Updating the Composite Indexes
The procedure for calculating the monthly updates of the composite indexes has four distinct steps.
In the notation below, the "t" and "t-1" subscripts refer to the current and prior month, respectively, and the "x" and "m" subscripts refer to a particular component of the index
Step 1 - Month-to-month changes are computed for each component.
If the component X is in percent change form or an interest rate, simple arithmetic differences are calculated: xt=Xt-Xt-1. If the component is not in percent change form, a symmetric alternative to the conventional percent change formula is used: xt=200*(Xt-Xt-1)/(Xt+Xt-1). If the component X is a diffusion index (e.g. ISM New Orders Index) or an interest rate spread the monthly level is used x t=X t (Diffusion indexes are first normalized by subtracting their sample mean and dividing by their standard deviation).
Details on symmetric percent change formula.
An example for Step 1 for BCI series 1 of the U.S. Leading Index.
|
March |
April |
|
|
Average Weekly Hours, Mfg. |
41.8 |
41.4 |
|
Symmetric percent change |
-0.96 |
Step 2 - The month-to-month changes are adjusted using standardization factors that equalize the volatility of each component.
An example for Step 2 for BCI series 1 of the U.S. Leading Index.
|
March |
April |
|
|
Average Weekly Hours, Mfg. |
41.8 |
41.4 |
|
Symmetric percent change |
-0.96 |
|
|
Standardized (-0.96*.278) |
-0.27 |
Step 3 - The adjusted month-to-month changes are summed across the components to obtain the growth rate for the current month. The growth rates for the leading and lagging indexes are then adjusted each month so that their long-term trends will be equal to that of the coincident index. This is accomplished by adding an adjustment factor to the growth rate of the leading and lagging indexes each month. The trend adjustment factor for the leading index is computed by subtracting its average monthly growth rate from the average monthly growth rate of the coincident index.
An example for Step 3 for the U.S. Leading Economic Index.
Sum of contributions in April = 0.09
Trend adjustment factor = -0.0321
Trend-adjusted sum of contributions = 0.09 + (-0.0321) = 0.06 (to 2 deci. pl.)
Step 4 - With the previous month's index level, use the trend-adjusted growth rate to compute the updated level of the index.
March’s level = 105.2
Trend-adjusted sum of contributions in April = 0.06
March's level of 105.2 *(200+(0.06))/(200-(0.06)) = April's level of 105.26.
The above formula is consistent with (i.e., inverts) the symmetric percent change formula in Step 1.
All index levels are rounded to one decimal. Thus, March = 105.2, and April = 105.3
The most up-to-date standardization factors and trend adjustment factors can be found in the monthly press release technical notes here.
2001 Revisions
Prior to 2001, an additional adjustment was made to equalize the volatility of the composite indexes. For the U.S. leading and lagging indexes, each monthly sum (it) was multiplied by an index standardization factor (f) that equalizes the volatility these indexes relative to the coincident index. This factor is the ratio of the standard deviation of the percent changes for the coincident index (vcoin) to the standard deviation of the unadjusted percent changes for the particular composite index (flead = vcoin/vlead, flag = vcoin/vlag). The Conference Board decided to remove this step as it was proven not have any meaningful difference to the composite indexes' analytical value.
The leading, coincident and lagging indicators that are not available at the time of publication are estimated using statistical imputation. An autoregressive model is used to estimate each component. The resulting indexes are constructed using real and estimated data, and will be revised as the data unavailable at the time of publication become available. Such revisions are part of the monthly data revisions, now a regular part of the U.S. and global business cycle indicators program. The main advantage of this procedure is to utilize available data sooner. Empirical research by The Conference Board suggests there are real gains in adopting this procedure to make all the indicator series as up-to-date as possible.