8> <Lecture 5. Uncertainty: Theories of Uncertainty Surprisingly, uncertainty has a rather short history in economics. The very idea that uncertainty might be relevant for economic analysis was only really suggested in 1921, Risk, Uncertainty and Profit by Frank H. Knight (1885-1972). Risk vs. Uncertainty His famous dissertation Risk, Uncertainty and Profit (1921) remains one of the most interesting reads in economics even today. In it, Knight made his famous distinction between "risk" and "uncertainty." Risk: Situations where the decision-maker can assign mathematical probabilities to the randomness which s/he is faced with. Uncertainty: Situations when this randomness cannot be expressed in terms of specific mathematical probabilities. Many economists dispute this distinction, arguing that Knightian risk and uncertainty are one and the same thing. For instance, they argue that in Knightian uncertainty, the problem is that the agent does not assign probabilities, and not that s/he actually cannot, i.e. that uncertainty is really an epistemological and not an ontological problem, a problem of knowledge of the relevant probabilities, not of their existence. Going in the other direction, some economists argue that there are actually no probabilities out there to be known because probabilities are really only beliefs. In other words, probabilities are merely subjectivelyassigned expressions of beliefs and have no necessary connection to the true randomness of the world. Post Keynesian Keynes saw his theory as a critique of neoclassical economics. However, the neoclassical economists selectively chose a few ideas from Keynes's General Theory and elaborated and developed these ideas. During the 1970s and 1980s, a group of economists revived the ideas of Keynes that were not compatible with neoclassical economics. They asserted the radical side of the Keynesianism tradition. Post Keynesians have argued that Knight's distinction is crucial. In particular, they argue that Knightian uncertainty may be the only relevant form of randomness for economics especially when that is tied up with the issue of time and information. In contrast, situations of Knightian risk are only possible in some very contrived and controlled scenarios when the alternatives are clear and experiments can conceivably be repeated such as in established gambling halls. Knightian risk, they argue, has no connection to the murkier randomness of the real world that economic decision-makers usually face: where the situation is usually a unique and unprecedented one and the alternatives are not really all known or understood. In these situations, mathematical probability assignments usually cannot be made. Thus, decision rules in the face of uncertainty ought to be considered different from conventional expected utility.
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The "risk vs. uncertainty" debate is long-running and far from resolved at present. The Knightian distinction may be useful, in that it permits us to roughly divide theories between those which use the assignment of mathematical probabilities those and which do not make such assignments. In this manner, the expected utility theory with objective probabilities of von Neumann and Morgenstern is clearly one of "risk", whereas the state-preference approach of Arrow and Debreu in which there are no assignments of probabilities whatsoever is one of "uncertainty". However, the intermediate theory of Savage, which yields expected utility with subjective probabilities, is not clearly in one camp or another: on one hand, the very assignment of numerical probabilities even if subjective implies that it represents choice under "risk"; on the other hand, these probabilities are merely expressions of what is ultimately amorphous belief and thus may seem more like "uncertainty". Expected Utility Theory with Objective Probabilities State-Preference Approach The basic proposition of the state-preference approach to uncertainty is that commodities can be differentiated not only by their physical properties and location in space and time but also by their location in "state". By this we mean that "ice cream when it is raining" is a different commodity than "ice cream when it is sunny" and thus are treated differently by agents and can command different prices. Subjective Expected Utility In the von Neumann-Morgenstern theory, probabilities were assumed to be "objective". However many thinkers remained unhappy with this practical reasoning. Many statisticians and philosophers have long objected to this view of probability, arguing that randomness is not an objectively measurable phenomenon but rather a "knowledge" phenomena, thus probabilities are an epistemological and not an ontological issue. In this view, a coin toss is not necessarily characterized by randomness: if we knew the shape and weight of the coin, the strength of the tosser, the atmospheric conditions of the room in which the coin is tossed, the distance of the coin-tosser's hand from the ground, etc., we could predict with certainty whether it would be heads or tails. However, as this information is commonly missing, it is convenient to assume it is a random event and ascribe probabilities to heads or tails. In short, in this view, probabilities are really a measure of the lack of knowledge about the conditions which might affect the coin toss and thus merely represent our beliefs about the experiment. The subjective nature of probability assignments is can be made clearer by thinking of situations like a horse race. In this case, most spectators face more or less the same lack of knowledge about the horses, the track, the jockeys, etc. Yet, while sharing the same knowledge (or lack thereof), different people place different bets on the winning horse. The basic idea is that by observing the bets people make, one can presume this reflects their personal beliefs on the outcome of the race. Thus subjective probabilities can be inferred from observation of people's actions.
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Cf. http://cepa.newschool.edu/het/essays/uncert/choicecont.htm
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