# Business cycle indicators: upcoming revision of the composite indexes.

The Bureau of Economic Analysis (BEA) is revising its composite
indexes of leading, coincident, and lagging indicators, the key indexes
in its analytic system designed to help predict peaks and troughs in the
business cycle. This revision has two major features: (1) The
incorporation of revised data for the index components, partly to
reflect the results of the 1991 comprehensive revision of the national
income and product accounts (NIPA'S), and (2) improvements in the
methodology for calculating the composite indexes, mainly a change in
the weighting of the index components and the elimination of the trend
adjustment for the indexes.

The improved methodology for calculating the composite indexes is derived from the "modified" methodology, described in an article in the June 1992 Survey of Current Business, that has been used to calculate the alternative coincident index presented each month in the Survey on page C-21.(1) The improved methodology corrects a flaw in the current index formula that tends to distort the cyclical pattern of the composite indexes in periods of slow growth, such as the current expansion. The cyclical amplitudes and trends of the revised composite indexes differ from those of the currently published indexes, but with the exception of the improved cyclical pattern of the coincident index, the differences do not reflect any change in the ability of the indexes to signal cyclical peaks and troughs. Although this revision encompasses more changes than the usual annual updating of the composite indexes, its scope is smaller than that of the revision in 1989, which involved changes in the component composition of the indexes.(2) This revision, which will be effective with the release on December 3 of estimates for October 1993, covers the period from 1948 forward. The revised data for 1948-93 for the composite indexes and their components will appear in the "Business Cycle Indicators" section of the November Survey.

Each of the composite indexes measures the average behavior of a group of economic time series that show similar timing at business cycle turns but that represent widely differing activities or sectors of the economy. The procedures used to construct the indexes are designed to neutralize the tendency of the more volatile series to dominate the average, and they enhance the usefulness of the three indexes as a consistent system.

The first section of this article summarizes the changes that are incorporated in this revision. The second section briefly compares the performance of the current and revised indexes with respect to the business cycle. An appendix presents the formulas used to calculate the revised composite indexes.

Elements of the Revision

Revisions to component series

Each month, BEA updates the composite indexes by computing a preliminary index value for the latest data month and recomputing the index values for the 5 preceding months to incorporate revised component data. This monthly updating picks up most routine monthly revisions in the index components. To pick up longer term revisions, such as revisions of seasonal factors and benchmark revisions, the composite indexes undergo annual recomputations (usually in the fall) to incorporate revised component data for the current year and for the 5 preceding years. The annual recomputations normally do not include changes in composition, methodology, or statistical factors.

Since the last overall revision of the composite indexes in 1989, many component series have undergone revisions for periods earlier than those included in the regular monthly and annual updatings of the indexes. In particular, the 1991 comprehensive revision of the NIPA'S, which shifted to a 1987 base year for constant-dollar and price measures, resulted in data revisions for several index components. The revised composite indexes incorporate the latest available data for all components; the composition of the indexes is not changed.

Leading index components. - In the revised leading index, two components - "manufacturers' new orders for consumer goods and materials" and "contracts and orders for plant and equipment" - are revised to incorporate new deflators with a 1987 base year. Most of the current deflators used for these components are Bureau of Labor Statistics Producer Price Indexes (PPI'S); the revised deflators are those used for various detailed NIPA components, which are estimated using PPI'S and various other price measures. In addition, the composition of the new orders component is revised to include all nondefense durable goods not classified as capital goods. (New orders for nondefense capital goods are included in the contracts and orders component.) This change, which involves the addition of three minor durable goods categories and the elimination of some minor duplication with the contracts and orders component, has a negligible effect on the behavior of the new orders component.

The "change in sensitive materials prices" component is recomputed. Because this component is the percent change in a composite index of crude and intermediate materials prices, this recomputation uses the revised formulas for calculating composite indexes (see the appendix).

The "change in manufacturers' unfilled orders, durable goods industries" and "money supply M2" components are revised to incorporate the rebasing of their deflators to a 1987 base year.

Coincident index components. - In the revised coincident index, data prior to 1977 for the "manufacturing and trade sales" component, which were in 1982 dollars, are rescaled in order to link them to the level of the data from 1977 forward, which are now in 1987 dollars as a result of the NIPA revision.

Lagging index components. - In the revised lagging index, the "ratio of manufacturing and trade inventories to sales" is revised prior to 1977; the revision reflects the previously mentioned revision to manufacturing and trade sales and a similar revision to manufacturing and trade inventories. The "commercial and industrial loans outstanding" component is revised to incorporate the rebasing of its deflator to a 1987 base year. In addition, in the revised lagging index and in recent releases of the current lagging index, the labor cost portion of the "change in index of labor cost per unit of output, manufacturing" is adjusted separately to smooth yearend 1992 bonus payments (included in the latest annual NIPA revision) before the usual smoothing technique is applied.(3)

Statistical factors

As part of this revision of the indexes, an estimation period for computing standardization factors was chosen, the standardization factors - for the indexes and their components - were recomputed, and a new index base period was established. In general, the selected estimation period for standardization factors should encompass several complete business cycles. However, recent years are excluded from the estimation period because recent data values for many component series are preliminary and are subject to revision. The overall estimation period for the revised standardization factors is 1948-89. In the current index, the estimation period is 1948-85. Computations of composite index values beyond the estimation period use the standardization factors computed for the estimation period.

With the lengthy estimation period, it is likely that some component series may exhibit very different behavior for subperiods within the estimation period, and some may be available for only part of the estimation period. To handle these situations, the component standardization factors may be computed separately for subperiods. In some cases, data for a component may not be available at the beginning of a selected estimation period; in those cases, the period for computing the component standardization factor starts with the first month for which data are available.

Component standardization factors. - For the coincident index, the overall estimation period, 1948-89, is used to calculate component standardization factors; for the leading and lagging indexes, subperiods are used. For the leading index, one component (consumer expectations) is not available on a monthly basis before 1978; the available data prior to 1978 are interpolated to derive a monthly series. All component standardization factors for the revised leading index are based on the subperiods 1948-77 and 1978-89. For the lagging index, one component (the prime rate) changes very little until 1966 but is highly variable thereafter. All component standardization factors for the revised lagging index are based on the subperiods 1948-65 and 1966-89. (Current and revised component standardization factors are shown in table 1.)

[TABULAR DATA OMITTED]

Index standardization factors. - The application of index standardization factors ensures that the average absolute percentage change in the leading index and in the lagging index is the same as that in the coincident index. The overall estimation period, 1948-89, is used to calculate the index standardization factors for the three revised indexes. (Current and revised index standardization factors are shown in table 2.)

[TABULAR DATA OMITTED]

Base period for the indexes. - Each composite index is scaled so that its average monthly value equals 100 in the base year. As part of this revision, the base year of the composite indexes is changed from 1982 to 1987. (The NIPA estimates currently use 1987 as the base year for price and constant-dollar measures.) This change in the base year has no effect on the month-to-month percent changes in the index.

Changes in index formulas

The revised formulas for calculating the composite indexes (see the appendix) incorporate changes that affect the weighting of the index components and the trend adjustments for the indexes. These changes correct characteristics of the current index methodology that overweight the cyclical part of component changes (in relation to the trend part) and that may produce misleading patterns in an index. A June 1992 Survey article addressed these matters in the context of the coincident index and discussed characteristics of the current and the revised methodologies.(4)

Component weights. - In the current composite indexes, each component is implicitly weighted by a combination of the component's standardization factor and the number of components available in a given month. However, these weights are not constrained to sum to 1.0. The use of (combined) weights that sum to more than 1.0 has resulted in an overweighting of the cyclical part of component changes relative to the trend part. For the current indexes, the implicit component weights sum to 1.29, 1.83, and 12.10 for the leading, coincident, and lagging indexes, respectively. In the revised indexes, the component weights are explicitly defined, and their sum is constrained to 1.0 for each index; this applies equal weights to the cyclical and trend parts of the component changes and results in smaller cyclical amplitudes in the revised indexes than in the current indexes.

The component weights for the revised indexes and relative component weights for the current indexes are shown in table 3. These component weights are derived from the component standardization factors with the constraint that the sum of component weights is 1.0 for each index. (See formulas 2 and 3 in the appendix.)

[TABULAR DATA OMITTED]

Index trend adjustments. - The methodology used for the current composite indexes includes an adjustment that sets the trend in each index equal to the trend in real gross national product. (In earlier versions of the composite indexes, the target trend was the average of the trends in the coincident index components.) The use of an additive trend adjustment results in an index that may exhibit misleading patterns. The methodology used for the revised indexes does not include a trend adjustment. Instead, the revised methodology ensures that (apart from index standardization) the trend in the resulting index equals a weighted average of the trends in the component series.

The trends in the revised leading and lagging indexes are much lower than those in the corresponding current indexes. The trends in the revised leading, coincident, and lagging indexes for 1948-89 are 0.8 percent, 2.9 percent, and 1.8 percent per year, respectively. The corresponding trends in the current leading, coincident, and lagging indexes are 3.3 percent, 3.0 percent, and 3.2 percent per year.

Cyclical Patterns in the Composite Indexes

The revised and current composite indexes for January 1956 through April 1993 are shown in chart 1, and the lead or lag of each index at each business cycle turning point is shown in table 4. In general, the cyclical amplitudes of each pair of revised and current indexes are quite different, but the cyclical patterns and turning points are similar.

[TABULAR DATA OMITTED]

The average absolute percent change in each of the revised indexes is 0-44 percent, slightly more than half of that in each of the current indexes. Therefore, excluding the trend adjustments in the current indexes, a change of 1 percent in any of the revised indexes is roughly comparable to a change of nearly 2 percent in the respective current index. As a consequence, the cyclical amplitudes of the revised indexes are considerably smaller than those of the current indexes.

The leading index. - At business cycle peaks, the average lead of the revised index is 11.6 months, compared with 8.3 months for the current index. Much of the difference occurs at the last two peaks: At the July 1981 peak, the lead of the revised index is 6 months longer than that of the current index, and at the July 1990 peak, it is 16 months longer. The leads range from 5 to 20 months for the revised index and from 2 to 20 months for the current index.

At business cycle troughs, the average lead of the revised index is 3.1 months, compared with 4.2 months for the current index. The difference is almost totally accounted for by the 8-month shorter lead of the revised index at the February 1961 trough; the leads of the two indexes are the same for the five subsequent troughs. The leads for both indexes range from 1 to 10 months.

The coincident index. - At business cycle peaks, both the revised and current indexes have average leads of slightly more than 1 month. The leads of the two indexes match at every peak except two: The August 1957 peak, when the lead of the revised index is 1 month shorter than that of the current index, and the July 1981 peak, when the current index is exactly coincident and the revised index has a lag of 1 month. Except for the 1957 peak, both indexes reach their cyclical peaks within 3 months of the corresponding business cycle peaks.

At business cycle troughs, the revised index is exactly coincident at every trough except two The May 1954 trough, when it lags by 2 months and the November 1982 trough, when it matches the 1-month lag of the current index. The current index is exactly coincident at six of the nine troughs, with short lags at the May 1954 an November 1982 troughs and with a 10-month lag at the March 1991 trough.

The 1993 level of the revised coincident index exceeds the high reached in the last expansion, whereas the 1993 level of the current index does not. The revised index more accurately reflects the patterns of the four index components - all of which have exceeded their highs of the last expansion.

The lagging index. - At business cycle peaks, the average lag of both the current and revised indexes is 3.1 months. The lags of the two indexes match at six of the last eight peaks; at the July 1981 and July 1990 peaks, the timing of the two indexes differs by just 1 month. The revised index does not have an identifiable cyclical decline corresponding with the 1948-49 business cycle recession, but the current index's cyclical performance in that period is only marginally better.

At business cycle troughs, the average lag of the revised index is 9.3 months, compared with 8.5 months for the current index. The lags of the two indexes match at every trough except two: The October 1949 trough, when the revised index does not have an identifiable trough, and the March 1975 trough, when the lag of the revised index is 6 months longer than that of the current index. Neither index has an identifiable trough for the 1990-91 recession.

Appendix: Revised Formulas for

Composite Indexes

A. Initial calculation of a composite index

Let [Y.sub.jt] denote the value of the jth component of a composite index in period t, where t = 0, 1, 2,..., T, and let [y.sub.jt] denote the component's monthly percent change (sometimes called a symmetrical percent change), computed as

(1) [y.sub.jt] = 200 [Y.sub.jt] - [Y.sub.j,t-1] / [Y.sub.jt] + [Y.sub.j,t-1] for

t = 1,2,3,...., T; or

[y.sub.jt] = [Y.sub.jt] - [Y.sub.j,t-1] (for components

that could have zero or negative values).

For a chose estimation period or subperiod define [S.sub.j], the average absolute value of these changes (also called the component standardization factor) for each of the j components, as

(2) [S.sub.j] = [sigma.sub.t]\[y.sub.jt]\ / T].

Let [w.sub.j] denote the weight for each of the j components:

(3) [w.sub.j] = [beta.sub.j] / [sigma.sub.j][beta.sub.j], where [beta.sub.j] =

1 / [S.sub.j].

This formula for [w.sub.j] gives equal weight to each component's standardized change, [z.sub.jt], defined as [z.sub.jt] = [y.sub.jt] / [S.sub.j]. Note that [sigma.sub.j][w.sub.j] = 1. (If data for a component are not available in month t, then [beta.sub.j] = 0 and [w.sub.j] = 0 for that component.)

The (symmentrical) percent change, [c.sub.t], in the composite index is defined as

(4) [c.sub.t] = [sigma.sub.j] [w.sub.j] [y.sub.jt] / [F.sub.kappa], for t = 1,2,4,...., T,

where [F.sub.kappa] is an index standardization factor (explained in step B) that is initially assigned a value of 1 for each of the [kappa] indexes. [Note that if [F.sub.kappa] = 1, then [c.sub.t] = [mu] + [sigma.sub.j] [w.sub.j]([y.sub.jt] - [mu.sub.j], where [mu] = [sigma.sub.j] [w.sub.j] [mu.sub.j]. That is, the trend in the index, [mu], will by design equal a weighted average of the trends in the components, [mu.sub.j].

The level of the composite index in period t, [NDX.sub.t], is computed as

(5) [NDX.sub.0] = 100, and

[NDX.sub.t] = [NDX.sub.t-1] (200 + [c.sub.t]) / (200 - [c.sub.t]), for

t = 1,2,3,..., T.

B. Index standardization

This step ensures that the average absulute symmetrical percent change, [Z.sub.kappa], is the same for each of the [kappa] composite indexes in a given set.

First , from the [c.sub.t] values computed using formula 4 (with [F.sub.kappa] = 1), calculate a [Z.sub.kappa] value for each of the [kappa] composite indexes: (6) [Z.sub.kappa] = ([sigma.sub.t]\[c. sub.t]\) / T, for t = 1,2,3,... T.

Next, compute the index standardization factor, [F.sub.kappa], for each index by dividing its [Z.sub.kappa] valued by the Z value of the "primary" index: (7)

[F.sub.kappa] = [Z.sub.kappa] / [Z.sub.primary].

The set of leading, coincident, and lagging indexes uses the coincident index as the primary index, so the [F.sub.kappa] values for the leading (lead), coincident (coin), and lagging (lag) indexes are

[F.sub.lead] = [Z.sub.lead] / [Z.sub.coin], [F.sub.lag] = [Z.sub.lag] / [Z.sub.coin], and

[F.sub.coin] = 1.

Then, recompute the [c.sub.t] and [NDX.sub.t] values for each index using formulas 4 and 5 and the [F.sub.kappa] values from formula 7.

C. Index rebasing

As a final step, each index is rescaled so that its average value equals 100 in the desired base year: (8) [NDX.sub.t,rebassed] = 100 ([NDX.sub.t] / BASE), for t =

0,1,2,3,..., T,

where BASE is the average of the 12 monthly NDX values in the base year.

D. Index calculation beyond the estimation

period

The composite index estimates derived in steps A-C are extended beyond the last month of the estimation period using formulas 1, 3, 4, and 5 and the standardization factors derived for the estimation period. The standardization factors are not recomputed each month; they are usually recomputed only at the time of a subsequent overall revision of the composite indexes.

(1) See George R. Green and Barry A. Beckman, "The Composite Index of Coincident Indicators and Alternative Coincident Indexes," Survey of Current Business 72 (June 1992); 42-45. (2) The 1989 revision was described in Marie P. Hertzberg and Barry A. Beckman, "Business Cycle Indicators: Revised Composite Indexes," Survey 69 (January 1989); 23-28. (3) A smoothing technique developed by Statistics Canada, designed to clarify the cyclical movements of series with relatively irregular fluctuations, is used for this component, for one other component of the lagging index, and for two components of the leading index. The smoothed series F is derived from the actual series X by applying the following formula:

[F.sub.t] = 0.134[X.sub.t] + 1.451[F.sub.t-1] - 0.586[F.sub.t-2].

(4) See footnote 1.

The improved methodology for calculating the composite indexes is derived from the "modified" methodology, described in an article in the June 1992 Survey of Current Business, that has been used to calculate the alternative coincident index presented each month in the Survey on page C-21.(1) The improved methodology corrects a flaw in the current index formula that tends to distort the cyclical pattern of the composite indexes in periods of slow growth, such as the current expansion. The cyclical amplitudes and trends of the revised composite indexes differ from those of the currently published indexes, but with the exception of the improved cyclical pattern of the coincident index, the differences do not reflect any change in the ability of the indexes to signal cyclical peaks and troughs. Although this revision encompasses more changes than the usual annual updating of the composite indexes, its scope is smaller than that of the revision in 1989, which involved changes in the component composition of the indexes.(2) This revision, which will be effective with the release on December 3 of estimates for October 1993, covers the period from 1948 forward. The revised data for 1948-93 for the composite indexes and their components will appear in the "Business Cycle Indicators" section of the November Survey.

Each of the composite indexes measures the average behavior of a group of economic time series that show similar timing at business cycle turns but that represent widely differing activities or sectors of the economy. The procedures used to construct the indexes are designed to neutralize the tendency of the more volatile series to dominate the average, and they enhance the usefulness of the three indexes as a consistent system.

The first section of this article summarizes the changes that are incorporated in this revision. The second section briefly compares the performance of the current and revised indexes with respect to the business cycle. An appendix presents the formulas used to calculate the revised composite indexes.

Elements of the Revision

Revisions to component series

Each month, BEA updates the composite indexes by computing a preliminary index value for the latest data month and recomputing the index values for the 5 preceding months to incorporate revised component data. This monthly updating picks up most routine monthly revisions in the index components. To pick up longer term revisions, such as revisions of seasonal factors and benchmark revisions, the composite indexes undergo annual recomputations (usually in the fall) to incorporate revised component data for the current year and for the 5 preceding years. The annual recomputations normally do not include changes in composition, methodology, or statistical factors.

Since the last overall revision of the composite indexes in 1989, many component series have undergone revisions for periods earlier than those included in the regular monthly and annual updatings of the indexes. In particular, the 1991 comprehensive revision of the NIPA'S, which shifted to a 1987 base year for constant-dollar and price measures, resulted in data revisions for several index components. The revised composite indexes incorporate the latest available data for all components; the composition of the indexes is not changed.

Leading index components. - In the revised leading index, two components - "manufacturers' new orders for consumer goods and materials" and "contracts and orders for plant and equipment" - are revised to incorporate new deflators with a 1987 base year. Most of the current deflators used for these components are Bureau of Labor Statistics Producer Price Indexes (PPI'S); the revised deflators are those used for various detailed NIPA components, which are estimated using PPI'S and various other price measures. In addition, the composition of the new orders component is revised to include all nondefense durable goods not classified as capital goods. (New orders for nondefense capital goods are included in the contracts and orders component.) This change, which involves the addition of three minor durable goods categories and the elimination of some minor duplication with the contracts and orders component, has a negligible effect on the behavior of the new orders component.

The "change in sensitive materials prices" component is recomputed. Because this component is the percent change in a composite index of crude and intermediate materials prices, this recomputation uses the revised formulas for calculating composite indexes (see the appendix).

The "change in manufacturers' unfilled orders, durable goods industries" and "money supply M2" components are revised to incorporate the rebasing of their deflators to a 1987 base year.

Coincident index components. - In the revised coincident index, data prior to 1977 for the "manufacturing and trade sales" component, which were in 1982 dollars, are rescaled in order to link them to the level of the data from 1977 forward, which are now in 1987 dollars as a result of the NIPA revision.

Lagging index components. - In the revised lagging index, the "ratio of manufacturing and trade inventories to sales" is revised prior to 1977; the revision reflects the previously mentioned revision to manufacturing and trade sales and a similar revision to manufacturing and trade inventories. The "commercial and industrial loans outstanding" component is revised to incorporate the rebasing of its deflator to a 1987 base year. In addition, in the revised lagging index and in recent releases of the current lagging index, the labor cost portion of the "change in index of labor cost per unit of output, manufacturing" is adjusted separately to smooth yearend 1992 bonus payments (included in the latest annual NIPA revision) before the usual smoothing technique is applied.(3)

Statistical factors

As part of this revision of the indexes, an estimation period for computing standardization factors was chosen, the standardization factors - for the indexes and their components - were recomputed, and a new index base period was established. In general, the selected estimation period for standardization factors should encompass several complete business cycles. However, recent years are excluded from the estimation period because recent data values for many component series are preliminary and are subject to revision. The overall estimation period for the revised standardization factors is 1948-89. In the current index, the estimation period is 1948-85. Computations of composite index values beyond the estimation period use the standardization factors computed for the estimation period.

With the lengthy estimation period, it is likely that some component series may exhibit very different behavior for subperiods within the estimation period, and some may be available for only part of the estimation period. To handle these situations, the component standardization factors may be computed separately for subperiods. In some cases, data for a component may not be available at the beginning of a selected estimation period; in those cases, the period for computing the component standardization factor starts with the first month for which data are available.

Component standardization factors. - For the coincident index, the overall estimation period, 1948-89, is used to calculate component standardization factors; for the leading and lagging indexes, subperiods are used. For the leading index, one component (consumer expectations) is not available on a monthly basis before 1978; the available data prior to 1978 are interpolated to derive a monthly series. All component standardization factors for the revised leading index are based on the subperiods 1948-77 and 1978-89. For the lagging index, one component (the prime rate) changes very little until 1966 but is highly variable thereafter. All component standardization factors for the revised lagging index are based on the subperiods 1948-65 and 1966-89. (Current and revised component standardization factors are shown in table 1.)

[TABULAR DATA OMITTED]

Index standardization factors. - The application of index standardization factors ensures that the average absolute percentage change in the leading index and in the lagging index is the same as that in the coincident index. The overall estimation period, 1948-89, is used to calculate the index standardization factors for the three revised indexes. (Current and revised index standardization factors are shown in table 2.)

[TABULAR DATA OMITTED]

Base period for the indexes. - Each composite index is scaled so that its average monthly value equals 100 in the base year. As part of this revision, the base year of the composite indexes is changed from 1982 to 1987. (The NIPA estimates currently use 1987 as the base year for price and constant-dollar measures.) This change in the base year has no effect on the month-to-month percent changes in the index.

Changes in index formulas

The revised formulas for calculating the composite indexes (see the appendix) incorporate changes that affect the weighting of the index components and the trend adjustments for the indexes. These changes correct characteristics of the current index methodology that overweight the cyclical part of component changes (in relation to the trend part) and that may produce misleading patterns in an index. A June 1992 Survey article addressed these matters in the context of the coincident index and discussed characteristics of the current and the revised methodologies.(4)

Component weights. - In the current composite indexes, each component is implicitly weighted by a combination of the component's standardization factor and the number of components available in a given month. However, these weights are not constrained to sum to 1.0. The use of (combined) weights that sum to more than 1.0 has resulted in an overweighting of the cyclical part of component changes relative to the trend part. For the current indexes, the implicit component weights sum to 1.29, 1.83, and 12.10 for the leading, coincident, and lagging indexes, respectively. In the revised indexes, the component weights are explicitly defined, and their sum is constrained to 1.0 for each index; this applies equal weights to the cyclical and trend parts of the component changes and results in smaller cyclical amplitudes in the revised indexes than in the current indexes.

The component weights for the revised indexes and relative component weights for the current indexes are shown in table 3. These component weights are derived from the component standardization factors with the constraint that the sum of component weights is 1.0 for each index. (See formulas 2 and 3 in the appendix.)

[TABULAR DATA OMITTED]

Index trend adjustments. - The methodology used for the current composite indexes includes an adjustment that sets the trend in each index equal to the trend in real gross national product. (In earlier versions of the composite indexes, the target trend was the average of the trends in the coincident index components.) The use of an additive trend adjustment results in an index that may exhibit misleading patterns. The methodology used for the revised indexes does not include a trend adjustment. Instead, the revised methodology ensures that (apart from index standardization) the trend in the resulting index equals a weighted average of the trends in the component series.

The trends in the revised leading and lagging indexes are much lower than those in the corresponding current indexes. The trends in the revised leading, coincident, and lagging indexes for 1948-89 are 0.8 percent, 2.9 percent, and 1.8 percent per year, respectively. The corresponding trends in the current leading, coincident, and lagging indexes are 3.3 percent, 3.0 percent, and 3.2 percent per year.

Cyclical Patterns in the Composite Indexes

The revised and current composite indexes for January 1956 through April 1993 are shown in chart 1, and the lead or lag of each index at each business cycle turning point is shown in table 4. In general, the cyclical amplitudes of each pair of revised and current indexes are quite different, but the cyclical patterns and turning points are similar.

[TABULAR DATA OMITTED]

The average absolute percent change in each of the revised indexes is 0-44 percent, slightly more than half of that in each of the current indexes. Therefore, excluding the trend adjustments in the current indexes, a change of 1 percent in any of the revised indexes is roughly comparable to a change of nearly 2 percent in the respective current index. As a consequence, the cyclical amplitudes of the revised indexes are considerably smaller than those of the current indexes.

The leading index. - At business cycle peaks, the average lead of the revised index is 11.6 months, compared with 8.3 months for the current index. Much of the difference occurs at the last two peaks: At the July 1981 peak, the lead of the revised index is 6 months longer than that of the current index, and at the July 1990 peak, it is 16 months longer. The leads range from 5 to 20 months for the revised index and from 2 to 20 months for the current index.

At business cycle troughs, the average lead of the revised index is 3.1 months, compared with 4.2 months for the current index. The difference is almost totally accounted for by the 8-month shorter lead of the revised index at the February 1961 trough; the leads of the two indexes are the same for the five subsequent troughs. The leads for both indexes range from 1 to 10 months.

The coincident index. - At business cycle peaks, both the revised and current indexes have average leads of slightly more than 1 month. The leads of the two indexes match at every peak except two: The August 1957 peak, when the lead of the revised index is 1 month shorter than that of the current index, and the July 1981 peak, when the current index is exactly coincident and the revised index has a lag of 1 month. Except for the 1957 peak, both indexes reach their cyclical peaks within 3 months of the corresponding business cycle peaks.

At business cycle troughs, the revised index is exactly coincident at every trough except two The May 1954 trough, when it lags by 2 months and the November 1982 trough, when it matches the 1-month lag of the current index. The current index is exactly coincident at six of the nine troughs, with short lags at the May 1954 an November 1982 troughs and with a 10-month lag at the March 1991 trough.

The 1993 level of the revised coincident index exceeds the high reached in the last expansion, whereas the 1993 level of the current index does not. The revised index more accurately reflects the patterns of the four index components - all of which have exceeded their highs of the last expansion.

The lagging index. - At business cycle peaks, the average lag of both the current and revised indexes is 3.1 months. The lags of the two indexes match at six of the last eight peaks; at the July 1981 and July 1990 peaks, the timing of the two indexes differs by just 1 month. The revised index does not have an identifiable cyclical decline corresponding with the 1948-49 business cycle recession, but the current index's cyclical performance in that period is only marginally better.

At business cycle troughs, the average lag of the revised index is 9.3 months, compared with 8.5 months for the current index. The lags of the two indexes match at every trough except two: The October 1949 trough, when the revised index does not have an identifiable trough, and the March 1975 trough, when the lag of the revised index is 6 months longer than that of the current index. Neither index has an identifiable trough for the 1990-91 recession.

Appendix: Revised Formulas for

Composite Indexes

A. Initial calculation of a composite index

Let [Y.sub.jt] denote the value of the jth component of a composite index in period t, where t = 0, 1, 2,..., T, and let [y.sub.jt] denote the component's monthly percent change (sometimes called a symmetrical percent change), computed as

(1) [y.sub.jt] = 200 [Y.sub.jt] - [Y.sub.j,t-1] / [Y.sub.jt] + [Y.sub.j,t-1] for

t = 1,2,3,...., T; or

[y.sub.jt] = [Y.sub.jt] - [Y.sub.j,t-1] (for components

that could have zero or negative values).

For a chose estimation period or subperiod define [S.sub.j], the average absolute value of these changes (also called the component standardization factor) for each of the j components, as

(2) [S.sub.j] = [sigma.sub.t]\[y.sub.jt]\ / T].

Let [w.sub.j] denote the weight for each of the j components:

(3) [w.sub.j] = [beta.sub.j] / [sigma.sub.j][beta.sub.j], where [beta.sub.j] =

1 / [S.sub.j].

This formula for [w.sub.j] gives equal weight to each component's standardized change, [z.sub.jt], defined as [z.sub.jt] = [y.sub.jt] / [S.sub.j]. Note that [sigma.sub.j][w.sub.j] = 1. (If data for a component are not available in month t, then [beta.sub.j] = 0 and [w.sub.j] = 0 for that component.)

The (symmentrical) percent change, [c.sub.t], in the composite index is defined as

(4) [c.sub.t] = [sigma.sub.j] [w.sub.j] [y.sub.jt] / [F.sub.kappa], for t = 1,2,4,...., T,

where [F.sub.kappa] is an index standardization factor (explained in step B) that is initially assigned a value of 1 for each of the [kappa] indexes. [Note that if [F.sub.kappa] = 1, then [c.sub.t] = [mu] + [sigma.sub.j] [w.sub.j]([y.sub.jt] - [mu.sub.j], where [mu] = [sigma.sub.j] [w.sub.j] [mu.sub.j]. That is, the trend in the index, [mu], will by design equal a weighted average of the trends in the components, [mu.sub.j].

The level of the composite index in period t, [NDX.sub.t], is computed as

(5) [NDX.sub.0] = 100, and

[NDX.sub.t] = [NDX.sub.t-1] (200 + [c.sub.t]) / (200 - [c.sub.t]), for

t = 1,2,3,..., T.

B. Index standardization

This step ensures that the average absulute symmetrical percent change, [Z.sub.kappa], is the same for each of the [kappa] composite indexes in a given set.

First , from the [c.sub.t] values computed using formula 4 (with [F.sub.kappa] = 1), calculate a [Z.sub.kappa] value for each of the [kappa] composite indexes: (6) [Z.sub.kappa] = ([sigma.sub.t]\[c. sub.t]\) / T, for t = 1,2,3,... T.

Next, compute the index standardization factor, [F.sub.kappa], for each index by dividing its [Z.sub.kappa] valued by the Z value of the "primary" index: (7)

[F.sub.kappa] = [Z.sub.kappa] / [Z.sub.primary].

The set of leading, coincident, and lagging indexes uses the coincident index as the primary index, so the [F.sub.kappa] values for the leading (lead), coincident (coin), and lagging (lag) indexes are

[F.sub.lead] = [Z.sub.lead] / [Z.sub.coin], [F.sub.lag] = [Z.sub.lag] / [Z.sub.coin], and

[F.sub.coin] = 1.

Then, recompute the [c.sub.t] and [NDX.sub.t] values for each index using formulas 4 and 5 and the [F.sub.kappa] values from formula 7.

C. Index rebasing

As a final step, each index is rescaled so that its average value equals 100 in the desired base year: (8) [NDX.sub.t,rebassed] = 100 ([NDX.sub.t] / BASE), for t =

0,1,2,3,..., T,

where BASE is the average of the 12 monthly NDX values in the base year.

D. Index calculation beyond the estimation

period

The composite index estimates derived in steps A-C are extended beyond the last month of the estimation period using formulas 1, 3, 4, and 5 and the standardization factors derived for the estimation period. The standardization factors are not recomputed each month; they are usually recomputed only at the time of a subsequent overall revision of the composite indexes.

(1) See George R. Green and Barry A. Beckman, "The Composite Index of Coincident Indicators and Alternative Coincident Indexes," Survey of Current Business 72 (June 1992); 42-45. (2) The 1989 revision was described in Marie P. Hertzberg and Barry A. Beckman, "Business Cycle Indicators: Revised Composite Indexes," Survey 69 (January 1989); 23-28. (3) A smoothing technique developed by Statistics Canada, designed to clarify the cyclical movements of series with relatively irregular fluctuations, is used for this component, for one other component of the lagging index, and for two components of the leading index. The smoothed series F is derived from the actual series X by applying the following formula:

[F.sub.t] = 0.134[X.sub.t] + 1.451[F.sub.t-1] - 0.586[F.sub.t-2].

(4) See footnote 1.

Printer friendly Cite/link Email Feedback | |

Author: | Green, George R.; Beckman, Barry A. |
---|---|

Publication: | Survey of Current Business |

Date: | Oct 1, 1993 |

Words: | 3489 |

Previous Article: | Reliability and accuracy of the quarterly estimates of GDP. |

Next Article: | Merchandise trade of U.S. affiliates of foreign companies. |

Topics: |