Normative economics is generally opposed to positive economics. Positive studies aim at understanding the properties of economic systems, thus elucidating here the structure of the set of tax equilibria. Normative studies are concerned with the welfare effects of economic choices, here with the consequences, for the agents' welfare of different tax policies. Normative studies are not opposite but complementary and in fact logically consecutive to positive studies: the results of positive analysis are normally a prerequisite to a comprehensive welfare assessment. This logical order is the one adopted here. The study of the normative economics of taxation will utilize our understanding of the positive economics of taxation gained in the previous chapter.

The present chapter proceeds as follows:

Sections 3.1 and 3.2 are devoted to the welfare analysis of tax equilibria when at first only small changes are considered. The title ‘tax reform’ reflects both the normative emphasis of the analysis and the fact that small tatonnement changes - rather than the large once and for all changes suggested by optimal taxation - are a priori considered. These first two sections can indeed be viewed as extensions in the normative direction of the positive study of section 2.2, chapter 2; they provide a comprehensive welfare analysis of a neighbourhood of a given tax equilibrium whose structure has been ascertained in the just recalled ‘positive’ investigation. The third section, 3.3, gives up the purely local viewpoint by examining how the infinitesimal changes suggested in the previous subsections can be linked along a finite path of tax reform. This subsection is more technical and can be, at first, skipped by the reader.

Section 3.4 continues the discussion of tax reform in two directions. First, it transposes the analysis of tax reform of sections 3.1 and 3.2 to the case where the welfare of individual agents can be aggregated into a social welfare function. In subsection 3.4.1, a more specific algorithm of tax reform - of the gradient projection type - is suggested; a ‘Musgravian’-like interpretation of its instructions is proposed in subsection 3.4.2.

In the preface to this volume Mr Loveday explains that it is to be regarded as the first instalment of the second stage of the investigation of the League of Nations' inquiry into the Business Cycle, of which Prof, von Haberler's Prosperity and Depression was the first stage. The ultimate object is to apply statistical tests to the alternative theories of the Business Cycle catalogued by Prof, von Haberler. But this instalment is limited to an explanation of the statistical method which it is proposed to employ, followed by three examples. In the first chapter Prof. Tinbergen deals with some of the logical issues involved; in the second chapter he explains in general terms the method of multiple correlation analysis; and in the next three chapters he applies this method to three selected examples – namely, Fluctuations in Investment, Residential Building, and Investment in Railway Rolling-stock.

The second chapter, which gives in brief compass a most lucid account of the statistical method to be employed, is very good indeed. But the first chapter, which should deal with the difficult logical problems involved in applying to economic data methods which have been worked out in connection with material of a very different character, is grieviously disappointing. So far as it goes, it is helpful; but it occupies only four pages, and it leaves unanswered many questions which the economist is bound to ask before he can feel comfortable as to the conditions which the economic material has to satisfy, if the proposed method is to be properly applicable.

From the ‘Introduction’

The word ‘cause’ has been used in the preceding paragraphs to indicate proximate causes only. This means that the economic considerations upon which the relation tested is based must be directed towards finding, as far as possible ‘direct causal relationships’. The variables in the relation must be directly connected either in the minds of some persons (e.g., through the reaction of the consumer to a given income and price) or by some definition (e.g., value of sales equals volume times price). This is not always possible if the strictest sense of ‘direct’ is kept to. Investment activity may be linked up directly with profit expectations, and these are hardly measurable. The next step connecting profit expectations with actual profits and some other variables may then also be included, and investment activity may be ‘explained’ both by actual profits and by some other variables. The more, however, such combinations of successive steps can be avoided in the formulation of relations, the better. This combination may always be undertaken afterwards – in fact, it forms the very important next step in our work – but the more explicitly it is done, the better. By keeping to this principle, one obtains relations with what Professor Frisch calls the maximum degree of ‘autonomy’ – i.e., relations which are as little as possible affected by structural changes in departments of economic life other than the one they belong to. It is clearly the task of economic analysis to indicate the nature of those direct causal relationships.

Chapter III Fluctuations in Investment

The Relation Tested

In this and the two following chapters, a number of the results obtained in applying the method described above to one of the central relations in business-cycle theory will be discussed. The relation in question may be defined as that indicating the ‘proximate’ objective causes of changes in investment activity, looked at from the demand side – i.e., from the side of investing entrepreneurs and public authorities.

Calculations have been made for investment in general, as well as for residential building and railways as important special cases.

As emphasized in chapter I, the principles underlying the procedure are that economic theory has to suggest the factors to be considered, while the statistical testing process shows the maximum degree of accordance obtainable and the relative strength of each factor required to obtain the degree of accordance.

For the investigation of investment in general, the choice of the relevant factors has been based on the following considerations. Total investment activity is the sum of the investment activity of those individual entrepreneurs who decide to invest at all. The larger the number, the greater in general will the volume of investment be. Whether or not an entrepreneur decides to invest depends first of all on whether he expects to make profits or not. Therefore, the number of entrepreneurs planning investment will depend on profit expectations.

This book is the outcome of the extensive archival research on which Morgan (1990) is based. Despite being a relatively young discipline (the Econometric Society was founded in 1931), econometrics already has a substantial intellectual history concerned with making sense of empirical economic evidence. Reading the early studies in quantitative economics and econometrics highlighted the wealth of material that was no longer well remembered, and revealed the insights it could cast on current debates as well as the historical perspective it automatically provided. We discovered important correctives to some conventionalist views extant about earlier, and still famous, debates and we comment on these below. The value of reading the struggles of pioneers to see how perceptions of problems emerged and how solutions began, specifically then gradually were generalized, was brought home to us. And, of course, the pure fun of reading the views of the giants who founded a new discipline enlivened our study and motivated us to bring it to a successful conclusion. We also greatly enjoyed discussing the history of econometrics with many of those who helped create it.

Overall, the book aims to be a contribution to the history of econometrics. The papers reproduced below represent the tip of the pyramid of published material, but are sufficient to establish many key aspects of the historical record. As such, the book can also serve as a resource for courses on the history of econometrics, especially its conceptual foundations.

Chapter II: The Degree of Permanence of Economic Laws

If we compare the historic developments of various branches of quantitative sciences, 12 we notice a striking similarity in the paths they have followed. Their origin is Man's craving for ‘explanations’ of ‘curious happenings’, the observations of such happenings being more or less accidental or, at any rate, of a very passive character. On the basis of such – perhaps very vague – recognition of facts, people build up some primitive explanations, usually of a metaphysical type. Then, some more ‘cold-blooded’ empiricists come along. They want to ‘know the facts’. They observe, measure, and classify, and, while doing so, they cannot fail to recognize the possibility of establishing a certain order, a certain system in the behaviour of real phenomena. And so they try to construct systems of relationships to copy reality as they see it from the point of view of a careful, but still passive, observer. As they go on collecting better and better observations, they see that their ‘copy’ of reality needs ‘repair’. And, successively, their schemes grow into labyrinths of ‘extra assumptions’ and ‘special cases’, the whole apparatus becoming more and more difficult to manage. Some clearing work is needed, and the key to such clearing is found in a priori reasoning, leading to the introduction of some very general – and often very simple – principles and relationships, from which whole classes of apparently very different things may be deduced.

The chief difficulties in the computation of statistical laws of demand are due to changes that occur in the market during the period to which the statistics of prices and of quantities of commodities refer. In order that the statistical laws of demand shall have sufficient validity to serve as prediction formulae, the observations must be numerous; and in order to obtain the requisite number of observations, a considerable period must be covered. This usually means that, during the interval surveyed in the statistical series, important changes occur in the condition of the market. But in case of staple commodities, such as the agricultural products with which we shall have to deal, the effects of those changes in the condition of the market that obscure the relation between prices and amounts of commodity may be largely eliminated. As far as the law of demand is concerned, the principal dynamic effects that need to be considered are changes in the volume of the commodity that arise from the increasing population, and changes in the level of prices which are the combined result of causes specifically responsible for price cycles and of causes that produce a secular trend in prices. The effects of these two fundamental changes may be eliminated approximately by a single statistical device, namely, by deducing the law of demand from a generalized treatment of the elasticity of demand.

The problem

It is fairly familiar knowledge that we sometimes obtain between quantities varying with the time (time-variables) quite high correlations to which we cannot attach any physical significance whatever, although under the ordinary test the correlation would be held to be certainly ‘significant’. As the occurrence of such ‘nonsensecorrelations’ makes one mistrust the serious arguments that are sometimes put forward on the basis of correlations between time-series – my readers can supply their own examples – it is important to clear up the problem how they arise and in what special cases. Figure 9.1 gives a very good illustration. The full line shows the proportion of Church of England marriages to all marriages for the years 1866–1911 inclusive: the small circles give the standardized mortality per 1,000 persons for the same years. Evidently there is a very high correlation between the two figures for the same year: the correlation coefficient actually works out at +0-9512.

Now I suppose it is possible, given a little ingenuity and goodwill, to rationalize very nearly anything. And I can imagine some enthusiast arguing that the fall in the proportion of Church of England marriages is simply due to the Spread of Scientific Thinking since 1866, and the fall in mortality is also clearly to be ascribed to the Progress of Science; hence both variables are largely or mainly influenced by a common factor and consequently ought to be highly correlated.

Conditions of Inductive Study

Economic equations derived from experience, like Henry Schultz's demand curves for agricultural commodities, have, or strive to attain, this practical importance: they should make it possible to estimate the values which one of the variables, the ‘predictand’ (e.g., demand), will assume when other variables, the ‘predictors’ (e.g., income and price), are made to assume given values. There is, however, a proviso, silently admitted in this as in any other inductive work, whether quantitative or not. If we use the word ‘magnitude’ in a broad sense to include characteristics which can assume the values ‘presence’ or ‘absence’ but which cannot be measured; and if we use the words ‘observation period’ and ‘prediction period’ so as to include observations and predictions not only over time but, for example, within and between geographical areas (or any other samples), then we can formulate the proviso as follows.

Let y be the predictand, let x1, … xn be used by the investigator as predictors, and let a1, a2 … denote ‘all other magnitudes in the world’; some, but not all, of the a's enter the proposed relationship explicitly and are called its parameters. Then every a either must remain constant or its variations must have no significant influence on the value of y. This must be true both during the observation period and during the prediction period.

If the condition is not fulfilled during the observation period, the relationship between y and the x's is a ‘spurious’ one.

Introductory

In recent years various attempts have been made to construct econometric models of the business cycle mechanism. Some of them are very simple, others more complicated; some pay more attention to the mathematico-economic set-up, others give special care to a statistical determination of the coefficients involved. The latter group is notable for, in particular, the model by Radice of the post-war United Kingdom, that by De Wolff of post-war Sweden, and my own attempts for the Netherlands and the United States. As far as I am myself concerned, a ‘model under construction’ is that for the United Kingdom between 1870 and 1914.

An essential feature of an econometric model is, I think, that it combines mathematico-economic treatment with statistical measurement of some type. The ultimate objectives of these models are the same as of any system of business cycle research, viz. (i) to explain historical events; (ii) to forecast future developments under certain conditions; and (iii) to indicate the probable consequences of measures of business cycle policy. Within the framework of these ultimate objectives, one may distinguish more proximate objectives. These may be separately stated for the economic and the statistical parts of the task. The objectives of the economic part are, to my mind:

1. (a) to clarify notions and assumptions of various theories and to localise differences of opinion;

2. (b) to find the complete implications of any set of assumptions as to type of movement resulting, influence of given types of policy, etc.

The Empirical Approach

When Tycho Brahé and Johannes Kepler engaged in the systematic labour of measuring the positions of the planets, and charting their orbits, they started with conceptions and models of the planetary system which later proved incorrect in some aspects, irrelevant in others. Tycho always, and Kepler initially, believed in uniform circular motion as the natural basic principle underlying the course of celestial bodies. Tycho's main contribution was a systematic accumulation of careful measurements. Kepler's outstanding success was due to a willingness to strike out for new models and hypotheses if such were needed to account for the observations obtained. He was able to find simple empirical ‘laws’ which were in accord with past observations and permitted the prediction of future observations. This achievement was a triumph for the approach in which large scale gathering, sifting, and scrutinizing of facts precedes, or proceeds independently of, the formulation of theories and their testing by further facts.

The book by Burns and Mitchell, discussed here, approaches the problems of cyclical fluctuations in economic variables in the same empirical spirit. The book has two main purposes: first, a detailed exposition, with experimental applications, of the methods of measuring cyclical behaviour, developed by the National Bureau of Economic Research; secondly, a search, with the help of these methods, for possible changes in cyclical behaviour of economic variables over time, whether gradual, abrupt, in longer cycles, or otherwise.

4 Turning from empirical to theoretical analysis, we find in the econometric field many different theoretical approaches. We find a mosaic of theories, some of which are complementary, while others are competing; we find rather fragments of a theory than one unified theory. Now in view of the many factors in economic life and their great variability, it is but natural that economic theory should be fragmentary. An all-embracing theory would no doubt be too complicated to be useful. But are the existing fragments all right? Are there not too often too many alternative approaches and suggested solutions to the same problem? J. M. Clark has touched upon this question in the note already referred to, and has also pointed out the weak point of many of these theories, the questionable realism of the underlying premises.

This lack of realism can to some extent be explained by the main handicap of economic analysis: economic theory cannot be tested by experiments. Now thus handicapped we should be all the more careful in selecting our premises and assiduous in testing them by non-experimental means. But I fear that the opposite is in fact more true: the less the theories can be tested experimentally, the more freely they seem to be put forward. I think, accordingly, that much remains to be done towards rejecting the less realistic approaches so that we can concentrate on the more realistic ones.