Christian Ehemann, assisted by Mary W. Hook and Clifton Baldwin, directed the assembling of the database and prepared the alternative measures of real GDP and GDP prices. Robert P. Parker and Jack E. Triplett contributed to the development of the article.

This article presents quarterly estimates of the alternative measures of change in real output and prices that BEA introduced in April 1992./1/ It also updates the annual estimates for 1988–90 to incorporate the results of the annual revision of the national income and product accounts (NIPA's) in July 1992 and extends the annual estimates to 1991./2/ The alternative measures, which supplement BEA's featured fixed-weighted measures, are especially useful for studies of long-term economic growth, for comparisons of business cycles, and for gauging the effect of changes in the economy's relative price structure on the measurement of real gross domestic product (GDP). Beginning with the May issue of the SURVEY OF CURRENT BUSINESS, BEA will publish current quarterly estimates of the alternative measures in the regular presentation of the preliminary and final NIPA estimates.

BEA's featured measure of real GDP is a fixed-weighted measure in which quantities in all periods are weighted with 1987 prices./3/ The advantages of this type of measure are the following: (1) The index number formula itself is simple; (2) any two, or in fact any number of, periods can be compared on a consistent basis; and (3) the index may be stated in terms of real dollars (by using only the numerator of the formula). The third advantage makes it possible to "add up" the components of real output and to compute for each component the "real dollar share" of GDP and the "real dollar contribution" to the change in GDP.

The disadvantage of the fixed-weighted measure lies in the fact that it assumes the relative price structure of the economy does not change. It provides a good approximation for real growth in the economy as long as the change in the relative price structure remains fairly small, which is likely to be true over fairly short time periods. For longer periods, however, larger changes in price structure have taken place in the U.S. economy. The two alternative measures are designed to allow for changes over time in the relative price structure. For this reason, they provide a better basis for assessing long-term growth in the economy and for comparing business cycles.

The alternative measures also provide a way to monitor the extent to which changes in the relative price structure since 1987 are affecting the measurement of real GDP. If the difference between the 1987-weighted index and the alternatives becomes large and prolonged, the alternative indexes will be more appropriate than the 1987-weighted index for analysis of the most recent periods./4/ BEA will discuss such differences in the "Business Situation," the lead article in the SURVEY.

The first section of this article provides a summary description of the annual alternative measures for real GDP, explains the calculation of the quarterly values for these measures, and compares the quarterly measures of real GDP; the second section briefly describes and compares the GDP price measures.

Tables 1 and 2, at the end of this article, present the annual and quarterly estimates of the fixed-weighted and alternative quantity and price measures for 1988–92. Table 1 presents the index numbers for gross domestic product and its major components and for other selected aggregates, and table 2 presents percent changes for these series.

Unlike the fixed-weighted measure, the two alternative measures of real GDP
are not based on the price weights of a single base year. In one of the
alternative measures, the *chain-type annual-weighted quantity index*,
the weights change each year; in the other, the *benchmark-years-weighted
quantity index*, the weights change each benchmark year—that is,
at about 5-year intervals. These alternative indexes use the Fisher Ideal
index formula to provide a measure of change between two
periods./5/

*Chain-type annual-weighted quantity index*.—For this alternative,
a Fisher Ideal quantity index is used to calculate the change from year
*t-1* to year *t*. Thus, the annual change is provided by the geometric
mean of the year *t* values of two fixed-weighted quantity indexes,
one of which uses prices of year *t-1* as weights and the other, prices
of year *t* as weights. Annual changes computed in this manner are "chained"
(multiplied) together to form a time series./6/

*Benchmark-years-weighted quantity index*.—For this alternative,
the Fisher Ideal index formula is adapted to use weights from pairs of adjacent
benchmark years. (Benchmark years are used as weighting periods because,
for components of GDP that incorporate information from the quinquennial
economic censuses, the benchmark-year price and quantity estimates are considered
to be more accurate than those for other years.) For each pair of benchmark
years and for the interval between them, two fixed-weighted quantity indexes
are computed: One with the prices of the first benchmark year as weights,
and the other with the prices of the second benchmark year as weights. The
geometric mean of these indexes is the benchmark-years-weighted quantity
index. For example, for each year between the benchmark years of 1982 and
1987, the benchmark-years-weighted quantity index is the geometric mean of
the fixed-weighted quantity index that uses 1982 prices as weights and the
fixed-weighted quantity index that uses 1987 prices as
weights./7/ For years beyond the most recent benchmark
year, the benchmark-years-weighted quantity index is calculated as the geometric
mean of the fixed-weighted quantity index that uses prices of the most recent
benchmark year and the fixed-weighted quantity index that uses prices of
the most recent year./8/ Thus, at present, the index for
years beyond 1987 is calculated using 1987 and 1991 prices. When prices for
1992—the next benchmark year—become available during the 1993 annual
NIPA revision, the benchmark-years-weighted quantity index for the third
quarter of 1987 forward will be recalculated using prices for 1987 and 1992.
A year later, when prices for 1993 become available, the index will be extended
to 1993 using 1992 prices as those of the most recent benchmark year and
1993 prices as those of the most recent year.

The procedure for calculating the quarterly alternative measures is similar
to that for the annual measures. For the chain-type annual-weighted index,
the quarterly quantity indexes use the annual prices for adjacent years as
weights. (Annual prices rather than quarterly prices are used as weights
because annual prices are more stable and contain less statistical noise
than quarterly prices.) The calculation of the quarterly values are "centered"
between adjacent years—that is, price weights for year *t-1* and
year *t* provide the basis for calculating the quarterly values of the
chain-type index for the third and fourth quarters of year *t-1* and
for the first and second quarters of year *t*.

For the benchmark-years-weighted index, the quarterly quantity indexes use the annual prices for adjacent benchmark years as weights. These calculations are also centered—for example, the quarterly fixed-weighted quantity indexes that use 1982 and 1987 prices as weights are used to calculate the benchmark-years index from the third quarter of 1982 to the second quarter of 1987.

Because the calculation of the annual alternative measures is carried out in more detail than that for the quarterly measures, the quarterly measures are adjusted so that the annual average of the four quarterly values equals the corresponding annual measure. The number of detailed components in the quarterly and annual calculations is shown in table A.

*Most recent estimates*.—For the chain-type annual-weighted index,
the most recent quarterly values are calculated using annual prices for only
the most recently available year as weights. For the benchmark-years-weighted
index, the most recent quarterly values are calculated using the annual prices
for the most recent benchmark year and for the most recently available year
as weights. Each year, when more recent annual prices become available, the
index is recalculated for the period since the most recent benchmark year.
Table B illustrates the approaches used for the
two alternative indexes, including a modification to the above scheme for
the benchmark-years-weighted index that is necessary in the benchmark and
following year.

The trends in the quarterly real GDP measures reflect those in the annual measures that were described in the April 1992 SURVEY article. From the business cycle peak in the first quarter of 1960 to 1987, the alternative indexes increase 14 to 16 percent more than the featured measure: The fixed-weighted index increases 129.9 percent, the chain-type annual-weighted index increases 147.5 percent, and the benchmark-years-weighted index increases 150.0 percent. In contrast, from 1987 to the fourth quarter of 1992, the alternative indexes increase 3 percent less than the featured measure: The fixed-weighted index increases 9.9 percent, and both alternative indexes increase 9.6 percent. Over the complete period from the first quarter of 1960 to the fourth quarter of 1992, the alternative indexes increase 12 to 14 percent more than the fixed-weighted index: The fixed-weighted index increases 152.6 percent, the chain-type index increases 171.3 percent, and the benchmark-years index increases 174.0 percent.

The largest differences between the quarterly changes in the alternative indexes and those in the fixed-weighted index are more than 2.0 percentage points at an annual rate (table C). In the 1960's, such differences occurred in one or both of the alternatives in four quarters. In the 1970's, such differences occurred in three quarters. In the fourth quarter of 1973, the difference was 3.2 percentage points for the chain-type index. After 1984, there are no differences larger than 1.0 percentage point.

An analysis of the sources of the differences between changes in the fixed-weighted index and changes in the alternative indexes requires further work. It is clear, however, that changes in the prices and quantities of computers and peripheral equipment are a major source of the differences over both long periods and from quarter to quarter. The output of computers and peripheral equipment has increased much more rapidly than that of other components of GDP, and computer prices have declined very rapidly. As a result, the output of computers received a higher valuation in the alternative indexes, which reflect the higher prices in earlier years, than in the fixed-weighted index, which reflects the relatively lower price in 1987. The effect of the higher valuation of computers in the alternative indexes is largest in producers' durable equipment. Also affected are personal consumption expenditures, government purchases, exports, and imports.

*Cyclical comparisons*.—The timing of the business cycle peaks
and troughs in real GDP is the same for the alternative indexes as for the
fixed-weighted index.

The alternative indexes are particularly useful for measuring the amplitude of business cycle contractions and expansions. Generally, the amplitudes of cyclical contractions and expansions in earlier years have been reduced as the fixed-weighted measure has been rebased to a more recent year in each subsequent comprehensive revision. This phenomenon has occurred because the prices of the components of real GDP that are cyclically sensitive tend either to decline or to increase more slowly than the prices of the components that are not, with the consequence that the weight of the cyclically sensitive components—including computers and peripheral equipment—has become smaller in each rebasing.

Table D shows the amplitudes of cyclical contractions and expansions measured with the fixed-weighted index and the alternative indexes. In 1960 and in 1969–70, the cyclical contractions in the alternative indexes are about twice as large as those in the fixed-weighted index. In the 1973–75 contraction, the alternative indexes decline somewhat more than the fixed-weighted index. However, in 1980, the expected pattern does not hold, and in 1981–82, the results are mixed. In each of the complete expansions, the alternative indexes increase at a faster rate than the fixed-weighted index.

In the current business cycle, the differences between the fixed-weighted index and the alternative indexes are small. The chain-type annual-weighted index decreases somewhat less than the other indexes in the contraction following the peak in the second quarter of 1990. Both alternative indexes increase somewhat less than the fixed-weighted index following the trough in the first quarter of 1991. In the fourth quarter of 1992, the fixed-weighted index was up 1.8 percent from the second-quarter 1990 peak; the chain-type index was up 1.6 percent, and the benchmark-years index was up 1.7 percent.

The featured measure of GDP prices is the GDP price index with 1987 quantity
weights. The two alternative measures of GDP prices are the *chain-type
annual-weighted price index* and the *benchmark-years-weighted price
index*. On both a quarterly and an annual basis, these price indexes are
analogues to the alternative quantity indexes, with the variables for price
and quantity simply reversed in the index formulas.

The fixed-weighted price indexes for several components of GDP—producers' durable equipment, exports, and imports—and for total GDP and other aggregates containing these components are not shown in the NIPA tables for years before 1982, because the use of the relative quantity structure in 1987 to measure price change for those years is inappropriate. Before 1982, the combination of the high level and very rapid decline of the price index for computers and the large 1987 quantity weight for computers results in either declines or very small increases in the fixed-weighted price indexes for these series./9/

The quarterly alternative GDP price indexes are like the corresponding quantity indexes in that they increase more rapidly than the fixed-weighted index before 1987 and less rapidly after 1987. From the first quarter of 1982 to 1987, the alternative indexes increase 5 percent more than the fixed-weighted index: The fixed-weighted index increases 19.9 percent, the chain-type annual-weighted index increases 20.8 percent, and the benchmark-years-weighted index increases 20.9 percent. From 1987 to the fourth quarter of 1992, the alternative indexes increase 1 to 3 percent less than the fixed-weighted index: The fixed-weighted index increases 22.8 percent, the chain-type index increases 22.2 percent, and the benchmark-years index increases 22.5 percent. The largest differences between the quarterly changes in the alternative indexes and those in the fixed-weighted index are between 0.5 and 1.0 percentage point at an annual rate (table E).

1. See Allan H. Young, "Alternative Measures of Change in Real Output and Prices," SURVEY OF CURRENT BUSINESS 72 (April 1992): 32–48. Also see Jack E. Triplett, "Economic Theory and BEA's Alternative Quantity and Price Indexes," SURVEY 72 (April 1992): 49–52.

2. of the annual and quarterly alternative output and price
measures for 1959–87 are available in U.S. Department of Commerce, Bureau
of Economic Analysis, *National Income and Product Accounts of the United
States: Volume 2, 1959–88* (Washington, DC: U.S. Government Printing
Office, September 1992). Order information is on the preceding page.

3. In this article, in order to facilitate comparisons with the alternative measures, BEA's featured measure of real GDP is shown as a fixed-weighted quantity index in which the weights are 1987 prices. This index, divided by 100 and multiplied by the 1987 value of current-dollar GDP, is equal to real GDP in constant 1987 dollars—the form in which real GDP is customarily presented in the NIPA charts and tables. Percentage changes in these two forms of real GDP are identical.

4. As described in the article in the April 1992 SURVEY, BEA plans to introduce a fixed-weighted quantity index that is calculated using 1992 prices as a third alternative following the 1993 annual NIPA revision. This index will provide an advance indication of how the fixed-weighted index will be affected by the updating of the price weights in the next comprehensive revision. If changes in the relative price structure since 1987 become an important factor, this third alternative, like those presented in this article, would be more appropriate than the 1987-weighted index for analysis of the most recent periods. (None of the alternative indexes will indicate the extent to which measured growth may be affected by revised source data and changes in methodology in subsequent annual revisions or in the comprehensive revision. Such effects can be as large as or larger than the effect of the choice of price weights.)

5. A Fisher Ideal quantity index is the geometric mean of a Laspeyres and a Paasche quantity index. The Laspeyres quantity index uses the prices of the first of the two periods being compared to weight quantities. The Paasche quantity index uses the prices of the second period. Given that the Fisher Ideal index is a geometric mean, the change in the Fisher Ideal index falls between the changes in the Paasche and Laspeyres indexes.

6. For example, if the percent change from year 1 to year 2 is 4.0 percent and from year 2 to year 3 is 5.0 percent, the annual changes are chained together as follows: Year 1=1.00, year 2=1.00 × 1.04, and year 3=1.00 × 1.04 × 1.05.

7. Except for statistical and definitional revisions, the former index corresponds to the fixed-weighted GDP measure used before the comprehensive revision in 1991. The latter index is the presently featured fixed-weighted GDP measure.

8. In the context of the alternative measures, prices of the most recent year refer to estimates prepared in the annual NIPA revision. They do not refer to earlier, preliminary annual estimates that incorporate the current quarterly estimates for the third and fourth quarters of the year. Thus, until the 1993 annual NIPA revision provides detailed 1992 estimates, the most recent annual estimates are those for 1991.

9. Rates of change in the annual fixed-weighted GDP price index for periods before 1982 are shown for illustrative purposes in tables C and D in the article in the April 1992 SURVEY.