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Discussion Paper New Series

A study of the methodology of Arthur Lyon Bowley and Alfred Marshall

Discussion Paper New Series No.2015-2 March 2015

Masashi KONDO [email protected]

School of Economics

Osaka Prefecture University

Sakai, Osaka 599-8531, Japan A study of the methodology of Arthur Lyon Bowley and Alfred Marshall

Masashi KONDO1

Abstract

While the works of T.R. Malthus, W.S. Jevons, and F.Y. Edgeworth have long garnered scholarly attention, this is not the case for A. Marshall (1842–1924) and A.L. Bowley (1869–1957). This paper fills that gap. I examine the statistical methodology of Bowley, a follower of Marshall. I discuss his early work and Marshall’s influences on him. He was more a follower of Marshall’s applied economics than a theoretical economist like Keynes (1883–1946) or Pigou (1877–1959). Indeed, he applied theories from statistics and economics to contribute to the body of knowledge on social sampling.

Keywords: Cambridge School, Alfred Marshall, Arthur Lyon Bowley, methodology

1. Introduction Throughout the history of statistical thought, the works of T.R. Malthus (1766– 1834), W. S. Jevons (1835–1882), and F.Y. Edgeworth (1845–1926) have garnered scholarly attention. However, the equal contributions of A. Marshall (1842–1924) and A.L. Bowley (1869–1957) have received relatively insufficient attention in comparison. Given this gap in the literature, this paper examines the statistical methodology of Bowley, a follower of Marshall and a developer of his economic theories. It was generally said that Marshall had formulated Ricardo’s and Mill’s economic theories early in his career, therefore it seems as though he might have employed a deductive methodology. However, throughout his academic career, from his days as a young scholar to late in his life, Marshall was interested in research factories and in industry in the UK and the US, and he collected and analysed data,

1 Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku Sakai-city Osaka 599-8531, Japan. (E-mail [email protected]) Tel +81- 72-254-9558

1 statistics, and facts on these topics. In particular, he placed high value on these kinds of works in addition to attaching great importance to his own research. Under Marshall’s influence, Bowley considered the application of statistics to the social sciences for the improvement of society. In this way, he contributed to the development of applied economics, suggesting that he was more a follower of Marshall’s applied economics than a theoretical economist like Keynes (1883– 1946) or Pigou (1877–1959). Indeed, he applied theories from statistics and economics to contribute to the body of knowledge on social sampling. However, Bowley did not always receive appropriate scholarly recognition for his work. According to Darnell (1981: 143), for instance, Samuelson stated that “Bowley’s work on wages and National Income accounting is well known, if only through the unfortunately named ‘Bowley’s Law’”2. Blaug (1986: 34) also underestimated and severely criticised him, stating, “The task of the statistician as Bowley saw it was to assist economic theory, not to challenge it”3. In contrast, Darnell described Bowley as “an economic statistician of the highest rank” and stated, “His work was motivated by genuine concern for his fellowman”. He continued: “there was nothing he did that was without practical, or at least a potentially practical, application”. Darnell also appreciated Bowley’s practical approach towards social reform, claiming “all his work is concerned by the common theme of social enquiry with the goal of change for the better”4. The sociologist Tomoeda further noted that Bowley “contributed much to the birth of a sociometry”5. According to Darnell, Bowley made three novel contributions to economics. First, Bowley was a “collector and compiler of economic statistics particularly on wages and national income”, a field that Marshall argued was crucial. Second, he was a pioneer of statistical techniques in the social sciences, in the development of mathematical economics and econometrics. Darnell placed high value on this particular field even though Blaug underestimated it. Third, he was “a pioneer of

2 Darnell 1981, p.143. 3 Blaug 1986, p.34. 4 Darnell 1981 p.168. 5 Tomoeda 2001, p.316.

2 sampling techniques”6. Dale and Kotz (2011) also examined the relevance of each of Bowley's contributions but overlooked his relationship with Marshall. Similarly, Groenewegen (2012) failed to classify Bowley as one of the 10 most prominent “minor Marshallians”. Based on the foregoing, from the perspective of Bowley’s intellectual history and given the above-mentioned lack of previous studies in this regard, the relationship between Bowley and Marshall is important for our paper. This article clarifies that Bowley studied multiple social science fields and contributed to social sampling by applying the statistical and economics techniques he learned from Marshall. The remainder of this paper is organised as follows. Section 2 introduces and assesses Bowley’s earlier studies. Section 3 presents Marshall’s statistical and economic methodology. Section 4 discusses Bowley’s Elements of Statistics and describes Bowley’s statistical methodology. Section 5 compares the methodologies of Marshall and Bowley, while Section 6 concludes.

2. A biographical note on Bowley’s early life7 Bowley was born in Bristol on 6 November 1869. He won a major scholarship to Trinity College, Cambridge to study mathematics and graduated as tenth wrangler in 1891. After graduating from his mathematical Tripos, he studied physics and chemistry under R. Appleton, who subsequently introduced him to Marshall. Bowley studied economics in earnest under the guidance of Marshall and “obtained both the Cobden prize in 1892 and the Adam Smith prize in 1894”8. He later won the Adam Smith prize for his essay titled “Change in Average Wages (Normal and Real) in the United Kingdom between 1860 and 1891”, while “a revised version of the paper was read to the Royal Statistical Society on 19 March 1895”9. Marshall commented that he had been “struck by the brilliancy of the

6 Darnell 1981, p.142. 7 This biographical note draws from Allen and George (1957), Darnell (1981), Blaug (1986), Dale and Kotz (2011), and the Oxford Dictionary of National Biography. 8 ODNB, Bowley. 9 Dale and Kotz 2011, p.11, Darnell 1981, p.143.

3 plan by which Mr. Bowley proposed to extract some information from the great mass of wage statistics which had hitherto been almost useless because of its fragmentary character”10. His particular research interests lay in the application of economic analysis to problems of social reform11. In this sense, Bowley began “his career as a mathematician but turned to economics because of its relevance to problems of social reform with which he was passionately concerned”12. Hence, Bowley’s encounter with Marshall transformed him from a mathematician into an economic statistician. On leaving Cambridge, Bowley seemed to be destined to teach mathematics in schools and he was on the staff at Brighton College and St John’s School, Leatherhead, from 1892 until 1899. However, “on Marshall’s recommendation, Bowley was invited to become one of the initial and very small staff, as part-time lecturer in statistics” when the LSE was founded in 189513. “In 1900 Bowley was appointed as Lecturer in Mathematics at Reading College, where he became Professor of Mathematics and Economics in 1907” until he resigned from his post in 191314. “At the LSE, he became part-time reader in statistics in 1908 and was given the title of professor in 1915”15. “When the University of London created a full-time chair in statistics in 1919, tenable at the LSE, this was the first chair ever created chair in statistics in the social sciences”16. Bowley became the first occupant of this chair and he held this post until his retirement in 1936. Through Elements of Statistics (1901), An Elementary Manual of Statistics (1910), and the Mathematical Groundwork of Econometrics (1924), Bowley became a pioneer of statistical methods for social science and economics. According to Collard, “Marshall encouraged Bowley to use statistics as an aid in discovering concrete truth”17. He later wrote Livelihood and Poverty (1915) and Has Poverty

10 Bowley 1895, p.280, Darnell 1981, p.143. 11 ODNB, Bowley. 12 Blaug 1986, p.31. 13 Allen and George 1957, p.236. 14 Darnell 1981, p.141. 15 ODNB, Bowley. 16 ODNB, Bowley. 17 Collard 1990, p.187.

Diminished? (1925), which solidified his position as a leader in the field of social surveying. According to Darnell, “Bowley was the most successful practitioner of sampling in his day”. He continued: “In his appreciation of the care required at all stages of a survey, in planning the project, in questionnaire design, in field-working, in proper instruction of interviewers, and in scientific interpretation and analysis of results, he set an exemplary standard”18. In the next sections, we clarify the relationship between Bowley and Marshall from the perspectives of their respective methodologies.

3. Marshall’s statistical and economic methodology In the early stages of his study, Marshall was very concerned with statistics. His economics professor inaugural address in 1885 was titled the “Present Position of Economics”, while he also presented a paper at the 1885 International Statistical Congress entitled the “Graphic Method of Statistics” 19 . This paper was subsequently published in the jubilee volume of The Journal of the Royal Statistical Society. In it, Marshall stated the following:

The graphical method of statistics, though inferior to the numerical in accuracy

of representation, has the advantage of enabling the eye to take in at once a long series

of facts…. In accuracy the graphic method is inferior to the numerical. But ease and

rapidity are essential when we want to compare many sets of facts together; because, if

the mind is delayed long in taking in the general effect of one set, it meanwhile loses full

count of others: a chief function of the graphic method is to facilitate the comparison of

different sets of statistics. 20 Marshall further stated that English history could be explained and

18 Darnell 1981, p.162. 19 According to J.M. Keynes, the novel contributions in this paper were the definition of the “elasticity of demand” and proposals for “the construction of historical curves” (Pigou 1925, p.501). 20 Pigou 1925, p.175.

5 verified by statistical methods21. He pointed out that a method had already been extensively used in which a group of curves is arranged “on the same sheet of paper … each of which tells one of the constituent parts of a piece of history”22. His proposal was to extend this plan and apply it not only to one sheet of paper but to a great many pages, which may be bound into one large book23. Marshall pointed out that the graphical method of statistics facilitates the identification and comparison of the essence of the facts, confirming the necessity and importance of statistical methods. He also insisted, “The progress of economic science depends largely on the stock of trustworthy and appropriate statistics at its command”24. Moreover, Marshall insisted, “it may be possible to collect and arrange statistics of consumption in such a way as to throw light on difficult questions of great importance to public wellbeing”25. He also indicated, “We should know what quantitative measures of public interests are most needed and what statistics are required for them, and that we should set ourselves to obtain these statistics”26. Again, Marshall pointed out that “much of the failure and much of the injustice, in which the economic policies of governments have resulted, have been due to the want of statistical measurement”27. However, although Marshall emphasised the need to collect statistical data and improve on them, he did not directly produce research results himself; rather, such works were published by his disciples. This helps us understand his statistical methodology. In the early days of his academic career, Marshall translated Ricardo and Mill’s economics into mathematics using the deductive method. Nevertheless, in his inaugural address, he proposed harmonising deductive and inductive methods, as follows:

Greedy then as the economist must be for facts, he must not be content with

mere facts. Boundless as must be his gratitude to the great thinkers of historic school,

21 Pigou 1975, p.178. 22 Pigou 1975, p.176. 23 Pigou 1975, p.177. 24 Marshall 1923, p.273. 25 Marshall 1961, p.85. 26 Marshall 1961, p.492 27 Marshall 1961, p.492.

he must be suspicious of any direct light that the past is said to throw on problems of

the present. He must stand fast by the more laborious plan of interrogating facts in

order to learn the manner of action of causes singly and in combination, applying this

knowledge to build up the organon of economic theory, and then making use of the aid of

the organon in dealing with the economic side of social problems. He will thus work in

the light of fact, but the light will not be thrown directly, it will be reflected and

concentrated by science. 28 In The Principles, he emphasised inductive methods and maintained that “it is the business of economics, as of almost every other science, to collect facts, to arrange and interpret them, and to draw inferences from them”29. Moreover, he approved Schmoller’s methodology and insisted, “Induction and deduction are both needed for scientific thought as the right and left foot are both needed for walking”30. He also noted, “The study of theory must go hand in hand with that of fact”31. In the same vein, Marshall believed that “induction, aided by analysis and deduction, brings together appropriate class of facts, arranges them, analyses them and infers from them general statement or law”32. In the Social Possibilities of Economic Chivalry (1907), he also stated that the “analysis and search for facts are, like the right and left foot in walking, each nearly useless alone”33. He insisted on the importance of harmony between the inductive and the deductive methods. Thus, while the deductive method is a notable part of Marshall’s methodology, he attached great importance to both the inductive and the deductive approaches throughout his career. However, he did not directly work on induction or contribute to statistical work, unlike his disciple and successor.

4. Bowley’s statistical works and his methodology In 1895, Bowley started work as a part-time lecturer at the LSE on the recommendation of Marshall and later published Elements of Statistics. C.P.

28 Pigou 1925, p.171. 29 Marshall 1961, p.29. 30 Marshall 1961, p.29. 31 Marshall 1961, p.39. 32 Marshall 1961, p.781. 33 Pigou 1925, p.323.

Sanger (1871–1930), in his review in the Economic Journal, placed high value on Bowley’s book, claiming that it was “the best book written in English, French, German, or Italian” and adding that “the London School of Economics has since its foundation had systematic courses of lectures on the elements of statistics”34. According to Darnell, “Elementary statistics was not taught as a component of an economics degree until the late nineteenth century, and even in those cases where such a course did exist, students were not pressed to go, and were encouraged in the belief that a little common sense could easily take the place of regular training with tables of numbers”35. At the LSE, Bowley taught statistics; however, the teaching of statistics at Cambridge lagged behind that of the LSE. Bowley thought that “statistics only furnish a tool, necessary though imperfect, which is dangerous in the hands of those who do not know its use and deficiencies” and further added that the “a knowledge of methods and limitations is necessary, if only to avoid being misled by unscrupulous or unscientific arguments”36. In the first chapter of his book, Bowley stated that researchers must “consider the limits of science” when investigating the elements of statistics37. He also pointed out the significance and limitations of studying this particular field:

Statistics may, for instance, be called the science of counting. Counting

appears at first sight to be a very simple operation, which any one can perform or which

can be done automatically; but, as matter of fact, when we come to large numbers, e.g.,

the population of the United Kingdom, counting is by no means easy, or within the

power of an individual; limits of time and place alone prevent it being so carried out,

and in no way can absolute accuracy be obtained when the numbers surpass certain

limits. Great numbers are not counted correctly to a unit, they are estimated; and we

might perhaps point this as a division between arithmetic and statistics, that whereas

arithmetic attains exactness, statistics deals with estimates, sometimes very accurate,

34 Sanger 1901, p.193. 35 Darnell 1981, p.146. 36 Bowley 1910, p.5. 37 Bowley 1901, p.1.

and often sufficiently so for their purpose, but never mathematically exact38. In discussing the differences between statistics and arithmetic in more depth, Bowley suggested that “in the monographic method the individual is everything; in the statistical method, nothing” and added, “when we wish to obtain a measurement of the group, peculiarities of individuals receive no attention”39. Bowley learned the exact differences between the roles of statistics and economics from Marshall, and insisted, “The statistician furnishes the political economists with the facts, by which he tests his theories on which he bases them”40. Bowley also pointed out that statistics provide the method of analysis and data for economics and social science while discussing the role that statistics should ideally play. In Elements of Statistics, he pointed out the inadequacy of collecting data for administrative purposes41. Similarly, Marshall had also insisted on the need to collect and maintain governmental statistics. When governmental statistics did not suffice, however, Bowley provided a great service to this academic field. Indeed, despite acknowledging the limitations of statistics, he still frequently pointed out their role in contributing to economics and social science. Bowley seems to have been influenced by Marshall’s methods and his ideas of statistics and economics. According to Darnell, “Bowley acknowledges that the statistician may furnish the facts by which the economist may test his theories. This was a most underdeveloped role of statistics at that time”42. Bowley published a series of articles titled “The statistics of wages in the United Kingdom during the last hundred years” in the Journal of the Royal Statistical Society from 1898 to 1906, and supplied data on wages at that time. In this regard, Bowley inherited Marshall’s desire for collecting and improving statistics, but he did not “verify the

38 Bowley 1901, p.1. 39 Bowley 1901, p.7. 40 Bowley 1901, p.8. 41 Bowley 1901, p.10. 42 Darnell 1981, p.148.

9 educed implications of economic theory” as Blaug did43. Rather, Bowley stated, “It is better, in fact to define statistics a posteriori”44 and insisted that statistics support the inductive method. Indeed, Bowley argued that deductive and inductive reasoning were strict substitutes, not complements, which remained a point of difference between him and Marshall. According to Darnell, “Bowley rarely approached statistics with the intension of verifying a priori theory”; indeed, he processed “the information” and presented “it in a meaningful way”45. His methodological intent was thus “to examine information in an exploratory way”. This indicates that his statistical methodology followed the inductive approach. Therefore, “it would seem as if Bowley’s maxim was ‘Let the data speak for itself”’. Throughout the history of economics methodologies, the inductive method has been the approach for statistics. However, by the end of 19th century, after the marginal revolution, statistics were becoming analytical tools for examining economic theory. Therefore, statistics were treated as instruments for discovering laws by induction. The emphasis on this point was later moderated46. In summary, Bowley collected statistical data and placed high value on statistics, and he pushed the application of the inductive method in the 20th century. In this regard, Marshall influenced him but his methodology differed from that of his former teacher. Bowley sufficiently understood the limitations of statistics and recognised the principal differences between statistics and economics as well as the influence of each of them on social science. In contrast, Marshall emphasised the necessity of collecting statistical data, but could not accomplish this plan alone.

5. A comparison of Marshall and Bowley Marshall advised his disciples and other economists how to use mathematics in the field of economics. He emphasised the words of Pigou that mathematics “might

43 Blaug 1986, p.34. 44 Bowley 1901, p.4. 45 Darnell 1981, p.149. 46 Egashira 2010, p.294.

10 lead us astray in pursuit of intellectual toys” and “the need of accompanying sets of statistical curves with written notes of non-statistical events”47. In reviewing Jevons’ Theory of Political Economy, Marshall wrote that the book could have been be improved if the mathematics had have been omitted, but the diagrams retained48. Likewise, when Edgeworth published Mathematical Psychics, Marshall wrote that “this book shows clear signs of genius, and is a promise of great things to come”, adding that “it will be interesting, in particular, to see how far he succeeds in preventing his mathematics from running away with him, and carrying him out of sight of the actual facts of economics”49. When Marshall wrote to Bowley 20 years later, he noted, “Edgeworth might have done something great at it; but he has crushed his instincts between the cog wheels of his mathematics machinery”50. Although Marshall studied mathematics at school, he considered that mathematics played a supplementary role in economics. Nevertheless, he attached importance to those aspects that could not be expressed by mathematics or that were left out when mathematics was used. He stated that “in my view every economic fact, whether or not it is of such a nature as to be expressed in numbers, stands in relation as cause and effect to many other facts”51. When Bowley published Elements, Marshall pointed out “there was too much mathematics in your excellent book for the ordinary economic students”. Marshall then enquired:

Will you then be so very generous as to forgive me if I ask yourself whether,

having now brought out this great and successful book, it is not time to make some

further study of the broader relations between economic facts: to leave mathematics for

a little on one side; and join more heartily in the quest for the One in the Many, the

Many in the One52?

47 Pigou 1925, p.84. 48 Pigou 1925, p.99. 49 Whitaker 1975, Ⅱ- pp.265, 267. 50 Whitaker 1996, Ⅱ- p.307. 51 Whitaker 1996, Ⅱ- p.306. 52 Whitaker 1996, Ⅱ- p.302.

By quoting the proverb “the One in the Many, the Many in the One”, Marshall urged Bowley to review his usage of mathematics. Moreover, when Bowley accepted the chairmanship of the Economic Science and Statistics Section of the British Association for the Advancement of Science, Marshall advised him that “a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics … [simply] illustrate the examples that are important in real life [and] translate into English”53. In the preface to Elements, Bowley stated that when “mathematical symbols were unavoidable; the preliminary hypotheses have been first discussed without algebraic notation and at some length”54. Sanger wrote in his review of Elements “very little mathematics is used” and noted that Bowley had “very cleverly avoided the use of more than a very small amount of mathematics”55. Sanger, however, expressed his appreciation for the fact that Bowley had paid such careful consideration to mathematics for a beginner’s book. While it was true that Bowley briefly left mathematics to one side to meet Marshall’s wish, he also strived to examine the broader relations between economic facts. In this regard, it could be argued that his contributions broadened not only mathematical statistics but also social surveying.

6. Conclusion Bowley inherited Marshall’s statistical ideas and went on to become a scholar who achieved a high-level statistical education at the LSE. Despite the scarcity of research on the academic achievements of Bowley, it is worth paying attention to his contributions to the fields of statistics and economics. His transformation from a mathematician to an economic statistician was greatly influenced by Marshall. Indeed, while studying at Cambridge under the tutelage of Marshall, he produced a contribution on wage statistics. This was a research field that Marshall considered necessary, but one that he could not accomplish by himself.

53 Whitaker 1996, Ⅲ-p.130. 54 Bowley 1901, p.vii. 55 Sanger 1901, p.193.

Bowley contributed to statistical education and to the development of statistics at the LSE as one of its foundation teachers, while he was also appointed first Chair Professor of Statistics. In contrast, Marshall wanted to develop applied economics at Cambridge University but was limited by staff resources. Bowley, who was his disciple, accomplished Marshall’s desire to develop applied economics and statistics at the LSE. Thereafter, Bowley contributed to many branches of statistics from the publication of Elements to social surveys and data sampling. Marshall and Bowley shared a common interest in social reform, because they regarded economics and statistics to be tools for the attainment of this goal. Therefore, Bowley contributed to the multifaceted study of social problems under the influence of Marshall. Moreover, both shared a desire to develop statistics for economics by collecting and maintaining economic data. Bowley provided a great service in this field. However, the differences between Marshall and Bowley can be characterised by their respective methodologies. Marshall proposed a harmonisation between the deductive and the inductive methods, whereas Bowley thought them to be clearly separated. Marshall’s ideas about the close connection between the two methods were put into practice in Principles and Industry and Trade. Bowley further thought that statistics could contribute to analyses carried out using the deductive method and had much to offer economics. However, the differences between Marshall and Bowley were few and the gap in their methodologies derived from the fundamental difference between economists and statisticians.

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