Productivity in Manufacturing

turns that affected the three countries at the beginning of the
1990's.

Manufacturing output slowed in the three countries after
1973, particularly in the United States. But while U.S. out-
put recovered significantly after 1979, such a recovery is not
yet evident in German or French manufacturing.

In Germany and France, labor hours declined over the
1956-93 period. In France, labor hours increased a modest
0.5 percent per year before 1973, but experienced strong de-
clines since then. In Germany, labor hours fell in all the pe-
tiods. The average yearly declines in labor hours in both
countries frequently reached 2 percent to 3 percent. In the
United States, labor hours increased slightly in manufactur-
ing for the period as a whole, but U.S. labor input declined
after 1979. However, the U.S. rate of decrease since 1979 has
been much slower than in Germany or France.

In all three countries, capital inputs increased strongly
during the period as a whole, with growth occurring in all
sub-periods. In Germany and France, however, these in-
creases were much greater before 1973; their rates of increase
have declined steadily since then. In the United States, capi-
tal inputs grew quite vigorously and fairly steadily during
the period, with relatively little variation in growth rates

Footnotes

among the different time periods. In contrast to what occurred
in Germany and France, capital inputs grew faster after 1973
than before.

Combined labor and capital inputs increased in the three
countries before 1973. After 1973, combined factor in-
puts declined in Germany and France, as cuts in labor hours
more than offset increased capital service inputs. In
the United States, average annual increases of combined fac-
tor inputs occurred in each time period, except for a slight
decline in 1990-93, although the rate of increase slowed
somewhat.

The ratio of capital service inputs to labor hours increased
in the three countries, indicating that capital was being sub-
Stituted for labor. In Germany and France, this process was
especially noticeable before 1973. In the United States, on
the other hand, the more vigorous capital-for-labor substitu-
tion occurred after 1973.

Labor productivity increased in the United States in all
periods, although just barely in 1973-79, when output stag-
nated. The pre-1973 rate of increase was slightly faster than
the post-1973 rate. In Germany and France, labor productiv-
ity also increased in all periods, but the pre-1973 rates were
much stronger. Q

‘For a summary of the state of the art, see Dale W. Jorgenson, “Productivity
and Economic Growth,” in E.R. Berndt and J.E. Triplett, eds., Fifty Years of
Economic Measurement: The Jubilee of the Conference on Research in In-
come and Wealth (University of Chicago, 1990), pp. 19-118.

2 The principal reference to the method used in this study to measure multi-
factor productivity is Trends in Multifactor Productivity, 1948-81, Bulletin
2178 (Bureau of Labor Statistics, 1983).

* Before 1960, the source data series did not include West Berlin or the Saar
region. Results with and without these two areas were published for 1960; they
were used to link the data series.

“The Bureau of Economic Analysis has annouced that, later this year, it will
feature the index of real Go based on its “chain type" annual weights measure
instead of the "fixed weight" measure. However, BEA does not publish a chain-
type annual-weighted measure for manufacturing,

5 For a description of alternate ways to compute real output, and for a discus-
sion of changes in the U.S. statistical program, see Alian Young, “Alternative
Measures of Changes in Real Output and Prices,” Survey of Current Business,
April 1992, pp. 32-52.

For comparison, an index of French manufacturing real value added also
‘was computed using annual chain-weighted estimates. The results showed only
a slight difference in the growth rates of the two series, with the benchmark-
years-weighted series growing somewhat faster.

"The French employee compensation figures for 1956-58 and 1991-93 are
BLs estimates.

‘For a more complete discussion about the perpetual inventory method of
estimating capital stock, and of imputed rent calculations, see Trends in Multi-

52 Monthly Labor Review July 1995

factor Productivity, 1948-81, September 1983.

This also is true for capital input growth in the manufacturing industries of
Germany and France. This result is at least partly due to the method used to
estimate capital stock (the perpetual inventory method).

"” In general, for any number X, if the change in X (or AX) is sufficiently
small, then

In L+XX) AXIK= (XAAK 1) and Lrgin( +44) = ain x)

"Breaking down the difference between the two products ain(&) xy
isaccording to the following scheme, using a,b,-ab, as illustrative variables:

ap,- a,b, =}a,b, +4.4,b, -bayby -Layb, +4 (a,b, — a,b, +a,b, —a,b,)

=ta,(b, +b,)-4a,(0, +0, )+40,(a, +a,)-4,(a, +a,)
= (2, ~2,)4(6, +b,)+(b,-by)4(a, +a,)

"To examine the reasons for the European manufacturing slowdown rela-
tive to the United States, and what trend or cyclical forces are at work, factors
such as exchange rate movements and unit labor cost comparisons also must be
considered, Two recent studies of these issues are available in Bart van Ark,
“Manufacturing prices, productivity, and labor costs in five economies”, Monthly
Labor Review, July 1995, pp. 56-72; and Mary Greiner, Christopher Kask,
and Christopher Sparks, “Comparative manufacturing productivity and unit
labor costs,"Monthly Labor Review, February 1995, pp. 26-38.



Manufacturing output, labor and capital Inputs, and multifactor productivity, 1956-93.

Index, 1956=100 Index, 1956=100

400
350+ United States
300
250

200

400

Cr ee EO
1962 1968 1974 1980 1986 1992
400 400
350 Germany 7350
300 1 300
250 ‘Multifactor productivity 250
200 200
Labor and capital inputs
150 seooencees, eowces. | 150
Re awnnmenwnccecoe’ .
100 100
a
1956 1962 1968 1974 1980 1986 1992
400 400
350F France 1 380
300 300
Multifactor productivity |
250 250
200 200
150 Labor and capital inputs 4 150
+ 100
Lo 19
1986 1992
Monthly Labor Review July 1995 43



Productivity in Manufacturing

of the increases in labor productivity were accounted for by
strong growth in multifactor productivity. Although capital
service inputs were growing faster than labor inputs through-
out this period, the substitution of capital for labor was rela-
tively moderate, particularly when compared with Germany
and France.

This changed somewhat after 1973, as growth in multi-
factor productivity tended to weaken, while the substitution
of capital for labor became more intense. In the 1973-79
period, U.S. manufacturing multifactor productivity declined
slightly, but labor productivity still managed to grow an
annual average 0.8 percent because of very strong increases
in capital service inputs, and the resulting shift in the capi-
tal/labor input ratio. But while the increasing capital/labor
input ratio continued to be an important contributor to the
growth of labor productivity in U.S. manufacturing in the
1979-90 period, multifactor productivity growth also recov-
ered, and was again a more important factor in explain-
ing labor productivity growth. Multifactor productivity
growth also was the more important factor in the 1990-93
period.

Thus, of the two factors, capital-for-labor substitution and
multifactor productivity, the latter turned out to be more im-
portant in explaining changes in U.S. labor productivity. The
exception was 1973-79, when mrp showed a small decline.

In the German manufacturing sector, labor productivity
recorded impressive gains over the period as a whole, but
with declining annual increases. Over the 1956-90 time pe-
riod, and for most of the sub-periods examined in this study,
growth in multifactor productivity also was the more impor-
tant factor in explaining these increases. Capital-for-labor
substitution was particularly vigorous before 1973, but MFP
was still more important in explaining the improvement in
labor productivity. However, given the strong capital-for-la-
bor substitution in German manufacturing over most of this
same period, this factor was, not surprisingly, almost as im-
portant. Also, in the most recent 3 years, 1990-93, when MFP
declined, the capital/labor substitution effect was greater than
the rr effect.

Average increases in all periods, but on a declining trend,
also characterize labor productivity in the French manufac-
turing sector over the 1956-90 period. French manufactur-
ing multifactor productivity growth, despite somewhat
slower growth in the more recent time periods, also recorded
steady increases in all the time periods examined, except for
1990-93. And despite the strong capital-for-labor substitu-
tion in France, manufacturing multifactor productivity still
played the major explanatory role in determining the manu-
facturing sector’s growth in labor productivity during most
periods. As in German manufacturing, the exception was in
1990-93, when manufacturing multifactor productivity de-
clined. But the capital-for-labor substitution effect, while

48 Monthly Labor Review July 1995

playing a secondary role, did contribute significantly to the
improvement of labor productivity.

Within all three countries, manufacturing multifactor pro-
ductivity is therefore a more important explanatory factor
than capital-for-labor substitution in explaining labor pro-
ductivity growth (but not in explaining differences in labor
productivity growth between the countries, as will be seen in
the following section).

In sum, growth in each country’s capital/abor input
ratio is insufficient by itself to explain the strong growth in
labor productivity observed in the different countries and
time periods. Other factors—those that are encompassed
by the concept of multifactor productivity—must also be
considered.

Comparisons among countries

United States and Germany. Over the 1956-90 period,
German manufacturing multifactor productivity grew

‘slightly faster, at 2.6 percent per year, than its United States

counterpart, which grew at an annual 2.1 percent average.
However, the German multifactor productivity annual
growth rate has been declining: 1956-73, 3.4 percent; 1973—
79, 2.6 percent; and 1979-90, 1.3 percent. (Multifactor pro-
ductivity was negative in the 1990's.) On the other hand,
U.S. manufacturing multifactor productivity has recovered
from the 1973-79 decline, and increased faster than the Ger-
man equivalent in the 1979-90 period (and in 1990-93).

Output growth can be broken down into the two compo-
nents of growth in combined labor and capital inputs and in
multifactor productivity, although the relationship is only
approximate with annual data. (See table 3.) Before 1973,
manufacturing output grew strongly in both countries, al-
though the German growth rate was somewhat greater (4.6
percent per year in the United States and 5.9 percent per
year in Germany). During these same years, capital service
inputs increased about twice as fast in Germany.

However, while hours worked were declining in German
manufacturing at the rate of 0.6 percent per year, U.S. hours
increased at the rate of 0.8 percent per year. The net result
was that, although the use of combined factor inputs in-
creased more in Germany than in the United States (an an-
nual rise of 2.4 percent versus 1.6 percent), German multi-
factor productivity grew marginally faster over this 17-year
period; the average difference was 0.4 percentage points per
year.

After 1973, the dynamics in the two manufacturing sec-
tors changed somewhat. U.S. manufacturers increased their
capital service inputs at a more rapid pace than in Germany,
and, while U.S. labor hours increased less than previously,
or even declined, labor input in German manufacturing
shrank much more. The net result was that total factor in-



cessions. Growth was more than twice as fast during 1956~
73 (4.6 percent annually) than in 1973-90 (2.0 percent). There
was a significant drop in output from the 1973 peak to the
1975 trough (-18.3 percent), marking the post-1973 energy
crisis and recession, and overall growth was very slow in the
1973-79 period. However, after 1979, real output growth
picked up again, to an average annual rate of 2.5 percent
during 1979-90 and 2.6 percent during 1990-93.

On the input side, total hours worked grew slowly for the
period—only 0.1 percent annually during 1956-93. Labor
input increased overall during 1956-79, with very rapid in-
creases during the 1950’s and 1960’s, and a decline since
then. Labor hours rose slightly during 1973-79, then de-
clined during the post-1979 period; the pace of the decline
accelerated after 1990. Hours worked in 1993 were 10.6 per-
cent below their peak in 1979, but were 5 percent above their
1956 value.

Capital service inputs grew vigorously and fairly steadily
throughout the 1956-90 period, with no recorded annual de-
clines, This is true even for recession years.? For U.S. manu-
facturing, the rate of capital input growth varied relatively
little among the different time periods between 1956 and
1990, from a high of 4.5 percent annually during 1973-79
to a low of 3.7 percent annually during 1979-90. However,
capital service inputs rose only 2.6 percent annually in 1990-
93. What is unusual (compared with the other countries) is
that capital inputs increased as rapidly after 1973 as before
1973. It should be noted that the most rapid growth in capi-
tal service inputs occurred during the 1973-79 period, which
was marked by the first energy crisis, as U.S. manufacturers
adjusted to increasing energy and labor costs,

The combined labor and capital inputs resulted in a gen-
erally rising trend throughout the 1956-90 period. The in-
crease was most rapid before 1973, at an annual average of
1.6 percent, and lowest between 1979 and 1990, at 0.4 per-
cent per year, because of the decline in labor inputs. The
only negative average occurred during 1990-93, because of
a significant drop in labor hours and smaller increases in
capital services inputs.

There was an overall substitution of capital for labor as
capital service inputs increased faster than labor hours. This
is shown by the capital services/hours worked ratio, which
grew an average of 3.7 percent per year between 1956 and
1990. The ratio grew somewhat faster during the post-1973
period (4.3 percent annually), but in general, this rate of
substitution was quite stable throughout the entire 37 years.
In this aspect, the United States differs from Germany and
France, where the substitution of capital for labor in manu-
facturing proceeded at a faster rate over the entire 1956-93
period. However, the increases were front-loaded on the ear-
lier, pre-1973 period, with significantly slower substitution
in the more recent years.

Finally, the trends in capital productivity, defined as the
ratio of output per unit of capital service inputs, also should
be noted. The steady growth in capital inputs, and the sub-
stitution of capital for labor, resulted in an overall decline in
this ratio. The 1956-73 period was an exception, with a small
average increase of 0.7 percent annually. The decline in capi-
tal productivity since 1973, particularly prominent in 1973—
79 (-3.2 percent annually), resulted from rapid increases in
capital service inputs during a period of relatively slow manu-
facturing output growth. Relative stability, with some over-
all increase, has been a characteristic of this ratio since 1982.

A telatively optimistic picture of recent U.S. manufactur-
ing developments can be derived from the output and factor
input dynamics analyzed above. The negative manufactur-
ing multifactor productivity growth recorded during 1973-
79 was due to stagnating output combined with a spurt in
capital service inputs, while labor hours also increased. Both
output and multifactor productivity growth have since
recovered.

Germany. Although the manufacturing multifactor pro-
ductivity increase of 2.6 percent per year over the 1956-90
period (2.3 percent, 1956-93) represented substantial growth,
it slowed significantly after 1973 (1.8 percent per year, 1973-
90), and especially after 1979 (1.3 percent per year, 1979-
90). German manufacturing multifactor productivity growth
slowed even though combined labor and capital inputs were,
on average, decreasing after 1973. In 1990-93, multifactor
productivity declined 0.4 percent annually due to an output
decline of 2.2 percent per year that was not matched by an
equal decline in inputs. For 1992 and 1993, multifactor pro-
ductivity declined 2.5 percent and 1.2 percent.

German manufacturing output grew at an average rate of
3.6 percent annually during the 34-year period 1956-90,
slightly faster than U.S. manufacturing output. However, the
rate of growth has been dropping steadily. Similar to the
United States, very rapid growth occurred before 1973 (5.9
percent annually) and a slowdown took place after that (1.4
percent per year, 1973-90). But unlike the United States,
there was no recovery in the output growth rate during the
latter years of the 1973-90 period. On the contrary, the 1979-
90 period registered slower growth (1.2 percent per year)
than the 1973-79 period (1.8 percent per year). Thus, al-
though the 1973-79 period may be treated as an aberration
in the United States, with growth recovering after 1979, this
is not true for Germany, at least not yet.

Labor hours worked in German manufacturing show a
declining trend throughout the entire 1956-90 period, par-
ticularly in the 1973-79 period (and since 1990). All the
labor input period averages are negative. (See table 1.) It
was only in the 1984-90 period that some stability seems to
have been restored. The result has been respectable gains in

Monthly Labor Review July 1995 45



Productivity in Manufacturing

but it hit the United States and the two European countries
at very different cyclical stages. For the United States the
problem is less severe, because manufacturing output hit
its last low in 1991; by the end of 1993 a large proportion
of the cyclical recovery should have taken place. However,
German and French manufacturing output were still falling
from their peaks in 1991 and 1990; as of 1993 they were
moving in the opposite cyclical direction from the United
States.

Productivity measures for periods ending in 1993 reflect
the facts as we know them from the latest available informa-
tion, and are therefore important. As data arrive for 1994
and later, the results will be recorded. Given these facts, one
should not accept as definitive interna-

1979. It could be argued that the 1973-79 period, character-
ized by the first energy crisis and the measures taken by in-
dustry to adapt to it, was atypical. By treating the 1973-79
data as outliers—observations that vary abnormally from sta-
tistical averages—U.S. multifactor productivity may be back
on a growth trend similar to—though somewhat less rapid
than-the trend of the pre-1973 years.

Multifactor productivity trends can be explained by rela-
tive changes in manufacturing output and factor input growth
rates. U.S. manufacturing output (real gross product origi-
nating) grew at a 3.3-percent annual average during the 1956-
90 period, with slowdowns and declines during cyclical re-

tional productivity comparisons that have [SIMMS Growth rates of manufacturing output, factor inputs, and productivity,
1993 as the ending year. In the summary US., Germany, and France, selected periods, 1956-93
comparative tables, average rates of changes!
change are shown for 1956-90 and 1956- wwerege annvelperent d
93. Labor input
France |  Seyee | Germany | France
Trends, by country
Because Germany and France had not, as 36 08 43 48
of 1993, recovered from their cyclical ry) 8 ~6 5
downturns, much of the analysis concen- 28 3 3 a
trates on the period ending in 1990. 1.0 “7 -9 22
71.8 -1.3 -3.3 -3.0
United States. Manufacturing multifac- Labor and capital input
tor productivity registered an average France yatect Germany | France
annual increase of 2.1 percent the entire ee
1956-93 period. (See table 1). Growth 48 42 1.0 7
declined from an average of 2.9 percent 43 ‘6 2 2
annually before 1973 to 1.2 percent be- 28 8 =4 -9
tween 1973 and 1990. However, this 35 14 “8 74
slower multifactor productivity growth oH 23 ae ay)
was composed of an annual decline of 0.2
percent during 1973-79 (when labor and pli services per how Cute por howe
capital inputs grew faster than output), France Siares | cemony | France
followed by a recovery to 2.0 percent an-
nually in 1979-90 and 2.8 percent a year 5.4 a0 47 50
during 1990-93. ps * at aa es e3
While the average rate of increase 33 bys 3 re
since 1973 is clearly below the pre-1973 43 31 24 32
average growth rate, one cannot conclude 50 40 12 12
on the basis of this evidence alone that services Muttitactor productivity
there has been a fundamental shift—a United
decline—in productivity growth after Fronce stotes__| Sermony| Fronce
1973. While the fastest increase in manu- 0.4 24 26 34
facturing multifactor productivity oc- “7 24 23 34
curred during 1956-73 (2.9 percent an- “8 3 te 24
nually), it increased nearly as fast during <9 <2 26 3.0
1990-93 (2.8 percent annually) and has my) 38 4 ia
averaged 2.2 percent annually since

44 Monthly Labor Review July 1995



in 1990-93). The slowest growth in capital service inputs
occurred during 1982-86 (and in 1992-93).

The combination of increases in capital service inputs and
the generally declining labor inputs results in an average
annual growth rate of 0.7 percent in labor and capital in-
puts over the 34-year period of 1956-90. In the earlier, pre-
1973 years, the increases in capital service inputs dominated
this aggregate, so that combined labor and capital inputs
grew at an average annual rate of 2.3 percent. In the later,
post-1973 years of 1973-90, capital service inputs grew at a
slower rate and labor input declined. As a result, labor and
capital inputs also declined, at an annual rate of 0.9 percent.

The ratio of capital services input to hours worked, a
measure of the rate at which capital is being substituted for
labor, rose in each of the 37 years in the 1956-93 interval,
indicating that capital inputs were growing faster than labor
inputs during this entire period. The rate of capital-for-labor
substitution was relatively stable among the various time
periods, although it proceeded at a somewhat faster pace
before 1973. The ratio grew between a high average annual
rate of 6.1 percent during 1956-73 and a low 4.3 percent
annual rate in the more recent 1979-90 period.

Capital productivity rose slightly during 1956-73, but has
since declined because capital service inputs grew faster than
manufacturing output.

French manufacturing recorded respectable gains in mul-
tifactor productivity throughout the 1956-90 period as a
whole. Before 1973, manufacturing output rose nearly 7 per-
cent annually and multifactor productivity increased 4.4 per-
cent annually. After 1973, a worsening multifactor produc-
tivity trend can be observed as a steadily declining growth
rate of real manufacturing output is confronted with a rela-
tively stable combination of factor inputs. However, the 2.1
percent annual multifactor productivity growth rate during
1979-90 is still respectable, essentially matching the U.S.
figure for the same period of 2.0 percent per year. Neverthe-
less, these data show that a decline in French manufacturing
multifactor productivity occurred after 1973.

Sources of labor productivity growth
For notational convenience, equation 1 can be rewritten as!
()din(mep,) = din(GPO)— Wry Xd In( Le )— Wks Xd (Ke)

The term d In(X)) also serves as an expression for XK, -
1), to indicate the percent change in X at time ¢. Noting that
wy t + 1 =1, and re-arranging terms in equation (7), we
et

(8) ain 22. = din (ure) +a inl) inp,

This indicates that changes in labor productivity (output
per hour) can be analyzed as the sum of changes in multifac-
tor productivity and changes in the ratio of capital service
inputs to labor hours, the latter multiplied by capital’s share
of the output value. The term representing the product of the
capital services per hour ratio and the capital income share
@ In[K, / Lx, .t ) can be interpreted as a capital-for-labor
substitution effect. In this way growth in labor productivity
can be separated into a multifactor productivity effect and a
capital/labor substitution effect.

Labor productivity changes are examined in the three
countries, to determine the role of these two effects in those
changes, (See table 2.)

Labor productivity in U.S. manufacturing grew an an-
nual average 3.1 percent over the 1956-93 period, some-
what faster before 1973 (3.8 percent per year) than after-
ward (2.3 percent per year). Labor productivity barely grew
in 1973-79, when output rose little more than 1 percent per
year. (See table 2.) Of all the periods, the highest labor pro-
ductivity growth was registered in 1990-93 (4 percent per
year).

Vigorous capital-for-labor substitution contributed to this
growth in Jabor productivity, but it is only part of the expla-
nation, In most periods, MFP was more important in explain-
ing labor productivity gains. (See table 2.) Before 1973, most

bie 2 | Sources of manufacturing labor
Productivity growth, U.S., Germany, and France,
selected periods, 1956-93 (in percent)
Output per | “labor Muiitactor
hour substitution
effect

3.0 1.0 24
34 1.0 21
a8 08 29
23 14 12

8 41 -2
34 141 20
40 ia 28
47 20 26
44 2.0 23
65 34 34
29 41 1.8
43 17 26
24 8 13
12 1.7 ~4
5.0 15 34
46 15 31
63 18 45
3.7 13 24
45 15 30
3.2 12 21
12 17 -4

Monthly Labor Review July 1995 47


Wolodar Lysko

Wolodar Lysko is an
economist in the
Division of Foreign
Labor Statistics,
Bureau of Labor
Statistics.

Manufacturing

Manufacturing multifactor
productivity in three countries

Multifactor productivity growth in the United States

has been lower than the growth rates recorded

by Germany and France since 1956, but only the U.S. rates
show a pickup since the post-1973 slowdown

tor productivity between three G-7 countries

over the 1956-93 period, the largest average
annual rate of increase, 3.1 percent, occurred in
France. Germany followed at 2.3 percent and the
United States with 2.1 percent.

After 1973, the growth rates slowed in all
three countries, The rate in the United States
picked up in the 1979-93 period, but evidence
of such a recovery in Germany and France re-
mains to be seen. Because manufacturing multi-
factor productivity is strongly affected by the
business cycle, observers must wait for cyclical
disturbances to subside in those countries for a
more definite answer.

Labor hours in U.S. manufacturing rose
slightly over the full period studied; they de-
clined significantly in Germany and France, par-
ticularly after 1973. At the same time, capital
services inputs were increasing steadily in all
three countries. The result was an overall sub-
stitution of capital for labor, which was espe-
cially vigorous in Germany and France before
1973, and intensifying in the United States after
1973.

Over the period 1956-93, labor productivity
increased faster in Germany and France than in
the United States over this period because of
much larger average increases between 1956 and
1979, But in the more recent 1979-93 period
the United States had the highest average an-
nual labor productivity growth rate. German and
French growth rates were higher before 1973,
due mostly to a more rapid substitution of capi-
tal for labor. Following 1973, the rates of substi-

I: a comparison of manufacturing multifac-

tution became more similar; differences in
manufacturing multifactor productivity changes
decided the leadership in labor productivity
growth, often on a cyclical basis.

Multifactor productivity differs from the
traditional measure of labor productivity by ex-
plicitly including capital as a factor of produc-
tion. Including capital as an additional input not
only recognizes its importance as a factor of pro-
duction, but also makes it possible to analyze
and explain how other factors influence labor
productivity.

For many years, the Bureau of Labor Statis-
tics has compared manufacturing labor produc-
tivity among the United States and many of its
industrialized economic competitors. Likewise,
for more than a decade, Bis has published multi-
factor productivity measures for U.S. manufac-
turing industries and other broad sectors of the
U.S. economy. Now, Bs is applying similar tech-
niques to productivity trends in various coun-
tries, providing a new tool to understand what
shapes international competitiveness and why
labor productivity trends differ among countries.
Comparisons in this article between the United
States and two other G-7 countries, Germany
and France, are the beginning of a wider project
that will eventually include other industrial
economies,

The basic approach of this study follows the
methodology developed by Ls to measure mul-
tifactor productivity for broad sectors of the U.S.
economy.’ The study considers the aggregate
manufacturing sector, without an analysis of de-
velopments in individual manufacturing indus-

Monthly Labor Review July 1995 39



Productivity in Manufacturing

Mal Sources of differences in manufacturing labor
Productivity growth, United States versus Germany
and United States versus France, selected periods,
1956-93

Copttal- Muttttactor
Capital
‘Output | labor Produc:
Petiod perhour jeubsttution| ihe) Pity
difference difference
8 07 04 05
3 6 3 2
17 7 4
5 -2 2 5
35 3 3 28
a4 -5 A =7
2.8 8 0 9.2
19 5 1 13
15 5 1.0
25 c) 1 15
13 a 0 12
36 3 0 32
4 0 0 9
2.8 3 2 32

period of 1956-90, labor productivity grew faster in German
manufacturing, by an average 1.6 percentage points per year.
All three factors apparently played a role in this result. To
get a better understanding of the underlying forces at work,
it is better to examine the different periods separately.

In the 17 years before 1973, labor productivity in the Ger-
man manufacturing sector increased by an annual average
6.5 percent against 3.8 percent per year in the United States.
Most of the difference (2.8 percentage points) can be traced
to the capital-for-labor substitution difference. The capital
Share difference, though much less important, was the next
biggest contributor to the above outcome. It should be men-
tioned at this point that for most of the time period studied,
the capital share in German manufacturing was larger than
the corresponding variable in the United States, helping to
maintain faster growth in German manufacturing labor pro-
ductivity. The capital share in the United States fluctuated
between 0.23 and 0.30, while in Germany it began above
0.40 in 1956 and subsequently declined. In 1980 it reached
the U.S. range, and even fell below the U.S. value in the last
2 years, at 0.24 vs. 0.28 for the United States in 1993. Thus,
this factor played a somewhat more important role in the
earlier years of the period under study and has become less
important in more recent years.

During the period 1973-90, the increases in labor pro-
ductivity were very similar in the manufacturing sectors of
both countries, with Germany holding an advantage of an

50 Monthly Labor Review July 1995

average 0.5 percentage point per year. But the rate at which
capital was substituted for labor in U.S. manufacturing ap-
proached or surpassed the corresponding German rate (these
rates became more alike), so that the difference in multifac-
tor productivity became relatively more important. However,
this period must be broken down into the first stage, 1973—
79, during which German labor productivity grew much
faster, 4.3 percent vs. 0.8 percent per year, and the second
stage, 1979-90, when U.S. labor productivity pulled ahead,
3.1 percent vs. 2.1 percent per year.

During 1973-79, almost all of the faster increase in Ger-
man manufacturing labor productivity was accounted for by
more rapid increases in German manufacturing multifactor
productivity, which rose by an annual average 2.6 percent
while U.S, manufacturing multifactor productivity declined
by 0.2 percent per year. The two sectors’ capital/labor input
tatios grew by about the same amount, separated by less than
1 percentage point per year.

In the period 1979-90, U.S. labor productivity increased
faster, and the difference in manufacturing multifactor pro-
ductivity growth rates was again the primary reason, al-
though faster capital-for-labor substitution in the United
States also played a significant role. The capital share differ-
ence still favored German labor productivity, but its influ-
ence had become minimal (the two capital shares had be-
come very similar).

One may conclude that over the 1956-90 period, the capi-
tal-for-labor substitution difference was the major factor in
explaining the differences in labor productivity growth rates
in the U.S. and German manufacturing sectors.

The multifactor productivity difference was next in im-
portance. Note that the factors that explain labor productiv-
ity growth within a country’s manufacturing sector are not
necessarily the same factors that explain differences in labor
productivity growth between countries. In the previous sec-
tion about sources of labor productivity growth, multifactor
productivity was found to be more important than capital-
for-labor substitution in explaining each country’s increase
in labor productivity. Now, in comparing U.S. and German
labor productivities, the reverse is true. This overall outcome
was determined by the pre-1973 developments, where capi-
tal/hours growth rates in the two countries differed much
more, while multifactor productivity growth rates were more
similar. But multifactor productivity played a much more
important role in later years, when capital-for-labor substi-
tution slowed in Germany and accelerated in the United
States, bringing the two rates closer.

Before 1973, the capital share difference (the higher Ger-
man level) was a relatively important factor in keeping Ger-
man labor productivity growing faster. Over the years, as the
German capital share became more similar to the U.S. capi-
tal share, this difference became less important.



——
Contribution of labor and capital and multifactor-
Productivity to manufacturing output growth,
United States versus Germany and France,
selected periods, 1956-93
[Average annual percent changes and
country differences in rates of change]
Man re MTM) Labor and | Multoctor
Period and country output |Capital input! productivity
grown | ofowth |” growth
Germany-U.S.
36 10 26
33 12 24
3 72 5
31 8 23
32 WW a4
-. -3 2
59 24 34
United States .. 48 1.8 29
Difference .. 13 8 4
1973-80: .
Germany 14 -4 18
United States - 20 8 12
Difference -6 4 5
1973-79:
Germany 17 -8 26
United Sta 12 1.4 -2
6 22 28
12 0.4 13
25 4 20
413 -5 -7
22 48 “4
268 =2 28
48 16 ~32
44 2 34
33 12 24
8 -5 13
36 5 3.4
32 1 24
4 -6 1.0
68 23 44
46 18 29
22 6 15
15 -8 24
20 a 12
-5 “1.6 12
26 -4 3.0
United States 12 14 =2
Difference 14 18 32
1979-80:
France .... 1.0 4 24
United States 25 4 20
Difference ... 15 15 0
418 14 -4
26 ~2 28
45 12 33

puts in German manufacturing fell, although they still grew
in the United States. In the 1973-79 period, growth in U.S.
manufacturing output slowed to arate of 1.2 percent per year,
while combined factor inputs grew by 1.4 percent per year,
resulting in a small decline in multifactor productivity. Dur-
ing this same period, the German manufacturing sector
posted annual increases of 1.7 percent in output and 2.6 per-
cent in multifactor productivity, But in the later period,
1979-90, German manufacturing output growth averaged
only 1.2 percent annually and multifactor productivity 1.3
Percent annually, while U.S. output increased by 2.5 percent
per year and U.S. multifactor productivity increased by 2.0
percent per year.

These results suggest that comparative growth rates of
manufacturing multifactor productivity should not be viewed
as fundamental, secular trends, where one country dominates
another over extended periods of time. Rather, multifactor
productivity growth depends on relationships among outputs
and inputs that vary cyclically, and can change in a rela-
tively few years.

‘We can examine how changes in labor productivity (out-
put per hour) differ in the manufacturing sectors of the United
States and Germany. One can again begin with relationship

GPO.
(8) 7,

au 22) = din (urp,) + dint) xine,
Because we want to examine differences in growth rates
between the United States and Germany, let us call D(~) the
difference between the respective growth rates of the mea-
sures shown in the parentheses. Relationship 8 can then be
broken down into:"

D( See) = D( Ft) x[ ave. }+ O(m,)

x[ave.ain($.)]+ D(MFP,)

1)

wherelave.ves] and [ove ain €)] are the arithmetic averages of
these variables for the two countries being compared.

In this way the difference in labor productivity growth
between the two countries is expressed as a sum of three
additive factors: difference in changes in capital inputs per
hour, multiplied by the (two-country) average capital share
in the value of output; difference in capital shares, multi-
plied by the (two-country) average change in capital inputs
per hour; and difference in multifactor productivity growth.
These three factors may be designated by the summary terms
of: the capital-for-labor substitution difference, the capital
share difference, and the multifactor productivity difference.
It should be remembered that the above relationship holds
only approximately for annual data.

This analysis was carried out for the various time periods,
and the results are summarized in table 4. For the 34-year

Monthly Labor Review July 1995 49



Productivity in Manufacturing

labor productivity even during the 1970's, despite the slow-
down in production. The reductions in labor inputs were es-
pecially sharp in 1990-93, with a decline of 9.1 percent re-
corded in 1993. In 1990, hours worked were 22 percent be-
low their 1973 level, and almost 30 percent below their 1956
level (29 and 36 percent below as of 1993).

As in the United States, the input of capital services in
German manufacturing is characterized by steady growth
over the entire period under study. This is due in large part
to the way that capital inputs are measured: as a weighted
summation of past investments in capital assets. However,
great disparities separate the average growth rates of capital
inputs for the different time periods. While there was strong
average growth over the period as a whole, the increases
were much greater before 1973 than after 1973, and espe-
cially in the 1979-90 period. The average annual increases
declined from 7.4 percent during 1956-73 to 2.5 percent
during 1973-79, to a relatively anemic 1.8 percent per year
in the 1979-90 period; the slowest growth occurred in the
interval 1982-88. Capital service inputs increased at an av-
erage annual rate of 2.4 percent in the 1990-93 period.

The combination of increasing capital service inputs and
generally declining labor inputs resulted in only small net
annual increases of 1 percent in combined labor and capital
inputs for the whole 1956-90 period. In the earlier, pre-1973
years, capital input increases dominated, resulting in a net
average increase of 2.4 percent for labor and capital. The
decline in this series in all periods since then is due to reduc-
tions in labor hours, because capital inputs continued to in-
crease, although at decreasing average rates. During the
1979-90 period, the declines in labor inputs were roughly
offset by the capital input increases, resulting in only a slight
net decline in labor and capital inputs of 0.1 percent per
year, Combined factor inputs declined sharply—6.5 percent
in 1993—~because of the sharp drop in hours and only a small.
increase in capital services.

Changes in the ratio of capital service inputs to labor
hours are an indicator of capital for labor substitution; these
increased in each of the 37 years betwen 1956 and 1993.
Capital-for-labor substitution proceeded very rapidly during
1956-73, at an average rate of 8.1 percent annually, slowing
to a still significant average of 5.1 percent annual rate dur-
ing 1973-79, and slowing further to 2.7 percent annually in
1979-90,

Examining the changes in capital productivity, the aver-
age output to capital input ratio declined during all the time
periods. As a result, net capital investment in manufactur-
ing increased, on average, faster than manufacturing output
during every period.

Based on the developments in manufacturing output and
factor inputs described above, one can see that the declining,
trend in German manufacturing multifactor productivity

46 Monthly Labor Review July 1995

growth in recent years can be traced to a steady reduction in
the output growth rate, in combination with relative stability
of factor inputs. Thus, manufacturing multifactor productiv-
ity seems to be following and mirroring movements in manu-
facturing production.

France. Manufacturing multifactor productivity grew at an
impressive average 3.4 percent annually over the entire
1956-90 period (3.1 percent, 1956~93), above the corre-
sponding results for either the United States or Germany.
(See table 1.) This breaks down to an average annual in-
crease of 4.4 percent during 1956-73, and a still respectable
annual 2.4 percent during 1973-90.

But the average rate of increase declined over the latter
period, so that increases in manufacturing multifactor pro-
ductivity have been much smaller in more recent years, grow-
ing at only 2.1 percent annually during 1979-90. The 1973-
90 slowdown in manufacturing multifactor productivity
growth occurred despite declines in combined labor and capi-
tal inputs, because the growth rates of manufacturing output
declined more rapidly. Results for the early 1990's are worse,
with multifactor productivity declines of 1.4 percent in 1991
and 0.5 percent in 1993 due to declines in manufacturing
output that were not matched by equal declines in labor and
capital factor inputs.

French manufacturing output increased constantly until
1975, when the first downturn occurred, but growth rates
declined over time. Despite a brief growth spurt in the late
1980’s, French manufacturing output stagnated during the
1980's and the beginning of the 1990's. As in Germany, the
results since 1979 were worse than for 1973-79. Manufac-
turing output rose at an average annual rate of only 1.0
percent during 1979-90, and declined each year during
1991-93,

Labor input in French manufacturing grew at a moderate
upward trend of 0.5 percent annually during 1956-73, after
which a steady and steep decline set in. Total labor hours
fell 2.1 percent annually during the 1973-90 period and 3.0
percent annually in 1990-93. Total hours worked in 1990
were 30 percent less than in 1973, and 23 percent below the
number of hours worked in 1956. As of 1993, total hours
worked were down 36 from 1973 and 30 percent lower than
in 1956,

As with the other countries covered by the present study,
the French manufacturing industry has been increasing its
productive capital asset base throughout the period covered,
so that capital service inputs have grown every year in real
terms, even during recessions. However, as in Germany, the
rate of growth has been declining over the years. Therefore,
growth rates vary greatly for the different time periods, rang-
ing from a high average of 6.6 percent per year in 1956-73
to a low of 2.0 percent per year in 1979-90 (and even lower



Productivity in Manufacturing

Generally, published data series are not available for K,,
and c,,, the stocks of the different types of capital and of the
income that they earn. Therefore, both variables must be
estimated.

The capital stock levels of depreciable fixed assets are
estimated by applying the perpetual inventory method (pm),
which consists of cumulating past investments in each type
of asset, while making due allowances for the decline in effi-
ciency that accompanied the aging of assets, which ultimately
are scrapped. The Bis method assumes that efficiency de-
clines gradually early in an asset’s life and more quickly later.
Space limits permit only a very compressed description of
the pm method used at BLs. This is presented in the appen-
dix, where the effect of assumed asset service lives on capital
service inputs also is examined. Cther sources and methods
are used to estimate the stock levels of the nondepreciating
assets, inventories and land, as is indicated below.

Rental prices c,, are estimated by an imputed rent for-
mula, which calculates what each asset would earn if it could
be rented in a competitive market for capital assets. The
imputed rent formula requires data series on asset prices,
income and property tax rates, and asset depreciation.*
(See the appendix for more details about the rental price
formula.)

Theoretical considerations suggest that when applying
formula 5, the different types of asset categories should be
combined at as disaggregated a level as possible. The more
categories, the more homogeneous will be the assets that
comprise each category; as a result, the more accurate will
be the overall index (K,). For the United States, is aggre-
gates up to 25 types of capital assets for each of 20 manufac-
turing industries (that is, formula 5 is applied industry by
industry). Investment data by asset type and by industry are
obtained from BEA. The capital input series for U.S. manu-
facturing, used in the present study, is a summation of the
real aggregate capital input values across all manufacturing
industries.

For Germany and France, capital estimates are available
for only four asset categories: equipment, structures, inven-
tories, and land. Investment series for equipment and struc-
tures in German manufacturing, and for inventory levels,
are provided by national account statistics. For France, the
published national accounts provide only total fixed invest-
ments in manufacturing. The breakdown into equipment
and structures was provided by the French statistical insti-
tute, INSEE. French manufacturing inventories are estimated
from annual changes in inventories. None of the three coun-
tries being compared publishes data for land used in manu-
facturing. In all three cases, the value of land is estimated

42 Monthly Labor Review July 1995

by applying a land/structures ratio to the estimated stock of
structures.

The time periods

When comparing differences in manufacturing output and
productivity trends among different countries, care should be
taken that these trends not be unduly affected by cyclical fluc-
tuations. Productivity measures tend to reflect these cyclical
movements, because output (the numerator) is very sensitive
to changed demand conditions, while factor inputs (the de-
nominator) are more sluggish. A common way to remove such
effects is to measure changes only between years that corre-
spond to similar cyclical phases, preferably cycle peaks.

For the United States, during the years covered by this
study (1956-93), seven reference cycle peaks, certified by
the National Bureau of Economic Research (NBER) business
cycle dating committee, have occurred. Without imitating
the elaborate timing methods used by the NBER, we will de-
fine a local cycle peak in manufacturing output as a year
with positive or zero growth in real manufacturing Gpo that
precedes a year with negative growth in real Gpo. According
to this definition, U.S. manufacturing peaks generally coin-
cided with or slightly led all U.S. reference cycle peaks, with
the exception of the mild recession of 1960-61, when manu-
facturing output continued to grow.

The terminal years used for analysis in this study are 1956,
1973, 1979, 1990, and the most current year, 1993. Besides
being local maxima output years in the United States, 1973
and 1979 also stand out because they were the beginning
years of the first and second energy crises and because of the
severity of the following recessions. German manufacturing
output hit peaks during the same two years. In France, manu-
facturing output peaks occurred in 1974 and 1979, but
growth slowed substantially in 1973. For these reasons, 1973
and 1979 were selected as two of the years that would an-
chor periods of comparison in the present study. Manufac-
turing productivity measures are available for all three coun-
tries beginning in 1956. Manufacturing output in the United
States peaked in 1957, while the German and French manu-
facturing sectors were growing strongly at that time and did
not hit cyclical peaks until 1966 and 1974, Therefore, it does
not appear that 1956 output was influenced by cyclical move-
ments in any of the three countries.

On an annual average basis, U.S. manufacturing output
peaked again in 1989, German output in 1991, and French
output in 1990. Since U.S. manufacturing output peaked in
the third quarter of 1990 and German output was rising
Strongly in 1990 and 1991, 1990 was selected as another
terminal year for analysis.

The fifth pivot year, 1993, is more of a problem. It is the
most current year for which the comparisons are available,



Appendix

Factor input prices

Let us define an aggregate price for manufacturing output, Po, by
dividing output at current prices by real output; an hourly price of
Jabor, Pi, by dividing total labor compensation by total hours
worked; and a price of capital services, Pk, by dividing total in-
come to capital by capital service inputs. With these newly defined
variables, equation 1 can be restated as

MEPS © Ay, y4my,) x Fe) mets em Beh uf 2)

Po.

Equation A-1 is referred to as the dual formulation of equation
1, (see p. 40) which is then called the primal formulation.’ Whereas
in equation I multifactor productivity increases when output grows
more than the combined factor inputs, in equation A-1 multifactor
productivity increases when the output price grows less than the
combined factor prices. It should be noted that the variables MFP,
w, and w, are the same in both formulations. Table A-1 presents the
growth rates of these three price series, for the three countries and
the periods being compared. In all cases, the hourly price of labor is
seen to be growing more rapidly than the price of capital service
inputs. The capital service price increases appear particularly low
in German manufacturing.

The perpetual inventory method

‘To avoid additional subscripts, the following description is in terms
of a single asset category, A similar approach, but with different
Parameters, would be applied to each category in turn. The per-
petual inventory method is applied to depreciable assets only.

Although we are dealing with only one asset category, this cat-
egory consists of a large number of individual units, and these units
have differing useful lives (L). The actual lives for this asset cat-
egory are assumed to be distributed in the form of a symmetric
pattern, which can be approximated by a truncated normal prob-
ability distribution, P(L), which is assumed to be +2 standard de-
viations around the mean asset life.

‘The contribution that any unit of capita) makes to the production
process declines with the asset’s age. Here we assume a hyperbolic
age-efficiency function

(A-2) forOSi<L

where i is age, L is useful life, and efi) is the unit’s relative effi-
ciency at age i. Relative efficiency is equal to 1.0 when the asset is
new, and then declines to 0 when its useful life ends at age i=L.
‘The curvature parameter B determines the pattern of efficiency loss,
and lies between 0 and 1. This is a parameter of the particular asset
category. For the three countries, Bp is assumed to be 0.50 for equip-
ment and 0.75 for structures. The form of the hyperbolic age-effi-
ciency function implies that efficiency declines more rapidly as as-
sets age.

Next we define the relative efficiency of the entire asset cat-
egory at age i, or a(i), as the weighted average of the individual unit
efficiencies, each one weighted by its relative frequency P(L)

Lmax
(A-3) aiy= >, P(L)T

=i

Lmax is the maximum useful life of an asset belonging to this
particular category. The quantity of real productive capital stock on
hand at the end of year ¢, for this particular asset category, or K(t),
is then computed as a summation of all past investments (/) that
could still be in operation at time 1, with the investments of every
age (or vintage) being discounted by afi)

bay
(a4) K(t)= > aliyx ra)
2
The afi) are a decreasing function of i, so that the older the as-
sets the less their contribution to K(t).

Capital stock estimates and service lives

Formulas A-2, A-3, and A-4 indicate that the computed capital stock
level K{t) for a given depreciable asset category is affected by the
service lives of the units that comprise this category. For the manu-
facturing industry in Germany, the estimated average service lives
of the two asset categories used are based on a study by Wolfgang
Kirner, and are 22 years for equipment and 43 years for structures.

For the manufacturing industry in France, the service lives are
based on data published by the French national statistical insti-
tute,? and the estimated averages are: 10 years for transportation
equipment, 18.47 years for equipment other than transportation,
and 36.84 years for structures. Transportation and other equipment
were combined into a single equipment category for the analysis
performed for this article. The United States capital input series is
based on 29 categories of equipment and 29 categories of struc-
tures, The median service life of the former is 12 years, and the
median service life of structures is 38 years,

We will now examine the sensitivity of the estimated trends in
capital service inputs to the length of service life assumed for a
given asset category. Using equation A-4, subtract K(t)-K(t-1), then
on the right-hand-side multiply and divide each term by I(t-1-i),
and finally divide each side by K(t-1). The result is

heer of H-1-1)
ane -oyf G1 «(|
Dy K@~1)

The expressions %AK(t) and %Al(t-i) are year-over-year per-
cent changes in the capital stock and in the level of investment, in
years ¢ and (r-i) respectively. The terms in the square brackets are
weights that sum to one over the span of summation. Therefore, the
year-to-year changes in the estimated capital stock are trailing mov-
ing averages of past investment changes. From A-5 it is evident
that the less variation in the %Al series, the less important are the
parameters included in the weights. In the limiting case, if we were
to assume that investments were growing at a constant rate through-
out the period, then the capital stock would grow at exactly the
same rate, regardless of the average service life or the B that was
used, Although such an assumption is unrealistic, formula A-5
shows that %AK does not tend to vary systematically with length of
service life. A change in the length of service life will only shift
the period over which the %AlI are averaged, and also modify the
weights somewhat. However, the result will still be an average of
past investment growth.

(A-5) %AK() =

Monthly Labor Review July 1995 53



sons—lie in the data requirements. All ship- Fame
ments among firms in the same sector must be
identified, deflated, and subtracted from the

Growth in capltal stock, results of sensitivity test, selected periods

sector’s real gross output and from its pur-
chases of inputs of energy, materials, and ser-
vices. This is difficult and time-consut

Problems of international data availability

and timeliness were one factor in the decision
to use the value-added method in the multifac-
tor productivity comparisons reported in this
article. Another is that it is compatible with
the regular international comparisons of manu-
facturing labor productivity reported by BLs,
which also uses real value added as the mea-
sure of output. In addition, until recently, sLs
regularly reported on U.S. manufacturing mul-
tifactor productivity developments based on the
value added approach: It is believed that, based
on equation A-7, the difference in the results
from the two methods should not be large given
that the measures reported here deal with the
aggregated manufacturing sector.

France Germany
Average service ite
1956-90 | 1956-73 | 1973-90 1956-90 | 1956-73 | 1973-90
$37 8.18 2.64 5.22 8.20 2.33
5.42 a1 2.78 - - 2.48
5.46 8.00 2.97 - - 2.69
5.49 7.79 3.23 - - =
5.32 8.22 2.49 5.13 8.18 2.16
5.21 8.25 2.26 4.96 6.11 1.89
5.02 8.22 1.92 4.59 7.75 1.52
2.23 2.78 1.70 3.45 5.81 414
2.12 2.55 1.70 3.48 5.73 1.28
1.99 232 1.88 9.50 5.63 1.43
1.84 2.09 1,69 - - -
2.35 8.02 1.68 3.40 5.89 98
2.53 3.52 1.85 3.24 5.96 59
272 458 cs) 264 5.81 ~A4

Footnotes to the appendix

‘Fora recent discussion of primal and dual measures of multifactor produc-
tivity, see Edwin R, Dean and Mark K, Sherwood, "Manufacturing costs, pro-
ductivity, and competitiveness, 1979-93,” Monthly Labor Review, October
1994, pp. 3-16.

2 Wolfgang Kirner, Zeitreihen fur das Anlagevermégen der
Wirtschafisbereiche in der Bundersrepublik Deutschland. Beitrage zur
Strukturforschung, Heft 5. Berlin, Deutsches Institut fur Wirtschaftsforschung,
1968. .

> Institut National de la Statistique et des Etudes Economiques, Comptes de
patrimoine en base 1980, August 1991, Table 2.1.

* This conclusion does not hold for the computed capital stock level, which
varies directly with the assumed average service life.

_ ‘Because the imputed rents are a factor in estimating the Témqvist weights
used for combining the different categories of capital services (s,, in equation 5),
they should normally be non-negative. Negative imputed prices of capital ser-

vices may arise in years when the price of a capital asset increases rapidly. The
explanation for this is that, with sufficiently high capital gains, a capital asset
can be owned (and operated) even if the value of its productive services is nega-
tive. This is most likely to happen with nondepreciable assets (land and inven-
tories). While productive capital services with a negative price may occur, one
would not wish to come up with such an estimate merely as a result of excessive
noise in the underlying price series. Smoothing the price changes reduces the
risk of this happening. For a discussion of this issue see Michael J. Harper,
Emst R. Berndt, and David 0. Wood, “Rates of Retum and Capital Aggrega-
tion Using Alternative Rental Prices,” in Dale W. Jorgenson and Ralph Landau,
eds., Technology and Capital Formation, MIT Press, 1987.

*Wiltiam Gullickson, “Measurement of productivity growth in U.S. manu-
facturing,” Monthly Labor Review, July 1995, pp. 13-28.

7 Gullickson, “Measurement of productivity growth,” Monthly Labor
Review, July 1995, pp. 13-28.

Monthly Labor Review July 1995 55



and changes in value added. The latter can be obtained as a
tesidual. The change in the gross output of an industry is

Q) duly) =w, , xdin(X,)+ War, x din (GPo,)

whereY, is real gross output of industry i, X, are real interme-

diate inputs to industry i, and w, and w,,, are the share

weights of intermediate inputs and of value added in the

value of production. Then the change in real Gro (net out-

put) is (
dinl¥:)—wxi Xd inl Xi}

(3) ain(cro;) = [ain x)— Was inl Xi)

Woro,

and the change in total manufacturing Gpo is obtained as
an aggregate:

4) din(Gpo) = >, Xd 10 (cPo;)

i

In all cases, weights are taken from the two years over
which growth is being measured. Lastly, the annual cpo
growth rates are chained into the index shown.

This index is currently available for years up to 1992.
The 1993 value was estimated based on the trend shown
by the industrial production index published by the U.S. Fed-
eral Reserve Board. The manufacturing output series calcu-
lated by the annual-weighted method results in faster an-
nual growth rates before the benchmark year than would have
been obtained if fixed weights had been used. The follow-
ing tabulation shows the average annual rates of increase
in manufacturing output over 1979-87 based on the three
methods:

1987 fixed-price weights 1,5 percent
Benchmark-years-weighted 2.3 percent
Annual-chain-weighted index 3.1 percent

German manufacturing output is real product originating
in manufacturing, as reported in the national accounts regu-
larly published by the German national statistical office,
Statistisches Bundesamt. Germany normally introduces new
price weights every 5 years. This price structure is used for
the preceding 5 to 10 years. For earlier years, this price struc-
ture is used at the level of detail published, but the old price
structure is maintained at a finer level of detail.

For France, output is real ceo for the sectors here defined
as manufacturing, as reported in the national accounts by
the national statistical institute, the Institut National de la
Statistique et des Etudes Economiques (inseE). In the French
national accounts, alternative series are published, one us-
ing transactions valued at the prices of the previous year and
the other using transactions valued at the prices of a base

year. The base year is normally changed every 10 years, and
series on the different base years are linked. The measures
used for this article are the base-year linked measures.°

Labor input, Labor input is defined in this article as total
hours worked by all persons active in the manufacturing sec-
tor. This includes the self-employed and unpaid family work-
ers as well as employees (wage and salary workers). Labor
input is not distinguished by categories such as experience,
age, or gender, and no quality differentiation is assumed.
The labor input data are the same as those used in the inter-
national comparisons of labor productivity computed by BLs.

Labor compensation is used to calculate labor's share in
total value added (w, in equation 1). This includes direct pay-
ments (wages and salaries, paid vacations, bonuses, pay-
ments in kind) and indirect payments (employer contribu-
tions to social insurance, liealth, and pension benefits). The
data on employee compensation are from national accounts
sources.” The compensation of self-employed persons is es-
timated by assuming that the hourly compensation costs of
the self-employed are the same as for employees.

Capital inputs, Capital inputs to the production process are
defined as the value of services per year from stocks of pro-
ductive capital assets, both stocks and services valued in real
terms. Capital service flows are assumed to be proportional
to the capital stock. Consequently, the measurement of capi-
tal inputs depends on the proper calculation of the capital
stock level, at constant prices. Capital used in manufactur-
ing comes in many forms and categories, although these can
be summarized in the four broad classes of fixed business
equipment (including vehicles), structures, inventories, and
land. The various types of capital stock are combined into an
aggregate capital stock index by applying appropriate
weights in a Térnqvist formula

K\_Wa Kix
(6) uf an ) “dts, +s,) uf Kin }

the real, weighted aggregate value of all asset
categories in year ft.

= the real value of capital asset category i in year t,
the weights used in combining the capital
Categories.

Ral
"

Taking an approach similar to that used in equation 1 and
making related assumptions, the weight s,, of each asset cat-
egory i is set equal to the asset’s estimated share of total
capital income in year t. Assuming competitive markets for
the different categories of capital, each category receives a
rent equal to its contribution. And if Y, denotes the total
income to capital, and ¢,, the rent earned by a unit of capital
in category i, then

Monthly Labor Review July 1995 41



Productivity in Manufacturing

tries. This follows the approach of BLs international labor
productivity comparisons in which the aggregate manufac-
turing sector is, with some exceptions, the unit of analysis.

Methodology

The multifactor productivity measures in this study are based
on a generalized production function for a country’s manu-
facturing sector, and are estimated from the following rela-
tionship: *

MFP.\__( GPO,\_1 f 2)
a oe WZ) (ia +m)

4)
Ky

Fm +W.4) XA

where MFP = =_-: multifactor productivity
GPO = the real gross product originating (or value
added) in manufacturing
L = input of labor services
K = input of capital services
wy, = labor’s share of current price value added
w, = capital’s share of current price value added

An assumption underlying the weights (w, and w,) used
in this model is that the two primary factors of production,
jabor and capital, divide all the value added between them-
selves, each being paid the value of its marginal contribu-
tion to output (its marginal product). This implies competi-
tive markets for the factors of production. Multifactor pro-
ductivity is a residual that registers those changes in the
sector’s real output (Gpo), which are not due to variations in
labor and capital inputs. This would include technological
changes, gains in organizational efficiency, changes in the
skill composition of labor input, and the benefits from re-
search and development. The multifactor productivity mea-
sures and comparisons presented in this article are in the
form of indexes or percent changes, and no level compari-
sons are made. An alternative, the dual formulation of equa-
tion 1, is shown in the appendix.

Defining manufacturing. The definition of manufacturing
is not identical among the United States, Germany, and
France. The German definition differs from the United States
in that it includes some quarrying and also the repair of elec-
trical equipment for households, and the repair of motor
vehicles, railroad equipment, and tires, which are classified
in the industries that produce these products. Data for Ger-
many apply to the former West Germany.’ The French data
apply to mining and manufacturing less energy-related prod-

40 Monthly Labor Review July 1995

ucts, As a result, the French definition excludes petroleum
refining and includes the quarrying and mining of
nonenergy-related products. The processing of agricultural
products and foodstuffs is added to the manufacturing sector
as defined in the French national statistics, which excludes
these industries.

Manufacturing output. Real (deflated) gross product origi-
nating in manufacturing (value added) is the output mea-
sure for each of the three countries. Another possible output
measure is discussed in the appendix. However, price-base
years used to measure real output and the frequency and
methods of changing price weights, which can lead to differ-
ences in real output growth rates, are different among the
three countries.

Until the 1990's the U.S. national accounts were only de-
flated using fixed weights, that is the prices in a particular
year. In this method the base year is changed every 5 years,
but the new base prices are then applied to the entire time
Series, so that data for all previous years are deflated using
the price structure of the most recent benchmark year. The
result is that the growth in real output for years before the
benchmark year is generally underestimated. This is still the
featured measure of U.S. output, but the Commerce
Department's Bureau of Economic Analysis also computes
and publishes alternate output measures, including a bench-
mark-years-weighted measure of manufacturing real output.‘

This deflation method uses the Fisher Ideal Index for-
mula and weights from two benchmark years, customarily 5
years apart. For each pair of adjacent benchmark years, the
weights are computed as the geometric mean of fixed-
weighted quantity indexes based on each of the two bench-
mark years.* These measures share one important character-
istic with the output measures computed for German and
French manufacturing: the two Nations use different weights
for different periods, rather than using the same fixed-
weighted structure for all years.

However, the benchmark-years-weighted measures also
have some limits. The benchmark years correspond to the
years for which Census of Manufactures data are available,
and relative prices in these years may be affected by cyclical
factors that are less relevant to other years. In addition, the
current BEA benchmark-years-weighted measures of manu-
facturing output have not been applied before 1977 and end
with the latest benchmark in 1987; the data for subsequent
years use constant 1987 weights.

Therefore, a chain-type annual-weighted index developed
by BLs is being used. This index is compiled by means of a
Térmqvist-aggregation of deflated output values for detailed
manufacturing industries, using moving weights. The index
is based on the assumption that changes in gross output are
equal to the sum of weighted changes in intermediate inputs



United States and France. Over the 1956-90 period,
manufacturing multifactor productivity in France grew at a
faster pace than multifactor productivity in U.S. manufac-
turing, at an annual average rate of 3.4 percent vs. 2.1 per-
cent. (See table 3). However, the French multifactor produc-
tivity annual growth rate slowed over the period: 1956-73,
4.4 percent; 1973-79, 3.0 percent; and 1979-90, 2.1 per-
cent. The vigorous turn-around in multifactor productivity
growth shown by U.S. manufacturing in the 1980’s and
1990’s was not matched by French manufacturing.

The reason for the better overall French performance was
that, while manufacturing output in France grew somewhat
faster during the 1956-90 period, U.S. combined factor
(labor and capital) inputs increased at nearly twice the rate
of the French (1.2 percent vs. 0.7 percent per year). This
greater improvement in the use of factor inputs by French
manufacturing was accomplished in part by saving labor.
Although capital service inputs rose strongly in both manu-
facturing sectors (France somewhat more, 4.6 percent per
year vs. 3.9 percent per year in the United States), French
labor hours declined by about 1 percent annually, while
manufacturing labor hours kept growing in the United States
until the 1980's.

After 1973, U.S. capital service inputs grew faster than
those in French manufacturing, especially after 1979, With
labor hours in French manufacturing continuing to decline
faster than in the United States, this further widened the gap
between U.S. and French labor and capital inputs. French
factor inputs declined throughout the 1973-90 period, even
as manufacturing output grew at an average 1.5 percent per
year. During this same period, combined U.S. factor inputs
kept increasing. This contributed to better French multifac-
tor productivity performance. U.S. multifactor productivity
grew faster than French manufacturing multifactor produc-
tivity only in the most recent 1990-93 period, when French
output fell and French manufacturing multifactor productiv-
ity turned negative.

To examine differences in labor productivity growth rates
in the manufacturing sectors of the United States and France,
we will use the same analytic tool that was used in the Ger-
man comparisons breaking down differences in labor pro-
ductivity growth into three additive factors: the capital-for-
labor substitution difference, the capital share difference,
and the multifactor productivity difference (equation 9).

For the entire 1956-90 period, French labor productivity
increased at a faster annual rate, 5 percent vs. 3 percent in
the United States, for a difference of 2 percentage points (see
table 4). French labor productivity grew faster in all periods
(except 1990-93), although the difference was negligible in
the 1979-90 period. Most of this difference in growth rates
was accounted for by more rapid multifactor productivity in-
creases in the French manufacturing sector (3.4 percent vs.

2.1 percent per year). The substitution of capital for labor
(i.e. changes in the ratio capital/flabor inputs) proceeded at a
faster pace in French manufacturing in most of the periods
studied, but the margin above the corresponding U.S. rate
diminished over time.

This difference in substitution rates (growth in capital ser-
vices per hour) equaled 3.1 percentage points per year in
1956-73, 1.3 percentage points per year in 1973-79, and
essentially no difference in 1979-90. While the capital-for-
labor substitution difference had a relatively greater weight
before 1973 than after 1973, multifactor productivity was
always the most important factor in explaining differences
in U.S.-French labor productivity growth. This is unlike the
German-U.S. comparison, in which the capital-for-labor sub-
stitution difference before 1973 was more important. In
1979-90, all three factors were approximately nil; labor pro-
ductivity grew at approximately the same average rate in
both countries.

Although multifactor productivity was the most impor-
tant factor, the rapid substitution of capital for labor in
French manufacturing also contributed significantly to the
labor productivity growth differential. The capital share dif-
ference played a negligible role in explaining differences in
labor productivity.

While multifactor productivity is important in explaining
labor productivity differences, there is no clear indication
that one country's long-term trend in manufacturing sector
multifactor productivity is inherently stronger. As in the
U.S.-German comparisons, cyclical considerations play a
part in determining comparative advantage, as the post-1990
switch in U.S.-French leadership in multifactor productivity
demonstrates.”

General observations

In all three countries, multifactor productivity increased
in most years, with the fastest growth rates recorded before
1973. But multifactor productivity declines occurred in all
three countries during periods in which output was cut
severely, as in 1973-79 in the United States and 1990-93
in Germany and France. Although Germany and France
had better multifactor productivity growth results for the
period as a whole, their rates of multifactor productivity
growth declined steadily over the years, showing negative
rates in 1990-93. By contrast, multifactor productivity
growth resumed in the United States after 1979, and although
U.S. manufacturing multifactor productivity increased most
tapidly in 1956-73 (2.9 percent per year), it grew nearly
as fast after 1979. Such a resumption in multifactor pro-
ductivity growth has not yet been observed in Germany
and France. However, unlike the United States, Germany
and France have not yet recovered from the economic down-

Monthly Labor Review July 1995 51

—————,—-


Productivity in Manufacturing

The form of the equation suggests that estimates of average capi-
tal service growth should be fairly robust for moderate changes in
the estimated service lives. To examine this assumption, average
annual changes in the capital stock of equipment and structures
were estimated for Germany and France, using different service
lives. The results are shown in table A-2. The base service lives
refer to the averages given in the first paragraphs of this section.
These were increased and decreased by given fixed percentages
(410 percent, 25 percent, and 50 percent), and the resulting aver-
age annual capital stock changes tabulated. The dash refers to cases
where the investment series do not go back far enough to permit the
calculations indicated.

In general, the more the service life departs from the base as-
sumption, the more does the computed capital growth differ from
the base solution, although this is not always true (e.g., compare
the 1956-73 results for German structures, base vs. base-50 per-
cent). In most cases the differences are less than 0.5 percentage
point, although there are two cases where the difference is over 1
percentage point (both for base-50 percent: French structures 1956—
73, and German structures 1973-90). In particular, it should be
noted that the average growth rates computed for the different time
periods vary more among each other than do the growth rates in
each time span, computed using different service life assumptions.

imputed rental price of capital

An imputed rental price is calculated for each asset category, using
the following equation

(1-mzy erat + Pret 2 -m)

OS) as iy, : + Pritt
where:

c Capital rental price

u Corporate income tax rate

Zz Present value of tax deductions for depreciation

e Investment tax credit

Pp Asset price

r Rate of return on investment

B Real value of depreciation

K Real capital stock

Ap, Capital gains (smoothed asset price change)*
x Property tax rate (taxes on capital)

Although the rate of return (r) appears as an independent vari-
able on the right-hand side of equation A-6, it is actually deter-
mined simultaneously with ¢ as a function of these same indepen-
dent variables and of the total property income. For Germany and
France, it is assumed that, for every year, all assets have the same
rate of return. This rate of return is determined for each country and
in each year using the total property income for that year and using
the value of the other variables in equation A-6 that pertain to that
year. For the U.S., the rates of return are permitted to differ by
industry; within industries all assets have the same rate of return.
for a particular year.

Sectoral output or value added

Sectoral multifactor productivity also can be measured by replac-
ing the output term (real gross product-cpo- or value added) in
equation Iwith a sector’s real gross output. To the primary factor

54 Monthly Labor Review July 1995

inputs of labor and capital are added other inputs purchased from
outside the sector (energy, materials, and business services). For
consistency, gross output is defined as output sold outside the sec-
tor, or “sectoral output.”* This approach is particularly appropriate
when dealing with detailed industries. The finer the industry break-
down, the smaller the value added as a proportion of sectoral out-
put, and the greater the value of inter-sectoral purchases as a pro-
portion of total factor inputs. Conversely, as sectors become more
aggregated, the proportion of value added in sectoral output in-
creases and the proportion of intermediate inputs coming from other
sectors declines.

At the total economy level, excluding imports and exports,
sectoral output is identical to value added (everything is sold to
final users), and the only input factors are labor and capital (noth-
ing purchased from other sectors). If we designate by MrP,, and MFP,
the multifactor productivity indexes calculated for a given sector by
the sectoral output and the value added methods respectively, then
it can be shown that in general

%AMFP,, value added, at current prices
%AMFP,, _ sectoral output, at current prices

The advantages of using the sectoral output definition of multi-
factor productivity are evident. It allows an analysis of the effects
on multifactor productivity trends of all intermediate factor inputs,
not only of the two primary factors of labor and capital.

The main disadvantages of the sectoral output approach—these
become especially formidable in the case of international compari-

(A-7)

Tab! Growth rates of prices of manufacturing output
‘and factor Inputs, U.S., Germany, and France,
selected periods, 1956-93

(Average annual percent changes}

Output Labor
price price price
29 59 26
27 58 23
44 50 15
48 69 37
86 96 48
29 55 3.2
0 48 18
31 85 1
34 83
29 10.3 4
34 68 18
40 93 18
31 55 19
26 64 85
57 10.5 63
5A 99 55
a7 96 53
77 13 73
98 159 63
66 89 78
16 37 35