Keynesian Uncertainty vs Knightian Uncertainty
Marcello Basili
Dear All,
100 years since the publication of Risk Uncertainty and Profit (RUP) and A Treatise on Probability (TP) I read them one more time. Both of them are interesting and well known books, even if they are so irreducible and incomparable that I would like to ask you why many decision theorists defines uncertainty as Knightian Uncertainty instead of Keynesian Uncertainty.
I think that Knightian uncertainty was not a good choice and induced misunderstanding. There is a clear asymmetry between Keynes and Knight in uncertainty analysis.
In TP Keynes was involved in definition of a coherent notion of uncertainty and a consistent probabilistic theory. RUP is a book about perfect competition, imperfect competition and business cycle, in particular in dynamics, and in fact Knight did not analyze uncertainty after 1921.
Keynes devoted to uncertainty a book, Knight a few pages. Borel, Russell and even Edgeworth appreciated the TP and Keynes approximation of non-numerable probabilities by intervals, but unbelievably many decision theorists still talk about Knightian uncertainty.
Knight defined uncertainty as a non-measurable, in his language non-insurable, situation as distinguished from risk, a measurable and insurable condition. Measurable means insurable that is a consumer can transform a possible large loss in a sure sunk cost. Moreover, recent studies show that there is an essential methodological disagreement between Knight and Keynes.
In what Knight’s definition of uncertainty is different from Ramsey’s definition of subjective probability based on betting? As well-known Savage (and De Finetti) uses a choice-based approach (or preference approach) to define subjective probabilities.
Bet and Insurance refer to attitude about money, i.e. about the consumer’s Certainty Equivalent, in fact in the S-shaped expected utility function, for example Marschak-Savage expected utility function, a consumer bets and insures at the same time.
Keynes calls non-numerable a situation where a consumer does not have a unique, additive and fully reliable probability distribution and her belief can be represented by an interval of probabilities, that is when a consumer has an upper and lower probabilities about the occurrence of a given event. With respect to the real meaning of “non-numerical probability” and its representation by an interval of probabilities, recent studies show, unequivocally, that the solution is in TP, where the reference to an interval of probabilities, that is a set of probabilities or numbers, is explicit such as in Ch. XV, titled: Numerical measurement and approximation to probabilities. In TP Keynes refers to Boole (Note 2, 161) as the ancestor of his imprecise probability approach. Keynes defines an interval of probabilities as an approximate evaluation of non-numerical probabilities that a consumer elicits when facing uncertainty. Keynes, also, suggests a formal method to find the bounds of the probability interval, or lower probability and upper probability that many decision theorists use currently.
Moreover, Keynes investigates the reliability of such an interval of probabilities and introduce the notion of weight of argument. Knight simply talks about confidence in estimation. Keynes defines in a clear and unique way the conventional coefficient of risk and weight and call it as c (Ch. 26, 315), and c=2pw/[(1+q)(1+w)], where w is the weight of argument, or a parameter between 0 and 1. Then probabilities are distorted in decision weights when w<1.
Summarizing, in TP Keynes introduces intervals of probabilities, distorted probabilities by the conventional coefficient of risk and weight, degrees of similarity as measures of uncertainty, but all of these definitions are echoed in current decision theory: Multiple Priors and Imprecise Probabilities, State-Dependent and Cumulative Prospect Theory, Case-Based Decision Theory, or by a Capacity, simply.
In the perspective of an historical scientific reconstruction, then Keynes’s and Ellsberg’s representations of uncertainty as distinguished from risk share the same notion. This fact makes Ellsberg’s urn example not a chance but, rather, a unique representation of the same intuition. Methodological and theoretical derivation of current decision theory from Ellsberg is a fact, consequently, it should be straightforward to consider Keynes not a noble father, but the ancestor of modern decision theory, and it would be straightforward using the definition of Keynesian Uncertainty.
In such a way, Keynes is for Decision Theory What The Beatles are for Pop Music.
Best Regards
Marcello Basili
Peter Wakker
Hi Marcello et al.,
Here is my understanding, negative on Knight (1921). He made great contributions to economics, but not to uncertainty. Several, including the references below, criticized him. Recently,
Cambridge Journal of Economics. Volume: 45. Issue: 5. 2021
was entirely dedicated to KK21. Somewhere there I read a possible explanation: Keynes’ ideas on macro are controversial. His opponents lobbied (manipulated?) for the term to be Knightian uncertainty and not Keynesian uncertainty. Successfully. Unfortunately. Keynes (1921) is of better quality and quantity on uncertainty than Knight (1921).
Best, Peter
{% https://doi.org/10.1093/cje/beab022
They criticize Knight (1921) for making mistakes. For instance, they write: “we argue that Knight made a combination of errors and poor modelling choices” %}
Brooke, Geoffrey & Lydia Cheung (2021) “Uncertainty and General Equilibrium: An Evaluation of Professor Knight’s Contributions to Economics,” Cambridge Journal of Economics 45, 901–918.
{% Risk versus Uncertainty; historical comments. Argue that, for Knight, the case of subjective nonobjective additive probability was uncertainty and not risk. Also that Knight’s writing is confused. %}
LeRoy, Stephen F. & Larry D. Singell, Jr. (1987) “Knight on Risk and Uncertainty,” Journal of Political Economy 2, 398–406.
{% %}
Skidelsky, Robert (2009) “Keynes: The Return of the Master.” Penguin, London.
Debraj Ray
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Ernesto Savaglio
Hi All,
let me add two references that -I hope- (partially) satisfy Debraj Ray's request.
1) Robert Skidelsky, (1992) - John Maynard Keynes: The Economist as Savior, 1920–1937, chapter 3 with appendix 1,2,3
Chapter 3 is about The Treatise of Probability, in particular it discusses the criticisms of Russell, Wittgenstein and Ramsey to the Treatise as theoretically weak
2) Anna Carabelli (2021) Keynes on uncertainty and tragic Happiness: complexity and expectations - Palgrave.
claims that The Treatise represents the logic behind The General Theory:
In chapter 16, Skidelsky (1992) writes "The American
economists reviewed The General Theory with a mixture of hostility and
misunderstanding [...] The special issue
of QJE (November 1936)
on The General Theory was
predominantly critical. [...] Among the leading American reviewers,
Knight was particularly disapproving... Later on, Hayek helped make the
Keneysian revolution unfinished. (market economy vs public intervention)
Keynes was the enemy to defeat.
Hence, everything that was Keneysian had to be downgraded or better ignored...
Thank you for bringing me back to my memories of History of Economic Thought,
regards,
Ernesto
David Dillenberger
This is a fantastic exchange, and Peter’s references are, as always, super useful. I should say that what probably helps many to understand Macello’s point is what confused me the most… (and, for this forum, is perhaps the least important part of his post): given that I think I understand the distinction between the two notions, there is A sense in which the Beatles are indeed the ancestor of popular music, but I can give some (good) arguments for why they were the noble fathers instead... I will stop here but, as you can imagine, there is a big literature on the evolution of popular music (even academic!).
For sure they were the original “Gang of Four”….
Now back to DT…
David
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Subject: Re: [DT_Forum] Keynesian Uncertainty vs Knightian Uncertainty
Debraj Ray
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