Tuesday, February 5, 2013

Probability Theory vs. Knightian Uncertainty: Is It Simply Semantics?

My Micro II course this semester is being taught by Bryan Caplan, who many readers may recognize as a frequent blogger over at EconLog. As an introduction to the course, the initial assigned readings included Caplan’s papers, “The Austrian Search for Realistic Foundations” and "Probability, Common Sense, and Realism: A Reply to Hülsmann and Block." The latter paper is a reply to Austrian criticisms of claims made in the former. Although the former paper’s focus on microeconomic discrepancies between Austrians and neoclassicals was personally intriguing (since I normally think along macro lines), the latter paper raises questions worth addressing.

Caplan’s reply can seemingly be divided into two distinct halves: the first half attempts “to spell out the philosophical side of [his] original thesis in greater depth” (p. 69) and the second half directly responds to the numerous critiques. Since Caplan is especially adept at undermining the validity of these critiques, the ensuing discussion will be directed solely at the first half of his paper.  

The paper begins by furthering discussion of probability as it relates to the Austrian-Neoclassical divide:

In Caplan (1999), my central counter to the full-blown Misesian rejection of quantifiable probability was a reductio ad absurdum. If we cannot quantify the probability of an “individual, unique, and nonrepeatable” (Mises 1966, p. 111) event, then we can never quantify probability at all, because strictly speaking, all events are “individual, unique, and nonrepeatable.” Naturally, though, this reductio is only persuasive if, ex ante, you acknowledge the absurdity of rejecting all real-world applications of probability theory.2 (p. 70)
Reading this passage for the first time I wondered, are the quantifiable probabilities being subjectively or objectively determined? Based on my previous readings of Mises’ and general perception about the debate, I presume Caplan is referencing subjective probabilities. However, as I understand the typical Austrian position, the trouble with subjective probabilities is not that they can’t be or aren’t formed. The issue is that, ex ante, it remains unclear and possibly unknowable how accurately those estimates will align with future observed outcomes. When predictions diverge from realistic probabilities, the chance of human action working against a desired end rises along with the likelihood of disequilibrium states.

Only a few pages later Caplan sufficiently answers this question while clarifying an important, yet often overlooked, distinction within neoclassical economics:
this conflates a fundamental tenet of neoclassicism—subjective-but-quantifiable probabilities—with a popular subsidiary neoclassical hypothesis—rational expectations (1997, p. 56). Rational expectations is a hypothesis linking subjective-but-quantifiable probabilities to objective frequencies. Empirical evidence of systematically mistaken beliefs (Caplan 2001a) counts only against rational expectations, not probability. (p. 73)
Personally I was caught a bit off guard by this neoclassical division since my subjective experiences suggest practically all neoclassical economists currently adhere to rational expectations. Whether this perception is due to my proclivity for macroeconomics or sampling bias remains an open question. Regardless, it was precisely this view about neoclassical (mainstream) economics that drove me away from the discipline in my undergraduate years and towards Lachmann’s radical uncertainty more recently.

Although Caplan is trying to disprove the existence of radical (Knightian) uncertainty, specifying his neoclassical position garnered my full attention. Extending his original argument against uncertainty and in favor probability theory, Caplan appeals to our common sense:
The basic principles of probability are simply self-evident. It is self-evident that one holds beliefs with some degree of certainty.3 It is self-evident that the degree of belief must vary from impossible to certain. (p. 70-71)
Denying the truth in these self-evident claims would be foolish, yet I still fail to see how these statements lead to the conclusion that “Knightian uncertainty is incoherent.” (p. 75) Strangely enough, a similar appeal to common sense may help show why the two concepts are not mutually exclusive.

As I understand it, Knightian (radical) uncertainty refers to the actual experience of outcomes that were previously unforeseeable. Caplan doesn’t appear to disregard this possibility, but instead claims this is effectively the same as having “a perceived probability of 0.” (p. 73) This appears to relegate the disagreement to one of mere semantics, but a little introspection suggests otherwise. Have you ever heard someone state the following?

“That possibility never crossed my mind.”
“I had not considered that possibility.”
“If I had known that was possible...”

Assuming your answer is yes, it is self-evident that one believes possibilities exist that were previously unconsidered. It is also self-evident that some events seem unpredictable. Therefore it is equally self-evident that true uncertainty exists.

Contrary to Caplan’s conclusion, Knightian uncertainty and “the basics of probability theory are self-evident and, rightly understood, are highly intuitive.” (p. 75) The seemingly semantic differences in effective behavior appear to be borne out by subjective experience. Ultimately these infrequent instances, though providing a sharp critique of rational expectations, fail to either contradict or materially add to probability theory. I’m therefore resigned to agree with Caplan that “any attempt to deny probability theory inevitably winds up presupposing it.” (p. 75)

Note: Within this debate about probability theory versus Knightian uncertainty, Caplan also argues that “Mises is correct to point out that beliefs about the efficacy of action are implicit in action. But he at best misspeaks when he characterizes this necessary feature of action as knowledge of “causality.” Instead, the necessary belief component of action is weaker; we don’t need to know—or even believe we know—any exceptionless causal laws. We merely require beliefs about conditional probabilities. (p. 72) This leads Caplan to conclude that “probability theory deserves to take the place of causality as a fundamental implication of the action axiom.” (p. 75)

This view raises a much deeper philosophical question about human action. Unfortunately that conversation will be postponed to a later date. In the meantime, here are a couple questions to ponder...

Are beliefs about conditional probabilities and/or knowledge of “causality” actually necessary for action? Or, would an individual without those characteristics still act, but in an unforeseeable manner?



1 comment:

  1. See Lars Syll, On the non-equivalence of Keynesian and Knightian uncertainty