Combining Forecasts: Why Decision Makers Neglect Correlation

We suggest a framework to analyse how individuals combine multiple sources of information to form predictions. We assume that individuals understand each source of information separately, but they are not certain about the correlation between them. We bound the ability of individuals to grasp such correlations by a notion of “correlation capacity”. We show that given this capacity there is a set of predictions which is completely characterised by two parameters: the correlation capacity parameter and the naive combination of forecasts which ignores correlation. The analysis yields two countervailing e¤ects on behaviour. A higher correlation capacity creates more uncertainty and therefore possibly conservative behaviour. On the other hand, when the naive combination is relatively precise, it can induce risky behaviour. We show how this trade-o¤ a¤ects behaviour in di¤erent applications, including …nancial investments and CDO ratings. Speci…cally we show that complex assets are likely to lead to complete neglect of correlation by individuals. “...If we assumed that states had the same overall error as in the FiveThirtyEight pollsonly model but that the error in each state was independent, Clinton’s chances would be 99.8 percent, and Trump’s chances just 0.2 percent. So assumptions about the correlation between states make a huge di¤erence. Most other models also assume that state-by-state outcomes are correlated to some degree, but based on their probability distributions, FiveThirtyEight’s seem to be more emphatic about this assumption,”Nate Silver, FiveThirtyEight discussing his predictions about the 2016 US Presidential election.