I now turn to the second class of question, namely that concerned with testing hypotheses or theories. The usefulness of observation and measurement in testing economic theories arises because the theorems of economics are supposed to relate to the actual world. Any economic theorem rigorously deduced from given postulates may be regarded as an hypothesis about the actual world which experience may show to be false. Indeed, the whole economic as opposed to mathematical interest in the theorem lies in its truth or falsity and not merely in its logical relationship to the postulates. But theorems which say something about the actual world cannot be derived solely from postulates which do not, but instead are purely formal in character. Consequently, the postulates which by their very nature cannot be tested directly by economic experience require to be tested by testing the theorems. This is the normal method of science and is clearly not without its difficulties from a logical point of view. For the argument runs as follows. If postulates, then theorems: as the theorems are verified, therefore the postulates are verified. But this is only true if there is a one-one relationship between the postulates and theorems which in general there will not be. Consequently, it is much easier to show that a theory is false than that it is highly probable that it is true.

It has been suggested that economics, unlike the natural sciences, can and in fact does proceed by a direct verification of the postulates. If this were possible it would indeed be a great gain since we could avoid the fallacy of affirming the consequent noted above. I shall return to this question after a brief treatment, by way of example, of the theory of choice.

The theory of choice, or preference, is perhaps the most highly developed branch of economics and is of particular interest since, like many branches of the natural sciences, it possesses a fully worked out, deductively formulated theory. Such a theory, by which I mean one in which the theorems are rigorously deduced from an initial set of objects and relationships which are concepts by postulation, does not in economics or any other empirical science suddenly arise in the mind of a great philosopher without any considerations of an empirical kind. Rather the procedure is somewhat as follows.

For the United States of America over the years 1929-41 I have carried out demand analyses on a more extended plan with the aid of the series provided in the Survey of Current Business. Table 4 (at end) sets out in nearly all cases a number of analyses using different combinations of determining variables. The reason for this is not that each analysis is believed to be of equal interest and reliability as an expression of the demand relationship, but simply that by studying a number of equations for each commodity we can trace the influence of adding (or leaving out) variables in making demand analyses. In view of the frequent use of the regression of the amount demanded on income alone or on income and a trend it will be of particular interest to see how these combinations of variables work out in relation to other possible sets.

The conclusions to be drawn from this table may be summarized, in the order adopted in the last section, as follows.

(1) The Use of Untransformed Data

Most of the analyses shown here had been completed before the utility of using transformed series had been recognized. It was not thought worth while to recalculate the equations using first differences and so no justification can be given for the choice of untransformed variables. As will shortly be seen the residuals in the larger subsets at any rate show, on the average, values of von Neumann's ratio similar to those expected for random series of the same length. But this may be due to the ‘bias towards randomness’ discussed by Cochrane and Orcutt§ and does not ensure that the standard errors bear their usual interpretation and can be accepted as measures of reliability in the ordinary sense. However, the failure to use an appropriate transformation will mean not so much that the estimates of the regression coefficients will be biased as that we may, by calculating standard errors, mislead ourselves as to the accuracy of these estimates. Thus the regression coefficients may be of interest in themselves and the findings of the last section suggest that the standard errors may not be altogether unreliable.

It is obvious that there is an enormous amount of descriptive material, sometimes called natural history data, about economic activity in all its forms. A great deal of this will not involve measurement at all, since it will consist of descriptions of the organization and working of institutions and agreements and arrangements of all kinds. In addition to this qualitative descriptive material there is a vast mass of quantitative descriptive material. Part of the latter arises from the labours of bookkeepers, clerks and others engaged in recording, classifying and presenting records of some form of activity. This part of the quantitative descriptive material normally relates to the records of a single organization or concern, though this may of course be very large and have many branches. Another part arises from an attempt to collect information from a number of separate units as exemplified by the greater part of official statistics. Classified and tabulated information of this kind contributes to the body of knowledge known as economic statistics.

In addition to this body of descriptive material, consisting of what I propose to call primary facts, there is on the quantitative side a further type of information which may be called empirical constructs. It may be that from a philosophical point of view these constructs are not to be sharply differentiated from primary facts and that the difference, if any, is only one of degree. By primary facts I mean such things as the originating entries in a cash book or the quantity of some commodity produced over a particular period. It is not as a rule hard to find a definition for items of this kind and the problem of obtaining information about them lies largely in the administrative and technical difficulties of collection. On the other hand there are many items, similar to primary facts in having a counterpart in the actual world, but which are not capable of being apprehended in the same simple manner. These empirical constructs are well illustrated by the example of the income of an individual or a nation. No amount of searching in primary records, that is the originating entries, actual or imputed, in the books of a firm or individual, will enable us to detect the income that has been made.

It was my privilege to give the Newmarch Lectures for the academic year 1948-9 at University College, London. In preparing them for publication I have thought it best to leave the topics in their original order, but not to divide the text of this essay into four sections corresponding to the individual lectures. The ground covered by each of these is contained in Sections I-VI, VII-XIII, XIV-XXI, and XXII-XXIX respectively, and the only extensions I have made are as follows. The topics of Sections VI and x were barely touched upon in the lectures themselves and are expanded here. The numerical illustration of Section XVI has been revised in the light of the national income White Paper which appeared in April 1949 and a detailed explanation of the way in which these figures have been derived has been added. Time did not permit any reference to the details of Section XVII or to the studies described in Sections xxvn and XXVIII.

I am indebted to two members of the Department of Applied Economics for the help they have given in preparing this book for publication. Section VI has benefited from the criticisms of Mr J. Durbin and I was assisted in the presentation of Section x by Mr S. F. James.

The temerity of attempting to cover so large a subject in so small a space is obvious. For the benefit of any who may wish to pursue the various topics further I have included a number of references, mostly to the literature of the last decade. The list is in no sense comprehensive; it contains simply those books and articles which have seemed to me most relevant among those I happen to have come across.

As I am going to talk about the part played by measurement in economics I propose at this point to say a little about these terms. The essentially economic aspect of a problem has been defined by Professor Robbins in saying that ‘economics is the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses’. This way of putting the matter brings out the important point that, while many situations iṅ actual life have an economic aspect, few if any can be analysed wholly in economic terms. Taken literally, however, it would bring the applied economist practically to a full stop since he cannot in general estimate the importance of economic factors unless he is prepared to make assumptions about, and if necessary arrange to hold roughly constant, certain non-economic factors such as changes in tastes. In fact he can frequently do this for himself in a rough-and-ready way although undoubtedly it would be again if he could fall back on other branches of the social sciences for help in such matters. The moral of Robbins's definition is that in applied work much more integration of the social sciences is needed.

Measurement is concerned with finding an expression for the degree of difference in distinguishable qualities or characteristics. It is possible if a means can be found for bringing the amount of any characteristic under investigation into a certain relationship with a set of numbers. Thus we may bring the weight of pig-iron produced at different blast furnaces into relation with a set of numbers and express the different outputs as so many tons in each case. But evidently there is no need for the set of numbers to be unique; for in the above instance, by a mere change of unit, we should obtain a new set of numbers, e.g. if we expressed the result in pounds or in kilograms. But all these different sets of numbers can be obtained from one another by multiplication by a constant; for example if y is the weight expressed in pounds and x is the weight expressed in tons then y = 2240x and so on. Different measures obtained from one another by multiplication by a constant are related by a straight line relationship which passes through the zero-point on the scale of each measure simultaneously.

I have emphasized from the outset that the main interest in this field lies in the presentation of the structure of transactions, and the simplest form of this structure which I believe brings out all the essential features, but avoids unnecessary complications, is contained in Diagram 3. Let us now consider the relationship between this structure and such familiar aggregates of transactions as the national income, the gross national product and the like.

The flow from production to consumption, £9,636 m., represents the income of the factors of production arising from services contributed to British enterprises, enterprises being understood in this context in a broad sense to include individuals working on their own account, landlords, professional persons and those who render individual services. This total may conveniently be termed the domestic product, since it represents the net value of production taking place within the limits of the United Kingdom. The national income is usually denned as the income accruing to the factors of production normally resident in or owned by persons normally resident in the United Kingdom independently of whether their contribution to production is made in this country or abroad. Consequently in order to get the national income we must add to the domestic product the net income from overseas investment, which was £40 m. in 1948, giving a total of £9,676 m. for the national income.

In setting out to explain the structure of a system of transactions I took as my point of departure the primitive economic concepts of production, consumption and adding to wealth. We may think of production, to take an example, as mainly centred in business enterprises, but it is clear that not all the transactions of business enterprises will appear in the form of activity production in my system. For example, business enterprises will very frequently save something out of their income, and as we have seen all the saving in the system is represented by a flow from the form of activity consumption to the form of activity adding to wealth. In a similar way we may think of the form of activity consumption as mainly taking place in households, but again households may acquire assets, e.g. a family may purchase a new house and as we have seen all expenditure of this kind takes place between the form of activity adding to wealth and the form of activity production. Consequently we cannot identify the three basic forms of economic activity with any particular entities in the economic system, and accordingly the question arises: Is there anything else with which we can identify them? I shall now try to show that the three basic forms of economic activity are isomorphic with the three basic statements of an orthodox accounting structure.

An accounting structure for a business enterprise may be said to consist of a profit and loss account and a balance sheet. The profit and loss account may be subdivided into an operating section and a non-operating section, while we may form a third account by taking the differences in the entries between the balance sheets at the beginning and end of the period. I shall now try to demonstrate two things: first, that the transactions entering into the three forms of economic activity, production, consumption and adding to wealth, are isomorphic respectively with those appearing in the operating section of a profit and loss account, the non-operating section and an account summarizing the capital incomings and outgoings of the period, which in consolidated form would show the balance sheet differences over the period and which I shall call a resting account. Secondly, I shall demonstrate that this structure is fundamental to all entities and is in no way special to business enterprises.

Prediction in one of its many forms is the goal of economics as it is of other sciences concerned with the actual world. But prediction may be attempted in so many different ways which are logically distinct that it will probably be best if I begin by discussing and illustrating the basis needed for a full prediction even if this ideal is still a long way from being realized in practical work.

Prediction in this sense requires that we can define the state of the system, or some part of it, in terms of a knowledge of the values of certain variables and that we possess a dynamic theory by means of which we can derive future states of the system by logical implication from a knowledge of the present state. In terms of a saving-investment example which I shall use as an illustration, this means that we have, let us say, a system of relationships connecting saving, investment and income of such a kind that if we know the parameters of the system and the present values of the three variables we can deduce the values which these variables will take in each future period.

If we are to be able to do this it is evident that the values of the variables connected by the relationships of the system must not all relate simply to the levels of those variables in a single period of time. A system of this kind would be static and its solution would yield only the equilibrium values of the variables. In physics it is usual to make this connexion between consecutive periods by reducing to the limit the length of the period and by introducing derivatives of the first and higher orders, i.e. rates of change, accelerations and so forth. In economics on the other hand the differential equations of physics are commonly replaced by finite-difference equations, i.e. dx/dt is replaced by Δx/ Δt, where Δt is some unit period, say the month or the year. In this way past values of at least some of the variables are introduced into the system and a link is thus created between the past and the present and, by extension, between the present and the future.