The diffusion index forecasts of the CPI (table 3) also represent substantial improvements over the benchmark models. Unlike the IP forecasts, the estimated factors do not account for all of the predictable dynamics in CPI inflation, and adding lags of CPI inflation to the diffusion index forecasts improves their performance, both for fixed к and к selected by recursive BIC. The results for fixed numbers of factors and the autoregressive correction indicate that the MSE attains a minimum at five or six factors. In contrast to the case of IP, the best fixed-к forecast is considerably better than the BIC-selected forecast, in both the balanced and unbalanced panel (the relative RMSEs are .62 v. .71 for the balanced panel with the autoregressive terms, respectively).

It is interesting to note that, in constrast to the results for IP, the leading indicator forecast based on a recursively BIC-selected subset of the leading indicators is considerably worse than using all leading indicators and in fact is worse than just using an autoregressive forecast. This is consistent with the view that the correlations between the individual leading indicators and inflation are unstable over time, so that variables selected on the basis of good prior performance become unreliable and thus produce poor out of sample forecasts.

It is also noteworthy that the Phillips curve model without the wage and price control variable performs almost as well as the leading indicator forecast, although not nearly as well as the autoregressive-augmented diffusion index forecasts. When the wage-price variable is added, simulated real time performance of the Phillips curve forecast actually deteriorates and barely improves upon the autoregressive forecast.

It should be stressed that the multivariate leading indicator models are sophisticated forecasting models that provide a stiff benchmark against which to judge the diffusion index forecasts. In fact, the performance of the leading indicator models in table 2 arguably overstates their out of sample potential performance, because the lists of leading indicators used to construct the forecasts were chosen by model selection methods using data similar to these, cf. Stock and Watson (1989) and Staiger, Stock and Watson (1997). In this light, we consider the performance of the diffusion index models to be encouraging.