Chart 3. Growth rates of alternative capital stock measures, total manufacturing,

1963-81
Annual Annual

percent change percent change
8.0 : 8.0
75 Gross perpetual 4 75
7.0 | °° Inventory measure 470°,
66 F 4,65
60 + ., + 60
55 + 4 65
5.0 + 4 50
45 + 4 45
40 + 4 40
35 - 4 35
3.0 + 4.30)
25 - 4 25
2.0 - 4 2.0
1.5: 4 15
10 - 41.0
05 F 4 05
0.0 [a a A LAN SO 0.0

1981

The discard assumption used was identical to the BLS
discard assumption. In using the perpetual inventory
method to measure capital, BLS assumes capital assets are
discarded as.a function of the average useful life of an
asset. For..each industry, capital assets. of similar
characteristics are. grouped into asset-type categories. An
average useful life for each type of asset’ is estimated by
the Bureau of Economic Analysis. Because each type
contains many different, although similar, assets, a
particular. asset may have a slightly different average
useful: life than that determined for its asset type. In
addition, capital assets of a given description may exhibit
variation in their useful lives as a result of random
variations in breakage, loss, or obsolesence. Because of
this, discards are assumed to, be normally distributed
around the average service life.

Initially, gross perpetual inventory capital stock meas-
ures were constructed for each detailed asset type within
each 2-digit sic manufacturing industry. The detailed
asset-type measures in each industry were then summed
to obtain the 2-digit industry. gross capital stock measure.
The durable, nondurable, and total manufacturing indus-
try. gross capital stock measures were: similarly: obtained
by summing .the appropriate 2-digit sic manufacturing
industry measures.'®

Measurement of multifactor productivity

The impact on multifactor productivity of using a static
assumption to:estimate capital discards was examined by
comparing alternative measures of multifactor productiv-
ity. The measures were'constructed by methods similar to
those used in constructing the BLS published multifactor
productivity measures for major sectors. The growth
rate of multifactor’ productivity for each industry ‘is
defined as the growth rate of output minus the weighted
growth rates of labor and capital inputs, where the
weights are the cost shares of the respective inputs in total
cost.'® Multifactor productivity was measured using first
the gross book value capital stock measure and, alterna-
tively, the gross perpetual inventory capital stock measure
for each industry for the years 1962-81.

Results.

As noted, actual capital discards, derived from the
gross book value data, increase and. decrease substantially
with economic slowdowns and. expansions, respectively,
in. each: industry studied.!?: This ‘isin: contrast to: the
smooth capital discard pattern assumed in the BLS capital
measures. For each industry, the growth. rate of gross
book value capital ‘stock showed substantially more

31


MONTHLY LABOR REVIEW June 1988 e Capital Discards in Productivity Measurement

percent in 1973-86. For further information on trends in multifactor
Productivity, see Multifactor Productivity Measures, 1986, USDL, 87-436
Bureau of Labor Statistics, Oct. 13, 1987). °

7A detailed explanation of the multifactor productivity measure
published by BLS is available in Trends in Multifactor Productivity,
1948-81, Bulletin 2178 (Bureau of Labor Statistics, September 1983).

*Output is defined as real gross product originating in a given
industry, which is net of its intermediate inputs. The multifactor
productivity measurement formula is derived from an assumed ptoduc-
tion relationship: Q(t) = A(W//(K(1),L (9), where Q(t) is real output, K(t)
is real capital input, L(t) is real labor input, and A(t) is an index of
neutral technological progress, or multifactor productivity. Taking the
logarithmic differential of this production function with respect to time,
and assuming perfect competition and constant .returns to scale, a
measure of multifactor productivity growth can be derived from
observed input and output quantities and prices:

where P* is the price of labor services, P* is the rental price of
capital services, P is the price of output, and the “dot” notation refers to
the rate of change of the variable over time. The growth rate of
multifactor productivity is equal to the growth rate of output minus the
cost-share-weighted growth rates of labor and capital inputs. The cost
share of labor input is the expenditure on labor, calculated as the price of
labor services multiplied by the quantity of labor services, PL, divided
by total input cost, calculated as the price of output multiplied by the
quantity of output, or PQ. Similarly, the cost share of capital input is
calculated as expenditure on capital input, P*K, divided by total input
cost, PQ. Under constant returns to scale and perfect competition, total
input cost is equal to the value of total output.. That is,

PQ = (PL+PXK )

“The BLS measures capital stock using the perpetual inventory
method. This method is described below.

SBLS estimates capital discards using a constant discard pattern based
on the estimated average useful lives of capital assets. An assumption of
a constant discard pattern has generally been made when measuring
capital stock using the perpetual inventory method. For example, see L.
Christensen and D. Jorgenson, “The Measurement of U.S. Real Capital
Input, 1929-1967,” Review of Income and Wealth, 1969, pp:
293-97; E. Denison, Accounting for United States Economic: Growth,
1929-1969 (Washington, The Brookings Institution, 1974), pp.
156-57; D. Jorgenson and Z. Griliches, “The Explanation of Produc-
tivity Change,” Survey of Current Business, May 1969, pp. 31-38; Fixed
Reproducible Tangible Wealth in the United States, 1925-79 Us.
Department of Commerce, March 1982), pp. T-1—T-15;.Capital Stock
Estimates for Input-Output Industries: Methods and Data, Bulletin 2034
Bureau of Labor Statistics, 1979), pp. 1-24; and Trends in Multifactor
Productivity, 1948-81, pp. 40-45; y

‘This study, of course, does not attempt a complete analysis of the
business cycle movements of capital discards, capital stock, and
multifactor productivity. The focus of the empirical work performed is
annual variation in capital discards, using alternative measures of
discards, and the effects of the discard series on trends in multifactor
productivity. Additional study of the capital discard-data, and related
data, within the context of the business cycle is contemplated. Some
exploratory work has examined movements in capital discards over the
business cycle by correlating the level of capital discards and the rate of
growth of output for each industry. These correlations, performed using
data for 1964-81, are negative for 18 of the 20 2-digit sic manufacturing
industries and for the durable, nondurable, and total manufacturing
sectors. These results indicate a decline in the level of discards as the rate
of growth of output increases during business cycle expansions and an
increase in the level of discards as the rate of output growth declines
during business cycle contractions.

"For further analysis and discussion of this issue, see Susan G. Powers,
“Cyclical Variation in Capital Stock Measures: Implications for

34

Multifactor Productivity,” Ph. D. thesis (State University of New York

at Binghamton, 1985):

"For a discussion of capital discarding, see A. Marston, R. Winfrey,
and J. Hempstead, Engineering Valuation and Depreciation (New York,
McGraw-Hill Book Company, Inc., 1953), pp: 139-42.

°Capital discards are measured for 1963-81, rather than 1962-81,
because of the lagged term in the discard definition.

1°Net capital stock measures are. constructed by BLS using the
Perpetual inventory method. Capital in the ‘current year is equal to
capital in the previous year, plus new investment, minus capital discards
and decay. Capital discards are determined based on the average useful
lives of capital assets. Decay in the productive efficiency of assets is

. approximated using a hyperbolic functional form. The hyperbolic

function is concave, implying slower decay during the early life of an
asset and faster decay during the later years.

"Net capital stock measures are used more frequently than gross
measures. However, net book value data often reflect an accounting, rather
than an economic, concept of depreciation. Comparing gross book value
and gross perpetual inventory, capital stock measures avoid. the bias that
might result from comparing net capital stock measures based on different
depreciation concepts. Note that capital discards measured using the gross
book value capital stock series reflect the original value of the capital
asset, rather than the remaining value of the asset after adjusting for
loss in productive efficiency of the asset over time. Similarly, discards
implied by the gross perpetual inventory capital stock measures are not
adjusted for loss in productive efficiency.

"°These data are available for manufacturing industries at the 2- ,3- ,
and 4-digit levels of the Standard Industrial Classification of industries.
The first year of available data, 1957, is not used. Values for the missing
observations, years 1965 and 1966, were interpolated to complete the
data series for 1962-81. The Census Bureau gross book value data were
regressed on gross book value data series constructed using Bureau of
Economic Analysis gross investment data and a discard assumption. The
fitted values for the Census Bureau gross book value series in 1965 and
1966 from this regression were used as estimated values.

This method is described in John Kendrick, Improving Company
Productivity: Handbook with Case Studies (Baltimore, The Johns
Hopkins University Press, 1984), pp. 42-46.

“Gross book value price deflators were developed for each industry
from 1962-81. First, the deflators were constructed for each industry’s
indiyidual asset types. Total gross book value price deflators for each
industry were then constructed as weighted sums of the individual
‘detailed-asset-type gross book value price deflators. The weights used to
construct the industry gross book value price deflators were the sum of
constant-dollar investment in asset i in years X-L to X, divided by the
sum of constant-dollar investment in total assets in years X-L to X. L is
the average service life of a capital asset. The weights constructed were
variable weights, changing each year.

The individual-asset-type deflators for each industry were constructed
using a method that considers the vintage composition of an industry’s
‘gross book value in any given year. The gross book value of capital for a
given year is defined as the original cost valuation of existing capital
assets, and so includes capital assets of different vintages. This method
estimates the vintage distribution of assets included in a given year’s
gross book value figure. Vintages from the previous L years were
assumed to remain in a given year’s gross book value. The proportion of
investment in each vintage within the gross book value figure was
determined by the original level of gross investment in the vintage.

The method used can be summarized as follows. The gross book value
price deflator value in year X is the sum of historical-dollar gross
investment in years X-L to X, divided by the sum of constant-dollar gross
investment in years X-L to X, This general formulation was constructed
using data on each asset type for each industry. The historical- and
constant-dollar gross investment data for each asset type in each
industry were obtained from the Bureau of Economic Analysis, as were
the average useful life values for each asset type by industry.

'SThe Bureau of Economic Analysis estimates of the average useful
lives of assets, and a truncated normal distribution ranging from 2


MONTHLY LABOR REVIEW June 1988 © Capital Discards in Productivity Measurement

capital discards. This contrasts with the smooth pattern of
capital discards that underlies the BLS capital stock

measures. The BLS uses the perpetual inventory method to °

construct net capital stock measures, that is, measures of
capital stock net of the decay in the productive efficiency
of existing. capital assets.'° The perpetual inventory

method measures net capital stock as the cumulated value.

of investment minus cumulated discards and cumulated
decay of capital assets. Under ‘the perpetual inventory

“method, capital discards are determined by a static
assumption, and this results in a smooth pattern of capital
discards over the business cycle.

For each industry, gross capital stock measures are -

constructed using the perpetual inventory method, and

are used to derive the capital discard series implied by the’

method’s discard assumption for the years 1963 to 1981.
Gross, rather than net, capital stock measures are created,
to facilitate’comparison with the gross book value capital
stock measures.'! Under the perpetual inventory method,
“gross capital stock is defined as the cumilated value of
investment; minus the cumulated value of discards. This
measure can be expressed as:

GPIM, = GPIM,, + GI, - DI
where:

GPIM, is the gross perpetual inventory method capital
stock in period f; ©
Gl, is gross investment in period f; and
DI, is capital discards in period ¢.

Capital discards, implicit in the gross perpetual inven-
tory capital stock measure, can be defined in terms of
gross investment and the gross capital stock measure:

DI; =: GI, = (GPIM, -°GPIM, ,)

This measure of capital discards is computed for each
industry. The gross investment series is measured using
gross investment data from the Commerce Departnient’s
Bureau of Economic’ Analysis. The gross perpetual
inventory capital stock measures are developed using the
gross investment data, and the discard assumption used in
BLS methods.

Measurement of capital stock

Gross book value estimates. Gross book value capital
stock is measured for each industry for the years 1962-81,
and used to compute the discard measures described
above. The gross book value capital stock measures are
also useful because movements in these measures over
time can be compared, by industry, to movements in ‘the
gross perpetual inventory capital’ stock measures. This
comparison is made to.determine whether the use of gross
book value data'to reflect actual capital discards signifi-
cantly affects: cyclical: movements. in capital stock. The

30

sensitivity of the multifactor: productivity’ measure: to
movements in discards is also studied using the book

“value capital measures. Multifactor productivity is com-

puted for each industry using the gross book value capital
stock measures, and compared to multifactor productivity
measures computed using the gross perpetual inventory
method measures of capital stock.

As indicated earlier, the. gross book value capital stock
measures are constructed. by deflating historical-dollar
gross book value data for each industry for the years
1962-81. Gross book value data are obtained from the
Annual Survey of Manufactures and ‘the Census of
Manufactures. Census gross book value is defined as the
gross book value of all fixed depreciable assets (buildings,
structures, machinery, and equipment) on the books of

» establishments at the end of the year. Data are available

by detailed manufacturing industry’? for 1957, 1962-64,
‘and 1967-81.

Price deflators for the historical-dollar gross book value
data were constructed for each industry ‘following a
methodology suggested by John Kendrick.’ For a given
year, the gross book value of capital is the value of the
existing capital assets, based on the original cost of the
assets. The existing capital assets include capital pur-
chased in different years, that is, of different vintages.
Development of a capital stock measure using the gross
book value data is possible if the value of the various
vintages of capital assets can be expressed in constant
dollars. This requires a price deflator that considers the
vintage distribution of assets in the gross book value for a
given year, and adjusts.the valuation of capital assets
from historical dollar to constant dollar, based on. this
vintage distribution. The price deflators: developed re-
flected estimates ofthe vintages of capital includedin:a
specific year’s gross book value data, and the proportion
of investment in each vintage, in the.form of Bureau ‘of
Economic Analysis gross investment data and avetage
useful life estimates.'*

Perpetual inventory method ‘estimates. Gross perpetual
inventory method capital stock measures were created for
each industry for the years 1962-81. As indicated above,
the perpetual inventory method measures net capital
stock. as cumulated new capital investment adjusted for
decay and discarding of previously accumulated capital
stock. For a gross capital stock measure, cumulated new
investment is adjusted for the cumulated value of dis-
carded investment, but not for decay.

Constructing ‘a gross perpetual inventory capital stock
measure requires a long historical ‘series: of new capital
investment data foreach‘ year in the capital series and ‘an
assumption regarding capital discards. The’capital invest-
ment data ‘used’ were Bureau of Econorfiic’ Analysis
constant-dollar gross investment data by ‘asset type’ for
each industry, from 1880-1981.


MONTHLY LABOR REVIEW June 1988 e

movement over the business cycle than did the growth
rate of the perpetual inventory-based stock. In contrast,
multifactor productivity based on the gross book value
capital stock measure, which reflects actual capital
discards, displays virtually the same cyclical pattern as
multifactor productivity computed using the gross perpet-
ual inventory capital stock measure, which reflects a
smooth pattern of capital discards. Thus, even though

_ Capital discards do vary over the business cycle, and
incorporating these variations into. the capital stock
measure does increase the cyclical movement of that
measure, this pattern of capital discards is not an
important factor in explaining cyclical variation in the
multifactor productivity measures.

A measure summarizing cyclical movement in the book
value and perpetual inventory method series on capital
discards, capital stock, and multifactor productivity was
computed for each industry. This measure uses the
deviation of the actual series values from trend values as a
proxy for the cyclical movement in the series. The
summary measure of cyclicality is the absolute value of
the percentage difference between the actual and the trend
values of a series, summed over the years 1969 to 1981.7°
Those years respectively contained the initial and the final
business cycle peaks occurring during the study period. A
higher value of the measure indicates that a series has
more extreme movements over the business cycle than a

Capital Discards in Productivity Measurement

series with a lower value. The summary measures of
cyclicality for each industry are presented in table 1.

Actual capital discards in each industry vary substan-
tially over the business cycle, compared to capital
discards implied by the gross perpetual inventory capital
‘stock measures. The summary measure of cyclicality for
capital discards based on the gross book value data, as
shown in table 1, is consistently of a much higher
magnitude than the same measure based on the static
perpetual inventory discard assumption.

The second set of columns in table 1 presents the
summary measures of cyclicality for gross book value and
gross perpetual inventory capital stock in each industry.
Although the perpetual inventory capital stocks do
exhibit some cyclical movements as a result of variation in
gross investment over the business cycle, the book value
measures in each industry consistently exhibit more
extreme cyclical movements. The book value capital stock
measures reflect variation in capital discards, as well as
gross investment, over the business cycle.

The third set of columns in table 1 presents the
summary measures of cyclicality for’ the alternative
measures of multifactor productivity. Multifactor produc-
tivity is first measured using gross book value capital
stock, and then using gross perpetual inventory capital
stock. The resulting multifactor productivity measures
demonstrate similar patterns of cyclical variation, as
evidenced by the small difference between the summary

Table 1. Summary measures of cyclicality in alternative measures of capital discards, growth rates of gross capital stock, and
multifactor productivity, by industry, 1969-81
Standard Capital discards Capital stock growth rates Muttfactor productivity indexes
indeattal Industry Book | Perpetual Book — | Perpetual Book | Perpetual
(Ciassification value | inventory || Difference .| value | inventory | Difference | value | inventory | Difference

hese basis basis basis basis basis basis

3.56 05 3.51 3.74 115, 2.69 17 A7 00

2.92 04 2.88 3.56 1.42 2.44 18 18 00
20 2.62 113 2.49 4.86 1.19 3.67 28 ‘26 02
2 598 01 595 | 10.17 520 497 50 39 aT
22 4.47 12 4.36 18.58 5.31 13.27 52 51 01
23 22.72 or | 2271 | 51.66 216 | 49.50 30 33 08
26 5.05 05 5.00 4.24 274 1.50 39 40 =01
27 4.35, 04 4.31 7,50 1.88 5.62 21 21 00
28 424 a 413 521 2.49 272 3 29 02
29 7.86 06 7:80 7.48 2.69 459 44 45 =.01
30

17.86 02 17.84 10.36 2.83 7.53 31 36 05
ka 2.62 02 2.60 26.46 4.22 22.24 34 =.01

440 05 4.35 4.04 1.48 2.56 15 16 ~01
24 14.75 02 14.73 14.09 2.78 11.31 24 A7 07
25 5.58 02 566 | 10.34 3.55 6.79 38 ‘37 =01
32

6.60 04 656 | 11.06 2.84 8.22 2 28 -01
33 2.09 02 207 5.94 2.53 3.41 53 54 =.01
34 15.49 06 | 15.43 7.85 1.75 6.10 3 32 =01
36 3.16 13 3.03 24a 1.49 93 22 24 o
36 ant ‘93 4.08 4.30 242 218 37 39 02
37 5.27 04 5.23 6.47 2.28 4.19 53 53 :00
38 34.22 07 34.15, 5.24 243 3.1 34 36 01
39 .

475. 7 468] . 12.14 237 a7 33 33 00

The summary measure is the sum of the absolute values of the percentage differences between actual and trend values for the specified series, for the years 1969-61.

32


percent to 198 percent of the average useful life of an asset L, are used by
BLS in determining discards. Capital assets are discarded as a function of
their average useful life. Variation in the discarding of capital assets
around the average useful life.is described. by the truncated. normal
distribution. The value of discards in a-given year, X, is calculated: by
summing the product of the constant-dollar value of a capital asset times
the probability of the asset’s: retirement at that age, for capital assets
ranging in age from 2 percent to 198 percent of the asset’s average life.
The truncated normal distribution includes two standard deviations or
95 percent of the area under the discard distribution. An expanded
discussion of the discard assumption used by BLS is contained in Trends
in Multifactor Productivity, 1948-81, appendix C.

* For each 2-digit sic manufacturing industry, the gross perpetual
inventory capital stock measure was obtained as an unweighted sum of
the industry's detailed-asset-type gross perpetual inventory capital stock
measures. This is similar to the methodology underlying the gross book-
value capital stock measures for each industry, because an industry’s
total gross book value is an unweighted sum of the gross book value of
existing capital assets. This approach also simplified the construction of
the gross perpetual inventory capital stock measures.

"For further discussion of the methodology underlying the published
BLS multifactor productivity measures, see Jerome A. Mark and William

H. Waldorf, “Multifactor. productivity: a new BLS measure,” Monthly
Labor Review, December 1983, pp. 3-15; Trends in Multifactor
Productivity, 1948-81; and Multi factor Productivity Measures, 1986,"

**Bureau of Economic Analysis data on output quantity were used in

“each industry, whereas labor services data were obtained. from. BLS

2-digit industry data sources. Labor income, capital income, and total
income estimates were ‘obtained from Bureau of Feonomic ‘Analysis
2-digit industry data.

For example, capital discards in total manufacturing fncredsedhiring
the peak-to-trough years, and decrease during the trough-to-peak years.
This is particularly noticeable during the 1973~75 and 1980 recession
periods. During the 1969-70 recession, discards increased slightly and
then jumped substantially in 1971) For a graphical presentation of
capital discards in total manufacturing for 1963-81, see chart 2.

The summary measure ‘of’ cyclicality for a given ‘series was
constructed using trend values which were estimated by regressing the
actual series values on a constant, time, and time squared, and obtaining
the fitted values from this regression. The meastire was constructed
using a sum over the years 1969 to 1981, in order to provide a peak-to-
peak comparison of the measures.

Excessive hours and productivity

Economists have tended to assume that 1 hour of labor supplied by a
worker is much like another. Karl Marx, who cited a variety of evidence
to show that long hours of work. were detrimental to health and to.
longevity, did not go on to deduce that those who worked long hours
must, because'of their poor health, produce less. The most fundamental
connection between. hours of work and production exists: at this
physiological level. People are able to sustain work for remarkably long.
continuous periods, and for remarkably high proportions of their total
daily hours. But long hours are accommodated by an adjustment of pace
or work intensity—by.a slowing of movements and.an interpolation of
more pauses between ‘movements. In addition, long hours (which must
also be judged relative to the arduousness of the work) tend to give rise to"
a high rate of absence and sickness, which has particularly serious éffects
in production involving the interdependence of workers and: complex

planning and scheduling.

—MICHAEL WHITE

Working Hours: Assessing the Potential for

Reduction (Washington, International
Labour Office, 1987), pp. 40-41;

35


The role of capital discards |
in multifactor productivity measurement

Discarding of plant and. equipment
varies over the business cycle,

but new measures of capital input
in 20 industries suggest the effect
on multifactor productivity is minor

SusAN G. POWERS

Since the early 1970’s, the United States has experienced a
marked slowdown in productivity growth, in ‘comparison
with. the experience of the early postwar years.'. The
slowdown focused increased attention on long-term pro-
ductivity, trends. This article examines a second pattern in
productivity growth, prevalent since World War. IL
Productivity growth increased during business cycle
expansions, and.décreased.during downturns. The cycli-
cal pattern is illustrated:in chart 1, using. the Bureau of
Labor Statistics multifactor productivity measure for the
private business sector from 1948 to 1986. The multifac-
tor productivity . measure is . the ratio. of output #6
combined capital and labor inputs.”

The cyclical pattern: in the: multifactor productivity
measure has not been satisfactorily explained, although
various factors that may’ contribute to such movements
have’ been identified. Change in multifactor productivity
is measured as the difference between the growth rate of
output.and the growth rate: of labor and capital inputs.’
Growth in this measure reflects increase in output due to
factors other than growth in capital and labor inputs. One
of these factors is technical change—the increased effi-
ciency of production resulting from better management or

Susan G. Powers is an economist in the ‘Division of Productivity
Research, Bureau of Labor Statistics.

organization of resources and improved. technology.
However, the. multifactor productivity measure. also
reflects the impact. on output of. changes. in capacity
utilization, in the composition of labor, and in.economies
of scale. In addition, the measure can be affected by errors
in the measurement of output and of capital and labor
inputs.

One possible explanation for the cyclical pattern of
multifactor productivity focuses on the measurement of
capital, input, specifically, the. measurement of capital
discards, Capital input in- production is defined as the
flow of services from the available stock of capital, which
is composed of capital assets of various vintages. The
stock of capital changes over time as a result of new
investment, in capital assets, discarding of capital assets,
and decay or loss in economic value of existing capital
assets, In the BLS framework, capital stock is measured
using gross investment data and some assumptions about
how capital assets decay and when they are discarded.*
The assumption used to estimate when capital assets are
discarded does not allow for increases and decreases in
discards over the business cycle.’ However, capital
discards generally increase when the economy is experi-
encing a slowdown, and decrease when economic activity
is at a peak.

Because this fluctuation in capital discards over the
business cycle. is not reflected by the capital input

27


Chart 4. Indexes of alternative multifactor productivity measures, total
manufacturing, 1962-81

Index Index
(1977 = 100) 1977 = 100]
108 108 =
104 + 4 104
too + 4 100
96 + + 96
92 4.92
88 4 88
84 + 4 84
80 4 80
76 + 4 76
72 1 1 1 4 1 1 J. 1 1 1 iL 1 1 1 4 1 1 i 1 1 72

1962 1965 1969 1973 1977 1981

measures of cyclical variation for the alternative multifac-
tor productivity measures in each industry.

These results are illustrated for total manufacturing in
charts 2, 3, and 4. Chart 2 shows actual capital discards
with implied capital discards derived from the gross
perpetual inventory capital stock measure. For ‘total
manufacturing and for detailed manufacturing industries,
actual capital discards derived from gross book value data
increase and decrease over the business cycle, while
discards implied by the perpetual inventory discard
assumption have a smooth, upward-trending pattern.
Chart 3 shows that, while the perpetual inventory capital
stock measure does vary over the business cycle, the book
value measure exhibits more extreme cyclical variation.
Chart 4 compares two alternative multifactor productiv-
ity measures, one based on the gross book value capital
stock, and a second based on the gross perpetual
inventory capital stock. The two multifactor productivity

measures show similar patterns of cyclical movements.
Accounting for increases and decreases in capital
discards over the business cycle demonstrates that varia-
tion in capital discards is a minor factor in explaining the
cyclical pattern exhibited by multifactor productivity
measures. This finding supports the conclusion that, the
BLS technique of measuring capital stock using the static
discard assumption in the perpetual inventory method
does not create a large cyclical bias. in the multifactor
productivity measure. However, the issue of explaining
the relationship between multifactor productivity and the
business cycle remains open. Possible explanations in-
clude fluctuations over the business cy¢le in the rates of
capital and labor utilization, which are not accounted for
by the capital or labor input measures. BLS is conducting
further research investigating these and other factors that
may explain the cyclical fluctuations in multifactor
productivity measures. o

——— FOOTNOTES ————_

ACKNOWLEDGMENT: Edwin Dean and Michael Harper of the
Division of Productivity Research provided valuable comments and
editorial assistance on this article. The author also thanks William
Waldorf of the State University of New York at Binghamton, who
provided guidance in the completion of this research.

"In the private business sector, growth in labor productivity—output
per unit of labor input—decreased from a rate of 2.9 percent annually in
1948-73 to a rate of 1.0 percent in 1973-86. Growth in multifactor
productivity—output per unit of combined capital and labor input—
decreased from a rate of 2.0 percent in the earlier period to a rate of 0.3

33



MONTHLY LABOR REVIEW June. 1988

© Capital Discards in Productivity Measurement

Chart 1. Index of multifactor productivity in the private business sector, 1948-86
Index Index
11977 = 1001 11977 = 1001
106 106
102 | a + 102
98 | : + 98
94 -_ . 94
90 . | o 90
86 2 | 86
82 | | ; | 82
738 . 738
m4 b y : 4

.
70 7 70
. 4
66 | 66
62 + . : 62
58 py mo imal a L Ee 58
1948 «1953 —s« 1958-1963. ss«1968-=Ss«1973.=S «1978 ==: 1983 1986
NOTE: ‘Shaded areas indicate recessionary periods, as designated by the National Bureau of Economic Research.

measure, variation in capital input over the business cycle
may be understated. The capital input measure will reflect
only cyclical movements in the gross investment series
and changes in the distribution of the average age of assets
over time. When multifactor productivity is measured
using this smooth capital input series, cyclical movements
in the’ output ‘series. may be more extreme than the
understated cyclical movements in capital input. The
result will be exaggerated cyclical movements in the
multifactor productivity measure.

BLS has conducted research that develops direct meas-
ures of capital discards, in order to examine whether
capital discards increase and decrease over the business
cycle, and, if so, what implications this may have for
cyclical movements in the multifactor productivity meas-
ure.® Direct capital discard measures are developed for
each 2-digit Standard Industrial Classification (sic) man-
ufacturing industry, and for durable, nondurable, and
total manufacturing, for the period 1963-81. The capital
discard measures are constructed using data on the gross
book value of depreciable capital assets.

Gross book value measures

For a firm in a particular year, the gross book value of
capital is defined as the sum of the original purchase cost

28

of all existing capital assets. When a company discards
capital assets, the gross book value is. reduced. by the
original cost of the asset. Data on the gross book value of
capital, then, directly reflect actual capital discards as
they occur. The method used to obtain the direct
measures of discards is described below.

This research provides a sensitivity test for-the impact
that an assumed smooth pattern of capital discards may
have on business cycle movements in capital input and in
multifactor. productivity.’ The direct capital discard
measures are compared to the smoothed measures to
assess the implications of increases and decreases in
discards over the business cycle. The gross book value
data, which are in historical dollars, are deflated to obtain
constant-dollar gross book value measures. These gross
book value capital stock measures reflect actual move-
ments in capital discards over time and are developed for
each 2-digit sic industry for the years 1962-81.

Next, the gross book value capital stock series, which
reflect increases and decreases in discards over the
business cycle, are used to construct multifactor produc-
tivity measures for each industry for 1962-81. Finally, for
each industry, the capital discard, gross ‘book value
capital stock, and multifactor productivity: measures that
reflect actual capital discards are. compared to corre-
sponding measures that reflect-a static capital discard
assumption.


Measurement of capital discards

Capital may be discarded for a variety of reasons.* The’

physical condition of capital assets deteriorates over time
and as the result of wear and tear from use. The benefit to
a firm of keeping an asset in use- eventually may be
eclipsed by the cost of maintaining the asset. The asset
may become obsolete, or a company, may discontinue the
production of a good or service for which the asset was

_ tequired. Capital also may be discarded as the result of
accidental destruction.

Discarding an asset involves removing the asset from
useful service. A discarded asset may be physically
removed from a plant or left in place but not used. An
asset no longer in use is considered to be discarded when
the firm’s account of the value of capital assets in service
is adjusted to remove the original cost of the asset.

Capital discards can be measured using data on the
gross book value of depreciable capital assets. The gross
book value of capital for a firm in a given year is the
historical dollar value of existing capital assets. These
data reflect capital discards as they occur, because the
original cost of an asset is removed from the gross book
value when the asset is retired.

This research developed a measure of actual capital

discards by deflating historical dollar gross book value:

data to obtain gross book value capital stock measures.

The gross book value capital stock measure for a given
year may be expressed as:
GBV,. = GBV,, + GI - DI,

where:
GBV, is the gross book value of capital stock in period ;

GI, is gross investment in period ¢; and
DI, is discards in period t.

” “When the expression for gross book value capital stock is

rearranged, a measure of actual capital discards can be
defined in terms of gross investment and gross book value
capital stock:

‘DI, = GI, - (BV, - GBV,.)

For the period 1963-1981, capital discards for each
industry were measured using this expression and data on
gross investment and the gross book value of capital
stock.? Census Bureau data on new. capital expenditures
were used for the gross investment series. Gross book
value capital stock measures were developed by deflating
data on the gross book value of depreciable capital assets
from Annual Survey of Manufactures and Census of
Manufactures, published by the Census Bureau.

The capital discard measures derived using the gross
book value data reflect the actual cyclical pattern of

Chart 2. Discard measures’ by type of gross capital stock estimate, total
manufacturing, 1963-81

Millions of Millions of

1972 dollars 1972 dollars
24,000 24,000
22,000 + -| 22,000
20,000 + + 20,000
18,000 - 4 18,000
16,000 - 4 16,000
14,000 + 14,000
12,000 + 4 12,000
10,000 | +} 10,000"
8,000 -- + 8,000
6,000 ~ 4. 6,000
4,000 + + 4,000
‘2,000 | + 2,000

o iene 1 1 1 [EERE nF n 1 1 1 1 1 L n 1 1 0.

4963 1968 1973 1978 1981