Why the ergodic theorem is not applicable in economics
from Lars Syll
At 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.