The More Timely Leading Index: How Well Does It Work?
Last month's article introduced a new procedure for calculating the composite index of leading economic indictors, which uses the data more efficiently. The new procedure allows the Leading Index to be constructed about four weeks earlier by combining projected values for data not available in the publication period with the data already available. As a result, this new Leading Index is more up-to-date than the current Leading Index published by The Conference Board. We also demonstrated that the new Leading Index had a significant advantage in tracking the historical benchmark Leading Index over the current method.
This month, we describe another test, based on out-of-sample forecasts, of the new Leading Index. We examine how well the current and new Leading Indexes help forecast the U.S. Coincident Index. The results support the finding in last month's article that the new Leading Index offers improvements over our current procedures.
Out-of-Sample Forecasts of the Coincident Index
The U.S. Coincident Index provides a good measure of the overall performance of the economy and the test of the new procedure uses forecast models that predict this index. We ask whether the Leading Index adds significant predictive powers for the Coincident Index after taking into account the predictive power of the Coincident Index lagged one period. In other words, we ask whether adding the Leading Index adds to a simple first order autoregressive forecast model for the Coincident Index by reducing errors in out-of-sample forecasts. Thus, we estimate four basic forecast models, a model using the lagged Coincident Index alone and models using the benchmark historical, current, and new Leading Indexes. The square root of the mean of the squared forecast errors (RMSE) summarizes differences between the forecast models. If adding the Leading Index to the models improves the forecasts of the Coincident Index, then the forecast model will have lower errors. In this way, we compare the predictive abilities of the three Leading Indexes.
For each of the four forecast models, there are 12 separate forecasts to allow for the various timing specifications for the Leading Index. Analysts typically use rules of thumb to make predictions about movements of the economy with the Leading Index. These specifications accommodate the different ways the Leading Index is used to make forecasts. Analysts and forecasters mainly use the Leading Index by looking at alternative numbered lags and different lag periods (columns 2 and 3).
The historical data from January 1970 through January 2000 are used (i.e., 361 monthly observations) to create one-month-ahead, out-of-sample forecasts of the Coincident Index. We begin with regressions that cover the period January 1970 to December 1973, producing a one-month-ahead forecast for January 1974. Thus, the first forecast is based on the 48 observations from January 1970 to December 1973. At this point, we add one more month of observations (i.e., the actual values for January 1974), re-estimate all coefficients, and form a second one-step-ahead forecast for February 1974 based on the 49 observations from January 1970 to January 1974. This process continues until the entire sample of observations is exhausted, and we are left with 313 regression forecasts (361 monthly observations minus the 48 observations used for the first set of forecasts). A sequence of simulated "real-time" forecast errors is then constructed by subtracting the forecasts from the actual value of the Coincident Index for each of the forecast models. RMSEs serve to summarize these numbers.
The RMSEs are reported in columns 4-7 of Table 1, and the ratios of the RMSEs, in percent, are in columns 8-11. Negative RMSE ratios indicate that the addition of Leading Index terms reduces the forecast errors relative to the forecast errors with Eq. (1), (2) and (3) or the forecasts with the current Leading Index (Eq. (4)). A glance at Table 1 shows the prevalence of minus signs in the last four columns. All but eight of the 48 entries (83 percent) are negative.
The New Procedure Consistently Outperforms the Current One
The results clearly support implementing the new procedure. The model that uses the new Leading Index to forecast the Coincident Index has lower RMSEs than the model that uses the current Leading Index in 11 of the 12 cases covered. Throughout, as we would expect, the model with the benchmark historical index data ranks first with the lowest RMSEs. Unfortunately, the model cannot be used in practice. The model with the new Leading Index data ranks second and the model with the current Leading Index data ranks third in predicting the Coincident Index. The consistency of the results shown by the superscripts in columns 5, 6, and 7 provides strong evidence for the superiority of the new procedure.
Simple averages of the RMSEs are 3.59 for the regression forecasts of the Coincident Index with the benchmark Leading Index; 3.76 for those with the new Leading Index; 3.86 for those with the current Leading Index; and 4.09 for the autoregressive forecasts (referring to means of columns 5, 7, 6, and 4).
The new approach to constructing the Leading Index uses available information more efficiently than the current method. Combining projected values for data missing in the publication period and actual values for the available data such as stock prices and interest rate spread appears to have significant advantages over the current method, which waits a month and reports late.
Because of such consistent improvements, the proposed approach will be adopted by The Conference Board. The practical implication of this is that, beginning in February 2001, the press release will report the value of the Leading Index through the end of the most recent month, in this case January. (Until now, that press release would have reported data through the end of December.) Therefore, after the 2001 revisions, the Leading Index reported by The Conference Board will refer to the latest month instead of the previous one.
Table 1: Predicting Log Changes in the U.S. Coincident Index, Monthly:
Autoregression and Contributions of Log Changes in the U.S. Leading Indexa
[Insert Oct BCI Table]