Knight’s Risk, Uncertainty and Profit

Knight, Frank H Risk, Uncertainty and Profit. Boston: Houghton Mifflin, 1921

Knight introduces ‘Knightian uncertainty’ in Part III Chapter VII The Meaning of Risk and Uncertainty:

“Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated…. The essential fact is that ‘risk’ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character; and there are far-reaching and crucial differences in the bearings of the phenomena depending on which of the two is really present and operating…. It will appear that a measurable uncertainty, or ‘risk’ proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all.”

This is widely quoted. Knight distinguishes the following:

“1. A priori probability. Absolutely homogeneous classification of instances completely identical except for really indeterminate factors. …

“2. Statistical probability. Empirical evaluation of the frequency of association between predicates, not analyzable into varying combinations of equally probable alternatives. … . The main distinguishing characteristic of this type is that it rests on an empirical classification of instances.

“3. Estimates. The distinction here is that there is no valid basis of any kind for classifying instances. This form of probability is involved in the greatest logical difficulties of all, and no very satisfactory discussion of it can be given, but its distinction from the other types must be emphasized and some of its complicated relations indicated.”

Knight gives the following:

“To illustrate, suppose we are allowed to look into the urn containing a large number of black and red balls before making a wager, but are not allowed to count the balls; this would give rise to an estimate of probability in the correct sense; it is something very different from either the mere consciousness or ignorance on which we act if we know only that there are balls of both colors without any knowledge or opinion as to the numbers or the exact knowledge of real probability attained by an accurate counting of the balls.”

This affects decision-making:

“… The business man himself not merely forms the best estimate he can of the outcome of his actions, but he is likely also to estimate the probability that his estimate is correct. The “degree” of certainty or of confidence felt in the conclusion after it is reached cannot be ignored, for it is of the greatest practical significance. The action which follows upon an opinion depends as much upon the amount of confidence in that opinion as it does upon the favorableness of the opinion itself.

“A man may act upon an estimate of the chance that his estimate of the chance of an event is a correct estimate. To be sure, after the decision is made he will be likely to sum all up in a certain degree of confidence that a certain outcome will be realized, and in practice may go farther and assume that the outcome itself is a certainty.

“… It is this true uncertainty which by preventing the theoretically perfect outworking of the tendencies of competition gives the characteristic form of “enterprise” to economic organization as a whole and accounts for the peculiar income of the entrepreneur. “

Some have proposd that Knightian uncertainty is simply uncertainty about a probability, but this does not seem to fit with the following.

In the Introduction, Knights says:

“We shall accordingly restrict the term “uncertainty” to cases of the non-quantitive type. It is this “true” uncertainty, and not risk, as has been argued, which forms the basis of a valid theory of profit and accounts for the divergence between actual and theoretical competition.”

And later …

“… if the actuarial chance of gain or loss in any transaction is ascertainable, either by calculation a priori or by the application of statistical methods to past experience, the burden of bearing the risk can be avoided by the payment of a small fixed cost limited to the administrative expense of providing insurance.

… both schools have followed everyday speech into the fallacy of treating risk as a substantially homogeneous category, where a fundamental difference in kinds of risk is in fact the key to the whole mystery. ” 

“The liability of opinion or estimate to error must be radically distinguished from probability or chance of either type, for there is no possibility of forming in any way groups of instances of sufficient homogeneity to make possible a quantitative determination of true probability. Business decisions, for example, deal with situations which are far too unique, generally speaking, for any sort of statistical tabulation to have any value for guidance. The conception of an objectively measurable probability or chance is simply inapplicable. … in fact it appears to be meaningless and fatally misleading to speak of the probability, in an objective sense, that a judgment is correct. As there is little hope of breaking away from well-established linguistic usage, even when vicious, we propose to call the value of estimates a third type of probability judgment, insisting on its differences from the other types rather than its similarity to them.”

More generally, Knight was in fluenced by Bergson.

Comments

Knight makes an important distinction. But:

  • He regards ‘the chance of an event’ as being represented by a single number, so that an estimate is an estimate of a number. 
  • One could reasonably envisage different ways of producing probability numbers as having differing chances of being within some margin of error, and so suppose that that the differences that he highlights could be captured qualitatively.
  • Examples using urns are too simple and those concerning business too general to motivate abandoning ‘tried and tested’ Bayesian techniques.
  • Whilst the business experience should motivate Knight’s distinction, the academic part of the discussion seems much too narrow.

There seems to me a very real danger that someone reading Knight’s work might be unpersuaded, while others might be persuaded but gain too limited a view of uncertainty.  Keynes’ Treatise, which was published in the same year, gives a fuller account, covering broader uncertainties. Some economists have suggested to me that Knight has given a simpler, more accessible, account of uncertainty than Keynes. So he has, but it also seems simplistic. Or does Knight give a fuller account elsewhere?

Dave Marsay

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