Five sectors — research and development, business travel and office supplies, scrap and used goods, and inventory valuation adjustment — appeared in some
years, but not in others the earlier years for the first three sectors and the later years for the last two sectors. In order to make the accounting framework
consistent over the four years of analysis, we eliminated these sectors from both gross and final output. This was accomplished by distributing the inputs used by
these sectors proportional to either the endogenous sectors which purchased the output of these five sectors or the final output.
5
Data on the ratio of RD expenditures to GDP were obtained from the National Science Foundation, Research and De6elopment in Industry, various years,
for 32 manufacturing industries covering the period 1958 to 1987. We were able to allocate these figures to 48 manufacturing industries in the input – output data.
6
5. Results
Table 1, upper panel, shows the standard forward multipliers for the 68 indus- tries in each of the four years. In 1987, not surprisingly, wholesale and retail trade
is the sector with the highest forward linkage, since, by construction, it supplies almost all industries in the economy. The second most important supplier is the
business service sector, followed by primary iron and steel, transportation, utilities, and industrial chemicals. On the bottom of the list are the consumer-oriented
sectors, including tobacco products, ordinance that is, armaments, household appliances, and footwear and leather products. Cross-industry correlations in
forward linkages are very high, though they tend to attenuate over time. The correlation coefficient between the 1987 and 1977 forward linkages is 0.96, com-
pared with a correlation of 0.92 between the 1958 and 1987 linkages; the respective rank correlations are 0.97, 0.96, and 0.90.
We next compute the new forward linkages based on matrix C. Results on forward linkage multipliers based on Eq. 7 with a = 0.003, b
1
= 0.106, b
2
= 1.101
and b
3
= 0.753 following Wolff, 1997 are shown in Table 1, lower panel. There
are now some interesting differences between these new multipliers and the stan- dard forward linkage multipliers. On the basis of the 1987 multipliers, the trade
sector ranks first and the construction sector ranks second, which is not unexpected since new investment is incorporated in the multiplier calculation. Business services
5
The allocation of the scrap sector was handeled differently in the make-use framework of the 1967, 1977 and 1987 tables. See ten Raa and Wolff 1991 for details.
6
This was calculated in two steps. First Company RD from the Federal Trade Commission Line of Business Data was averaged over 1974, 1975 and 1976 and then divided by the average of industry GDP
over the same 3 years. Second, using the National Science Foundation data, we computed the average ration RD expentitures to net sales at the 32-industry level for the 1958 – 1987 period and adjusted the
first set of RD to gross output ratios accordingly. It should be noted that the RD data at this level of detail are not available prior to 1958, which prevented us from aldso including the 1947 – 1958 period
in the regression analysis. The net sales are net of intra-company sales.
482 T
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Structural Change
and Economic
Dynamics
11 2000
473 –
489
Table 1 Ranks and values of forward linkage multipliers based on pˆApˆ
− 1
traditional and matrix C spillovers, 1958–1987, with sectors ranked by 1987 multipliers top 10 only
1967 1977
1987 1958
Traditional 3:
4.18 1:
5.71 5.08
2: 1:
Trade, restaurants 59
4.79 4:
3.40 2:
4.32 3:
3.89 2:
63 4.77
Business services 1:
4.79 2:
4.41 4.83
Primary iron and steel 28
1: 3.55
3: 3.77
Transportation 5:
3.37 5:
3.31 4:
3.35 3:
55 8:
2.52 7:
3.07 58
Utilities 5:
3.19 10:
2.34 6:
3.28 6:
3.30 3.09
19 6:
3.19 6:
Industrial chemical 4:
3.88 10:
2.74 61
Real estate 7:
2.95 5:
3.31 11:
2.30 11:
2.69 2.26
6 12:
2.59 8:
Construction 4
16: Crude petroleum and gas
2.06 4:
3.37 9:
2.57 13:
2.21 7:
2.87 9:
2.79 2.78
7: 29
Primary non-ferrous metals 10:
2.51 Correlations with 1987 forward linkages
0.917 0.929
0.956 0.957
0.973 0.903
Rank correlations with 1987 forward linkages Matrix C spillo6ers
3: 6.06
2: 8.22
7.72 1:
2: 6.93
59 Trade, restaurants
1: 7.16
1: 6
8.44 Construction
2: 8.11
1: 7.83
4: 5.54
4: 5.12
4.35 63
5: 6.44
3: Business services
Primary iron and steel 6.35
2: 6.10
3: 5.69
4: 4.33
28 3:
6: 4.30
6: 4.25
4.85 Transportation
55 4:
4.21 5:
4.23 Real estate
5: 4.96
9: 3.72
6: 3.93
6: 61
9: 58
2.97 Utilities
8: 3.75
7: 3.83
11: 2.77
7: 3.85
7: 3.95
3.66 19
7: 3.75
8: Industrial chemicals
17: 2.40
5: 4.27
4 Crude petroleum and gas
9: 3.07
12: 2.62
8: 3.51
11: 3.42
3.39 29
8: 2.94
10: Primary non-ferrous metals
0.945 0.966
Correlations with 1987 forward linkages 0.938
0.909 0.952
Rank correlations with 1987 forward linkages 0.944
0.905 0.880
0.903 Correlations with traditional forward linkage multiplier
0.898 0.890
Rank correlations with traditional forward linkage multiplier 0.916
0.963 0.927
now rank third, followed by primary iron and steel and transportation. The correlation coefficients between the new forward linkage multipliers and the stan-
dard forward linkage multipliers are now around 0.9, and the rank correlations range from 0.89 to 0.96. Cross-industry correlations in these new forward link-
ages are high and increase over time. The correlation coefficient between the 1987 and 1958 forward linkages is 0.94, that between the 1987 and 1967 multi-
pliers is 0.95; and that between the 1987 and 1977 multipliers is 0.97; the corresponding rank correlations are 0.91, 0.94, and 0.95.
We next look at the major spillover sectors over the 1958 – 1987 period. These are defined as sectors i with high spillover terms p
i
c
i1
… c
in
which reflect both the strength of their forward linkages and their TFP growth. These sectors,
shown in Table 2, are the ones which contributed most to the overall TFP growth of the economy. Over the whole 1957 – 1987 period, the most important
source of overall growth was the trade sector, reflecting its very high forward linkage value. The second most important sector was computer and office equip-
ment, a reflection of its very high TPF growth. Indeed, in the 1977 – 1987 period, it made by far the greatest contribution to embodied TFP growth. The third
most important sector over the 1958 – 1987 period was electronic components, followed by transportation and plastics and synthetics. At the bottom of the list
are the low actually negative TFP growth sectors, including crude petroleum and gas, finance and insurance, business services, radio and TV broadcasting,
and metallic mining.
It is also of interest that there is very little correlation over time in the rank order or values of sectors in terms of pC. The correlation coefficient between
the 1958 – 1967 and the 1977 – 1987 values is 0.27 and the rank correlation is 0.22; the corresponding figures between the 1967 – 1977 and 1977 – 1987 values are
− 0.03 and 0.12. This is a reflection of the fact that sectoral TFP growth is very
variable over time. Our final step is to decompose overall TFP growth into sectoral contributions.
The decomposition is based on Eq. 14 and the figures are percentages of the positive growth contributions only, to avoid engines of growth making more
than 100. The results are shown in the bottom panel of Table 3. The results are quite striking. Over the full 1958 – 1987 period, the computer and office
equipment industry was directly or indirectly responsible for over one fifth of the positive contributions to TFP growth of the economy. It was the leading sector
in both the 1967 – 1977 and the 1977 – 1987 subperiods. Indeed, in the 1977 – 1987 period, it accounted for one fifth of the positive contributions to overall TFP
growth. A reason for this large effect is that TFP growth in computers and office equipment averaged 9.94 per year during this period. The next largest
growth rates during this period were for electronic components and accessories, at 3.88 per year, and non-metallic minerals mining, at 3.70 per year. It is
also of interest that annual TFP growth in computers and office equipment accelerated from 1.22 in the 1958 – 1967 period to 2.58 in 1967 – 1977 and
9.94 in 1977 – 1987. The next leading
484 T
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Raa ,
E .N
. Wolff
Structural Change
and Economic
Dynamics
11 2000
473 –
489
Table 2 Embodied total factor productivity growth rates, based on p
i
c
i1
… c
in
in Eq. 9, 1958–1987, with sectors ranked by 1958–1987 values top 10 only, figures in percent per annum
1958–1987 1958–1967
1967–1977 1977–1987
3: 7.4
2: 8.9
4: 5.9
7.9 1:
Trade, restaurants 59
7: 3.5
1: 41
14.5 Computer and office equipment
2: 6.4
50: 0.7
5: 4.7
3: 7.6
4.0 9:
47 Electronic components
3: 5.7
2: 7.6
58: −
1.9 55
Transportation 4:
5.1 1:
10.0 4:
5.3 6:
4.8 4.9
20 6:
5.1 5:
Plastics and synthetics 3:
6.5 1:
12.9 62:
− 2.9
61 6:
Real estate 4.9
6: 4.0
11: 3.0
2.0 1
29: 3.1
7: Agriculture
10: 2.8
25: 2.0
53 Ophthalmic and photographic equipment
8: 2.5
18: 3.1
23: 1.4
12: 2.9
3.1 10
17: 2.4
9: Fabrics, yarn and thread mills
14: 3.2
43: 0.3
9: 3.7
10: 24
2.4 Rubber, miscellaneous plastics
Correlations with 1977–1987 values 0.274
− 0.028
Rank correlations with 1977–1987 values 0.222
0.120
485 T
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E .N
. Wolff
Structural Change
and Economic
Dynamics
11 2000
473 –
489
Table 3 Percentage decomposition of overall TFP growth by sector, based on Eq. 4 Domar and Eq. 14 sources of growth, with sectors ranked by 1958–1987
values top 10 only, figures in percent per annum, with denominator the sum of positive elements only 1967–1977
1977–1987 1958–1987
1958–1967 Domar
2: 16.0
1: 21.6
19.1 2:
1: Trade, restaurants
59 11.4
1: 11.9
1: 30.6
66: −
8.3 61
2: Real estate
16.5 4:
7.8 4:
5.5 4.1
Agriculture 1
6: 8.6
3: 9.0
Transportation 3:
8.4 59:
− 1.8
4: 7.3
3: 55
5: 5.1
5: 3.5
5: 3.6
8 5:
Food products 5.5
14: 1.5
2: 8.2
0.2 3.6
52: 41
Computer and office equipment 6:
1.8 Apparel
11: 1.9
7: 3.1
7: 2.9
16: 12
10: 2.0
11: 2.5
21 Drugs and cleaning products
8: 2.4
19: 1.4
12: 1.7
6: 3.1
1.1 Electronic components
47 23:
2.3 9:
2.2 Communications
6: 3.1
58: −
1.4 10:
2.2 12:
56 0.31
0.11 Rank correlations with 1977–1987 values
Engines of growth 1:
14.3 1:
1: 19.2
Computer and office equipment 18.0
19: 0.8
41 3:
11.8 2:
47 5.9
Electronic components 2:
9.2 8:
3.6 4:
9.2 5:
1.9 4.2
20 6:
5.7 3:
Plastics and synthetics 68:
− 0.5
8: 3.8
3: 3.6
4: 52
4.3 Scientific and control instruments
62: −
0.5 55:
0.0 15.3
Aircraft and parts 50
1: 4.2
5: 6.9
Audio, video and communications equipment 13:
2.3 6:
1.8 6:
3.8 4:
46 11:
2.2 5:
5.9 8:
1.5 21
Drugs and cleaning products 7:
3.7 2:
13.0 68:
− 4.8
7.2 3.2
3: 49
Motor vehicles 8:
1.8 Rubber, miscellaneous plastics
19: 1.2
7: 1.8
9: 2.5
12: 24
7: 44
4.5 Household appliances
14: 0.4
10: 2.3
9: 2.9
Rank correlations with 1997–1987 values 0.400
0.231 0.812
0.691 0.809
0.807 Rank correlations with Domar values
sector was electronic components, which accounted for 14 of the positive con- tributions of overall TFP growth over the full 1958 – 1987 period and for 6 in
1977 – 1987. Plastics and synthetics ranked third over the three decades, followed by scientific and control equipment and then aircraft and parts. Together, the
top five industries were responsible for 41 of the positive contributions of overall TFP growth over the full 1958 – 1987 period and for 31 in 1977 – 1987.
It is also notable that the top 10 industries are all manufacturing industries.
There is very little correlation over time in the rank order of sectors in terms of their contribution to overall TFP growth. The rank correlations between the
1958 – 1967 and the 1977 – 1987 values is 0.40 and that between the 1967 – 1977 and 1977 – 1987 values is 0.23. This again is a reflection of the fact that sectoral
TFP growth in the US economy can change radically over time. It also suggests that the engines of growth in the US economy can change radically over time.
In the real estate sector, for example, annual TFP growth, after rising from 1.42 in the 1958 – 1967 period to 2.97 in 1967 – 1977, plummeted to − 0.76
in 1977 – 1987. This, together with its linkages to other industries in the econ- omy, also accounts for its very low ranking in the 1977 – 1987 period.
A comparison with the standard decomposition of overall TFP growth based on Domar factors Eq. 4 is also instructive see the top panel of Table 3.
Here, the top four industries, in rank order, over the 1958 – 1987 period are wholesale and retail trade including restaurants, real estate, agriculture, and
transportation. Computers and office equipment rank only sixth, compared with their top rank on the basis of matrix C. Like the engines of growth, there is a
positive but low correlation in rank order of these industries over time, because of the high variability of TFP growth between periods. However, overall, the
Domar rankings are similar to those based on matrix C, with rank correlations of 0.8 or so for most periods and for the entire 1958 – 1987 period. This result
reflects the fact that industry-level TFP growth is the main determinant of the contribution of an industry to overall TFP growth.
6. Conclusion
