This paper examines the theoretical and empirical properties of a supervised factor model based on combining forecasts using principal components (CFPC),in comparison with two other supervised factor models (partial least squares regression,PLS,and principal covariate regression,PCovR) and with the unsupervised principal component regression,PCR.The supervision refers to training the predictors for a variable to forecast.We compare the performance of the three supervised factor models and the unsupervised factor model in forecasting of U.S.CPI inflation.The main finding is that the predictive ability of the supervised factor models is much better than the unsupervised factor model.The computation of the factors can be doubly supervised together with variable selection,which can further improve the forecasting performance of the supervised factor models.Among the three supervised factor models,the CFPC best performs and is also most stable.While PCovR also performs well and is stable,the performance of PLS is less stable over different out-of-sample forecasting periods.The effect of supervision gets even larger as forecast horizon increases.Supervision helps to reduce the number of factors and lags needed in modelling economic structure,achieving more parsimony.