On the Use of Density Forecasts to Identify Asymmetry in Forecasters' Loss Functions

Abstract: We consider how to use information from reported density forecasts from surveys to identify asymmetry in forecasters' loss functions. We show that, for the three common loss functions - Lin-Lin, Linex, and Quad-Quad - we can infer the direction of loss asymmetry by just comparing point forecasts and the central tendency (mean or median) of the underlying density forecasts. If we know the entire distribution of the density forecast, we can calculate the loss function parameters based on the first order condition of forecast optimality. This method is applied to forecasts for annual real output growth and inflation obtained from the Survey of Professional Forecasters (SPF). We find that forecasters treat underprediction of real output growth more dearly than overprediction, reverse is true for inflation.