Box: Using Chained-Dollar Estimates for Computing Contributions to Economic Growth: A Cautionary Note

The Bureau of Economic Analysis (BEA) measures real output and prices using chain-type annual-weighted indexes computed with a Fisher formula. These measures, which were introduced in the most recent comprehensive revisions of the national income and product accounts and of the gross product originating by industry (GPO) estimates, allow for the effects of changes over time in relative prices and quantities. By eliminating the substitution bias inherent in the previously featured fixed-weighted measures of real output and prices, these new indexes provide significantly more accurate measures of growth in real GDP and other major economic aggregates./1/

As a convenience for data users, BEA also prepares dollar-denominated real output series that are consistent with the chain-type indexes and that retain some of the computational advantages of constant-dollar series. The real chained (1992) dollar estimates for a GDP expenditure component or for a GPO industry are derived as the product of the chain-type quantity index (divided by 100) and the corresponding 1992 current-dollar value. Because the formula for the chain-type quantity indexes uses weights of more than one period, the corresponding chained-dollar estimates are usually not additive.

For many analytical purposes, these chained-dollar estimates are appropriate and informative. Growth rates and percent changes based on chained dollars are always equivalent to those derived from the quantity indexes and can be used confidently over any time period. Contributions to change computed from published chained dollars are usually appropriate for periods close to the reference year, especially for components or industries whose prices have not changed substantially relative to GDP prices.

However, if relative prices for individual GDP expenditure components or for GPO industries have changed substantially, then calculations of contributions to economic growth based on published chained-dollar estimates may be misleading and inappropriate even for short periods close to the reference year. Even for highly aggregated expenditure categories or for industry groups, the calculations will usually be misleading over long periods, because relative prices are likely to change substantially./2/

The accompanying exhibit shows the contributions of industry groups to the change in real GDP for 1977–82 based on chained (1992) dollars and on chained (1977) dollars. (The period 1977–82 was chosen for illustrative purposes because it is relatively far from the reference year for published chained (1992) dollars.) Contributions to the change in real GDP were computed by dividing the change in chained dollars for an industry group by the change in chained dollars for GDP for the period. For many industry groups, the contributions are very similar using either 1977 or 1992 as the reference year, but for some industry groups, they differ substantially. As measured using chained (1992) dollars, services account for 37 percent of real GDP growth in 1977–82; as measured using chained (1977) dollars—a more appropriate (contemporaneous) reference period—services account for 28 percent. Similarly, the contribution of finance, insurance, and real estate (FIRE) is 39 percent based on chained (1992) dollars and 31 percent based on chained (1977) dollars. These differences arise because the GPO prices of services and of FIRE increased substantially relative to GDP prices from 1977 to 1992, whereas the GPO prices of most other industry groups declined relative to GDP prices. Thus, using the relative prices of 1992 for services and FIRE overstates their contribution to real economic growth in the earlier period.

The contributions to real GDP growth computed from chained-dollar estimates can be misleading not only for industry groups over long time periods, but also for detailed industries during periods of rapid changes in relative prices, even for periods that are relatively close to the chained-dollar reference year. To illustrate, the contributions of detailed industries to the change in GDP for 1997 were computed using the published chained (1992) dollars and using an alternative measure based on chained (1996) dollars. For most industries, the alternative measure yields the same or similar estimates of contributions to real GDP growth. However, for two industries for which GPO prices have increased much slower relative to GDP prices—industrial machinery and equipment (which includes computers) and electronic and other electric equipment (which includes semiconductors)—the contributions are substantially overstated using chained (1992) dollars: For industrial machinery and equipment, 11.6 percent, compared with 8.6 percent using chained (1996) dollars; and for electronic and other electric equipment, 17.5 percent, compared with 10.6 percent. Conversely, the contribution of the insurance carriers industry is somewhat understated—2.1 percent, compared with 2.7 percent—because the GPO price for this industry increased much faster than GDP prices.

For analyses of contributions to the change in real GDP, BEA strongly recommends the use of the published contribution-to- growth tables. Table 2 in the monthly GDP news release and NIPA table 8.2, which is on page D–25 of this issue, provide accurate measures of the contributions of the major GDP expenditure components to the percent change in real GDP for all periods; these tables use exact formulas for attributing growth to the components of GDP. Table 2 in this article provides estimates of annual contributions to the percent change in real GDP for industry groups based on approximations to the exact formula. The estimates for each year are based on the prior year's current-dollar estimates, and the average annual contribution for 1992–97 is computed as the average of the annual percentage-point contributions.

For some analytical purposes, it may be desirable to compute contributions to growth for more than a single period or for aggregates other than GDP. Users can prepare close approximations of these contributions using chain-type annual-weighted indexes. In effect, users compute a chained-dollar series for a particular period using the percent changes in the chain-type annual-weighted indexes to compute chained-dollar series indexed to the current dollars of the reference period appropriate for the analysis (see footnote 1 for a reference to additional information on these calculations). Another alternative is to use the same procedure as that used for table 2 in this article. In table 2, the contributions of industry groups to real GDP growth for 1993 were computed by (1) extrapolating the 1992 estimates of current-dollar GDP and GPO by the percent changes in the corresponding GDP and GPO chain-type quantity indexes from 1992 to 1993, (2) calculating each industry group's percentage contribution to the change in real GDP for 1993 based on chained dollars, and (3) multiplying these percentages by the percent change in real GDP for 1993. The contributions for 1994 were computed by extrapolating the 1993 current-dollar estimates by the percent changes in the chain-type quantity indexes from 1993 to 1994. These estimates were then used to calculate the contribution of each industry group to the change in real GDP for 1994 based on chained (1993) dollars. As with the calculations for contributions to real GDP growth for 1993, these percentage contributions to growth for 1994 were then multiplied by the percent change in real GDP for 1994. This procedure was repeated to calculate each industry group's percentage-point contribution to real GDP growth for each year (1993, 1994, 1995, 1996, and 1997). The average annual contribution for 1992–97 was then computed for each industry group as the simple average of each year's percentage-point contribution.

Footnotes:

1. For more information, see J. Steven Landefeld and Robert P. Parker, "BEA's Chain Indexes, Time Series, and Measures of Long-Term Economic Growth," SURVEY OF CURRENT BUSINESS 77 (May 1997): 58–68.

2. Comparisons among the chained (1992) dollar estimates of components or industries may be particularly misleading for periods before 1982. For example, during the World War II era, the share of GDP accounted for by government consumption expenditures and gross investment increased substantially, and prices throughout the economy were tightly controlled and very different from postwar levels. These changes in the structure of the economy, while relatively short lived, seriously affect computations of contributions to GDP growth in this period.