Box: The Measurement of the Change in Real GPO by Industry

In this article, BEA departs from its traditional use of a fixed-weighted quantity index for measuring real manufacturing GPO and total real GDP for 1977–87. Instead, BEA uses one of the alternative measures—the benchmark-years-weighted index—that were introduced in April 1992 as part of the most recent comprehensive revision of the national income and product accounts. (See Allan H. Young, "Alternative Measures of Change in Real Output and Prices," SURVEY OF CURRENT BUSINESS 72 (April 1992): 32–48.)

Measuring real growth

Manufacturing GPO and GDP, 1977–87.—A fixed-weighted index is a good measure of real growth as long as the relative price structure of the economy does not change very much from that in the base year. Because of substantial changes in the relative price structure in manufacturing—changes that were largely traceable to the rapidly declining prices of computers and peripheral equipment—the currently used fixed-weighted measure with 1987 price weights is appropriate for only a fairly short period of years around 1987. For timespans covering earlier years, the use of fixed 1987 price weights understates the growth in manufacturing GPO, because the rapid growth in the output of the computer industry is weighted not by the price of computers in those years but by the lower 1987 price. Similarly, the use of fixed 1987 price weights understates the growth in GDP in these timespans. However, the understatement of GDP growth is less than that of manufacturing GPO, because the output of the computer industry accounts for a smaller portion of total GDP.

A benchmark-years-weighted index, unlike a fixed-weighted index, is not based on the price weights of a single year; the weights change each benchmark year—that is, at about 5-year intervals./1/ Over time, the weighting periods are shifted forward to reflect the prices that prevailed in the timespan being measured. For example, the period 1977–82 uses price weights for 1977 and 1982, and the period 1982–87 uses price weights for 1982 and 1987. As a result, the benchmark-years-weighted index is a more accurate measure of growth from benchmark year to benchmark year.

Exhibit 1 shows growth rates for manufacturing GPO using the benchmark-years-weighted measure and three fixed-weighted measures with 1977, 1982, and 1987 prices as weights.

In part A of the exhibit, the benchmark-years-weighted measure, the preferred measure of growth for 1977–87, shows an average annual increase of 2.5 percent. The three fixed-weighted measures show that the measurement of the growth rate for manufacturing is quite sensitive to the choice of weights. For example, the average annual growth rate for manufacturing for 1977–87 is 4.3 percent using weights from the beginning of the timespan (the fixed-1977-weighted measure), and it is only 1.7 percent using weights from the end of the timespan (the fixed-1987-weighted measure).

Both the 1977-weighted measure and the 1987-weighted measure present certain problems when they are used to measure output over the period 1977–87. The 4.3-percent growth rate calculated using the 1977-weighted measure is too high, largely because the change in output for 1982–87 is measured using 1977 prices, which were quite different from the actual prices that prevailed in the period. In contrast, the 1.7-percent growth rate calculated using the 1987-weighted measure is too low, largely because the change in output for 1977–82 is measured using 1987 prices.

Part B of the exhibit shows the growth rates for the previously published estimates of manufacturing GPO, which were calculated using fixed 1982 weights. The differences between the changes for this measure and those for the fixed-1982-weighted measure in part A indicate the effects of incorporating the revised source data and the improvements in methodology described in this article.

Part C of the exhibit reproduces a table from the April 1992 SURVEY article on the alternative measures of real output and prices. The growth rates in the table, which were calculated from provisional estimates that incorporated some of the revised data from the December 1991 comprehensive revision, are similar to those shown in part A.

Nonmanufacturing GPO, 1977–87.—For 1977–87, the fixed-1987-weighted measure is used for nonmanufacturing industries. For these industries, the choice of relative price weights has much less effect than it did for manufacturing; in addition, considerable additional work would be required to calculate the benchmark-years-weighted indexes, especially for the industries for which double deflation is not used in their estimation. When the growth of a nonmanufacturing industry is compared with that of manufacturing or of GDP, the fixed-weighted measure for the nonmanufacturing industry is, in effect, serving as a proxy for a benchmark-years-weighted measure.

GPO for all industries, 1987–90.—For 1987–90, the fixed-1987-weighted measure is used for all industries and for GDP. The differences between this measure and a benchmark-years-weighted measure in which 1990 is treated as if it were a benchmark year are fairly small.

Measuring industry shares

As noted in the April 1992 SURVEY article, a benchmark-years-weighted index has somewhat different properties than the traditional fixed-weighted index. Its use in the calculation of change in real GPO by industry means that questions such as whether manufacturing is becoming a larger or smaller part of the total economy must be addressed in somewhat different ways. (One should note that if the question is simply the relative size of manufacturing at a point in time, the current-dollar share provides the answer.)

With the traditional fixed-weighted measures, the question of whether manufacturing is becoming a larger or smaller part of the total economy could be answered either by comparing growth rates in real manufacturing GPO with those in real GDP or by calculating the change in the constant-dollar share of manufacturing GPO in GDP. The following example (in which the manufacturing share is increasing) illustrates that the two approaches are equivalent.

Period Real GDP Real manufacturing GPO "Constant-dollar" share
Percent change10.0 15.04.5

The constant-dollar share of manufacturing increases 4.5 percent—from 20.0 percent to 20.9 percent of total GDP. The same result may be obtained directly from the changes in manufacturing GPO and GDP by stating them as ratios of the period 2 values to the period 1 values as follows: (1.15/1.10)×100–100=4.5%.

It is sometimes not appreciated that the use of constant-dollar shares relies on a unique property of fixed-weighted indexes: Only with fixed-weighted indexes can real GDP be expressed as the sum of real GDP components. Because benchmark-years-weighted indexes do not share this "additive" property, one cannot convert these indexes into dollar values and then compute time series of shares of real GDP that add up precisely.

The simplest way to use the benchmark-years-weighted indexes to answer the question is to compare growth rates, but it is also possible to calculate approximations of the manufacturing share. Exhibit 2 shows two such approximations. Approximation A is calculated by extrapolating forward and backward the 1982 levels of current-dollar manufacturing GPO and GDP using the benchmark-years-weighted indexes. Approximation B is calculated in the same way except that the extrapolations are from the 1987 current-dollar levels. Approximations calculated in this way will not produce shares that add up precisely to 100 percent, but the approximation error will usually be small when the calculations do not extend far from the base year. It should be noted that a difference in the levels of approximations A and B does not indicate a change in the real manufacturing share; it reflects the change in the relative price structure of manufacturing from 1982 to 1987.

Shares for all industries calculated using approximation B for manufacturing and for GDP and fixed-weighted measures for the nonmanufacturing industries are shown in table 2 of the article. The sum of the industry shares is 1.6 percent larger than the GDP approximation in 1977, and it is 0.3 percent larger in 1982; these differences are included in "percentage not allocated by industry" in the table. BEA plans to further explore the properties of various approximations in the future.

1. For the benchmark-years-weighted index, the Fisher Ideal index formula is adapted to use weights from pairs of adjacent benchmark years. For each pair of benchmark years, two fixed-weighted quantity indexes are computed: One with prices of the first benchmark year as weights, and the other with prices of the second benchmark year as weights. The geometric mean of these two indexes is the benchmark-years-weighted index.