## R. C. O. Matthews, C. H. Feinstein, and J. Odling-Smee

Print publication date: 1982

Print ISBN-13: 9780198284536

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198284535.001.0001

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# (p.599) Appendix J Correlations Among Manufacturing Industries

Source:
British Economic Growth 1856-1973
Publisher:
Oxford University Press

We present here the results of a simple correlation analysis performed on the growth rates of output, labor, etc. and on the absolute values of other variables for 12 manufacturing industry groups (the 13 discussed in Chapter 8, with the exclusion of textiles, for which the data are unsatisfactory). The analysis is in two parts: (1) correlation coefficients between two different variables in the same period (calculated for 1924–37, 1951–64, and 1964–73), and (2) correlation coefficients between the same variables in successive periods. Nineteen variables, listed in Table J.1, were used, and throughout there were 12 observations

Table J.1 Variables Used in the Correlation Analysis

Variable

Abbreviation

Annual percentage growth rates of:

Output

$q ∧$

Labor

ĉ

Capital

$k ∧$

TFI

$f ∧$

TFP

$x ∧$

Labor productivity

$q ∧$ − ĉ

Capital per man‐hour

$k ∧$ − ĉ

Capital per unit of output

$k ∧$$q ∧$

Buildings

$b ∧$

Plant and machinery

$m ∧$

Implicit output prices

$p ∧$

Average hourly earnings (first year of period)

w

Average hourly earnings (last year as percent of first year)

(1 + ŵ)t

Average profit rate (first year of period)

r

Average profit rate (last year as percent of first year)

(1 + $r ∧$)t

Capital per man‐hour (first year of period)

k/n

Output per man‐hour (first year of period)

q/n

Capital‐output ratio (first year of period)

k/q

Proportion of output exported in value‐added term (intermediate years)a

e

(a) The years used, which were dictated by the availability of input‐output tables, were as follows: 1935 was used for the 1924–37 period; 1954 for 1951–64; and 1968 for 1964–73.

(p.600)

Table J.2 Within‐Period Correlation Coefficients for Twelve Manufacturing Industries, 1924–1937, 1951–1964, and 1964–1973

Variable

ĉ

$k ∧$

$f ∧$

$x ∧$

$q ∧$ − ĉ

$k ∧$ − ĉ

$k ∧$$q ∧$

$b ∧$

$m ∧$

$p ∧$

w

(1+ŵ)t

r

(1+$r ∧$)t

k/n

q/n

k/q

e

Variable

$q ∧$

0.82*

0.52

0.88*

0.81*

0.52

−0.45

−0.80*

0.46

0.26

−0.30

−0.08

−0.21

−0.20

0.40

−0.18

−0.15

−0.15

−0.01

$q ∧$

0.67*

0.60*

0.71*

0.57

0.65*

0.07

−0.48

0.50

0.29

−0.60*

0.52

0.07

−0.19

−0.11

0.52

0.47

0.40

0.31

0.59*

0.66*

0.74*

0.81*

0.88*

0.37

−0.69*

0.61*

0.71*

−0.73*

−0.01

−0.15

0.48

0.23

0.06

0.32

−0.19

0.13

ĉ

0.35

0.97*

0.36

−0.06

−0.75*

−0.70*

0.31

0.08

0.03

−0.14

0.20

0.14

0.16

0.01

0.17

−0.03

−0.02

ĉ

0.59*

0.86*

−0.07

−0.13

−0.25

−0.12

0.50

0.18

−0.07

0.64*

−0.12

0.00

−0.22

0.28

0.46

0.22

0.44

0.68*

0.80*

0.16

0.13

0.04

−0.11

0.59*

0.60*

0.02

−0.18

0.16

0.18

0.24

−0.24

−0.08

−0.35

−0.30

$k ∧$

0.54

0.31

0.38

0.36

0.10

0.84*

0.85*

−0.39

0.07

−0.24

0.10

0.12

−0.34

−0.08

−0.46

−0.15

$k ∧$

0.87*

−0.18

0.20

0.63*

0.41

0.78*

0.82*

−0.09

0.69*

0.13

−0.01

−0.33

0.66*

0.70*

0.56

0.60*

0.91*

0.17

0.40

0.75*

0.10

0.75*

0.90*

−0.31

−0.25

0.10

0.51

0.07

−0.10

0.17

−0.29

−0.24

$f ∧$

0.43

0.09

−0.59*

−0.64*

0.50

0.22

−0.06

−0.07

0.13

0.07

0.22

−0.08

0.11

−0.13

0.00

$f ∧$

−0.17

0.07

0.21

0.14

0.69*

0.60*

−0.10

0.70*

0.10

0.04

−0.33

0.65*

0.76*

0.53

0.54

0.21

0.44

0.52

−0.10

0.71*

0.85*

−0.39

−0.05

0.09

0.37

0.45

0.11

0.37

−0.11

−0.20

$x ∧$

0.88*

−0.14

−0.72*

0.25

0.22

−0.50

−0.07

−0.54

−0.47

0.49

−0.25

−0.41

−0.13

−0.01

$x ∧$

0.83*

−0.15

−0.84*

−0.10

−0.29

−0.73*

−0.09

−0.03

−0.33

0.53

−0.03

−0.23

−0.06

−0.21

0.90*

0.09

−0.91*

0.27

0.30

−0.72*

0.03

−0.37

0.37

0.29

−0.01

0.15

−0.19

−0.02

$q ∧$ − ĉ

0.32

−0.35

0.33

0.34

−0.56

0.07

−0.66*

−0.55

0.46

−0.33

−0.51

−0.21

0.02

$q ∧$ −ĉ

0.36

−0.52

0.16

0.21

−0.73*

0.04

0.21

−0.26

0.37

0.42

0.16

0.31

−0.05

0.44

−0.77*

0.39

0.51

−0.90*

0.09

−0.29

0.48

0.14

0.22

0.43

−0.03

0.01

$k ∧$ − ĉ

0.78*

0.29

0.52

−0.30

0.19

−0.37

−0.07

−0.08

−0.25

−0.23

−0.30

−0.09

$k ∧$ −ĉ

0.61*

0.45

0.82*

−0.04

0.22

0.26

−0.02

−0.18

0.52

0.39

0.45

0.29

0.23

0.49

0.69*

−0.44

−0.18

0.01

0.53

−0.12

0.08

0.30

−0.09

−0.06

$k ∧$$q ∧$

0.06

0.29

0.08

0.15

0.07

0.30

−0.38

−0.03

0.11

−0.15

−0.10

$k ∧$$q ∧$

0.28

0.57

0.58*

0.17

0.06

0.20

−0.48

0.12

0.23

0.15

0.31

−0.08

−0.07

0.66*

−0.23

0.37

−0.14

−0.23

−0.17

−0.27

−0.03

−0.05

$b ∧$

0.58*

−0.25

0.28

−0.24

0.07

0.14

−0.23

0.03

−0.38

0.01

$b ∧$

0.56

0.12

0.40

0.26

0.04

−0.11

0.47

0.46

0.55

0.37

0.83*

−0.18

−0.04

0.17

0.48

0.26

−0.20

0.12

−0.31

−0.15

$m ∧$

−0.41

−0.07

−0.38

0.11

0.05

−0.40

−0.24

−0.49

−0.39

$m ∧$

−0.01

0.43

0.27

0.28

−0.41

0.60*

0.66*

0.38

0.34

−0.43

−0.18

−0.16

0.61*

0.22

−0.09

0.23

−0.28

−0.19

$p ∧$

0.35

0.85*

−0.17

0.40

0.46

0.24

0.51

0.39

$p ∧$

−0.41

0.23

0.08

0.11

−0.23

−0.29

0.02

−0.01

−0.25

0.46

−0.23

0.21

−0.54

−0.65*

−0.32

−0.22

ŵ

0.29

−0.48

0.36

0.71*

0.52

0.62*

0.34

w

−0.18

0.05

−0.66*

0.43

0.71*

0.20

0.66*

−0.01

−0.65*

−0.33

0.78*

0.76*

0.81*

0.65*

(1 − ŵ)t

−0.11

0.19

0.41

0.33

0.40

0.30

(1−ŵ)t

−0.07

0.18

0.48

0.25

0.53

0.09

−0.05

−0.22

−0.18

−0.09

−0.12

−0.13

r

−0.68*

−0.13

0.37

−0.35

−0.28

r

−0.47

−0.23

0.25

−0.52

−0.30

0.55

−0.54

−0.21

−0.72*

−0.60*

(1 − $r ∧$)t

0.06

−0.28

0.24

0.19

(1−$r ∧$)t

−0.20

−0.62*

0.06

−0.36

−0.59*

−0.36

−0.68*

−0.52

k/n

0.79*

0.92*

0.39

k/n

0.82*

0.87*

0.46

0.90*

0.95*

0.59*

q/n

0.52

0.07

q/n

0.52

0.46

0.76*

0.40

k/q

0.50

k/q

0.50

0.67*

Source: Basic statistics (Appendix N); Barna 1952; Input‐Output Tables, 1954, 1968, UK [9], [16].

Note: The first figure in each cell refers to 1924–37, the second to 1951–64, and the third to 1964–73. An asterisk refers to a correlation coefficient significantly different from zero at the 5% level (the critical value is ± 0.576).

(p.601) (p.602) corresponding to the 12 industry groups. In this appendix we do no more than present the results and draw attention to some of the more significant figures. Some of the correlation coefficients are quoted elsewhere to support or refute particular hypotheses.

The within‐period correlation coefficients are shown in Table J.2. The more interesting facts are as follows.

1. (1) Output growth was correlated both with input growth and with the growth of labor productivity (Verdoorn law).

2. (2) There was an inverse correlation between output growth and the growth of output prices, more pronounced in the postwar period than in the interwar period.

3. (3) There was no significant correlation between the growth of TFI (or of capital or labor) and the growth of TFP. This tends to refute the hypothesis that there were economies of scale associated with inputs. Nor was the growth of TFP correlated with the growth of capital per unit of labor.

4. (4) The growth of TFP was positively correlated with the growth of both labor productivity and capital productivity. The other input did not, as it were, fully account for inter‐industry differences in one input's productivity.

5. (5) The growth of output prices was inversely correlated with both the growth of labor productivity and the growth of TFP. In the interwar period and to a lesser extent in the postwar period, there was also a positive correlation between the rate of growth of prices and the rate of growth of wages.

6. (6) There was a tendency for those industries with high capital intensity (relative to either labor or output) and high absolute labor productivity, all of which were related, to have high average earnings of labor, as well. On the other hand, there was no tendency for industries with rapidly increasing labor productivity to have rapidly increasing wages; indeed, in the interwar period, the opposite was the case.

7. (7) There was a positive correlation between capital intensity and the proportion of output exported.

8. (8) In 1951–64, but not in 1964–73 or in the interwar period, industries with rapidly growing output, labor input, and capital input had high wages.

9. (9) In 1951–64, but not in 1964–73 or in the interwar period, the rate of growth of TFI was positively correlated with capital intensity.

10. (10) In the interwar period the rate of growth of TFI was inversely correlated with the increase in capital intensity. In the postwar period the tendency was in the opposite direction.

Between‐period correlations are shown in Table J.3. There was a tendency for the same industries to have high capital intensity, high labor productivity, high wages, and high export proportions in all periods. The between‐period correlations of the variables referring to growth rates are in general remarkably low. There is no growth‐rate variable that gets an asterisk in both columns, though there is a moderately high correlation in output growth in both. In general, though not without exceptions, there was more resemblance between the two parts of the postwar period than between the interwar period and 1951–64. (p.603)

Table J.3 Between‐Period Correlation Coefficients for Twelve Manufacturing Industries, 1924–1937, 1951–1964, and 1964–1973

Variable

Between 1924–37 and 1951–64

Between 1951–64 and 1964–73

Variable

Between 1924–37 and 1951–64

Between 1951–64 and 1964–73

$q ∧$

0.46

0.55

$p ∧$

−0.14

0.47

ĉ

0.85*

0.12

w

0.50

0.76*

$k ∧$

−0.21

0.08

(1−ŵ)t

−0.08

0.29

$f ∧$

0.61*

0.20

r

0.14

0.49

$x ∧$

0.10

0.57

(1−$r ∧$)t

−0.07

0.00

$q ∧$ĉ

0.10

0.55

k/n

0.88*

0.94*

$k ∧$ĉ

−0.15

0.40

q/n

0.68*

0.81*

$k ∧$$q ∧$

−0.35

0.65*

k/q

0.50

0.84*

$b ∧$

−0.05

0.47

e

0.90*

0.93*

$m ∧$

−0.64*

0.36

Source: Same as Table J.2.

Note: An asterisk refers to a correlation coefficient significantly different from zero at the 5% level (the critical value is ± 0.576).

Thus there was a tendency for the same industries to have high rates of growth of TFP in both parts of the postwar period, but not in 1924–37 and 1951–64. There was a surprising negative correlation in the growth of plant and machinery ($m ∧$) between 1924–37 and 1951–64: those industries where the stock of machinery grew relatively rapidly in 1924–37 had a relatively slow rate of growth in machinery in 1951–64. On the other hand, the growth of labor (and hence of TFI) was strongly correlated between 1924–37 and 1951–64 but not between 1951–64 and 1964–73 (see Chapter 8, pp. 242–43).