Expectations

BIBLIOGRAPHY

Economics is concerned in large part with expectations. Consumers planning to smooth their spending over a lifetime form expectations about future income, prices, interest, and other factors in their decision-making processes. Producers spreading investment expenditures over future time periods form expectations of future costs and returns. Government policy makers aiming to stabilize the economy use monetary and fiscal policies to achieve their expected targets. In the global economy, gains from free trade occur because traders expect a country to produce at the lowest opportunity cost. Economists try to measure expectation, to analyze their effects on the economy, and to study how they are formed.

In a competitive economy, expectations are realized at the equilibrium state. A Keynesian view of expectation equilibrium is that planned savings should equal planned investments. One reason that expectations may not be correct in a competitive economy is that prices and output vary, creating problems for producers who incur costs now and are uncertain about future prices. One can analyze uncertain outcomes in order to assign a probability or likelihood to their occurrences. If uncertainty is too risky, one may choose to be risk averse, as in the case of oligopolistic firms that are unable to guess their rival’s conduct. To understand and coordinate expectation, one can collect anticipation data on business plans, ask people about their expectation and attitude, or survey experts to learn about their consensus.

One forms expectations with the aid of logic, psychology, and probability. Cognitive psychologists, for instance, found that agents make future decisions based on the similarity of present evidence, playing down probabilities and even the quality of the evidence. An expected outcome may follow from conscious behavior or habits, which may be self-fulfilling, nonmaterial, and altruistic. Agents may be content with little achievements, not necessarily looking for maximum outcomes.

An individual may be certain of his or her expectations. Certainty means one assigns a high probability or likelihood to the occurrence of the event. Besides high and low probability events, one finds some uncertain events to which one cannot possibly attach a probability. One distinguishes between measurable and unmeasurable uncertainty, assigning the term risk when uncertainty can be measured.

A workhorse in expectation analysis is the expected utility hypothesis (EUH). The EUH is a function that captures all of an individual’s expectations about an outcome, assigns a numeric value for one’s choices among alternatives, and allows one to maximize the expected outcome. But its results can be paradoxical. The St. Petersburg paradox, a “let’s make a deal” situation, offers the player a fixed amount of money (say $20), or an uncertain outcome that pays one dollar if heads turn up when a fair coin is tossed N times. The outcome is 2ⁿ, each with a probability of one half, so that the expected value of the game is infinite, the limit of . The paradox is that no one is willing to pay a large sum to play the game. The probabilist Daniel Bernoulli (1700–1782) thought that the problem was that as a person wins more and more money in the game, one experiences diminishing returns for money. To capture diminishing utility, Bernoulli used a log utility function on the outcome, showing that the payoff becomes a small sum: . The solution was not definitive in the sense that one can choose a utility sequence that would still yield an infinite payoff. What is needed is a bounded utility function.

From a microeconomic perspective, the economist Milton Friedman presented a lucid explanation of the utility concept that has telescoped further development. With a stream of income, I_i, and associated probabilities, P_i, the expected value is the sum of their products. Utility enters when one forms a function of income, F (I ), whose products with their respective probabilities give a special function, . In the special instance where income is expected with certainty, P_i = 1, both the G and F functions have the same value or utility. A plot of F (I ), against, income, I, highlights a concave or convex utility function, indicating risk aversion, and risk lover (plunger), respectively. A risk averse person prefers the expected value over the EUH outcome. A risk lover prefers the EUH to the expected value. If one eliminates scale and origin from the utility function by the restrictions I = 0, F (I ) = 0, and I = 1, F (I ) = 1 F (I ) I = 0, then one can determine utility values for any amount of income. Without such restrictions, however, the utility function can take on a recurrent concave shape, explaining why someone will not pay a large sum to play the St. Petersburg game.

From the macroeconomic perspective, one starts with the English economist John Maynard Keynes’ equation where national income, φ(N), equal to investment demand, D ₂, plus consumption x (N), could be solved for full employment, N. Given the state of employment, consumers, investors, and employers expect to consume, invest, and earn a prospective amount, respectively, which fluctuates with the state of long-term expectation. Keynes’ concept of long-term expectation can be clothed in modern notations. Long-term expectation takes the form of a random variable, y, within a time frame of three months to a year, t, in a mass psychology “atmosphere”, ω_it, given state of the news, Ω_it. Investors, i, calculate the average expectation, E, such as in a beauty contest where competitors must pick out the prettiest face among photographs that are published in a newspaper. In this competition, the average is an intersubjective representation, which may be expressed as = y_it = λ_i E(y_it |Ω_it + w_it, and the competitor whose choice comes nearest to this average will win the competition.

Keynes’ work created several research programs in expectations. John Hicks used a day-to-day model for up to a week to develop his elasticity of expectation hypothesis. Following Hicks in dating commodities, the Arrow-Debreu model of competitive equilibrium found current and expected prices that jointly clear supply and demand equations in present and future markets, and Jean-Michael Grandmonth formulated an intertemporal model, that extended the Arrow-Debreu model for sequences of time periods. On the other hand, G. L. S. Shackle steered expectation analysis away from a probability base. One makes several nonprobabilistic statements about the next period output, x, such as that it is impossible, possible, surprising if it would reach a specified high or low level, or very surprised it occurs. One can attach a corresponding number, y, to represent the degree of potential surprise those outcomes mean. One can further place a corresponding value on the surprise value when it reaches a maximum potential surprise, ŷ. The result is a function y = f (x ) that is bowl shaped, and centered at a neutral output level where x = 0. Further, one can assign numbers to the degree of surprise numbers to measure the degree of stimuli, A (x, y (x )), from the surprise function associated with the potential outcome.

Since the 1950s, economists have been using an adaptive expectation model to show how expectation is formed over time. The adaptive version follows the dictum that an individual learns from his or her mistakes. A rifleman calibrates his weapon by observing how far off his previous shot deviated from the target.

In macroeconomic forecasts, the adaptive model was employed to study the effect of expected prices and unemployment on present wages and inflation rates. In the Phillips Curve, the coefficient of the expected price variable was zero. A coefficient of the expected price variable equal to one would mean that expectations are fully adjusted into inflation and wage rates. For instance, if the expected rate of inflation, π̂, is set by some proportion, γ, between the actual inflation, π and the expected inflation, then one can use the equation: π̂–π̂_-1 = γ(π_-1 π̂_-1) 0 < γ < 1 to represent the formation of expectations. Full adjustment means γ= 1, but empirically it was mostly less than unity, implying that the Phillips Curve was downward sloping.

The adaptive expectation model was integrated into the MPS model of the Federal Reserve Board, one of the first large-scale econometric models that were built in the 1960s. Expectation was captured in the form of lag structure both to parameters and error terms. The model, however, failed to capture drifts in the parameters of structural equations. The Rational Expectation Hypothesis (REH) has explained some of those problems and added other novelties to the formation and measurement of expectations.

The concept of REH is based on equilibrium analysis as opposed to Keynesian disequilibrium analysis. Under ideal conditions of competition, one expects economic agents to have perfect information or knowledge of the relevant market variables. Absent complete information, one settles for all the information that is available before making a forecast.

Robert Lucas is credited with making the REH practical. One incorporates information into REH models by replacing the expected variable with an equation or variable that measures the expectation. For instance, Thomas J. Sargent and Neil Wallace wrote equations for Aggregate Supply, IS, LM, and monetary policy. Some of the equations require that the expected price level prevailing at time t be set at time t –1. In other words, one replaces the expression of the form E(p_it | Ω_it ) with values resulting from applying the mathematical expectation operator, E, on them, conditioned by the information one has at the time t–1.

Faith in the RE hypothesis is still being determined. Edmund Phelps advocated dropping the equilibrium framework, for a more non-Walrasian framework in which economic agents are not price takers, which yields results more in line with Paul A. Samuelson’s views that oppose the REH. Large-scale econometric models for the REH are still not within reach. To improve predictions, Finn Kydland and Edward Prescott have used time-consistent computational experiments in econometric models, subsequent to the REH revolution. These models allow policy makers such as the Federal Reserve Board, to have no concern about wrong models or wrong goals, or even histories and reputation, because they need only choose sequentially.

SEE ALSO Adaptive Expectations; Beauty Contest Metaphor; Expectations, Implicit; Expectations, Rational; Expectations, Static; Expected Utility Theory; Friedman, Milton; Game Theory; Keynes, John Maynard; Lucas, Robert E., Jr.; Macroeconomics; Phillips Curve; Risk; Sargent, Thomas; Uncertainty; Utility, Von Neumann-Morgenstern

BIBLIOGRAPHY

Bernoulli, Daniel. [1738] 1954. Exposition of a New Theory on the Measurement of Risk. Trans. L. Sommers. Econometrica 22: 23–36.

Borel, Emile. 1962. Probabilities and Life. Trans. Maurice Baudin. New York: Dover Publications.

Fisher, Irving. 1930. The Theory of Interest. New York: Macmillan.

Fisher, R. A. 1957. The Underworld of Probability. Sankya 18: 201–210.

Fisher, R. A. 1973. Uncertain Inference. In Collected Papers of R. A. Fisher, Vol. 3, ed. J. H. Bennett, 451–464. Adelaide: University of Adelaide.

Friedman, Milton. 1976. Price Theory. Chicago: Aldine Publishing.

Grandmonth, Jean-Michael. 1983. Money and Value. London: Cambridge University Press.

Hicks, John R. 1946. Value and Capital. Oxford: Clarendon Press.

Hicks, John R. 1984. The Economics of John Hicks, ed. Dieter Helm. Oxford: Basil Blackwell.

Katona, George. 1972. Theory of Expectations. In Human Behavior in Economic Affairs, eds. Burkhard Strumpel, James N. Morgan, and Ernest Zahan, 549–581. Amsterdam: Elsevier.

Keynes, John M. 1921. A Treatise on Probability. London: Macmillan.

Keynes, John M. 1937. The General Theory of Employment. The Quarterly Journal of Economics 51 (2): 209–223.

Knight, Frank H. 1971. Risk, Uncertainty and Profit. Chicago: University of Chicago Press.

Kydland, Finn E., and Edward C. Prescott. 1977. Rules Rather Than Discretion: The Inconsistency of Optimal Plans. Journal of Political Economy 85: 473–491.

Kydland, Finn E., and Edward C. Prescott. 1996. The Computational Experiment: An Econometric Tool. The Journal of Economic Perspectives 10 (1): 69–85.

Laffont, Jean-Jacques. 1989. The Economics of Uncertainty and Information. Trans. John P. Bonin and Helene Bonin. Cambridge, MA: MIT Press.

Lucas, Robert E., Jr. 1972. Econometric Testing of the Natural Rate Hypothesis. In The Econometrics of Price Determination Conference, ed. Otto Eckstein. Washington, DC: BOG of the Federal Reserve System and SSRC.

Lucas, Robert E., Jr. 1972. Expectations and the Neutrality of Money. Journal of Economic Theory (4): 103–124.

Lucas, Robert E., Jr. 1975. Econometric Policy Evaluation: A Critique. In The Phillips Curve and Labor Markets, eds. Karl Brunner and Allan Meltzer. New York: Elsevier, 1976.

Lucas, Robert E., Jr., and Thomas J. Sargent. 1994. After Keynesian Macroeconomics. In The Rational Expectation Revolution, ed. Preston J. Miller, 5–30. Cambridge, MA: MIT Press.

Muth, John. 1961. Rational Expectation and the Theory of Price Movements. Econometrica (July): 315–335.

Papademos, Lucas, and Franco Modigliani. 1990. The Supply of Money and the Control of Nominal Income. In Handbook of Monetary Economics, Vol. 1, eds. B. M. Friedman and F. H. Hahn, 399–494. Amsterdam: North-Holland.

Pesaran, M. Hashem. 1987. The Limits to Rational Expectation. Oxford: Basil Blackwell, Inc.

Phelps, Edmund S. 2006. Prospective Shifts, Speculative Swings. In Samuelsonian Economics and the Twenty-First Century, eds. Michael Szenberg, Lall Ramrattan, and Aron A. Gottesman, 66–87. New York: Oxford University Press.

Popper, Karl. 1959. The Logic of Scientific Discovery. New York: Harper and Row Publishers.

Samuelson, Paul A., 1986. The Collected Scientific Papers of Paul A. Samuelson. Vol. 5. Ed. Kate Crowley. Cambridge, MA: MIT Press.

Sargent, Thomas J. 2002. Commentary: The Evolution of Economic Understanding and Postwar Stabilization Policy. In Rethinking Stabilization Policy: A Symposium Sponsored by The Federal Reserve Bank of Kansas City, 79–94. Kansas City, MO: Federal Reserve Bank of Kansas City.

Savage, Leonard J. 1972. The Foundation of Statistics. New York: Dover Publications.

Shackle, G. L. S. 1952. Expectation in Economics. Cambridge, U.K.: Cambridge University Press.

Shackle, G. L. S. 1961. Decision Order and Time in Human Affairs. Cambridge, U.K.: Cambridge University Press.

Shackle, G. L. S. 1970. Expectation, Enterprise and Profit. London: George Allen and Unwin Ltd.

Shackle, G. L. S. 1974. Keynesian Kaleidics. Chicago: Aldine Publishing Company.

Simon, Herbert A. 1976. From Substantive to Procedural Rationality. In Method and Appraisal in Economics, ed. Spiro Latsis, 129–148. Cambridge, U.K.: Cambridge University Press.

Tversky, A., and D. Kahnemann. 1974. Judgment under Uncertainty: Heuristics and Biases. Science 185: 1124–1132.

Young, Warren, and William Darity Jr. 2001. The Early History of Rational and Implicity Expectations. History of Political Economy 33 (4): 773–813.

Lall Ramrattan

Michael Szenberg