1Computing is a crucial task in econometric practice. Before the invention of digital computers in the 1940s, the term “computer” in general referred to human “computors”, who were a group of (usually) females sitting in a room with their mechanical calculators to hand. The computor’s responsibility was to check, enter and calculate all the tasks assigned by scientists. Given that this term is almost obsolete nowadays, computor as a human job has already been relegated to the history of the twentieth century. For illustrative purposes, this paper uses the term “computer” for computing machines performing statistical regressions and mathematical simulations, and “computor” for human calculators undertaking repetitive computing assignments.
2To characterize the historical transition from computors to computers in econometric practices, historians have primarily focused on a general picture of development. One received view summarized by Gilbert and Qin (2006) outlines the chronology of econometric computation from a labor-intensive to a capital, technology-intensive mission:
In the interwar period, regression was often performed by hand or by a mixture of calculating machines (used for moment calculations) and manual solution. In the early postwar years, econometricians would sometimes thank the “computors” (the people, almost invariably young ladies, who operated the computing machines) for their assistance. Rapid progress in computer technology during the 1960s greatly facilitated macro modellers work (Gilbert and Qin, 2006, 139).
3The received view clearly indicates that econometricians relied on human computations to begin with and switched to digital computers in the postwar years. In a similar fashion, other literature examines the history of econometric computation within a period or across different periods. Morgan (1990) mentions the practical aspect of computation in the 1920s. Gilbert and Qin (2006) briefly cover this aspect from the 1930s to the 1980s. Renfro (2004; 2009) surveys the history of econometric software since the 1950s. Renfro (2011) reviews the meaning of computer programs for econometricians since the 1940s. Backhouse and Cherrier (2017) provides an overview of computers in empirical economics from the 1940s to the 1980s.
4However, while the existing historiography is interested in the long-run development of econometric computations, an integrated narrative and analysis revealing the transition dynamics is lacking. How exactly did econometricians work with computors and convert to digital computers? What conditions made using computers in macro modelling possible? Recognizing these shortcomings, this paper considers the evolution of econometric computations within a coherent, case-specific setup. By narrowing down the unit of analysis, this paper puts more weight on the intertwined relationship between organization, econometricians and the generating of econometric knowledge.
5Examining the case-specific history of econometrics has advantages in answering two intercorrelated questions. On the one hand, what happened during the historical transition from computors to computers? To this end, this paper proposes a focusing study that accounts for various factors during the production process of econometric computations. More precisely, it considers not only how certain estimation methods were invented by econometricians, but what other factors, e.g. (wo)manpower, data, computing machines, and programming expertise made these computations available. On the other hand, unveiling the conditions during the transition ventures the second question: To what extent did the emergence of computing technologies reshape the division of computing labor within econometric practices? The question is worth answering for two reasons. Firstly, when new types of computing labor emerge following new technology, the meaning of performing econometric computations may also vary. Thus, studying the changing division of computing labor would be useful for historians to clarify what it meant to be an econometrician in different periods. Secondly, the history of “computing ladies” has been a well-researched topic in recent histories of computing (Abbate, 2012; Hicks, 2017). While the history of econometric computation is no doubt one of scientific computations, this paper speaks to this “hidden figure” aspect and brings female computors and programmers into the historical narrative of econometrics.
- 1 For a history of econometrics at the DAE, see Smith (1998) and Thomas (2017).
6The paper uses the history of the Department of Applied Economics (DAE) at the University of Cambridge as a case study.1 One obvious reason justifying this choice is that the DAE has been a representative econometric institution since the postwar period. Founded in 1946, the DAE is known for its contributions to national accounting statistics and econometrics during its first ten years. These works were facilitated under the direction of Nobel laureate Richard Stone (1913-1991), who was the DAE’s director from 1946 to 1955. Under Stone’s directorship, the DAE developed extensive cooperation between its econometricians. Time-series econometricians formed the main group of econometricians at the DAE in 1946-1950, with microeconometricians following in 1949-1955. Both groups made significant contributions to their respective fields of econometric analysis. According to Angus Deaton’s (2008b, 6) assessment, the DAE experience was a story of successful leadership and cooperation that “has perhaps been equalled only by the work of the Cowles Commission.”
7Most importantly, the story of the DAE witnesses several turning points in econometric computation which fit in the received chronology. The DAE’s works on macro- and micro- econometrics were the research products of two distinct ways of computation, that is, computor and computer. When the DAE was first established, it followed the old-fashioned way of computation that relied on female computors and mechanical calculators. In 1947, a notable advancement was the “regression analyzer” (RA), an analog machine invented by DAE affiliate Guy H. Orcutt (1917-2006; Backhouse and Cherrier, 2017; Cheng, 2020; 2021, chapter IV). Despite the introduction of this new tool, evidence suggests that Orcutt was still looking for other ways, including computors, to handle his time-series data. Since then, doing computation gradually became separated into the twin tasks of data processing and computer programming, though the boundary between them remained ambiguous. Data punching, checking, and computing persisted as the computor’s essential job. Only some computing tasks, especially those of Orcutt’s, were replaced by analog computers.
8After 1949, the DAE’s research agenda shifted to the analysis of new large-scale microdata. This demand was successfully fulfilled by the new digital computer, the Electronic Delay Storage Automatic Calculator (EDSAC), which was entered operation the same year. Cambridge microeconometricians were one of the first groups of programmers to use the EDSAC in econometric analysis (Slater, 2004; Renfro, 2011). In the 1950s, programming digital computers became a crucial and demanding skill for econometricians in producing econometric knowledge. The boundary between data-processing and programming tasks was eventually made explicit, and the former role was almost completely taken over by computors.
9The situation further changed after a new demand for programming emerged. Without a coherent programming procedure, regressions on the EDSAC were not economical. Performing a regression analysis was divided into various stages of computation. In 1956, the DAE employed Lucy Joan Slater (1922-2008) as its programming specialist. Following Slater’s appointment, the DAE innovated a series of regression programs that were widely adopted across the University. Until the 1980s, Slater headed the DAE’s computing center and managed the computations of the Cambridge Growth “Rocket” Project in building a macro, computerized model of the British economy. The employment of a programming specialist such as Slater, who did not have any background in economics, signaled the professionalization of programming expertise in the late 1950s. A more sophisticated division of labor within econometrics was thus developed.
10A decade ago, Aldrich (2010) proposed the label “econometricians’ statisticians” to capture some statisticians whose works had inspired econometricians. Adopting this concept, this paper outlines the historical dynamics of econometric computations at the DAE into four themes: econometricians’ computors, econometricians as computer builders, econometricians as computer programmers, and econometricians’ programmers. The thematic setting does not suggest that the latter were fully replaced by the former, but rather that the latter’s divisions of labor further complicated the former’s following by the emergence of computers, new data, and the specialization of programming expertise. The sections are organized according to the following themes: Section 1 sketches the origin of the DAE and its initial reliance on computors; Sections 2 and 3 document the arrival of Orcutt’s RA and econometricians’ adoption of the EDSAC, respectively; Section 4 illustrates how DAE econometricians further outsourced their programming tasks to Slater, making her a special figure during the transitioning divisions of computing labor, and Section 5 concludes.
11On 5 March 1938, in a letter from John Maynard Keynes (1883-1946) to Colin Clark (1905-1989), who had determined to stay in Australia, Keynes eagerly urged his previous colleague to return to England for a new “statistical realistic department”:
- 2 Letter from Keynes to Clark, 5 March 1938, in Keynes (1978, 800-801).
Don’t make too quick a decision. Come back here [Cambridge] in the first instance anyhow. You will be able to get back to Australia at any subsequent moment you may choose. The problem of doing anything here might be more difficult—indeed it is—but it may be more important. It is very necessary to lay the foundations for a proper department of statistical realistic economics at Cambridge.2
- 3 For Keynes’s role in the development of national accounts, see Tily (2009).
12Keynes never offered a clear definition of “statistical realistic” economics. What he had in mind was probably work on national accounting statistics, which had been Clark’s significant contribution since the 1930s. At the time, Keynes was convinced that producing some quantitative evidence on the British economy would help with a sound evaluation of economic policies and generate a dependable measurement of his “multiplier” in General Theory.3 With Keynes’s huge endorsement, Clark undoubtedly appeared as the best candidate to lead the new department.
13Although Clark did not ultimately return, Keynes managed to continue his statistical economics project at Cambridge. Back in early 1938, a new initiative called the Cambridge Research Scheme had been established by a grant from the National Institute of Economic and Social Research (NIESR). The steering committee included Keynes, Richard Kahn, Piero Sraffa, David Champernowne, Austin and Joan Robinson, and Michał Kalecki. The committee clearly stated that the goal of the scheme was to improve the quality of economic measurements:
- 4 “Research Scheme”, JRNS/3/2/19A, Papers of John Richard Nicholas Stone (JRNS), King’s College Archi (...)
The ultimate purpose of this investigation is to provide trustworthy short period measurements of the main components of the economy such as real income, investments, consumption, output of different branches of activity, output for home and foreign market, and so on.4
14The foundation of the scheme reflected Keynes’s dissatisfaction with the precision of economic statistics, as noted in General Theory: “our statistics are not accurate enough … to allow us to infer more than high approximate estimates” (Keynes, 1936, 127). The scheme remained rather loose and informal with different participants pursuing various tasks of data collection and calculation. Notable examples included Kalecki on prices and prime costs and Keynes himself on the measurement of saving (Pesaran, 1991, 96-97). Constructing these datasets required not only delicate arrangements of data recordings and computation, but smooth cooperation with other agencies such as the Board of Trade or the NIESR, and with those needs in mind, the scheme called for more manpower and sources of data.
- 5 In Trends, Stone wrote monthly reviews of European economies using a wide range of economic data. H (...)
- 6 Letters from Michał Kalecki to Richard and Winifred Stone, 27 Nov 1938 and 6 Jan 1393, JRNS/3/2/19A
- 7 Letter from Richard and Winifred Stone to Noel Hall, 10 Nov 1938, JRNS/3/2/19A; Letter from Noel Ha (...)
- 8 Letter from Austin Robinson to Richard Stone, 25 Apr 1939, JRNS/3/2/19A.
15The names that popped up on the list of potential cooperators were Richard and Winifred Stone, who were both Cambridge alumni employed in the City of London. After the couple married in 1936, they spent most of their spare time undertaking empirical economic research. Richard Stone, who was a business professional and former pupil of Clark, had been interested in economic data collection and its statistical analysis back in his first academic publication, “A Study of Cost” (Tweddle and Stone, 1936). In June 1937, before Clark’s visit to Australia, Stone took over Clark’s position as managing editor of Trends, a supplementary series of Industry Illustrated.5 Stone gradually became known to the people at Cambridge and NIESR and was included in the scheme. In 1938-1939, the Stones received several research requests, including data collection from Kalecki,6 potential research proposals from Noel Hall,7 then Director of the NIESR, and taking with Keynes on “his plan to measure saving” from Austin Robinson.8 Moreover, the communications indicate that Richard Stone also sought statistical assistance from the scheme. To address Stone’s request, Robinson continued to search for a computer, writing to Stone kindly about it:
What about statistical assistance? Has [Noel] Hall been able to give you any direct help? If not, is there anything that we can do for the moment?
- 9 Letter from Austin Robinson to Richard Stone, 27 Feb 1939, JRNS/3/2/19A.
We have just been advertising for a statistical assistant here, and in the process of finding one we have discovered that there is a lady in Cambridge … who was at one time assistant to [Harold] Hotelling … It seems to me not impossible that we might rope her in to help either you, or Keynes, or both, in your investigation.9
- 10 Letter from Austin Robinson to Richard Stone, 17 Oct 1939, JRNS/3/2/19A.
16It is unclear whether the female candidate was ultimately hired, but the scheme did guarantee the Stones £60 out of the total budget of £600 for hiring a “lady” computor.10 This budget allocation suggested that the hiring of computing labor had become increasingly crucial for data-intensive work. However, communications ceased around the summer of 1939. The scheme was almost suspended in September 1939 after the UK’s declaration of war on Nazi Germany.
17Already involved with other institutions, the Stones proceeded to publish two articles on statistical economics. Both articles involved huge statistical data collections and calculations. Stone and Stone (1938) applied three different methods and datasets to estimate the Keynesian marginal propensity to consume. The article used a wide range of economic data on income and consumption collected from scholars such as Kalecki, Jan Tinbergen, and Simon Kuznets. In another paper, Stone and Stone (1939) compared the industrial output indices produced by three different institutions and tried to create a new benchmark for those statistics. The two articles were research highlights of the Stones and crucial contributions to Richard Stone’s pre-academic career.
18Later, Keynes decided to make the scheme more formal. In November 1939, the Faculty of Economics and Politics approved Keynes’s proposal and named the new institution the “Department of Applied Economics” (DAE). The department’s Committee of Management included mostly the same members as the Cambridge Research Scheme but replaced Kahn and Kalecki with Gerald Shove and Dennis Robertson. At this point, however, the DAE’s main goal was still not clearly defined, as Austin Robinson recalled,
When the National Institute [NIESR] was born a little belatedly into this family of struggling infants … neither Maynard Keynes nor I, concerned with planning and negotiating what ultimately became the Cambridge DAE, knew the answer in those early days. (Robinson, 1988, 63)
19With such a vague remit, neither Keynes nor Robinson could prioritize the setting up of the new department, especially since both began working at Whitehall in 1939. The foundation of the DAE was therefore delayed until the war reached its end. In 1944, the Committee of Management relaunched discussions on the DAE and soon made an offer to Richard Stone to become the DAE’s founding director from July 1945.
- 11 The Stones separated in 1940 and Winifred did not work in academia afterwards. In 1941, Richard Sto (...)
20The committee’s final decision was not surprising, since the 31-year-old Stone, with his Cambridge background, was indeed a qualified economic statistician at the time. During the war, Stone had gradually distinguished himself as a national account statistician as well as an applied econometrician. On the one hand, in mid-1938, after stepping down from the management of Trends, Stone joined the Ministry of Economic Welfare and then the Offices of the War Cabinet in the summer of 1940. Along with James Meade (1907-1995), he produced three British national accounts for 1938 and 1940. These estimates immediately interested Keynes at the Treasury and were circulated as a part of a White Paper on Budget Day of 1941 (British Parliamentary Papers, Cmd 6261). Until 1944, Stone acted as an assistant to Keynes and continued working on producing national accounting statistics. On the other hand, through Robinson and his second wife Feodora Leontinoff (1909-1956), Secretary to the NIESR, Stone maintained close connections with the wartime Institute.11 In 1941, he formed a small research group working on analysis of consumer behavior. The results, titled “The Analysis of Market Demand”, were published at the end of the war (Stone 1945). The 97-page article was one of the first econometric analyses of market demand using national accounting data of expenditure and consumption.
21As director of the DAE, Stone was given “extremely liberal and congenial” (Pesaran, 1991, 99) guidelines from the Committee of Management. In his proposal submitted to the Nuffield Foundation, Stone clarified the three research aims of the department:
The Department will concentrate simultaneously on the work of observations, i.e. the discovery and preparation of data; the theoretical appraisal of problems, i.e. the framing of hypotheses in a form suitable for quantitative testing; and the development of statistical methods appropriate to the special problems of economic information. The special character of the Department’s approach to the problems of real world [sic] will lie in this attempt at systematic synthesis. (Stone, cf. Pesaran and Harcourt, 2000, F149-F150)
22These aims guided three practical goals for the department: (a) National Income, Product and Social Accounting Projects, (b) Statistical Methods in Economics, (c) Verification and Estimation of Economics Relationships (DAE, 1948, 10-16). In a nutshell, what Stone had in mind in current terms were (a) construction of a UK-wide national accounting time series, (b) investigation of the statistical properties of those time series, and (c) econometric analysis using different sources of information. To fulfill those tasks, he recruited Roy C. Geary (1896-1983), Orcutt, Gerhard Tintner (1907-1983), James Durbin (1923-2012), Geoffrey Watson (1921-1998), and Andrew D. Roy (1920-2003) to the department. Under Stone’s direction, this initial group of DAE econometricians began to work on different applied econometrics projects on the top floor of the Marshall Library.
- 12 For instance, obtaining a two-variable linear regression coefficient required two sums of squared t (...)
23Both constructing new statistical data and analyzing these data required an immense number of computations. For the former, the work included data collection, checks, and numerical operations. For the latter, calculating just a single regression coefficient could involve even more numerical processes.12 Therefore, from the very beginning, Stone was clearly aware of the demand for human computors for the DAE research projects:
The scale of its [the DAE’s] operation has meant that its staff must be sufficiently large to permit of the appointment of several types of specialist research worker, and that its facilities must include a computing staff and mechanical equipment that are adequate to the extensive econometric researches that need to be undertaken. (DAE, 1948, 7)
- 13 While exact models of these desk calculators are not recorded, it is unknown whether different mode (...)
24Stone expected that such computing facilities would not only serve for the department’s staff members, but also for the Faculty of Economics, which also required computational assistance (DAE, 1948, 8). As a result, when the department moved to a new building next to the Marshall Library in September 1947, the new floor plan consisted of a computing room with four computors and six electric calculating machines, comprising four Marchants, one Monroe and one Madas calculator (DAE, 1948, 24). Figure 1 shows a typical Marchant model of desk calculator at the time. Until the late 1940s, the department relied mainly on these machines and computors to perform econometric computations.13 Durbin and Slater recalled the early situation of the DAE’s computing facilities:
… one of the assets of the DAE was that we had a room there with perhaps eight or ten young ladies operating desk calculators, supervised by an older lady of forbidding demeanor. They did the computing. (Durbin in Phillips, 1988, 131)
- 14 Slater, An interview conducted by Janet Abbate for the IEEE History Center, April 9, 2001.
… there was no computing in the economics department, except for the inevitable woman room—a room full of about ten or twelve women, all desperately churning away on ordinary Marchant calculators. It was to get the [economics department’s] data ready.14
Figure 1. Merchant Model 10FA, Introduced in 1948
Source: National Museum of American History (https://americanhistory.si.edu/collections/search/object/nmah_689952, retrieved 03/11/2023).
25In the early days of the DAE, hand calculators and female computors were the most intuitive setup both from Stone’s own experience and taking account of technological constraints. Since the 1920s, hand calculators had been the only kind of computing machine available to applied economists. Stone was without doubt familiar with using them, having received a Monroe calculator as a twenty-first birthday present in his final undergraduate year. He spent a summer estimating the Cobb-Douglas function by fitting British time-series indices of output, labor, capital with time trends (Pesaran, 1991, 89). He took his machine with him to Whitehall where, as Meade later recalled, he “established himself with a quill pen and a Monroe hand calculator” (Deaton, 1993, 479). Furthermore, computations at the time still resembled those Stone had performed in the 1930s: they were time-consuming tasks comprising repetitive checking and typing jobs at office desks. Every operation needed to be done from scratch and the hand calculator was the only tool available. For instance, as reported in Bean (1929, 394), a four-variable curvilinear regression of thirty observations required eight working hours from an experienced computor. Consequently, the solution to this time constraint was either simplifying calculation methods to minimize the computation burden (Morgan, 1990, 139n), or simply hiring more computing labor. While the former depended on the advancement of econometric knowledge, the latter came about naturally as a practical solution.
- 15 For more details about Orcutt’s early years and his design of RA, see Orcutt (1990) and Cheng (2021 (...)
26Stone kept searching for alternative computation solutions. In 1946, another new computing facility was installed, the “regression analyzer” (RA), an analog machine invented by Orcutt. Controlled by punched cards, the RA included electric circuit designs that processed the input current and made calculations. After numerical data were punched in, different circuit designs would yield combinations of summations, subtractions, and multiplications to solve the least-square problems. The outcome was measured by voltmeters and visualized on a cathode ray oscilloscope. In his doctoral years, Orcutt had been interested in applying his engineering expertise to solve econometric problems. During his first job at MIT, Orcutt completed the first viable version of the RA that could perform multiple regressions.15 During the summer of 1945, Orcutt was introduced to Stone, who was looking for new faculty members to join the DAE. In a letter to Stone, Orcutt emphasized that his machine was constructed to facilitate the computation process:
- 16 Letter from Orcutt to Stone, 22 Aug 1945, JRNS/3/1/96.
It is a machine for rapidly finding means, standard deviation, regression coefficients, standard errors of estimate, correlation coefficients, etc., directly from the data without the necessity of computing the sums of squares and sums of cross products of the series involved and then solving a set of normal equations.16
- 17 Letter from Orcutt to Stone, 15 May 1946, JRNS/3/1/96.
27In this regard, the RA was akin to a computerized regression program: once the punch cards had been arranged, the machine would run and solve a specific least-square problem automatically. In the finalized version, the RA could accommodate up to three time series, each with up to 30 observations (Orcutt, 1990, 10) and solve one simple regression in 40 to 50 seconds.17 The machine was first demonstrated at the 1945 annual Christmas meeting of the Econometric Society, titled “A Machine for Determination of Correlation and Regression Coefficients” (Journal of the American Statistical Association, 1946, 78).
- 18 Letter from Orcutt to Stone, 14 January 1946, JRNS/3/1/96.
- 19 Letter from Orcutt to Stone, 15 May 1946, JRNS/3/1/96.
- 20 Letter from Orcutt to Stone, 1 Nov 1946, JRNS/3/1/96.
28During the 1946 academic year, while Stone was visiting the Institute of Advanced Study at Princeton University, he stopped by MIT and made Orcutt an offer of a senior research position at the DAE. After two weeks of consideration, Orcutt accepted the two-year contract with a £715 annual salary.18 While everything seemed to be proceeding smoothly, an interesting episode occurred when Stone tried to import the RA. Since the RA was originally designed for a weather-forecasting project funded by the U.S. Air Forces, Orcutt first needed the permission of the project convenor George Wadsworth, professor of mathematics at MIT. Wadsworth basically approved Orcutt’s request but expressed some reservations from the military perspective.19 Furthermore, importing the RA to the UK induced concern from British bureaucrats, to the extent that Stone even told Orcutt that the permission “may not go through.”20 In his defence of the RA’s legitimacy, Stone wrote very sincerely to a customs officer on how much the DAE yearned for this machine:
- 21 Draft letter from Stone to F. W. Lawfield, 11 Nov 1946, JRNS/3/1/96.
This machine is unique and is able to make certain types of calculation arising in statistical economics very much more rapidly than any other known device. It is essential for certain of the research purposes of the Dept.21
- 22 Letter from Stone to F. W. Lawfield, 11 Nov 1946, JRNS/3/1/96.
I ought perhaps to explain that I have only seen the machine once when it was under construction. It is a small piece of apparatus about the size of a large table wireless set and was invented by Mr. Orcutt … You will understand that we are very anxious to have the use of this machine, which will be of immense value to our research.22
29Stone’s letter reflected the DAE’s lack of an effective computational device, and the arrival of Orcutt’s machine would ease the department’s computational burden. The RA was finally approved for import after further exchanges between Stone and UK customs officials regarding the license permission. In November 1946, along with his RA, Orcutt arrived at the University of Cambridge and became the DAE’s first employee from the US.
- 23 The attendance list and correspondences are found in JRNS/4/12.
- 24 Letters from Orcutt to Oatley, 24 Feb 1947 and 25 Feb 1947, JRNS/4/12.
30On 21st January 1947, Orcutt made the first demonstration of the RA to his Cambridge colleagues. Fellow DAE economists (Geary, Austin Robinson, Kahn, and Sraffa) were invited, along with other people who were interested in new computers, including Maurice Wilkes (1913-2010), director of the Mathematical Laboratory, Ronald Fisher (1890-1962), professor of genetics, and staff members of the Engineering Laboratory.23 After the demonstration, Stone and Orcutt began their communication with Charles Oatley, lecturer at the engineering department. With Oatley’s help, Orcutt refurbished the RA from electronic components purchased by the university from the Ministry of Supply.24 The refurbished RA was described in the technical report published as Orcutt (1948a).
- 25 Letter from Stone to Brigadier Hickman, 14 May 1947, JRNS/4/12. The design of this machine was not (...)
- 26 Letters from Stone to Hugh Young, 15 Jul 1947 and 31 Jul 1947, JRNS/4/12.
- 27 The main result was published in Orcutt (1948b).
31With the improved RA, Orcutt commenced work on a project examining the autoregressive nature of the annual economic series used by Tinbergen (1939, Appendix C, 205-207). The project required massive computations of correlation coefficients to obtain the correlograms of Tinbergen’s series. To relieve this burden, at Orcutt’s request, the DAE loaned another “autocorrelation machine” from the Radar Research and Development Establishment (RRDE) of the Ministry of Supply.25 The autocorrelation machine was constructed by Edward Shire and Keith Runcorn of the Cavendish Laboratory while they were both working at the RRDE. After Shire’s introduction, Orcutt and Stone then visited the RRDE in London to collect the machine.26 Once the machine had been reallocated to Cambridge, Orcutt concluded that the autoregressive behavior of Tinbergen’s series could be captured by the equation: 27
yi+2=1.3yi+1-0.3yi+εi+2
32Despite this result, it seems that the DAE facilities were still insufficient for computations. In a letter to Feodora Stone, Orcutt again eagerly requested computational assistance from the NIESR:
- 28 Letter from Orcutt to Feodora Stone, 20 Aug 1947, JRNS/4/12.
As you probably know we are very short of computing helps here [at the DAE] and Dick suggested that perhaps your Miss Potter [the NIESR’s computor] might be able to do some more work for me.28
33After showing his equation, Orcutt elaborated on the “some more work” he requested:
What we would like to do now is determine empirically the frequency distribution of correlations to be expected by chance between series generated by such a model. We plan to carry out the necessary correlations on my machine but there will still be the big job of constructing the series to be correlated.
I have to come into London in the near future to see about a meter and will bring the details concerning the work I would like Miss Potter to do if you think you can spare some of her time for my problem.
- 29 Letter from Orcutt to Feodora Stone, 25 Aug 1947, JRNS/4/12.
34As clearly illustrated in his letter, Orcutt used the analog machines for computing correlation coefficients, whereas the computors performed “the big job of constructing the series”, suggesting that data arrangement was an essential task for computors. In the event, Orcutt did not come to London, but Potter came to Cambridge instead.29 Consequently, Orcutt completed another paper that constructed a quasi-Tinbergen series with random numbers to test their autocorrelative structure. The results, coauthored with Diploma student S. F. James, included 36 series of computations of autocorrelations featuring 90 items each (Orcutt and James, 1948). While the computations at the DAE were “considerably facilitated” (Orcutt and James, 1948, 400) by the RA, computors contributed most to the fundamentals of data processing such as preparation and construction.
35In sum, the introduction of analog machines in 1947 did indeed change the DAE’s divisions of computing labor, but during this transition, the computing room and computors remained indispensable for econometricians. On the one hand, as shown in Orcutt’s case, when complicated computing works were taken over by the RA and the autocorrelation machine, computors gradually diverted their time and skills to data processing, enabling econometricians to deal with larger datasets. However, even with computors fully engaged, the shortage of computing labor was severe. In order to overcome this constraint, Orcutt had to borrow another female computor from the NIESR for new data arrangement, indicating that the demand for computors increased with the emergence of new computers. Therefore, in a letter to Nina Wilkes, Orcutt recollected his time at Cambridge with an emphasis on the contributions of the DAE’s female computors:
- 30 Letter from Orcutt to Nina Wilkes, 9 Mar 1949, JRNS/3/1/96.
I have many fond memories of Cambridge and particularly of my association with the Department [DAE] there and I would appreciate it if you would let the computers [computors] know how much I appreciate the work that they have done for me.30
36On the other hand, self-built computers only partially substituted for the original method of desk-computing work since the analog machines were not satisfactorily reliable, as in Watson’s reminiscence:
… there was little digital computer [at the DAE] and the students’ legs were sticking out the back – all vacuum tubes and wires and punched hole tape … it’s where the reliability problem first came up … Another time Jim Durbin and I had 10 equations and 10 unknowns and the analog computer did it. There were flashing lights, and the iterations converged, less and less flashing lights. I remember people were saying, “Now we’ll be able to get the eigenvectors” or other things we’d been writing about. (Beran et al., 1998, 91)
- 31 One possibility could be that the analog machine was subjected to random noise that would bias the (...)
37Watson’s example of obtaining eigenvectors indicates that the unspecified analog computer was perhaps used for matrix inversions, but he did not explain what caused the reliability problem.31 No matter the real reason, Durbin and Watson may have relied less on results from analog machines and more on those from desk calculators for higher accuracy. To this end, Durbin recounted a “game” of organizing computing works under a limited number of computors:
We were very concerned about the accuracy of these tables, as everybody was, doing computing in those days. What we tried to insist on was for the girls to do all calculations twice. But, of course, this was rather boring from their point of view. To some extent you had to play a game when you were organizing this type of computing, in getting the right amount of checking done and getting it done properly. We ourselves, although neither one of us liked computing, had to do some checking of those tables. (Durbin in Phillips, 1988, 131)
- 32 As Orcutt (1990, 11) recollected, “Stone arranged for me to have the use of a laboratory room in th (...)
38Another feature of the changing divisions of computing labor was the emergence of cooperation between different departments on computing facilities. When Orcutt’s machine arrived, the demonstration not only interested the DAE economists, but people from various laboratories. These laboratories were pivotal in facilitating construction of the new machines and therefore Orcutt’s computations. Once cooperation had begun, the Engineering Laboratory helped distribute the electronic components for building machines, and the Cavendish Laboratory mediated the DAE’s loan of the autocorrelation machine and provided Orcutt with a facility for modifying machines.32 The Mathematical Laboratory, which later became better known as the Computer Laboratory, seems not to have played an important role in the DAE’s early stages of computation. However, although no record of communications exists in the archives, one letter copied from Maurice Wilkes to the DAE is particularly interesting. In the letter, Wilkes introduced the Electronic Discrete Variable Automatic Calculator (EDVAC), a digital general-purpose computer built by the University of Pennsylvania, and then, he hinted the emergence of a new computer that would dominate the DAE’s computation for the next decade:
- 33 Copied letter from Wilkes to Stone, 3 Sep 1947, JRNS/4/12.
The EDVAC is, as far as ideas go, the forerunner of all the machines now being built or projected and I had this in mind when I chose a name which rhymed with EDVAC for my own machine.33
- 34 Orcutt went to the International Monetary Fund to work under J. J. Polak in 1948. Durbin joined the (...)
39When Orcutt and Durbin left Cambridge in the late 1940s,34 the DAE’s research on time-series econometrics had gradually established its reputation based on two new empirical tools. First, Durbin and Watson developed a statistical test of serial correlation in the least-square regressions where the time series were generated from an autoregressive process. These were recognized in the literature as the Durbin-Watson statistics (Durbin and Watson, 1950; 1951). Second, based on his previous research which verified the autoregressive nature of Tinbergen’s economic time series, Orcutt came to question whether this feature could be removed through numerical operations. Along with Stone’s supervisee Donald Cochrane (1917-1983), Orcutt developed a method of first differences to adjust the non-randomness of error-term that was credited as the Cochrane-Orcutt transformation (Cochrane and Orcutt, 1949; Orcutt and Cochrane, 1949). Those empirical tools, as shown in the former section, were built under circumstances of limited computing power. Given this constraint, at the beginning of the 1950s, the DAE’s computing room was enlarged to six computors and nine hand calculators.
40The creation of the Durbin-Watson test and Cochrane-Orcutt transformation had even deeper influences on the DAE. A significant outcome was that Stone became more skeptical of the validity of aggregate economic time series. Stone had recalled this skepticism towards the Tinbergen-Haavelmo-style program when writing his monograph on demand analysis (Stone and Rowe, 1954), where he referred to the methodological flaws of time series:
The statistical analysis [of Stone and Rowe, 1954] owed much to my colleagues and particularly to Durbin and Orcutt. It is perhaps surprising that I did not discuss Haavelmo’s simultaneous equation system. In principle, I fully agreed with it but in practice I thought that, with the many other difficulties in time series regression analysis, this one could perhaps be left over for the time being. (Stone in Pesaran, 1991, 103)
41The practical difficulties of time series caused Stone to move away from macro-level to micro-level information. As a clear sign of this shift in emphasis, in early 1949, Stone launched a new project on the social accounts of Cambridgeshire, led by J. E. G. Utting and assisted by Durbin. This project aimed to use regional micro-surveys to construct a Leontief-style input-output table to infer regional economic performance (Stone et al., 1950). Following three pilot studies, the survey of Cambridgeshire covering around 4,000 addresses began in 1953 (DAE, 1954, 9). Such a shift in practical concerns would call for more demands for computing power while more data would need to be properly handled.
42Booms in micro-level surveys on household expenditure also explain why Stone and the DAE switched to research on microeconometrics at the beginning of the 1950s. In Stone and Stone (1938), Stone had applied multinational microdata to estimate the propensity to consume, but the scale of the dataset was quite small. After the end of the war, the scale of newly available microdata skyrocketed. In 1947, two interwar surveys conducted by UK officials were first coded and made available for academic purposes. These were the 1937-1938 working-class household expenditure survey of 10,762 families from the Ministry of Labour and the 1938-1939 middle-class survey of 1,361 families from the Civil Service Statistical Bureau. In 1950 and 1951, the UK Ministry of Food conducted two more surveys of household expenditure covering 1,143 families and approximately 6,000 families, respectively. Responding to the emergence of large-scale microdata, Stone began to seek other possibilities in order to expand his work on demand analysis.
43Based on previous experience, it seemed to be clear that developing novel empirical research required manpower, especially horizontal cooperation between junior scholars. Among the DAE’s notable time-series econometricians, Orcutt and Durbin were early-stage academics, and Cochrane and Watson were doctoral students. Stone adopted a very similar philosophy when recruiting new people to study microeconometrics. From 1949, a new group of econometricians arrived at the DAE in succession, including James Tobin (1918-2002, active 1949-1950), Hendrik S. Houthakker (1924-2008, active 1949-1952), Michael J. Farrell (1926-1975, active 1949-1975), Sigbert J. Prais (1928-2014, active 1950-1957), J. A. C. (Alan) Brown (1922-1984, active 1952-1965), and John Aitchison (1926-2016, active 1952-1956). Among this group, Tobin and Houthakker were early-stage academics. Tobin was a Junior Harvard Research Fellow who had just defended his doctoral dissertation in which he combined annual economic time series and family budget surveys to study the U.S. consumption function. Moreover, his study on U.S. food demand (Tobin, 1950) was in the last stages of completion before he moved to the UK. Houthakker had received his doctorandus from Amsterdam and had already published a paper on price elasticity in the Dutch electricity sector (Houthakker, 1949). Farrell and Prais started their graduate degrees under Stone. Under Stone’s direction, Farrell focused his project on the demand for durable goods, and Prais on empirical analysis of the Engel curve. Brown had a degree in economics from Cambridge and had previously worked in the statistical division of the Ministry of Agriculture, Fisheries, and Food. His practical experience with food budget surveys led him into academia (Stone, 1985, 191). Aitchison was trained in statistics at Cambridge and was just embarking upon his academic career.
- 35 For a history of constructions of the EDSAC, see Ahmed (2013, 44-65).
- 36 UA/COMP A.9 (1), Archives of the Mathematical Laboratory and its successor, the Computer Laboratory (...)
44In parallel with the arrival of new members at the DAE, construction of a new electrical computer was in progress at the Mathematical Laboratory. Following his visit to the US in 1946, Wilkes was determined to construct an automatic calculator akin to John von Neumann’s EDVAC (Ahmed, 2013, 41). In 1947, Wilkes joined the race to invent the first electrical computer in the UK alongside other universities and institutions. The new machine’s name was the Electronic Delay Storage Automatic Calculator (EDSAC), as shown in Figure 2.35 On May 1949, the EDSAC ran its first program to compute a table of square numbers, demonstrating that the machine was officially in operation. The EDSAC was soon attracting users from various departments to run their scientific computations, initially under informal arrangements. Around 1951, in order to allocate the increasing demand for computations more efficiently, Wilkes asked EDSAC users to propose their research projects that he would then authorize, and announced that only registered users would be able to run their authorized projects.36 The EDSAC Priorities Committee would organize a meeting to review the process of ongoing projects and discuss the allocation of total computation hours for the following six months.
Figure 2. The EDSAC (ca. October 1947)
Source: Department of Computer Science and Technology, University of Cambridge, (https://www.cst.cam.ac.uk/news/70-years-first-computer-designed-practical-everyday-use, retrieved 03/11/2023).
45After the EDSAC was opened for research purposes to staff members at Cambridge, the DAE’s econometricians soon discovered its uses in their econometric analyses. Particularly, Stone expected that the machine could solve the “statistical complications” when estimating non-linear regression models:
[The EDSAC] has proved to be invaluable for mathematical calculations of the most varied kinds. It has great possibilities for statistical work, especially regression analysis, and for certain calculations in production theory. Statistical complications such as non-linear restraints on regression coefficients, that have so far been avoided because of computational difficulties, may now be attacked directly and some attempts of this nature are being considered. (DAE, 1951, 24)
Table 1. EDSAC Jobs by DAE Staff Members, 29 May 1951 to 10 January 1956
|
Job No.
|
User
|
Job Title
|
Project
|
|
14
|
Houthakker – Prais – Prais (Brown)
|
Correlation work
|
Family budgets inquiry
|
|
15
|
Houthakker – Prais – Prais (Brown)
|
Inversion of matrix
|
Family budgets inquiry
|
|
55
|
Prais
|
Non-linear regression
|
Family budgets inquiry
|
|
76
|
Prais (for Fisher)
|
Time series correlation
|
|
|
102
|
Prais (for Stone)
|
Time series correlation
|
|
|
106
|
Prais – Brown – Brown & Aitchison
|
Post-war budgets
|
Family budgets inquiry
|
|
107
|
Prais – Brown
|
Equivalent adult scales
|
Family budgets inquiry
|
|
112
|
Brown
|
Anthropometric measurements
|
(For Clothing Industry Development Council)
|
|
127
|
Brown
|
Inversion of matrix arising in Import/Export study
|
|
|
151
|
Brown
|
Tests of normality
|
|
|
202
|
Brown
|
Regression analysis
|
Demand analysis
|
|
212
|
Brown
|
Linear expenditure systems
|
Analysis of consumers’ expenditure 1920-1938
|
|
294
|
Brown
|
Social accounts of Cambridge
|
Consumers’ expenditure
|
Source: UA/Comp A.9 (1), “Current list of EDSAC Job Numbers”, summarized by the author.
- 37 Slater (2004, 119) confirmed that “Economists were among the earliest users of the programmable ele (...)
- 38 The list is found in UA/COMP A.16.
- 39 The full name of the school was Summer School in Programme Design for Automatic Digital Computing M (...)
46Working with the Mathematical Laboratory, the DAE’s econometricians were among the first group of programmers to utilize the EDSAC for econometric computations.37 Table 1 summarizes the authorized jobs performed by the econometricians between 1951 and 1956 from the archival records. The first name to appear on the EDSAC’s registration list was Houthakker,38 who had learned programming skills at a summer school held in Cambridge “on the behalf of the Department” (DAE, 1951, 24).39 Under the project named “Family budgets inquiry”, Houthakker’s proposed tasks included “correlation work” (no. 14) and “inversion of matrix” (no. 15), clearly indicating that the new machine was used for regression analysis. The numbers of the jobs also confirm that he was aware of the EDSAC’s potential at an early stage. Then, he was succeeded as the main user of the machine by Prais, who also proposed a new task on “non-linear regression” (no. 55). The family budgets inquiry remained the most crucial project until 1953, when Brown and Aitchison appeared on the registration list. A new project on consumer expenditure replaced the previous inquiry and they remained the key users of the project until 1956. The dominance of Brown suggests that he was the main programmer at the time. His jobs ranged from regression analysis and statistical tests to linear expenditure systems with some other occasional jobs. The results were reported accordingly:
analyses of up to thirteen variables at a time can now be completed with facility within a day of the elementary series being completed … In addition to the programmes for regression analysis and for the analysis of family budgets, which include programmes capable of carrying out an analysis of covariance, much use has recently been made of ‘Monte Carlo’ methods … Matrix inversion, which arises in the computations already described, is also an important feature of input-output analysis and applications have been made in this field. (DAE, 1954, 11)
- 40 For a summary of Stone’s contribution to input-output analysis, see Marangoni and Rossignoli (2016)
47In short, the EDSAC assisted the DAE econometricians in three aspects. The first was linear and non-linear regression analyses in the family budgets inquiry relating to the recently available household surveys. Second, matrix inversion was used in the input-output analysis that was one of Stone’s works at the time.40 Last, the Monte-Carlo idea had been previously applied by Orcutt and James (1948) to Tinbergen’s data. Once the random samples had been constructed, hypotheses on statistical distributions or laws could thus be examined.
48Brown, Houthakker and Prais reported their practical experiences of using the EDSAC in econometrics in the Journal of the American Statistical Association (Brown et al., 1953). The article, perhaps for the first time in the history of economics literature, offered a non-technical review on how empirical works in economics were organized on a large-scale digital computer. The proceeding logic and terminology used by the EDSAC were very similar to those of modern computers: the machine took “orders” such as addition and multiplication as logical operations and the numerical data were fed through punched cards; the orders and data were stored in the “memory” where each location could either hold an order or a 17 digit binary number; a sequence of orders which was called a “program” would be executed by the “control unit” automatically. The EDSAC’s material breakthrough brought great efficiency and increased capacity. First, the EDSAC could repeat programs until certain conditions established by its users were satisfied, meaning that higher degrees of mathematical iteration could be calculated. Second, the EDSAC required only 1.5 milliseconds for an addition and 6 milliseconds for a multiplication. Last, the EDSAC contained 1,000 memory locations that allowed scientists to handle large-scale datasets (Brown et al., 1953, 417).
49While the arrangement of punch cards still relied on human computors, Brown et al. (1953) argued that the superiority of the EDSAC to other mechanical machines lay in its ability to estimate empirical relationships. In regressions on large-scale datasets, since “the ratio of input plus output time to computing time is large” (Brown et al., 1953, 418), it was not economical to ask computors simply to repeat mundane tasks such as matrix inversion, addition, and multiplication. The EDSAC’s advanced speed was documented as comparable to human computors when calculating the moment matrix of variables:
It takes about 7 minutes on the Edsac to compute all the 55 weighted sums of squares and cross-products of 10 variables with 40 observations in addition to about 4 hours for punching and checking the number tape and verifying the results by a sum-check. A human computer with an electric desk machine would probably need about 75 hours for this job, so that 71 hours of labor are replaced by 7 minutes of machine time. (Brown et al., 1953, 423)
50This reduction in labor was not only impressive relative to the former method of organizing computations, but also when compared to Orcutt’s RA, a relatively recent technology adopted by the DAE. Orcutt once reported the RA’s efficiency in computing 1890 sums of cross products of deviation from means: “The punching of the cards took about four to five minutes per card, and it took about 30 seconds, using the machine, to obtain each sum of cross products of deviations from means …” (Orcutt, 1948a, 68-69). Judging from the ratio of total card punching time to machine time, the EDSAC (240 mins/7 mins) represented a still more efficient computing solution than the RA (4-5 mins/0.5 mins).
- 41 Rowe was an affiliate of the NIESR who frequently co-authored with Stone on demand analysis.
51With the EDSAC and new microdata on household expenditures, Cambridge econometricians consolidated the first series of collective contributions to post-war microeconometrics. Largely connected to the computing jobs presented in Table 1, these contributions utilized the surveys of 1937-1938 on the working classes and of 1938-1939 on the middle classes to estimate the demand structure of commodities and marginal propensity to consume. A series of journal articles authored by Aitchison, Brown, Houthakker, Prais, and Stone were published in leading journals. The EDSAC helped the DAE to complete three departmental monographs, including Measurement of Consumers’ Expenditure and Behaviour in the United Kingdom, 1920-1938 (Stone and Rowe, 1954),41 The Analysis of Family Budgets (Prais and Houthakker, 1955), and The Lognormal Distribution (Aitchison and Brown, 1957). These three books attracted wide attention from econometricians and distinguished the DAE as a top-tier research institution in econometrics. For instance, Roy G. D. Allen, professor of statistics at the London School of Economics, praised the Stone-Rowe study highly (Allen, 1954, 124). By 1960, the Prais-Houthakker study had been reviewed 16 times and the Brown-Aitchison study 13 times.
52First, in the interwar period, Stone (1945) had estimated the market demand for commodities in the UK in 1920-1938. Stone and Rowe (1954) further extended the previous analysis by combining the results from microdata. The quantity-price equation was decomposed into price effect, income effect, and time trend. While price elasticities were obtained from the original national-accounting statistics, income elasticities were estimated from budget materials which contained household expenditures on different commodities. A dummy variable was included to distinguish between the two surveys of different classes, and the Cochrane-Orcutt transformation was adopted to eliminate time trends. To account for the gap between income and total expenditure elasticity, Stone and Rowe applied a 10 % reduction of the result from household surveys to approximate income elasticity based on Houthakker (1952, 20)’s estimate of the marginal propensity to consume. By doing so, Stone and Rowe (1954) argued that the variations in consumption due to price fluctuations and individual preferences could be successfully isolated:
… the variation in consumption per equivalent adult thus attributable to changes in income per equivalent adult is removed from consumption per equivalent adult in the time series, and the residue is related to changes in relative prices and to time as an indicator of the slowly changing effects of tastes and habits. (Stone and Rowe 1954, 310)
53Based on the 1954 study, Stone (1954) presented his model of linear expenditure systems (LES). The LES adopted the idea of simultaneous equation modelling to synthesize those individual commodity demand equations into a compact system. A system of demand equations in 1920-1938 could thus be used to project future national demand for commodities. Stone’s LES paper pioneered the entire field of demand analysis that aggregated a universal demand system with the fewest assumptions and empirical estimates. Deaton evaluated the LES as “a major breakthrough, not only in demand analysis, but also in applied econometrics in general” (Deaton, 2008a, 17). Although Stone had clearly noted that the calculations were performed by “Miss Potter and Miss Ayling” (Stone, 1954, 511n) at the NIESR, the project also appeared on the EDSAC job list (Table 1) assisted by Brown.
- 42 Those specifications being double-log, log inverse, semi-log, linear, and hyperbola.
54Second, Prais and Houthakker (1955) estimated the UK Engel curves using the same interwar budget surveys. The study applied five model specifications to find the best econometric model for the estimation of income elasticity.42 The EDSAC was used in all schemes of computation and Chapter 6 elaborated upon the computational methods and procedures based on Brown et al. (1953). The study found that double-log specification provided “a fairly satisfactory description” for most commodities and semi-log for most foodstuff expenditures (Prais and Houthakker, 1955, 103). Detailed estimates were reported under both specifications. Based on the results, the authors diverted to explore different topics on consumer behavior and income elasticities.
55Finally, Aitchison and Brown (1957) investigated the mathematical features of lognormal distribution and its empirical applications in economics. At first, they constructed 65 artificial random samples and used the EDSAC to test their lognormality. Then, they explored the practical applicability of lognormal distribution in describing the actual behavior of household budgets. Based on the results, they argued that the assumption of lognormal distribution of total expenditure was a proper approximation to aggregate household behaviors (Aitchison and Brown, 1957, 123). Results from the 1937-1938 working-class survey further illustrated this argument. At the end, this study also devoted a single chapter to discussion of the technical issues around use of the EDSAC.
56In the early 1950s, a new division of computing labor emerged at the DAE following the operation of the EDSAC. The growing scale of emerging microdata suggested that the old way of computation was impractical. The epistemic need for large-scale regressions encouraged junior researchers, such as Aitchison, Brown, Houthakker, and Prais, to learn programming expertise in order to solve practical issues. Once econometricians had become computer programmers, programming skill as a unique asset for producing econometric knowledge gradually gained respect, as Stone noted that advancing econometric knowledge could not be a single-handed practice:
the coordination of economic facts and theories involves essentially more than just a knowledge of economics; in addition, there are mathematical problems of formulation, statistical problems of estimation and the testing of hypothesis and problems of computation. (Stone and Rowe, 1954, xxvi)
- 43 One exception is Stone and Rowe (1954), where the calculations were done at the NIESR and undertake (...)
57Stone’s perception showed that the meaning of practicing econometrics was experiencing a fundamental change. With the emergence of new computing technologies, expertise in data processing and computer programming had been separated into two distinct tasks. While the former task was outsourced to computors, econometricians took on the latter and learned how to work with digital computers. Consequently, the DAE econometricians developed close cooperation with the Mathematical Laboratory and continued their reliance on computors for other desk computing works such as data punching and checking, and diagram sketching. For instance, Houthakker (1952) in his footnotes acknowledged not only the DAE’s senior computor Mrs. E. M. Chambers for her supervision of a “large amount of computation” (Houthakker, 1952, 359n), but also Wilkes and his collaborators for “the no less formidable task of computing weighted sums of squares and cross-products of 10 variables … carried out on the EDSAC” (Houthakker, 1952, 366n). In many other cases, such as Prais and Houthakker (1955) and Aitchison and Brown (1957), acknowledgements were expressed in parallel to Wilkes and the DAE computors,43 indicating that the new divisions of labor had solidified.
- 44 The meeting minutes noted: “Professor Stone drew attention to the fact that with the departure of M (...)
- 45 “Minutes of the 60th meeting of the Committee of Management”, 1 Mar 1956, UA/Min.V.392.
- 46 “Minutes of the 61st meeting of the Committee of Management”, 25 Apr 1956, UA/Min.V.392.
58In the mid-1950s, the EDSAC and its programming knowledge became significant parts of the production process of econometric knowledge. At the time, the DAE’s main programmers were Aitchison and Brown. However, at the end of 1955 when Aitchison decided to resign, Stone, who had just stepped down from his directorship, initiated discussions on the employment of a new programmer at the Committee of Management meeting.44 At the next meeting, a research plan to investigate the productivity of coal mines for the UK government was proposed by Farrell, who expected that the project “would require initial assistance from a research worker able to design and carry out Edsac programming.”45 To accommodate this need, the Committee of Management quickly arrived at the conclusion that the DAE’s research worker for programming would have to be Slater, who was “extremely suitable” for this appointment.46
- 47 Slater (2013, 215) confirmed that she was the second woman to use the EDSAC.
59This decision did not come out of nowhere. Slater had studied mathematics at Bedford College of London University (BA 1944; MA 1949; PhD 1951; DLitt 1956) and Cambridge University (PhD 1953; ScD 1968). Before coming to Cambridge, she completed her PhD thesis on hypergeometric equations that would eventually make her a well-known mathematician. Since 1951, she had been working at the Mathematical Laboratory under Wilkes and programming with the EDSAC. As one of the earliest EDSAC programmers,47 Slater had assisted other users outside the Laboratory, including Brown, with small computing jobs. She recalled an occasion around 1953 when Brown had asked her to provide a short program to conduct repetitive calculations of various input data:
By this time [1953], the computer could calculate and print decimals with the point in the correct place. The main difficulty was that double length floating point numbers were only just being developed and the calculation required the difference of two nearly equal sums of squares, that is the difference of the sum of squares of the observed data and the sum of squares of the theoretical data. There was a lot of programming and testing work for me to do before I got a routine which could do that calculation fairly accurately. (Slater, 2004, 120)
- 48 For technical improvements to the EDSAC II, see Wilkes (1992).
- 49 Slater (2013, 244) referred to it as “Edsac 1 ½”.
- 50 Slater, An interview conducted by Janet Abbate for the IEEE History Center, April 9, 2001.
60Slater’s technical support became more valuable with the further development of the EDSAC. In 1956, the Mathematical Laboratory began to modify its old machine into EDSAC II, a second-generation EDSAC with improved design and components “at least ten times faster” (121) speed.48 Slater was one of the few members of the Laboratory who programmed the early EDSAC II while it was under construction.49 From early 1956, she performed some small jobs using the EDSAC II for the DAE econometricians, including one that computed all the balance sheets of companies from the London Stock Exchange for Prais. Slater then “managed to form some sums and cross-products for him and Siggy seemed pleased” (Slater, 2013, 244-245). Therefore, it was no surprise that Slater appeared at the top of the DAE’s list of candidates for programmer when Brown “wanted to start a proper computing unit that could get the work done for preparing the programs and the data to be put into EDSAC II.”50
- 51 An episode was recalled by Slater during the interview. In response to the issue of (card) punching (...)
61In May 1956, nominated by Brown, Slater was interviewed by the DAE’s Selection Committee, including Denis Robertson, Austin Robinson, Stone, and new director Brian Reddaway. Although Robertson, who was sceptical of the use of computing machines,51 expressed doubts, the department made Slater the offer of a position as Junior Research Officer with Stone’s strong support. Slater accepted the offer and began what she described as “a long and happy collaboration with the DAE” (Slater, 2013, 250).
Table 2. EDSAC Jobs by DAE Staff Members, 1 November 1956 to 24 October 1960
|
Job No.
|
User
|
Job Title
|
|
389
|
Slater
|
Pilot study of productivity of coal mines
|
|
390
|
Slater
|
Life-income cycle of dentists
|
|
391
|
Slater
|
Inversion of matrices for Dep. of Applied Economics
|
|
392
|
Slater
|
Development of linear regression programs
|
|
422
|
Slater
|
Regression on car price cycles
|
|
81/4
|
Slater (for Brown)
|
Covariance analysis
|
|
459 & 84/6
|
Slater
|
Probit analysis
|
|
460
|
Slater
|
Regression analysis
|
|
85/6
|
Slater (for G. S. Watson)
|
Probability distributions
|
|
507
|
Slater (for Stone)
|
5 dimensional probit analysis
|
|
547 & 90/8
|
Slater (for A. Ghosh)
|
Inversion of matrices for input-output analysis
|
|
550 & 90/9
|
Slater & Mr. Fieldhouse (for Brown)
|
Linear programing
|
|
97/4
|
Slater (for A. D. Bain)
|
Estimation of growth curves for television
|
|
98/7
|
Slater (for Brown)
|
Covariance analysis of price and quantity data
|
|
101/21
|
Slater (for Brown)
|
Extension and application of a project 98/7
|
|
101/22
|
Slater
|
Development of probit analysis programs
|
|
102/11
|
Slater (for J. R. S. Revell)
|
Local authority calculations
|
|
103/4
|
Mr. Longden with Slater present (for A. R. Prest)
|
Regression analysis to test a method of computing income elasticities of tax yield
|
|
103/18
|
D. G. Champernowne (Faculty of Economics)
|
Mechanical composition of four-part harmony
|
Source: UA/Comp A.9 (2-6), “Current list of EDSAC Jobs”, summarized by the author.
- 52 According to Slater (2013, 250), “I was given a desk in a pre-fabricated building [of the DAE] on t (...)
- 53 It is worth noting that Champernowne appeared in the list (no. 103/18) as the first person applying (...)
- 54 UA/Comp A.9 (4).
62Continuing to work in the Mathematical Laboratory,52 Slater began heading the DAE’s computor unit and taking charge of programming responsibilities for the department. Table 2 summarizes the EDSAC jobs done by DAE staff members since mid-1956, at which point Slater became almost the sole user. These computation jobs included her own projects developing linear and probit regression programs (no. 392 and 101/22), and projects proposed by Brown, Stone and others.53 At the time, econometricians often submitted their research descriptions themselves, and Wilkes would approve the requests as long as Slater programmed. Despite this, the computing time requested by the DAE still occupied a very small proportion of that approved by the Laboratory. From 1st August to 31st October 1958, the DAE’s five projects (459, 460, 507, 547, and 550) only used 2 hours and 47 minutes of computing time that accounts for just 0.73 % of the total time approved.54 Slater also occasionally acted as supervisor of the first students to enter the field of programming (no. 550, 97/4, and 103/4).
- 55 The project was known as the “Rocket Project”.
63As directed by Stone and Brown, Slater’s major task was to solve the “computer bottleneck” to make “calculations carried out accurately and quickly” (Slater, 2013, 248) for Stone’s idea of building a computerized model of the British economy, which would later become the “Cambridge Growth Project” (1960-1987).55 However, as Stone and Brown had not been fully ready to initiate the project, they asked Slater to design a regression program that could perform regressions faster and more accurately. At the time, obtaining regression coefficients from a large-scale dataset still required computing various numerical elements separately, meaning that the machine could only “calculate” “a bit at a time, as the women did using the hand machines” (Slater, 2013, 248), but not “run” the whole regression as one continuous, coherent process. The problem led Slater to her first task, assisting Farrell in sorting out the coal mine data (no. 389), which consisted of 818 British coal mines punched on 80 column Holorith cards. To this end, Slater described the technical problems when constructing a regression program on the EDSAC II:
The central problem was that of inverting a matrix … A second problem was that the process involved subtracting one number from another which was nearly equal to it. So this part of the process had to be carried out using double-length arithmetic. This also was a problem I had encountered before. (Slater, 248-249)
- 56 Slater recollected: “In those days, we could only invert a three-by-three on EDSAC I, and that was (...)
64The first matrix inversion issue was raised due to the transition between the two EDSACs. Matrix inversion is an essential procedure for obtaining multiple-regression estimates, and it was a general problem at the time. Adding another dimension to a square matrix resulted in a lot of calculations for its inversion. In the early 1950s, inverting a three-by-three matrix was considered satisfactory due to the limited speed of the EDSAC.56 Later, to accommodate the improving speed of the EDSAC II, a new regression program with larger matrix inversion sizes must have been redesigned. The second subtraction issue was akin to what Slater had encountered around 1953. With the greater accuracy of point numbers on the EDSAC II, the problem apparently became manageable a few years later.
65Apart from technical issues, another practical concern was data preparation, as Slater confirmed that the “problem was that the data was on punched cards and we had no punched-card reader in the laboratory. So the engineers had to make a machine which would transfer punch cards onto paper tape. This they did quite quickly” (Slater, 2013, 252). Even with the transformation problem solved, Slater still needed computors to do other punching and checking works, as she later recalled:
- 57 Slater, An interview conducted by Janet Abbate for the IEEE History Center, April 9, 2001.
I had a girl called Ruth Loshack. Harry Loshack was the secretary for the department, and she was his daughter. So I trained her to do some punching for me. It was a typing job, but she had to be able to check that the pattern of holes was correct … And it was a long, slow job because of the checking. In those days, it had to be done twice, and then the two tapes compared through a machine which compared them, and stopped if there were holes that were was different—that didn’t agree. You needed two copies, because paper tapes tore very easily. So it was a long job, and it took her all day to do it, and then I ran it in the night.57
66The case of Loshack verifies that the computors’ job remained largely unchanged between the EDSACs. The duties of the computing room still existed, and the only difference was that its supervisor had been replaced by Slater. As a result, with Slater’s assistance, Farrell wrote an EDSAC program for regression analysis, which was, as Slater stated, “as far as I know … the first attempt in England to produce a program which could do an elementary regression,” and “quickly became very popular among other research units in the University” (Slater, 2004, 121). Final computations of the Coal Mine project were obtained through the EDSAC II. The results were published later as Farrell and Fieldhouse (1962) and Farrell and Jolly (1963).
67With Slater’s engagement, regression programs continued to be developed at the DAE. In the early 1960s, a series of programs tackling multiple regression analysis had been completed (Slater, 1962, 289). The very first version on the EDSAC II was named “REG I”, where its specification was described as following:
- 58 “Specification of Regression Programme for E.D.S.A.C. II: ‘REG I’”, UA/Comp A.9 (3).
Given a set of data either plain {au, v} or weighted {wu ,, au, v} with u = 1, 2, …n, v = 1, 2, …k + 1, where n is unlimited, but k≤10, this program performs a general regression analysis a with a number of special option.58
- 59 “REG II” and “REG III”, UA/Comp A.9 (3).
68In short, the REG I could allow at most 11 variables of unlimited observations and compute regression coefficients as direct output. The program also contained other options such as weighted, logarithmic and first-difference transformations. Later, the size of matrix inversion further expanded. The “REG II” could invert any square matrix to a maximum of 21 dimensions, and then could be fed as part of the inputs into the “REG III”, which had a capacity of 27 dimensions and could also export coefficients directly.59 In the 1960s, the DAE played a crucial role in developing these general regression subroutines that made estimations more economical. These programs became valuable assets of the Mathematical Laboratory that benefitted not only the DAE’s econometricians but also scientists from other departments.
- 60 Applying the TITAN to the DAE’s econometric works was not successful due to machine failures (DAE, (...)
- 61 As Documented in DAE (1973, 12), “A major task for the computing staff, under Dr L. J. Slater, aros (...)
- 62 For Slater’s contribution to the developments of software for the Project, see Barker et al. (2004)
- 63 This episode was from Slater’s reminiscence, “we had a party to celebrate the [Stone’s] Nobel Prize (...)
69In 1960, Slater took over programming duties for the Cambridge Growth Project, receiving a special appointment from the DAE as Assistant Director of Research in 1962 as a result. Thereafter, computing technology kept advancing. In 1963, the newly designed TITAN computer was completed at the Mathematical Laboratory, indicating that a third-generation computer would replace the old EDSAC II.60 The Laboratory organized a funeral for EDSAC II. People dressed in black and prepared wreaths and cards to mourn the demise of their machine, which was officially switched off permanently after finishing its last task (Slater, 2013, 264). In 1972, the Laboratory held a funeral for the TITAN and welcomed the arrival of the IBM 370, which also operated on the Fortran language unlike the TITAN (Slater, 2013, 267). Every time these machines were switched from one to other, Slater had to translate the existing programs so that they would be compatible with the new system.61 Until her retirement in 1982, Slater worked on a series of Fortran programs for economic research and the Project.62 During these years, Slater was, as once praised by Stone, “dea ex machina” (goddess behind the machine) of the DAE who “ought to have had a share in the [Nobel] prize.”63
70Indeed, it is now difficult to judge the fairness of Stone’s claim as he won the Nobel Prize due to his work on systems of national accounts. However, Slater’s arrival as programming specialist signified the transition to a more precise division of computing labor at the DAE. As the problems of computation became further complicated following the invention of new computers, the demand for an econometricians’ programmer naturally emerged to tackle these practical issues. In this sense, the employment of Slater marked that programming skills had become a separate but inevitable profession, and the DAE stood out as one of the first econometric institutions that appreciated this expertise, as confirmed by herself:
There were no such jobs as computer officers or systems analysts. Those jobs had just not been invented at that time. But, from my point of view, it sounded like a good offer, provided that they [the DAE] did not mind my knowing little or nothing about economics. (Slater, 2013, 250)
71Slater’s impact on the DAE’s research exemplifies that econometricians’ programmers deserve a place in the history of econometric computations. While the computing expertise was becoming irreplaceable, it did not matter whether the econometricians’ programmer knew anything about economics, but they had to master the “economics of programming” (Brown et al., 1953) in order to make every computation work efficiently. In other words, they had to be capable of translating the econometrician’s idea into the practical domain, supervising the women in the computing room on data-punching using as little labor as possible, considering the arrangement of sub-routines under certain computing time constraints, designing the whole ensuing procedure on computers, checking the accuracy of estimates once every run was done, and striving to improve the existing programs for future use. As such, the DAE’s case showed the exact point of historical transition where econometricians began to outsource the computing work to professional programmers. Another story in parallel could also be found across the Atlantic from former DAE affiliate Orcutt. In the mid-1950s, Orcutt initiated a microsimulation project at Harvard. One of the successful elements of his Monte-Carlo simulation was the project’s main programmer Martin Greenberger. Lacking a proper programmer was instrumental in his failure to construct a new microsimulation model at Wisconsin (Cheng, 2020).
- 64 Slater confirmed that “My unit, the room with twelve women with calculators, gradually changed to a (...)
72From the late 1950s, the DAE under Brain Reddaway’s directorship gradually moved away from econometrics, leaving the complicated programming and laborious data collection mainly to Stone’s Growth Project (Smith, 1998, 99-101). From the 1960s onwards, the number of computors at the DAE continued to decrease. In 1964, the DAE hired sixteen computing staff including thirteen females (DAE, 1965, 32). The adoption of the IBM 370 in 1972 signaled the beginning of the end for the old-fashioned computors. In 1974, after the program transfer from the TITAN to the IBM 370 was confirmed to have gone smoothly, DAE’s “data processing staff”, a professionalized name for computors in the 1970s, was reduced from five to three (DAE, 1975, 18).64 The overall budget of the computing unit remained unchanged, implying that the computors’ salary on average were improved to reflect the increasing workloads. Many of the DAE computors were relieved from their desk-computing jobs during this transition.
73In the 1960s, following the commercialization of digital computers and the standardization of programming language, software packages gradually came to play a crucial role in econometric computations. Programming packages written in Fortran boomed, exemplified by Slater and her collaborators at Cambridge and practitioners from other worldwide institutions such as the London School of Economics, the Massachusetts Institute of Technology, and the Universities of Michigan, Pennsylvania, and Wisconsin (Renfro, 2004). Econometricians from these universities became programmers again or, in more specific terms, Fortran programmers for IBM computers. Among these cases, did the econometricians have their “Slaters” during the construction processes behind the software packages? This paper cannot answer whether there were always hidden figures behind econometric practices, but Slater’s story is a fair start in documenting the contributions of professional programmers to the computerization of economics.
74Transitioning from computors to computers, the story of the DAE is a fruitful and representative chapter in the history of econometric computations in the postwar era. With emerging computing technologies, the division of computing labor in econometric practices gradually switched from one to the other, intertwined with, analog machines, econometricians, digital computers, and professional programmers. Econometric practices are driven not only by econometricians’ ideas and available data, but also by those computors and programmers hidden behind the scenes. As the historical picture is complicated, an integrated narrative accounting for these computing labors is needed. While this paper contributes to such a need, more case studies could be done to further fill this gap in the history of econometrics.
I thank editors of this special issue, two anonymous referees, and participants of the 2022 workshop on “The Computerization of Economics” for helpful comments.