# The composite index of coincident indicators and alternative coincident indexes.

The composite index of coincident indicators (ICI) is designed to
approximate movements in aggregate economic activity; in particular, it
is designed to have turning points that coincide with those of the
business cycle. The Bureau of Economic Analysis (BEA) constructs the ICI
from four components: Employees on nonagricultural payrolls
(employment), real personal income less transfer payments (income),
industrial production (production), and real manufacturing and trade
sales (sales).

This article reviews the cyclical patterns of the ICI and describes a characteristic of the method for calculating the ICI that has distorted its recent movements; it then discusses a modification to the methodology and presents several alternative coincident indexes.(1)

Cyclical patterns of the ICI

In the last eight business cycles, all but one of the turning points in the ICI were in the same quarter as, or in an adjacent quarter to, the business cycle turning points, which are designated by the National Bureau of Economic Research (NBER). For the most recent cycle, the peak designated by NBER was in July 1990, and the ICI peak was in June 1990; NBER has not yet designated the trough, but the ICI shows an apparent cyclical low in January 1992. Two ICI components--employment and income--have cyclical lows in that month; the cyclical low for production is in March 1991, and the low for sales is in January 1991 (chart 1).

One way of assessing the plausibility of the recent ICI low as a signal of the cyclical trough is to compare its timing with that of the trough of real gross national product (GNP), a broad measure of economic activity.(2) With one exception (1970), the cyclical lows for the ICI and for GNP have occurred in the same or adjacent quarters in each of the past eight recessions. In the current business cycle, the cyclical low for GNP occurred in the first quarter of 1991, much earlier than that for the ICI.

The disparity in the timing of the apparent cyclical lows for the two series is traceable to a characteristic of the method used to calculate the ICI. In the current cycle, the effects of this characteristic have become noticeable because of an extended period of very slow growth in the ICI components. In past cycles, the ICI components generally made more rapid and sustained recoveries from their cyclical lows.

ICI methodology

The method used by BEA to calculate the ICI is based on the standard composite index methodology developed by NBER researchers Geoffrey H. Moore and Julius Shiskin in the 1950's. Briefly, that method consists of the following steps: (1) Monthly symmetrical percent changes are

calculated for each of the four component

series. (2) To prevent the more volatile component series

from dominating the index, each series

of changes is standardized so that its average

absolute value is 1.0; this standardization

is accomplished by dividing each series of

changes by its average absolute value. (3) For each month, the standardized component

changes are averaged. (4) The series of average standardized changes is

cumulated into a preliminary ICI, beginning

with a value of 100 for the initial month. (5) The trend of the preliminary ICI is subtracted

from the trend in real GNP to derive a trend

adjustment factor. (6) The trend adjustment factor is added to the

average standardized changes calculated in

step 3. (7) The trend-adjusted average standardized

changes from step 6 are cumulated into an

ICI. (8) The final ICI is calculated by dividing each

month of the ICI in step 7 by its average value

in 1982.

A characteristic of this methodology is that steps 2 and 3, taken together, implicitly apply two sets of weights to symmetrical component changes. For the currently published ICI the sum of these combined weights is 1.833. The technical description of the ICI methodology in the accompanying box shows that the change in the ICI can be separated into a trend part and a cyclical part. The use of (combined) weights that sum to more than 1.0 overweights the cyclical part (which has been weak in recent months) relative to the trend part. The modified methodology described in the box constrains the sum of the weights to 1.0 and gives the same weight to the cyclical and trend parts of changes in the ICI.

Alternative coincident indexes

Chart 2 shows the patterns during the current cycle for the currently published ICI (index A) and four alternative coincident indexes (indexes B, C, D, and E). The four alternative indexes incorporate revised component data and updated parameters that are estimated using data for the period 1948-85. Indexes B and C were prepared using the same methodology as index A, but the trend of index C was not forced to equal that of real GNP. Index D was prepared using a modified ICI methodology that forces the sum of weights on component changes to equal 1.0. Index E was prepared by applying a very different, experimental methodology developed by James H. Stock and Mark W. Watson to the four components used by BEA.(3)

As shown in chart 2, the levels and patterns of the indexes A and B are very similar--each shows a downward drift in recent periods. Indexes A, B, and C each show a cyclical peak in June 1990. However, indexes A and B each show an apparent cyclical low in January 1992, but index C shows an apparent cyclical low in March 1991. The timing of the cyclical low in index C agrees closely with that in real GNP; however, the trend of index C from the first quarter of 1959 to the fourth quarter of 1990 is 5.24 percent at an annual rate, much higher than the 2.99-percent trend of real GNP or the trends for any of the four ICI components for the same period. (Comparable estimates of GNP are not yet available for periods before 1959.)

Index D shows a cyclical peak in June 1990 and an apparent cyclical low in March 1991. After increasing during the second and third quarters of 1991, this index declines to a January 1992 level that is 0.3 percent higher than its March 1991 level. Since January, this index has increased. The trend of index D is 2.83 percent at an annual rate, close to the 2.99-percent trend of real GNP.

The overall pattern of index E is similar to that of index D. Index E declines from a cyclical peak in August 1990 to an apparent cyclical low in March 1991. After increasing during the second and third quarters of 1991, this index declines to a January 1992 level that is 1.3 percent higher than its March 1991 level. Since January, this index has increased. The trend of index E is 3.25 percent at an annual rate.

The percentage increase from March 1991 to January 1992 is larger in index E than in index D because of differences in the component weights used in the two indexes. In index E, over 70 percent of the weight is assigned to production, so it closely mirrors the pattern of production. In index D, over 70 percent of the weight is assigned to employment and income; these are the two components that have the lowest standardization factors, and they are the two that do not show a clear uptrend after March 1991.

BEA will examine the properties of indexes D and E and their performance in past business cycles. While that examination is being carried out, a chart for these indexes will be included in the "Business Cycle Indicators" section (C-pages) of future issues of the Survey. (1.) BEA is indebted to James H. Stock (of Harvard University) and Mark W. Watson (of Northwestern University) for pointing out the characteristic in the ICI methodology and for suggesting a modification. (2.) The timing of peaks and troughs in real GNP and real gross domestic product (GDP) is virtually identical. Real GNP is used here because it is used to establish the trend in the currently published ICI. (3.) Stock and Watson's methodology for calculating their experimental ICI involves complicated and advanced statistical methods. (See James H. Stock and Mark W. Watson, "A Probability Model of the Coincident Economic Indicators," in Leading Economic Indicators, edited by Kajal Lahiri and Geoffrey H. Moore (Cambridge, UK: Cambridge University Press, 1991).) For example, determination of appropriate weights involves maximum likelihood estimation using Kalman filters and gamma functions. Three of the four components they use are identical to those used by BEA, and their fourth component, employee hours in nonagricultural establishments, is similar to the employment component used by BEA. Recent estimates of their experimental indexes of coincident (and of leading) indicators are released each month by NBER.

This article reviews the cyclical patterns of the ICI and describes a characteristic of the method for calculating the ICI that has distorted its recent movements; it then discusses a modification to the methodology and presents several alternative coincident indexes.(1)

Cyclical patterns of the ICI

In the last eight business cycles, all but one of the turning points in the ICI were in the same quarter as, or in an adjacent quarter to, the business cycle turning points, which are designated by the National Bureau of Economic Research (NBER). For the most recent cycle, the peak designated by NBER was in July 1990, and the ICI peak was in June 1990; NBER has not yet designated the trough, but the ICI shows an apparent cyclical low in January 1992. Two ICI components--employment and income--have cyclical lows in that month; the cyclical low for production is in March 1991, and the low for sales is in January 1991 (chart 1).

One way of assessing the plausibility of the recent ICI low as a signal of the cyclical trough is to compare its timing with that of the trough of real gross national product (GNP), a broad measure of economic activity.(2) With one exception (1970), the cyclical lows for the ICI and for GNP have occurred in the same or adjacent quarters in each of the past eight recessions. In the current business cycle, the cyclical low for GNP occurred in the first quarter of 1991, much earlier than that for the ICI.

The disparity in the timing of the apparent cyclical lows for the two series is traceable to a characteristic of the method used to calculate the ICI. In the current cycle, the effects of this characteristic have become noticeable because of an extended period of very slow growth in the ICI components. In past cycles, the ICI components generally made more rapid and sustained recoveries from their cyclical lows.

ICI methodology

The method used by BEA to calculate the ICI is based on the standard composite index methodology developed by NBER researchers Geoffrey H. Moore and Julius Shiskin in the 1950's. Briefly, that method consists of the following steps: (1) Monthly symmetrical percent changes are

calculated for each of the four component

series. (2) To prevent the more volatile component series

from dominating the index, each series

of changes is standardized so that its average

absolute value is 1.0; this standardization

is accomplished by dividing each series of

changes by its average absolute value. (3) For each month, the standardized component

changes are averaged. (4) The series of average standardized changes is

cumulated into a preliminary ICI, beginning

with a value of 100 for the initial month. (5) The trend of the preliminary ICI is subtracted

from the trend in real GNP to derive a trend

adjustment factor. (6) The trend adjustment factor is added to the

average standardized changes calculated in

step 3. (7) The trend-adjusted average standardized

changes from step 6 are cumulated into an

ICI. (8) The final ICI is calculated by dividing each

month of the ICI in step 7 by its average value

in 1982.

A characteristic of this methodology is that steps 2 and 3, taken together, implicitly apply two sets of weights to symmetrical component changes. For the currently published ICI the sum of these combined weights is 1.833. The technical description of the ICI methodology in the accompanying box shows that the change in the ICI can be separated into a trend part and a cyclical part. The use of (combined) weights that sum to more than 1.0 overweights the cyclical part (which has been weak in recent months) relative to the trend part. The modified methodology described in the box constrains the sum of the weights to 1.0 and gives the same weight to the cyclical and trend parts of changes in the ICI.

Alternative coincident indexes

Chart 2 shows the patterns during the current cycle for the currently published ICI (index A) and four alternative coincident indexes (indexes B, C, D, and E). The four alternative indexes incorporate revised component data and updated parameters that are estimated using data for the period 1948-85. Indexes B and C were prepared using the same methodology as index A, but the trend of index C was not forced to equal that of real GNP. Index D was prepared using a modified ICI methodology that forces the sum of weights on component changes to equal 1.0. Index E was prepared by applying a very different, experimental methodology developed by James H. Stock and Mark W. Watson to the four components used by BEA.(3)

As shown in chart 2, the levels and patterns of the indexes A and B are very similar--each shows a downward drift in recent periods. Indexes A, B, and C each show a cyclical peak in June 1990. However, indexes A and B each show an apparent cyclical low in January 1992, but index C shows an apparent cyclical low in March 1991. The timing of the cyclical low in index C agrees closely with that in real GNP; however, the trend of index C from the first quarter of 1959 to the fourth quarter of 1990 is 5.24 percent at an annual rate, much higher than the 2.99-percent trend of real GNP or the trends for any of the four ICI components for the same period. (Comparable estimates of GNP are not yet available for periods before 1959.)

Index D shows a cyclical peak in June 1990 and an apparent cyclical low in March 1991. After increasing during the second and third quarters of 1991, this index declines to a January 1992 level that is 0.3 percent higher than its March 1991 level. Since January, this index has increased. The trend of index D is 2.83 percent at an annual rate, close to the 2.99-percent trend of real GNP.

The overall pattern of index E is similar to that of index D. Index E declines from a cyclical peak in August 1990 to an apparent cyclical low in March 1991. After increasing during the second and third quarters of 1991, this index declines to a January 1992 level that is 1.3 percent higher than its March 1991 level. Since January, this index has increased. The trend of index E is 3.25 percent at an annual rate.

The percentage increase from March 1991 to January 1992 is larger in index E than in index D because of differences in the component weights used in the two indexes. In index E, over 70 percent of the weight is assigned to production, so it closely mirrors the pattern of production. In index D, over 70 percent of the weight is assigned to employment and income; these are the two components that have the lowest standardization factors, and they are the two that do not show a clear uptrend after March 1991.

BEA will examine the properties of indexes D and E and their performance in past business cycles. While that examination is being carried out, a chart for these indexes will be included in the "Business Cycle Indicators" section (C-pages) of future issues of the Survey. (1.) BEA is indebted to James H. Stock (of Harvard University) and Mark W. Watson (of Northwestern University) for pointing out the characteristic in the ICI methodology and for suggesting a modification. (2.) The timing of peaks and troughs in real GNP and real gross domestic product (GDP) is virtually identical. Real GNP is used here because it is used to establish the trend in the currently published ICI. (3.) Stock and Watson's methodology for calculating their experimental ICI involves complicated and advanced statistical methods. (See James H. Stock and Mark W. Watson, "A Probability Model of the Coincident Economic Indicators," in Leading Economic Indicators, edited by Kajal Lahiri and Geoffrey H. Moore (Cambridge, UK: Cambridge University Press, 1991).) For example, determination of appropriate weights involves maximum likelihood estimation using Kalman filters and gamma functions. Three of the four components they use are identical to those used by BEA, and their fourth component, employee hours in nonagricultural establishments, is similar to the employment component used by BEA. Recent estimates of their experimental indexes of coincident (and of leading) indicators are released each month by NBER.

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Title Annotation: | includes related article on methodology design |
---|---|

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

Publication: | Survey of Current Business |

Date: | Jun 1, 1992 |

Words: | 1461 |

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