During his honours research on an index of industrial production at the University of Western Australia, Salter gained an understanding of the composite commodity theorem. The applied work on the index of industrial production provided him with the analytic foundations for his two famous contributions to economic theory, in capital theory and international trade theory. In his Ph.D. thesis at the University of Cambridge he agreed with Joan Robinson that it is impossible to measure the aggregate capital stock because the assumptions of the composite commodity theorem do not hold in a general equilibrium framework. But Salter was not bothered by the elusive nature of capital because he saw no need to measure the capital stock in the first place. He developed a vintage model of capital, in which technical progress occurs at the margin of the capital stock, when new investment goods are installed. In the dependent economy model Salter, however, accepted the aggregation of exportables and importables because in a small open economy the terms of trade are unaffected by domestic economic policy. Thus, Salter recognised that the capital stock is an invalid aggregate in a macroeconomic model, but internationally traded goods are a valid aggregate in the dependent economy model. His success as an economic theorist lies in the fact that he understood when to apply the composite commodity theorem as an analytic tool, and when to avoid it.
In 1953, Wilfred Edward Graham Salter submitted his honours thesis at the University of Western Australia, in which he constructed an index of industrial production for Australia. The thesis was well received by the faculty and, after some revisions, it was published in a monograph series of the Department of Economics. In this paper the connection between Salter’s honours research and his pioneering contributions to economic theory and policy is considered. Salter was a gifted student who had the good fortune to be involved in a fruitful research project at the beginning of his professional career. During the honours year, he learnt to apply the analytic tools of economics, and he worked with new production data that had become available in many countries, including Australia, after World War II. Both, the analytic skills and the applied statistical work were critical for his Ph.D. research at the University of Cambridge and his distinguished career as an economist in the public service, which was tragically cut short at a young age.
Born in 1929, Salter spent his childhood during the Great Depression and he experienced World War II as a teenager.1 From 1948 to 1953, he studied economics at the University of Western Australia, graduating with first-class honours. Frank Richard Edward Mauldon served as supervisor, and Salter also acknowledged the help of Frank Benson Horner, who worked at the New South Wales Bureau of Statistics in the early 1950s. After the honours thesis, Salter embarked on an ambitious, if not hectic, schedule of research and writing. The honours thesis is dated February 1953 and the revised thesis was published by the University of Western Australia Press in 1954.2 In January 1953, Mauldon asked Salter and Ronald William Peters to conduct a feasibility study on regional income measures for Western Australia. In September, Salter submitted a preliminary report with sectoral income measures at the state level, leaving it to Peters to disaggregate the state figures to the regional level. Pointing out some limitations of his study, Salter (1953a, p. i) mentions that he had been forced to complete it “by a certain date”, which was given by his departure for England in the second half of 1953.
In the Department of Applied Economics at the University of Cambridge, Salter found a research culture that was conducive to his research interests. In 1954, he won the Stevenson Prize for the best graduate essay, and in 1955 he submitted his Ph.D. thesis on technical change and labour productivity. The supervisor, William Brian Reddaway, was an authority on the British index of industrial production who shared Salter’s enthusiasm for applied statistical work. Salter was also helped by Laszlo Rostas, who was an expert on taxation and the measurement of productivity. A post-doctoral fellowship enabled Salter to spend the academic year 1955/56 at Johns Hopkins University, where he added American data to his thesis. At Johns Hopkins University he discussed his work with Fritz Machlup, an eminent Austrian-American economist, and his student Edith Elura Tilton Penrose, who is known for her theory of economic growth, which is based on the acquisition of knowledge by the firm.3 Salter returned to Australia in September 1956 – only three years after he had left the country. He had used his time well since he had hastily submitted the report on income measures for Western Australia in September 1953. The revised honours thesis had been published, his graduate essay had won him the Stevenson Prize, the Ph.D. had been completed, and he had spent a productive postdoctoral year in America.
Back in Australia, Salter spent four years as a research fellow at the Australian National University, a still young institution that had been established ten years earlier. At the ANU Trevor Winchester Swan, the co-author of the Solow-Swan model of economic growth, and Ivor Frank Pearce took an interest in Salter’s research on productivity and technical change. Two works published in this period established Salter’s reputation as a first-rate economic theorist. In Productivity and Technical Change (1960), which was based on his Ph.D. thesis, he developed a vintage model of capital in which technical progress can take place only if there is investment. The second work is the article on ‘Internal and External Balance: The Role of Price and Expenditure Effects’, which appeared in the Economic Record in 1959. In this article Salter put forward a model of international trade for a small open economy – Australia – in which output is divided in internationally traded goods and non-traded goods. Salter’s work on productivity and technical change and his model of international trade are commonly regarded as two independent contributions to economic theory. Andrea Maneschi (1997) writes that “Admirers of Wilfred Salter can be divided into two distinct sets who appear to be unaware of each other, those who praise his work on productivity and technical change, and those who praise his Australian open-economy model.” In this article it will be shown that both contributions of Salter to economic theory have a common source: his honours thesis, which gave him a firm understanding of John Robert Hicks’ composite commodity theorem.
In 1960, Salter became an assistant secretary in the Prime Minister’s Department in Canberra. It seems that he preferred public service and the involvement in the formulation and implementation of economic policy to academic research. One reason for his reluctance to pursue an academic career, which undoubtedly would have been distinguished, was his passion for national income and output data. In the mid-twentieth century, the collection of income and output data became an undertaking of national statistical offices. The League of Nations investigated the feasibility of national income and output statistics and, after World War II, national statistical offices adopted the new system of national accounting of the United Nations. In his honours thesis Salter constructed the first index of industrial production for Australia, and in the report that he submitted to Mauldon on the eve of his departure for England he estimated state income for Western Australia. But he quickly realised that universities lacked the resources needed for the construction of national economic data sets. Salter was not interested in an academic position because the public sector became the driving force behind the collection of quantitative economic information in the mid-twentieth century. In the report on income in Western Australia he commented:
“During the course of this study it has become increasingly obvious that income studies cannot be carried out completely satisfactorily except in a well-equipped research bureau and by a team of research workers. Income research demands complete and detailed knowledge of virtually all statistics and their sources. An individual cannot hope to master completely the intricacies of all the figures he uses. … For these reasons, a University research worker can only hope to present a framework within which future effort can be directed.” (Salter 1953a, p. i)
Salter’s interest in quantitative economic information was not limited to Australia. Taking leave from the Australian public service in 1962, he joined the development advisory service of Harvard University to become an economic advisor to the government of Pakistan. He was attracted to Pakistan because it provided a laboratory for the theory of technical change that he had developed in his Ph.D. thesis. Salter (1955/60) and Leif Johansen (1959, 1961) independently pioneered the vintage model of capital. In Salter’s model machines that are installed now use new technology, whereas old machines that had been installed earlier incorporate obsolete technologies. New and old technologies coexist at the same point in time, with the owners of new machines earning economic (Ricardian) rents. One of the most striking features of a developing economy is the coexistence of new and traditional technologies. In Pakistan lorries coexisted with donkey carts, plantations coexisted with subsistence farming, and factories coexisted with street workshops that were run by artisans. Yet, Salter did not have the time to make a lasting mark on development economics. In 1963, he died in Lahore of heart failure, leaving behind two children and a wife who had loyally supported him during his studies, typing his honours thesis at the University of Western Australia.
2. Relative Prices and Economic Aggregates
In the first chapter of his honours thesis Salter discusses the conceptual difficulties that arise when different goods are aggregated to a quantity index. The three text boxes that are displayed in this article are the first three sections of Chapter I of the honours thesis. The same headings are used as in the honours thesis and the complete text of each section is reproduced. The text of these sections is virtually unchanged in the revised version of the honours thesis, which was published by the University of Western Australia Press in 1954. The same does not apply to other parts of the honours thesis, which Salter revised for publication.
Salter starts his analysis with the premise that the ultimate goal of economic activity is the satisfaction of human wants. Applying standard price theory, he notes that the ‘utility dimension’ of goods is reflected by prices. For this reason, economists are interested in the value of an economic aggregate, and not in its weight or some other physical dimension. It follows that “at one point or another, the price factor must be introduced if a measure [of industrial production] is to be economically significant.” This argument is much deeper than the common quip that prices must be used ‘because it is not possible to add apples and bananas’. According to Salter, a quantity index is an economically meaningful measure because the price weights give it a ‘utility dimension’. Text Box 1 displays the section on the problem of aggregation in Salter’s honours thesis.
Text Box 1
I – THE PROBLEM OF AGGREGATION
The first problem may be stated as: How can we aggregate a series of different goods and services in some way that is economically significant?
While a transport engineer may be interested in their total weight or volume, to the economist the only significant aggregation is total value. This, of course, springs from the economist’s point of view. We are interested in a “thing” not because of its size or weight but its ability to satisfy human wants. Our concern is its “utility dimension”, which we approximate by price. Physical measures only have economic significance to the extent that they are a useful means of expressing price per unit.
The important point for our purpose is that economic measures of quantities cannot be divorced from prices. Whatever else we may do, at one point or another, the price factor must be introduced, if a measure is to be economically significant.
In the next section, Salter considers the difficulties that arise when prices change. He observes that the value of an economic aggregate can change for three reasons: (1) the quantity of goods changes, (2) a change in tastes causes an adjustment in relative prices, and (3) the value of money changes. The price effects – items (2) and (3) – break the link between the value of the aggregate and the quantity of goods that it represents. A change in the value of the aggregate unambiguously reflects a change in the quantity of goods only if relative prices and the value of money remain constant. Salter elaborates “… if relative prices and the value of money are constant and the quantities have doubled, we can say that the economic significance of the aggregation of goods is twice as great.” This section of the honours thesis is reprinted in Text Box 2.
Text Box 2
II – COMPARISONS BETWEEN AGGREGATES
For a comparison at one point of time few difficulties arise since the “utility dimensions” of goods are fixed and the relationship between utility and money is constant. Thus aggregates can be compared simply on the basis of their total values.
It is when we attempt a comparison over time that difficulties arise. Over a period three types of changes can occur that will affect the value totals.
A change in the quantity of goods.
A change in “tastes” or the “utility dimension” of goods. This change is reflected in relative prices.
A change in the value of money or the “money-utility” relationship.
Changes (ii) and (iii) are reflected in price.
Thus while we can aggregate quantities of coal, apples and locomotives on the basis of period A’s relative prices and value of money, and we can similarly aggregate quantities of the same goods at period B’s relative prices and value of money, we cannot compare them. This is because there is no connecting link between the two sets of values. At least two of the three factors must be constant before a comparison can be made.
Thus if relative prices and the value of money are constant and the quantities have doubled, we can say that the economic significance of the aggregation of goods is twice as great.
If quantities and the value of money are constant and relative prices have changed, we can say the economic significance has increased or decreased by so much.
If quantities and relative prices are constant and the value of money has changed, we can use a comparison in the value totals to measure the change in the value of money.
In practice all three changes occur over time. This means we cannot compare changes in the economic significance of quantities without making artificial assumptions about prices. To the extent these assumptions are artificial, any quantity index is only an approximation. Since we can make alternative assumptions (equally artificial) about prices, no unique measure of the economic significance of quantities is possible.23
(2) Value of money only refers to its value within the aggregate under consideration, not to an overall general value of money for the whole economy.
(3) See R. Wilson (2) p. 11 for an extreme example of different results obtained by different approximations.
Finally, in the third section Salter tackles the aggregation problem from a somewhat different angle, enquiring in what sense an index of industrial production measures a ‘real’ change in production. He distinguishes between two distinct concepts of ‘real’: an index that uses the same prices for the aggregation of goods in every year is expressed in “base year prices”, whereas an index that uses current prices for every year is expressed in “constant pounds (or dollars)”. The first type of index is a Laspeyres index and the second is a Paasche index, which Salter introduces at this point:
Qi indicates the output of some industry in year i and Pi is its price. Both indexes provide measures of the real change in production because prices are held constant, but the concept of “real” is ambiguous because base year prices are used in the Laspeyres index and current prices are used in the Paasche index. For this reason, the two indexes yield different values for the change in industrial production. In his honours thesis, Salter uses the Laspeyres index, which he transforms into a form that can be easily measured. Text Box 3 presents the section of the honours thesis that deals with the meaning of the term “real”.
Text Box 3
III – THE MEANING OF THE TERM “REAL”
Index numbers of Industrial Production are in “real terms”. In view of what has been said, it may prove profitable to enquire what exactly this means.
Obviously it cannot mean simply an aggregation of goods and services for as we have seen this is impossible except in terms of a set of prices.
We can mean a comparison over time between two aggregations of goods and services each totalled according to their appropriate set of prices, but with some allowance for changes in the value of money. It should be noted that value totals derived in this way need not be identical even if equal quantities of the same goods are compared.
Or we can mean a comparison between two aggregations of goods on the basis of one single set of prices. One aggregation of goods and services, at least, would have to be totalled on prices appropriate* to it.
The upshot seems to be that the term “real” can have various meanings which are not always distinguished in its usage. The better procedure seems to be to use the phrase “in constant pounds (or dollars)” if we mean the value of money is assumed constant but relative prices have changed, and the phrase “in 1938-39” prices” if we are using a fixed set of prices.
These phrases represent alternative concepts by which changes in industrial production may be compared.
* “inappropriate” in the published version of the honours thesis.
Since relative prices change over time, a quantity index involves an error. Referring to the Laspeyres index, Salter (1953b, p. 5) notes that “the further from the base year a comparison is made, the greater is the likely error caused by aggregating goods and services on an inappropriate set of prices”. And on the Paasche index he comments “Since such index numbers are not really comparable because of changes in relative prices, the further apart we attempt to make them the greater the error.” The problem of relative prices in the aggregation of goods was naturally well known at the time Salter wrote his honours thesis. Wassily Wassilyovitch Leontief (1936, 1947) and John Hicks (1939/46) put forward the so-called composite commodity theorem, which – according to Hicks – holds that “a group of goods behaves just as if it were a single good”4 if relative prices between the goods do not change. Leontief’s version of the theorem is more general, stating that the aggregation of goods is valid if the marginal rates of substitution inside the aggregate are independent of variables outside the aggregate. Hicks had considered the simple case where marginal rates of substitution (relative prices) are constant. It seems that Salter was not aware of Leontief and Hicks’ work on the composite commodity theorem when he wrote his honours thesis, but he must have become aware of it during his Ph.D. research at Cambridge.
The list of references at the end of the honours thesis gives an indication of the applied research culture that Mauldon fostered in the Department of Economics at the University of Western Australia. Only nine works are listed, with a note that two of them include extensive bibliographies. In the introduction to the honours thesis, Salter mentions the United Nations report on ‘Index Numbers of Industrial Production’, which was released in 1950. In Chapter I, which deals with the aggregation problem, he refers to an article of Ronald Wilson (1947), who – like Salter – abandoned a promising academic career in favour of the Australian public service.5 In the main body of the thesis where the index of industrial production is developed and estimated, Salter refers to two studies on output and productivity by Reddaway (1950), his future Ph.D. supervisor, and Carter, Reddaway and Stone (1948).6 Finally, Salter (1953b, p. 15) mentions a method of measuring the output of an industry that was first proposed by Wilson (1937), although Fabricant (1940) and Geary (1944) “have been given the credit [for it] in overseas publications.”7
A trait that served Salter well in his research was his ability to focus on the issue at hand. He did not get sidetracked, keeping his references short and to the point. In his honours thesis he did not mention the pioneering research on index numbers by Francis Ysidro Edgeworth, and he also omitted the article of Ragnar Anton Kittil Frisch (1936) on the index number problem. Irving Fisher’s The Making of Index Numbers, which was first published in 1922, is mentioned just once, in Chapter II of Part II of the honours thesis where the time reversal test for index numbers is used. Salter did not refer to these major works on index number theory because his research interests were applied, involving the construction of an index of industrial production for Australia. Besides, the established literature on index numbers mostly dealt with price indexes, whereas he was interested in the aggregation of production across industrial sectors and the construction of a quantity index. Chapter I of Salter’s honours thesis would, however, have benefited from a reference to the works of Leontief (1936, 1947) and Hicks (1939/46) on aggregation and the composite commodity theorem.
3. Productivity and Technical Change
Salter arrived in Cambridge in 1953, the year when Joan Robinson started off the controversy about the measurement of the capital stock in the economy. Physical capital, which is used for the production of goods, consists of a myriad of objects and devices – shovels, computers, and so on. Like other economic aggregates, the value of the capital stock can be calculated by adding up the value of each single capital good in the economy. This is neither better nor worse than in the case of other economic aggregates – that is, a quantity index of the real capital stock is distorted if relative prices of capital goods change over time. The problem is not so much the measurement of the capital stock, but its use in the production function in macroeconomic models. The price of a capital good depends on the interest rate because it equals the present value of the flow of extra output that it produces during its life. As a consequence, the price of a long-lasting capital good falls relative to that of a short-lived capital good if the interest rate rises. Robinson (1953) pointed out that the inclusion of the capital stock in the production function is circular because macroeconomic models are used to determine the interest rate, and the interest rate is needed to determine the aggregate capital stock.