Note.—This article was written by J. Steven Landefeld and Robert P. Parker. The note that accompanies the article was written by Jack E. Triplett.

*As previously announced, BEA plans to release the results of its next
comprehensive revision of the national income and product accounts (NIPA's)
at the end of 1995. This revision will be the tenth of its kind; the last
such revision was released in December 1991. Comprehensive revisions differ
from annual NIPA revisions because of the scope of the changes incorporated
and because of the number of years subject to revision. This year's comprehensive
revision will include the elements of the annual revision covering 1992–94,
which would usually have been published in this issue. *

*Major improvements that will be incorporated in this comprehensive revision
include the following: The introduction of new featured measures of real
output and prices, the implementation of an improved empirical basis for
the estimates of depreciation and capital stocks, and the treatment of government
purchases of structures and equipment as investment. As in the past, the
revised estimates will also reflect other definitional and statistical changes,
including the incorporation of newly available source data—such as the
1987 benchmark input-output tables, data from the 1992 Economic Censuses,
and several annual surveys for 1993 and 1994—and of improved estimating
methodologies. *

*This article discusses BEA's new featured measures of real output and
prices. Forthcoming SURVEY OF CURRENT
BUSINESS articles will address the other changes to be introduced
in the comprehensive revision. *

*It is important to note that the estimates that result from the comprehensive
NIPA revision will reflect the incorporation of new and revised source data
and improved estimating methodologies, which mainly affect the current-dollar
estimates, as well as the change in methodology used to calculate the featured
measures of real output and prices. *

When BEA releases the results of its upcoming comprehensive, or benchmark, revision of the national income and product accounts (NIPA's) at the end of this year, the featured measures of real output and prices will be calculated using chain-type annual-weighted indexes. At present, the featured measures are calculated using fixed-weighted indexes, which are usually updated at the time of a comprehensive revision. The change in the featured measures recognizes the need in estimating real GDP and prices to use weights that are appropriate for the specific periods being measured.

Changes in the new featured measures of output and prices will be calculated using the weights of adjacent years. These annual changes are "chained" (multiplied) together to form a time series that allows for the effects of changes in relative prices and changes in the composition of output over time. In contrast, fixed-weighted measures are calculated with a single set of weights over the entire time period. Use of fixed-weighted measures of real GDP and prices for periods other than those close to the base period results in a "substitution bias" that causes an overstatement of growth for periods after the base year and an understatement of growth for periods before the base year. For example, in the currently featured fixed-weighted measure of real GDP, which is based on 1987 prices:

- Real GDP growth is overstated by 0.7 percentage point in the second quarter of 1995: Growth was 0.5 percent according to the fixed-1987-weighted measure, compared with a decline of 0.2 percent according to BEA's alternative chain-type measure, which provides unbiased estimates of growth.
- During the current expansion, average annual real GDP growth is overstated by 0.5 percentage point; in past expansions, it is understated by about 0.5 percentage point.

BEA's new featured measures will eliminate the inconvenience and confusion associated with BEA's past practice of updating the weight and base periods—and thus rewriting economic history—about every 5 years. By minimizing substitution bias, the new measures of real GDP growth will also improve analyses of issues such as productivity, returns to investment, and the long-term growth potential for the economy. For example, projections of long-term economic growth based on the new measures will avoid the consistent overestimation of output inherent in forecasts based on out-of-date fixed-weighted measures. Likewise, analyses of long-term growth trends and changes in these trends will be free of the distortions caused by fixed-weighted measures.

The measures that BEA will feature are similar to the chain-type annual-weighted measures that BEA has been publishing in the SURVEY OF CURRENT BUSINESS since 1992. These measures, which are calculated independently for each aggregate and detailed component, are currently expressed as index numbers and as percent changes. To facilitate sectoral, trend, and current-period analyses, BEA will expand presentations of the estimates to include contributions of changes in major components to the growth of real GDP and dollar-denominated series that are calculated from the featured output indexes.

The remainder of this article provides additional information about the substitution bias in measures of real GDP and about the availability of the new measures. The accompanying note discusses the concepts and methods used in calculating output and price indexes.

In recent years, rapid changes in the composition of output and in relative prices have brought into question the longstanding methods that underlie real, or constant-dollar, GDP and other NIPA estimates. The currently featured constant-dollar estimates are expressed in 1987 dollars; that is, they value each component at its price in the base year, currently 1987. Use of the same fixed price weights over all time periods provides a set of indexes that convert to dollar-denominated measures in which the components add up precisely to the totals. BEA has featured such measures partly because many users consider this additive property to be useful; for example, it facilitates analysis of contributions to growth and provides flexibility in aggregating the detailed components. (It also facilitates verification of calculations using these detailed components.)

Within the index number literature, it has been long recognized that output measures that use fixed price weights of a single period tend to misstate growth as one moves further from the base period. This tendency, often called substitution bias, reflects the fact that the commodities for which output grows rapidly tend to be those for which prices increase less than average or decline. Thus, when real GDP is recalculated using more recent price weights, the commodities with strong output growth generally receive less weight, and growth in the aggregate measure is reduced. These recalculations provide more accurate measures of growth in current periods, because the weights more closely reflect the prices of the economy in current periods; for earlier periods, however, the recalculations provide less accurate measures of growth, because the weights are even further away from the prices appropriate to those periods.

Until recently, this bias (and the associated revisions in growth rates due to weight and base-year shifts) was small enough to be safely ignored. Two developments contributed to the need to investigate alternatives. First, beginning in the 1970's, changes in the prices and quantities of the energy and food components of GDP were large enough in certain periods for the choice of price weights to significantly affect the measurement of change in real GDP. Second, computer prices declined at an average annual rate of 17 percent during 1982–87, while computer output increased at a 34-percent rate; as a result, computers caused significant revisions in the GDP estimates when the weights and base period were updated. For example, when BEA shifted the weights and base period from 1982 to 1987 as part of the 1991 comprehensive NIPA revision, computers contributed significantly to the downward revision of 0.2 percentage point in the annual growth rate of real GDP for 1977–90.

In the late 1980's, BEA initiated a research program to investigate alternative measures of output and prices./1/ In April 1992, BEA published two alternative measures of annual change in real GDP for 1959–90, and in March 1993, BEA began publishing them for quarterly changes. The two alternative measures are not based on the price weights of a single year; rather, they are indexes that account for changes in relative prices over the periods for which growth rates are computed. In the chain-type annual-weighted quantity index, the weights are from adjacent years; in the benchmark-years-weighted quantity index, the weights are from adjacent benchmark years—about 5-year intervals./2/

Comparisons of BEA's alternative chain-type annual-weighted real GDP measure with BEA's currently featured fixed-1987-weighted measure indicate the degree of substitution bias in the fixed-weighted measure (chart 1):/3/

- For 1959–87, BEA's featured measure of annual growth in real GDP is understated by an average of 0.3 percentage point.
- Between 1987 and 1992, there is no significant substitution bias evident in BEA's featured measure of real GDP growth.
- In 1993 and 1994, BEA's featured measure of real GDP growth is overstated by an average of 0.6 percentage point.

For business cycle analysis, use of a chain-type index presents a more accurate picture of the strength of expansions and the depth of contractions. It also ends what has appeared to have been the "gradual smoothing" of changes in these periods that resulted largely from the lower rate of growth attributable to successive updating of the base period in the fixed-weighted measures./4/

- Since the recession trough of the first quarter of 1991, average annual real GDP growth has been overstated by an average of 0.5 percentage point (chart 2). For the five economic expansions between 1960 and 1990, real GDP growth is understated by an average of 0.5 percentage point. As a result, comparisons of the strength of the current expansion with that of past expansions using the present fixed-weighted measures may be overstated by as much as 1 full percentage point.
- The average annual rate of decline in real GDP during the six contractions between 1960 and 1991 is understated by an average of 0.3 percentage point.

Use of BEA's new featured measure will provide a more accurate picture not only of overall growth during past business cycles, but also of the growth of the individual components of GDP and their contribution to overall growth. For example, use of the chain-weighted index lowers the average contribution of producers' durable equipment (PDE)—which includes computers—to real GDP growth in the current expansion from 38.9 percent to 32.4 percent and raises the contribution of PDE in the five economic expansions between 1960 and 1990 from 10.7 percent to 13.3 percent.

For productivity analysis, use of a chain index has a significant effect on assessments of the magnitude of the slowdown in labor productivity (real output divided by hours worked) and in the growth of potential output since the early 1970's./5/ The chain-type measure shows an average real GDP growth rate of 4.1 percent for 1959–72 and 2.5 percent for 1973–94, while the fixed-weighted measure shows 3.7 percent and 2.4 percent, respectively (chart 3). Thus, use of the chain index shows that the slowdown in real GDP growth since 1972 was 1.6 percentage points, 0.3 percentage point more than indicated by the fixed-weighted index.

For investment analysis, the use of single-year weights has significantly overstated the impact of recent investment in computers in relation to investment in other types of assets. For example, in 1977, a small mainframe computer may have cost $800,000, over 18 times the $43,000 cost of a new single-family home. By 1987, technological innovation had reduced the cost of a computer system with the same capacity as the 1977 mainframe to $80,000, less than the $102,000 average cost of a new home. Today, that same system may cost as little as $30,000, less than one-fourth the cost of a new home. Use of relative prices from 1977, or even 1987, will significantly overstate the relative value and impact on the economy of the explosive growth in computers that has occurred since the late 1970's. Thus, in 1987, the purchase of a new computer had a "real" value roughly equal to a new home, but use of this relative price to value such an investment in 1995 overstates by fourfold the value and impact of that investment—in terms of jobs, wages, profits, and intermediate products—relative to investments in homes and in other capital goods.

% Analyses of particular periods can also be significantly affected by substitution bias, especially in periods far from the base period or when the components that grow the most are those whose relative prices have declined the most. Since the third quarter of 1994, differences among the measures of change in real GDP have widened; the average quarterly change at an annual rate in the chain-type index is 0.8 percentage point less than the average change in the currently featured fixed-weighted index (chart 4).

Although computers are often an important factor behind the substitution bias and usually explain most of particularly large differences, they are not the only source of this bias. For example, computers account for about three-fifths of the overstatement of real GDP in the fourth quarter of 1994 and about three-fourths of the overstatement in the first quarter of 1995. In some quarters, they are not a factor. Over the recent expansion, they have accounted for about three-fifths of the overstatement./6/

BEA's alternative measures of real GDP and GDP prices are now published monthly in tables 7.1, 7.2, and 7.3 (index numbers) and in table 8.1 (percent changes) in the "Selected NIPA Tables" section of the SURVEY. Since November 1994, the alternative measures also have been available online from STAT-USA on the third working day after the release of each quarterly GDP estimate./7/ A few months ago, to assist users in adapting to the new measures, alternative indexes for almost all the detail for which constant 1987-dollar estimates are shown in the "Selected NIPA Tables" were added to the set of estimates available from STAT-USA. Beginning with the release of preliminary GDP estimates for the second quarter of 1995 on August 30, 1995, selected alternative measures series will be included in the news release, and the more detailed alternative measures series will be available from STAT-USA at the same time as the "Selected NIPA Tables."

When BEA introduces the new featured measures of output and prices for the comprehensive NIPA revision, additional information will be made available to facilitate their use. (The change in the featured measure will not affect the availability of any current-dollar NIPA estimates; implicit price deflators will also be available.) Index numbers, which will be calculated with 1992 as the base period, and percent changes will be available at the same level of component detail now shown for the constant-1987-dollar series in the "Selected NIPA Tables." Summary tables showing the chained dollar-denominated indexes and the contributions of the major components to the growth in real GDP will be available for recent periods in the GDP news release. More detailed dollar-denominated indexes based on both the new featured measure and on fixed-1992 weights will be made available from STAT-USA shortly after the news release.

BEA also will present tables showing the contributions of the major components to the growth in real GDP for periods of particular interest to users. Users will find that they can easily prepare close approximations of contributions to real GDP growth or to the growth of other aggregates. Table 1 shows how to estimate these contributions to real GDP growth using the last cyclical expansion as an example./8/ First, the levels of real GDP and its major components for the initial quarter are set equal to the published current-dollar levels. Second, corresponding dollar series for the second quarter of 1990 are computed by extrapolating (multiplying) the third-quarter 1982 level for each component by the percent change in the chain output index for that component. Finally, the contribution of each component to the change in GDP is calculated as the ratio of the dollar change in each component to the dollar change in GDP. Table 2 presents approximations of the contributions of the major components to the growth in real GDP for each economic expansion since 1960.

In addition to a table that shows contributions of the major components to the growth in real GDP, BEA will also provide constant-dollar denominated series using both the new featured measure and the fixed-1992-weighted measure./9/ Because the formula used to calculate the new featured measure uses weights of more than one period, the corresponding constant-dollar denominated series will not be additive. Nevertheless, for years close to the base year, the detailed components of these dollar series will be useful because they will be virtually additive (that is, the sums of the detailed-component dollar series will be very close to the independently calculated aggregates). However, as one moves away from the base period, the additivity of the components of the series will diminish. For the fixed-1992-weighted dollar series, the components will be additive in all periods. However, as one moves away from the base period, the substitution bias in the aggregate fixed-weighted measures will grow, and these measures will present an inaccurate picture of economic activity in those periods. As a result of these problems, BEA's chain-weighted annual indexes and tables of contributions will provide a better basis for assessing long-term growth in the economy and for comparing business cycles.

As part of the comprehensive revision, BEA is working on developing methods for calculating chain-weighted estimates of inventory investment that facilitate the evaluation of the impact of inventories on changes in real GDP. As part of its research on alternative measures, BEA is also working on developing capital stock estimates that will be consistent with the new chain-weighted measures of output and prices.

1. For a discussion of this research, see the following SURVEY articles: Allan H. Young, "Alternative Measures of Change in Real Output and Prices, Quarterly Estimates for 1959–92" in March 1993; Allan H. Young, "Alternative Measures of Change in Real Output and Prices" in April 1992; Jack E. Triplett, "Economic Theory and BEA's Alternative Quantity and Price Indexes" in April 1992; and Allan H. Young, "Alternative Measures of Real GNP" in April 1989.

2. For recent periods, modified procedures are used to calculate the alternative measures, because annual weights for the most recent year are not available. For the currently published chain-type measure, the estimates beginning with the third quarter of 1993 are calculated using 1993 weights—that is, they are calculated using a fixed-1993-weight formula. For the currently published benchmark-years measure, the estimates beginning with the third quarter of 1992 are calculated using weights for 1992 and 1993. For additional details, see pages 32–33 of the March 1993 SURVEY.

3. For recent periods, the substitution bias in prices is smaller than that in output. For example, the rate of increase in prices—as measured by the fixed-1987-weighted measure of gross domestic purchases prices—is overstated by 0.2 percentage point in the second quarter of 1995, compared with the 0.7-percentage-point overstatement in real GDP. In 1993 and 1994, the rate of increase in prices is also overstated by an average of 0.2 percentage point, compared with 0.6 percentage point for output. The smaller overstatement in prices occurs mainly because for goods with falling relative prices—such as computers—changes in output have been so much greater than changes in prices.

4. Because contractions are shorter than expansions, it should not be assumed that the effects of the introduction of chain-type measures will offset one another.

5. The Bureau of Labor Statistics (BLS) prepares annual
measures of multifactor productivity and quarterly measures of labor productivity
for major sectors. Since July 1994, the annual BLS measures of multifactor
productivity have been prepared using a chain-type annual-weighted output
series provided by BEA. In late 1995 or early 1996, the quarterly labor
productivity series also will be prepared using new measures of output in
the nonfarm business sector based on the chain-weighted real GDP. This change
will be discussed in a forthcoming article in the *Monthly Labor Review*.
The effects of using chain-type measures for productivity analysis were also
discussed on page 97 of the *1995 Economic Report of the President*.

6. For information about the difference in the second quarter of 1995, see the "Business Situation" article in this issue.

7. BEA's economic information is available online through subscription to STAT-USA's Economic Bulletin Board or Internet service. For more information, call (202) 482–1986.

8. The methodology used to estimate the component contributions to the rate of growth of GDP is a close approximation, as indicated by the "residual" line in table 1. The tables of component contributions that BEA will present as part of the comprehensive revision will use exact formulas for attributing growth to the components of GDP or of other aggregates.

9. For the forthcoming comprehensive NIPA revision, 1992 will be used as the base period for preparing constant-dollar series at the most detailed component level, because 1992 is the latest year for which the current-dollar estimates will not be subject to revision until the next comprehensive NIPA revision. These detailed series provide the inputs used for calculating the chain-weighted measures.