Optimal combination of survey forecasts

We consider the problem of combining individual forecasts of real gross domestic product (GDP) growth and Harmonized Index of Consumer Prices (HICP) inflation from the Survey of Professional Forecasters (SPF) for the Euro area. Contrary to the common practice of using equal combination weights, we compute weights which are optimal in the sense that they minimize the mean square forecast error (MSFE) in the case of point forecasts and maximize a logarithmic score in the case of density forecasts. We show that this is a viable strategy even when the number of forecasts to be combined gets large, provided that we constrain these weights to be positive and to sum to one. Indeed, this enforces a form of shrinkage on the weights which ensures a reasonable out-of-sample performance of the combined forecasts.