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The Rise and Fall of the Williamson Curve

Published online by Cambridge University Press:  03 March 2009

Charles Feinstein
Charles Feinstein
Affiliation:
Nuffield College, Oxford
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Type
Review Article
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The Journal of Economic History , Volume 48 , Issue 3 , September 1988 , pp. 699 - 729
Copyright
Copyright © The Economic History Association 1988

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References

The author is Reader in Recent Social and Economic History, University of Oxford, Nuffield College, Oxford, OXI INF. The paper was written in 1987 while I was a Visiting Scholar at Stanford University. I should like particularly to acknowledge the cooperation I received from Jeffrey Williamson. I am also grateful to Gregory Clark, Nick Crafts, Paul David, Anne Digby, Stanley Engerman, Leon Feinstein, Peter Lindert, Daniel Raff, Peter Solar, Peter Temin, and Mark Thomas for their extremely helpful comments on an earlier draft. None are responsible for any remaining errors of fact or interpretation; and some would, I know, wish me to say explicitly that they do not necessarily agree with either the substance or the style of this final version.

1 The main themes were stated earlier in Linder, Peter H. and Williamson, Jeffrey G., “English Workersapos; Living Standards during the Industrial Revolution: A New Look,” Economic History Review, 36 (02. 1983);Google Scholar and Williamson, Jeffrey G., “Urban Disamenitirs, Dark Satanic Mills, and the British Standard of Living Debate,” this JOURNAL, 41 (03. 1981), pp. 74–83.Google Scholar

2 Kuznets, Simon, “Economic Growth and Income Ineqality,” American Economic Review, 45 (03 1955), pp. 1–28.Google Scholar

3 Williamson, , book here under review[hereafter Inequality], p. 50.Google Scholar

4 Kuznets, Simon, “Economic Growth and Income Ineqality,” American Economic Review, 45 (03. 1955), p. 65.Google Scholar

5 Thus Williamson opens Part II (Kuznets, Simon, “Economic Growth and Income Ineqality,” American Economic Review, 45 (03. 1955), p.77) with the categorical Statement:“Part I has established that the industrial revolution generated inequality trends that appear to confirm the Kuznets curve…” and the first sentence of Part III (p.107) similarly begins: “Having documented a British Kuznets curve in Part I, how do I account for it?” (italics added).Google Scholar

6 For the American study, Williamson, Jeffrey G. and Lindert, Peter H., American Inequality: A Macroeconomic History (New York, 1980);Google Scholarthe quote comes from Williamson, , Inequality, p. 77.Google Scholar

7 The last of the Williamson indicators is based on size distributions of houses by number of windows assessed, derived from the window tax data. I have not looked closely at these estimates, but it is clear that a forbidding set of guesses and assumptions is required to convert the distributions of dwellings by numberof windows into corresponding distributions of rentals, and to convert these in turn to distributions of income. Confidence in the results was not enhanced by consideration of the many problems encountered with the relatively more straightforward exercise with the Inhabited House Duty data, see Section 111(a).

8 Notable earlier studies which have emphasized the broad stability of pay ratios in Britain, both in the nineteenth century and later, include Rowe, J. W.F., Wages in Practice and Theory (London, 1928)Google Scholar; Knoles, K. G. J. C. and Robertson, D. J., “Differences between the Wages of Skilled and Unskilled Workers,” Bulletin of the Oxford University Institule of Statistics, 13 (04. 1951)Google Scholar; Brown, E. H. Phelps and Hopkins, S. V., “Seven Centuries of Building Wages,” Economic 22 (08. 1955)Google Scholar; Routh, G., Occupation and pay in Great Britain, 1906–60 (Cambridge, 1965);Google Scholar and Brown, Henry Phelps, The Ineqality of Pay (Oxford, 1977).Google Scholar

9 The series is carried backn to the eighteenth century in Williamson, Jedffrey G., “The Structure of Pay Britan, 1710–1911,” in Uselding, P, ed., Research in Economic History, 7 (1982). The corresponding series for the earlier period, however, almost certainly suffer from precisely the same defects. In addition, it may be noted that Williamson uses one source for 1710, 1737, and 1755, a second for 1781, and a third from 1797 onwards; this is likely to have added significantly to the problems of comparability.Google Scholar

10 It should be emphasized that this striking contrast is not the result of comparing individual series with an average which has been smoothed by offsetting fluctuations. None of the seven constituents of the average display the volatility which figures so prominently in each of the five separate series.

11 The exception is Williamson's series for the annual earnings of clergymen, which after rising from £272 in 1861 to £337 in 1891, drops by 40 percent to £206 in 1911. This movement, however, can be attributed largely to the fact that the estimates for 1861 and 1911 are net of deductions for various payments made by clergymen out of their gross salaries, whereas the 1891 estimate is gross. (The intervening years are obtained by interpolation between these benchmarks.) For discussion of this point, and general comments on other deficiencies in the underlying sources, see Orr, K. W., “Change in the Methods of Financing of the Church of England, c. 1870–1914, with special reference to theparochial Clergy” (D. Phil. Thesis, University of Oxford, 1983), pp. 9–29Google Scholar, estimates for both gross and net income show a slight rise from 1891 to 1911 (Kuznets, Simon, “Economic Growth and Income Ineqality,” American Economic Review, 45 (03. 1955) pp. 189–90). I am indebted to E. Newell for drawing my attention to this excellent study.Google Scholar

12 The Estimates are also the source for three of the earnings series for unskilled occupations. These display some of the same problems as those documented below for the skilled (see pp. 706–709 and fn. 22), but in much lees extreme form. The principal source for the “well-behaved” occupations is, by contrast, the long-established data on earnings published by Bowley, A. L. and Wood, G. H. in a famous series of articles in the Journal of the Royal Statistical Society; they are supplemented by two new series compiled by Williamson for teachers and clergymen. The latter is subject to the reservations noted in fn. II.Google Scholar

13 A friendly critic of an earlier draft has noted that incredulity is no substitute for hard evidence. I accept this, but can only report if nineteenth-century legal earnings were marked by such volatility it has escaped attention of the historians of the profession. For solicitors, see, for example, Christian, E. V. B., A Short History of Solicitors (London, 1896), pp. 172–202Google Scholar; Kirk, Harry, Portrait of a Profession (London, 1976), pp. 87–92Google Scholar and Offer, Avner, Property and Politics, 1870–1914 (Cambridge, 1981), pp. 11–22, 61Google Scholar. For the smaller number of barristers, a recent sutudy reports a pattern quite unlike that suggested by Williamson: “After 1820 incomes levelled off and remained stationary until the mid-1830s. After 1835 incomes declined. By 1850 incomes had begun to rise again and by the second half of the decade they reached new levels which were maintained until 1875” (Duman, Daniel, The Judicial Bench in England, 1727–1875 [London, 1892], pp. 105–11).Google Scholar

14 Loudon, IrvineMedical Care and the General Practitioner 1750–18, (Oxford, 1986), pp. 249–66Google Scholar. For very similar evidence for the late nineteenth century, see Peterson, M. Jeanne, The Medical Profession in Mid-Victorian London (Berkeley, 1978). pp. 209–21. Her main conclusion is that medical incomes were at roughly the same level in 1870 and 1913. 1 am indebted to my advisor on the social history of medicine, Anne Digby, for guidance on this topic.Google Scholar

15 There is no continuous series for privately employed clerks. The statement in the text is based on the fragmentary data in sources such as Bowley, A. L., (Sec.) “Report of the Committee[of the British Association] on the Amount and Distribution of Income… below the Income Tax Exemption Limit in the United Kingdom,” Journal of the Royal Statistical Society, 74 (12. 1910), p. 63Google Scholar; Klingender, F. D., The Condition of Clerical Labour in Britain (London, 1935), pp. 1–24Google Scholar; Routh, G., “Civil Service Pay, 1875 to 1950,” Economica, 21 (09. 1954), pp. 207–13CrossRefGoogle Scholar; Banks, J. A., Prosperity and Parenthood (London, 1954), pp. 105–7Google Scholar; Feinstein, C. H., National Income Expenditure and Output of the United Kingdom 1855–1965, (Cambridge, 1972), pp. 172–73Google Scholar; and Anderson, Gregory, Victorian Clerks (Manchester, 1976).Google Scholar

16 Routh, , “Civil Service Pay” p. 211.Google Scholar

17 The data are taken from the Inland Revenue Reports and cover both higher grade government offcials and those employed by public companies. The average assessment was adjusted on the basis of Stamp, J. C., British Income and Property (London, 1916), pp. 481, 488, to allow for the rise in the exmption limit from £100 to £150 in 1876 and the further rise to £ 160 in 1894.Google Scholar

18 Since this general comment was written, a brilliant reconstruction of the Pay series for lawyers and doctors has been published by Jackson, R. V., “The Structure of Pay in Nineteenth-Century Britain,” Economic History Review, 40 (11. 1987), pp. 561–70. This shows definitively that Williamson's samples for these two professions are absurdly unrepresentative.CrossRefGoogle Scholar

19 Because there were very few doctors, lawyers, or engineers in the public sector Williamson is forced to rely on very small samples, often fewer than 20; see Jackson, , “Structure of Pay”, pp. 564–66. The averages for these occupations are thus very sensitive to a few extreme values, and to small changes in the relative numbers at the upper or lower end of the income range.Google Scholar

20 If skilled and unskilled pay in any occupation are respectively, Si and Ui and the corresponding (fixed) weights are »i and θi, then the skill ratio in year I is: (∑ »iS i)/(∑ θiU i1), and an index of the ratio in year 2 relative to year I can be written as [(∑ »iS i2)/(∑ »S i1)]. [( ∑θU i1)/(∑ θiUi1)/(∑θiU i2)]. The contribution of each skilled occupation to the change in the pay ratio can thus be expressed as: (S i1/∑»iS i1). (S i2/S i1.). »i with a corresponding expression for the unskilled. The effect of the exceptionally high level of earnings attributed to lawyers and other occupations with a low weight is thus that it permits S i, to rise steeply relative to ∑ »iS i, at the same time as the big swings in their earnings contribute to a high value for the ratio S i2/S i1.

21 If, as is usually the case, skill is measured simply by pay, then there is little doubt that coal hewers should be classified as skilled. In 1913 they were the highest paid of the five grades of skilled workers recorded by Rowe, (Wages in Practice and Theory, p. 42) in his classic study of skill differentials. If Williamson has some other criterion in mind, it should be specified and defended. The issue is particularly important since miners' earnings rose exceptionally rapidly between 1881 and 1911, and their inclusion with the unskilled thus makes a major contribution to the decline of the pay ratio over this period.Google Scholar

22 The preceding comments have concentrated on the issue of the trends and fluctuations in the earnings series. It should also be noted, however, that the sampling and other problems already highlighted must also cast doubt on the level of earnings given for many occupations. Among the skilled, this is clearly the case for lawyers, doctors, and engineers. Among the unskilled, the estimates imply, for example, that for most of the century an unskilled messenger or porter was earning more than a skilled worker in manufacturing. Williamson's estimates of the accumulation of skill at selected dates (see below, p. 726–727) are based directly on differences in the levels of pay shown by these earnings series, and will thus be adversely affected by any errors in the levels.Google Scholar

23 Williamson, , Inequality, pp. 36–43. The estimates given in the text are based on my calculation of the level of the inequality index in row 2 of Table 3. Williamson, ,Google Scholaribid., p. 41 gives only the changes in the index.

24 Earlier studies of the distribution of earnings were based on the Wage Inquiries of 1886 and 1906. See, in particular, the work by Bowley, A. L., The Change in the Distribution of the National Income, 1880–1913 (Oxford, 1920)Google Scholar and Wages and Income in the United Kingdom since 1860 (Cambridge, 1937)Google Scholar. For the extension to later periods, see Ainsworth, R. B., “Earnings and Working Hours of Manual Wage-Earners in the United Kingdom in 1938”, Journal of the Royal Statistical Society, 112 (Part I, 1949)Google Scholar; Routh, , Occupation and PayGoogle Scholar; and Thatcher, A. R., “The Distribution of Earnings of Employees in Great Britain,” Journal of the Royal Statistical Society, 130 (Part 11, 1968)Google Scholar. See also Brown, Phelps, Inequality of Pay, for general discussion of the “remarkable stability …of the distribution of earnings of British male manual workers, from 1886 to the present day” (p. 319).Google Scholar

25 Williamson, , Inequality, p. 40.Google Scholar

26 Exclusion of the professions would not be sufficient to obtain a reliable measure of the changing distribution of earnings. There are several other aspects of the data which are unsatisfactory. In particular, the series for clerks in the private sector, already criticized in Section 11 (a), accounts for much of the remaining variation in the inequality index.

27 Williamson, , “Distribution of Earnings,” Appendices A and B.Google Scholar

28 Williamson, , Inequality, p. 72.Google Scholar

29 An earlier, and slightly different version of IHD had been introduced in 1778 and was repealed in 1834. The account of Schedule A and IHD given in the text ignores certain minor complications of no relevance to these estimates; see Stamp, , British Incomes and Property, pp. 107–41, for the full story.Google Scholar

30 I have recently done this for another purpose, and the procedure is explained in Feinstein, Charles H. and Pollard, Sidney, eds., Studies in Capital Formation in the United Kingdom, 1750–1920 (Oxford, 1988), pp. 413–15.Google Scholar

31 Williamson, , Inequality, pp. 224–27.Google Scholar

32 Thatcher, A. R., “The Distribution of Earnings of Employees in Great Britain,” Journal of the Royal Statistical Society, 130 (Part 11, 1968), p. 61. The two additional estimates, for 1823 and 1915, add nothing of substance to the story.Google Scholar

33 Thatcher, A. R., “The Distribution of Earnings of Employees in Great Britain,” Journal of the Royal Statistical Society, 130 (Part 11, 1968), p. 225.Google Scholar

34 Mitchell, B. R. and Deane, P. M., Abstract of British Historical Statistics (Cambridge, 1962), pp. 236–38. From 1874 the Inland Revenue Reports give not only the total number and GAV of the exempt dwelling houses, but also a subdivision into three classes: average GAV less than £10, £10 and under £15, and £15 and under £20. For earlier years estimates can be derived by the procedure referred to in fn. 30.Google Scholar

35 The scale of the resulting error can be illustrated by the estimate for 1830 reproduced by Williamson as a specimen of his procedure (Inequality, p. 229). The first class, “Untaxed,” shows average income at 1890/1 prices as £50.4. This is calculated from (In R - in α)/bgr;, with R = £5.0, In α = 0.7141, and β = 0.83. Williamson's price index for 1830 (1890/1 = 100) is 126.6, and if R is first deflated, as it is for all other classes, average income is cut to £37.94. Total income is thus reduced from £104.000m to £78.275m.Google Scholar

36 Williamson, , “Two Centuries of British Income Inequality,” p. 23.Google Scholar

37 Thatcher, A. R., “The Distribution of Earnings of Employees in Great Britain,” Journal of the Royal Statistical Society, 130 (Part 11, 1968), pp. 29–37Google Scholar; Inequality, p. 58.Google Scholar

38 The Pareto coefficient is a measure of the relationship between given income levels and the number of persons with incomes in excess of those levels. If X = any given income, and N = the number of persons with incomes of X or more, the Pareto coefficient, b, is given by the expression: In N = In a – b In X.

39 Williamson, , Inequality, pp. 62–63.Google Scholar

40 Thatcher, A. R., “The Distribution of Earnings of Employees in Great Britain,” Journal of the Royal Statistical Society, 130 (Part 11, 1968), p. 65.Google Scholar

41 Since the distributions are available annually, the effect of the two changes in classification can be measured quite precisely. The inverse Pareto coefficient was 0.835 in 1865/66. The first fall occurs in 1866/67, when the exclusion of public companies reduces it abruptly to 0.766. The second occurs in 1898/99, when the exclusion of firms reduces the coefficient to 0.602, compared to 0.729 a year earlier. The first discontinuity is unavoidable; the second is not, since a separate distribution is given for firms.

42 Stamp, , British Incomes and Property, p. 238. There are a number of other factors discussed by Stamp (pp. 238–56) which may have affected the distribution to a lesser degree, for example, the introduction of abatements in 1863 and the resultant classification of net rather than gross assessments.Google Scholar

43 The estimates derived from Baxter and Bowley and Stamp were initially given in Williamson, Jeffrey G., “British Income Inequality, 1688–1913: Political Arithmetic and Conventional Wisdom” (unpublished manuscript, University of Wisconsin, 1978)Google Scholar. Revised estimates based on Patrick Colquhoun were given in Lindert, Peter H. and Williamson, Jeffrey G., “Revising England's Social Tables, 1688–1812,” Explorations in Economic History, 19 (10 1982)CrossRefGoogle Scholar. The combined results were presented and analyzed in Lindert, Peter H. and Williamson, Jeffrey G., “Reinterpreting Britain's Social Tables, 1688–1913,” Explorations in Economic History, 20 (01 1983)CrossRefGoogle Scholar; and are briefly discussed in Williamson, , Inequality, pp. 65–73.Google Scholar

44 Williamson, , Inequality, pp. 67, 69.Google Scholar

45 Soltow, Lee, “Long-Run Changes in British Income Inequality,” Economic History Review, 21 (04. 1968), p. 22.CrossRefGoogle Scholar

46 One example of the problems associated with these social tables must suffice. For incomes subject to tax R. Dudley Baxter assumed that the distribution of assessments under Schedule D could be taken as representative of the distribution of all incomes. But, as already emphasized in Section 111(b), the basis of the Schedule D classification was not a distribution of incomes. Each taxpayer could have more than one assessment, and each assessment could relate to more than one taxpayer. The latter is likely to have been particularly important in 1867, when unincorporated firms were still the most common form of enterprise, and each partnership assessment would cover the income of at least two partners. There is also no reason to assume that the distribution of other forms of income was similar to that of income assessed under Schedule D.

47 In Baxter's original estimates the taxpaying class were also enumerated individually, but Williamson replaced this by Stamp's estimate of the actual number of taxpayers. Since the Inland Revenue treated families as a single unit for tax purposes, this is the appropriate definition for comparison with Colquhoun. It means, however, that the degree of inequality within the 1867 distribution is appreciably enhanced, since income at the upper end of the distribution is concentrated in families, while that at the lower end is dispersed over individuals.

48 Note also that Williamson uses the distribution given by Baxter without any recognition of the peculiarly hybrid nature of his size classes. These were based on the earnings of adult males, but also included women and juveniles employed in the same range of occupations. For example, Baxter's subdivision IV, lower skilled labor, includes 1,000,000 adult males with weekly earnings of 21s to 23s, 300,000 women with weekly earnings of 10s, and 540,000 boys and girls earning only 6s to 7s 6d. In addition, over a million female domestic servants, with earnings of 11s to 14s, are allocated to this class. See Baxter, R. Dudley, The National Income (London, 1868) p. 94. Such heterogeneous groups should surely not be treated as single-size classes for the purpose of calculating measures of distribution.Google Scholar

49 Bowley, , Wages and Incomes, p. 46Google Scholar. For the original estimate, see Mackenzie, W. A., “Changes in the Standard of Living in the United Kingdom, 1860–1914,” Economica, 3 (10. 1921), pp. 211–17.CrossRefGoogle Scholar

50 Mackenzie, , “Changes in the Standard of Living,” pp. 215–16.Google Scholar

51 Bowley, , “Report on the Amount and Distribution of Income,” pp. 63, 66.Google Scholar

52 I refer here and elsewhere to the estimates “without paupers”. As Williamson notes, there are massive problems of definition and estimation still to be resolved before estimates can be made “with paupers”.

53 This overstates the true number of families, but the same assumption is made below for the 1913 estimate.

54 The only other possibility with the data available would be to assume that the earnings of women and children were directly proportional to those of the male head of household. Since it seemed likely that the opposite would be true in many cases (that is, in families where the husband had below-average pay, the wife would be forced to compensate for this by seeking relatively higher wages), the assumption of equal distribution was thought preferable. In any event, comparability is again preserved by making the same assumption for 1913.

55 Routh, , Occupation and Pay, pp. 52, 166–68.Google Scholar

56 Williamson, , Inequality, p. 155.Google Scholar

57 For example, Williamson, Jeffrey G., “The Impact of the Irish on British Labor Markets During the Industrial Revolution,” this JOURNAL, 46 (09 1986) pp. 693–720; and “The Impact of the Corn Laws Just Prior to Repeal”, Harvard Institute for Economic Research, Discussion Paper No. 1279 (1986).Google Scholar

58 Williamson, , Inequality, p. 160.Google Scholar

59 The debate has already started, though mainly in relation to the period of the industrial revolution. See for example, Heim, Carol E. and Mirowski, Philip, “Interest Rates and Crowding-Out during Britain's Industrial Revolutiion,” this JOURNAl, 47 (03. 1987), pp. 117–39Google Scholar: the reply by Williamson, , “Interest Rates and Crowding-Out during Britain's Industrial Revolution,” this JOURNAL, 47 (03 1987), pp. 214–16Google Scholar; N. F. R. Crafts, “British Economic Growth, 1700–1850; Some Difficulties of Interpretation,” Jeffrey G. Williamson, “Debating the British Industiral Revolution,” Mokyr, Joel, “Has the Industrial Revolution Been Crowded Out? Some Reflections on Crafts and Williamson,” Explorations in Economic History, 24 (07 1987), pp. 245–68, 269–92, 293–319.CrossRefGoogle Scholar

60 Williamson, , Inequality, p. 247.Google Scholar

61 This is effectively the same as the procedure used by Williamson to calculate the total factor productivity growth rates for 1861 to 1911 ( Williamson, Jeffrey G., “The Impact of the Irish on British Labor Markets During the Industrial Revolution,” this JOURNAL, 46 (09 1986), pp. 249–50). The calculation is as follows: the per annum growth rates for the aggregate supplies of labor and capital are given as 1.40 percent and 2.50 percent (p. 247). The shares taken by the agricultural sector in 1821 and 1861 repsectively are given as 0.284 and 0.275 for labor, and 0.473 and 0.2 15 for capital (pp. 243, 238). The implied per annum growth rates for these two inputs are thus 1.32 percent and 0.50 percent, and the growth rate for the third input, farm land, is given as 0.03 percent. These inputs can then be weighted by their shares in total income of the sector (given on p. 241) to obtain a growth rate for total agricultural inputs of 0.81 percent per year. The growth rate for output is taken to be 1.49 percent (p. 130), giving a productivity growth rate for agriculture of 0.68 percent per year.Google Scholar

62 See Crafts, , “British Economic Growth,” pp. 248–56, and Mokyr, “Has the Industrial Revolution Been Crowded Out?” pp. 305–12 for further discussion of this topic.Google Scholar

63 Williamson, , Inequality, p. 250.Google Scholar

64 I have very strong reservations about the method used to calculate these initial estimate of growth in skills per worker ( Williamson, Jeffrey G., “The Impact of the Irish on British Labor Markets During the Industrial Revolution,” this JOURNAL, 46 (09 1986), pp. 232–36)Google Scholar. See, among other things, the comment in fn. 22, and the more substantial comment in Jackson, R. V., “Industrialisation and the Structure of Pay: Was there a Kuznets Curve in Nineteenth Century Britain?” Australian National University, Working Papers in Economic History, (07 1987), pp. 22–24. I have suppressed these reservations, however, in order to concentrate on the subsequent stages in Williamson's estimation process.Google Scholar

65 Case B rates are lower because agricultural labor is growing more slowly in the first period and falling absolutely in the second.

66 Williamson, , Inequality, p. 237 for the first, p. 248 for the second.Google Scholar

67 Williamson, Jeffrey G., “The Impact of the Irish on British Labor Markets During the Industrial Revolution,” this JOURNAL, 46 (09 1986), p. 246.Google Scholar

68 The value of manufacturing output at current prices in 1821 and 1861 was reconstructed from the sources quoted by Williamson, , “The Impact of the Irish on British Labor Markets During the Industrial Revolution,” this JOURNAL, 46 (09 1986), p. 239.Google Scholar

69 Value added in services was based on an estimate by Deane, P. and Cole, W. A., British Economic Growth, 1688–1959 (Cambridge, 1962), p. 166. The total wage bill in the sector was then independently estimated by Williamson, and the share of capital obtained as a residual. The trouble with this procedure is that the Deane and Cole estimate was itself the sum of income from employment and profits. It follows logically that any revision to one of their components must be carried through into their total. The extent of the problem can be seen in the results for 1891. The Deane and Cole estimate gives the shares of labor and capital as 68 percent and 32 percent, whereas the corresponding Williamson estimates are 48 percent and 52 percent.Google Scholar

70 Williamson, , Inequality, pp. 113–4, 118–9.Google Scholar