Probability elicitation and the formation of expectations : an experimental approach

Abstract

This research deals with subjective probabilities and their use in decision-making. Two theories that predict behavior in this context are tested using the methods of experimental economics. An articulation of the theory of scoring rules leads to weak and strong predictions about behavior under an improper rule--the only kind of predictions that can be directly observed. The weak prediction was tested under controlled laboratory conditions using subjects with linear utility over the range of rewards. One-step-ahead probability forecasts were elicited from eight subjects under a proper (quadratic) scoring rule and from eight subjects under an improper (linear) scoring rule. Using the entire 40 forecast periods, the prediction that subjects under the linear rule will forecast with significantly "tighter" probability distributions was confirmed. However, there was no significant difference in "tightness" attributable to scoring rules over the first 15 periods, suggesting that a training or feedback effect is required before the predicted behavior is manifested. It is thus possible that, for a limited number of forecasts, the linear scoring rule may be the reward mechanism of choice since it has the advantage (particularly in field elicitation studies) of being easily understood by subjects. The theory of quasi-rational expectations was tested under controlled conditions of the economics laboratory. Five experiments were conducted with a variety of stochastic processes. In each experiment, subjects produced one-step-ahead forecasts of the variable generated by a Monte Carlo process. Comparisons of the performance of an aggregate of subjects' forecasts versus an ARIMA model showed that for relatively simple series (such as those generated by autoregressive processes of first or second order) the aggregate forecast was indistinguishable from that of the model. These results lend support to the theory that forecasts from an ARIMA model can serve as substitutes for aggregate expectations in macroeconomic policy models.