Using the Entire Yield Curve in Forecasting Output and Inflation

Following Diebold and Li (2006), we use the Nelson-Siegel (NS, 1987) yield curve factors. However the NS yield curve factors are not supervised for a specific forecast target in the sense that the same factors are used for forecasting different variables, e.g., output growth or inflation. We propose a modifed NS factor model, where the new NS yield curve factors are supervised for a specific target variable to forecast. We show that it outperforms the conventional (non-supervised) NS factor model in out-of-sample forecasting of monthly US output growth and inflation. The original NS yield factor model is to combine information (CI) of predictors and uses factors of predictors (the entire yield curve). The new supervised NS factor model is to combine forecasts (CF) and uses factors of forecasts of output growth or inflation conditional on each point of the yield curve. We formalize the concept of supervision, and demonstrate, both analytically and numerically, how supervision works. For both CF and CI schemes, principal components (PC) may also be used in place of the NS factors. In out-of-sample forecasting of U.S. monthly output growth and inflation, we find that supervised CF-factor models (CF-NS and CF-PC) are substantially better than unsupervised CI-factor models (CI-NS and CI-PC), especially at longer forecast horizons.