along with nuclear power, pesticides and genetically engineered crops.

  2. Much of my research has been based on assuming non-ergodicity as a condition and then asking how can we obtain reliable decision-making in such an environment, where reliability is within known limits. The answer is it is not possible to just handle arbitrary Keynesian uncertainty. It is, however, possible to obtain reliable decision-making within bounds defined by some weaker condition than ergodicity. Ergodicity is just an invariance condition - a very strong one holding that the future and past are statistically symmetrical - which leads us to the possibility of using weaker invariances instead. I have been looking at entropic invariance conditions but there are any number of other ways to frame bounding assumptions instead.

  3. By the way, saying that a system is ergodic is also equivalent to saying that it has no self-reference, hence no paradoxes. Non-ergodic systems are non-ergodic because underlying logical paradoxes limit knowing within the logical context of the system.