RDP 2000-10: Monetary Policy-Making in the Presence of Knightian Uncertainty 3. Risk versus Uncertainty
December 2000
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One of the first economists to make a distinction between risk and uncertainty was Frank Knight (1933). Knight's interest in this subject was spurred by the desire to explain the role of entrepreneurship and profit in the production process. Knight held the view that profits accruing to entrepreneurs are justified and explained by the fact that they bear the consequences of the risks (uncertainties) inherent in the production process that cannot be readily quantified.
There is a fundamental distinction between the reward for taking a known risk and that for assuming a risk whose value itself is not known. It is so fundamental, indeed, that, as we shall see, a known risk will not lead to any reward or special payment at all (p 44).
Known risks arise in situations where outcomes are governed by physical laws, e.g. a dice roll, or the factors affecting future outcomes remain more or less constant over time, e.g. mortality tables. In these cases, past observations of the distribution of outcomes will be a good guide for the distribution of outcomes that can be expected in future. At some point, however, the processes that need to be forecast become sufficiently complex and interrelated with the outcomes of the decisions of other agents, that the past does not provide such reliable information about the likelihood of future events occurring.
The fact is that while a single situation involving a known risk may be regarded as ‘uncertain’, this uncertainty is easily converted into effective certainty; for in a considerable number of such cases the results become predictable in accordance with the laws of chance, and the error in such prediction approaches zero as the number of cases is increased (p 46).
LeRoy and Singell (1987) summarise Knight's distinction between risk and uncertainty by defining uncertainty as a situation where no objective, or publicly verifiable, probability distribution exists. In situations where a single objective probability distribution does not exist, LeRoy and Singell argue that Knight's exposition is consistent with the idea that the decision-maker forms some subjective probability. When a single probability distribution is available, it is straightforward to evaluate the expected value of pay-offs to different actions. However, forming a unique subjective probability distribution may not be straightforward as the Ellsberg paradox helps to illustrate.
Suppose we have a box of 300 balls, 100 of which are red and the rest are blue and green in undisclosed proportions. A ball is chosen at random from the box. Suppose we are offered the choice of betting on whether a red ball or a blue ball would be selected. Which should we choose to gamble on? Now suppose we are faced with a different gamble. We have to choose between betting on whether the ball is not red or not blue. Which gamble do we select in this case?
In most instances, individuals will pick red and not red in response to these two questions (Kreps (1990) based on Ellsberg (1961)). If red is selected in the first gamble, the participant has implicitly evaluated their subjective probability of getting a blue ball to be less than the probability of a red ball. The paradox here is that in order for the same individual to act rationally according to the axioms of expected utility theory when faced with the second choice, they should bet that a blue ball will not be chosen. The Ellsberg paradox highlights the fact that people prefer situations when the probabilities are known to those where they are unknown. This, in turn, implies that individuals do not always employ a single subjective probability distribution to resolve their uncertainty. Red may be chosen in the first gamble, not because we believe the probability of getting a red ball is greater than a blue ball, but because we know the exact probability of getting the red ball.
The question is, how should an individual make rational decisions when a range of probability distributions are possible? The Bayesian approach to this problem would be to decide on a probability distribution over the possible probability distributions, which essentially reduces the problem to one in which there is a single probability distribution. This solution assumes that the decision-maker is willing to make definite statements about the distribution of future outcomes. The problem with using a uniform distribution over alternatives or a diffuse prior, is that there is no information to justify using this distribution. Schmeidler (1989) argues that it is unreasonable to apply equal probabilities to unknown events when the information about these events is limited. He argues that only when symmetric information about these events is abundant should equal probabilities be applied. Therefore, the interest in the problem arises from the fact that decision-makers are either unwilling or unable to make such a strong assumption about probabilities at the first stage of the decision-making process.
Another approach is to recognise that some of the axioms underlying expected utility theory may not apply in an environment where a range of probability distributions is possible. The corollary of this is that it will not be possible to use standard expected utility solutions for these decision problems. Two ways of relaxing the assumptions underlying expected utility theory to allow for Knightian uncertainty are discussed in the next section and the implications for the conduct of monetary policy are discussed in Section 5.