On the Estimation of Forecaster Loss Functions Using Density Forecasts

We suggest a novel approach to use density forecasts from surveys to identify asymmetry in forecaster loss functions. We show that we can calculate the loss function parameters for Lin-Lin and Quad-Quad loss functions based on the first order condition of forecast optimality. Since forecasters form their point forecasts based on what they believe to be the data generating processes and their loss functions, we can reverse this process and learn about forecaster loss functions by comparing their point forecasts and density forecasts for the same target. The advantage of this method is that we can relax the two assumptions needed in Elliott, Komunjer and Timmermann’s (2008) GMM method: the point forecasts and density forecasts need not to be rational and the loss function parameters need not to be constant over time. Moreover, we do not need to know the actual values of the target variable. This method is applied to density forecasts for annual real output growth and inflation obtained from the Survey of Professional Forecasters (SPF) during 1968-2023. We find that forecasters treat underprediction of real output growth more dearly than overprediction, reverse is true for inflation.