# Composite indexes of leading, coincident, and lagging indicators.

Composite Indexes of Leading, Coincident, and Lagging Indicators

THE current economic expansion, which marked its 60th month in November, has surpassed in length all other expansions since World War II except that of 1961-69 (table 1). Both the longevity of the current expansion and recent developments, such as the sharp drop in prices on the stock market, have focused attention on business cycles and business cycle research.

One technique developed in business cycle research and widely used as a tool for analyzing current economic conditions and prospects is the cyclical indicators approach. This approach identifies as cyclical indicators specific economic time series that tend to lead, coincide with, or lag the broad movements of the business cycle.1 Much of the original work on cyclical indicators was conducted by the National Bureau of Economic Research, Inc. (NBER), which published its first list of cyclical indicators in 1938. In 1961, the Bureau of the Census began reporting on business conditions in the monthly Business Cycle Developments, which emphasized the cyclical indicators approach.

1. Business cycles have been defined as sequences of expansion and contraction (recession) in various economic processes that show up as major fluctuations in aggregate economic activity--that is, in comprehensive measures of production, employment, income, and trade. While recurrent and pervasive, business cycles of historical experience have been nonperiodic and have varied greatly in duration and intensity, reflecting differences in economic systems, conditions, policies, and outside disturbances.

In 1972, the Bureau of Economic Analysis (BEA) assumed responsibility for the cyclical indicators and the publication, which had been renamed Business Conditions Digest (BCD). BEA then carried out--with the cooperation of NBER--a comprehensive review of the cyclical indicators system that led to the introduction in 1976 of a new set of cyclical indicators. One major purpose of this new set--arrived at by adding some indicators, deleting some, and modifying others--was to take into account the effect of inflation in the dating and analysis of business cycles. Subsequently, revisions were made in 1979 and in 1983. BEA now has underway another comprehensive review, drawing on the work done at the Center for International Business Cycle Research at Columbia University.

At the forefront of BEA's cyclical indicators system are the composite indexes of leading, coincident, and lagging indicators. These summary measures, which are designed to signal changes in the direction of aggregate economic activity, have been published since 1968. Each index measures the average behavior of a group of economic time series that show similar timing at business cycle turns but represent widely differing activities or sectors of the economy (table 2). The series that tend to lead at business cycle turns are combined into one index, those that tend to coincide into another, and those that tend to lag into a third.

The components of the indexes were selected with the help of a formal, detailed scoring system that places particular emphasis on cyclical timing.2 The indexes incorporate the best-scoring series from many different economic-process groups and combine those with similar timing behavior, using their overall performance scores as weights. Because the combination of prompt availability and reasonable accuracy is an especially important requirement of composite indexes, only monthly series that are available on a timely basis and are not subject to large revisions are considered when selecting components of the three composites.

2. All cyclical indicators are evaluated according to seven major characteristics: Cyclical timing, economic significance, statistical adequacy, conformity to business cycles, smoothness, prompt availability (currency), and revisions. Table 7 of the Handbook of Cyclical Indicators presents the scores for the cyclical indicator series.

Because they are based on series of historically tested usefulness and given timing characteristics, with diversified economic coverage and a minimum of duplication, composite indexes give more reliable signals over time than do any of the individual indicators. Furthermore, independent measurement error and other "noise" in the included series are smoothed out in the composite indexes.

Method of construction

The procedures used to construct the composite indexes help counter certain difficulties of combining economic time series--the tendencies of volatile series to dominate the average and of some series to perform better than others with regard to relevant criteria. Further, the procedures enhance the usefulness of the three composite indexes as a consistent system. Important aspects of these procedures--the component standardization of amplitude, weighting, index standardization of amplitude, and trend adjustment-- are highlighted in the explanation that follows.3

3. For an alternative, algebraic explanation of the material in this section, see the Handbook of Cyclical Indicators, p. 69.

1. Measures of change, standardization, and weighting of the components.

a. Month-to-month percent changes or differences are calculated for each component series. To ensure symmetrical treatment of positive and negative changes, the percent changes are computed using the formula 200(B - A)/(B A), where A is the value for the first month and B is the value for the second month.4 For series (such as first differences) that can contain zero or negative values, and for series that already are in percentage or ratio form, simple month-to-month differences (B - A) are computed.

4. The conventional formula for calculating the percent change over a given timespan is 100(B - A)/A, where A is the beginning value and B is the ending value. In the modified formula, the sum of A and B is used as the denominator to keep positive and negative percent changes symmetrical. For example, consider a series with consecutive values of 4, 8, 4, 8, 4, 8, and 4. Although there is no upward trend in this series, the conventional percent-change formula yields an average change of 25 percent, because there are an equal number of 100-percent increases and 50-percent decreases. The modified formula yields an average change of zero, because there are an equal number of increases and decreases of 67 percent. (Adapted from Signals of Recession and Recovery, by Julius Shiskin, National Bureau of Economic Research, 1961.)

b. To prevent the more volatile component series from dominating the index, the monthly changes (percent changes or differences, as computed in the preceding step) for each component are standardized to make the average of their absolute values equal to one. This standardization is accomplished for each component by dividing the monthly changes by their long-run historical average change, without regard to sign. This average is the component standardization factor. (Long-run average changes are recomputed only when the composite index undergoes a comprehensive revision.)

c. For each month, a weighted average of the standardized changes for all available components is computed. The weight for each component reflects the overall performance score of that series as a cyclical indicator. (See footnote 2 for a list of the factors that determine a series' score.) Thus, the better-performing series are assigned higher weights in the composite index. The weights and standardization factors for the components of the three major composite indexes are shown in table 3.

2. Standardization and cumulation of the index.

a. For the leading and lagging composite indexes, the weighted averages computed in the preceding step are subjected to an index standardization procedure that makes their long-run averages, without regard to sign, equal to the corresponding average for the coincident index. This is done to facilitate the use of the three composite indexes as a consistent system. To standardize the leading index, its average weighted changes (as computed in step 1c) are divided by the ratio of their long-run average to the corresponding average for the coincident index. The lagging index is standardized in the same manner. These ratios of the long-run averages are the index standardization factors and are shown in table 4.

b. The standardized average changes computed in the previous step are cumulated into a raw index, which is used in deriving the trend adjustment factor. This raw index is computed using the following procedure: A value of 100 is assigned to the index for the initial month (month C), and the value for the following month (month D) is computed by applying the formula D = C(200

r)/(200 - r), where r is the standardized average change between months C and D. The value for the third month (month E) is computed from the relationship E = D(200 r)/(200-r), where r is the standardized average change between months D and E. The index values for subsequent months are computed in the same manner. The factor (200 r)/(200 - r) in these formulas converts the symmetrical percent changes (see step 1a) to conventional percent changes.

3. Adjustment of the trend. A trend adjustment procedure is used to make the trends in the three composite indexes equal to the average of the trends in the components of the coincident index.5 This trend can be considered a linear approximation of the secular movement in aggregate economic activity. Although the purpose of the composite indexes is to indicate directional changes in aggregate economic activity, many users also view them as indicators of levels of activity. The trend adjustment procedure facilitates the use of the indexes as cyclical measures within a consistent system.

5. This trend adjustment procedure is derived from the "reverse trend adjustment" technique developed by Julius Shiskin and applied to the leading index prior to November 1976. (Julius Shiskin, "Reverse Trend Adjustment of Leading Indicators," The Review of Economics and Statistics, Vol. XLIX, No. 1, February 1967, pp. 45-49.) The earlier technique removed the original trend from the leading index and replaced it with the trend of the coincident index. The trends of the coincident and lagging indexes were not altered.

a. Establishing the target trend:

(1) Using the business cycle average method, a log-linear trend is computed from the original seasonally adjusted data for each of the components of the coincident index. First, the average monthly value for the initial cycle (measured between specific cycle peak dates) and the corresponding value for the terminal cycle are determined. Then, the percent change from the initial cycle average to the terminal cycle average (each centered at the middle of its cycle) is converted to a monthly rate by the compound interest formula.

(2) The trends derived in the preceding step for the individual components of the coincident index are averaged (with equal weights) to obtain the target trend. Table 5 illustrates the computation of the target trend.

b. Trend adjusting the composite indexes:

(1) Trends are computed for the raw indexes of the leading, coincident, and lagging composites using the method described in step 3a(1).

(2) The differences between the target trend and the raw index trends computed in the preceding step are the trend adjustment factors. For each index, the trend adjustment factor is added to the standardized average changes derived in step 2a. The raw index trends and the trend adjustment factors are shown in table 6.

(3) The trend-adjusted changes resulting from the preceding step are cumulated, using the method described in step 2b, to produce the leading, coincident, and lagging composite indexes.6

6. Because of the sequence used in the adjustment procedures, the trends of the three composite indexes are equal, but the average monthly changes, without regard to sign, are only approximately equal. If the index standardization described in step 2 had been applied after--rather than before--the trend adjustment, the average monthly changes in the three indexes would be equal, but the trends would be only approximately equal. Because the trend adjustment can affect the cyclical timing of the indexes and the index standardization cannot, precise equalization of the trends is considered more important than precise equalization of the average monthly changes.

c. Finally, each index is converted to the desired base year (currently 1967) by dividing each term by the average value of the index in the base year and multiplying by 100.

Monthly updating

Near the end of each month, the composite indexes are updated by computing the preliminary estimates for the previous month and recomputing the preceding 11 monthly values. For each index, one or two component series typically are not available in time to be included in the preliminary estimate for a month. The first computation of the indexes normally includes 9 of 11 leading index components, 3 of 4 coincident index components, and 4 of 6 lagging index components. Preliminary data for the missing components and revisions for the other components are included the following month when the indexes are recomputed. Because a composite index averages the behavior of its available components, the absolute contribution of an unrevised component will decline from the preliminary index computation to the following month's recomputation as the number of components being averaged increases.

Chart 6 shows the composite indexes of leading, coincident, and lagging indicators from 1968 to the present. Data and percent changes for the last year are shown in table 7. For a discussion of recent movements in the index of leading indicators, see the "Business Situation" article in this issue of the SURVEY.

The box on this page describes BEA's publications and other products that feature the composite indexes.

The composite indexes of leading, coincident, and lagging indicators are featured in the Business Conditions Digest (BCD), a monthly publication containing charts and tables for more than 300 economic time series. BCD includes more than 100 cyclical indicators, plus other series that help evaluate current and prospective economic conditions. Appendixes provide historical data, cyclical comparison charts, and data sources. The Handbook of Cyclical Indicators (1984), a supplement to BCD, contains series descriptions and historical data (1947-82) for all series that appear in BCD. Both publications are available from the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402:

Business Conditions Digest. List ID: BCD, price $44.00 per year, $4.00 single issue.

Handbook of Cyclical Indicators. Stock No. 003-010-00127-5, price $5.50.

Payment may be by check or money order (made payable to Superintendent of Documents) or charged to a GPO deposit account number, VISA, or MasterCard. To order by phone, call (202) 783-3238.

Current data for the composite indexes of leading, coincident, and lagging indicators also are available in summary form in monthly BEA Reports. These reports are available from Economic and Statistical Analysis/BEA, U.S. Department of Commerce, Citizens and Southern National Bank, 222 Mitchell Street, P.O. Box 100606, Atlanta, GA 30384:

BEA Reports: Composite Indexes of Leading, Coincident, and Lagging Indicators. Monthly reports. Accession No. BEA-16-S, price $18.00 per year.

Order must include a check or money order payable to Economic and Statistical Analysis /BEA. For information, call (202) 523-0777.

Data for most of the series shown in BCD are available on diskettes and on computer tape. For more information about these products, call (202) 523-0535, or write to Statistical Indicators Division (BE-60), Bureau of Economic Analysis, U.S. Department of Commerce, Washington, DC 20230.

Table: 1.--Business Cycles, 1945 to the Present

Table: 2.--Classification of Composite Index Components by Economic Process

Table: 3.--Standardization Factors and Weights for Composite Index Components

Table: 4.--Index Standardization Factors

Table: 5.--Target Trend Computation

Table: 6.--Trend Adjustment Factors

Table: CHART 6 Composite Indexes of Leading, Coincident, and Lagging Indicators

Table: 7.--Recent Data and Percent Changes for Composite Indexes of Leading, Coincident, and Lagging Indicators

THE current economic expansion, which marked its 60th month in November, has surpassed in length all other expansions since World War II except that of 1961-69 (table 1). Both the longevity of the current expansion and recent developments, such as the sharp drop in prices on the stock market, have focused attention on business cycles and business cycle research.

One technique developed in business cycle research and widely used as a tool for analyzing current economic conditions and prospects is the cyclical indicators approach. This approach identifies as cyclical indicators specific economic time series that tend to lead, coincide with, or lag the broad movements of the business cycle.1 Much of the original work on cyclical indicators was conducted by the National Bureau of Economic Research, Inc. (NBER), which published its first list of cyclical indicators in 1938. In 1961, the Bureau of the Census began reporting on business conditions in the monthly Business Cycle Developments, which emphasized the cyclical indicators approach.

1. Business cycles have been defined as sequences of expansion and contraction (recession) in various economic processes that show up as major fluctuations in aggregate economic activity--that is, in comprehensive measures of production, employment, income, and trade. While recurrent and pervasive, business cycles of historical experience have been nonperiodic and have varied greatly in duration and intensity, reflecting differences in economic systems, conditions, policies, and outside disturbances.

In 1972, the Bureau of Economic Analysis (BEA) assumed responsibility for the cyclical indicators and the publication, which had been renamed Business Conditions Digest (BCD). BEA then carried out--with the cooperation of NBER--a comprehensive review of the cyclical indicators system that led to the introduction in 1976 of a new set of cyclical indicators. One major purpose of this new set--arrived at by adding some indicators, deleting some, and modifying others--was to take into account the effect of inflation in the dating and analysis of business cycles. Subsequently, revisions were made in 1979 and in 1983. BEA now has underway another comprehensive review, drawing on the work done at the Center for International Business Cycle Research at Columbia University.

At the forefront of BEA's cyclical indicators system are the composite indexes of leading, coincident, and lagging indicators. These summary measures, which are designed to signal changes in the direction of aggregate economic activity, have been published since 1968. Each index measures the average behavior of a group of economic time series that show similar timing at business cycle turns but represent widely differing activities or sectors of the economy (table 2). The series that tend to lead at business cycle turns are combined into one index, those that tend to coincide into another, and those that tend to lag into a third.

The components of the indexes were selected with the help of a formal, detailed scoring system that places particular emphasis on cyclical timing.2 The indexes incorporate the best-scoring series from many different economic-process groups and combine those with similar timing behavior, using their overall performance scores as weights. Because the combination of prompt availability and reasonable accuracy is an especially important requirement of composite indexes, only monthly series that are available on a timely basis and are not subject to large revisions are considered when selecting components of the three composites.

2. All cyclical indicators are evaluated according to seven major characteristics: Cyclical timing, economic significance, statistical adequacy, conformity to business cycles, smoothness, prompt availability (currency), and revisions. Table 7 of the Handbook of Cyclical Indicators presents the scores for the cyclical indicator series.

Because they are based on series of historically tested usefulness and given timing characteristics, with diversified economic coverage and a minimum of duplication, composite indexes give more reliable signals over time than do any of the individual indicators. Furthermore, independent measurement error and other "noise" in the included series are smoothed out in the composite indexes.

Method of construction

The procedures used to construct the composite indexes help counter certain difficulties of combining economic time series--the tendencies of volatile series to dominate the average and of some series to perform better than others with regard to relevant criteria. Further, the procedures enhance the usefulness of the three composite indexes as a consistent system. Important aspects of these procedures--the component standardization of amplitude, weighting, index standardization of amplitude, and trend adjustment-- are highlighted in the explanation that follows.3

3. For an alternative, algebraic explanation of the material in this section, see the Handbook of Cyclical Indicators, p. 69.

1. Measures of change, standardization, and weighting of the components.

a. Month-to-month percent changes or differences are calculated for each component series. To ensure symmetrical treatment of positive and negative changes, the percent changes are computed using the formula 200(B - A)/(B A), where A is the value for the first month and B is the value for the second month.4 For series (such as first differences) that can contain zero or negative values, and for series that already are in percentage or ratio form, simple month-to-month differences (B - A) are computed.

4. The conventional formula for calculating the percent change over a given timespan is 100(B - A)/A, where A is the beginning value and B is the ending value. In the modified formula, the sum of A and B is used as the denominator to keep positive and negative percent changes symmetrical. For example, consider a series with consecutive values of 4, 8, 4, 8, 4, 8, and 4. Although there is no upward trend in this series, the conventional percent-change formula yields an average change of 25 percent, because there are an equal number of 100-percent increases and 50-percent decreases. The modified formula yields an average change of zero, because there are an equal number of increases and decreases of 67 percent. (Adapted from Signals of Recession and Recovery, by Julius Shiskin, National Bureau of Economic Research, 1961.)

b. To prevent the more volatile component series from dominating the index, the monthly changes (percent changes or differences, as computed in the preceding step) for each component are standardized to make the average of their absolute values equal to one. This standardization is accomplished for each component by dividing the monthly changes by their long-run historical average change, without regard to sign. This average is the component standardization factor. (Long-run average changes are recomputed only when the composite index undergoes a comprehensive revision.)

c. For each month, a weighted average of the standardized changes for all available components is computed. The weight for each component reflects the overall performance score of that series as a cyclical indicator. (See footnote 2 for a list of the factors that determine a series' score.) Thus, the better-performing series are assigned higher weights in the composite index. The weights and standardization factors for the components of the three major composite indexes are shown in table 3.

2. Standardization and cumulation of the index.

a. For the leading and lagging composite indexes, the weighted averages computed in the preceding step are subjected to an index standardization procedure that makes their long-run averages, without regard to sign, equal to the corresponding average for the coincident index. This is done to facilitate the use of the three composite indexes as a consistent system. To standardize the leading index, its average weighted changes (as computed in step 1c) are divided by the ratio of their long-run average to the corresponding average for the coincident index. The lagging index is standardized in the same manner. These ratios of the long-run averages are the index standardization factors and are shown in table 4.

b. The standardized average changes computed in the previous step are cumulated into a raw index, which is used in deriving the trend adjustment factor. This raw index is computed using the following procedure: A value of 100 is assigned to the index for the initial month (month C), and the value for the following month (month D) is computed by applying the formula D = C(200

r)/(200 - r), where r is the standardized average change between months C and D. The value for the third month (month E) is computed from the relationship E = D(200 r)/(200-r), where r is the standardized average change between months D and E. The index values for subsequent months are computed in the same manner. The factor (200 r)/(200 - r) in these formulas converts the symmetrical percent changes (see step 1a) to conventional percent changes.

3. Adjustment of the trend. A trend adjustment procedure is used to make the trends in the three composite indexes equal to the average of the trends in the components of the coincident index.5 This trend can be considered a linear approximation of the secular movement in aggregate economic activity. Although the purpose of the composite indexes is to indicate directional changes in aggregate economic activity, many users also view them as indicators of levels of activity. The trend adjustment procedure facilitates the use of the indexes as cyclical measures within a consistent system.

5. This trend adjustment procedure is derived from the "reverse trend adjustment" technique developed by Julius Shiskin and applied to the leading index prior to November 1976. (Julius Shiskin, "Reverse Trend Adjustment of Leading Indicators," The Review of Economics and Statistics, Vol. XLIX, No. 1, February 1967, pp. 45-49.) The earlier technique removed the original trend from the leading index and replaced it with the trend of the coincident index. The trends of the coincident and lagging indexes were not altered.

a. Establishing the target trend:

(1) Using the business cycle average method, a log-linear trend is computed from the original seasonally adjusted data for each of the components of the coincident index. First, the average monthly value for the initial cycle (measured between specific cycle peak dates) and the corresponding value for the terminal cycle are determined. Then, the percent change from the initial cycle average to the terminal cycle average (each centered at the middle of its cycle) is converted to a monthly rate by the compound interest formula.

(2) The trends derived in the preceding step for the individual components of the coincident index are averaged (with equal weights) to obtain the target trend. Table 5 illustrates the computation of the target trend.

b. Trend adjusting the composite indexes:

(1) Trends are computed for the raw indexes of the leading, coincident, and lagging composites using the method described in step 3a(1).

(2) The differences between the target trend and the raw index trends computed in the preceding step are the trend adjustment factors. For each index, the trend adjustment factor is added to the standardized average changes derived in step 2a. The raw index trends and the trend adjustment factors are shown in table 6.

(3) The trend-adjusted changes resulting from the preceding step are cumulated, using the method described in step 2b, to produce the leading, coincident, and lagging composite indexes.6

6. Because of the sequence used in the adjustment procedures, the trends of the three composite indexes are equal, but the average monthly changes, without regard to sign, are only approximately equal. If the index standardization described in step 2 had been applied after--rather than before--the trend adjustment, the average monthly changes in the three indexes would be equal, but the trends would be only approximately equal. Because the trend adjustment can affect the cyclical timing of the indexes and the index standardization cannot, precise equalization of the trends is considered more important than precise equalization of the average monthly changes.

c. Finally, each index is converted to the desired base year (currently 1967) by dividing each term by the average value of the index in the base year and multiplying by 100.

Monthly updating

Near the end of each month, the composite indexes are updated by computing the preliminary estimates for the previous month and recomputing the preceding 11 monthly values. For each index, one or two component series typically are not available in time to be included in the preliminary estimate for a month. The first computation of the indexes normally includes 9 of 11 leading index components, 3 of 4 coincident index components, and 4 of 6 lagging index components. Preliminary data for the missing components and revisions for the other components are included the following month when the indexes are recomputed. Because a composite index averages the behavior of its available components, the absolute contribution of an unrevised component will decline from the preliminary index computation to the following month's recomputation as the number of components being averaged increases.

Chart 6 shows the composite indexes of leading, coincident, and lagging indicators from 1968 to the present. Data and percent changes for the last year are shown in table 7. For a discussion of recent movements in the index of leading indicators, see the "Business Situation" article in this issue of the SURVEY.

The box on this page describes BEA's publications and other products that feature the composite indexes.

The composite indexes of leading, coincident, and lagging indicators are featured in the Business Conditions Digest (BCD), a monthly publication containing charts and tables for more than 300 economic time series. BCD includes more than 100 cyclical indicators, plus other series that help evaluate current and prospective economic conditions. Appendixes provide historical data, cyclical comparison charts, and data sources. The Handbook of Cyclical Indicators (1984), a supplement to BCD, contains series descriptions and historical data (1947-82) for all series that appear in BCD. Both publications are available from the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402:

Business Conditions Digest. List ID: BCD, price $44.00 per year, $4.00 single issue.

Handbook of Cyclical Indicators. Stock No. 003-010-00127-5, price $5.50.

Payment may be by check or money order (made payable to Superintendent of Documents) or charged to a GPO deposit account number, VISA, or MasterCard. To order by phone, call (202) 783-3238.

Current data for the composite indexes of leading, coincident, and lagging indicators also are available in summary form in monthly BEA Reports. These reports are available from Economic and Statistical Analysis/BEA, U.S. Department of Commerce, Citizens and Southern National Bank, 222 Mitchell Street, P.O. Box 100606, Atlanta, GA 30384:

BEA Reports: Composite Indexes of Leading, Coincident, and Lagging Indicators. Monthly reports. Accession No. BEA-16-S, price $18.00 per year.

Order must include a check or money order payable to Economic and Statistical Analysis /BEA. For information, call (202) 523-0777.

Data for most of the series shown in BCD are available on diskettes and on computer tape. For more information about these products, call (202) 523-0535, or write to Statistical Indicators Division (BE-60), Bureau of Economic Analysis, U.S. Department of Commerce, Washington, DC 20230.

Table: 1.--Business Cycles, 1945 to the Present

Table: 2.--Classification of Composite Index Components by Economic Process

Table: 3.--Standardization Factors and Weights for Composite Index Components

Table: 4.--Index Standardization Factors

Table: 5.--Target Trend Computation

Table: 6.--Trend Adjustment Factors

Table: CHART 6 Composite Indexes of Leading, Coincident, and Lagging Indicators

Table: 7.--Recent Data and Percent Changes for Composite Indexes of Leading, Coincident, and Lagging Indicators

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Publication: | Survey of Current Business |
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Date: | Nov 1, 1987 |

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