A More Timely and Useful Index of Leading Indicators 

Robert H. McGuckin, Ataman Ozyildirim, and Victor Zarnowitz*

The Conference Board 

Economics Program, 845 Third Avenue, New York, New York, 10022

Abstract 

Effectively predicting cyclical movements in the economy is a major challenge. While there are other approaches to 

forecasting, the U.S. leading index has long been used to analyze and predict economic fluctuations. We describe and test a 

new procedure for making the index more timely. The new index significantly outperforms its less timely counterpart and 

offers substantial gains in real-time out-of-sample forecasts of changes in aggregate economic activity and industrial 

production. It provides timely and accurate ex-ante information for predicting, not only the business cycle turning points, but

the monthly changes in the economy. 

1. INTRODUCTION 

1.1 The Problem 

Most of the macroeconomic data for the United States require considerable time to collect, process, and release. Lags of one 

month are common for principal monthly indicators. For the quarterly data, including the national income and product 

accounts (NIPA), the lags are longer. Moreover, many of these indicators are subject to sizable revisions that are only 

realized over long time intervals. The data revisions presumably reduce measurement errors but they add to uncertainty and 

forecasting errors, as do gaps and lags in the availability of the data. 

The actual recognition lags are considerably longer than these publication lags as it is difficult to recognize signals in noisy 

data. As a result, not just private but even public decision and policy makers are faced with long delays and much uncertainty 

about the current (let alone the future) conditions of the economy. Although government is the main source of 

macroeconomic statistics, its access to the data is not much more timely than that of the public. 

At the same time, the publication lags and revision schedules vary greatly and some indicators are everywhere available 

promptly. In particular, financial market price and yield data are available electronically in real time during each trading day. 

The U.S. leading index includes stock prices and interest rate spreads that have no significant data lags and relatively few, if 

any, revisions. The financial market indicators convey a great deal of information with predictive value, yet, until recently, 

they were represented in the leading index, not by their most recent monthly values, but by their values in the preceding 

month for which data for other indicators were also available. For these series the timely availability of accurate data is not an 

issue, but indexing procedures did not take advantage of the most recent information. 

The failure to use the most current available data in the leading index is a likely major source of forecast errors. Some 

nonparametric rules and probability model applications of the leading index performed well in forecasting recent cyclical 

developments, even using real-time data, as reported by Andrew J. Filardo (2002). However, some other studies have 

suggested that the composite leading index was not a good predictor of industrial activity in real time. Aside from the path 

breaking work by Francis X. Diebold and Glenn D. Rudebusch (1991) on the importance of real time evaluations, studies by 

Arturo Estrella and Frederic S. Mishkin, (1998), suggested similar conclusions. They emphasized the importance of selected 

financial indicators such as interest rate spreads and bond and stock price indexes as better predictors of business cycle 

turning points. At least in part to address these criticisms, in addition to the new index procedures, we evaluate the accuracy 

of LI, both the old and new leading indexes. 

 

*

 We would like to thank Phoebus Dhrymes, Jan Jacobs, Chris Sims, Peter Zadrozny, members of The Conference Board 

Business Cycle Indicators Advisory Panel, seminar participants at the CIRET Conference (2000), the ASA (2002) annual 

meetings, participants in the University of Groningen seminar and an anonymous referee for helpful comments and 

suggestions. We would also like to thank Tim Jones for excellent research assistance. All remaining errors are, of course, 

ours. The views expressed in this paper are those of the author(s) and do not necessarily represent those of The Conference 

Board. Address for correspondence: The Conference Board, Economics Program, 845 Third Avenue, New York, New York, 

10022. 

Page 65
1.2 The Attempted Solution 

How should one deal with the data shortcomings and make the composite indexes less vulnerable to them, more timely, and 

more useful for economic analysis and forecasting? The old composite index of leading economic indicators is replaced by a 

new index, which uses more timely and more complete data. The missing-data problem encountered in the construction of 

the composite indexes calls for a practical solution that combines three principles. (1) Use the most recent complete monthly 

data for those components where they are available. (2) Use the simplest uniform methods of forecasting that will produce 

acceptable estimates for those components where the data for the most recent complete month are not available. (3) Apply 

strictly consistent tests to the old and new indexes to compare their predictive performance, and accept the results of the new

procedure only if they pass these tests. 

This paper describes in detail how The Conference Board solved the above problem. It also assesses the accuracy of the new 

composite leading index using out-of-sample tests with both historical and “real-time” data. This is in contrast to many 

earlier tests of the leading indicators that rely only on historical, revised data series, not on information available at the time 

of publication. We find that the new procedure yields significant gains and that the resulting leading index is more timely and

useful, in the sense that the leading index significantly improves forecasts across a broad range of models. 

1.3 Outline 

Part Two of the paper describes the traditional method of constructing a composite leading index, sets out its rationale, and 

provides its critique. An alternative method that is capable of producing a timelier and more useful index is then developed. 

The availability of component data and the implied production schedules are given full consideration in defining the new 

index calculation procedures and comparing it formally with the conventional one. This portion of the paper ends with a 

discussion of the expected costs and benefits of the new approach. 

Part Three analyzes the structure of the underlying data and the role of data revisions. It compares the historical leading 

index, defined as the leading index calculated with the latest available data, with successive vintages of the old and new 

leading indexes. By using real-time data for each of their ten components in the current set of leading indicators (see The 

Conference Board, Business Cycle Indicators Handbook, 2001), we put the indexes on a strictly consistent and comparable 

basis. Charts comparing the old and new indexes show that they are nearly identical in the early parts of the time series, 

which comprise revised data. But they differ increasingly in the later pre-revisions parts of the series. In its last section, part 

III discusses the coincident or current conditions index (CCI), which the leading index (LI) is designed to predict. 

Part Four asks how well the leading index predicts CCI; it considers briefly other measures of overall economic activity as 

well. The equations or models and the procedures designed for testing the performance of the index are presented and 

discussed. So are the tables providing the evidence on the summary measures of the associated forecast errors. 

The last section (V) draws together our conclusions and places them in the context of some other related findings in the 

literature. 

2. CONSTRUCTION OF THE COMPOSITE LEADING INDEX 

2.1 The Logic and Consequences of the Traditional Method

There is much variation among business cycles in duration and magnitude, causes and consequences. The contributions of 

specific factors differ over time. This helps to explain why composite indexes designed to describe and predict economic 

growth and fluctuations generally work better over time than do their individual components (different indicators selected for 

the best past performance). The leading index, for example, represents better the multicausal, multifactor nature of the 

economic movements than does each of its following components: the average workweek, initial claims for unemployment 

insurance, new investment commitments (orders, contracts, housing permits), real money supply, yield spread, stock prices, 

and consumer expectations. The contributions of these components vary over time, depending on the characteristics of each 

cycle. The leading series themselves vary in timing, smoothness, currency, etc. The index gains from this diversification.1

 

 

1

 The indicator approach is just one of many approaches to business cycle analysis. Introduced first by Mitchell and Burns 

(1946), it has been a major component of the NBER business cycle program and has proved useful over the years. 

Page 66
However, many technical problems arise from this diversity, perhaps none more vexing than those stemming from the fact 

that some indicators are available promptly, others with substantial lags. 

The traditional method employed since the early post-World War II years successively by the National Bureau of Economic 

Research (NBER), the Bureau of Economic Analysis (BEA) in the U.S. Department of Commerce, and lately The 

Conference Board incorporated two rules. First, all components of the index refer to the same month. Second, only actual 

data – no forecasts – are used. 

This first adopted and long used procedure had its logic. The set of the data used was time-consistent, since it covered the 

same period, as usual in index construction. In addition, by consisting of actual data, the index avoided errors inevitably 

associated with forecasting. 

However, the methodology suffered from failing to use the latest available financial and other data with presumably more 

relevance and more predictive value than the data actually used, which were one month older. While forecasting the missing 

variables introduces error, it also improves the timeliness of the composite index. 

The old procedure also had no good way of coping with the serious problem of missing data. The practice followed 

occasionally in the U.S. and routinely in most foreign countries has been to calculate the indexes with a partial set of 

components – e.g., a minimum of 40 to 60 percent depending on the country according to the Organization for Economic 

Cooperation and Development (OECD).2

 An equally arbitrary rule of at least 50 percent of components was used in the 

United States until recently. 

While any rule based on less than the full complement of the data allows the indexes to be more up-to-date, all such rules 

raise serious problems. First, there is the very undesirable trade-off between the coverage and the timing of the index: the 

more complete its coverage, the less timely is the index. Second, without a full set of components, the volatility adjustment 

(standardization) factors used to calculate the contributions of the components often change dramatically depending on which 

series, and how many of them, are missing. 

The only effective way to avoid these problems while adhering to the rules of the traditional method was to delay the 

issuance of the index until preliminary data became available for all of its components. For the monthly indicators used in 

the most recent version of the traditional index this meant a production lag of almost two months.

2.2 The Gain in Timeliness from the New Method 

In the old procedure, the index released during the current month (t) referred to the month (t-2). In the new procedure, 

implemented by The Conference Board since January 2001, the index released in the same month (t) refers to the month (t-1). 

This is a major advantage of greater timeliness. 

Let Y be the vector of indicator series with data lags such that they are not available in the current publication period. 

Variables in Y are generally data on real macroeconomic activity and price indexes. Specifically, for the present U.S. 

Leading Index they include new orders for consumer goods and materials, new orders for nondefense capital goods, and real 

money supply. (Nominal money supply is available but the personal consumption expenditure deflator used to adjust it is 

not.) 

Let X be the vector of the indicator series that are available for the most recent complete month. These include the promptest 

financial indicators such as stock prices, bond prices, interest rates, and yield spreads. They also include many other, less 

prompt but frequently reported series. Seven of the ten components of the U.S. Leading Index fall in this category.3

Table 1 shows the availability of the components of LI in the two most recent complete months, using March (t) as an 

example (the situation in any other month is analogous). It also illustrates the publication schedules of the old and the new 

index. In our example, the old index would be calculated in the first week of March (t) for January (t-2), the month with a 

complete set of components. The new index would be calculated in the third week of March for February (t-1), the month for 

 

2

 See Nilsson (1987). Also see web page http:// www.oecd.org/std/li1.htm 

3

 This count depends on the publication date of the Business Cycle Indicators report during each month. The statement holds 

for the present publication schedule adopted in January 2001. 

Page 67
which 70 percent of the components are available and 30 percent are forecast. Before the introduction of the new method, 

users of the indicator approach had to wait for two more weeks until April for the February index. 

A simple formalization of the old and new indexing procedure may be given as follows: 

( , ) −2, = t−2 t−2

old LI tt XI Y (1)

and 

)

ˆ

( , 1, 1 1

^

− = t− t−

new

LI tt XI Y (2)

Here denotes the indexing procedure4

I ⋅)( used; )(

, = ⋅ − LI I

itt

 denotes the value of the index for the month t-i published in 

the month t, where i denotes the publication lag. The first subscript on the index gives the month of release; the second 

subscript, the month of the target or reference. The symbol ^ refers to a magnitude based at least in part on some kind of 

forecasting. 

2.3 The Costs and Benefits of the New Procedure 

The indicators used to construct the leading index tend to move ahead of the business cycle as represented by CCI, its 

components, and other measures of overall economic activity in real terms. For example, businesses adjust hours before 

changing employment by hiring or firing; new orders for machinery and equipment are placed before completing investment 

plans; etc. Thus, by design, the composite index of leading indicators helps predict changes in the economy. The old 

leading index performed this function with errors due largely to missing data and other measurement problems. In the new 

index, some of these problems are reduced but new errors are introduced by the forecasts ofY 1 . 

^

t−

For the new procedure to be preferred, it is necessary that the errors of be smaller than those of so that 

does a better job of forecasting the economy. Conceivably, could be inferior to . However, using Xt-1 instead of 

Xt-2 results in a substantial advantage of greater timeliness, as the new index is available more than half a month earlier than 

the corresponding old index. Furthermore, the Y forecasts are typically short, hence they should produce relatively small 

errors. Also, the individual errors of the components of the vector may offset each other when combined to form the 

composite index. Thus, there are three good reasons why the new procedure can be expected to be an improvement.5

new

LI

^

1

old LI

new

LI

^

new

LI

^

old LI

1

^

t−

^

Y t−

Of course, there exist a great variety of ways to forecast Yt

. However, the advantages of simplicity, stability, and low costs 

argue for concentrating on easily implemented autoregressive models that pass some fairly strict tests. For practical reasons 

associated with production of the indexes on a monthly basis, frequent changes in the forecast model are avoided. The 

Conference Board uses the same model for fixed periods of at least a year or two, but re-estimates it every month. The model 

will be tested every year or so and, if necessary, replaced with a better working one. Therefore, simple and easily 

implemented lag structures were the focus of The Conference Board’s search for a forecasting method. 

 

4

 In this paper we take to be fixed and identical to the Conference Board’s indexing procedure. The Conference Board 

follows longstanding practice of using standardization factors to equalize the volatility of the index components so that 

relatively more volatile series do not exert undue influence on the index. On details of indexing, see The Conference Board, 

Business Cycle Indicators Handbook,

I ⋅)(

 2001. 

5

 The Y forecasts for the U.S. are restricted to one-month ahead forecasts, but for other countries multi-step forecasts for 

some Y variables are necessary. In most foreign countries there are fewer weekly and monthly and more quarterly and 

annual series, and for this and other reasons the lags tend to be longer, up to 3-5 months. Hence, outside the U.S. the need for 

the new procedure is even greater than for the U.S., although the potential errors from forecasting the Y variables are greater, 

too. 

1

^

t−

Page 68
Robert H. McGuckin et al. (2001) examined AR (i) models with lag lengths, i, of one to four months. The forecasts improve 

strongly for i = 1, 2 and only marginally at best for i = 3, 4. Unconstrained processes work better than the constrained ones.6

 

Hence, the simple second order autoregressive hotbox imputation method was adopted after much experimentation and due 

consideration of the practical needs of monthly production schedules. 

3. COMPARING THE LEADING INDEXES AND THEIR PREDICTIVE TARGET 

3.1 Calculating the New and the Old Indexes in a Consistent Manner 

The long history of the leading and coincident indexes has been punctuated from time to time by changes in the composition 

of these indexes and some of their technical properties. The reasons for these alterations lie in advances of the research on 

business cycles and the indicators, and in changes in the availability and quality of the underlying statistical time series.7

There is no support for the notion that component series were added to and subtracted from the index to obtain high 

correlations with measures of aggregate economic activity.8

In order to compare the new and old leading indexes on a consistent basis, we calculated the indexes using real time data on 

each of their ten components. This puts the new and old indexes on strictly equal footing, eliminating all changes in 

composition or methodology (base years, standardization factors, etc.) – and hence all possible discontinuities or differences 

due to these factors. 

Old Index.

The real time data used in this study were first electronically archived in 1989 by the former Statistical Indicators Division of 

the U.S. Department of Commerce and later, since 1995, by The Conference Board. The data available in January 1989 are 

called the “January 1989 vintage” and consist of a monthly sample covering the period January 1959 to November 1988. 

Each consecutive monthly vintage adds the next month’s observation. Thus, the next vintage consists of the comparable data 

available in February 1989, covering the sample period January 1959 to December 1988, and so on, through August 2002, 

which is reported in the September 2002 vintage. Hence, there are 165 vintages and 165 corresponding sets of data that are 

used to create 165 series of the old index, each starting in January 1959. 

New Index.

The above is a stylized description of the real time data because the components are not all published at the same time. 

Rather there is a steady stream of new data on the components of the leading index throughout a given month. The following 

example explains how we create the new leading index with the real time data we have: Assume we are in the third week of 

January 1989. The December 1988 values of the three Y components of the index (see Table 1 and text above) have not been 

published yet. The latest data available for these components end in November 1988 and are saved in the January 1989 

vintage. The December 1988 values of the remaining seven components have already been published at various dates in 

January. Note that under the schedule for the old leading index these seven components will not be archived until February 

1989. 

We use the three components from the January 1989 vintage and forecasts of their values for December 1988 and combine 

them with the values of the seven components that are saved in the February 1989 vintage to get the new leading index 

 

6

 The simplest model was Y = Yt-1, i.e., an autoregressive process of order one where the constant is zero and the coefficient 

is one. Even this model improved a little on the old index but less so than the corresponding unconstrained version. The 

available data on X could help forecast the missing Y series, but their use would result in overweighing the X variables in the

index and does not repay the effort. 

t

^

7

 For comprehensive information on the structure and evolution of cyclical indicators and composite indexes, see Klein 

(1999a, b) and Zarnowitz (1992) chs. 10 and 11. 

8

 The NBER and the U.S. Bureau of Economic Analysis (BEA) conducted no fitting exercises to improve forecasting with 

LI, but producers of cyclical indicators must be sensitive to the effects of real changes in the economy’s structure, 

institutions, and policies. A good example is the addition of real money supply to LI in the 1973-75 review and 

benchmarking. There are also occasional efforts to improve the index by removing or replacing a component that became 

unduly volatile or otherwise deteriorated like the index of sensitive materials prices (included in LI prior to the 1996 revision 

by The Conference Board). 

Page 69
covering the period January 1959 to December 1988. We call this the January 1989 vintage since it would have been 

published in the third week of January 1989 if the new procedure were in place. The next vintage of the leading index is 

constructed similarly. Thus, each vintage of the new leading index has one more monthly observation than the old leading 

index. The 165 data sets of real time data described above give 165 vintages of the new leading index. The last vintage of 

the new index we use is the September 2002 vintage, which covers January 1959 through August 2002. 

Page 70

The formal and general representation of such a data structure as laid out in Diebold and Rudebusch (1991) is a matrix with 

1...s columns, one for each successive vintage, and with 1...r rows, one for each successive period covered by the data 

available within each vintage. Here Lrs is the value of the leading index (old or new), which covers month r and which has 

been published in month s. 

3.2 Real-Time Vintages of the New and Old Leading Indexes 

Chart 1 compares five randomly selected vintages of the new Leading Index with each other and the historical index. The 

vintage series end one month before the publication dates of 1/89, 11/91, 7/98, 3/00, and 6/01, respectively, while the 

historical index incorporates all revisions in the data through September 2002. All six series start in January 1959, and all 

have common index base, 1987 = 100. 

By construction, all six indexes have the same composition and the same computational characteristics. Hence, any difference 

between them must be due to the effects of (1) data revisions and (2) forecasting the missing data. But at any time historical

post-revision values account for the great bulk of all observations, and they are generally identical in the different vintages. 

Forecasts for missing data apply only to the most recent values (end months for each vintage) of three of the components of 

LI. This explains why the differences between the vintages tend to be so limited. 

Indeed, it is mainly the new orders for consumer goods and materials and the new orders for nondefense capital goods, which 

have large revisions, partly due to their deflators. Similarly, revisions affect at times importantly the implicit deflator for 

personal consumption expenditures used to adjust M2, money supply. The other leading indicators either have no revisions 

at all (stock prices, the yield spread) or have only rare and relatively small revisions. 

A closer look at the chart reveals that the patterns of cyclical change are virtually identical in the different vintages of the new 

LI; moreover, even the short irregular fluctuations also look closely similar.9

 However, the successive vintages show an 

upward tilt. The historical index, which is the last (9/2002) vintage, shows the strongest upward trend; the earlier vintages 

start from somewhat higher levels and end at somewhat lower levels. Underestimation of growth and inflation appears to be 

a frequent characteristic of preliminary data in long expansions like the 1960s and 90s.10

 

While inter-vintage discrepancies appear more visible around some of the past turning points, in the 1960s, the 1970s, and 

1982, the specific-cycle peaks and troughs in the leading index fall on the same dates for all different vintages in a whole

succession of business cycles. Indeed, the historical index agrees on the dates of cyclical turns with the earlier vintages. The 

agreement is exact in a large majority of cases and close in the few instances where the timing is not identical. 

For the period since 1959, Chart 1 shows the consensus peak and trough dates for the leading index. They are marked P and 

T where they precede the onset of business cycle recessions and recoveries, respectively, and x where there are “extra” turns 

not associated with general economic declines and rises. In 1959-2002, seven recessions occurred in the United States, as 

shown in the chart by shaded areas; the beginning and end dates of these phases, i.e., the U.S. business cycle peaks and 

troughs, respectively, are listed at the top of the chart. All vintages of the leading index share the property of turning down 

ahead of business cycle peaks, and up ahead of the troughs. The length in months of each of these leads is shown in Chart 1 

by a negative number placed next to each of the eight P and each of the eight T markings.11 The leads at peaks range from 6 

 

9

 Analysis of this issue must await another paper. Moreover, reliance on charts requires some care. When 1959, the initial 

year of the real-time data sample, is used as the index base, the five vintages and the historical data all are just about 

indistinguishable on a graph for the first six or seven years covered. Later on, discrepancies between the vintages appear and

increase gradually. When a later year such as 1987 is chosen as the base, the vintages get to differ on that account in both the 

early and the late periods, and the differences tend to disappear in the mid–1980s (see Chart 1). 

10 Zarnowitz (1992), ch. 13, shows a similar pattern for related forecasts. On how data revisions can interact with the 

differences between real-time perceptions and ex-post realizations of important macroeconomic variables, see Orphanides 

(2001). 

11 By convention, leads are represented by negative numbers, lags by positive numbers. 
to 21 months and average 11 months; for those at troughs, the numbers are 1 to 8 and about 4.5 months. In addition, the 

algorithm developed by Gerhard Bry and Charlotte Boschan (1971), which mimics closely the procedures of NBER 

researchers for selecting turning points, picked three “extra” declines (six x turns). 

A plot of the corresponding vintages of the old index looks very much like Chart 1 and including it here would not repay the 

additional space required (the chart is available upon request). For both the old and the new indexes, the set of the specific

cycle turning points is the same, as presented in Table 2. Data revisions have caused a few small shifts between the earlier 

and the later vintages; these are listed in the footnotes to Table 1 and refer to irregular or flat turning zones (see Chart 1). 

Because their cyclical timing is essentially identical, the new and old leading indexes cannot be distinguished by how well 

they anticipate the onset of business cycle recessions and recoveries. With the same composition, they face the same data 

and produce the same leads. But the new procedure reduces the delays involved in publication and results in a more timely 

index, which should prove helpful in actual recognition of turning points. 

3.3 Comparing the Old and New Indexes Directly 

Chart 2 plots the new LI and the old LI for the period since 1989 covered by our “real time” sample. Each point on the graph 

represents the end value of each of the 165 vintages of data. covers the period December 1988 – August 2002; 

covers November 1988 – July 2002. The lower panel of the chart shows the percent differences between the two real-time 

level series plotted in the upper panel. It is evident that these differences are very small most of the time: and 

practically overlap. Further, the time series of the differences is essentially random and has little if any bias: most of the

time, the positive and negative differences balance each other. 

new

LI

^

old LI

old LI

new

LI

^

In addition, Chart 2 in its upper panel shows the “historical LI,” that is the last vintage which incorporates all revisions to

date. This historical index series deviates from both the old and the new LI by much more than they deviate from each other, 

but mainly in the level, not in the pattern of cyclical change which is shared by all three series. Much of the time during the 

1990s the historical index runs slightly above the other indexes reflecting the aforementioned tendency of the indicators to 

understate growth and inflation during expansions. 

The randomness of the differences between the old and the new LI is certainly a welcome feature as it means that forecasting 

the missing components of the index introduces no net systematic error. So is the fact that the discrepancies are generally 

small, fractions of one percent. This suggests that any errors caused by the new procedures are likely to be more than offset 

by improved timeliness. Nonetheless, the differences in timing between the two indexes occasionally cause them to differ 

strongly because of large benchmark revisions in some components: in a few scattered months, uses pre-benchmark 

data while uses post benchmark data. 

new

LI

^

old LI

Chart 2 also confirms that the old and new real-time leading composites available since 1989 can hardly be distinguished by 

their cyclical timing. Since differences in forecasting the turning points is not an issue, we base all our tests on how well the 

new vs. old LI does in forecasting times series that represent total economic activity. These tests are both more general and 

more demanding than turning point comparisons: They use a regression framework and distinguish quantitatively between 

historical and real-time data. 

3.4 The Coincident Index as a Measure of Current Economic Conditions 

The Leading Index is widely used as a tool to forecast changes in the direction of aggregate economic activity and in 

particular business cycle turning points. The reference chronologies of the latter are determined historically by the National

Bureau of Economic Research. In this task, NBER relies to a large extent on the principal coincident indicators: nonfarm 

establishment employment, real personal income less transfers, real manufacturing and trade sales, and industrial production. 

Hence, business cycle peaks and troughs are well approximated by the dates of peaks and troughs in the current conditions 

index (CCI). 

Page 71
Chart 3 demonstrates the close correspondence between the timing of CCI and the chronology of U.S. expansions and 

contractions. It also shows that the LI leads the CCI at all business cycle peaks and troughs. Finally, it demonstrates that 

CCI and real GDP, which is the most comprehensive measure of U.S. output, are very closely associated. 

Page 72

While highly correlated with real GDP, CCI has several advantages over GDP as a target measure for testing the new 

composite leading economic index. The leading index is developed to predict the CCI, which, unlike GDP, is available 

monthly. CCI is made up of several variables, not just output. Its four components, together, cover all economic activities 

that are important for our present purposes. GDP is the most comprehensive measure of output but it is subject to long 

strings of revisions, which are often large; CCI is revised less, partly because the revisions of its components frequently 

offset each other. Hence, the linkage to the cyclical turning points is closer for CCI than GDP (Zarnowitz, 2001a). For these

reasons, our main focus is on the CCI as a measure of current economic activity. 

Because of the interest in and importance of real GDP as the most comprehensive economic variable, we performed 

forecasting exercises using this aggregate, too. Tests of how well LI predicts GDP must first solve the problem of how to 

transform the two series to common frequencies. One would like to take advantage of the fact that the leading indicators are 

monthly, but interpolations of quarterly to monthly real GDP can adversely affect the results. This is because they arbitrarily 

smooth real GDP, which is the series that is used both as the dependent variable and, lagged, as one of the explanatory 

variables. In the absence of a reliable monthly GDP12, it is preferable to work with quarterly LI. Although this 

transformation causes a considerable loss of information, it does not distort the results in any obvious way. Hence, we 

decided to use quarterly LI in the form of the average observations for each successive quarter.13 We find that the tests with 

real GDP and LI are supportive of the new procedure. These results are presented in an appendix. 

The problems with using quarterly GDP are the main reason why many studies use industrial production (IP) as the target 

variable. But IP is only one of the components of CCI, and it covers a relatively small and declining part of the economy 

(manufacturing, mining, and electric and gas utilities). On the other hand, the use of IP means that transactions in materials

and intermediate products are explicitly accounted for in large measure, which is probably appropriate. Hence, we report, in 

addition to the results for CCI, tests based on the industrial production index. This provides a benchmark of the results for 

critics who argue that the leading index does not do well when based on real-time data (See Diebold and Rudebusch, 1991). 

4. HOW WELL DOES THE LEADING INDEX PREDICT? 

4.1 The Testing Models and Procedures 

Before proceeding with our primary task of evaluating the new procedure for estimating the U.S. Leading Index, it is logical 

to ask whether the old LI adds useful information to forecasts of basic measures of aggregate economy. This is particularly 

important in light of recent criticisms of the LI as a forecasting tool. At the same time we also investigate the new LI, but 

absent the timing improvements, which are taken-up in a separate section. This simplifies and clarifies the discussion by 

allowing us to examine the importance of timing by building on the analysis of the old LI and the new LI, first without and 

then with taking account of the timeliness issue. 

In approaching this issue we use the following standard for our tests: LI should improve on simple autoregressive forecasts 

for the monthly measures of aggregate activity: CCI or IP. We begin by asking whether the historical leading index 

improves on the standard forecast. This, of course, is a well-traversed path in the literature with well-expected results. 

A much more ambitious task is to construct an out-of-sample, real-time test of whether the leading index improves on the 

basic autoregressive forecast of aggregate economic activity (changes in CCI). To ensure that the leading indicator data 

conform to the data available at the time of original publication, we continue to employ the indexes and 

introduced in part 3 above, both of which consist of real-time data for the ten components on the present (1996) list of 

leading indicators. 

new

LI

^

old LI

 

12 The new estimates of monthly GDP by Macroeconomic Advisers, a private forecasting firm, were unavailable to us at the 

time, and are still limited to the 1990s and not widely accepted. 

13 An alternative transformation might be to use the value of the LI in the final month of each quarter, but we decided against 

this method because it would ignore the other monthly observations. 
Each of the 165 vintages in our real-time sample provides data for a forecast of monthly change in CCI (or IP). The first 

month in our sample period is December 1988, the last month is August 2002. Thus the sample period provides a series of 

165 estimated regressions for each forecast model. Each estimated model is based on observations starting in January 1959 

and ending in the following successive months: December 1988, January 1989,..., August 2002. 

Forecast regressions have the same structure for each vintage and are used to create a sequence of forecast errors. These 

forecast errors are summarized by an estimate of a mean square error based on differences between the forecast and the 

historical values of the corresponding actual growth rates in the target economy-wide aggregate. This procedure is repeated 

for a series of forecasting exercises that vary the forecast horizons (1,3, 6 months-ahead), spans over which growth is 

measured in the estimating equation (1,3,6, 9 months) and lags of the forecast variables (1,3, 6, 9). 

We use real-time data for LI so as to reproduce fairly the actual forecasting situation for the old and new leading index alike. 

For CCI, however, we use historical data so this target variable remains the same over all vintages and forecast models. Here 

we follow the common practice requiring the forecaster to use preliminary estimates to predict data incorporating future 

revisions in the target variable. This allows a comparison of our results to those of other studies that pursue the same 

strategy.14

The Forecast Models.

The forecast regression models are specified in changes in natural logarithms for both the coincident index and the leading 

indexes. This is done in order to avoid spuriously high correlations due to common trends that obtain in the levels of the 

indexes. As noted by Maximo Camacho and Gabriel Perez-Quiros (2002, pp. 62-63), the augmented Dickey-Fuller test 

cannot reject the null hypothesis of a unit root in the levels of the LI series but is consistent with stationarity of log 

differences of LI. Given the trends in the LI and the even stronger trend in CCI, the use of the change model is most 

appropriate (See Chart 3). But the monthly changes in CCI are quite volatile and those in LI even more so. Further, the lags 

of the former behind the latter index tend to be considerably longer than one month, even on average, and particularly long 

near the peak capacity utilization. Some coordinated extensions of the forecasts horizons and numbers and spans of the 

growth rates used seemed to be appropriate here, but we opted for a broad range of simple specifications so as to avoid any 

risks of data or model mining. Combining forecasts 3- and 6- months ahead with 3-, 6- and 9- month growth rates and the 

same numbers of lagged explanatory terms was deemed reasonably safe and sufficient for our present exploratory purposes.

Let ∆jCCI t denote the growth rate over the past j months ending in month t. The span j is allowed to vary from one to 3, 6, 

and 9 months. To provide a standard for evaluating the forecasting power of the leading index, a simple autoregressive 

equation is used in which ∆jCCIt

 is related to its own lags, ∆jCCIt-1 to ∆jCCIt-k, with the number of lagged terms, k, varying 

from one to 3, 6, and 9. 

 (3) 







=

=

∆ = + ∑ ∆ +

=

+−−

7,4,1

, 9,6,3,1

,1

1

1 ,1 1

p

jk

CCI CCI t

k

i

j t ji pit α β ε

There follow tests of whether adding lags of the old or new leading index to this equation reduces out-of-sample forecast 

errors. Equation (4) adds lags of the old index to the benchmark Eq. (3): 

 (4) 







=

=

∆ = + ∑ ∆ + ∑ ∆ +

=

+−−

=

+−−

7,4,1

, 9,6,3,1

,2

1

,2

1

2 ,2 1

p

jk

CCI CCI LI t

k

i

old

pitji

k

i

j t ji pit α β δ ε

Equation (5) adds lags of the new leading index instead: 

 (5) 







=

=

∆ = + ∑ ∆ + ∑ ∆ +

=

+−−

=

+−−

7,4,1

, 9,6,3,1

,3

1

,3 1

1

3 ,3 1

p

jk

CCI CCI LI t

k

i

new

pitji

k

i

j t ji pit α β δ ε

This gives 16 different combinations of the spans of growth rates (j) and number of lags (k) for each of the above three 

models. We repeat the same exercise for forecasts three and six months ahead (p = 4 and p = 7). This provides us with 48 

forecast exercises classified by three factors: the length of forecast horizon, the number of the lagged explanatory terms, and

transformation of the data (span of the growth rates). 

 

14See in particular Diebold and Rudebusch (1991). The revised data are believed to be closer to the truth. However, the use of 

revised data in lagged values of the dependent variable gives the autoregressive element an advantage vis-à-vis the 

contribution of the leading index term which is based on preliminary data. Assessments of the forecasts thus mix forecasting 

and measurement errors. This approach makes it more difficult for the LI to improve the forecast. 

Page 73
No effort was made to optimize the predictive regression specifications (this belongs in another paper). Rather, we tried to 

get a sufficiently comprehensive and diverse picture of what the alternative leading indexes –historical and real time, old and

new – can contribute, even under relatively unfavorable conditions. This approach – looking at a broad and symmetric set of 

models – was modified in one way: Only results for models for which the span of growth in the variables in the model is 

greater than or equal to the forecast horizon are reported. Longer forecasts are not well served by short growth rates and the 

use of short spans in the longer forecasts provided unreliable results. Nonetheless, we include these clearly inferior forecast

exercises when we calculate the summary MSE’s across all the models and forecast horizons. 

 

4.2 Out of Sample Forecasts of Changes for Common Forecast Horizons.

Table 3 reports the mean square errors (MSE) for the forecasts which use growth rate spans of one, three, six, and nine 

months (j = 1,3,6,9) and one, three, six, and nine month lags for each explanatory variable (k = 1,3,6,9). It covers 36 forecast 

exercises, 16 for one-month ahead, 12 for 3-month ahead, and 8 for 6- month-ahead forecasts. This covers all possible

models where the span of the forecast variables is greater than or equal to the forecast horizon. The reported entries are MSE 

x105

. The table compares the accuracy of one, three, and six month ahead autoregressive forecasts of changes in CCI 

(column 4) with the forecast accuracy of models that use, in addition, the lagged changes in LI: the historical, old, and new 

indexes (columns 5, 6, and 7, respectively). 

The equations with the historical index reduce the MSE’s in all cases for the six-month ahead forecasts and in all but one case

each for the one-month and three-month ahead forecasts (cf. columns 4 and 5). The exceptions are the two shortest forecasts 

with models that use only one lag. This is consistent with the often-noted view among leading index users that the shortest 

changes do not produce good forecasts. Nonetheless, the difference between these entries and the corresponding entries in 

column 4 is very small and probably of low significance. Compared with the old and new real-time leading indexes, the 

historical index delivers the most accurate forecasts throughout (cf. column 5 with columns 6 and 7). 

These findings confirm the prior results and expectations. Earlier studies repeatedly found the historical index to be a good 

forecasting tool, whereas some questioned the usefulness of the real time indexes. The historical leading index, like the 

target historical coincident index (CCI), is essentially free of revision (measurement) errors; in contrast, a real-time leading 

index is preliminary as its critical latest values are subject to revisions. This is true of the new as well as the old real-time 

index. 

Adding the lagged changes in the old index to the autoregressive equations reduces the MSE’s in 30 out of the 36 cases (cf. 

columns 4 and 6). The six adverse results all refer to forecasts with short growth rate spans, mostly of one month. Much the 

same applies to the equations that include lagged changes in the new index, except that here in two cases MSE’s improved 

among the 6-month forecasts. 

What is clear is that the LI reduces forecast errors across most models and forecast horizons. In addition the costs of the new

procedure do not appear large, based on a comparison with the MSE’s of the old and historical LI. This suggests these costs 

will be outweighed by the gains to the timeliness of the new index, an issue we turn to next. 

4.3 More Timeliness Implies a Gain in Forecasting Accuracy 

In the last section we neglected the fact that the identity of the target period “one month ahead” means something different 

for the old index than for the new index, which is much prompter. Here we address this issue explicitly to evaluate the gain 

from the timelier procedure 

Page 74

The old leading index is one month behind the new one (see section II.B.). For example, Chart 1 shows that the first vintage 

in our real-time sample gives a new index forecast for January 1989, but the old index based on the same data would predict 

instead December 1988. To see how this gain in timeliness affects the relative predictive performance of the new LI vs. the 

old LI, we now evaluate how the two indexes forecast for sequences with the same target periods.15

 

We deal with the problem of using ∆jLIold

t-2 to forecast ∆jCCIt

 in two ways. The first is a direct (one-step) prediction in the 

regression framework: ∆jLIold

t-2 and ∆jCCIt-2 are used to jointly predict ∆jCCIt

 . The second is a two-step prediction: a 

 

15 Let us restate that this cannot be done with the aid of Table 3, which shows how the two indexes perform over the same 

forecast horizons but with different target periods. 
second-order autoregressive model is employed to estimate ∆jLIold

t-1 and then the latter value, along with ∆jCCIt-1, is used to 

predict ∆jCCIt

. This provides a forecast consistent with the simple autoregressive process used throughout this analysis. 

Page 75

Table 4 retains the format of Table 3 and restates the MSE’s for the equations with lagged CCI and LInew terms. As would be 

expected, using the equations with ∆jLIold

t-2 to predict ∆jCCIt instead of ∆jCCIt-1 results mostly in substantially higher errors. 

The MSE’s in Table 3, column 6, are lower than their counterparts in Table 4, column 5 and 6, in 67 out of 72 cases (they 

lose out to the direct forecasts in lines 1-4, and to the two-step forecasts in line 1). Whereas the predictions with the old 

index terms are entirely competitive in Table 3, they are clearly not in Table 4, where the new index outperforms the old 

index heavily. 

A comparison of the direct and two-step forecasts with the old index discloses a very mixed picture (cf. columns 5 and 6). 

For forecasts three months ahead, the two-step ahead predictions are more accurate, but for the shorter forecast horizon, the 

direct predictions tend to be more accurate. For the longer horizon, the picture is mixed, with the two-step dominating for the

9-month and the direct for the 6-month spans. The overall score here is even, 18 for the direct and 18 for the two-step 

forecasts. 

Table 5 confirms for all of our real-time out-of-sample forecasts of log changes in the U.S. Current Conditions Index between 

1989-2002 that the U.S. Leading Index improves on the autoregressive benchmark model. The overall MSE’s (averages for 

16 models) are lower for the regressions with lagged CCI and LI terms than for the regressions with lagged CCI terms only. 

This is true for one-month, three-month, and six-month ahead predictions alike, and not only for the historical index (column 

2) but even for the real-time new index (column 3) and old index when differences in the targeted calendar months are 

ignored (column 4). Only when the same calendar months are targeted do the MSE’s of the equations using the old index 

data exceed the autoregressive benchmark MSE’s (cf. cols. 5 and 6 with col. 1). The average standard deviations show much 

the same relations as the average MSE’s (see the entries in parentheses). To facilitate the comparisons, Table 5 provides also

the ratios of the MSE’s of the models with the LI terms to the autoregressive model. 

We conclude that there can be no doubt about the incremental (net) predictive content of the leading index, even when its 

preliminary real-time data are used to forecast the “final” or “true” data for the coincident index. Section IV.E shows the 

same for the forecasts of other measures of the industrial production index. The contrary findings in the literature are, we 

strongly suspect, explained by the use of leading indexes that incorporate definitional (composition) changes rather. 

4.4 More on the Properties of Forecasts with Leading Indicators 

The two basic findings of our study, then, are: (1) the leading indicators, properly selected and collected in an index, convey

significant predictive information about the economy’s change in the next several months, beyond what can be learned from 

the economy’s recent past. (2) The new index is dramatically more accurate than the old index in forecasting growth of CCI 

in the same impending target months. In addition, our results inspire confidence because they make sense in the light of what 

is known from many past studies about some tendencies common in short-term economic forecasts. 

Thus, a very general property here is perhaps the simplest one: the longer the forecast horizon, the larger the error. Tables 3 

and 4 clearly conform to this rule when one compares forecasts with all but the shortest growth rate spans (compare the one, 

three, and six-month horizons). We would also expect that the larger the number of explanatory (lagged) terms, the smaller 

generally will be the MSE’s. This effect also tends to be a characteristic of Tables 3 and 4. 

We also observe that, given the forecast horizon and lags, MSE’s generally increase with the span in months over which the 

growth rates are calculated. This is a very strong tendency, in the range of 20-80 percent. This is true for each of the four 

models covered in columns 4-7. 

Such a steep rise in the errors may seem alarming, but in fact it is not and has an easy explanation. The longer its span (j), the 

larger is the growth rate ∆jCCIt reflecting the economy’s upward trend. The means of ∆1, ∆3, ∆6, and ∆9 for our dependent 

variable are 0.0021, 0.0066, 0.0132, and 0.0220, respectively. Thus, ∆jCCI grows a little faster in size than in length, e.g., ∆6, 

is 6.3 times ∆1 and ∆9 is 10.5 times ∆1. This is a faster progression than that of the corresponding MSE’s. Hence the errors 

actually tend to decrease in relative terms, while increasing in absolute terms. Table 6 uses of the ratios of root mean square 

errors of the forecasts to the means of ∆jCCI to show that the so measured relative MSE’s drop steadily as j and k increase. 

The declines are surprisingly large and uniform for the different forecast horizons and models. This tempers the first 

impression that increases in the spans of change and the number of lagged terms affect the accuracy of the forecasts 

adversely. 
Page 76

4.5 The Leading Index Also Helps to Predict Industrial Production 

In European countries, it is mainly the index of industrial production that is used as the principal target of leading index 

forecasts, and some U.S. analysts prefer it as well (despite the fact that it is narrow, declining in coverage, and itself only one 

of the components of CCI). For comparability with this work, therefore, we add Tables 7 and 8, which parallel for U.S. 

industrial production what Tables 3 and 4 show, respectively, for CCI. The findings are very similar. 

Table 7 shows that the historical LI improves on the autoregressive benchmark forecasts in all but two of the 36 cases listed. 

(There are no Xs in columns 5, 6, and 7, respectively). This is very similar to the forecasts of CCI growth (see Table 3 and 

section IV.B above). The good representation of manufacturing by the leading indicators tends to favor forecasts of industrial 

production; the processes of component selection and construction of LI may be favoring the forecasts of CCI. 

Table 8 shows that the old index performs generally much worse than the new index when the same calendar month is 

targeted by both. As indicated by the Xs, the direct forecasts with LIold yield larger MSE’s than their counterparts with LInew

in all but two of the 36 cases (note that the exceptions are six-month forecasts with short growth rates; see column 5). For the 

two-step forecasts with LIold, the score is 32 worse than the forecasts with LInew and four better (all of the latter looking sixmonths ahead; see column 6). Once more, all of this parallels the results for the CCI predictions reported in Table 4. 

5. CONCLUDING THOUGHTS

The new procedure for calculating the U.S. Leading Index combines seven current financial and non-financial indicators with 

simple forecasts of three other indicators that are only available with lags. This makes the new index much timelier and 

demonstrably superior to the old index with the same components. The latter had eschewed forecasting but at the expense of 

being less complete, less timely, and less accurate for its targets. We show this directly by evaluating forecasts for the same

calendar months with both the new and old index. The more efficient and more complete use of the available data, along with 

a workable procedure to fill temporarily the gaps due to missing data, combine to provide a better leading index. 

Aside from the gains to the new procedure, the analysis also shows, using real time out-of-sample evaluation methods, that 

the index of leading indicators provides useful forecasting information. This appears to contradict the empirical evidence 

from several recent studies that find fault with the ex ante performance of the composite index of leading economic 

indicators. 

A priori we expected that the poor real time performance found by some researchers might have been caused by the leading 

index not having been as up-to-date as the financial indicators. The old procedure for calculating the index left out the most

recent financial data, which are likely to provide first signals of weakening and downturns in profits and early investment and

credit commitments.16 The real-time out-of-sample tests presented in this paper show that the new more timely leading index 

contains useful ex-ante information for predicting fluctuations in economic activity. 

We expect the leading index to do better than a few components because the sources and profiles of business cycles differ 

over time. This means that a leading index that contains both the financial and the real indicators should be better than its 

individual components over time, and according to many historical tests actually is. The more comprehensive and 

diversified, and the better selected, its components, the more effective the index. In some periods, financial indicators 

outperform real activity indicators in their ability to lead; in other periods, the opposite is the case. Thus, it is unlikely that 

the composite index would be inferior to its financial sub-index over more than short periods. 

A full examination of this issue is well beyond the scope of this paper. We are now beginning a deeper investigation of the 

problem of how to use the indicators best by extending the sample periods to include more cyclical events and concentrate on 

recessions and recoveries; also by improving the specifications of our forecasting models. We are also extending the 

examination to countries outside the United States. But in light of our results to date, we conclude that our expectation that

the composite index methodology provides a useful tool for predicting and assessing business cycles is still a very viable 

hypothesis. 

 

16 On the empirics and theory of interconnected movements in real, financial, and expectational variables, see Zarnowitz 

(1999), esp. 80-82; also Evans, et al. (1998). 
APPENDIX: THE LEADING INDEX ALSO HELPS TO PREDICT REAL GDP 

Page 77

Many economists prefer real GDP as the broadest and comprehensive measure of aggregate economic activity. Although, as 

discussed above, the coincident index (CCI) as a monthly measure of economic activity is highly correlated with real GDP 

and has some advantages over real GDP, we also repeated our tests to see if the leading index helps to predict growth in real 

GDP. For completeness, therefore, this appendix presents Table A1, which parallels Table 3 in the text. In order to perform 

our tests with real GDP we transformed LI into the quarterly frequency by taking the average of monthly observations within 

a quarter as noted in section III.D of the paper. This avoids problems with interpolating real GDP to make it monthly and 

uses all available LI information in a given quarter. The forecasting exercises are analogous to those presented in section 

IV.A. The findings are very similar to those reported earlier in the paper. 

Let ∆jRGDP t denote the growth rate over the past j quarters ending in quarter t. The span j is allowed to vary from one to 2, 

3, and 4 quarters. To provide a standard for evaluating the forecasting power of the leading index, a simple autoregressive 

equation is used in which ∆jRGDPt

 is related to its own lags, ∆jRGDPt-1 to ∆jRGDPt-k, with the number of lagged terms, k, 

varying from one to 2, 3, and 4. 







=

=

∆ = +∑ ∆ +

=

+−−

4,3,1

, 4,3,2,1

,1

1

1 ,1 1

p

jk

RGDP RGDP t

k

i

j t ji pit α β ε (A1)

There follow tests of whether adding lags of the old or new leading index to this equation reduces out-of-sample forecast 

errors. Equation (A2) adds lags of the old index to the benchmark Eq. (A1): 







=

=

∆ = +∑ ∆ +∑ ∆ +

=

+−−

=

+−−

4,3,1

, 4,3,2,1

,2

1

,2

1

2 ,2 1

p

jk

RGDP RGDP LI t

k

i

old

ji pit

k

i

j t ji pit α β δ ε (A2) 

Equation (A3) adds lags of the new leading index instead: 







=

=

∆ = +∑ ∆ +∑ ∆ +

=

+−−

=

+−−

4,3,1

, 4,3,2,1

,3

1

,3 1

1

3 ,3 1

p

jk

RGDP RGDP LI t

k

i

new

ji pit

k

i

j t ji pit α β δ ε (A3) 

This gives 16 different combinations of the spans of growth rates (j) and number of lags (k) for each of the above three 

models. We repeat the same exercise for forecasts two and three quarters ahead (p = 3 and p = 4). This provides us with 48 

forecast exercises classified by three factors: the length of forecast horizon, the number of the lagged explanatory terms, and

transformation of the data (span of the growth rates). 

Table A1 reports the mean square errors (MSE) for the forecasts which use growth rate spans of one, two, three and four 

quarters and one, two, three and four quarter lags for each explanatory variable. It covers 36 forecast exercises, 16 for onequarter ahead, 12 for 3-quarter ahead, and 8 for 3-quarter-ahead forecasts. This covers all possible models where the span of 

the forecast variables is greater than or equal to the forecast horizon. The reported entries are MSE x105

. The table compares 

the accuracy of one, two, and three quarter ahead autoregressive forecasts of changes in real GDP (column 4) with the 

forecast accuracy of models that use, in addition, the lagged changes in LI: the historical, old, and new indexes (columns 5, 6, 

and 7, respectively). 

The equations with the historical index reduce the MSE’s in all cases for the two- and three-quarter ahead forecasts and in all

but two cases for the one-quarter ahead forecasts (cf. columns 4 and 5). As before, compared with the old and new real-time 

leading indexes, the historical index delivers the most accurate forecasts throughout (cf. column 5 with columns 6 and 7). 

Adding the lagged changes in the old index to the autoregressive equations reduces the MSE’s in 27 out of the 36 cases (cf. 

columns 4 and 6). The nine adverse results all refer to the shortest, i.e., one-quarter ahead forecasts, and all use the shortest, 

i.e., one and two quarter growth rates. Much the same applies to the equations that include lagged changes in the new index, 

where adding the lagged changes in the old index to the autoregressive equations reduces the MSE’s in 28 out of the 36 cases 

(cf. columns 4 and 7). 

The LI reduces forecast errors across most models and forecast horizons. In addition, the reductions in MSE’s when the new 

index is used are slightly better in almost all cases (cf. columns 6 and 7) suggesting the new procedure has improved the 

information content of the LI. 
Table A1: Out-of Sample Forecasts of Quarterly Growth Rates in RGDP, U.S. 1989- 2002: 

Contribution of Autoregression and the Leading Index*

 

 

Span of Months over 

which Growth Rate is 

Calculated (j) 

Number of Lags of 

Growth Rates of 

RGDP, LI (1 

to k) 

Mean Square Errors (MSE) for Model with Lagged Terms in 

Line 

RGDP only RGDP and LIh 

(historical index)

RGDP and LIold 

(real-time, old 

index) 

RGDP and LInew 

(real-time, more 

timely index)

(1) (2) (3) (4) (5) (6) (7) 

One Quarter Ahead Forecasts 

1 1 1 2.919 2.929*

 3.134* 3.109*

2 1 2 2.805 2.763 3.038*

 2.966*

3 1 3 2.817 2.680 2.955*

 2.865*

4 1 4 2.795 2.675 2.941*

 2.868*

5 2 1 4.043 3.955 4.425*

 4.217*

6 2 2 3.666 3.864*

 4.313* 4.168*

7 2 3 3.395 3.321 3.634*

 3.537*

8 2 4 3.334 3.177 3.455*

 3.381*

9 3 1 5.251 4.207 4.434 4.238 

10 3 2 4.833 4.008 4.330 4.113 

11 3 3 4.456 3.899 4.336 4.111 

12 3 4 3.900 3.550 3.973*

 3.777 

13 4 1 5.624 4.391 4.430 4.362 

14 4 2 4.753 4.146 4.224 4.209 

15 4 3 4.448 4.037 4.126 4.112 

16 4 4 4.523 4.118 4.223 4.216 

 Two Quarter Ahead Forecasts

17 2 1 7.806 7.053 7.477 7.269 

18 2 2 7.762 7.023 7.606 7.319 

19 2 3 7.783 6.965 7.457 7.234 

20 2 4 7.859 6.910 7.271 7.060 

21 3 1 11.257 9.445 9.883 9.362 

22 3 2 9.563 8.513 9.296 8.746 

23 3 3 9.608 8.113 8.959 8.384 

24 3 4 9.633 8.369 9.241 8.743 

25 4 1 13.771 10.471 10.536 10.167 

26 4 2 10.949 9.115 9.278 9.005 

27 4 3 10.705 9.127 9.323 9.086 

28 4 4 10.581 9.307 9.426 9.273 

Three Quarter Ahead Forecasts

29 3 1 16.368 14.623 14.595 14.234 

30 3 2 16.217 13.879 14.115 13.581 

31 3 3 16.665 14.013 14.582 14.024 

32 3 4 16.945 14.672 15.274 14.845 

33 4 1 21.795 18.571 18.735 18.172 

34 4 2 18.892 16.680 17.035 16.614 

35 4 3 19.216 16.726 17.094 16.679 

36 4 4 19.077 17.210 17.546 17.239 

*NOTE: LI converted to quarterly frequency by using average of three months as the quarterly observation. 

n

n

t

t

e

MSE

∑

=

=

1

2

, t = 1,...,55. Because are 

very small, the entries in columns 4-7 show MSEx105

. The x’s denote the cases where the models with lagged LIold and LInew terms are less accurate than the 

autoregressive model, that is, where the entries in columns 4 and 6 are smaller than the corresponding entries in column 4.

2

t

e

Page 78
 

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Page 79

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_____. “The Leading Indicators in Historical Perspective.” Business Cycle Indicators, 1999b, 4(11), pp. 3-4. 

McGuckin Robert H.; Ozyildirim, Ataman, and Zarnowitz, Victor. “The Composite Index of Leading Economic Indicators: 

How to Make It More Timely.” National Bureau of Economic Research (Cambridge, MA) Working Paper No. 8430, August 

2001. 

Nilsson, Ronny. “OECD Leading Indicators.” Organization for Economic Co-operation and Development Economic Studies, 

1987 No. 9. 

Orphanides, Athanasios. “Monetary Policy Rules Based on Real-time Data.” American Economic Review, September 2001, 

91(4), pp. 964-985. 

Zarnowitz, Victor. “On Functions, Quality, and Timeliness of Economic Information.” Journal of Business, 1982, 55, pp. 87-

119. 

_____. Business Cycles: Theory, History, Indicators, and Forecasting, Chicago, Illinois: The University of Chicago Press, 

1992, pp. 316-356. 

_____. “Theory and History Behind Business Cycles: Are the 1990s the Onset of a Golden Age?” Journal of Economic 

Perspectives, Spring 1999, 13(2), pp. 69-90. 

_____. “Coincident Indicators and the Dating of Business Cycles.” Business Cycle Indicators, 2001a, 6(8), pp. 3-4. 

_____. “The Record of the U.S. Leading Index and Its Components.” Business Cycle Indicators, 2001b, 6(9), pp. 3-4. 
Table 1: Data Availability and Old/New Index Publication Schedules: An Example

 

Available in March: 

Data for 

Included in March 

Publication Data for 

Line Indicator Seriesa January February 

January 

Old

t

I

February 

New

t

I

ˆ

(1) (2) (3) (4) (5) (6) 

1 New orders, consumer goods and 

materials Y1 Yes No Yes Yes 

(Estimated) 

2 New orders, nondefense capital 

goods Y2 Yes No Yes Yes 

(Estimated) 

3 Money supply, M2 Y3 Yes No Yes Yes 

(Estimated) 

4 

Average weekly hours, 

manufacturing X1 Yes Yes Yes Yes 

5 Ave. weekly initial claims for unemp. 

insurance X2 Yes Yes Yes Yes 

6 Vendor perf., slower deliveries 

diffusion index X3 Yes Yes Yes Yes 

7 Building permits, new private 

housing units X4 Yes Yes Yes Yes 

8 Stock prices, 500 common stocks X5 Yes Yes Yes Yes 

9 Interest rate spread X6 Yes Yes Yes Yes 

10 Index of consumer expectations X7 Yes Yes Yes Yes 

a

 Each series is identified with title first and by symbol second. Series in lines 1,2 ,and 3 are in constant 1996 

dollars, calculated by The Conference Board using chain weighted price deflators. Series 5 is used in inverted 

form. The series are seasonally adjusted, except those that do not require seasonal adjustment (e.g., the S&P 

500 stock price index). For complete information, including sources, see The Conference Board Business 

Cycle Indicators Handbook (2001). 

Page 80
Table 2 

Dates of Cyclical Turns in Old and New Leading Indexes, 

Six Selected Vintages, 1960 – 2002

Line 

(1) 

Vintages 

(2) 

Trough 

(3) 

Peak 

(4) 

1 Jan-89, Nov-91, Jul-98, Mar-00, Jun-02, Aug-02 3/1960 3/1966 

2 Jan-89, Nov-91, Jul-98, Mar-00, Jun-02, Aug-02 3/1967 1/1969 

3 Jan-89, Nov-91, Jul-98, Mar-00, Jun-02, Aug-02 4/1970a 2/1973b 

4 Jan-89, Nov-91, Jul-98, Mar-00, Jun-02, Aug-02 2/1975 4/1978 

5 Jan-89, Nov-91, Jul-98, Mar-00, Jun-02, Aug-02 4/1980 10/1980 

6 Jan-89, Nov-91, Jul-98, Mar-00, Jun-02, Aug-02 3/1982c 6/1988 

7 Nov-91, Jul-98, Mar-00, Jun-02, Aug-02 6/1989d 1/1990 

8 Nov-91, Jul-98, Mar-00, Jun-02, Aug-02 1/1991 12/1994 

9 Jul-98, Mar-00, Jun-02, Aug-02 5/1995 1/2000 

10 Aug-02 3/2001 

a

 For both the old and the new indexes, the January 1989 series show a trough in October 1970, 

not April 1970. This exception reflects a double-trough pattern and a revision shifting the low 

from October to April. 

b

 For both the old and the new indexes, the January 1989 and the November 1991 vintage series 

have peaks in January 1973, not February 1973. 

c

 For both the old and the new indexes, the January 1989 series show troughs in January 1982, 

not March 1982. 

d

 For both the old and the new indexes, the November 1991 vintage series have troughs in July 

1989, not June 1989. 

Page 81
Table 3 

Out-of Sample Forecasts of Growth in the Current Conditions Index, U.S. Jan. 1989- Sep.2002:

Contribution of Autoregression and the Leading Index 

 

Page 82

Span of Months over 

which Growth Rate 

is Calculated 

(j) 

Number of Lags 

of Growth Rates 

of CCI, LI 

(1 to k) 

Mean Square Errors (MSE) for Model with Lagged Terms in 

Line 

CCI only CCI and LIh 

(historical index)

CCI and LIold 

(real-time, old 

index) 

CCI and LInew 

(real-time, more 

timely index)

(1) (2) (3) (4) (5) (6) (7) 

One Month Ahead Forecasts 

1 1 1 0.863 0.873x

 0.877x 0.863 

2 1 3 0.747 0.732 0.752x

 0.739 

3 1 6 0.764 0.719 0.733 0.729 

4 1 9 0.770 0.713 0.723 0.719 

5 3 1 1.044 1.022 1.063x

 1.061x

6 3 3 1.090 1.074 1.104x

 1.102x

7 3 6 0.953 0.904 0.939 0.940 

8 3 9 0.949 0.882 0.907 0.905 

9 6 1 1.207 1.099 1.133 1.121 

10 6 3 1.299 1.180 1.202 1.193 

11 6 6 1.351 1.235 1.282 1.271 

12 6 9 0.929 0.850 0.879 0.867 

13 9 1 1.500 1.333 1.361 1.356 

14 9 3 1.543 1.369 1.386 1.381 

15 9 6 1.566 1.397 1.388 1.392 

16 9 9 1.574 1.369 1.339 1.337 

Three Month Ahead Forecasts 

17 3 1 2.436 2.486x

 2.663x 2.656x

18 3 3 2.608 2.440 2.629x

 2.622x

19 3 6 2.561 2.281 2.459 2.462 

20 3 9 2.549 2.088 2.272 2.284 

21 6 1 3.549 3.058 3.283 3.315 

22 6 3 3.393 2.942 3.188 3.196 

23 6 6 2.999 2.675 2.868 2.874 

24 6 9 2.913 2.430 2.592 2.576 

25 9 1 4.734 3.517 3.696 3.745 

26 9 3 4.488 3.435 3.642 3.689 

27 9 6 4.321 3.398 3.600 3.643 

28 9 9 3.968 3.174 3.333 3.381 

Six Month Ahead Forecasts 

29 6 1 8.172 7.768 8.039 8.214x

30 6 3 8.174 7.537 7.904 8.208x

31 6 6 8.088 7.182 7.422 7.703 

32 6 9 8.381 7.124 7.164 7.404 

33 9 1 11.713 9.385 9.362 9.583 

34 9 3 10.598 8.585 8.811 9.030 

35 9 6 10.387 8.336 8.457 8.717 

36 9 9 10.473 8.369 8.462 8.729 

Note: 

n

n

t

t

e

MSE

∑

=

=

1

2

, t = 1,...,165. Because e are very small, the entries in columns 4-7 show MSEx105

. The x’s denote the cases where 

the models with lagged LIold and LInew terms are less accurate than the autoregressive model, that is, where the entries in columns 4 and 6 are 

smaller than the corresponding entries in column 4. All the differences between MSE’s in column 4 and either column 5, 6 or 7 for one month 

ahead forecasts are significant at the 5 % level based on the encompassing test statistic (ENC_NEW) developed by Clark and McCracken (2001) 

to test for one-step ahead forecast accuracy in nested models. The test statistic is not applicable to 3 and 6-month ahead forecasts, but research is 

underway to develop the appropriate tests for multi-step ahead forecasts. 

2

t
Table 4 

Comparable Forecasts of Growth in the Current Conditions Index Are More Accurate for the New Index Than for the 

Old Index, Jan. 1989- Sep.2002 

 

Span of Months over 

which Growth Rate 

is Calculated (j) 

Number of Lags of 

Growth Rates of 

CCI, LI (1 to k) 

Mean Square Errors (MSE)a

For Model with Lagged Terms in 

Line 

CCI and LInew b CCI and LIold

Direct 

CCI and LIold

Two-Step 

(1) (2) (3) (4) (5) (6) 

One Month Ahead Forecasts

1 1 1 0.863 0.724x

 0.816x

2 1 3 0.739 0.702x

 0.760 

3 1 6 0.729 0.716x

 0.780 

4 1 9 0.719 0.691x

 0.752 

5 3 1 1.061 1.709 1.230 

6 3 3 1.102 1.753 1.474 

7 3 6 0.940 1.601 1.383 

8 3 9 0.905 1.428 1.452 

9 6 1 1.121 1.940 1.472 

10 6 3 1.193 1.985 1.632 

11 6 6 1.271 1.942 1.705 

12 6 9 0.867 1.568 1.745 

13 9 1 1.356 2.204 1.724 

14 9 3 1.381 2.188 1.761 

15 9 6 1.392 2.272 1.785 

16 9 9 1.337 2.068 1.814 

Three Month Ahead Forecasts 

17 3 1 2.656 2.870 3.164 

18 3 3 2.622 2.813 3.057 

19 3 6 2.462 2.632 2.755 

20 3 9 2.284 2.409 2.492 

21 6 1 3.315 4.929 5.111 

22 6 3 3.196 4.944 5.761 

23 6 6 2.874 4.346 5.711 

24 6 9 2.576 3.874 5.516 

25 9 1 3.745 5.252 5.900 

26 9 3 3.689 5.167 6.630 

27 9 6 3.643 4.990 6.462 

28 9 9 3.381 4.647 6.602 

Six Month Ahead Forecasts 

29 6 1 8.214 8.514 9.264 

30 6 3 8.208 8.367 7.103 

31 6 6 7.703 8.017 6.893 

32 6 9 7.404 7.927 6.662 

33 9 1 9.583 11.631 12.290 

34 9 3 9.030 11.072 11.900 

35 9 6 8.717 10.510 12.227 

36 9 9 8.729 10.971 13.325 

Note: 

n

n

t

t

e

MSE

∑

=

=

1

2

, t = 1,...,165. Because e are very small, the entries in columns 4-6 show MSEx105. The entries in column 4 are 

identical to those in Table 3, column 7. The x’s denote the cases where the models with lagged LIold terms are more accurate than the models 

with lagged LInew terms, that is, where the entries in columns 5 and 6 are smaller than the corresponding entries in column 4. 

2

t

Page 83
 

Table 5 

Out of Sample Forecasts of Log Changes in the U.S. Current Conditions Index, All 16 Models: A Summary: January 1989- August 2002

(1) (2) (3) (4) (5) (6) (7) (8)

 

 

Page 84

Forecast Horizon 

(Number of Months 

Ahead)

Lagged Dependent Variables Used in the Regression Model 

 

 

 

CCI and LIold

CCI only CCI and LIh CCI and LInew Different

targets 

Same Target 

 Direct

Forecast 

Two-step 

forecast 

Line 

1 One Month 1.134 

(0.303) 

1.047 

(0.245) 

1.061 

(0.243) 

1.067 

(0.242) 

1.593 

(0.578) 

1.393 

(0.401) 

2 

 

 

Three Months 2.718 

(1.375) 

2.305 

(1.024) 

2.470 

(1.107) 

2.305 

(1.024) 

3.249 

(1.747) 

3.901 

(2.292) 

3 Six Months 5.711 

(4.117) 

4.980 

(3.304) 

5.225 

(3.472) 

5.083 

(3.365) 

5.819 

(4.167) 

5.932 

(4.648) 

MSE Ratio to Autoregressive Model 

4 One Month 1.000 0.923 0.936 0.941 1.405 1.228 

5 

 

 

Three Months 1.000 0.848 0.909 0.848 1.185 1.435

6 Six Months 1.000 0.872 0.915 0.890 1.019 1.039

 Percent of models with smaller MSE’s than the autoregressive model 

7 One Month - 93.75 87.50 75.00 - - 

8 

 

Three Months - 93.75 62.50 56.25 - - 

9 Six Months - 62.50 43.75 62.50 - - 

Note: The entries in lines 1, 2, and 3 are averages of the MSE’s in each category; those in parentheses are the corresponding average standard deviations. The 

entries in lines 4, 5, and 6 are ratios: the average MSE in each class is divided by its counterpart for autoregressive model (set equal to 1.000 in column 3). The 

entries in 7, 8, and 9 (columns 4, 5, and 6) are percentages of the regression models in each category with MSE’s smaller than those of the autoregressive 

benchmark model.
Page 85
Table 6 

Relative Errors of Out-of-Sample Forecasts of Growth in the Current Conditions Index, U.S. 

Jan. 1989- Sep.2002:

 

Page 86

Span of Months over 

which Growth Rate 

is Calculated 

(j) 

Number of Lags 

of Growth Rates 

of CCI, LI 

(1 to k) 

For Model with Lagged Terms in 

Line 

CCI only CCI and LIh 

(historical index)

CCI and LIold 

(real-time, old 

index) 

CCI and LInew 

(real-time, more 

timely index)

(1) (2) (3) (4) (5) (6) (7) 

One Month Ahead Forecasts 

1 1 1 1.328 1.335 x 1.338 x 1.328 

2 1 3 1.235 1.223 1.239 x 1.229 

3 1 6 1.249 1.212 1.224 1.220 

4 1 9 1.254 1.207 1.215 1.212 

5 3 1 0.488 0.483 0.493 x 0.492 x

6 3 3 0.499 0.495 0.502 x 0.501 x

7 3 6 0.466 0.454 0.463 0.463 

8 3 9 0.465 0.449 0.455 0.454 

9 6 1 0.264 0.252 0.256 0.255 

10 6 3 0.274 0.261 0.264 0.263 

11 6 6 0.279 0.267 0.272 0.271 

12 6 9 0.232 0.222 0.225 0.224 

13 9 1 0.176 0.166 0.167 0.167 

14 9 3 0.178 0.168 0.169 0.169 

15 9 6 0.180 0.170 0.169 0.169 

16 9 9 0.180 0.168 0.166 0.166 

Three Month Ahead Forecasts 

17 3 1 0.746 0.753 x 0.780 x 0.778 x

18 3 3 0.771 0.746 0.775 x 0.773 x

19 3 6 0.764 0.721 0.749 0.750 

20 3 9 0.763 0.690 0.720 0.722 

21 6 1 0.453 0.420 0.436 0.438 

22 6 3 0.443 0.412 0.429 0.430 

23 6 6 0.416 0.393 0.407 0.408 

24 6 9 0.410 0.375 0.387 0.386 

25 9 1 0.312 0.269 0.276 0.278 

26 9 3 0.304 0.266 0.274 0.276 

27 9 6 0.298 0.264 0.272 0.274 

28 9 9 0.286 0.256 0.262 0.264 

Six Month Ahead Forecasts 

29 6 1 0.687 0.670 0.682 0.689 x

30 6 3 0.687 0.660 0.676 0.689 x

31 6 6 0.684 0.644 0.655 0.667 

32 6 9 0.696 0.642 0.643 0.654 

33 9 1 0.491 0.440 0.439 0.444 

34 9 3 0.467 0.420 0.426 0.431 

35 9 6 0.462 0.414 0.417 0.424 

36 9 9 0.464 0.415 0.417 0.424 

Note: The entries in column 4-7 represent ratios of root mean square errors of the forecasts to the means of the dependent variable 

(∆jCCIt). The x’s mark the cases where the relative errors are on the average smaller for the autoregressive model than for the model

with the lagged leading index terms. The x’s in this table are in the same positions as in the corresponding Table 3; but note that these 

differences tend to be small and of doubtful significance. 
Table 7 

Out-of Sample Forecasts of Growth in the Industrial Production Index, U.S. Jan. 1989- Sep.2002: 

Contribution of Autoregression and the Leading Index 

 

Span of Months over 

which Growth Rate 

is Calculated 

(j) 

Number of Lags 

of Growth Rates 

of IP, LI 

(1 to k) Mean Square Errors (MSE) for Model with Lagged Terms in 

Line 

IP only IP and LIh 

(historical index)

IP and LIold 

(real-time, old 

index) 

IP and LInew 

(real-time, more 

timely index)

(1) (2) (3) (4) (5) (6) (7) 

One Month Ahead Forecasts 

1 1 1 2.639 2.636 2.633 2.577 

2 1 3 2.533 2.235 2.261 2.247 

3 1 6 2.602 2.329 2.350 2.354 

4 1 9 2.586 2.224 2.211 2.225 

5 3 1 3.558 2.971 3.032 3.054 

6 3 3 3.657 3.309 3.374 3.369 

7 3 6 3.338 2.936 2.972 2.989 

8 3 9 2.899 2.501 2.512 2.520 

9 6 1 4.773 3.746 3.775 3.770 

10 6 3 4.776 3.961 3.993 4.006 

11 6 6 4.948 4.115 4.118 4.120 

12 6 9 3.641 2.970 3.009 3.009 

13 9 1 4.394 3.440 3.509 3.470 

14 9 3 4.144 3.423 3.458 3.461 

15 9 6 3.994 3.458 3.440 3.442 

16 9 9 4.055 3.537 3.412 3.410 

Three Month Ahead Forecasts 

17 3 1 10.642 9.216 9.579 9.719 

18 3 3 10.941 9.567 9.888 9.970 

19 3 6 10.480 8.703 8.979 9.156 

20 3 9 9.913 8.078 8.257 8.502 

21 6 1 17.528 12.764 13.126 13.470 

22 6 3 16.508 13.382 13.598 13.805 

23 6 6 14.753 11.752 11.866 12.089 

24 6 9 13.378 10.325 10.433 10.565 

25 9 1 18.322 12.525 12.936 13.256 

26 9 3 14.20 11.620 11.926 12.223 

27 9 6 13.716 11.218 11.449 11.736 

28 9 9 13.248 12.439 12.640 12.878 

Six Month Ahead Forecasts 

29 6 1 35.563 32.695 34.257 35.466 

30 6 3 35.341 31.931 33.210 34.589 

31 6 6 34.730 30.914 31.453 32.871 

32 6 9 34.875 30.833 31.007 32.173 

33 9 1 47.959 39.044 39.188 40.228 

34 9 3 41.177 35.474 36.234 37.298 

35 9 6 39.866 35.063 35.523 36.653 

36 9 9 39.972 36.354 36.488 37.555 

Note: 

n

n

t

t

e

MSE

∑

=

=

1

2

, t = 1,...,165. Because e are very small, the entries in columns 4-7 show MSEx105. The x’s denote the 

cases where the models with lagged LIold and LInew terms are less accurate than the autoregressive model, that is, where the entries in 

columns 4 and 6 are smaller than the corresponding entries in column 4. All the differences between MSE’s in column 4 and either 

column 5, 6 or 7 for one month ahead forecasts are significant at the 5 % level based on the encompassing test statistic (ENC_NEW) 

developed by Clark and McCracken (2001) to test for one-step ahead forecast accuracy in nested models. The test statistic is not 

applicable to 3 and 6-month ahead forecasts, but research is underway to develop the appropriate tests for multi-step ahead forecasts. 

2

t

Page 87
 

Page 88

Table 8 

Comparable Forecasts of Growth in the Industrial Production Index 

Are More Accurate for the New Index Than for the Old Index 

Jan. 1989- Sep.2002 

Span of Months over 

which Growth Rate is 

Calculated (j) 

Number of Lags of 

Growth Rates of IP , 

LI (1 to k) 

Mean Square Errors (MSE)a

For Model with Lagged Terms in 

Line 

IP and LInew b IP and LIold

Direct 

IP and LIold

Two-Step 

(1) (2) (3) (4) (5) (6) 

One Month Ahead Forecasts 

1 1 1 2.577 2.283x

 2.583 

2 1 3 2.247 2.273 2.349 

3 1 6 2.354 2.352 x 2.533 

4 1 9 2.225 2.316 2.510 

5 3 1 3.054 5.654 4.173 

6 3 3 3.369 6.144 5.829 

7 3 6 2.989 5.307 5.057 

8 3 9 2.520 4.679 5.003 

9 6 1 3.770 7.199 5.597 

10 6 3 4.006 7.860 6.722 

11 6 6 4.120 7.261 7.136 

12 6 9 6.177 6.830 

13 9 1 3.470 7.070 5.590 

14 9 3 3.461 6.730 5.824 

15 9 6 3.442 6.675 5.889 

16 9 9 3.410 6.954 6.113 

3.009 

Three Month Ahead Forecasts 

17 3 1 9.719 11.852 10.257 

18 3 3 9.970 11.870 11.379 

19 3 6 9.156 10.488 10.611 

20 3 9 8.502 10.111 9.690 

21 6 1 13.470 20.367 19.770 

22 6 3 13.805 20.926 28.318 

23 6 6 12.089 17.948 27.199 

24 6 9 10.565 16.463 25.024 

25 9 1 13.256 20.756 23.782 

26 9 3 12.223 19.593 28.758 

27 9 6 11.736 18.959 29.137 

28 9 9 12.878 19.784 32.123 

Six Month Ahead Forecasts 

29 6 1 35.466 37.279 30.532 x

30 6 3 34.589 35.855 27.544 x

31 6 6 32.871 35.312 27.003 x

32 6 9 32.173 35.697 29.236 x

33 9 1 40.228 48.259 42.067 

34 9 3 37.298 45.130 44.676 

35 9 6 36.653 44.651 45.689 

36 9 9 37.555 46.668 50.854 

Note: 

n

n

t

t

e

MSE

∑

=

=

1

2

, t = 1,...,165. Because e are very small, the entries in columns 4-6 show MSEx105. The 

entries in column 4 are identical to those in Table 6, column 7. The x’s denote the cases where the models with lagged 

LIold terms are more accurate than the models with lagged LInew terms, that is, where the entries in columns 5 and 6 are 

smaller than the corresponding entries in column 4. 

2

t
65

70

75

80

85

90

95

100

105

110

115

120

60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02

Chart 1: Historical LI (as of September 2002) and Five Selected Vintages of the New Leading Index

January 1959 - August 2002

Historical LI

\

Mar. '00

Vintage

\

Jul. '98

Vintage

\

Nov. '91 Vintage

\

\

Jan. '89

Vintage

Jun. '01

Vintage

\

Index (1987 = 100)

The shaded areas represent U.S. busines cycle recessions as dated by the National Bureau of Economic Research. The latest shading

relates to the recession of 2001 and is dated according to the cyclical contraction of the CCI (the U.S. current conditions or coincident index).

P denotes the specific-cycle peaks and T the troughs in the historical LI and the vintages of the new LI. The numbers at the P and T markings

denote the leads in months at the business cycle peaks and troughs respectively.

12/00

11/01

Historical LI

Jul. '98 Vintage

\

_

7/90

11/82 3/91

7/81

7/80

1/80

3/75

11/73

11/70

12/69

2/61

4/60

P

P

P

P

P

P

P

X

X

X

X

X

X

T

T

T

T

T

T

T

Page 89
95

100

105

110

115

120

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

New LI Old LI Historical LI

-2

-1

0

1

2

1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002

Ratio, Old to New

Chart 2: Old and New Composite Leading Indexes, November 1988 - August 2002

Mean 0.027244

Std. Dev. 0.227264

Percent Index (1987 = 100)

7/90

7/90

3/91

3/91

12/00

12/00

11/01

11/01

Page 90
0

0

0

0

-2

0

0

0

0

+1

-1

0

0

0

-11

-3

-11

-7

-9

-1

-21

-3

-3

-8

-6

-2

-11

-8

T

P

T

T

T

T

T

T

T

T

T

T

T

T

T

P

P

P

P

P

P

P

P

P P

P

P

P

X

X

X

X

X

X

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02

Leading Index

Current Conditions Idex

Real GDP

Chart 3: U.S. Current Conditions Index, U.S. Leading Index and Real GDP

January 1959 - August 2002

Current Conditions Index

Leading Index

\

\

LI (1987 = 100)

CCI (1996 = 100)

4/60 12/69 11/73 1/80 7/81 7/90 12/00

2/61 11/70 3/75 7/80 11/82 3/91 11/01

_

_

_

_ 100

60

80

40

The shaded areas represent U.S. busines cycle recessions as dated by the National Bureau of Economic Research. The latest shading

relates to the recession of 2001 and is dated according to the cyclical contraction of the CCI (the U.S. current conditions or coincident index).

P denotes the specific-cycle peaks and T the troughs in the Leading and Current Conditions Indexes. The numbers at the P and T markings

denote the leads or lags in months at the business cycle peaks and troughs respectively.

Real GDP

\

Real GDP

Page 91