September 2000

The current procedure for calculating the composite index of leading indicators does not use the most up-to-date information. The composite index methodology ignores currently available data on stock prices, bond prices, and yield spreads in favor of a time-consistent set, (i.e., data for a past month for which most, if not all, components of the index are available). This is a major shortcoming. For the United States, for example, the index of leading indicators published on August 30th uses data from July despite the availability of August values for at least two of the components, namely interest rate spread and stock prices. The problems are more acute in most foreign countries where many indicator series are available with lags of more than one month, sometimes as long as 3 to5 months. In order to address these problems, we propose an alternative index procedure, which uses current financial information along with estimates of the values of variables that measure the "real" state of the economy, but are only available with a lag.

Faced with lags in the availability of many series, the practice has been to calculate the index with a partial set of components in most foreign countries and occasionally in the U.S. Typically, at least half of the components of an index are required before this procedure is used. For example, according to the rules used by the OECD, the minimum percentage of component series required before a composite index can be calculated lies between 40 and 60 percent depending on the country (see OECD web page http://www.oecd.org/std/li1.htm).

While such rules create a more up-to-date index, they raise many serious problems. The effective weights used to calculate the contributions of the components, for example, often change dramatically without a consistent set of components. Thus, there is a trade-off between the coverage and the timeliness of the leading index. The more complete its coverage, the less timely is the index.

Current Procedure

In constructing the leading index, the present approach is to use data with the shortest available lag relating to the common past month. Let Xt- be the vector of the indicator series that are available in "real time," (i.e., in the current publication period, t). Variables in Xt- are generally financial indicators such as stock prices, bond prices, interest rates, and yield spreads. Let Yt be the vector of the indicator series that are available only with lags, (i.e., those variables that are not available in the current publication period). Variables in Yt- are generally data on various aspects of real macroeconomic activity and price indexes. In the U.S., these variables usually lag by one month. Thus, the most recent value of the index for month t is ; its previous value is , and so on. The Xt values are not used, which amounts to throwing away the most up-to-date information.

The Proposed Alternative

The new index procedure uses current financial information, along with estimates of the values of variables that measure the "real" state of the economy but are only available with a lag.The proposed index is constructed with a complete set of components using actual and forecasted data. The historical series for the index would be revised each month as the data unavailable at the time of publication become available. Such revisions would be treated as part of the monthly data revisions, now a regular part of indicator programs.

The main idea behind the more timely Leading Index we are proposing is that it should incorporate the most recent available values for the X variables and good, cost-effective estimates of the Y variables for the matching period. Thus, instead of the current index, , we have an alternative index , for all t = 1... T. Here, the symbol ^ refers to a magnitude based at least in part on some kind of forecasting and t refers to the latest complete month at the time the value of the index is released (e.g., August for the index published on August 30th).

Conceivably, it is possible that is inferior to . However, using Xt instead of Xt-i should give considerable advantage. Other reasons for expecting the procedure to be an improvement are: (1) the errors of the forecast should be limited, since they typically will be for short intervals (one or a few months), (2) the individual errors of the components of the vector may offset each other when combined to form the composite index.

The Choice of Forecast

There are various ways to forecast Yt. Here, we focus on simple autoregressive models: Yt is predicted by estimating an i-th order autoregressive model. For example, if i = 1, let = I (Xt, (Yt-1)) denote the index which uses an AR-1 model to forecast and so on. For practical reasons associated with production of the indicators on a monthly basis, it is necessary to fix the forecast model used for particular countries for fixed periods of a year or two. Therefore, we focus on relatively simple lag structures that can be easily implemented and these are fixed for the entire sample period. As will be shown below, this approach tends to give results that improve strongly for i = 1,2 and only mildly for i = 3, 4, and are generally acceptable.

Defining the Complete or "Ideal" Benchmark Index Evaluating the alternative indexes is facilitated by a benchmark to compare the current and proposed procedures. We use for this purpose the current definition of the Leading Index for the U.S. produced by The Conference Board. Let the benchmark index, , be the actual value of this index at time t based on complete data for all components of both the set Xt and the set Yt. For simplicity, think of as a historical index, which is no longer revised. (However, this is not an innocuous assumption, since in practice the recent values of the index are subject to revisions; only after some time (perhaps a year or more) has elapsed can the values of be taken as given). Because the data for several components of the complete benchmark index are available only with lags, it is impossible to construct in real time for the publication period t. However, apart from any data revisions and assuming complete information can be had with a one-month lag, the current index would equal the ideal index for period t-1. That is, is used as a substitute for -- essentially, a crude first-order autoregressive forecast of . In this sense, the current method is itself a simple projection of the (t-1) data to the t-th period. The one-month lag applies to the U.S. index, but for other countries the lags are generally longer and more varied.

Simple Comparisons with Current and Alternative Indexes

Chart 1 shows the benchmark index IB and the current index IC for the period January 1970 - January 2000 (361 monthly observations). The two series are very close but IB tends to be above IC. The differences (IB - IC) are plotted separately to a larger scale on the left-hand side. By far most of the time, these discrepancies due to missing data and other measurement errors are positive, generally between zero and two on the index scale (and very similar in percentage terms). This bias is most likely the result of data errors and subsequent revisions, which presumably affect IC more strongly and more adversely than they affect IB. Over time, as the data gaps are filled and the data errors are reduced, the discrepancies between IB and IC remain largely random and relatively small. Interestingly, their volatility appears to be larger in the first half of the period covered (1970-85) than in the second half (1986-1999).

Chart 2 compares in the same way IB and the alternative AR-2 index IA. It is important to note that the discrepancies from IB are here smaller (generally in the range of -1 to +1) and that they are not biased in the sense of being predominantly positive or negative but are approximately symmetrical around the zero line. Again, however, the series of differences (IB - IA) shows greater volatility in 1970-85 than in 1986-99.

Root mean square errors (RMSE) of (IB - IC) and (IB - IA) allow us to compare these discrepancies over time. We consider not only the AR-2 model as in our charts (i.e., ) but also AR-1, AR-3, and AR-4 models (i.e., by , , and respectively). The RMSE of (IB - IC) is 1.011, (IB - ) is 0.646, and (IB - ) is 0.592. They show in each case substantial reductions of the discrepancies from IB as we move from to and , much smaller (or no) improvements with shifts to , and . Thus, for simplicity and uniformity, we choose the AR-2 model as the preferred one. This new composite index procedure could go a long way towards improving the ex-ante forecasting performance of the leading index. It includes current financial information along with estimates of the values of variables that measure the "real" state of the economy, but are only available with a lag. This approach to constructing the leading index uses available information more efficiently than the current method and appears to have significant advantages over it.

In next month's article, we will briefly describe some simple tests of the quality of our choice of benchmark or ideal index and compare the forecasting performance of the current and alternative indexes. These tests as well as many others are regularly a part of the evaluation by The Conference Board of its composite indexes. The purpose of the leading indexes is to predict changes in the coincident indexes, which reflect the present state of the economy. The current leading index, , performs this function with errors that are due largely to missing data and other measurement problems. In the proposed index, , the main source of errors is presumably the deficient forecasts of . In addition to the evidence we presented here, we will show next month that the forecast errors of are generally over time smaller than those of .