Jason Smith replies to Lars Syll (and Paul Davidson).
What comes out of assuming ergodicity? All of basic thermodynamics and much of basic economics. If we assume economic (or thermodynamic) systems aren't ergodic -- what does that give us?
Essentially, assuming non-ergodicity is analogous to the assumption that I(A) < I(B) in the information transfer framework (ergoditicy is the assumption that I(A) ≈ I(B) ... the information in the two macro observable is the same, from which you can derive supply and demand).
What can we get from the assumption I(A) < I(B)? Nothing.
That is to say that while ergodicity is a useful assumption, non-ergodicity is a completely useless assumption. It doesn't prove that economies are quasi-periodic chaotic systems or that they are some other kind of complex system -- you need evidence for that! Show us a model that that is empirically successful. Or at least more empirically successful than assuming ergodicity.
Yes, that's a point that Keynes made and which Davidson and Syll elaborate:
Many thanks for sending me your article I enjoyed it very much. I am sure these matters need discussing in that sort of way. There is one point, to which in practice I attach a great importance, you do not allude to. In many of these statistical researches, in order to get enough observations they have to be scattered over a lengthy period of time; and for a lengthy period of time it very seldom remains true that the environment is sufficiently stable. That is the dilemma of many of these enquiries, which they do not seem to me to face. Either they are dependent on too few observations, or they cannot rely on the stability of the environment. It is only rarely that this dilemma can be avoided.
Letter from J. M. Keynes to T. Koopmans, May 29, 1941
Of course, that is a bit of a hand wave but Keynes is much more specific about it in other places. But the idea is that the basis for neoclassical assumptions is too non-representation of the subject matter to yield a useful methodology. Neoclassical methods are not useful for telling us what we really need to know, in particular for policy formulation. Keynes proposed a new economic method based on a monetary production economy in which money is non-neutral and uncertainty dominates.
Keynes was not only a theoretician but an economic "engineer" who are active in the world of policy at the time of the Great Depression and his ideas are credited with saving the day — other than by neoclassical economists that have sought to "correct" this, for which the world is now suffering another prolonged contraction.
In the Keynesian view, econometric models are essentially a waste of time. According to old Keynesians and Post Keynesians, Paul Samuelson "bastardized" Keynes by introducing key assumptions that Keynes specifically rejected.