>This makes no sense. An "aggregate," by definition, is the sum of
>its "components."
<http://www.bea.gov/bea/an/nipaguid.pdf>
Chained-dollar measures
BEA also prepares measures of real GDP and its components in a dollar-denominated form, designated "chained (1996) dollar estimates." For GDP and for most other series, these estimates are computed by multiplying the 1996 current-dollar value by a corresponding quantity index number divided by 100. For example, if a current-dollar GDP component equaled $100 in 1996 and if real output for this component increased 10 percent in 1997, then the chained (1996) dollar value of this component would be $110 ($100 * 1.10) in 1997. (For a list of the chained-dollar series that are not calculated this way, see the box "Chained Measures in the NIPA's That Are Not Calculated as Fisher Indexes.")
For analyses of changes over time in an aggregate or in a component, the percentage changes calculated from the chained-dollar estimates and from the chain- from year t-1 to year t is calculated as type quantity indexes are the same; any differences will be small and due to rounding. Thus, chained-dollar estimates are most appropriately interpreted as index numbers with a reference value other than 100. However, because the relative prices used as weights for any period other than the reference year differ from those used for the reference year, the chained-dollar values for the detailed GDP components will not necessarily sum to the chained-dollar estimate of GDP or of any intermediate aggregate. A measure of the extent of such differences is provided by a "residual" line, which indicates the difference between GDP (or another major aggregate) and the sum of the most detailed components in the table.
For periods close to the reference year, when there usually has not been much change in the relative prices that are used as the weights for the chain-type index, the residuals tend to be small, and the chained (1996) dollar estimates can be used to approximate the contributions to growth and to aggregate the detailed estimates.
As one moves further from the reference year, the residual tends to become larger, and the chained-dollar estimates become less useful for economic analysis. For this reason, most of the chained-dollar series for detailed components are shown beginning with 1987.
In general, the use of chained-dollar estimates to calculate component shares or component contributions to real growth may be misleading for periods away from the reference year. Thus, contributions to percent change shown in tables 8.2-8.6 provide better measures of the composition of GDP growth and that of its major aggregates. In particular, for components for which relative prices are changing rapidly, such as computers and peripheral equipment, calculations of contributions using chained-dollar estimates may be misleading even very close to the reference year (and the residuals in the corresponding chained-dollar tables may be large).
Tables 8.2-8.6 use exact formulas for attributing growth to the components of GDP and of other aggregates, but the presentation is limited to the contributions to change from the preceding year or quarter.
For some analytical purposes, it may be desirable to calculate contributions to growth for more than a single quarter or year or to calculate contributions to growth for aggregates not shown in tables 8.2-8.6. An article in the SURVEY provides information on how to prepare chained-dollar series with different reference years that permit the calculation of close approximations of contributions to real growth for any period.26 This article shows how to calculate a chained-dollar series for any period by using the percent changes in the chain-type indexes to compute chained-dollar series indexed to the current dollars of whatever reference year is appropriate for the analysis. In the article, different reference years are used depending upon the time period analyzed; for example, for decades and business cycles, the midpoints of the periods are used.
In this publication, tables 1.2A, 1.2B, 1.2C, and 1.2D present annual estimates of real GDP and its major components in chained (1937) dollars, chained (1952) dollars, chained (1972) dollars, and chained (1982) dollars, respectively. However, users should be aware that contributions calculated from these tables are approximations and may produce misleading results for periods far from those reference years or when relative prices are changing rapidly, such as during the energy crisis of 1973-75.
The presentation in this publication of chaineddollar estimates before 1987 has been limited to key aggregates. However, detailed quantity indexes, which are accurate for all periods, are presented in tables 7.3-7.14 and 7.17-7.20, most of which begin with 1929. These quantity indexes can be used in place of chained-dollar estimates in analyses that require data on real GDP or its components over time, as well as to calculate percent changes. For GDP and its major components and for other measures of output, annual growth rates beginning with 1930 and quarterly growth rates beginning with the second quarter of 1947 are presented in table 8.1.