16 From what we have just seen [the last section], for a commodity which exchanges freely in a given market, between a group of producers and a group of consumers, if each individual always remains free at each instant to fix his own price, and to increase or decrease his production or consumption, there will finally be convergence, in the market, towards a certain equilibrium price p, for a certain quantity x of goods produced and consumed, p and x being well determined by the curves, say, Γand C. In fact, for a large number of goods, these conditions are roughly realized, and one can accept that the price which establishes itself in reality is nearly the theoretical equilibrium price.

The price depends: on the general economic situation (always supposed constant, in all of this study), on supply and on demand. Now these three elements never stop varying, and, during the course of time, the price follows their variations. In the second part of this study an attempt is made to distinguish by observation between these complicated influences. But we are able to predict here the direction of the variation which will tend to produce a change in each of the two last factors, supply and demand.

We shall say that the supply increases when the indifference curve Γ of the producers passes from Γ2 to Γ'2 (figure 17.1); then to the same indifference price there corresponds a greater quantity produced, and to the same indifference production there corresponds a lower price.

The traditional approach to the analysis of the price formation process and of market phenomena in general is that the demand schedules and the supply schedules together determine the prices, so that, if both sets of schedules are assumed, it has no sense to ask what will happen if such and such a change in price occurs. If it is wanted to consider the effect of price changes in the traditional scheme, this effect must be looked upon only as a potential effect, say the effect that would be produced on the quantities demanded if the demand schedules remained unchanged while shifts (sufficient to produce the given price changes) occurred, in the supply schedules. Or vice versa. For many purposes it is more satisfactory to work with a theoretical scheme which is such that it is possible to assume at the same time a given demand and supply structure and still ask the question of how the quantities traded will react under the impact of price changes. An outline of – or rather prolegomena to – such a theory is given in this paper.

Such a modification of the traditional demand–supply set up seems particularly necessary for analytical purposes in international trade, and in what follows I shall most of the time speak about ‘countries’, ‘International trade’, etc. But the argument is general and has obvious applications to other parts of economic theory.

Introduction

The Object of Confluence Analysis, the Danger of Including too Many Variates in a Regression Analysis

In a paper ‘Correlation and Scatter …’ in Nordic Statistical Journal 1928 I drew attention to the fact that in statistical regression analysis there exists a great danger of obtaining nonsensical results whenever one includes in one and the same regression equation a set of variates that contain two, or more, subsets which are already – taken by themselves – highly intercorrelated. Suppose, for instance, that we have three statistical variates x1, x2, x3 (measured from their means), and that we know for a priori reasons that there exist not only one but two independent linear equations between them (since the variates are measured from their means, we may assume the equations to be homogeneous). Further, suppose that a great number of observations are made, each observation giving the values of the three variates and being represented as a point in the three dimensional (x1, x2, x3) space. All these observation points would then lie on a straight line through origin in (x1, x2, x3) space. From the distribution of these points it would be absurd to try to determine the coefficients of any of the two equations that we know a priori should exist between the variates. Indeed, a set of points lying in a line does not contain enough information to determine a plane.

This is one of those rare books which, if only they are received with the serious attention that they deserve, sometimes succeed in forcing an entirely new orientation in the field of scientific endeavour with which they deal. The book would deserve the closest attention, even if its specific arguments were found to be either unsound or of little permanent value for further research along positive lines, by virtue of the vision of its conception, the saneness with which it sets limits to the discussion, and the boldness with which it states its conclusions. It required an imaginative vision to pull one's self consciously away from the details both of present methods of ‘business forecasting’ and of the ‘cycle theories’ which, consciously or unconsciously, lie at the base of those methods, in order to examine the methodological assumptions common to all methods and theories. It required a saving sense of balance to prevent the inevitably abstract and formal nature of the treatment from leading to fruitless juggling with metaphysical subtleties of doubtful relevance. It required courage of high order to issue a challenge, couched in the most uncompromising terms, to the vested interests represented by those ‘Institutes’, commercial and ‘scientific’, which are at this moment devoting a huge expenditure, in time and effort, to the study of business forecasting.

1 In the daily market reports, and other statistical publications, we continually find comparisons between numbers referring to the week, month, or other parts of the year, and those for the corresponding parts of a previous year. The comparison is given this way in order to avoid any variation dueto the time of year. And it is obvious to everyone that this precaution is necessary. Every branch of industry and commerce must be affected more or less by the revolution of the seasons, and we must allow for what is due to this cause before we can learn what is due to other causes.

2 Merchants and manufacturers are of necessity intimately acquainted, by experience or by tradition, with such periodic fluctuations as occur in their own branches of industry. By the skill and rule-of-thumb knowledge which each one acquires in his own pursuits, they make allowance for such variations, and thus very rude comparisons of prices, stocks, and sales enable them to detect irregular changes in their own market, which is all that they require.

3 But the unwritten knowledge of commercial fluctuations is not available for scientific purposes, and it is always of very limited extent; so that, if we come to inquire into the causes of more obscure fluctuations, such as those of credit, bankruptcy, bullion, currency, rate of interest, etc. theorists and practical men alike disagree.

Methods Used

For this purpose the materials used for the statistical calculations are chiefly two: ‘P’, the index number of wholesale prices of the United States Bureau of Labor Statistics, and ‘T’, the Index of Trade of Professor Warren M. Persons. The period covered by the trade series is from August, 1915, to March, 1923, inclusive.

I take this opportunity to advocate the use of an index of the physical volume of trade in place of the vague and most meaningless index of ‘business’ so commonly employed hitherto. ‘Business’ is a cloudy concept. An index of ‘business’ consisting of a mixture of three such essentially different categories as quantities, prices, and values, seems to me as absurd as an index of ‘weather’ which would jumble together, in a single average, such unlike elements as temperature, humidity, cloudiness, barometric pressure, and wind velocity. No meteorologist would insult his science by such an average index of the weather. The atmospheric weather is not to be put in any one figure. No more is the economic weather. But physical volume of trade has a definite and important meaning or set of meanings, just as it does temperature or barometric pressure.

In a theory of economic dynamics, the ophelimity function of individuals must be supposed to depend on the quantities of goods consumed and the sacrifices brought, not only at the moment considered, but also at later moments. Their offer and demand schemes for each moment then depend not only on the prices governing at that moment, but also on the price expectances the individuals have for the future. Among those expectances, those relating to the near future will be of more importance than those relating to a further period. As a first approximation it might be supposed that only the expectances relating to a certain time period (the ‘horizon’) are of importance, and all of the same importance. That means that the subject is at every moment t making a definite plan for the period from t to t + τ, and then realizes certain parts of that plan. Before other parts could be realized, the subject makes a ‘revision’ at the moment t + 1, say, for the period from t + 1 to t + τ + 1, etc.

The purpose of the present paper is to discuss, with the help of these notions, some results of statistical analysis, which cannot be explained by static theory, and which seem to teach something about horizons or expectances.

Relation between Total Annual Supply of Non-Perishable Crops and Amounts Handled

The amount handled is always smaller than the total supply (crop plus carry-over), the difference being the next year's carry-over.

‘The Law of Demand’

Statistical Laws of Demand

Two fundamental defects in the current theoretical method of treating economic 66 questions are exemplified in the case of the theory of demand: first, the assumption is made that all other things being equal (the old cœteris paribus), an increase in the supply of the commodity will lead to a corresponding fall in the price; secondly, it is assumed that the concrete problem of the relation of price and supply of commodity will be simplified by attacking first the constituent elements of the question rather than by attacking directly the problem in its full concreteness. Neither assumption is satisfactory nor indeed admissible. The ‘other things’ that are supposed to remain equal are seldom mentioned and are never completely enumerated; and consequently the assumption that, other unmentioned and unenumerated factors remaining constant, the law of demand will be of a certain type, is really tantamount to saying that under conditions which are unanalysed and unknown, the law of demand will take the supposed definite form. The burden of proof is upon anyone using this method to show that the assumption does not at least involve a physical impossibility.

The second of the above two assumptions is not more satisfactory than the first. It reproduces the defects of the first assumption with others superadded.

Introduction

Measurement of parameters occurring in theoretical equation systems is one of the most important problems of econometrics. If our equations were exact in the observable economic variables involved, this problem would not be one of statistics, but a purely mathematical one of solving a certain system of ‘observational’ equations, having the parameters in question as unknowns. This might itself present complicated and interesting problems, such as the problem of whether or not there is a one-to-one correspondence between each system of values of the parameters and the corresponding set of all values of the variables satisfying the equation system. For example, if we have, simultaneously, a demand curve and a supply curve, the set of possible observations might be just one single intersection point, and knowing that only would not, in general, permit us to draw any inference regarding the slope of either curve.

Real statistical problems arise if the equations in question contain certain stochastical elements (‘unexplained residuals’), in addition to the variables that are given or directly observable. And some such element must, in fact, be present in any equation which shall be applicable to actual observations (unless the equation in question is a trivial identity). In other words, if we consider a set of related economic variables, it is, in general, not possible to express any one of the variables as an exact function of the other variables only.

Introductory: Superposed Fluctuations and Disturbances

If we take a curve representing a simple harmonic function of the time, and superpose on the ordinates small random errors, the only effect is to make the graph somewhat irregular, leaving the suggestion of periodicity still quite clear to the eye. Figure 10.1 (a) shows such a curve, the random errors having been determined by the throws of dice. If the errors are increased in magnitude, as in figure 10.1(b), the graph becomes more irregular, the suggestion of periodicity more obscure, and we have only sufficiently to increase the ‘errors’ to mask completely any appearance of periodicity. But, however large the errors, periodogram analysis is applicable to such a curve, and, given a sufficient number of periods, should yield a close approximation to the period and amplitude of the underlying harmonic function.

When periodogram analysis is applied to data respecting any physical phenomenon in the expectation of eliciting one or more true periodicities, there is usually, as it seems to me, a tendency to start from the initial hypothesis that the periodicity or periodicities are masked solely by such more or less random superposed fluctuations – fluctuations which do not in any way disturb the steady course of the underlying periodic function or functions. It is true that the periodogram itself will indicate the truth or otherwise of the hypothesis made, but there seems no reason for assuming it to be the hypothesis most likely a priori.

Endogenous and Exogenous Variables

In static or dynamic economic theory, the criteria employed in determining whether or not a system of equations is complete are derived from the purpose for which such systems are constructed: the explanation of economic phenomena. In each case a distinction is drawn between the endogenous variables that the economist sets out to explain and the exogenous variables that he takes as given. The number of equations required for the explanation of the values or, in the dynamic case, of the movements of the endogenous variables, then equals the number of such variables.

Exogenous Variables in Economic Theory

In determining which variables are set aside as exogenous, two main principles are implicitly or explicitly applied in economic literature. They might be described as the departmental principle and the causal principle. The departmental principle treats as exogenous those variables which are wholly or partly outside the scope of economics, like weather and climate, earthquakes, population, technological change, political events. The causal principle, which does not always lead to the same result, regards as exogenous those variables which influence the remaining (endogenous) variables but are not influenced thereby.

The causal principle is often used also if it applies only approximately, that is, if the influence of the endogenous variables on those treated as exogenous is presumed to be small.

Overview

It is conventional to believe that econometrics is primarily a post-1950 development. This is correct only in the sense that it was in the twenty years after 1950 that econometrics became the primary method of applied economics. Yet, as work on the history of econometrics has recently shown, the foundations of econometric analysis were laid in the period of its early development during the half century before 1950. Our readings and commentary show how the basic methods, practices and conceptual framework of econometrics were developed in the context of applied economics and statistics in this early period. Although the earliest extract in fact dates from 1861 and the latest from 1952, all but three of the forty-five readings originally appeared between 1900 and 1950.

Our choice of readings is not designed to provide a complete history of all the elements of econometrics; rather, our aim has been to put together what we consider to be the most important papers in the development of both structural and time-series elements in econometrics. We need to draw the distinction between those papers in early econometrics which are remembered now, and those which were important in the process of developing ideas then. For example, many economists are familiar with Trygve Haavelmo's simultaneous equations paper of 1943, but not so many people knew (particularly before Haavelmo won the Nobel Prize in 1989) of his more important contributions in The Probability Approach in Econometrics of 1944.

The application of the theory of correlation to economic phenomena frequently presents many difficulties, more especially where the element of time is involved; and it by no means follows as a matter of course that a high correlation coefficient is a proof of causal connection between any two variables, or that a low coefficient is to be interpreted as demonstrating the absence of such connection. In many cases, indeed, the existence of a causal connection between two phenomena is more clearly deduced from mere inspection of diagrams than from mathematical calculation. But simple inspection will not enable us to measure the degree of correspondence, and many points will often remain hidden which may be revealed by a judicious use of correlation.

Comparatively little use has as yet been made in the domain of economics of the methods elaborated chiefly by Mr F. Galton and Professor K. Pearson; the most noteworthy contributions to the Statistical Journal being perhaps those of Professor Edgeworth and Mr Yule. One of the chief difficulties encountered in determining whether the movements of two sets of variables may be attributed to a particular cause arises from the fact that, especially in economics, phenomena which can be completely explained by the action of a single cause are extremely rare. And although there may actually be one, or more than one, cause affecting two phenomena, yet these may frequently be influenced by several other conditions which are not common to both.