Call the random variable being forecasted X. If X is a discrete event, then it has the value zero or one. Forecasts of X depend on the information set available to the forecaster. Assume that there are two information sets Io and II, where Io is a subset of II. A forecaster with information set I, knows everything that the forecaster with in- formation set Io knows, and more.3 Denote the optimal forecast of X given the information set Io by E(X1IO). We are interested in forecasts of forecasts, which are useful when agents need to forecast behavior of other agents. An agent with information set I, who forecasts the forecast of an agent with information Io is estimating E[E(X1I0)1I11]
The law of iterated expectations states that if I, includes Io, then E[E(X1I0)1I1] must equal E(XIIo) (Chow and Teicher 1978, p. 204). Better-informed agents should ignore their additional information when forecasting the forecasts of less-informed agents. When the curse of knowledge occurs, the forecaster with information I, overesti- mates the scope of Io. Formally, the curse of knowledge means that E[E(X|Io)|I1 ] is not equal to E(X|IO), but is somewhere between E(X|Io) and E(X|II). A simple model we test in our experiments is
E[E(XI0)1I11] = wE(XIIi) (1 - w)E(XIIo).
If w = 0, an agent is applying the law of iterated expectations cor- rectly. If w = 1, agents who know II think that all other agents know II too. The parameter w thus measures the degree of curse of knowl- edge.