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A New View of Economic Growth$

Maurice FitzGerald Scott

Print publication date: 1991

Print ISBN-13: 9780198287421

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198287429.001.0001

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(p.524) Statistical Appendix

(p.524) Statistical Appendix

Source:
A New View of Economic Growth
Publisher:
Oxford University Press

1 Introduction

This appendix gives some further details of the sources and methods used to derive the basic statistics analysed, mainly, in Chapters 10 and 11. The statistics themselves are also given: those for periods in Table SA I, and those for individual years for the USA, Japan, and the UK in Table SA II.

While it is hoped that enough explanation has been provided for most readers, it seemed impractical to describe all the estimates in full. The next three sections deal with particular topics—the derivation of the variable used to measure the scope for catch‐up, cu, the derivation of the weights used in the regressions, and an explanation of how the effects of changes in hours of work on labour productivity were estimated. These three sections are followed by four more describing the sources and methods used for the USA, Japan, the UK, and the continental European countries.

2 The Scope for Catch‐Up, cu

As noted in Chapter 10, a variable measuring the scope for catch‐up, cu, was introduced to help explain differences in growth rates between different countries in the years since the Second World War. This section describes how the variable was estimated.

The aim was to measure output per man in non‐residential businesses (but excluding agriculture) in each country in each year relative to the corresponding output per man in the USA, taken as being the leading country. For any particular period, cu was then the arithmetic mean of those relatives for the years in the period. Agriculture was excluded because it was thought that relative output per man there was not a good indicator of the scope for catch‐up, since productivity was much influenced by special factors such as the availability of good‐quality land and heavy protection.

In principle, output in each country needed to be valued, for this comparison, at the same prices as for the USA. This could be done using either the country's own prices or US prices, the former showing, in general, an appreciably lower level of output relative to that of the USA than the latter. Countries tend to produce relatively more output of goods that are relatively cheaper. It seemed best to take the geometric mean of these two price comparisons, i.e. an intermediate set of price weights. If one were to imagine the lower‐productivity country growing over a period so as to catch up the USA, while that country stood still, then growth in the catching‐up country would on average be measured using an intermediate set of price weights, assuming some approximation to a Divisia index. If one were instead to use either the country's own initial price weights or US price weights to measure (p.525) growth, it would either exceed or fall short of this and so would not correspond to the gap that actual growth performance would reveal.

In principle, the input of labour in the productivity comparison needed to be quality‐adjusted, since some of the differences between countries were due to differences in labour quality, and, in so far as this was the case, there were no corresponding differences in the scope for catch‐up. There might be corresponding differences in the scope for improving labour quality, but that would show up in g L, not in ϱ.

The main sources used for labour inputs were Denison with Poullier (1967), and Denison and Chung (1976). Each country was compared with the USA in 1960, except for Japan, for which the comparison was made in 1970. Denison provides estimates of the differences in labour input arising from: annual hours of work (allowing for differences in the efficiency of work, owing to differences in hours of work); the age and sex composition of employment; education; and the proportion of self‐employment and unpaid family workers (excluding agricultural workers). Outputs were compared using the work of Gilbert and Kravis (1954), Gilbert and associates (1958), and Kravis et al. (1975). The first two of these are cited in Denison with Poullier (1967) and were used for all countries except Japan, for which the last was used.

Both outputs and labour inputs were adjusted so far as possible to correspond to NRB, excluding agriculture, for the year of comparison (1960 or 1970). However, extrapolating the ratios to earlier or later years, index numbers of Q/L for the country concerned relative to those for the USA were used as the best indicators readily available. These index numbers refer to the whole of NRB.

Output per (quality‐adjusted) man employed in NRB (excluding agriculture) in each country relative to the USA in the base year was estimated. These figures are given in Table SA.1.

Table SA.1 Output Per (Quality‐Adjusted) Man Employed in Non‐Residential Businessa in Each Country

Country

Relative output per quality‐adjusted man employed (USA = 1)

Base year

Japan

0.563

1970

UK

0.443

1960

Belgium

0.572

1960

Denmark

0.544

1960

France

0.588

1960

Germany

0.567

1960

Italy

0.471

1960

Netherlands

0.492

1960

Norway

0.621

1960

(a) Excluding agriculture.

(p.526) 3 Weights Used for the Regressions

As noted in Section 10.2, in fitting equations by least squares to the twenty‐six observations for different countries and periods, each observation was multiplied by a weight. These weights consisted of the square roots of the products of three variables: namely, for each period, the number of years in the period, the mean population of the relevant country in that period, and an index of statistical reliability of the data for that period. Mean populations were taken simply as the geometric means of populations in the first and last years of each period, the sources used being as follows.

  • USA: 1929–73; Survey of Current Business, Special Supplement, July 1981, Table 8.2; 1889–1929, linked at 1929 using Historical Statistics of the United States 1789–1945, series B31.

  • Japan: 1889–1970, Ohkawa and Shinohara (1979), Table A53, interpolating to get mid‐years; 1970–3, United Nations Monthly Bulletin of Statistics, October 1982.

  • UK: 1856–1962, Feinstein (1972), Table 55, column (1); 1962–1973, CSO Monthly Digest of Statistics, November 1982.

  • Continental European countries: OECD Manpower Statistics 1954–1964, 1965, Table 1.

The three components of the weights are shown in Table SA.2, together with their rounded products. The observations were multiplied by the square roots of this last column of figures.

4 The Effects of Changes in Hours of Work on Labour Productivity

This section provides a fuller explanation and discussion of that in Section 2.2. When hours of work are long, a reduction can generally be expected to result in some offsetting increase in output per man‐hour. The offset is greater the longer are hours per week or per year; indeed, hours can be so long that a reduction in hours per year actually increases output per year. As Sidney Webb and Harold Cox (1891, 4) concluded, ‘in the arithmetic of labour, as in that of the Customs, two from ten is likely to produce, not eight, but even eleven’ (quoted in Denison with Poullier 1967, 59). As Denison points out,

Shorter hours result in less fatigue, greater intensity of work, fewer mistakes, better quality of output, less wastage, and less absenteeism. This personal effect is greatly reinforced by an institutional factor. Many jobs require an individual's presence so long as an establishment is open, but do not fully occupy him throughout this time so that he can readily compress the same amount of work into fewer hours. (Denison with Poullier 1967, 59)

Denison mentions several other studies which have concluded that the offset exists, some of which have estimated its magnitude, and these include studies by the International Labour Organization, an expert report to the European Economic Community, the French Planning Commission, the Dutch Planning Bureau, the Norwegian government, the National Institute of Economic and Social Research, a (p.527)

Table SA.2 Weights Used for the Regressions

Country

Period

No. of years

Mean population (m)

Statistical reliability

Weighting factor

UK

1856–73

17

30.0

0.5

255

1873–1901

28

36.6

0.5

512

1901–13

12

43.5

0.5

261

1913–24

11

45.3

0.333

166

1924–37

13

46.1

1

599

1937–51

14

48.8

0.5

341

1951–64

13

52.1

1

677

1964–73

9

54.9

1

494

USA

1889–1900

11

68.6

0.5

377

1900–13

13

86.1

0.5

560

1913–29

16

108.9

0.5

871

1929–48

19

133.7

1

2540

1948–73

25

175.7

1

4392

Japan

1887–99

12

40.8

0.333

163

1899–1911

12

46.5

0.333

186

1911–28

17

55.7

0.333

316

1928–36

8

66.0

0.333

176

1952–61

9

89.7

1

807

1961–73

12

101.1

1

1214

Belgium

1955–62

7

9.0

1

63

Denmark

1955–62

7

4.5

1

32

France

1955–62

7

45.2

1

316

Germany

1955–62

7

54.6

1

382

Netherlands

1955–62

7

11.3

1

79

Norway

1955–62

7

3.5

1

25

Italy

1955–62

7

49.2

0.5

172

German research institute for the German government, and P. J. Verdoorn and L. Reynolds. (See Denison with Poullier 1967, 59–62, for details.) Matthews et al. (1982) also allowed for a productivity offset in their study.

While the weight of expert opinion is therefore very much on the side of making some allowance for increased productivity as hours fall, authors disagree as to how much should be allowed. I have adopted Denison's estimates so far as he provided data for the USA, Japan, and continental Europe, and I have attempted to follow his assumptions in constructing estimates for the UK and for years not covered by him for other countries. The method used is described below. Apart from the evidence in favour of some adjustment, some econometric evidence in favour of the particular adjustments made here is discussed in Section 10.5. While this is not compelling, I think that labour input is better measured with the adjustment made (p.528) than without. However, both measures are provided (L is with and H without the adjustment).

Denison applies his adjustment only to full‐time non‐farm workers. In 1960, male workers in this category in the USA worked an average of 42.3 hours per week, after reductions to allow for vacations, other holidays, sickness, and absences for other reasons. Denison assumes that a small reduction in hours of work (whether as a result of a shortening of the normal working week, or increased vacations, etc.) would have led then to a 30 per cent offset in output per man‐hour. He further assumes that, had average hours worked per week been ten hours longer, at 52.3 hours per week, the offset would have been complete, so that output per year would have been unaffected by a small reduction in hours of work. ‘Intermediate points are set by proportional interpolation’.1

While Denison does not set out his assumptions in terms of a formula, it is convenient to do so here. Let y be output per man‐hour, h be average hours worked per week by full‐time male workers, and k be the proportionate productivity offset. Then, by definition,

k = h y d y d h .
(SA.1)
Assume that k increases linearly with hours worked, so
k = a + bh
(SA.2)
where a and b are constants. Integrating (SA.1), and using (SA.2) to eliminate k, we get
ln y = a ln h + bh + c
(SA.3)
where c is a constant which depends on choice of units. The values of a, b, and c, can be obtained as follows. First, when h = 42.3, we have k = 0.3, and when h = 52.3, k = 1. From (SA.2) it follows that
1 0 . 3 = 10 b . b = 0 . 07
and
a = 2 . 661 .
If we now, for example, choose to set y = 1 when k = 42.3, then from (SA.3) we can find
c = 7 . 00388 .
Equation (SA.3) then enables y to be determined for given values of h. The adjusted index of man‐hours can then be obtained by multiplying unadjusted man‐hours by y. The results so obtained agree with Denison's.

In using this method to obtain adjusted man‐hours for the UK, some modifications of Denison's procedure were necessary. First, only data on average (p.529) hours worked by male and female full‐time workers taken together were available whereas Denison used separate series for males and females. An adjustment to ‘male‐equivalent’ hours was made to allow for this. Second, the y‐index was used to multiply all man‐hours worked, including those by part‐time workers, the self‐employed, and farmworkers. Denison treated these groups differently, assuming that for part‐time workers k = 0, and for farmworkers and the self‐employed k = 1. Since these groups are small in the UK for much of the period covered, and since they offset each other to some extent, it is not thought that the difference is important. Finally, the above formula implies that when (male‐equivalent) hours per week fall below 38.0, k becomes negative. In other words, further reductions in hours worked below 38.0 reduce rather than increase productivity. It seemed preferable to assume that there was simply no further change.2

5 USA: Sources and Methods

General

For the period 1889–1929, the main source was Kendrick (1961). For the period 1929–73, the main sources were the National Income and Product Accounts of the United States 1929–76 (abbreviated to NIPA 1929–76), together with Denison (1979) and Kendrick with Pech (1973) for labour input. For the period 1973–85 the main sources were NIPA 1929–82, the Survey of Current Business, July 1986 (henceforth SCB July 86), and Denison (1985). Alaska and Hawaii are partly omitted before 1960 in the NIPA statistics, but, so far as possible, adjustments are made to remove this discontinuity.

Output at Constant Prices, Q

The main steps in the calculation were as follows.

1. Conventional estimates of GDP at constant prices were obtained. Up to 1929 the estimates are at market prices, and thereafter at factor cost.

2. These were adjusted by subtracting gross domestic investment expenditure as conventionally estimated at constant prices and adding back gross domestic investment expenditure at current prices deflated by the implicit price index of private plus public consumption.

3. Further adjustments consisted in subtracting output at constant prices as conventionally estimated of government (but not government enterprises), households and non‐profit institutions (but see below for 1889–1928), and dwellings.

The base years used for weighting are mentioned below. For 1889–1928, Kendrick (1961) gives all the series required except the output of households and non‐profit institutions and dwellings. The output of households and non‐profit institutions was, accordingly, not subtracted in step 3. (I am not clear, in any case, how far it is included in the original estimates.) However, the output of government (excluding government enterprises) is given by Kendrick, and subtracted, and an estimate was made of the output of dwellings to be subtracted in each year using estimates of (p.530) consumers' outlay on rent in Kuznets (1946, 144). These estimates are for overlapping decades at current and 1929 prices, from which annual estimates were constructed by trial and error. Kendrick's estimates are given in 1929 prices, but are based on a chain index with price weights varying every few years (Kendrick 1961, 54–5). For 1929–73, NIPA 1929–76 gives all the series required. My understanding of the explanation given in the source of the weighting system adopted is that all quantities were weighted by 1972 prices (NIPA 1929–76, xiii). In general, one would expect this to result in a downward bias in the quantity index, as compared with a chain‐linked index in which the prices are changed every few years. However, at least over the period 1929–53, Kendrick found very little difference between a chain‐linked index and one using 1929 weights (see Kendrick 1961, 55). It is also noteworthy that the rate of growth of real GNP over the period 1948–74 was scarcely affected by the revisions made when the base year for price weights was shifted from 1958 to 1972 (see SCB, p. 1, January 1976, 25–6). For 1973–85, NIPA 1929–82 gives all the series required up to 1982, and this was updated to 1985 using SCB, July 1986. The price weights are 1982.

Output at Current Prices, Y

The main steps in the calculation were as follows.

1. The gross domestic product at factor cost as conventionally defined was estimated. The average of estimates from the expenditure and income approaches was taken where both were available (i.e. from 1929 onwards).

2. From this, the output of government (but not government enterprises), households and institutions, and dwellings was subtracted.

For the period 1889–1929 the main source was Kendrick (1961). However, no estimate of GDP at current factor cost is given by him. Accordingly, the starting point was GNP at current market prices in Kendrick's Table A‐IIb. From this was subtracted his estimate of net factor income from abroad at 1929 prices (Table A‐III), converted to current prices using the implicit price index for GNP (see Kendrick 1961, 248). The correction from market prices to factor cost was combined with a general proportionate adjustment of the resulting estimate for 1929 to make it equal that derived from NIPA 1929–76 and referred to below. It was assumed that this proportionate adjustment was constant throughout the period. Output of government was obtained by converting Kendrick's estimates at 1929 prices to current prices using three linked deflators. The first, for 1909–29, was the implicit deflator for government output in NIPA 1929–76. The second, for 1890–1909, was an index of average earnings of clerical workers in manufacturing and steam railroads from Historical Statistics of the US, 1789–1945, series D142. This gave similar results to the third index, Kendrick's implicit deflator for government purchases of goods and services, which was used to link 1889–1890. Output of households and institutions was not subtracted, but some allowance is made for it by the proportionate adjustment in the 1929 figure, assumed constant in other years, already referred to.

Finally, output of dwellings was obtained by multiplying the output at 1929 prices (see ‘Output at constant prices Q’ above) by an index of rents. For the years 1913–29 the Bureau of Labour Statistics (BLS) index given in Historical Statistics series L44, (p.531) was used, which seems consistent with Kuznets (1946), Table III‐10, p. 144, and also p. 105 so far as can be judged. Kuznets (1946, 138 and 105) implies that he used Carl Snyder's index for rents for years prior to 1913, and that that index ‘practically does not change from 1875 to 1895, then rises gradually from 1895 to 1913’. This statement, plus Kuznets's overlapping‐decades estimates, guided the annual estimates made here. For the period 1929–73, all the series required were obtained from NIPA 1929–76. For the period 1973–85 they were obtained from NIPA 1929–82 and SCB July 1986.

Domestic Gross Investment at Current Prices, S

This is domestic gross investment as conventionally defined, including the value of the physical change in inventories, but excluding gross investment in dwellings and gross investment by government and institutions. For 1889–1929 the main source was Kendrick (1961), starting from gross private domestic investment (Table AIIb, the sum of columns (7) and (8)) and subtracting gross investment in dwellings and institutions using other sources. For non‐farm residential investment Grebler, Blank and Winnick (1956, 338, Table B‐6), was used. For farm residential investment 1897–1929, Goldsmith (1955, 761) was used, his estimates being extrapolated back to 1889 by guesswork. For institutions, Goldsmith (1955, 619–20) was used. For 1929–73, all the statistics are from NIPA 1929–76, and for 1973–85 they are from NIPA 1929–82 and SCB July 1986.

Labour Income at Current Prices, W

This is the sum of compensation of employees (including taxes and contributions for social insurance and employers' contributions for private pension and welfare funds) and the estimated labour component of income from self‐employment, excluding compensation of employees in government (but not government enterprises), households, and institutions. For the period 1889–1928, no annual estimates were made. However, averages for the standard periods (1889–1900, 1900–13, 1913–29) were constructed as follows. The first two periods were based on Budd (1960, 387 and Appendix C), which provides estimates for overlapping decades from 1869 to 1913. However, his estimates of the deemed labour earnings of self‐employed workers were reduced by a small amount in the light of Dension's comments on them (Budd 1960, 402) and my use of Denison's estimates for 1929 and later (see below).

It should be noted that the resulting averages of labour income share (λ = W/Y) are not strictly comparable with those for later periods or other countries, since recession years are not excluded. As λ tends to be high in recession years, it is somewhat overstated in 1889–1900 and 1900–13 by comparison with those other estimates. The estimate for 1913–29 was based on Kuznets with Epstein and Jenks 1941, 216–17, Table 22), which gives annual estimates for compensation of employees and ‘entrepreneurial income’ for 1919–38. These were each linked to corresponding items for the series from 1929 onwards and are described below. Adjustments were made to exclude labour income of government, households, and institutions. It was assumed that 0.74 of linked entrepreneurial income was labour (p.532) income, since this was the ratio for 1929 which corresponded to the estimate (based on Denison) for that year described below. In making the estimate of λ for 1913–29, as for later periods and other countries, recession years, war years, and the final year of the period were excluded. In this case, however, 1913 was also excluded since no estimate for that single year was available. For the period 1929–73 the source for total compensation of employees, and for the amounts subtracted for employees in government and households and non‐profit institutions, was NIPA 1929–76. Labour income of unincorporated business was as estimated in Denison (1979), and derived from his Tables G‐1 and G‐3 (pp. 170, 172). For the period 1973–85 similar estimates were made using NIPA 1929–82, SBC July 1986, and Denison (1985). The latter's estimates of labour income of unincorporated business were, however, adjusted upwards. This was because they were based on estimates of unincorporated business earnings as in NIPA 1929–76, and these were appreciably increased in the revised estimates in NIPA 1929–82 (see SCB December 1985, p. 10). Following this adjustment, the estimates of λ for 1973 based on NIPA 1929–82 agreed closely with that based on NIPA 1929–76.

Numbers Employed, Full‐Time Equivalents, N

The sources used give employment in terms of full‐time equivalents. For the period 1889–1929, Kendrick (1961, 305–6, Table A‐VI) was used, taking his estimate for the total private economy (which includes government enterprises). Employment in households and institutions was not subtracted as no separate estimates were available. For the period 1929–48, Kendrick with Pech (1973, 243–4, Table A‐19) gives an index of persons engaged in the private domestic economy which was linked to the preceding series at 1929. Again, no subtraction for households and institutions was made. For the period 1948–73, a series consisting of the following items from NIPA 1929–76 Table 6.11B was used, linked to the preceding series at 1948: persons engaged in production in private domestic industries plus government enterprises less full‐time equivalent employees (Table 6.8B) in educational services, social services, and membership organizations, private households, and half of those in health services. These figures exclude unpaid family workers, and so the estimates of these in Denison (1979, 154 Table B‐1) were added. For the period 1973–85, similar estimates were made using NIPA 1929–82, SCB July 1986, Denison (1985), and the US Bureau of Labour Statistics Employment and Earnings, issues for January 1983–6.

Man‐Hours Worked Per Annum, H

The only difference between H and L is the allowance made for the changing efficiency of hours worked. This section is therefore best read after that describing L, which follows immediately. For the years covered by Denison (i.e. 1929, 1940–1, 1947–82), the adjustment to L consisted simply in removing the index of ‘efficiency of an hour's work as affected by changes in hours due to intra‐group changes’, as in Denison (1979, Table 3‐1, column (5)) for the years up to 1973 and in Denison (1985, Table 3‐1, column (5)) for the years 1973–82. Changes in efficiency arising from ‘specified intergroup shifts’ were not removed (see Denison 1979, 40–1, and (p.533) Denison 1974, 42–3). The removal was effected in a similar way to that in which the addition of the reallocation effect was made, which is described in the note to L below. For the interpolated years 1930–9 and 1942–6, two changes were involved in the procedure described in the note to L. First, the input of labour to farm business was measured in man‐hours rather than in persons engaged, and, second, the adjustment made for changes in the efficiency of hours worked in non‐farm business was omitted. For the years 1889–1929 the same two changes were made to the procedure described in the note to L. For the years 1982–5 Denison's index of changes in efficiency arising from intra‐group changes was projected (and used to adjust L as described above) by regressing the index, for the years 1972–82, on average annual hours worked per full‐time equivalent employee in private business plus government enterprises (r 2 = 0.988). The latter were obtained from NIPA 1929–82 Table 6.7B and 6.11, and was also available for 1983–5 in SCB July 1986.

Labour Input, L

The quality‐adjusted index of labour input after 1928 is based on Denison's estimates as in Denison (1979) for the years 1929, 1940–1, and 1947–73, and in Denison (1985) for the years 1973–82. It is convenient to describe this first, and then to describe the sources used to interpolate the other years, 1930–9, 1942–6, and, finally, the sources used for the years 1889–1929 and 1983–5.

Denison provides an index of labour input into the non‐residential business sector which adjusts for changes in age and sex composition, for education, and for changes in hours worked. The allowance made for the last of these includes an allowance for changes in the efficiency of hours worked which is discussed in Section 4 above. In addition, Denison estimates the contribution made to the growth of output resulting from the transfer of labour from farming, and from non‐farm self‐employment, to the rest of the sector. I have combined these effects with the other quality and quantity changes in labour input to produce an index of labour input including them all. For the years covered by Denison, it is this adding on of the reallocation of labour effects that is the only modification made here to Denison's labour input series. The adding on is most simply described for the years for which Denison gives a continuous series, i.e. for 1947–82. He estimates the contribution of the change in labour input from, for example, 1947 to 1948 to the proportionate growth of national income in non‐residential business between those years as

λ D 47 L D 48 L D 47 L D 47 ,
that is, as the product of the labour share of national income in non‐residential business in 1947, λD47, and the proportionate increase in his index of labour input (L D). He also provides an estimate of the proportionate growth of national income in non‐residential business arising from the reallocation of labour. Let us call this R 47/48. I add these together to obtain my proportionate increase in the quality‐adjusted labour input as
L 48 L 47 L 47 = · λ D 47 L D 48 L D 47 L D 47 + R 47 / 48 × / λ D 47 .

(p.534) It follows that, if the proportionate increase in my index is multiplied by λD47, I will get the same contribution to proportionate growth of national income as does Denison from his index of labour input plus his reallocation effect. My index of labour input is then obtained by accumulating the year‐to‐year proportionate changes obtained as just described. For the years up to 1973 the source used was Denison (1979). For the years 1973–82, linked at 1973, the source used was Denison (1985).

For years where a continuous series is not provided by Denison (i.e. 1929, 1940, 1941, 1947), one can follow a similar method, making the assumption that the proportionate rates of growth of output and labour input are uniform over each period. While this was not the case, it is thought that any resulting error is small.

For the years 1930–9 and 1942–6, not covered by Denison, the following sources were used to estimate an index of labour input (which included 1929, 1940–1, and 1947) which was then used to interpolate between the years he covered. Index numbers of persons engaged in farm business and man‐hours worked in non‐farm business were obtained from Kendrick with Pech (1973, Table A‐22 and A‐21). Index numbers of the age‐sex compositional effect and of the education effect were obtained by interpolation of Denison's figures. An index of average hours worked in non‐farm business was obtained from Kendrick with Pech (1973), and this was used to calculate an index of the changing efficiency of hours worked as described in Section 4 above. The index of persons employed in farm business was not adjusted for changes in hours worked following Denison (1979, 40), who points out that full‐time farmworkers work very long hours, so that any changes in hours worked are likely to be fully offset by changes in efficiency. However, in so far as shifts in average hours worked in non‐farm business were due to what Denison calls ‘intergroup effects’, e.g. a shift from full‐time to part‐time work, my attempt to allow for changes in the efficiency of hours worked departs from his more careful calculations. My index of labour input for interpolation was calculated from the above series by combining the index of persons employed in farm business with the index of man‐hours worked in non‐farm business (after first multiplying by the age‐sex and the hours‐efficiency effects) using the labour earnings weights for 1948 given in Kendrick with Pech (1973, 231). The resulting combined index was then multiplied by the education effect index. Its increase over the period 1929–47 was 35 per cent as compared with the increase of 40 per cent of the index based directly on Denison.

For the years 1889–1929, the method used was similar to that just described for the interpolating series. Index numbers of persons engaged in farm business and man‐hours worked in non‐farm business were obtained from Kendrick (1961, Tables A‐VI and A‐X), as also was an index of average hours worked in non‐farm business. The last was used to calculate an index of the efficiency of hours worked in non‐farm business as described in Section 4 above. It was assumed that there was no change in age‐sex composition. An index of education effect is given in Denison (1962, 72 and 85). This extends from 1909 to 1958. A comparison with Denison's later estimates (Denison 1979) suggests that the earlier ones are upward‐biased as compared with the later ones. Since I have used the later ones above, I adjusted the earlier ones downwards by one‐third. I also assumed that the index 1889–1909 grew at the same rate as from 1909 to 1920. The weights used to combine farm and non‐farm (p.535) labour inputs were obtained from Kendrick (1961, 267) and refer to the years 1919–29.

For the years 1983–5 a series was built up from the components described below and this was linked on at 1981 (not 1982, because, while Denison's estimate was retained for that year, it was thought to be likely to be subject to more revision than his estimate for 1981. Also, in reconstructing the series back to 1972, there was closer agreement with Denison's series for 1981 than for 1982.) The components used were the index of N, described above; an index of annual hours per full‐time equivalent employee in private business plus government enterprises (described in the note to H); an index of the efficiency of an hour's work as affected by changes in hours arising from intra‐group changes (also described in the note to H); an index of age and sex composition effects using data from Earnings and Hours and following Denison's method so far as possible; an index of the effect of education, which was simply a projection of Denison's index for 1972–82; and an index of gains from reallocation of labour based on employment data from NIPA 1929–82 and SCB July 1986. The resulting index of L agreed reasonably well with the index already described for 1972–82.

6 Japan: Sources and Methods

General

For the period 1952–65 (and for some series 1952–71), the data are based mainly on Denison and Chung (1979); for subsequent years they are based on various official sources mentioned below, but mainly the Annual Reports on National Accounts of the Economic Planning Agency of the Government of Japan (referred to as ‘EPA (1981)’ etc.). For the period 1941–51 no data are given. For the period 1885–1940 the main source was Ohkawa and Shinohara (1979). Annual estimates of the share of wages could not be made for this last period, although some very rough averages were estimated for the standard sub‐periods (see below). While the post‐Second World War series were linked to the earlier ones, so that Q, N, H, and L are all expressed as index numbers on the base 1913 = 100, this link is especially weak.

Output at Constant Prices, Q

The main steps in the calculation were as follows.

1. Conventional estimates of GNP or GDP at constant prices were obtained.

2. These were adjusted by subtracting estimates of gross domestic investment expenditure at constant prices, as conventionally measured, and adding back gross domestic investment expenditure at current prices deflated by the implicit price index of private plus public consumption.

3. Further adjustments consisted in subtracting output at constant prices as conventionally measured of public administration and defence, professional services (to cover health and education), domestic servants and dwellings, and also net factor income from abroad at constant prices where appropriate.

The price weights used are noted below for each period. For 1885–1940, steps 1 and 2 were based on Ohkawa and Shinohara (1979, Tables A1, A2, A3, A38 and (p.536) A39), using the series at current and constant 1934–6 prices. Their Table 3.2 was also used to provide estimates of inventory investment for years for which such estimates are not given in the other tables. For step 3, net domestic product at 1934–6 prices in ‘public administration’ (which includes defence), ‘professional’ and ‘domestic servants, etc’ as in Table A25 was subtracted, as also was personal consumption expenditure at 1934–6 prices on housing from Table A36. For 1952–65, steps 1 and 2 were based on Denison and Chung (1976), supplemented by EPA 1969 and 1973 for gross domestic investment at current and constant prices. For the constant price series, 1965 price weights were used. Outputs of general government, households, and institutions, and dwellings at constant prices were subtracted for step 3 using Denison and Chung (1976). The link from 1938 to 1952 was based mainly on data from Ohkawa and Shinohara (1979) at 1934–6 prices, supplemented by Denison and Chung (1976) and Ohkawa and Rosovsky (1973). The output of public administration and defence, and professional services and domestic servants, was based on employment data which may not be comparable, since it came from different sources for 1938 and 1952. For 1965–73, the constant price series use 1975 price weights and are mainly from EPA 1981 for all three steps but are supplemented by Denison and Chung (1976) to adjust EPA series for dwellings and the output of households and non‐profit institutions to a basis comparable with that of Denison and Chung. For 1973–84, EPA 1986 was mainly used, with similar adjustments, using 1980 price weights.

Output at Current Prices, Y

The main steps in the calculation were as follows.

1. Conventional estimates of GNP (up to 1940) or GDP (from 1952 on) at market prices were obtained using the mean of estimates from the income–output approach and from the expenditure approach. For the earlier period it was necessary to correct for bias in the estimates before calculating the mean (see Ohkawa and Shinohara 1979, 66–8).

2. Net indirect taxes, the output of public administration and defence, professional services, domestic servants, dwellings, and (for the GNP series) net factor income from abroad were subtracted. Up to 1940, the main source was Ohkawa and Shinohara (1979); for 1952–65 the main source was Denison and Chung (1976); for 1965–73 the main source was EPA 1981; for 1973–84 the main source was EPA 1986. For the period 1952–65, the categories subtracted for public administration and defence, professional services, and domestic servants are those labelled by Denison and Chung as ‘general government’, ‘private households’, ‘private non‐profit institutions’ (which includes private medical, health, and education institutions, as well as religious and other non‐profit institutions), and ‘foreign governments’ (i.e. income of Japanese employees of foreign governments in Japan). For later years similar categories are given in the EPA figures, but, whereas the ‘general government’ figures agree closely with Denison and Chung's, the EPA figures for households and non‐profit institutions are much smaller. According to Denison and Chung (1976, 140), this is because private education and health are excluded. The EPA figures were therefore increased proportionately to make them comparable with those of Denison and Chung.

(p.537) Domestic Gross Investment at Current Prices, S

This equals gross domestic capital formation (including the value of the physical change in stocks) as conventionally defined but excluding investment in dwellings and government structures (or ‘general government’ post‐Second World War). Military investment is excluded. Loss of stocks in 1923 arising from the Kanto earthquake is allowed for, but not damage to ‘buildings’, since it is assumed that most was to dwellings. However, damage to ‘factories’ and ‘ships’ is allowed for. The sources were the same as for Y, except that for 1952–65 EPA 1969 and 1973 were used.

Labour Income at Current Prices, W

Annual estimates are given only for 1952 onwards. For earlier years the data are unreliable, but some rough estimates for our standard periods are given. These are based on annual data for non‐agriculture and five‐year averages for agriculture given in Ohkawa and Shinohara (1979, Tables A47 and 4.5). The non‐agricultural data are for net domestic product, so capital consumption from Table A7 was added. The agricultural data are for shares of total costs of production, and these were converted to current yen using the data in Table A16. Wages of self‐employed workers were imputed as described in the source. Income from dwellings is excluded, and wages of public administration and defence, professions, and domestic servants were subtracted as for Y. The period averages exclude recession and war years. That for 1899–1911 is based on data for 1906–11, 1906 being the earliest year for which data for non‐agriculture are given in the source. The estimate for 1887–99 is simply the same as for 1899–1911. For 1952–65 the estimates are derived from Denison and Chung (1976), these being linked at 1965 to the estimates for 1965–73. The latter were based on EPA 1981, being the sum of compensation of employees in the whole economy, plus 0.6834 times income from unincorporated enterprises in agriculture, forestry, and fishing, plus 0.8917 times other income of unincorporated enterprises, less income of general government, households, and non‐profit institutions as in Y. The multiplying factors of 0.6834 and 0.8917 are the estimated labour components of the income of unincorporated enterprises, and are those estimated by Denison and Chung for 1970, and used by them for other years in their study (Denison and Chung 1976, 174). For 1973–84 the same method was followed using data from EPA 1986.

Numbers Employed, N

For the period 1885–1940, the numbers of ‘gainful workers’ in the whole economy are given in Ohkawa and Sinohara (1979, Table A53). These appear to include the armed forces, but not those overseas. For the years 1920, 1930, and 1940, Lockwood (1954, 465, Table 40) gives the numbers in the civilian labour force and the armed forces. His estimates agree closely with those in Ohkawa and Shinohara. Lockwood also specifies the number in ‘government and the professions’ and ‘domestic’. For 1920, 1930, and 1940, these categories, together with the armed forces, were subtracted from the Ohkawa–Shinohara series to give numbers in non‐residential business. For other years, the Lockwood figures for the subtraction were projected (p.538) backward, or interpolated, using the output at constant prices of public administration and defence, professional services, and domestic servants as in Q. No corrections for part‐time workers could be made. For the period 1952–71, the estimates of employment in non‐residential business in Denison and Chung (1976, Table 3‐4) were taken. The link from 1938 to 1952 used the ‘gainful workers’ series in Ohkawa and Shinohara (1979, Table A53), subtracting, for 1938, the numbers in the armed forces, the government, the professions, and domestic servants as obtained above and, for 1952, numbers employed in general government and households and non‐profit institutions and foreign governments (i.e. their Japanese employees in Japan) as in Denison and Chung (1976, Tables A‐1 and A‐2). In view of the different series used for prewar and postwar years, the change over the war period is of doubtful reliability. For the period 1971–3, the following series was linked to the Denison–Chung figures at 1971. Total numbers employed were obtained from Monthly Statistics of Japan, Statistics Bureau, Prime Minister's Office, and from these were subtracted numbers employed in government, households, and non‐profit institutions as in EPA 1981. For the period 1973–84 numbers employed in the whole economy and in government, households, and non‐profit institutions were all obtained from EPA 1983 (for 1973–80) and EPA 1986 for 1980–4, linking at 1980. For the years 1952–72, no adjustment was made for part‐time workers. From statistics given by Denison and Chung (1976, Table F‐1–F‐3), it seems likely that N would have grown slightly faster, perhaps by 0.2 per cent per annum, owing to a decline in the proportion of part‐time workers, had an adjustment been made. For the years 1973–84, an adjustment was made, counting those working thirty‐four hours or less a week as one‐half of a full‐time worker, using data from Monthly Statistics of Japan. Over this period, part‐time working increased as a proportion of the whole, and the adjustment reduces the rate of growth of N by about 0.2 per cent per annum.

Man‐Hours Worked Per Annum, H

For 1885–1940, and for the link 1938–52, this is the same as L (q.v.), since no adequate data on hours of work were available for these years,3 and hence no hours efficiency offset was calculated. According to Minami and Ono, from 1888 to 1969 ‘there was no substantial changes in hours and days worked per worker’ (see Ohkawa and Shinohara 1979, 210). For 1952–71 the figures are derived from the series for L (see below) by the same method as that adopted for the USA, that is, the effect of changes in the efficiency of an hour's work as affected by changes in hours arising from ‘intra‐group’ changes was removed, this being the only difference. This effect is as calculated by Denison and Chung (1976, Table 4‐3, column (5)). The effect arises from the improvement in productivity resulting from a fall in hours worked by full‐time workers. (See Section 4 above for further discussion.) In the (p.539) case of Japan, hours of work were so long in this period that virtually the whole of any fall in full‐time hours was assumed to be offset. For 1971–3, there is a negligible difference between the H and L series, since available figures suggested little change in average hours of work. For 1973–84 average annual hours worked in the whole economy (from estimates kindly supplied by A. Maddison, and which include the effects of part‐time working) were used in place of the allowance made for changes in hours and efficiency in calculating L (see below). Apart from that, the series is the same as L.

Labour Input, L

Five components of the index of labour input may be distinguished: (i) the growth in numbers, (ii) the increase in productivity arising from shifting workers out of agriculture and into the rest of the economy and, in the years 1952–71 only, out of non‐farm self‐employment into the rest of the economy, (iii) changes in hours of work, including the resulting effects on the productivity of an hour's work, (iv) changes in the age and sex composition of the work‐force, and (v) changes in the amount of education received by members of the work‐force. For the years 1952–71, Denison and Chung's (1976) estimates of all five components were taken, but for earlier and later years only some of the components could be estimated.

For these other years, the method used to estimate (ii), while similar to Denison and Chung's (see their Appendix J), is not exactly the same, although it is thought that the results of the two methods are close to each other. It seemed both simpler and more straightforward to combine (i) and (ii) together in the following way. As with their method, the calculation proceeds one year at a time. It is assumed that the marginal product of labour is directly proportionate to its wage in each sector. Suppose that employment in sector i from year t to year t + 1 increased in proportion n it. Suppose that the share of wages in GDP in sector i, at current factor cost in year t, is λit. Suppose that we are measuring output at constant prices of base‐year T, and that the share of sector i in GDP at factor cost at base‐year prices in year t is y it. Then the proportionate growth of labour input from t to t + 1 arising from (i) and (ii) together is given by

Σ i ( n it λ it y it ) Σ i ( λ it y it ) .

In words, the proportionate growth of L from one year to the next is given by the weighted sum of the proportionate growth of employment in each sector, the weights being proportionate to output elasticities of employment in each sector4 and to the shares of total output of each sector. Denison and Chung assume that the output elasticity in non‐agriculture is proportionate to the share of labour, but for (p.540) agriculture they assume an output elasticity of 0.25, which is much lower than the share of labour income (0.65–0.75, according to them), ‘because labour could be withdrawn from many farms with little loss of output (and it was, of course, from such farms that it predominantly was drawn)’ (Denison and Chung 1976, 226–7).5 Denison and Chung remark that, when Ohkawa and Watanabe saw their estimates of the gains from the reallocation of labour, they thought they were too small. However, a careful examination by Denison and Chung of possible explanations for this leads them to the conclusion that they do not need to revise their estimates. Indeed, as they point out, it would not greatly increase the gain from reallocation if they were to assume that labour lost from agriculture (or unincorporated business) caused no drop in output there (pp. 229–34).

The opposite view, i.e. that there were no gains from reallocation, at least before the First World War, has been expressed by Kelley and Williamson (1974, 44–50). They argue that some wage differential between agriculture and industry is to be expected because of cost‐of‐living differences and quality differences, but that these are consistent with a close‐to‐perfect labour market. In the period 1887–1915 there is no evidence, they say, that industrial wages rose faster than rural ones (although average labour productivity did), and this is also consistent with a close‐to‐perfect labour market. However, I do not myself find their arguments persuasive. Although the data they give (Table A.2) do not suggest a large gap between daily wage rates in agriculture and manufacturing before the First World War (and see also Ohkawa and Shinohara 1979, Figure 13.1), there does seem to have been a large gap between average annual labour earnings in agriculture and the rest of the economy. Kelly and Williamson appear to dismiss annual earnings data as being ‘less useful’ (1974, 223). As only a small fraction of employment in agriculture consisted of wage labourers (Ohkawa and Shinohara 1979, 238), it seems quite possible that the marginal annual product of workers leaving agriculture was much below that of labour hired by the day. It is also quite possible for the gap to persist for many years, while migration proceeds, and yet for daily wage rates in agriculture to keep in step with those in industry. One needs to know more about the locality and seasonality of employment of daily workers, and about the unpleasantness of the tasks they were asked to perform, before one can judge whether there is much validity in Kelley and Williamson's arguments. In the absence of such information, I prefer to accept the more orthodox view that the reallocation of workers from agriculture to the rest of the economy contributed substantially to economic growth as conventionally measured.

For the years 1885–1940, components (i) and (ii) were estimated as above using the numbers of gainful workers in agriculture and forestry, and in non‐agriculture, as in Table A.53 of Ohkawa and Shinohara (1979). GDP or GNP in each sector was estimated from the same source (see Q and Y above), as also was the share of wages in non‐agriculture at current prices (see their Table A. 47: this commences at 1906, and for earlier years the average for 1906–14 of 0.7 was assumed). For agriculture, Denison and Chung's output elasticity of 0.25 was assumed. Employment in public administration and defence, professional services, and domestic services was (p.541) removed using the series calculated for Q and Y above. Component (v), changes in labour quality owing to education, was estimated using data and weights given in Ohkawa and Rosovsky (1973, Table 3.6 and pp. 56–8). Their data start at 1900, and it was assumed that the rate of growth of educational quality from 1885 to 1900 was the same as from 1900 to 1910. No direct information on the remaining components (iii) and (iv), hours and age–sex composition, was available. Ohkawa and Rosovsky (1973, 55) take the view that the effect of changes in age and sex composition were probably slight, and, as already quoted, Minami and Ono state that changes in hours of work were probably small. However, it was decided to make a small upward adjustment in the index of L of 0.00264 per year, mainly to allow for a possible understatement of quality improvements arising from education and for reallocation out of self‐employment in non‐agriculture. This figure was the difference between the rate of growth of labour input over the years 1953–63, after quality adjustment, and after allowing for reallocation between sectors, in Denison and Chung (1976) over the rate of growth for the same period calculated using the same sources and methods as for 1885–1940. There were several sources of difference between those two estimates, and it is uncertain that their magnitudes would have been the same in 1885–1940. The estimate of the growth of L in that period is correspondingly uncertain.

For the link between 1938 and 1952, essentially the same sources and methods were used as for 1885–1940. However, it was assumed that there were no net changes in quality arising from hours, age and sex composition, and education. Since employment in agriculture grew rather faster than in the rest of the economy (excluding government, etc.) over this period, the index of L grew rather more slowly than that of N.

For 1971–3, the method used for components (i) and (ii) was similar to that for 1885–1940, the data coming from EPA 1981 and from Monthly Statistics of Japan (as for N). However, the output elasticities in agriculture and non‐agriculture were assumed constant, and were based on Denison and Chung's figures for 1963 (Denison and Chung 1976, 227). There was a negligible change for (iii), hours of work. The effects of changes in age and sex composition, item (iv), were calculated using data in Monthly Statistics of Japan using weights based on Denison and Chung (1976, Table G‐1 and G‐3) for 1971. Quality improvements owing to education were simply projected at the same rate as for 1961–71 as in Denison and Chung (1976, Table 4.3). The addition of 0.00264 mentioned above for 1885–1940 was not made.

For 1973–84, components (i) and (ii) were calculated in the same way as for 1971–3, except that the employment and GDP data were from EPA 1983 and 1986. Component (iii), changes in hours of work and in the efficiency of an hour's work, was assumed to be given by the index of N divided by the index of numbers employed with no adjustment for part‐time working. Consequently, this component reflected only that part of the reduction in average hours worked which was due to the increase in part‐time working (and, by counting part‐time workers as equal to 0.5 of a full‐time worker, when their hours of work were probably a smaller proportion than this, closer to 0.4 (see Denison and Chung 1976, Tables F‐1–F‐3), made an allowance for greater efficiency of part‐time workers' hours). It was assumed that the remaining reduction in hours (which was small) was wholly offset (p.542) by increased efficiency of work. Components (iv) and (v) were calculated as for 1971–3.

7 UK: Sources and Methods

General

Up to 1920, Southern Ireland is included in the UK; thereafter it is excluded.

Output at Constant Prices, Q

The main steps in the calculation were as follows.

  1. 1. A ‘compromise’ index of conventional GDP at constant factor cost was obtained by taking the equally weighted arithmetic mean of index numbers based on output, expenditure, and income data.

  2. 2. This was adjusted by subtracting gross domestic investment expenditure at constant prices, as conventionally measured, and adding back gross domestic investment expenditure at current prices deflated by the implicit price index of private plus public consumption.

  3. 3. Further adjustments consisted in subtracting output at constant factor cost as conventionally measured of dwellings, professional and scientific services (to cover health and education), public administration and defence, and domestic servants. From 1970 to 1985, the output of the industries extracting mineral oil and natural gas was excluded (their output was negligible before then).

The price weights used varied between periods. In the main, 1900 prices were used for 1856–1913, 1938 prices were used for 1913–38, and a Fisher ‘Ideal’ index of 1938 and 1948 prices was used for 1938–48. However, in some cases weighting was done using other years' price weights, depending on availability of data. For the years after 1948 the system of price weighting is described in the Blue Books. Broadly speaking, the price weights are updated every five years or so, and the base year is used to calculate output at constant prices for the years adjacent to the base year both before it and after it. Series over longer periods are the result of linking together the five‐year series. This method gives an approximation to a Divisia index, and seems preferable to either a Laspeyres or a Paasche index in which the base year remains fixed for long periods. Up to 1948 the principle source was Feinstein (1976, 1972), and thereafter various issues of Economic Trends Annual Supplements and the Blue Books of National Income and Expenditure.

Output at Current Prices, Y

The main stages in the calculation were as follows.

  1. 1. Conventional GDP at factor cost was obtained as the equally weighted arithmetic mean of estimates based on income and expenditure data.

  2. 2. This was adjusted by subtracting output at current factor cost of dwellings, professional and scientific services (to cover health and education), public administration and defence, domestic servants, and the imputed rent of public capital. From 1970 the output of industries extracting mineral oil and natural gas (p.543) was also excluded. (Their output was negligible before then.) The main sources used were the same as for Q.

Domestic Gross Investment at Current Prices, S

This is gross domestic capital formation (including the value of the physical change in stocks) as conventionally defined but excluding investment in dwellings, social and other public services investment (including highways and bridges), and, from 1970 onwards, gross fixed investment in the petroleum and natural gas industries. The main sources used were as for Q, but prior to 1920 the gross fixed investment series in Feinstein (1976, 1972) was replaced by a revised series kindly provided by Feinstein which was consistent with the series used in Matthews et al. (1982), although still subject to further revision.

Labour Income at Current Prices, W

This is the sum of income from employment (including taxes and social security contributions) and the estimated labour component of income from self‐employment, excluding income from employment in professional and scientific services, public administration and defence, domestic servants, and, from 1970 onwards, income from employment in petroleum and natural gas extraction industries. The main sources used were the same as for Q. For the years up to 1973, the share of income from self‐employment which was deemed to be labour income is that underlying Figure 6.1, p. 165 in Matthews et al. (1982), the figures being kindly supplied by Feinstein. The method used to estimate this was to subdivide the economy into twelve sectors, and to assume that, within each sector, labour earnings per self‐employed worker were the same as per employee. For years prior to 1920, however, rougher methods were used. After 1973 my own estimates were rough, the 1973 estimate being extrapolated using numbers of self‐employed (as in Economic Trends Annual Supplement) and average income from employment per employee in the whole economy.

Numbers Employed, Full‐Time Equivalents, N

The following magnitudes were estimated:

  1. 1. total numbers employed in the whole economy (including self‐employed), N T;

  2. 2. the proportion of these consisting of part‐time workers, p;

  3. 3. the ratio of hours worked by part‐time workers to full‐time workers, r;

  4. 4. the ratio of man‐hours worked in non‐residential business to those worked in the economy, h.

Then N = hN T (1 − p + pr).

As regards magnitude 1, up to 1959 the main sources were Feinstein (1976, Table 57) and Matthews et al. (1982, Table D.1), which gives benchmark years. For subsequent years, the Department of Employment Gazette for October 1975, December 1976, and later issues, and Economic Trends Annual Supplements were the main sources. For magnitude 2, Matthews et al. (1982, Table D.1) gives (p.544) benchmark years 1856–1973, and intervening years were interpolated. For subsequent years annual estimates were made using various issues of the New Earnings Survey of the Department of Employment. For magnitude 3, estimates were made of average full‐time hours per week and average part‐time hours per week. For the former, the estimates were mainly based on Matthews et al. (1982), supplemented by Department of Employment and Productivity (1971) and also the British Labour Statistics Yearbooks and various New Earnings Surveys. The same sources were used to estimate average part‐time hours. For magnitude 4, see the note for H below, item (2).

Man‐Hours Worked Per Annum, H

(1) An estimate of man‐hours worked in the whole economy was first prepared, and then multiplied by (2) the estimated ratio of man‐hours worked in the non‐residential business sector to those in the whole economy. This was then multiplied by a further factor (3), which adjusted for changes in age and sex composition and also for education. Item (1) used the series N T (1 − p + pr) described above in the note for N, multiplied by average full‐time hours per week, and adjusted further so as to allow for annual and public holidays, absences for sickness, and days lost through strikes, estimates for these being derived from the same sources. For the years 1973–85 estimates of annual hours per worker were kindly supplied by A. Maddison. The ratio (2) for years 1856–1913 was that for 1913 (see below) multiplied by the ratio of (total employment in the whole economy less employment in the armed forces and employment in the rest of public and professional services) to total employment in the whole economy. The latter was obtained as in item 1 of the note for N above. Employment in the armed forces is from Feinstein (1976, Table 57), and employment in the rest of public and professional services was obtained by interpolation and extrapolation of the figures for census years, 1861–1911, in his Table 60. For years 1913–73, Matthews et al.'s estimates of man‐hours worked by industry for benchmark years 1924–73 was the main source, and they provide a rough estimate for 1913 in Table 8.1. Interpolation was done on the basis of annual figures of employment by industry. The preceding estimates did not remove domestic servants from total man‐hours, and for this (and for man‐hours in oil and natural extraction gas from 1970) a different method of adjustment was used, based on the ratio of earnings by domestic servants (and oil and natural gas extraction workers) to total earnings (obtained as for W above). In effect, man‐hours were then weighted by earnings per hour. The adjustments for item (3) followed those estimated by Matthews et al. (1982, 4.7), which gave rates of growth arising from these factors between benchmark years 1856 and 1973. The rates of growth were assumed to be constant between benchmark years, and also to be the same in the non‐residential business sector as in the whole economy. For 1973–85 estimates were made based on New Earnings Survey Data, and (for education) on a projection of the rate of growth for 1964–73 from Matthews et al. (1982, Table 4.7).

Labour Input, L

Labour input equals man‐hours worked adjusted for age and sex composition and for education (i.e. H) multiplied by a further factor, y, which allows for the (p.545) changing efficiency of an average hour's work. (See Section 4 above for further discussion.) This factor is a function of the average hours worked in a year by a full‐time worker estimated from the sources mentioned in the note to N, item 3. For 1973–85, y was assumed constant, being close to its maximum value according to the formula used.

8 Continental European Countries: (Belgium, Denmark, France, Germany (Federal Republic), Italy, Netherlands, Norway): Sources and Methods

General

The statistics throughout refer to the years 1955–62 since it was only for these years that a quality‐adjusted index of employment was available from Denison (Denison with Poullier 1967). The various national income statistics needed were, in the main, derived from the same sources as those used by Denison, namely, the OECD's National Accounts Statistics 1955–1964, (Paris, 1966) (henceforth referred to as OECD 1966) and, for France and Germany, the OECD's General Statistics, January 1965. The latter was needed so as to enable a link to be formed between earlier and later series on slightly different bases. In what follows, only OECD 1966 is referred to, although this should be taken to include the January 1965 publication as well. In addition to these sources, some reference to national sources was necessary, as detailed below.

Output at Constant Prices, Q

The main steps in the calculation were as follows.

  1. 1. Conventional estimates of GDP at constant 1958 factor cost were obtained for 1955 and 1962.

  2. 2. These were adjusted by subtracting gross domestic investment expenditure as conventionally estimated at constant 1958 prices and adding back gross domestic investment expenditure at current prices deflated by the implicit price index of private plus public consumption.

  3. 3. Further adjustment consisted in subtracting output at constant 1958 prices as conventionally estimated of dwellings and of public administration, defence, education, and health.

All the figures were from OECD 1966. For France and Germany, GDP at market prices was used. For Denmark, France, Italy, Netherlands, and Norway, the growth rate of GDP was adjusted by the same amount as the growth rate of national income was by Denison for irregularities in the pressure of demand and in agricultural output (see Denison with Poullier 1967, 302–16). Because of these adjustments, the growth rate was measured as simply the average exponential growth rate between the end‐years of the period, 1955 and 1962. Denison made no adjustment to the German growth rate for the above reasons, and his adjustment to the Belgian growth rate for the government deflation procedure was irrelevant, since the output of government is excluded here. His adjustment for construction deflation procedures in France was also irrelevant here, since investment expenditures are deflated by the price index of consumption. For the Netherlands, since the output of dwellings at (p.546) constant 1958 prices was not shown separately in the source, output at current prices was deflated by the implicit price index of consumers' expenditure on rent.

Output at Current Prices, Y

This is GDP at factor cost less the output of dwellings and of public administration, defence, health, and education, the figures coming from OECD 1966. For France and Germany, output of dwellings is at market prices, but no correction to factor cost was made, so the result is to understate Y for them slightly, and overstate s and λ. Estimates for each year 1955–62 were made. Only one estimate of GDP at factor cost was available for each year in the source, so there was no averaging of estimates made from the income and expenditure approaches, as in the USA, Japan, and the UK.

Domestic Gross Investment at Current Prices, S

This is gross domestic fixed asset formation plus change in stocks less gross domestic fixed asset formation in dwellings and less gross fixed asset formation by general government. Estimates for each year 1955–62 were made. The source used was OECD 1966.

Labour Income at Current Prices, W

This is compensation of employees plus the estimated labour component of the income of independent traders less compensation of employees in public administration, defence, health and education. Denison with Poullier (1967, 38) gives the share of the first two components of W (i.e. without the deductions for public administration, etc.) in national income as conventionally defined for the average of 1955–9 and also of 1960–2. From OECD 1966 annual estimates of national income were obtained, and the average ratio of it to Y for 1955–62 was calculated. This, combined with Denison's estimates, then gives an estimate of the average ratio of W to Y for 1955–62 before deductions for public administration, etc. Annual estimates of compensation of employees in public administration (etc.) were made using OECD 1966 by subtracting depreciation and other operating provisions in general government from GDP in this sector. Again, the average ratio to Y for 1955–62 was estimated, and this ratio was then subtracted from the preceding ratio of W (without deductions) to Y to give the final estimated average ratio of W to Y for 1955–62. This average ratio was all that was needed, and annual estimates of W were therefore not made.

Numbers Employed, Full‐Time Equivalents, N

According to Denison (Denison with Poullier 1967, 65), only in Italy, of the countries considered here, was there an important change in the ratio of full‐time to part‐time workers. Hence, with that exception, N was simply taken as total numbers employed excluding those in the armed forces, as in Denison with Poullier (1967, 47, 49), and also excluding those in public administration, health, and education. These last were estimated using mainly national statistical yearbooks. Estimates were made only for (p.547) 1955 and 1962. For Italy an adjustment was made to allow for the sharp fall in the proportion of part‐time workers based on information given in Denison with Poullier (1967, 65, 369).

Man‐Hours Worked Per Annum, H

The only difference between L and H is the allowance made for the changing efficiency of hours worked. This section is therefore best read after that describing L, which follows immediately. From Denison with Poullier (1967, 66 Table 6.6), one can, for each country, compute three index numbers for 1962, with 1955 = 1, which are for non‐agricultural wage and salary workers only, viz.: (1) average annual hours per person employed (columns (1) and (3) of the table), (2) the (improved) quality of an hour's work arising from the fall in annual hours (columns (4) and (6)), and (3) the quality of a year's work (columns (7) and (9)). The third of these is simply the product of the first two, and is the one that was used in estimating L. For H, the only difference is that the first index number was used in place of the third.

Labour Input, L

For each country, for 1955 and 1962, numbers employed in three different groups were estimated: (1) agriculture, forestry, hunting, and fishing, (2) non‐agricultural employers and own‐account workers and unpaid family workers, and (3) wage and salary workers in the rest of NRB. All the necessary figures are given in Denison with Poullier (1967, 47, 49), except that it was necessary to exclude wage and salary workers in public administration, health, and education from group (3). This was done using the estimates mentioned in the section above on N. Quality‐adjusted index numbers of employment for each of these groups for 1962, with 1955 = 1, were then constructed and combined using estimated relative marginal products of labour in each as weights, and this weighted index of employment was L. The quality adjustments were as follows. For each of the three groups it was assumed that the adjustments for changes in age and sex composition, and for improved education, were the same, and were as given in Denison with Poullier (1967, Tables 7.7, p. 77 and Table 8.6 (A), p. 89). For group (3) only, the index of quality of a year's work given in Denison with Poullier (1967, 66, Table 6.6, columns (7) and (9)) was used to adjust employment in that group. This allowed both for changes in hours worked in the group and for the assumed effect on efficiency of falling hours of work. For groups (1) and (2), no allowance was made for changes in hours of work (either here or by Denison). It is quite likely that any changes that did occur were wholly offset by changes in the efficiency of each hour worked. The weights used to combine the index numbers of employment for each group were as follows: for group (1), one‐quarter of national income per worker in the sector, except for Denmark, where the proportion was 0.33, and for Italy, where it was 0; for group (2), one‐quarter of estimated average earnings of non‐agriculture employees; for group (3), estimated average earnings of non‐agricultural employees. All the weights were derived from estimates for 1955, and are based on the assumptions made in Denison with Poullier (1967, 214, 216). (p.548)

Table SA I Data for Periods

Country

Period

g

g L

g N

g H

s

λ

cu

π

UK

1856–73

0.02413

0.01418

0.00834

0.01066

0.0993

0.5419

0.5909

0.06

1873–1901

0.02116

0.01798

0.00999

0.01715

0.1059

0.5995

0.5752

0.29

1901–13

0.01613

0.01930

0.01143

0.01760

0.0961

0.6190

0.4806

0.58

1913–24

−0.00125

−0.00354

−0.00400

−0.01283

0.0532

0.6540

0.4417

0.91

1924–37

0.01939

0.01570

0.00893

0.01672

0.0812

0.6717

0.4360

0.46

1937–51

0.01876

0.00768

0.00335

0.00548

0.0903

0.6900

0.4316

0.36

1951–64

0.02650

0.00680

0.00448

0.00592

0.1690

0.7072

0.4347

0.15

1964–73

0.02721

−0.01200

−0.00933

−0.01247

0.1938

0.7298

0.4794

0.00

1973–85

0.00563

−0.01065

−0.00842

−0.01062

0.1820

0.7435

0.5553

0.75

USA

1889–1900

0.04018

0.02597

0.01840a

0.02285

0.1684

0.7436

1

0.27

1900–13

0.03335

0.03340

0.02387

0.02833

0.1731

0.6771

1

0.31

1913–29

0.03164

0.02012

0.01305

0.01504

0.1353

0.7266

1

0.31

1929–48

0.02366

0.01855

0.00987

0.01508

0.0879

0.7257

1

0.68

1948–73

0.03352

0.01554

0.00804

0.01511

0.1424

0.7261

1

0.16

1973–85

0.02400

0.02253

0.01877

0.02171

0.1633

0.7247

1

0.42

Japan

1887–99

0.03280

0.01892

0.00539

0.01892

0.1323

0.5420

0.4655

0.33

1899–1911

0.01541

0.01466

0.00344

0.01466

0.1127

0.5420

0.4182

0.50

1911–28

0.02438

0.02530

0.00258

0.02530

0.1387

0.5636

0.4070

0.41

1928–36

0.05275

0.03034

0.01137

0.03034

0.1360

0.5179

0.3801

0.00

1952–61

0.09605

0.04848

0.01961

0.04991

0.2510

0.6761

0.3203

0.00

1961–73

0.08869

0.03470

0.01312

0.03438

0.3175

0.6126

0.4537

0.00

1973–84

0.03148

0.01744

0.00712

0.01715

0.2576

0.6849

0.5529

0.18

Belgium

1955–62

0.03469

0.01257

0.00449

0.00949

0.1647

0.6807

0.5689

0.14

Denmark

1955–62

0.04027

0.01496

0.01008

0.01091

0.1914

0.6959

0.5389

0.00

France

1955–62

0.05003

0.01607

−0.00226

0.01516

0.1829

0.6875

0.5743

0.00

Germany

1955–62

0.05867

0.01491

0.01157

0.00586

0.2228

0.6546

0.5462

0.00

Netherlands

1955–62

0.03956

0.01625

0.01048

0.01340

0.2278

0.6578

0.4885

0.14

Norway

1955–62

0.03443

0.00236

−0.00162

−0.00169

0.2839

0.6363

0.6086

0.14

Italy

1955–62

0.06133

0.03441

0.00607

0.02913

0.1931

0.6386

0.4655

0.00

Note

For the meaning of the symbols, see List of Main Abbreviations and Symbols at the front of the book. All growth rates are exponential, and the way in which the various averages were calculated is explained in Chapter 2.

(a) Owing to an error, g N for this period was taken as 0.01527 in all the regressions in which it appears.

(p.549) (p.550)

Table SA II Annual Data for USA, Japan, and the UK (Years Marked by an Asterisk Are Those Judged to Be Substantially Affected by Excess Capacity or War, and So were Excluded in Fitting Trends of Output and Employment or in Calculating Averages of Wage Shares.)

USA, Non‐Residential Business

Year

Index numbers (1913 = 100)

Ratios

Q

L

N

H

s

λ

1889

38.61

46.43

57.59

50.65

0.1243

1890

41.50

48.43

59.50

52.97

0.1918

1891

43.34

50.13

61.01

54.77

0.1794

1892

47.72

52.13

62.83

57.12

0.2097

1893*

44.92

52.03

62.57

56.34

0.1687

1894*

43.79

50.83

61.22

53.82

0.1643

1895

49.78

54.32

64.41

58.14

0.1811

1896*

48.71

54.81

64.72

58.16

0.1497

1897

53.93

57.00

66.62

60.52

0.1642

1898

55.02

57.70

67.17

61.02

0.1503

1899

61.69

62.28

71.29

66.70

0.1686

1900

62.28

63.73

72.40

67.77

0.1887

1901

69.26

67.37

75.43

71.58

0.1889

1902*

68.68

71.55

78.75

75.64

0.1988

1903

71.78

74.40

81.11

78.41

0.1879

1904*

70.40

74.37

80.72

77.11

0.1593

1905

76.40

78.91

84.46

81.94

0.1585

1906

87.06

83.07

87.80

86.03

0.1865

1907

87.81

85.66

89.80

88.50

0.1824

1908*

78.29

83.49

87.51

84.04

0.1278

1909

89.55

89.06

92.02

89.81

0.1775

1910*

89.39

92.13

94.41

92.86

0.1758

1911

92.38

94.22

95.82

94.90

0.1495

1912

96.15

97.91

98.60

98.57

0.1686

1913

100.00

100.00

100.00

100.00

0.1808

1914*

90.16

98.81

98.63

97.50

0.1073

1915*

93.07

99.61

98.98

97.15

0.0997

1916*

108.6

108.1

105.6

106.1

0.1445

1917*

103.7

110.9

107.5

108.5

0.1201

1918*

109.8

111.4

107.3

107.6

0.1043

1919*

116.1

111.8

107.5

104.2

0.1658

1920

118.7

112.6

108.0

105.8

0.2192

1921*

111.6

105.2

102.1

95.28

0.0969

1922*

117.4

113.1

107.8

103.7

0.1155

1923

135.8

123.0

114.8

113.8

0.1648

1924

140.1

120.9

112.8

111.0

0.1025

1925

142.3

125.4

115.8

115.8

0.1477

1926

152.6

130.5

119.2

121.0

0.1475

1927

153.5

131.6

119.2

121.5

0.1295

1928

154.8

133.6

120.4

123.0

0.1182

1929

166.0

138.0

123.6

126.5

0.1502

0.7123

1930*

148.4

130.6

117.4

117.7

0.1118

0.7432

1931*

132.7

119.8

109.1

106.9

0.0672

0.7837

1932*

109.9

107.5

100.2

94.07

0.0024

0.8376

1933*

106.4

108.1

99.54

94.30

0.0216

0.8437

1934*

115.1

112.9

105.9

95.01

0.0537

0.7802

1935*

128.9

119.3

109.3

101.2

0.0994

0.7691

1936*

144.4

130.2

114.1

111.9

0.1150

0.7398

1937*

159.6

138.0

119.1

119.8

0.1456

0.7557

1938*

145.1

128.5

112.2

110.0

0.0723

0.7674

1939*

159.1

136.6

116.1

117.7

0.0951

0.7524

1940*

175.5

144.6

120.9

125.0

0.1304

0.7226

1941*

208.2

163.9

130.5

142.0

0.1455

0.6992

1942*

232.8

177.3

137.5

155.5

0.0631

0.6983

1943*

249.3

185.3

139.5

165.1

0.0305

0.7059

1944*

255.4

182.6

136.4

163.9

0.0386

0.7043

1945*

248.5

175.9

132.2

155.9

0.0609

0.7233

1946*

242.7

184.9

140.3

160.0

0.1450

0.7635

1947

246.3

193.1

146.8

165.8

0.1221

0.7391

1948

267.2

196.0

149.8

168.6

0.1484

0.7254

1949*

258.4

187.7

144.3

160.5

0.1038

0.7299

1950

286.9

194.9

147.4

167.0

0.1500

0.7102

1951

306.6

208.0

153.0

178.4

0.1600

0.7049

1952

314.0

213.6

154.5

182.2

0.1275

0.7274

1953

326.3

219.3

156.5

186.9

0.1229

0.7380

1954*

319.5

211.2

151.4

180.3

0.1146

0.7443

1955

348.0

219.3

154.4

186.9

0.1440

0.7172

1956

358.6

224.5

157.2

191.7

0.1492

0.7373

1957

360.8

224.0

157.1

190.5

0.1412

0.7412

1958*

351.3

215.8

150.2

183.5

0.1176

0.7458

1959

378.5

225.2

153.6

191.5

0.1388

0.7304

1960

381.4

226.5

154.2

192.7

0.1347

0.7432

1961

386.0

225.8

152.1

191.9

0.1279

0.7389

1962

407.0

231.6

154.1

197.5

0.1384

0.7276

1963

423.1

235.7

154.6

201.6

0.1371

0.7209

1964

447.9

241.2

157.0

206.1

0.1406

0.7190

1965

479.0

250.6

162.1

214.6

0.1604

0.7078

1966

506.7

260.8

167.8

222.6

0.1724

0.7068

1967

516.3

264.6

170.6

224.9

0.1599

0.7183

1968

541.9

271.5

174.1

230.7

0.1538

0.7213

1969

557.9

278.3

178.9

236.5

0.1612

0.7361

1970*

550.2

275.7

177.2

233.4

0.1498

0.7526

1971

566.4

275.6

176.2

233.4

0.1502

0.7398

1972

604.3

284.3

180.9

240.5

0.1546

0.7362

1973

644.6

298.0

189.6

251.6

0.1706

0.7370

1974*

632.4

300.3

192.3

252.7

0.1673

0.7520

1975*

625.8

291.6

185.7

245.2

0.1377

0.7282

1976

662.9

300.9

191.4

252.6

0.1533

0.7268

1977

703.2

312.6

199.3

262.2

0.1642

0.7204

1978

749.6

328.6

210.2

275.4

0.1763

0.7189

1979

766.1

340.9

218.0

285.5

0.1735

0.7287

1980*

755.3

339.6

217.3

283.7

0.1603

0.7388

1981

773.8

344.7

219.3

287.4

0.1807

0.7275

1982*

746.4

338.0

214.6

281.8

0.1525

0.7385

1983*

770.2

348.5

216.5

291.2

0.1443

0.7253

1984

830.5

372.2

228.7

311.2

0.1789

0.7135

1985

852.6

384.0

234.1

320.7

0.1648

0.7169

Japan, Non‐Residential Business

Year

Index numbers (1913 = 100)

Ratios

Q

L

N

H

s

λ

cu

1885

47.46

62.35

88.33

62.35

0.0915

0.3994

1886

51.07

62.45

88.40

62.45

0.0989

0.4258

1887

55.04

63.01

88.60

63.01

0.1056

0.4513

1888

58.35

64.58

89.18

64.58

0.1348

0.4633

1889

61.76

66.92

90.01

66.92

0.1256

0.4696

1890*

58.04

68.36

90.62

68.36

0.1200

0.4192

1891

65.28

69.85

91.14

69.85

0.1275

0.4574

1892*

63.86

71.66

91.72

71.66

0.1217

0.4119

1893

68.43

73.24

92.18

73.24

0.1294

0.4579

1894

70.25

71.15

91.81

71.15

0.1338

0.4849

1895

75.14

71.38

92.03

71.38

0.1432

0.4860

1896

77.31

75.80

93.31

75.80

0.1595

0.4856

1897*

75.39

78.37

94.05

78.37

0.1588

0.4302

1898*

76.98

79.39

94.47

79.39

0.1274

0.4303

1899

81.90

80.96

95.00

80.96

0.1032

0.4321

1900*

79.13

82.13

95.37

82.13

0.1039

0.4172

1901*

81.86

82.64

95.51

82.64

0.1017

0.4077

1902*

78.38

83.58

95.86

83.58

0.0909

0.4134

1903*

75.71

83.20

95.83

83.20

0.0975

0.3991

1904*

82.38

81.13

95.50

81.13

0.0936

0.4539

1905*

80.94

81.20

95.45

81.20

0.1385

0.4356

1906*

82.86

83.05

96.44

83.05

0.1324

0.4028

1907

89.01

88.91

97.69

88.91

0.1249

0.4132

1908*

88.79

90.25

97.92

90.25

0.1198

0.4439

1909

90.60

93.13

98.23

93.13

0.1113

0.4094

1910

93.13

96.11

98.76

96.11

0.1343

0.4453

1911

99.99

95.99

98.98

95.99

0.1475

0.4495

1912*

96.80

97.85

99.45

97.85

0.1347

0.4262

1913*

100.0

100.0

100.0

100.0

0.1424

0.4231

1914*

101.2

101.7

100.4

101.7

0.1460

0.4614

1915*

110.9

111.2

101.0

111.2

0.1409

0.4516

1916*

121.3

114.4

101.4

114.4

0.1568

0.4466

1917*

133.0

112.8

101.5

112.8

0.2068

0.5335

1918*

136.4

118.0

100.6

118.0

0.2278

0.4962

1919*

128.2

109.3

98.30

109.3

0.1806

0.4779

1920

132.6

120.2

100.8

120.2

0.1876

0.4428

1921

135.7

123.2

101.4

123.2

0.1305

0.4393

1922

138.4

127.0

101.8

127.0

0.1369

0.4442

1923*

131.9

134.7

102.2

134.7

−0.0907

0.3753

1924*

133.7

133.5

101.8

133.5

0.1443

0.3657

1925*

137.4

139.3

102.6

139.3

0.1224

0.3678

1926

140.0

142.4

102.9

142.4

0.0966

0.3557

1927

151.0

144.1

103.0

144.1

0.1473

0.3801

1928

157.1

145.7

103.3

145.7

0.1277

0.3937

1929

157.4

151.1

105.2

151.1

0.1349

0.3664

1930

162.3

159.9

107.7

159.9

0.1443

0.3780

1931

167.1

164.8

109.4

164.8

0.1420

0.3873

1932

168.2

167.0

110.6

167.0

0.0913

0.4169

1933

187.1

170.9

111.0

170.9

0.1078

0.4706

1934

209.6

176.0

111.7

176.0

0.1625

0.4943

1935

222.9

183.1

112.6

183.1

0.1777

0.4767

1936

228.4

187.8

113.9

187.8

0.1889

0.4640

1937*

250.8

187.6

112.3

187.6

0.2424

0.4891

1938*

261.7

195.1

114.0

195.1

0.2194

0.5026

1939*

275.9

200.6

114.9

200.6

0.2375

0.4996

1940*

288.4

211.8

118.7

211.8

0.2507

0.4747

1941

1942

1943

1944

1945

1946

1947

1948

1949

1950

1951

1952

236.0

232.4

137.5

232.4

0.2516

0.7100

0.2923

1953

255.2

247.2

146.1

247.8

0.2051

0.7075

0.2936

1954

272.7

254.9

147.9

257.2

0.1891

0.6852

0.2992

1955

300.6

261.6

152.3

264.2

0.2155

0.6935

0.3064

1956

334.2

278.2

155.1

283.2

0.2712

0.6869

0.3182

1957

383.0

299.5

159.5

305.3

0.3149

0.6547

0.3359

1958

388.6

312.4

160.7

317.6

0.2414

0.6642

0.3233

1959

427.3

326.2

161.6

331.0

0.2669

0.6584

0.3298

1960

500.7

343.9

165.7

349.3

0.3032

0.6243

0.3658

1961

572.6

356.4

166.5

360.2

0.3973

0.6131

0.3977

1962

610.9

371.7

168.9

368.0

0.3119

0.6220

0.3957

1963

656.2

382.9

170.2

376.1

0.3113

0.6313

0.4040

1964

723.9

398.7

172.3

390.2

0.3211

0.6253

0.4137

1965

750.2

415.9

175.7

419.0

0.2769

0.6314

0.3993

1966

835.1

434.2

179.7

437.4

0.2817

0.6179

0.4189

1967

942.7

448.7

183.4

454.1

0.3160

0.6075

0.4556

1968

1065

464.4

186.4

464.7

0.3279

0.6018

0.4861

1969

1201

476.7

187.7

476.0

0.3340

0.5903

0.5318

1970

1308

492.4

189.6

489.4

0.3446

0.5817

0.5632

1971

1326

506.5

189.8

501.5

0.3020

0.6109

0.5390

1972

1433

519.7

189.5

515.6

0.2853

0.6177

0.5489

1973

1584

544.9

194.1

539.7

0.2989

0.6468

0.5686

1974*

1565

550.4

192.5

528.0

0.3090

0.6744

0.5713

1975*

1534

550.7

189.9

524.3

0.2601

0.6990

0.5492

1976

1584

573.7

194.8

549.4

0.2471

0.7044

0.5303

1977

1646

586.5

197.3

562.8

0.2370

0.7016

0.5279

1978

1721

597.3

199.5

574.7

0.2309

0.6909

0.5344

1979

1832

609.2

200.9

590.5

0.2517

0.6942

0.5662

1980

1925

622.4

202.2

604.5

0.2585

0.6770

0.5884

1981

1971

629.9

203.6

608.1

0.2558

0.6786

0.5898

1982

2006

637.1

204.8

615.5

0.2484

0.6827

0.6033

1983

2048

650.9

207.8

630.6

0.2366

0.6882

0.6024

1984

2143

658.2

208.2

644.8

0.2480

0.6816

0.6174

UK, Non‐Residential Business

Year

Index numbers (1913 = 100)

Ratios

Q

L

N

H

s

λ

cu

1856

31.06

39.22

60.07

46.02

0.0979

0.5763

0.5902

1857

31.25

39.32

59.93

46.15

0.0569

0.5577

0.5878

1858

31.74

38.29

58.07

44.94

0.1016

0.5403

0.6084

1859

32.35

41.11

62.03

48.24

0.0750

0.5755

0.5731

1860

33.18

41.90

62.91

49.17

0.0774

0.5739

0.5723

1861

34.26

41.65

62.17

48.76

0.0991

0.5438

0.5899

1862

34.24

41.04

60.93

47.95

0.0808

0.5299

0.5938

1863

34.66

42.23

62.34

49.22

0.1091

0.5247

0.5796

1864

35.98

43.99

64.57

51.15

0.1247

0.5229

0.5732

1865

37.26

44.63

65.13

51.77

0.1330

0.5363

0.5806

1866

37.73

44.72

64.94

51.88

0.1072

0.5368

0.5823

1867*

36.86

43.52

62.85

50.37

0.0783

0.5464

0.5800

1868

38.77

43.75

62.82

50.52

0.1228

0.5348

0.6022

1869

38.72

44.75

63.91

51.56

0.0745

0.5335

0.5835

1870

42.42

46.40

65.90

53.34

0.1091

0.5265

0.6118

1871

45.29

48.09

67.91

55.16

0.1362

0.5084

0.6255

1872

45.21

49.69

69.21

54.89

0.1047

0.5491

0.5996

1873

46.93

50.63

69.78

54.09

0.1269

0.5660

0.6062

1874

47.36

51.12

69.69

52.83

0.1082

0.5724

0.6012

1875

48.29

51.56

69.74

53.29

0.1292

0.5709

0.6032

1876

48.53

51.55

69.17

53.27

0.1302

0.5770

0.6016

1877

48.61

51.71

68.83

53.44

0.1208

0.5888

0.5962

1878

48.58

51.22

67.65

52.93

0.1093

0.5781

0.5969

1879

49.63

49.35

64.65

50.99

0.1100

0.5908

0.6281

1880

51.44

53.45

69.46

55.23

0.1125

0.5596

0.5964

1881

53.50

55.37

71.40

57.22

0.1019

0.5736

0.5942

1882

55.52

57.38

73.40

59.30

0.1398

0.5799

0.5905

1883*

55.20

58.23

73.89

60.17

0.0983

0.5960

0.5741

1884*

54.90

55.54

69.92

57.39

0.0894

0.5890

0.5941

1885*

54.30

55.63

69.49

57.49

0.0792

0.5924

0.5821

1886*

55.10

55.95

69.32

57.82

0.0729

0.5846

0.5828

1887

58.12

58.90

72.41

60.87

0.0953

0.5860

0.5795

1888

61.23

62.00

75.61

64.07

0.0867

0.6006

0.5755

1889

66.11

65.43

79.16

67.61

0.1435

0.6127

0.5843

1890

66.34

66.63

79.98

68.86

0.1198

0.6306

0.5588

1891*

64.65

66.71

79.42

68.81

0.0760

0.6416

0.5391

1892*

61.48

65.95

77.90

68.02

0.0605

0.6600

0.4898

1893*

61.28

66.28

77.65

67.62

0.0559

0.6652

0.5150

1894

67.35

68.12

79.18

69.69

0.1032

0.6374

0.5519

1895

69.89

70.48

81.28

72.16

0.1005

0.6385

0.5204

1896

73.55

73.91

84.54

75.58

0.1101

0.6412

0.5385

1897

74.29

75.33

85.49

76.78

0.1039

0.6419

0.5013

1898

78.61

77.32

87.05

78.60

0.1275

0.6321

0.5128

1899

83.12

79.53

88.83

81.05

0.1359

0.6109

0.5074

1900*

82.22

79.91

88.55

81.27

0.1165

0.6135

0.5063

1901*

80.85

80.35

88.33

81.55

0.1332

0.6236

0.4707

1902*

82.30

81.14

88.50

82.37

0.0866

0.6102

0.5082

1903*

81.03

82.13

88.87

83.24

0.0836

0.6267

0.4918

1904*

81.99

82.09

88.13

83.07

0.0979

0.6151

0.5074

1905

84.92

84.41

89.90

85.40

0.1167

0.6067

0.4997

1906

88.44

87.47

92.43

88.33

0.1143

0.6077

0.4640

1907

90.48

89.15

93.46

89.88

0.0928

0.6250

0.4761

1908*

84.93

86.13

89.59

86.55

0.0524

0.6329

0.5057

1909*

87.68

87.63

90.42

88.18

0.0904

0.6243

0.4786

1910

90.80

92.30

94.51

92.61

0.0980

0.6250

0.4876

1911

93.97

95.80

97.31

95.94

0.0963

0.6229

0.4811

1912

95.55

97.07

97.87

96.76

0.0913

0.6264

0.4821

1913

100.00

100.00

100.00

100.00

0.1170

0.6204

0.4809

1914*

98.69

97.92

97.35

99.22

0.1181

0.6428

0.5312

1915*

98.16

92.70

91.70

95.34

−0.0341

0.6363

0.5450

1916*

93.63

89.35

87.93

91.81

−0.0756

0.6582

0.5016

1917*

91.48

86.49

84.70

88.75

0.0243

0.6189

0.5440

1918*

91.56

86.84

84.61

89.01

0.0835

0.6227

0.5144

1919*

89.89

95.93

93.99

91.66

0.1101

0.6587

0.4339

1920*

93.51

104.3

104.8

95.05

0.0651

0.6729

0.4090

1921*

84.61

88.77

91.78

79.00

0.0607

0.6708

0.4321

1922*

90.94

91.30

92.59

81.90

0.0584

0.6553

0.4615

1923*

93.85

93.95

94.27

84.60

0.0578

0.6675

0.4351

1924

98.63

96.18

95.70

86.84

0.0768

0.6703

0.4256

1925

105.1

97.53

96.80

87.83

0.1182

0.6359

0.4567

1926*

98.97

95.87

96.54

85.30

0.0765

0.6606

0.4246

1927

108.3

103.3

99.97

94.11

0.0841

0.6710

0.4323

1928

109.6

103.9

100.3

94.21

0.0862

0.6654

0.4378

1929

113.4

106.0

101.8

96.07

0.0898

0.6593

0.4277

1930*

112.2

102.8

99.40

92.26

0.1045

0.6490

0.4619

1931*

104.3

99.89

96.47

89.44

0.0745

0.6900

0.4533

1932*

105.3

101.2

96.90

90.40

0.0650

0.7061

0.4890

1933*

109.3

103.9

98.36

93.44

0.0392

0.7154

0.5140

1934

116.9

107.7

102.2

97.67

0.0798

0.6954

0.5120

1935

122.3

113.2

104.1

103.3

0.0774

0.6855

0.4809

1936

129.0

117.8

107.6

107.8

0.0841

0.6909

0.4749

1937

134.8

122.8

111.2

112.6

0.1078

0.6769

0.4565

1938

135.5

120.3

110.8

108.0

0.1102

0.6559

0.4797

1939*

139.5

129.1

115.2

118.1

0.1149

0.6655

0.4462

1940*

143.3

125.5

110.7

115.4

0.1288

0.6419

0.4524

1941*

152.5

126.0

109.4

117.1

0.0879

0.6224

0.4582

1942*

152.0

127.4

109.8

118.3

0.0467

0.6221

0.4370

1943*

154.8

125.0

107.0

116.0

0.0634

0.6232

0.4427

1944*

145.2

120.6

103.5

110.2

0.0094

0.6403

0.4140

1945*

136.9

114.4

99.6

102.8

0.0092

0.6750

0.4074

1946*

140.0

120.1

104.9

107.2

0.0635

0.6823

0.4271

1947

150.4

126.5

111.9

111.8

0.1395

0.7058

0.4483

1948

159.5

129.7

114.0

114.6

0.1379

0.6972

0.4338

1949

166.1

131.6

115.1

116.1

0.1331

0.6939

0.4409

1950

170.0

134.6

116.2

119.0

0.1113

0.7100

0.4126

1951

181.6

137.3

117.1

121.5

0.1877

0.7083

0.4315

1952*

177.9

135.8

116.2

119.8

0.1344

0.6915

0.4286

1953

186.5

138.0

116.9

121.9

0.1407

0.6834

0.4368

1954

193.8

141.2

118.5

124.9

0.1416

0.6907

0.4363

1955

204.2

144.2

120.1

127.7

0.1675

0.7021

0.4292

1956

206.4

145.1

120.6

128.3

0.1701

0.7113

0.4283

1957

209.4

145.0

120.5

127.9

0.1778

0.7103

0.4312

1958*

207.3

142.9

119.0

125.8

0.1711

0.7119

0.4286

1959

215.2

145.3

119.6

128.1

0.1757

0.7062

0.4238

1960

229.0

147.7

121.9

129.9

0.1993

0.7050

0.4428

1961

234.2

148.6

123.3

130.4

0.1911

0.7195

0.4434

1962

235.2

147.9

123.2

129.5

0.1683

0.7275

0.4352

1963

246.3

148.3

122.7

129.8

0.1713

0.7151

0.4449

1964

261.2

151.7

124.2

133.0

0.2054

0.7144

0.4459

1965

267.1

151.1

124.7

132.2

0.1972

0.7199

0.4448

1966

271.3

147.7

124.3

128.9

0.1907

0.7281

0.4547

1967

274.8

144.4

121.1

126.0

0.1934

0.7278

0.4690

1968

287.2

143.8

119.7

125.5

0.1979

0.7252

0.4812

1969

294.7

144.1

119.3

125.8

0.2006

0.7348

0.4906

1970

300.5

141.7

118.4

123.6

0.1990

0.7563

0.5110

1971

304.6

136.2

115.4

118.8

0.1858

0.7310

0.5233

1972

314.3

135.3

115.0

118.2

0.1742

0.7307

0.5256

1973

344.0

139.6

117.1

121.8

0.2098

0.7265

0.5479

1974*

339.5

137.1

116.5

119.6

0.2067

0.7656

0.5655

1975*

329.9

135.0

115.2

117.8

0.1509

0.7909

0.5476

1976*

334.9

132.5

112.6

115.6

0.1755

0.7645

0.5517

1977*

338.0

132.1

112.6

115.3

0.1888

0.7419

0.5470

1978

347.3

132.1

113.0

115.3

0.1934

0.7384

0.5542

1979

353.5

134.2

114.6

117.2

0.2073

0.7656

0.5637

1980*

341.7

131.5

114.0

114.8

0.1689

0.7982

0.5619

1981*

331.1

121.6

108.1

106.2

0.1583

0.8100

0.5833

1982*

330.5

120.8

105.5

105.4

0.1656

0.8013

0.5958

1983*

340.7

117.8

103.5

102.9

0.1758

0.7847

0.6293

1984*

350.3

121.0

105.4

105.6

0.1824

0.7890

0.6240

1985

367.3

122.7

105.8

107.1

0.1870

0.7730

0.6484

(p.551) (p.552) (p.553) (p.554) (p.555) (p.556) (p.557) (p.558)

Notes:

(1) See Denison with Poullier (1967, 63) and Denison (1979, 37–8), where revised estimates of hours worked in the USA in 1960 are given.

(2) In fact, no change was assumed in y for the UK for 1973–85. Owing to an oversight, some very minor reductions in y were left in for 1970–3.

(3) Ohkawa and Rosovsky (1973, 49) remark that ‘pre‐World War II working‐hour statistics are extremely limited, and therefore not usable for present purposes’. They quote some estimates for particular years 1923–39 which do not suggest any clear or marked trend, up or down, but say that ‘In the opinion of most experts, these figures are not reliable enough to indicate changes in actual working hours. They pertain rather to [regular or standard working hours].’

(4) If the marginal product of labour equals its wage, then λi = w i L i/Y i = (L i/Y i) (∂ Y i/∂ L i), which is the output elasticity of employment in sector i. This is the conventional justification for using λi. According to the theory in this book, the output elasticity (with perfect markets) is not λi but λi / (1 − s i) in steady growth. Hence it has to be assumed that s i is the same in all sectors for the formula in the text to apply. With imperfect markets there is a further assumption of uniformity required, and it is clear that the formula is, at best, only a rough approximation.

(5) For labour moving out of non‐farm unincorporated business, Denison and Chung assume that the marginal product of each worker there was only one‐fourth as much as that of labour in the rest of the economy (excluding agriculture).