Bowley, Arthur Lyon

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Bowley, Arthur Lyon



Arthur Lyon Bowley (1869–1957), British statistician, was born at Bristol and brought up in a conventional and religious family. Before he went to Trinity College, Cambridge, in 1888 with a major scholarship in mathematics, he spent nine years at Christ’s Hospital, a boarding school of a strictly religious foundation where pupils wore a traditional costume and were subject to spartan conditions. The school left a lasting impression on his character; later in life he was governor of the school for some years.

Bowley followed a conventional course in mathematics at Cambridge, graduating as a wrangler in 1891, but an interest in economics and social problems, which was to be the mainspring of his life’s work, was already evident in his undergraduate days. He was in contact with Alfred Marshall and others active in the developing social sciences, and he was deeply affected, not so much by refinements of economic analysis as by the problems of social reform in Britain at the end of the century.

In studying these problems Bowley used both contemporary and historical material. His first work was A Short Account of England’s Foreign Trade in the Nineteenth Century (1893), for which he received the Cobden Prize at Cambridge in 1892. Foreign trade was a subject on which he continued to write throughout his life, but a more important early interest was the relation between movements of wages and prices, the subject of the first paper he read to the Royal Statistical Society in March 1895 (1895a). From 1895 to 1906 the Journal of the society and the more recently established Economic Journal published many papers by him on this topic, sometimes by Bowley alone and sometimes with G. H. Wood as coauthor. Bowley approached the subject with statistical and historical care verging on the pedantic, yet at the same time with a deep and sympathetic appreciation of the human problems involved.

It was on Marshall’s recommendation that Bowley was invited to join the small and mainly part-time staff of the London School of Economics when the first session began in 1895. Thus was laid the main path of his professional career. Over a period of more than forty years, until his retirement in 1936, Bowley taught statistics to successive generations of students of the social sciences at the school. He developed an intimate friendship with Edwin Cannan and remained to take his place as an elder statesman in a large and distinguished faculty of economists, historians, and social and political theorists. He was never a socialist in the sense of Webb and other founding fathers of the school, but as a good liberal he found the senior common room a congenial and stimulating back-ground to his activities in teaching and research.

The London School of Economics, although increasingly the locus of his work, did not for many years provide Bowley with his livelihood. In 1895, when living and teaching mathematics at a school in Leatherhead, he bicycled from there on the Wednesday half holidays to lecture at the London School in the early evening. Later, from 1900 to 1913, he was a member of the mathematics staff at University Extension College, Reading, and remained as a lecturer in economics there until 1919. Meanwhile he became a part-time reader in statistics at the London School in 1908, receiving the title of professor in 1915. It was only in 1919, with the establishment of a chair in statistics in the University of London, of which he was the first holder, that he became a full-time member of the school’s faculty.

As a mathematician Bowley was competent without being very original, and he became increasingly old-fashioned in his mathematical formulations. He published relatively little, and nothing of real substance, either in mathematical statistics or in mathematical economics, although both fields developed rapidly in very exciting directions in his middle and later life. Much of his work was in mathematical form as a matter of convenience, but the mathematics itself was incidental to his main purposes. First and foremost Bowley was a practitioner in applied statistics, with the whole of the social sciences as his field, and for most of his career he had to make bricks with very little straw. Always a severe critic of British official statistics, and highly respected in official quarters, he was called upon far too seldom to advise on the development of government statistics. British economic and social statistics in the 1920s and 1930s would undoubtedly have been improved, particularly by the use of sampling techniques, if he had had more to do with them. His main influence was through his private researches and in discussions at the international level.

There can be little doubt that Bowley’s major contribution was to the development of sampling techniques and their application to economic and social studies. While he was forming his ideas in the 1890s, the great debate on the “representative method” was taking place among official statisticians in Europe and the United States. It was from these discussions against the rather narrow back-ground of official statistics that the modern corpus of sampling techniques developed, with applications in all fields of scientific inquiry. Anders N. Kiaer (1838–1919), the distinguished chief of the Norwegian Bureau of Statistics for 46 years, led the case for sampling at a series of sessions of the International Statistical Institute from 1895 (Bern) to 1901 (Budapest). He was at first opposed by a majority of leading official statisticians, but his ideas rapidly gained ground, being greatly supported by the report of Carroll D. Wright, at Budapest, on sampling experience in the U.S. Department of Labor. Bowley, elected to the institute in 1903, was immediately attracted by the possibilities of the “representative method.” With characteristic care, he explored for himself both the appropriate mathematical formulation of sampling precision and the best ways of interpreting the results of sample surveys to laymen.

Between 1912 and 1914 Bowley directed sample surveys of working-class households in five English towns, and in presenting his results in Livelihood and Poverty (Bowley & Burnett-Hurst 1915), he was far ahead of his time in explaining both the method and the errors of sampling. He devoted a chapter to the four sources of error: incorrect information, loose definitions, bias in selection of sample, and the calculable errors of sampling. It is true that he did not distinguish the method of cluster or systematic sampling he adopted (selection of 1 in n down a listing of the frame) from simple random sampling. Even so, his exposition of 1915 would have been readily accepted two generations later.

It was only appropriate, therefore, that Bowley became a member of the committee set up by the International Statistical Institute in 1924, presenting their “Report on the Representative Method in Statistics” (Jensen 1926) at the Rome session in 1925. Bowley’s hand is clearly visible in the major recommendation “that the investigation should be so arranged wherever possible, as to allow of a mathematical statement of the precision of the results, and that with these results should be given an indication of the extent of the error to which they are liable” (Jensen 1926, p. 378), as well as in Annex A to the report “Measurement of the Precision Attained in Sampling” (1926a). Bowley himself continued to practice what he preached, notably in his resurvey of the five English towns published in Has Poverty Diminished? (1925) and in The New Survey of London Life and Labour, Volume 3 (1932a; 1932b) and Volume 6 (1934).

Another pioneering work undertaken by Bowley was the estimation of the distribution of national income, a task in which he was in the end rather less successful than might have been expected. His first essays were “The Division of the Product of Industry” and “The Change in the Distribution of the National Income: 1880−1913.” Later he worked with Josiah Stamp on the more elaborate “The National Income: 1924” (see Bowley 1919–1927) and with the National Institute of Economic and Social Research on Studies in the National Income: 1924–1938 (1942), a series that was curtailed by the outbreak of World War n. This work was a natural development of his early interest in wages and of his continuing concern with the redistribution of income as a tool in social reform. In the years between the two world wars he found British data quite inadequate for his purpose; economists did not agree on even the concept of national income. His work was influential when the first official estimates of the British national income were made, under the inspiration of J. M. Keynes, during World War n. But it was not in his careful and precise nature to take undue risks in handling scattered data. This he left to others, notably to the more adventurous, almost buccaneering, spirit of Colin Clark.

A third area in which Bowley’s pioneering was influential was his regular reporting on and analysis of the current economic position for the London and Cambridge Economic Service. This service began publication as a private venture, dependent on subscriptions for its bulletins, in January 1923. At first it was a cooperative project with the Harvard University Committee on Economic Research, which had issued its Harvard Economic Service bulletins for some time, and the aims were set out by William H. Beveridge in an introductory article on the study of business cycles. Bowley was the first editor of the service, serving in this capacity for more than twenty years, until 1945, and continuing as a regular contributor until 1953. Under his guidance the service was soon set on a very profitable course of its own, independent of its Harvard parent (which failed to survive the crisis of 1929) and of various schools of business cycle research.

Two characteristics of Bowley as an editor were outstanding. One was the skill with which he listened at editorial meetings to the diverse and out-spoken views of economists before writing his own pithy assessment of the economic position in order to represent just as much as, and no more than, the majority of economists could agree upon at that moment. The other was his conviction that any analysis of the present or forecast of the future was dependent on long runs of carefully prepared statistical series covering the whole range of economic and social matters. He and his research associates were indefatigable in designing and improving index numbers and in devising ways of presenting them most effectively. From the beginning he showed his series in graphical form, often by the use of ratio scales and often after adjustment for seasonal variations. He was one of the earliest champions of these now well-recognized devices. In these and other aspects he never shirked the task of explaining highly technical matters to a lay public.

Bowley was an effective if rather dour committeeman, and he held many offices, in the British Association, in the Royal Statistical Society, and in the International Statistical Institute, among others. He received many honors, which culminated in his appointment as knight bachelor soon after his eightieth birthday.

R. G. D. Allen

[For discussion of the subsequent development of Bowley’s work in sampling, seeEconomic data; Index numbers; Sample surveys.]


(1893) 1922 A Short Account of England’s Foreign Trade in the Nineteenth Century: Its Economic and Social Results. 3d ed. London: Allen & Unwin.

1895a Changes in Average Wages (Nominal and Real) in the United Kingdom Between 1860 and 1891. Journal of the Royal Statistical Society 58:223–278.

1895b Comparison of the Rates of Increase of Wages in the United States and in Great Britain: 1860-1891. Economic Journal 5:369–383.

1897 Relations Between the Accuracy of an Average and That of Its Constituent Parts. Journal of the Royal Statistical Society 60:855–866.

(1900) 1937 Wages and Income in the United Kingdom Since 1860. Cambridge Univ. Press.

(1901) 1937 Elements of Statistics. 6th ed. New York: Scribner; London: King.

(1910) 1951 An Elementary Manual of Statistics. 7th ed. London: Macdonald & Evans.

1911 The Measurement of the Accuracy of an Average. Journal of the Royal Statistical Society 75:77–88.

1915 Bowley, Arthur L.; and Burnett-Hurst, A. R. Livelihood and Poverty: A Study in the Economic Conditions of Working-class Households in Northhampton, Warrington, Stanley and Reading. London: Bell.

(1919–1927) 1938 Three Studies on the National Income. London School of Economics and Political Science. → Contains “The Division of the Product of Industry”; “The Change in the Distribution of National Income: 1880–1913,” by Arthur L. Bowley; and “The National Income: 1924,” by Arthur L. Bowley and Josiah Stamp.

1924 The Mathematical Groundwork of Economics: An Introductory Treatise. Oxford: Clarendon.

1925 Bowley, Arthur L.; and Hogg, Margaret H. Has Poverty Diminished? A Sequel to Livelihood and Poverty. London: King.

1926a Measurement of the Precision Attained in Sampling. International Statistical Institute, Bulletin 22, part 1:6–62.

1926b The Influence on the Precision of Index-numbers of Correlation Between the Prices of Commodities. Journal of the Royal Statistical Society 89:300–319.

1928 Notes on Index Numbers. Economic Journal 38: 216–237.

1930a Area and Population. Pages 58–83 in London School of Economics and Political Science, The New Survey of London Life and Labour. Volume 1: Forty Years of Change. London: King.

1930b London Occupations and Industries. Pages 315–340 in London School of Economics and Political Science, The New Survey of London Life and Labour. Volume 1: Forty Years of Change. London: King.

1932a The House Sample Analysis. Pages 29–96 in London School of Economics and Political Science, The New Survey of London Life and Labour. Volume 3: Survey of Social Conditions: 1. The Eastern Area. London: King.

1932b Bowley, Arthur L.; and Smith, H. Llewellyn. Overcrowding. Pages 216–253 in London School of Economics and Political Science, The New Survey of London Life and Labour. Volume 3: Survey of Social Conditions: 1. The Eastern Area. London: King.

1934 The House Sample Analysis. Pages 29–117 in London School of Economics and Political Science, The New Survey of London Life and Labour. Volume 6: Survey of Social Conditions: 2. The Western Area. London: King.

1935 Allen, Roy G. D.; and Bowley, Arthur L. Family Expenditure: A Study of Its Variation. London School of Economics and Political Science, Studies in Statistics and Scientific Method, No. 2. London: King.

1942 Bowley, Arthur L. (editor). Studies in the National Income: 1924–1938. Cambridge Univ. Press.


Jensen, Adolph 1926 Report on the Representative Method in Statistics. International Statistical Institute, Bulletin 22, part 1:359–380.

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Bowley, Arthur Lyon

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