## May 7, 2015

### Heterodoxy simply does not apply ergodicity

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

Blog-Reference

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.*

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.

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.

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.

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.

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.

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.

Egmont Kakarot-Handtke

References
Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: Behavior. SSRN Working Paper Series, 2600523: 1–17. URL

*   For the complete formalism see here and for the graphical representation here