Model uncertainty and ergodicity

from Lars Syll

Post Keynesian authors have offered various classifications of uncertainty … A common distinction is that of epistemological versus ontological uncertainty, with the former depending on the limitations of human reasoning and the latter on the actual nature of social systems …

Models of ontological uncertainty tend to hinge on the existence of information that is critical to the decision-making task. Fundamental uncertainty occurs in “situations in which at least some essential information about future events cannot be known at the moment of decision because this information does not exist and cannot be inferred from any existing data set” (Dequech 1999, 415-416). For Davidson (1991, 131), “true” uncertainty arises when “the decision maker believes that no information regarding future prospects exists today and therefore the future is not calculable.”

In the model-based view of uncertainty, by contrast, it is not the existence of information that determines uncertainty, but the credibility of the model(s) used to encode available information. By focusing on the existence of information, or its completeness, these Post Keynesian accounts of ontological uncertainty implicitly accept the possibility that if economic agents had sufficient information they could apply that information to a model without uncertainty. Yet a suitably complex deterministic system … can prompt model uncertainty even if future outcomes are in principle knowable … Model uncertainty is thus epistemological rather than ontological in nature. It occurs even in environments with stable data generating processes.

Owen F. Davis

An interesting paper that merits a couple of comments.

To understand real-world ”non-routine” decisions and unforeseeable changes in behavior, 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 those that will rule the future.

Time is what prevents everything from happening at once. To simply assume that economic processes are ergodic and concentrate on ensemble averages – and a fortiori in any relevant sense timeless – is not a sensible way of dealing with the kind of genuine uncertainty that permeates open systems such as economies.

What is important in recognizing that real social and economic processes are nonergodic is the fact that uncertainty – not risk – rules the roost. That was something both Keynes and Knight basically said in their 1921 books. Thinking about uncertainty in terms of “rational expectations” and “ensemble averages” has had seriously bad repercussions on the financial system.

Knight’s uncertainty concept has an epistemological founding and Keynes’ definitely has an ontological founding. Of course, this also has repercussions on the issue of ergodicity in a strict methodological and mathematical-statistical sense. I think Keynes’ view is the most warranted of the two.

The most interesting and far-reaching difference between the epistemological and the ontological view is that if one subscribes to the former, the Knightian view, you open up to the mistaken belief that with better information and greater computer power we somehow should always be able to reduce model misspecification and/or invent new and better models to calculate probabilities and describe the world as an ergodic universe. As Keynes convincingly argued, that is often (unless we think we actually live our lives in Savage’s “small world”) not ontologically possible.

To Keynes, the source of uncertainty was in the nature of the real — nonergodic — world. It had to do, not only — or primarily — with the epistemological fact of us not knowing the things that today are unknown, but rather with the much deeper and far-reaching ontological fact that there often is no firm basis on which we can form quantifiable probabilities and expectations at all.

Sometimes we do not know because we cannot know.