Reconsidering ergodicity and fundamental uncertainty

Abstract

This paper studies the relationships between the concepts of ergodicity, stationarity, homogeneity, and Keynesian fundamental uncertainty in light of a recent debate between Rod O’Donnell (2014–15) and Paul Davidson (2015). The latter has long argued that Keynesian fundamental uncertainty is best viewed as an axiomatic ontological condition of nonergodicity of a system. This influential view is challenged by O’Donnell who favors an epistemological behavioral perspective based on people having imperfect knowledge. Whereas for Davidson it is Keynes overthrowing the axiom of ergodicity that is fundamental, for O’Donnell it is Keynes overthrowing the axiom of perfect knowledge. We shall find that both parties make valid points in this debate, but further clarification is needed. Both accept that while Keynes never used the term “ergodicity” in his writings, he did discuss problems of nonhomogeneity of data when critiquing the econometric methodology of Jan Tinbergen. While it is known that a stationary series may be nonergodic, such as a limit cycle, it is much less well known and not commented on by either of them that a nonstationary series may be ergodic. Furthermore, while a nonstationary series must be nonhomogeneous, a nonhomogeneous series may be stationary under proper transformations such as first differencing. Deeper connections of the development of ergodic theory and chaos theory and this link to the debate over fundamental uncertainty are also discussed.