Forecasting and Decision Theory

When forecasts of the future value of some variable, or the probability of some event, are used for purposes of ex ante planning or decision making, then the preferences, opportunities and constraints of the decision maker will all enter into the ex post evaluation of a forecast, and the ex post comparison of alternative forecasts. After a presenting a brief review of early work in the area of forecasting and decision theory, this chapter formally examines the manner in which the features of an agent's decision problem combine to generate an appropriate decision-based loss function for that agent's use in forecast evaluation. Decision-based loss functions are shown to exhibit certain necessary properties, and the relationship between the functional form of a decision-based loss function and the functional form of the agent's underlying utility function is characterized. In particular, the standard squared-error loss function is shown to imply highly restrictive and not particularly realistic properties on underlying preferences, which are not justified by the use of a standard local quadratic approximation. A class of more realistic loss functions ("location-dependent loss functions") is proposed.