Output Growth and the British Industrial Revolution: A Restatement of the Crafts-Harley View...

Output Growth and the British Industrial Revolution: A Restatement of the Crafts-HarleyViewAuthor(s): N. F. R. Crafts and C. K. HarleyReviewed work(s):Source: The Economic History Review, New Series, Vol. 45, No. 4 (Nov., 1992), pp. 703-730Published by: Blackwell Publishing on behalf of the Economic History SocietyStable URL: http://www.jstor.org/stable/2597415 .Accessed: 11/05/2012 12:22

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Economic History Review, XLV, 4(I992), pp. 703-730

Output growth and the British industrial revolution: a restatement

of the Crafts-Harley mew1 By N. F. R. CRAFTS and C. K. HARLEY

n the early i98os we published revised estimates of aggregate economic performance during the British industrial revolution which have stimulated

reappraisal of the beginnings of modern economic growth.2 These new estimates have led most scholars to abandon the previous orthodoxy which had been based on the pioneering work of Deane and Cole.3 We have subsequently explored further aspects of the industrial revolution using our i982/3 estimates of the rate of growth as acceptable best guesses.4 Recently, however, several papers published in this journal have, with varying degrees of hostility, expressed doubts about our estimates.5 We think it is now opportune to respond to these comments. Our critics have questioned the appropriateness of our estimation techniques and have suggested that our overall view of the industrial revolution is misconceived. While we do not wish to dismiss the points that have been made, we feel both that many of the specific criticisms of our estimating techniques have been erroneous and that our overall view of the late eighteenth and early nineteenth centuries has been misunderstood.

Initially in section I we present a brief summary of a coherent new view of British growth that emerged from our aggregate estimates. The bulk of the paper then takes up the technical issues that have recently been raised. In particular, we argue the following main points. First, that there is inevitably a range of possible estimates for industrial output growth given the inherent index number and data problems. Both Crafts's and Harley's original estimates fall within this range, as do Jackson's new estimates, whereas Deane and Cole's do not. Second, that we do not accept Jackson's case for preferring what he calls a Crafts rather than a Harley view of industrial output growth nor do we accept his dismissal of the indices of industrial output presented by Crafts, Leybourne, and Mills (CLM) and by Harley. Third, that Hoppit and Berg and Hudson substantially overstate

1 We are grateful to Maxine Berg, Brian Mitchell, Joel Mokyr, Patrick O'Brien, and an anonymous referee for helpful comments on earlier drafts. Any errors are, of course, our responsibility.

2 Harley, 'British industrialization'; Crafts, 'A review of the evidence'. 3Deane and Cole, British economic growth. 4 Crafts, British economic growth; idem, 'Difficulties of interpretation'; idem, 'International context';

Crafts, Leybourne, and Mills, 'Trends and cycles'; C. K. Harley, 'The state of the British industrial revolution: a survey of recent macroeconomic reassessment' (Univ. of Western Ontario discussion paper, no. 90I2).

5 Berg and Hudson, 'Rehabilitating the industrial revolution'; Hoppit, 'Counting the industrial revolution'; Jackson, 'Government expenditure'; idem, 'Rates of industrial growth'.

703

704 N.F.R. CRAFTS AND C.K. HARLEY

their criticisms and are confused and misleading in important respects. Fourth, that, while we recognize the need for some small revisions, our view of growth remains intact in all its essentials while no-one has made a case for reinstatement of the Deane and Cole view of growth during the industrial revolution.

The data for this period are, of course, imperfect and so any estimates of growth are controlled conjectures. Criticisms must be approached in that light. Useful critiques do not simply rehearse the known weaknesses of the sources but explore the robustness of the estimates and seek to examine the bounds of plausibility. It is inappropriate simply to counsel abandonment of effort in the face of uncertainty or to imagine that the range of possibilities is unlimited. In this spirit, in section II we review the construction of the industrial production indices and examine the impact of possible amendments to our earlier work. In section III we consider the wider implications of revisions to our understanding of overall growth, productivity change, and the industrial revolution.

Berg and Hudson have raised the important issue of the appropriate modelling of the development process during Britain's industrialization. Modelling has costs as well as benefits. We believe in the usefulness of the approach developed by Crafts, and formalized further by Harley, which places Britain firmly in the context of international economic relations and draws on international comparisons. We find, however, from reading others' reactions to our work that our view has not been expressed as clearly as we would like and we attempt to correct this in section I. At the same time, we fully accept that using this model may divert attention from other key features of the economy. Other models and approaches will be required to illuminate those aspects, but that we regard as a separate issue from the question of accurate measurement.

I

Our work is seen by some as denying a fundamental transformation of the British economy during the century I750-I850.6 This was not, however, the impression we intended to convey and our revisionism needs to be set in a proper perspective. In particular, by the early nineteenth century the old long-run equilibrium understood by Malthus had been swept away and rapid population growth no longer had catastrophic effects on real wages. The basic character of the economy changed from one dominated by the balance of land and population to one governed by technological change and capital accumulation. We are happy to agree with O'Brien that, notwithstanding the revisions we have proposed to estimates of growth, 'over the period I750-I850 the growth of the British economy was historically unique and internationally remarkable'.7

We do, of course, reiterate that industry overall grew much more slowly

6 For example, Stedman Jones, 'Changing face', p. 38; Clark, Revolution and rebellion, p. 38 suggests that recent work makes the idea of an industrial revolution a spurious one, a proposition we do not accept.

7 P. K. O'Brien, 'The industrial revolution: a historiographical survey', mimeo (I99I), p. 28.

OUTPUT GROWTH AND THE INDUSTRIAL REVOLUTION 705

than was once thought. Revolutionary changes in industrial technology were not widespread and productivity improvements contributed only modestly to the growth of GDP before the second quarter of the nineteenth century, probably causing a growth of national income of about one-third of one per cent annually (table 5). To be sure, industrial change helped to alter social structure, demographic behaviour, and savings habits, all of which may have stimulated growth. Nevertheless, it seems impossible to sustain the view that British growth leapt spectacularly in one generation as a result of innovations in manufacturing.

New estimates of national income per caput identify a longer period of transition. Growth had probably begun to accelerate by the early eighteenth century but modern economic growth only became fully established in Britain in the railway age. It should be remembered, however, that our estimates of slower growth of industry and GDP during the years I780-i830 imply a wealthier and more industrial economy in the mid eighteenth century than that previously envisaged. Britain's economy in I760 was certainly not that of a traditional agrarian society.8

Even though industrial innovations had a more modest impact on economic growth than was previously believed, they did create a genuine industrial revolution reflected in changes in Britain's economic and social structure.' By the second quarter of the nineteenth century, a combination of the rapid growth of the urban based textile industries that exported most of their product and the marked decline in agriculture's share of the labour force produced the first urban industrial economy-a development that was not inherent in the progress of the late seventeenth-century economy. Both industrial technology and mobility out of agriculture were important. Britain's external trading position was fundamentally changed and its situation in the international economy was unique. 10 By historical and international standards Britain's structural adjustment was very rapid. Not only do we regard this as a profound change, our modelling strategy has been orientated particularly to understanding this atypical industrialization, as section III discusses in more detail.

II

Our view of Britain's transformation into modern economic growth depends heavily on our assessment of the rate of industrial growth. Estimating aggregate growth requires accurate information both on the growth of output of different goods and on the relative importance-or appropriate weight- of each. The doubts expressed by our critics have concerned both these aspects of our estimates. In this section we address these doubts and examine the impact that they might have on our estimates. To anticipate, we find that, while many of the issues raised are of legitimate concern, reasonable

8 Innes, 'Jonathan Clark', pp. I77-8 is right to stress that 'pre-industrial' can be a misleading label for the eighteenth century.

9 Crafts, British economic growth, pp. 65-9 makes this argument quite plainly. 10 This is the theme of Crafts, 'International context' and of Harley, 'British industrial revolution'.


alternative decisions about how to deal with the problems do not substantially change the estimates of overall growth.

An aggregate grows at the weighted average of the growth of its individual components. Consequently, even if proper weights are unknown, an aggregate's growth must lie between that of its slowest and fastest growing components. The aggregate growth estimate may be quite sensitive to the weights given to very fast or slow growing sectors. In the construction of an index of industrial output for the industrial revolution period, weighting is absolutely central because a few particularly visible industries, notably cotton textiles, grew very much more rapidly than the others.11 Both Crafts and Harley in constructing their revised estimates argued that, although this was recognized by Hoffmann"2 and by Deane and Cole, their indices seriously exaggerated industrial growth by adopting inappropriate methods to deal with this problem. This point has been generally accepted and is not at issue now.

Reactions to our work in this regard differ sharply. On the one hand Hoppit argues that the fragility of the evidence on value added makes weighting very difficult and unreliable13 while Berg and Hudson repeat this claim and add that as a result there will always be wide margins of potential error in estimates of growth.14 On the other hand, Jackson accepts the weights used by Crafts as reasonably reliable and clearly preferable to those used by Harley, or in the CLM Best Guess index, both of which he regards as having been constructed so as to underestimate growth.15

We take an intermediate position, namely that there is insufficient evidence to be able readily to choose between Crafts, Harley, or for that matter Jackson's own new index but that the broad outline of the Crafts-Harley- Jackson view is much more robust than Hoppit or Berg and Hudson are willing to concede. The really big issue is undoubtedly the weighting of cotton rather than the correct distribution of value added weights among the other sectors. In comparison with the growth rate of cotton, other sectors, so far as we have indicators, grew at broadly similar rates. The range of possible growth rates for a sub-aggregate that excludes cotton and iron is correspondingly limited. We demonstrate this more specifically below. First, however, it is necessary to correct a number of serious misapprehensions in Jackson's article.

A well-known property of index numbers of output, which Harley employed to construct his estimates, is that a value added weighted index of quantity relatives is identical to a price weighted index. In particular, the use of initial year value added to weight quantity relatives defined on that same year gives a Laspeyres quantity index, and the use of final year value added to weight quantity relatives defined on that same year gives a Paasche quantity index. Paasche indices tend to give lower estimates of growth because the relative prices of rapidly growing sectors generally fall over time.

Crafts, British economic growth, pp. I7-28 deals with these points at length. 12 Hoffmann, British industry, pp. I7-23. 13 Hoppit, 'Counting the industrial revolution', pp. i8o-i. 14 Berg and Hudson, 'Rehabilitating the industrial revolution', p. 28. 15 Jackson, 'Rates of industrial growth', pp. 6-ia, I4.


Consistency must, of course, be maintained between the weighting base and the base for the quantity relatives. Given data on the quantity relatives and the value added shares in the base year, the implied value added shares in other years can be inferred using the quantity relatives. These points are demonstrated with a simple example in appendix I.

Failure to understand these elementary equivalences has led Jackson into serious error and it follows that his objections to the treatment of cotton in Harley's index numbers are misconceived. He confuses price weights with shares in value added. Thus, his statement that the I per cent weight given to cotton in the Laspeyres index was the maximum weight the industry received in his calculations for the period I770-I81516 is utterly misleading; recomputing the Laspeyres index from the data in Harley's tables I and 217 shows that the share of value added attributable to cotton in i8i5 = i9/0.8 X I = 23.75 out of a total index of 208-220, i.e. II per cent. As would be expected since cotton output is here valued at I770 prices, this is higher than the 8 per cent Harley estimates the share of cotton to have been in i8i5 at i8i5 prices. Except in the initial year with the Paasche index when the implied share of cotton in industrial value added is o.8 per cent, Harley's procedures always credit cotton with more than I per cent of industrial value added. As would also be expected, contrary to Jackson's claim,"8 Harley's Laspeyres index numbers give faster growth than the corresponding Paasche estimates.

A similar confusion permeates Jackson's discussion of the CLM index, although here it may be more understandable given the compressed exposition of the method of construction of that index occasioned by its place of publication. 19 Jackson's suggestion that the CLM index obtains results different from Hoffmann for reasons other than reweighting and that as a result comparisons over time are invalid20 is misleading, and his inference that the quantity relative for the industrial sector outside cotton and iron is unchanged over the period I783-I8oo is also incorrect.21 The adjusted weights in the CLM index were assumed to apply in i8oi and quantity relatives were worked back from there-in other words we have a Paasche quantity index with cotton ascribed a share of 6.7 per cent in industrial value added in i8oi, which seems to be, as described, a Harley variant of Hoffmann. It turns out that in this i8oi price weighted quantity index the quantity relative in I783 for the rest is 77 per cent of the i8oi level and the implied share of cotton in industrial value added in I783 at i8oi prices is about I.6 per cent. The implication is that one link in the Hoffmann chained index has been replaced but that is no reason not to make comparisons of trend growth over time.

Although the principles of index number construction using value added weights have been correctly applied in both these cases, the rates of growth

16 Ibid., p. 9. 17 Harley, 'British industrialization', pp. 269, 272. 18 Jackson, 'Rates of industrial growth', p. 7. 19 Crafts, Leybourne, and Mills, 'Trends and cycles', pp. 46-7. 20 Jackson, 'Rates of industrial growth', pp. io-i. 21 Ibid., p. io.


that they give are sensitive to the weighting for cotton, by far the fastest growing sector. Jackson opts for weighting using the value added shares given by Crafts22 and rejects the alternative (lower) weights used by Harley and by CLM.

It must be accepted, however, that the share of cotton in industrial value added prior to at least the mid nineteenth century cannot be established with precision-it will remain open to scholars to argue within a range of estimates which can be obtained using different methods, as may be illustrated by the work of Crafts and Harley. In i8oi, where the differences are largest, Crafts took the share of cotton in industrial value added as I7 per cent, compared with Harley's implied estimate of 5 to 6 per cent.

Harley was particularly concerned with the problems of estimating the size of the industrial sector in an economy with much labour in dual occupations and small-scale workshops, precisely the worries which are stressed by Berg and Hudson and by Hoppit. He concluded that 'the diversity of industrial activity was such that realistic estimation of its extent and of the relative importance of its components [could] only be constructed from systematic enumeration of the economy as a whole.'23 He chose occupational data in the census of I84i as the earliest reliable enumeration and projected backwards from this benchmark. The structure of relative prices in earlier years was taken to be the same as in i84I except for cotton and iron where the most important changes probably occurred. Corrections were made on the basis of the best available price information.24 This could perhaps lead to biased estimates through failure to allow for other important changes in relative prices in i8I5 or I770, but the direction of such bias is unclear contrary to Jackson's assertion that it is downward.25 In contrast, Crafts based his estimates of the structure of value added at benchmark years very largely on the work of Deane and Cole who in turn relied heavily on contemporary estimates together with the evidence, where available, of taxes and wages.26 Although in a sense these are based directly on price and quantity data, they are described by Deane and Cole as 'rough estimates' and the contemporary estimates are sometimes at variance with one another.

Comprehensive data on cotton textiles were not collected during the industrial revolution. Even after reasonably reliable estimation became possible in the I830s there remained uncertainty about the size of the industry. Table i shows a range of recent estimates of gross output of cotton for I84I (Harley's benchmark year) based on two procedures.

Moving from the value of gross output to value added involves the removal of cotton costs which is straightforward and the removal of other purchased inputs which is problematic; Deane and Cole took these other costs to be

22 Crafts, British economic growth, p. 22. 23 Harley, 'British industrialization', p. 268. 24 Ibid., pp. 270-2. 25 Jackson, 'Rates of industrial growth', p. 7. For example, competition with cotton suggests that for

traditional textiles relative prices in i84I would be lower relative to non-textiles than earlier. Harley's i8i5 weights would be too low for this slow-growing sector and this would cause an upward bias to his estimated aggregate growth rate.

26 Deane and Cole, British economic growth, chs. 5-6.


about one-third of the value of output less cotton.27 The output estimates in table I converted in this way to value added yield shares of Deane and Cole's estimate of manufacturing output in i84i ranging from i5 per cent to I2 per cent. Harley's I84I figure of I3.4 per cent is in this range. Crafts based his i83I weight for cotton on Deane and Cole's estimates but failed to follow their adjustment for purchased inputs other than cotton. Correcting this oversight reduces Crafts's cotton share to I7 per cent from 22 per cent in I83I. The impact of this change on his estimates is considered later in this section.

Table I. Estimates of the value of gross cotton output in i84i

?m. Deane and Cole 46.7 Blaug 43.0 Matthews 39.4 von Tunzelmann 38.4

Sources: Deane and Cole, British economic growth, p. i87; Blaug, 'Productivity of capital', p. 376; Matthews, Study in trade-cycle history, pp. I48-5I; von Tunzelmann, Steam power, p. 229. For details of these authors' various methods see app. 2.

A similiar assessment for the start of the nineteenth century is more difficult. Crafts interpolated his i8oi benchmark of ?9.2m. from Deane and Cole's figures of ?5.4m. for I798-i800 and ?ii.om. for i80I-3. When adjusted for purchased inputs the I798-i800 figure becomes ?3.6m. or about 6.5 per cent of industrial value added, very close to Harley's implied share. Deane and Cole's i8oi-3 value, when corrected for other purchased inputs, is ?7.3m. or about I3.5 per cent rather than Crafts's I7 per cent of manufacturing output.28 Chapman has speculated that the figures that Deane and Cole took from contemporary sources failed adequately to allow for the finishing of cotton textiles.29 Chapman and Chassagne's detailed work suggests that printed cottons gained between IO and 40 per cent in the finishing stage.30 Not all cottons underwent such expensive finishing but a figure towards the top end of this range would essentially restore Crafts's original estimate.

In sum, Crafts's and Harley's value added shares for cotton in i8oi are somewhere near the top and bottom of the likely range. Accordingly their two estimates of late eighteenth-century industrial growth probably bracket the range of possibilities. Our investigation of the weighting of the industry provides no support for Jackson's dismissal of the weighting of cotton in the Harley or CLM indices in favour of that in Crafts.

The data available to measure growth in the volume of output of different industries are, of course, imperfect. For some sectors there are clearly no usable figures while for others judgments are required as to the acceptability of the available evidence. The information available on an annual basis gives

27 Ibid., p. i88. 28 Ibid., p. i87; Crafts, British economic growth, p. 22. 29 Chapman, 'Cotton industry', p. 48. 30 Chapman and Chassagne, European textile printers, pp. 90, I39, 2i6-7.

7I0 N.F.R. CRAFTS AND C.K. HARLEY

a narrower coverage than that for benchmark years. Here we take up some of the comments that have been made in the recent literature concerning the reliability of the individual sector estimates used in our various indices.

All work in this area, including our own and Jackson's recent index,3' makes substantial use of customs and excise data. Hoppit has rehearsed a number of weaknesses of these records, including evasion and corrupt behaviour by excise officers which may have varied over time.32 Clearly, these problems did exist but Hoppit exaggerates the difficulties considerably and any bias is likely to be quite small. Mitchell notes that for most goods conditions of manufacture prevented much evasion and argues that the real problems lay in the area of candles, starch, and malt.33 Of these only the category of candles enters the Crafts index and only malt enters the CLM index-in each case with a very low weight-and none is in the Harley index. Moreover, the rate of growth of the candles series, if not the level of output, does seem to be reliable and increasing temptations to evasion were offset by the growing efficiency of the officials.34

While Jackson very largely endorses the use of data in the Crafts index, he objects strongly to some of the component series of the CLM index, particularly those for eighteenth-century woollens, coal, and iron.35 This is part of his general thesis that the CLM index underestimates growth in the period I76i-I8oo. The key requirement for the construction of this index was that it should be based on annual data since its purpose was to allow time series analysis of trends and cycles. Jackson's objections are considered in appendix 3 where it is argued that there are a number of possible biases working in different directions.

What would be the net effects of these different biases on the CLM index? For I770-I8oo where a comparison can most readily be made, the value added weighted average growth rate would be about 0.18 per cent per year too high. It should also be remembered, however, that this bias is offset by the choice of a Paasche quantity index for this period, whereas the more usual choice of weighting might be Fisher ideal which appears to have been Hoffmann's own aim. This opposite bias would probably cancel out the net effect of the excessive growth in coal, iron, and woollens and it seems reasonable to conclude that the CLM index can be used as a fair approximation on an annual basis of a Harley type index of industrial production in the late eighteenth century. Nevertheless, it is desirable to investigate Jackson's comments further and appendix 3 reports an alternative index, 'Revised Best Guess', which broadens the coverage and adjusts the weighting of the CLM index.

31 Jackson, 'Rates of industrial growth', tab. 9, p. i9. 32 Hoppit, 'Counting the industrial revolution', pp. I79-80. 33 Mitchell, British historical statistics, pp. 397-8. 34 Ibid., p. 398. Hoppit, 'Counting the industrial revolution', p. i8o also objects to the inexact data

available on the non-excised industries and their treatment by Crafts. Here too his complaints are much exaggerated and his reading of the literature is questionable. For the I790s he criticizes Crafts's estimates for copper and silk, yet the careful reworking of the sources by Jackson produces virtually identical growth rates; 'Rates of industrial growth', tab. 8, p. i8. Hoppit's discussion of copper is based on a misreading of Harris, The copper king, pp. I3I-4.

35 Jackson, 'Rates of industrial growth', pp. I3-4.

OUTPUT GROWTH AND THE INDUSTRIAL REVOLUTION 7II

There remains a problem raised both by Hoppit36 and by Berg and Hudson,37 namely that all indices of industrial production for the industrial revolution period are based on a sample of industrial activity rather than on data for the whole sector and that this sample may be unrepresentative. It seems likely, however, that this problem has led Harley and, even more so, Crafts to overestimate the rate of industrial growth, contrary to Berg and Hudson's belief. (It should be noted that they offer not a shred of quantitative evidence to support their claims.)

Adding more sectors to the index if data were available would of necessity reduce the value added shares of those sectors already included, among them cotton and iron (whose contribution to overall growth is higher using Crafts's methodology than using Harley's). Only if the weighted average growth rate of the omitted sectors exceeded that of the included sectors would there be a case for arguing that Crafts and Harley underestimated industrial growth. This is unlikely, but it would be desirable to expand coverage of the indices as and when more data are compiled.

We now present some estimates of alternative procedures in the measurement of industrial output growth. It is clear that some revision of Crafts's estimates is called for. As discussed in appendix 3, his iron output series can be improved by adopting Jackson's series based on Harley's original work, and his value added weighting for cotton in i83i needs to be corrected. It is also necessary to amend the series for building used by both Crafts and Harley. This was based on Feinstein's estimates which have since been revised and improved. The effect of these revisions, which are set out in table 2, is to reduce the estimates of industrial output growth by a small amount.

Table 2. Revisions to Crafts and Harley estimates of industrial output growth (per cent per

year)

Crafts Original Revised I760-80 I.5I I .29 I780-I800 2. I I I .96 i80I-3I 3.00 2.78

Harley Original Revised I770-i8I5 i.6 I.5 i8I5-4I 3. I 3.0

Sources: Original estimates from Crafts, British economic growth, tab. 2.6, p. 26, col. (I) for I760-80 and col. (4) for I780-i83i and from Harley, 'British industrialization', tab. 5, p. 276; revised Harley estimates for building use estimates based on Feinstein, 'National statistics', tab. x, col. (4), p. 446; revised Crafts estimates use same source for building and the value added weight of building now changed as a result to I4.2% in I770 and I7.0% for the I770-i80i average with other weights adjusted pro rata. Iron from estimates in Jackson, 'Rates of industrial growth', tab. 8, p. i8. Cotton is now assumed to be I7% of value added in i83I, not 22%, and other weights are adjusted pro rata.

36 Hoppit, 'Counting the industrial revolution', pp. i8I-2. 37 Berg and Hudson, 'Rehabilitating the industrial revolution', pp. 28-9.

7I2 N.F.R. CRAFTS AND C.K. HARLEY

Table 3. Industrial output growth between benchmark years (per cent per year)

Crafts Revised CLM Revised Jackson Hoffmann Crafts CLM

I700-60 0.7 0.7 o.8 o.8 o.8 I760-80 I.5 I.3 0.9 o.8 I.3 1.4 I780-i80i 2. I 2.0 I.9 I .7 2. I 3.9 i80i-30 3.0 2.8 2.7 2.7 2.9 2.8

Harley Revised CLM Revised Hoffmann Harley CLM

I770-i8I5 i.6 I.5 I.4 I.4 2.5

i8I5-4I 3. I 3.0 3.6 3.6 3.6

Sources: Jackson, 'Rates of industrial growth', tab. i, p. i, extended to include Crafts Revised and Harley Revised taken from tab. i above and Revised CLM which is derived from the Revised Best Guess index in tab. 2 above.

It is immediately apparent from table 3 that the revisions to the CLM index have very little effect on the pattern of estimated industrial growth. This is confirmed by time series analysis reported elsewhere.38 Figure I, which was estimated by the Kalman filter technique, also shows a similar pattern of trend growth to that shown by the original CLM index.39 In each case the distinguishing characteristic of the British case is a long period of

4.0

3.5-

3.0-

D 2.5 -

; 2.0-

pi 1.5-

1.0-

0.5-

0.0- 1700 1720 1740 1760 1780 1800 1820 1840 1860 1880 1900

Year

Figure i. Estimated trend rate of growth of industrial output of Revised Best Guess index Source: see text and app. 3 for details of construction of the index; see Crafts, Leybourne, and Mills, 'Britain', for exposition of econometric methodology employed.

38 Crafts, Leybourne, and Mills, 'Britain'. 39 Compare fig. I in this paper with fig. 4 in Crafts, Leybourne, and Mills, 'Trends and cycles', p. 53.

OUTPUT GROWTH AND THE INDUSTRIAL REVOLUTION 7I3

steady acceleration in the trend rate of industrial growth from the mid eighteenth century through to the second quarter of the nineteenth; the main difference with Revised Best Guess is that the trend rate of growth briefly touches 3.4 per cent at the peak compared with 2.9 per cent for the original CLM index. We would marginally prefer Revised Best Guess for time series work on the industrial revolution, but the main result here is that the principal findings are robust to quite substantial changes in weighting and coverage, given that Hoffmann's overweighting of cotton is avoided.40

Indeed the striking feature of table 3 is that whereas adjusting Hoffmann to use a realistic weight for cotton in obtaining the CLM index has a substantial effect on the estimated growth rate, particularly in the last two decades of the eighteenth century, all the further refinements make relatively little difference. This is not really surprising; Harley arrived at a similar conclusion-reweighting Hoffman for I770-i8I5 gave practically the same growth as Harley's own index, although this incorporated additional information on sectors not covered by Hoffmann.i

The major point is now clear. Estimates of late eighteenth-century industrial output growth are very sensitive to the weighting of cotton textiles but are only modestly affected by other variations of procedure. The CLM and Revised CLM indices are close to Harley for I770-i8I5 and are accordingly a little below Crafts in I780-I 8oi. Not surprisingly, a comparison of Jackson's index with Harley's shows that the difference in estimated growth rates comes almost entirely from the choice of weights rather than from different estimates of growth of sectoral outputs.42

If this is indeed the key to relatively reliable measurement of industrial growth during the industrial revolution, it seems at first sight very strange that Deane and Cole's estimates were so much higher than those of Crafts or Jackson who have essentially taken their weight for cotton from Deane and Cole's work. Had Deane and Cole constructed a quantity index for

40 This is apparent in other variants which were experimented with but are not reported here. We are grateful to Steve Leybourne and Terry Mills for their help with the econometric analysis.

41 Harley, 'British industrialization', tab. 5, p. 276. 42 Jackson may have found faster growth for either or both of the reasons that he estimated higher

growth rates for some sectors and gave higher weight to faster growing sectors. In fact for the years I760-i820 his sectoral growth rates are very similar to, and in some cases slightly lower than, Harley's for I770-i8I5 despite Jackson's finding an overall growth rate of i.9 per cent per year, some 0.3 per cent above Harley's:

Growth rates (% per year)

Jackson, I760-i820 Harley, I770-i8iS Cotton 6.7 7.0 Other textiles I.2 I. I Iron 2.7 3.2 Coal 2.4 2.5 Other 0.7 0.8-i.2

These growth rates are calculated from Jackson, 'Rates of industrial growth', tab. II, p. 20 and Harley, 'British industrialization', tab. 2, p. 272.


industrial output and based their growth estimates upon it rather than making indirect estimates,43 it seems certain that they would have arrived at much the same answer. They did construct a real output index for the textiles subset of industry based on their weights. This shows growth of textile output, which accounted for over 40 per cent of total industrial output, at o.9 per cent for I780-i800 and 4.I per cent for I800-32.44 Given this estimate it is unthinkable that the rest of industry could have grown enough to justify their estimates of 3.4 per cent and 4.4 per cent per year for I780-I800 and I80I-3I respectively.

In general, it appears that the critiques by Berg and Hudson, Hoppit, and Jackson of the Crafts-Harley view of industrial growth during the industrial revolution are at best much overstated and at worst seriously misleading and misconceived. There remains some doubt as to the exact rate of growth of industrial output, and we regard attempts to reconcile or to arbitrate between our original estimates as the pursuit of spurious precision, especially because of the difficulty of establishing an exact weighting for cotton. Many of the other doubts expressed could at most have had a very small impact on the estimates and there is no reason to think that there is any systematic downward bias in our indices. On the whole such corrections as now seem necessary tend slightly to lower our earlier estimates of growth.

Finally, it is important to recognize that whatever doubts remain on the details of the measurement of output growth, resurrection of the Deane and Cole view is not in prospect, as Jackson plainly recognizes. Two further propositions underline this point.

First, the 'missing sectors' on which Berg and Hudson dwell would have had to be both very large and very fast growing to restore the Deane and Cole estimates-for example, if they were as large again as the observed sector and grew at 4.8 per cent per year in I780-i80i and 6.o per cent per year in I8oi-3I, then combined with the revised Crafts estimates in table 2 this would approximately restore the Deane and Cole figures.

Second, as Harley pointed out in his original paper,45 his growth estimates are broadly in line with what we know independently about the growth in demand for industrial output, whereas the earlier figures were not. Further research has tended strongly to confirm this argument and would still support Harley's view of the growth of industrial demand.46

III This section reviews further aspects of the measurement of economic

growth and productivity during the late eighteenth and early nineteenth centuries and examines some of the wider implications of the growth estimates for the understanding of the industrial revolution.

43 Crafts, British economic growth, pp. i8-33 outlines and criticizes Deane and Cole's methodology. 44Deane and Cole, British economic growth, p. 2I3. 45 Harley, 'British industrialization', pp. 283-5. 46 More recent research on real wage rates and on investment bears on this point. In both cases the

implied revisions to the Harley demand index would very slightly increase the estimated rate of growth. See Crafts and Mills, 'Trends in real wages', and Feinstein, 'National statistics'.


Crafts and Harley were both concerned to look not just at industrial growth but also at growth of GDP as a whole. Both used for this purpose the estimates made by Crafts and originally published in I983.47 These estimates have also been subject to criticism, some of it well informed and some rather wild and woolly. We first review the changes (summarized in table 4) which we accept should now be made to those estimates, and then respond to other comments from recent papers in this journal which we do not accept.

Table .i. Revisions to Crafts's estimates of real GDP growth (per cent per year)

I760-I 780 I780-180i i80i-i831

Agriculture 0.I3 0.75 i.i8 Industry I.29 (I.5I) I.96 (2.II) 2.78 (3.00) Commerce o.64 (0-70) I.38 (I.32) 2.I3

GDP o.64 (0.70) I.38 (I.32) I.90 (I.97)

Note: earlier estimates are in parentheses. Sources: estimates in Crafts, British economic growth, ch. 2, with revisions described in text.

Table 4 shows the implications for Crafts's growth estimates of accepting the revisions to his industrial output growth figures, as reported in table 2, while retaining the methodology he established. They replace the estimates published in I985. The effect is to reduce estimated growth by 0.05 per cent per year for I760-80 and 0.07 per cent per year for i80i-3I. The figure for growth in I780-i80i is o.o6 per cent higher than previously estimated because the opportunity has been taken to correct an error in Crafts's original calculations pointed out by Jackson.48 Obviously, these estimates will in each period be a little too high if a revised Harley rather than a revised Crafts estimate for industrial output growth is used.

It certainly should be recognized that estimates of growth for sectors other than industry are distinctly less reliable. Crafts in his earlier work pointed to procedures used by Deane and Cole which seemed to be unreasonable and sought to replace them with more plausible ones. In particular, he drew attention to the danger of using population growth to proxy agricultural output growth in the eighteenth century and the implausible productivity growth implied by their unreliable deflation of current price estimates of national product in the early nineteenth century.49 The results seem to be generally agreed to be a more plausible set of 'controlled conjectures' and as yet few refinements have been proposed.

Two quantitative studies deserve attention, but they do not provide any

47 Crafts, 'A review of the evidence'; Harley, 'British industrialization', tab. 9, p. 286. 48 Jackson, 'Government expenditure', pp. 225-6, notes that the estimate for commerce is incorrect

and that overall output and commerce should both grow at I.43 per cent in the original estimate for I780-i80i. Commerce is assumed to grow at the same rate as GDP and so the estimates in tab. 5 allow for revised growth in this sector. The total effect of these revisions to commerce and industry is to leave overall income growth unchanged for I760-i80i and, accordingly, there is no need for further consideration of the formula used to estimate agricultural growth described on pp. 39-4I of Crafts, British economic growth.

49 Ibid., ch. 2.

7i6 N.F.R. CRAFTS AND C.K. HARLEY

figures with which further to revise Crafts's estimates. Jackson has correctly pointed out that Crafts failed to draw attention to the possible problems inherent in the government expenditure figures for the period, especially those resulting from the different composition of expenditure in peace and war.50 He himself recognizes, however, that an improved series is not readily achievable. Allen carefully reviews alternative approaches to the measurement of agricultural output and finds that Crafts's results match those from other methods over the long run. He notes that alternative approaches may suggest more even growth than Crafts found but concludes that the evidence does not permit confident choice between alternatives over short intervals.5

Accepting, then, that estimates of GDP growth for the period prior to I83I are less reliable than those for later in the nineteenth century, should we believe with Hoppit that the margins for error are very large and, for example, that growth in I80I-I83I may have been anything between I.49 per cent and 2.5I per cent?52 Hoppit argued that both the sectoral weights and the sectoral growth figures were liable to error. There are several strong reasons for thinking that this is a gross overstatement of the severity of the problems involved and ignores the need to achieve consistency with other quantitative evidence.

First, independently of the work on revising growth figures for I780-I83I, there has been a major research effort into improving estimates of real wage growth during the same period. The outcome of the debate between Crafts and Lindert and Williamson gives a 'best guess' figure for real wage growth over this period very similar to the per caput income growth figure implied by table 4 above.53 We would expect the two to show similar growth over these years.

Second, Hoppit conducts his 'sensitivity analysis' using a range from 24 per cent to 40 per cent for the weight of industry in GDP, with sectoral output growth figures subject to plus or minus 20 per cent. This is far too wide both because subsequent work has tended to confirm Deane and Cole's estimates for employment structure and because there is relatively reliable evidence that the share of industry in income was around 34 per cent in the I840s, not reaching 40 per cent until I90I.54

Third, table 3 suggests that the growth of industrial output is fairly well established for I80I-3I within a narrow range. Given this, the available evidence on employment structure, and the strong likelihood that labour productivity growth in services was no higher than in industry, we regard an upper bound on the growth of real output per head in I80I-3I of about

50 Jackson, 'Government expenditure'. It seems likely, however, that Jackson overstates the seriousness of the problem for comparisons of I760, I780, and i8oi since these were all periods of heavy wartime expenditure.

51 Allen, 'Agriculture during the industrial revolution'. 52 Hoppit, 'Counting the industrial revolution', p. i84. 53 For discussion of these estimates see Crafts, 'Real wages, inequality and economic growth' and

Crafts and Mills, 'Trends in real wages'. The 'Best Guess' estimate shows real wage growth of 0.48 per cent per year for I780-i83I, while the revised figures show that national income per head grew at 0.43 per cent per year.

54 For early nineteenth-century employment structure see Wrigley, 'Men on the land', and for later nineteenth-century shares of income originating see Deane and Cole, British economic growth, p. i66. Given these endpoints, the range of permutations of growth rates and shares is greatly narrowed.


0.5 per cent per year as the most that is plausible-compared with Hoppit's proposed upper bound of i.o6 per cent.55

Berg and Hudson assert that overall economic growth is underestimated, although characteristically they offer no quantitative evidence in support of this proposition which is stated as a matter of prior belief.56 We have already given reasons to doubt their optimism over industrial output growth. For GDP as a whole their arguments are no more convincing. The unsatisfactory basis of their case is reflected by the following points. First, although they repeatedly stress the radical nature of change in the period to bolster their scepticism of the slower growth story of Crafts and Harley, they themselves acknowledge that the well-documented examples of electricity and computers show that the impact of fundamental innovations on economic growth is often modest for a surprisingly long time.57 Second, they argue that early growth was often in activities that left no quantitative trace. Since we surely believe that the record became more (not less) complete as time passed, this is actually a reason to suppose that the national accounts approach overestimates rather than underestimates growth.58

Revisions to estimates of overall output growth strongly affect estimates of total factor productivity growth, the usual methodology for assessing the importance of productivity change for economic growth. On an economy wide basis, this procedure identifies productivity growth as the difference between the rate of growth of an index of output and the rate of growth of measured inputs (and, in consequence, reflects any economies of scale or improvements in organization as well as technological change). Berg and Hudson object that measurement of TFP growth during the industrial revolution is particularly unreliable, not only because they doubt the output growth estimates but also because they believe that the assumptions made in estimating TFP growth are fraught with problems.59 Once again, however, we believe their criticisms are seriously wide of the mark.

Table 5 reports conventional estimates of TFP growth. It shows that this increased much more slowly according to the revised estimates than would have been thought with the data used by writers in the I970s. Labour productivity growth, of course, is also slower. The reduced estimates of output growth are the chief reason for this. The growth rate of any aggregate of capital and labour input growth must lie between the rates of growth of the two series and thus must be in a very narrow range, as table 5 also reveals. Thus, as we show below, Berg and Hudson's worries over the effects of weighting procedures are of little practical import.

Berg and Hudson claim that this approach leads to the underestimation both of the extent and of the significance of productivity advance.60 In detail they object that these calculations are based on inappropriate weighting of

55 Using the labour force estimates in Wrigley, 'Men on the land', and the estimates and discussions in Crafts, British economic growth, ch. 2 and in Deane and Cole, British economic growth, ch. 4.

56 Berg and Hudson, 'Rehabilitating the industrial revolution', pp. 26, 30. 5 Ibid., p. 35. 58 Ibid., p. 29. 59 Ibid., pp. 32-3. 60 Ibid., pp. 30, 32-4.


Table 5. Estimates of total factor productivity growth (per cent per year)

I760-180i i80i-i83i

Feinstein AY/Y I.I 2.7 AK/K I.0 I.4 AL/L o.8 I.4 TFP 0.2 I.3

Craftsa

AY/Y I.0 2.0 AK/K I.0 I.5 AL/L o.8 I.4 TFP 0. I 0.55

New estimates AY/Y I.0 I.9 AK/K I.0 I.7 AL/L o.8 I.4 TFP 0.I 0.35

Note: a These figures are adjusted to identify only capital and labour as factors of production. Capital and labour are in each case both assigned weights of 0.5. Sources: Feinstein, based on his I978 capital stock estimates, comes from Feinstein, 'Capital accumulation', pp. I39-4I; Crafts is derived from Crafts, British economic growth, p. 8i; New estimates uses the revised growth estimates of tab. 5 and the new capital stock estimates in Feinstein, 'National statistics', tab. xvi, p. 459.

capital and labour because the economy did not correspond to a 'number of restrictive assumptions', that factors of production were often underutilized, that changes in factor quality are ignored, and that new products create enormous difficulties.6' They conclude that

If the most sensible way to view the course of economic change is through the timing and impact of innovation, it is arguable that the introduction of national accounting categories has frustrated this project. Emphasis has been placed on saving and capital formation at the expense of science, economic organization, new products and processes, market creativity, skills, dexterity, the knacks and work practices of manufacture.62

In fact, it can readily be shown that the degree of bias from the weighting of capital and labour is at most quite small.63 The extent of the possible bias in the TFP estimates depends on the extent of scale economies and the difference in the growth rates of capital and labour-if these were the same and returns to scale were constant, then weighting is completely irrelevant. Because capital and labour grew at quite similar rates and because for the economy as a whole returns to scale must have been quite close to constant,

61 Ibid., pp. 33-4. 62 Ibid., p. 34. 63 This exposition follows that in Thomas, 'Accounting for growth', pp. 57I-2.


the scope for errors in measurement of TFP is much less than Berg and Hudson assert. A technical demonstration of this can be found in appendix 4.

The maximum range given by the formula derived there and the new estimates in table 5 for TFP growth is o.I plus or minus 0.04 for I760-I80 I and 0.35 plus or minus o.i8 for I80I-3I. In practice it must be likely both that any bias would be much smaller than this and that it would be present to a similar extent in both periods. The big change in the pattern of increase in TFP growth which has come from the revisions to output growth estimates dwarfs any small bias that could have resulted from misweighting factor input growth, quite contrary to Berg and Hudson's assertions.

It is perfectly true that, as Crafts stressed, the estimates are 'crude' in the sense that it is not possible to measure changes in quality of labour or in hours worked.64 However, the implication of this and, in particular, Berg and Hudson's heavy stress on the underestimation of the growth of the labour force in these calculations because of an unrecorded increase in female and child labour inputs65 is that table 5 exaggerates total factor productivity growth-again the opposite of the bias they allege. Similarly it is ironic that Berg and Hudson bring up the difficulty of dealing with new goods in the measurement of TFP. The downward revision of estimates of TFP growth in recent work has been due primarily to the avoidance of the errors in index number construction which plagued earlier work and which were especially associated with the development of new processes and products in textiles.

We believe therefore that the estimates of TFP growth are more likely to be too high than substantially too low. We are not surprised to find a low rate of TFP growth during I780-I83I. It is surely one of the chief lessons of published work in the last three decades, particularly in new economic history, that the impact of apparently dramatic innovations on overall economic growth is modest, especially at the outset.

Nevertheless this does imply that part of Berg and Hudson's argument may be right. TFP should capture the impact of innovation but it may not be very sensitive in the short run to changes in innovativeness or to developments which will eventually have a strong impact on costs and output.66 In his discussion of sectoral productivity growth Crafts should have made it clear that in claiming that in much of the economy TFP growth was extremely low, he did not wish to suggest that these sectors did not experience any innovations.67

Crafts and Harley have both seen the revisions to macroeconomic estimates combined with some elementary economic modelling as promoting a better understanding of structural change in the economy during the century after I750.68 For many writers such changes were at the very heart of their definition

64Crafts, British economic growth, pp. 79-82. 65 Berg and Hudson, 'Rehabilitating the industrial revolution', pp. 35-7. 66 Cf. the case of electricity referred to earlier. 67 Crafts modified his earlier views somewhat and accepted that the data may leave rather more

possibility of productivity advance in the 'unmodernized sectors' than he allowed in British economic growth; see 'Difficulties of interpretation', p. 255. Harley, 'British industrial revolution', pp. 2I-2 reworks Crafts's I985 calculation in some detail and argues that its message nevertheless remains valid.

68 Crafts, British economic growth, chs. 3, 6, 7; idem, 'International context'; Harley, 'British industrial revolution'.


of the term 'industrial revolution'.69 The modelling strategy which both Crafts and Harley adopted was developed to try to explain Britain's unusual experience in its extreme degree of industrialization, to place this phenomenon firmly in the context of international trading relations, and accordingly to contribute to the development of more satisfactory generalizations concerning the international experience of economic growth in the nineteenth century than those embodied in the writings of Gerschenkron or Rostow.70

We believe that, on its own terms, this research programme has been fruitful and, in particular, has returned to prominence the notion of comparative advantage. There now exists a plausible and coherent account of structural change during British industrialization which encompasses the unevenness of productivity advance, the unusual productivity levels of and release of labour by British agriculture, and the combination of very rapid industrialization with quite modest overall growth.71 Moreover, the historical issues on which light is shed by considering the linked questions of comparative advantage and structural change are not trivial and were of much concern to politicians, major interest groups, and economists of the day.72

We are also convinced that the broad outlines of growth and structural change are reliably enough established to sustain this account despite the data problems, which, as we acknowledge, remain. Complete accuracy will never be possible but our estimates are robust enough to bear the weight of these interpretations. Thus, while Hoppit is surely right to remind us of the difficulties of a complete sectoral classification of employment, Wrigley's careful reviews of the evidence confirm the basic picture of the much greater reduction in the proportion of labour used in agriculture between I700 and I850 in Britain than elsewhere in Europe, which is at the centre of this story.73

In order to construct this (or indeed any other formal or informal) model to explain these interesting features of British development, it is necessary to simplify. Simplification entails both selection of assumptions on which to base the argument and edited presentation of facts. We would argue strongly that the simplifications made in our work have been fruitful. We would not, however, want to argue that they would be appropriate to address all questions nor would we dispute that there is a long agenda of other important issues. Once this is recognized it goes without saying that there are dangers or costs as well as benefits resulting from our research strategy. It is on some of these negatives that Hoppit and, especially, Berg and Hudson seize and we readily accept some of their arguments.

Thus, we are happy to agree with Hoppit (and never claimed otherwise) that focusing on national accounts can only illuminate a part of the social and economic change taking place in the period and we would readily accept that there are many different yet perfectly reasonable ways of defining

69 For example, Mathias, First industrial nation, p. 2 believes that the most important feature of the idea of 'industrial revolution' is 'the fundamental redeployment of resources away from agriculture'.

70 The development of this kind of research is reviewed in O'Brien, 'Typology'. 71 Crafts, 'International context'; Harley, 'British industrialization'. 72 Most obviously in the context of the corn laws. 73 Hoppit, 'Counting the industrial revolution', p. I78; Wrigley, 'Men on the land'; idem, 'Urban

growth and agricultural change'.

OUTPUT GROWTH AND THE INDUSTRIAL REVOLUTION 72I

'industrial revolution'.74 Similarly, we agree with Berg and Hudson that the division between 'traditional' and 'modern' sectors in industry which we have found very useful for our purposes is a simplification that in other contexts would be quite unacceptable.75 Perhaps the most important point raised both by Hoppit and by Berg and Hudson concerns the regional perspective on industrialization.76 We would agree that regional development varied considerably and that exploring this diversity offers the potential of a set of quite different and valuable insights into the experience of the industrial revolution. Nevertheless, it remains true that for some issues

77 analysis at the national level is appropriate. Perhaps Berg and Hudson will in due course achieve a full rehabilitation

(and provide an adequate definition) of an 'industrial revolution' as they conceive the notion and quite possibly this can co-exist with the present estimates of economic growth. But such rehabilitation would involve the documentation of the long list of speculative comments and assertions in their article and would entail a programme of research essentially complementary to the one we have undertaken.

IV Our main arguments can be re-stated briefly as follows. First, we would

stress that the considerable volume of work since our original papers does not provide any serious quantitative challenge to our main findings nor does it go any distance towards reinstating Deane and Cole's view, which was the previous orthodoxy. Second, we accept that measurement of growth yields only a range of best guess estimates. Nevertheless, it is important not to overstate the degree of uncertainty. Third, we have made revisions to our earlier estimates in the course of the paper; these are generally fairly small and tend to reduce slightly the estimated growth rates. Fourth, we reject Jackson's ill-informed attempt to discard the indices of industrial output prepared by Crafts, Leybourne, and Mills and by Harley, although we welcome his own index as a worthwhile contribution. Fifth, we demonstrate that total factor productivity estimation is much less problematic than the critics claim. Sixth, we accept that our approach to the industrial revolution has been shaped by the pursuit of particular questions and that other approaches are both valid and potentially important. Finally, we reaffirm the importance of the industrial revolution as an historical discontinuity.

University of Warwick University of Western Ontario

74 Hoppit, 'Counting the industrial revolution', p. i89. We do, however, reject his absurd claim that our use of national accounts reflects the belief that the industrial revolution and growth are virtually interchangeable concepts.

75 Berg and Hudson, 'Rehabilitating the industrial revolution', p. 32. 76 Ibid., pp. 38-9; Hoppit, 'Counting the industrial revolution', p. i86. 77 It should be noted that Crafts was well aware of regional differences, particularly in wages; British

economic growth, pp. 3-6, I04-7. Berg and Hudson fail to point out that his discussion of factor market integration was a comparison of internal and international integration. This view is, of course, at the heart of the Ricardian analysis of international trade and, when linked to the proposition that comparative


APPENDIX I: A numerical example to illustrate index number construction

The following example clarifies the relationship between quantity indices and value added weighting. Consider an economy with the following production of final goods (there are no intermediate goods).

Year o: i0 bricks at i (io% of current value added) 5 cakes at i 8 (90%)

Year I: 20 bricks at 2 (20%) 40 cakes at 4 (8o%)

The Quantity Relatives are as follows: QO = Year i: bricks = 2 Q1 = Year i: bricks = 0.5

Year o: cakes = 8 Year o: cakes = 0.I25

p0q, The Laspeyres Quantity Index, , gives output in year I = 740 (year o = ioo). p0qO

The Paasche Quantity Index, p1q, gives output in year o = 20 (year i = ioo). p1q0

-

As is generally the case, the rate of growth of the Laspeyres index is the faster of the two, the relative price of cakes having fallen.

It is easy to check that, valued in year o prices, in year i the value added share of bricks is 2.7 per cent and that of cakes is 97.3 per cent. Thus a Laspeyres calculation is tantamount to raising the value added share of the fast growing sector in the final year. Similarly, valued in year i prices, in year o the value added shares of bricks and cakes are both 50 per cent.

Denote shares of value added in current prices as VAo and VA1 for year o and year i respectively. Then calculate the following for the ratio of output in year i over year o:

IVAOQO = 0.2 + 7.2 = 7.4 which is the same as the Laspeyres estimate obtained earlier. For the ratio of output in year o over year i calculate

IVA1Q1 = o.i + 0.I = 0.2 which is the same as the Paasche estimate obtained earlier. Thus the appropriate sum of value added shares multiplied by quantity relatives is simply another (potentially more convenient) way of obtaining Laspeyres and Paasche quantity indices. However, it is vital to match up the correct quantity relatives and value-added shares. Consider IVA1Qo = 0.4 + 6.4 = 6.8; this is plainly neither a Laspeyres nor a Paasche equivalent calculation.

The CLM, Amended Best Guess, and Revised Best Guess indices are all Paasche quantity indices based on i8oi which are calculated using the quantities relative to that year and value added shares in i8oi as initial weights. The weights in each case were chosen to be broadly in line with Harley. The new indices are get out in appendix 3.

advantage is based on relative efficiency, explains why nineteenth-century British farmers suffered so much from imports despite their high productivity. The same farming efficiency transplanted elsewhere would have had a very different implication and here the national unit of analysis is the one which gives insight; cf. Crafts, 'International context'.


APPENDIX 2: The size of the cotton industry

One approach to the measurement of gross cotton output derives from Baines's estimate for i833 based on estimates of employment and wages, of costs for raw cotton and other inputs, and of profits. Matthews developed a time series of output from a benchmark of ?32.3m. in i833, based on Baines, conveniently assuming that the value of home consumption equalled that of exports and calculating a series of output value using raw cotton consumption, and the official and declared values of exports. Von Tunzelmann endorsed this series, although it may overestimate the value of the home trade.78

The second approach originated with Mann and was adopted with modifications by Ellison. Deane and Cole rely on this, as does Blaug.79 The weights of yarn and piece goods exports were deducted from estimates of the yarn produced, to give the weight of yarn consumed domestically. The domestic piece goods were then valued at a multiple of the average value of exports. There are two pitfalls with this procedure: guessing the valuation of domestic cloth, and converting the customs figures on yards of cloth exported into weight. The latter is a severe problem since cloth varied widely in its weight per yard. Blaug used ilb. = 5.47 yards and domestic goods value = I.33 times exports throughout, while Ellison used a variable conversion factor of between 6.i and 5.3 yards per lb. and a valuation ratio which varied for unexplained reasons between a low of I.I3 in i829-3i and a high of I.7 in i859-6i.

Ellison and Blaug both seem to have used quite high conversion ratios. Von Tunzelmann, for rather different purposes, adopted 5 yards per lb., Burn's i833 list of exports yields an average of 5.I yards, and an average of contemporary price quotations yields an estimate of about 4.75 yards to the lb.80 A revised calculation using Blaug's procedure but 5.o rather than 5.47 yards yields an i84I output of ?34.5m., which is only three-quarters of Deane and Cole's figure in table .

APPENDIX 3: Revisions to the CLM index of industrial output

Jackson's doubts about the CLM index require some discussion. In the case of woollens the series used is the only possible one, although, as Jackson remarks, it is based on Yorkshire production and does not tally with Deane's estimates for scattered benchmark years for the country as a whole which were used and interpolated by Crafts and by Jackson himself.82 Given the importance of the sector it would be particularly useful to include it. It is generally accepted that Yorkshire output growth was somewhat higher than that of Britain as a whole and a comparison of the two sources seems to confirm this: the Yorkshire series shows growth at i.i per cent per year in I74I-99 compared with 0.95 per cent for Deane's estimates. For I772-99 the discrepancy is rather greater with the Yorkshire series showing 0.42 per cent higher growth (o.96 per cent versus 0.54 per cent), although Deane's figure for I772 is a particularly tentative one. Jackson's criticism is correct to an extent but the bias may well not be large and, it must be remembered, would go

78 Matthews, Study in trade-cycle history (see p. I49 for acknowledgement of possible overestimate); von Tunzelmann, Steam power, p. 227.

79 Blaug, 'Productivity of capital'; Ellison, Cotton trade. 80 Burn's list can be found in Baines, History, p. 407. The price quotations are in the Economist and

in an appendix by Simmonds to Ure, Cotton manufacture, p. 5II. 81 This calculation uses the improved import data for raw cotton in Huberman, 'Prices and quantities',

p. I03 which provide some useful modifications without changing greatly the overall picture of cotton consumption.

82 Jackson, 'Rates of industrial growth', p. 22; Deane, 'Output of the British woollen industry'.


in the opposite direction to the general thrust of his objections to the growth estimates from the CLM index.

For coal, the series used is again the only possibility on an annual basis. For I760-i800 the Hoffmann coal series grows at o.9 per cent per year (0.4 per cent for I770-I8oo) which is less than the recent and surely more reliable estimates by Pollard.83 In this case the bias imparted will be a downward one. For iron, the CLM index used interpolations of Riden's figures for pig iron prior to I786;84 for I786-i800 the Hoffmann estimates agree very well with Jackson's own estimates. In general the CLM index avoided interpolation but it was felt that to omit iron would risk accusations of downward bias in trend growth estimates. Harley and Jackson both propose revisions to the Riden series to allow for changes in the ratio of other iron output to pig iron, and these imply that the series used by the CLM index for I760- 86 has too high a growth rate by about I.2 per cent per year for this sector, imparting an upward bias to the growth of the index. Crafts's own index also needs amendment to deal with the inadequacy of the Riden series for this purpose.

Amended Best Guess and Revised Best Guess are set out in table A3. i. Amended Best Guess corrects an error in transcription in the CLM index. Revised Best Guess expands the coverage of the CLM index to include all other available series for the eighteenth century rather than merely reweighting and slightly amending Hoffmann as the CLM index did.

Revised Best Guess is a Paasche quantity index based on i8oi and was calculated in the same way as the CLM index. Starting from i8oi quantity relatives, the i8oi value added weights were used to obtain the index numbers for earlier years working back from i8oi. When series dropped out of observation the weights of sectors other than cotton and iron were increased in proportion and the resulting new index was spliced to the old. The first of these adjustments occurs at I789. The initial value added shares of sectors in Revised Best Guess are listed for I789-I8oo in table A3.2. The earlier years in the table are also given to show the disappearance of sectors from observation and the consequent inflation of the weights of the remaining sectors.

APPENDIX 4: Biases in TFP measurement

Consider the following expression:

AA/A = AY/Y - aAK/K - (h - a) AL/L

where AA/A is the rate of growth of output not explained by input growth, i.e. TFP growth, a and (h - a) are weights reflecting the elasticity of output with respect to capital and labour respectively. Conventionally h is assumed equal to i, with a and (i - a) equal to the shares of profits and wages. With perfect competition, constant returns to scale, and a Cobb-Douglas production function, measurement of TFP growth is exact. More generally we might let h vary to reflect the extent of returns to scale; for example, if a doubling of inputs led to a quadrupling.of output, h = 2 and so on. We might also recognize that market imperfections may cause the shares of profits and wages to be poor indicators of the output elasticities.

It is now straightforward to assess how serious the biases suggested by Berg and

83 Pollard, 'New estimate'. 84 Riden, 'Output of the British iron industry'; this information was inadvertently omitted from the

published description of the CLM index.


Hudson might be. Clearly the output elasticities are non-negative and add up to h. Then the maximum range of estimates for AA/A equals h(AK/K - AL/L) since AA/A = AY/Y - hAK/K when a = h and AA/A = AY/Y - hall when a = o. Of course, it is unlikely that h will be much different from I-even in recent times when economies of scale are much more important, at the level of the whole economy h is probably no more than I.285-and both output elasticities will surely be well above zero, so that the likely range of estimates is much less than the formula suggests. The maximum figure reported in the text assumes h = I.2.

85See Crafts, 'Productivity growth reconsidered'.

Table A3. I. Indices of industrial production (I9I3 = IOO)

Amended Best Guess Revised Best Guess

I700 I.79 I.92 I70I 2.19 2.II I702 I.50 I.85

I703 I.83 2.I6 I704 I.88 2.40 I705 I.98 2.35 I706 i.6i 2.02

I707 I.65 2.08 I708 i.88 2.I9 I709 I.89 2.I5 I7I0 I.79 I.77

I7II I.79 2.I0

I7I2 I.79 2.I2

I7I3 I.97 2.26 I7I4 2.o6 2.I8

I7I5 2.19 2.22 I7I6 2.40 2.37

I7I7 2.53 2.58 I7I8 2.49 2.52

I7I9 2.33 2.62 I720 2.42 2.52 I72I 2.37 2.44

I722 2.7I 2.68 I723 2.66 2.69 I724 2.I5 2.58 I725 2.54 2.63 I726 2.46 2.70 I727 2.42 2.66 I728 2.24 2.5I

I729 2.27 2.4I

I730 2.43 2.54

I73I 2.33 2.50

I732 2.37 2.53 I733 2.66 2.65 I734 2.34 2.64 I735 2.62 2.65 I736 2.59 2.69 I737 2.40 2.63 I738 2.80 2.67 I739 2.65 2.70

I740 2.42 2.57 I74I 2.22 2.64 I742 2.45 2.58


Table A3.I. continued

Amended Best Guess Revised Best Guess

I743 2.34 2.63 I744 2.69 2.69 I745 2.57 2.64 I746 2.75 2.69 I747 2.84 2.76 I748 3.10 2.82 I749 2.77 2.87 I750 3.05 2.97 I75I 3.o8 2.95 I752 3.07 3-03 I753 3.II 3.02

I754 3.o8 2.94 I755 3.II 2.99

I756 2.83 2.83 I757 2.92 2.98 I758 2.90 2.94 I759 2.84 2.99 I760 2.80 2.99 I76I 2.96 3.09 I762 2.84 3.05 I763 2.86 3.03 I764 3.04 3.22 I765 2.99 3.I3 I766 3.20 3.25

I767 3.47 3.42 I768 3.32 3.29 I769 3.52 3.43 I770 3.43 3.39 I77I 3.52 3.49 I772 3.64 3.57 I773 3.52 3.50 I774 3.I4 3.23 I775 3.26 3.32 I776 3.42 3.46 I777 3.43 3.5I I778 3.56 3.62 I779 3.26 3.38 I780 3.38 3.49 I78I 3.55 3.6I I782 3.49 3.65 I783 3.69 3.73 I784 4.00 3.95 I785 3.97 3.96 I786 3.94 3.93 I787 4.I3 4.I3 I788 4.12 4.I6 I789 4.26 4.20 I790 4.27 4.30 I79I 4.42 4.42 I792 4.74 4.66 I793 4.45 4.49 I794 4.36 4.47 I795 4.45 4.64 I796 4.60 4.78 I797 4-54 4.56 I798 4.65 4.7I I799 5.26 5.I3 I8oo 5.20 5.07 i8oi 4.87 4.87


Table A3. I . continued

Amended and Revised Best Guess I802 5.I4 I858 27.I I803 5.I9 I859 28.8 I804 5.36 i86o 30.4 I805 5.48 i86i 30.0 i8o6 5.52 I862 30.2 I807 5.74 I863 30.0 i8o8 5.46 I864 3I.9 I809 5.6o I865 33.9 i8io 6.og I866 34.9 I8II 6.40 I867 34.4 I8I2 6.02 I868 35.5 I8I3 6.07 I869 35.3 I8I4 6.I7 I870 38.4 I8I5 6.7I I87I 4I.3 i8i6 6.55 I872 42.5 I8I7 7.I6 I873 43.7 i8i8 7.46 I874 44.2 I8I9 7.2I I875 44.2 I820 7.40 I876 44.7 I82I 7.7I I877 45.4 I822 8.I3 I878 44.6 I823 8.56 I879 42.8 I824 9.02 i88o 48.2 I825 9.85 I88I 50.9 I826 8.99 I882 53.5 I827 IO.2 I883 54.5 I828 I0.9 I884 52.2 I829 IO.5 I885 50.4 I830 II.5 i886 49.9 I83I ii.6 I887 53.7 I832 Ii.6 I888 57.2 I833 I2.2 I889 60.9 1834 12.9 1890 6i.8 I835 I3.4 I89I 62.3 I836 I4.7 I892 59.I 1837 14.0 1 893 58.o I838 I 5.3 i894 6i.8 1839 i6.6 1 895 64.2 I840 I6.2 I896 68.8 I84I i6.5 I897 69.6 I842 I5.7 I898 72.8 I843 i6.6 I899 76.3 I844 I8.7 I900 76.4 I845 I9.7 I9OI 75.8 I846 I9.7 I902 76.6 I847 I9.I I903 75.5 I848 20.9 I904 76.2 1 849 21.2 I905 81.7 i850 2I.2 i906 85.9

i85I ~~22.1 190 88.7 I852 23.9 igo8 82.6 I853 25.6 I909 83.6 1854 25.6 1910 84.9

i855 ~~25.5 1911 90. 8 i856 27.3 I9I2 93.3 I857 28.4 I9I3 IOO.O

Sources: 'Amended Best Guess' is the CLM Best Guess Index amended for the period 1853- 1913 where it is now based on the index for industrial output excluding construction from Lewis, Growth and fluctuations, pp. 248-50. This also eliminates an error in the CLM index kindly pointed out to Crafts by Brian Mitchell: the data for ig06-13 had been incorrectly transcribed from the original source. For 'Revised Best Guess' see text, app. 3, and app. tab. A3.2.


Table A3.2. Relative sectoral size by value-added of sectors included in the Revised Best Guess index of industrial production, I700-i800 (per cent)

I700-I7I0: Coal: I5.i, Tin: 2.3, Cotton: ii.6, Silk: I5.i, Linen: 27.9, Sugar: i.o, Beer: i8.4, Malt: 5.8, Tobacco: 2.8.

I7II-2: Coal: I4.i, Tin: 2.I, Cotton: io.8, Silk: I4.i, Linen: 26.0, Sugar: 0.9, Beer: I7.I, Malt: 5.4, Tobacco: 2.6, Candles: 6.9.

I7I3-9: Coal: I3.4, Tin: i.9, Cotton: I0.3, Silk: I3.4, Linen: 24.8, Sugar: o.8, Beer: i6.3, Malt: 5.I, Tobacco: 2.5, Paper: I.2, Soap: 3.7, Candles: 6.6.

I720-I: Coal: II.3, Iron: I5.6, Tin: i.6, Cotton: 8.7, Silk: II.3, Linen: 20.9, Sugar: 0.7, Beer: I3.8, Malt: 4.3, Tobacco: 2.I, Paper: i.o, Soap: 3.I, Candles: 5.6.

I722-6: Coal: 6.8, Iron: 9.5, Tin: o.9, Cotton: 5.3, Silk: 6.8, Linen: I2.6, Sugar: 0.4, Beer: 8.3, Malt: 2.6, Tobacco: I.3, Paper: o.6, Hides and skins: 39.6, Soap: I.9, Candles: 3.4.

I727-38: Coal: 6.7, Copper ore: o.6, Iron: 9.4, Tin: o.9, Cotton: 5.2, Silk: 6.8, Linen: I2.5, Sugar: 0.4, Beer: 8.3, Malt: 2.6, Tobacco: I.2, Paper: o.6, Hides and skins: 39.5, Soap: I.9, Candles: 3.4.

I739-60: Coal: 4.6, Copper ore: 0.5, Iron: 6.5, Tin: o.6, Cotton: 2.8, Wool: 32.0, Silk: 4.6, Linen: 8.6, Sugar: 0.3, Beer: 5.8, Malt: i.8, Tobacco: o.9, Paper: 0.4, Hides and skins: 27.0, Soap: I.3, Candles: 2.3.

I76I-70: Coal: 4.6, Copper ore: 0.5, Iron: 6.5, Tin: o.6, Cotton: 6.7, Wool: 3I.9, Silk: 4.6, Linen: 8.6, Sugar: 0.3, Beer: 5.8, Malt: i.8, Tobacco: o.9, Paper: 0.4, Hides and skins: 23.2, Soap: I.3, Candles: 2.3.

I77I-9: Coal: 4.5, Copper ore: 0.4, Iron: 6.5, Copper goods: 0.5, Tin: o.6, Cotton: 6.7, Wool: 3I.8, Silk: 4.6, Linen: 8.5, Sugar: 0.3, Beer: 5.8, Malt: i.8, Tobacco: o.9, Paper: 0.4, Hides and skins: 23.1, Soap: I.3, Candles: 2.3.

I780-6: Coal: 4.5, Copper ore: 0.4, Iron: 6.5, Copper goods: 0.5, Tin: o.6, Cotton: 6.7, Wool yarn: I4.4, Wool cloth: I7.4, Silk: 4.6, Linen: 8.5, Sugar: 0.3, Beer: 5.8, Malt: i.8, Tobacco: o.9, Paper: 0.4, Hides and skins: 23.I, Soap: I.3, Candles: 2.3.

I787-8: Coal: 4.5, Copper ore: 0.4, Iron: 6.5, Copper goods: 0.5, Tin: o.6, Cotton: 6.7, Wool yarn: I4.4, Wool cloth: I7.4, Silk yarn: I.5, Silk cloth: 3.5, Linen: 8.5, Sugar: 0.3, Beer: 5.8, Malt: i.8, Tobacco: o.9, Paper: 0.4, Hides and skins: 23.I, Soap: I.3, Candles: 2.3.

I789-I800: Coal: 4.4, Copper ore: 0.4, Iron: 6.5, Copper goods: 0.5, Tin: o.6, Ships: 2.2, Cotton: 6.7, Wool yarn: I4.0, Wool cloth: I7.0, Silk yarn: I.4, Silk cloth: 3.o, Linen: 8.3, Sugar: 0.3, Beer: 5.7, Malt: I.7, Tobacco: o.9, Paper: 0.4, Hides and skins: 22.5, Soap: I.3, Candles: 2.2.

Notes: The weighting of sectors and construction of the index is described in app. 3; note that not all industry is covered by the index and the shares of sectors other than iron and cotton and all weights prior to I76I are inflated to compensate; they are not therefore estimates of actual value added shares. Sources: The new or revised series added to the CLM index are taken from Mitchell, British historical statistics, pp. 404- 5, 4I2-3, 4I5-6, and 462-4 except for linen which is based on data for imports of yarn from Schumpeter, English overseas trade statistics, tab. xvI, p. 30.


Footnote references Allen, R. C., 'Agriculture during the industrial revolution, I700-i850', in R. C. Floud and D. N.

McCloskey, eds., The economic history of Britain since I700, I (Cambridge, 2nd edn., forthcoming). Baines, E., History of the cotton manufacture in Great Britain (0835). Berg, M. and Hudson, P., 'Rehabilitating the industrial revolution', Econ. Hist. Rev., XLV (I992),

pp. 24-50. Blaug, M., 'The productivity of capital in the Lancashire cotton industry during the nineteenth century',

Econ. Hist. Rev., 2nd ser., xiii (i96i), pp. 359-91. Chapman, S. D., 'The cotton industry in the industrial revolution', in L.A. Clarkson, ed., The industrial

revolution: a compendium (i990), pp. I-64. Chapman, S. D. and Chassagne, S., European textile printers in the eighteenth century (i98i). Clark, J. C. D., Revolution and rebellion (Cambridge, i986). Crafts, N. F. R., 'British economic growth, I700-I83I: a review of the evidence', Econ. Hist. Rev., 2nd

ser., XXXVI (I983), pp. I77-99. Crafts, N. F. R., British economic growth during the industrial revolution (Oxford, I985). Crafts, N. F. R., 'British economic growth, I700-I850: some difficulties of interpretation', Exp. Econ.

Hist., XXIV (I987), pp. 245-68. Crafts, N.F. R., 'Real wages, inequality and economic growth in Britain, I750-I850: a review of recent

research', in P. Scholliers, ed., Real wages in nineteenth and twentieth century Europe (Oxford, i989), PP. 75-95.

Crafts, N. F. R., 'British industrialization in an international context', J. Interdisc. Hist., xix (i989), pp. 4I5-28.

Crafts, N. F. R., 'Productivity growth reconsidered', Econ. Pol., xv (forthcoming, I992). Crafts, N. F. R., Leybourne, S. J., and Mills, T. C., 'Trends and cycles in British industrial production',

J. R. S. S., ser. A, CLII (I989), pp. 43-60. Crafts, N. F. R., Leybourne, S. J., and Mills, T. C., 'Britain', in R. Sylla and G. Toniolo, eds., Patterns

of European industrialization (i99i), pp. I09-52. Crafts, N. F. R. and Mills, T. C., 'Trends in real wages in Britain, I750-I9I3', Exp. Econ. Hist., XXX,

(forthcoming, I993). Deane, P., 'The output of the British woollen industry', J. Econ. Hist., XVII (I957), pp. 207-23. Deane, P. and Cole, W. A., British economic growth, i688-i959 (Cambridge, i962). Ellison, T., The cotton trade of Great Britain (i886). Feinstein, C. H., 'National statistics, I760-I920', in C. H. Feinstein and S. Pollard, eds., Studies in

capital formation in the United Kingdom, I750-I 920 (Oxford, I988), pp. 259-47I . Harley, C. K., 'British industrialization before I84I: evidence of slower growth during the industrial

revolution', J. Econ. Hist., XLII (1982), pp. 267-89. Harris, J. R., The copper king (Liverpool, i964). Hoffmann, W. G., British industry, I700-I950 (Oxford, I955). Hoppit, J., 'Counting the industrial revolution', Econ. Hist. Rev., 2nd ser., XLIII (I990), pp. I73-93. Huberman, M., 'How did labor markets work in Lancashire? More evidence on prices and quantities

in cotton spinning, I822-I852', Exp. Econ. Hist., XXVIII (I991), pp. 87-I20. Innes, J., 'Jonathan Clark, social history and England's "ancien regime"', P. & P., II5 (I987), pp. 165-

200. Jackson, R. V., 'Government expenditure and British economic growth in the eighteenth century: some

problems of measurement', Econ. Hist. Rev., 2nd ser., XLIII (I990), pp. 2I7-35. Jackson, R. V., 'Rates of industrial growth during the industrial revolution', Econ. Hist. Rev., XLV

(I992), pp. I-23. Lewis, W. A., Growth and fluctuations, I870-I9I3 (I978). Mathias, P., The first industrial nation (i969). Matthews, R. C. O., A study in trade-cycle history: economic fluctuations in Great Britain, i833-42

(Cambridge, 1954). Mitchell, B. R., British historical statistics (Cambridge, i988). O'Brien, P. K., 'Do we have a typology for the study of European industrialization in the nineteenth

century?', J. Eur. Econ. Hist., xv (i986), pp. 29I-333. Pollard, S., 'A new estimate of British coal production, I750-I850', Econ. Hist. Rev., 2nd ser., XXXIII

(I980), pp. 2I2-35. Riden, P., 'The output of the British iron industry before I870', Econ. Hist. Rev., 2nd ser., XXX (I977),

pp. 442-59. Schumpeter, E. B., English overseas trade statistics, I697-I808 (I960). Stedman Jones, G., 'The changing face of nineteenth century Britain', Hist. Today, Oct. I99I, pp. 36-

40. Thomas, M., 'Accounting for growth, I870-I940: Stephen Nicholas and total factor productivity

measurements', Econ. Hist. Rev., 2nd ser., XXXVIII (I985), pp. 569-75. Ure, A., Cotton manufacture (I86o).


Von Tunzelmann, G. N., Steam power and British industrialization to i86o (Oxford, I978). Wrigley, E. A., 'Urban growth and agricultural change: England and the continent in the early modern

period', J. Interdisc. Hist., xv (I985), pp. 683-728. Wrigley, E. A., 'Men on the land and men in the countryside: employment in agriculture in early

nineteenth century England', in L. Bonfield, R. M. Smith, and K.Wrightson, eds., The world we have gained (Oxford, I987), pp. 295-336.

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