Appreciation by Graham Pyatt

Sir Richard Stone: an appreciation

In 1984, when Richard Stone was awarded the Nobel Prize in Economics, there was some initial surprise among some younger economists who assumed they would be aware of anyone worthy of such an honour; and even greater surprise when they came to realise that Richard Stone was one of those giants, no less, on whose shoulders those of us who succeed him have been privileged to stand. The fact that some of Stone's seminal contributions - a 1941 U.K. Government White Paper; the United Nations' Standardised System of National Accounts (the SNA); and the subsequent Towards a System of Social and Demographic Statisticsare the main examples - do not appear in a bibliography of his published work may go some way to explaining why it is that Stone's name has not been one to conjure with over the years outside a limited circle of aficionados [endnote 1]. But, for the rest, it must be said that, among the pioneers of econometrics (he was elected a Fellow of the Econometric Society in 1938 and President in 1955) Stone was first and foremost an empiricist. In a little-known paper The a priori and the empirical in economicsStone argues that there is more than one way of approaching most problems in economics [endnote 2]. His personal preference for an empirical approach may be even less fashionable to-day than it was twenty years ago. Yet it did not prevent Stone from making important contributions to econometrics, to multi-sector modelling and to socio-demographic analysis. The essential point is that Richard Stone believed in a methodology that started with the facts, that recognised the need for conceptual frameworks to organise the collection and presentation of those facts, and for the formal analysis of the facts in order to draw inferences from them. His contributions to the second phase of this approach constitute his outstanding achievements. But they need to be appreciated in the context of the whole. The fact that others have not had to reinvent the architecture of the national accounts in particular is perhaps the most telling measure of the importance of Richard Stone's contributions and their enduring significance.

Richard Stone wrote a brief autobiography to accompany his 1984 Nobel Lecture [endnote 3]. It tells of his early attraction to economics via classics and the law, his tutorials in Cambridge with Richard Kahn and Colin Clark, and his initial exposure to Maynard Keynes as a graduate student. They were to meet again, following Stone's war-time secondment to the Civil Service and subsequent work with James Meade on a survey of the country's economic and financial situation. Some of their results were published as the second part of the U.K. government White Paper previously referred to - An analysis of the sources of war finance and an estimate of the national income and expenditure in 1938 and 1940 - which proved to be the start of the annual series of official estimates of national income and expenditure for the U.K. and the common point of departure for two subsequent lines of development. One of these saw the emergence of a set of international standards for national income accounts, melded from the largely independent efforts of various contributors in several countries and promoted by a succession of international bodies - but always, it seems, with Stone as a prime mover - and culminating in the 1968 United Nation's volume previously cited A System of National Accountswhich was Richard Stone's magnum opus.

Meanwhile, writing for a more academic audience, Meade and Stone collaborated on a book National Income and Expenditure which, following initial publication in 1944, ran into four editions; and then a further six editions followingmajor rewriting in 1961 by Richard and Giovanna Stone [endnote 3]. This was essential reading on the subject matter for thirty years, as was another volume inspired by the early work of Meade and Stone - John Hick's The Social Framework - which introduced the term social accountingto describe the subject matter [endnote 5].

As a consequence of these symbiotic developments, their subject matter evolved from the definition and consistent estimation of the national income as income, outlays (expenditures) and product into a framework for recording the inter-relationships between production, consumption, and accumulation within an economy, and the transactions between that economy and the rest of the world, all within a fully articulated system of double-entry accounts; and then beyond, into a single-entry social accounting matrix (SAM) format that embraces input-output (the interdependence of production activities) the flow-of-funds (which records how investment is financed via savings and credit creation) and a complementary system of accounts for assets and liabilities.

The table below illustrates the essential characteristics of a SAM in schematic form. The table is square and may have any number of rows and columns (which must, of course, be equal). However, every row and column must belong to one of six categories, which are defined by the row and column labels. The first five categories represent different aspects of our (i.e. the domestic) economy, while the sixth refers to the rest of the world. The elements of the matrix (table) record the total value of transactions of a particular type during a particular accounting period - usually a calendar year. By convention, each cell is to be interpreted as a receipt for the row in which it is located and an expenditure or outlay for the column. Accordingly, the block of transactions in the bottom-left corner records payments to the rest of the world for goods and services that are absorbed by domestic markets i.e. for imports. And the corresponding block of transactions in the top right-hand corner provides similar information on the value of exports.

Table: a typical SAM in schematic form

The size of these blocks will depend on the extent to which the categories (i) and (vi) of the table are disaggregated. There may be hundreds of different types of goods and services within the category (i) or there may be just a few. Similarly, the rest of the world may be an aggregate of all economies other than ours, or the rest of the world may be disaggregated to recognise different currency areas, trading blocks, or individual trading partners. The amount of detail is a matter of choice, subject only to the availability of raw data. And the choice needs to be exercisedin relation to the analysis to be served: too much detail can be a problem, albeit of a different genre to having too little.

To appreciate a SAM one needs to peruse it, and the interested reader will gain far more by letting their curiosity wander around the table than by reading any written commentary that I could offer. Let it suffice, therefore, to restrict my remarks to three features of the SAM that the curious reader can hope to discover for themselves.

First, it can be noted that the total of all entries in each row of the SAM must be equal to the corresponding column total. And this must be true no matter how much disaggregation there may be within each of the six categories of rows and columns. Aggregate demand for each and every type of good or service must be equal to aggregate supply (because for every sale there must be a matching purchase); the total revenue of every production activity must be equal to its total costs (because value added is defined to make it so); the income of each domestic institution (such as 'all households in Sydney') must be equal to its total outlays (because of the way savings are defined); and so on. Secondly, all the well-known national accounting identities are implicit in the table e.g. the fact that savings and investment must be equal. And, thirdly, it can be noted that the circular flow of income within our economy is captured within the pattern of non-zero entries.

The SAM format is a powerful way of presenting information on the size and structure of an economy as illustrated by the table. Moreover, it is even more flexible than the above discussion suggests, allowing not only the number of individual rows and columns to be chosen at will but also for some variation in the different types of accounts. For example, the SAM which defines the 1968 UN SNA does not include separate details for factor services (to the irritation of many analysts and model builders). But it does include asset accounts, the details of which show how stocks of assets of different types at the end of the accounting period depend on the stocks held at the beginning of the period, investment during the period (net of depreciation), and capital gains and losses that occur during the accounting period as a result of price changes.

As a complement to their role in presenting data, SAMs also provide the best of all frameworks for compiling these data in the first place and the reconciliation of inconsistencies between alternative data sources. To estimate a SAM requires information from a variety of censuses, surveys and administrative records to be collated and reconciled. In this context a SAM acts as a consistency framework within which it soon becomes evident that if the information from a particular data source is assumed to be correct, then the information contained in some other source(s) must be adjusted - and by specific amounts that can be calculated easily enough via the general rule that corresponding row and column totals must be equal.

The third sense in which SAMs have come to play an essential role in contemporary practice is in calibrating models. Every model has an accounting framework that can be represented as a SAM. And the results of every model scenario can also be presented in the same SAM format. It therefore follows that if the calibration of a model is consistent with the information contained in the relevant SAM for some base accounting period, then the changes generated by alternative model scenarios can be expressed as changes from the baseline SAM to the new SAMs that are generated by these alternative scenarios i.e. by a set of incremental SAMs [endnote 6].

This evolution in the role of SAMs was not an autonomous process that just happens to have produced results that some economic model builders find useful. Rather, the evolution was driven by the desire to support the models that economists wanted to build. Leontief's work in the 1930s was informed from the outset by a keen sense of the symbiotic relationship between his model and its accounting system. And much of Stone's work throughout the 1950s was taken up with the generalisation of the Leontief model to recognise products and production activities as different facets of economic activity, and to integrate both into his social accounting matrix conception. His success in doing so provided important foundations for what became the 1968 System of National Accounts. And it also left Stone, as the 1950s drew to a close, considering what to do next.

In 1947,Dick Stone had been appointed as Director of the newly-established Department of Applied Economics in Cambridge. This provided him with an ideal base from which to pursue his various interests, which were by no means confined to social accounting. In particular, Stone shared with many of his contemporaries a lively interest in the economics of consumer behaviour and, more especially, demand analysis. This was a direct consequence of war-time realities, which had made the availability of food and the adequacy of the nation's diet a primary concern that persisted in the aftermath. The modelling of consumer behaviour was important, therefore, in trying to predict the likely consequences of shortages and for the design of rationing systems to mitigate the potential difficulties. These realities encouraged not only the development of theory but also the collection of time-series and cross-section (household survey) data. One consequence was to provide the ingredients necessary for the development of demand analysis within the then fledgling branch of economics known as econometrics. Stone made the Department of Applied Economics the international centre for work in this field. His many personal contributions to it culminated in a two-volume study for which Stone was subsequently awarded the degree of ScD by Cambridge University [endnote 7].

A third consideration helped to make the late 1950s an auspicious time for a new beginning. Britain remained in the vanguard of computerised data processing, having capitalised on the early start provided by the code-crackers at Bletchley Park with the construction of Atlas computers in Manchester and Cambridge. Cambridge had now built EDSAC II (Electronic Data Sorter and Calculator) thereby creating the capacity to compute solutions for sizeable versions of the Leontief model as generalised by Stone.

In 1959, Richard Stone launched the Cambridge Growth Project in collaboration with Alan Brown, who brought to their partnership a comparative advantage in computing as well as his own considerable capabilities as an applied economist. It was he who gave the name Rocketto the model developed within the project since all of us who were involved at that time were well aware that, like Stephenson's original locomotive, the model was sure to offer considerable scope for development as technology advanced: but, meanwhile, it was a new sort of beast [endnote 8].

The Cambridge Growth Project continues to this day, albeit in a commercial guise, and Rocket has long-since evolved into a general equilibrium model. But it proved to be useful long before that happened by showing that any attempt to accelerate growth in the British economy in the early 1960s would generate an excessof aggregate demand over supply that would be difficult to accommodate. Later, in the Thatcher years, it was the first of the UK models to predict that the number of unemployed was destined to exceed two million.

Come the 1970s, Stone refocused his energies yet again, this time on demographic accounting. His initial ideas on the subject were given their first airing in the 1970 series of Radcliffe Lectures at Warwick University. And they finally evolved into a new treatise Systems of Social and Demographic Statistics that was published by the United Nations in 1975 [endnote 9]. The central concern in Systems is to account for people. Stone sets the problem in a dynamic context in which individuals are born into, and then move (migrate) between a set of mutually exclusive and exhaustive states or categories before they eventually die. Age groups provide the obvious example of a set of states that can be used to classify the population within this framework. But there are many other potentially interesting taxonomies relative to which Stone's framework of forward and backward stochastic differential equations can be deployed, such as in tracing the movement of a population through an education or health system, or the spatial location of a moving population. And here we should note that Stone's framework for socio-demographic data is analogous to his work on the SNA in so far as the framework serves not only as an interesting way of presenting the facts: it is also a powerful framework for collating the facts and reconciling inconsistent and fragmentary data; and the architecture of the system is at least suggestive of the way in which the facts might be modelled. All of which may explain why Systems is yet another of Stone's contributions over the years that relevant authorities consider to be seminal.

Richard Stone never stopped writing, and much of his time in later years was spent preparing short biographies of twelve of his heroes, published posthumously as Some British Empiricists in the Social Science, 1650 - 1900 [endnote 10]. They are all here - the political arithmeticians William Petty, Charles Davenant and Gregory King; the economic statisticians William Fleetwood (who pioneered index numbers), Arthur Young (the concept of value added) and Patrick Colquhoun; the demographers John Gaunt, Edmond Hailey (taking time-out from astronomy) and William Farr; and the early sociometricians Frederick Morton Eden (on poverty at the end of the 18th century) Florence Nightingale (on hospital reform) and Charles Booth (on the poor in London). These essays make fascinating reading. They illuminate the origins of modern economic and social statistics: and beyond that, they celebrate an intellectual tradition of which Richard Stone was himself the outstanding exemplar in modern times.

Graham Pyatt

Warwick, September, 2005

Endnotes

(i) The complete references are: U.K., Treasury (1941) An analysis of the sources of war finance and an estimate of the national income and expenditure in 1938 and 1940His Majesty's Stationery Office, London;United Nations,Statistical Office A System of National Accounts Studies in Sources and methods,Series F, No. 2, United Nations, New York; and United Nations, Statistical Office(1975) Towards a System of Social and Demographic StatisticsStudies in Methods, Series F, No. 18, United Nations, New York.

(ii) First published in L'industria No. 4, pp. 467-86 and subsequently reproduced in Stone,R. (1966) Mathematical Methods in the Social Sciences and other essays Chapman and Hall, London

(iii) Reproduced as an annex to Stone,R. (1997) Some British Empiricists in the Social Sciences, 1650-1900Cambridge University Press

(iv) See J.E. Meade and R. Stone (1944) National Income and Expenditure Oxford University Press; reprinted in 1966 by Bowes and Bowes in a substantially rewritten version by R. Stone & G. Stone.

(v) See Hicks, J.R. (1942) The Social Framework The Clarendon Press, Oxford.

(vi) Stone did not explore this particular feature beyond its application to input-output models. But it has since been developed considerably, to the point that it is now well-established as an aspect of best practice among general equilibrium model builders.

(vii) See Stone, R. with D.A. Rowe and others (1954 & 1967) The Measurement of Consumer Expenditure and Behaviour in the United Kingdom, 1920-38Volume I (1954) and Volume II (1967) Cambridge University Press.

(viii) See Stone, R. and J.A.C. Brown (1962) ''A long-term growth model for the United Kingdom" in Geary, R.C. (ed.) Europe's Future in Figures North Holland Publishing Company,Amsterdam.

(ix) See United Nations, Statistical Office (1975) Towards a System of Social and Demographic Statistics Studies in Method, Series F, No. 18 United Nations, New York.

(x) See Stone,R. (1997) Some British Empiricists in the Social Sciences, 1650-1900 Cambridge University press.

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