International Monetary Economics

APPENDIX

NOTE ON THE USE OF STATISTICAL CONSTRUCTIONS

IN several chapters theories based on comparisons between index-numbers of prices and on the “behaviour” of certain statistical series were submitted to critical analysis. It may be useful to state explicitly the foundations on which this analysis and criticism were built, and to discuss briefly the basic conceptions involved.

The conquest of economic thinking by the mathematical statistician has made much headway in the course of the last half century with the result that in criticizing some of the statistical methods which have been used in economics one has to question a good many “generally accepted” views and methods. The critical work to be done is considerable and the time is ripe for carrying it out without much further delay. The value of much of the work to be done in the next decades by the “econometricians” and even by the non-mathematical economists will depend upon the revision and adjustment of methods used and of conceptual and statistical instruments of research employed. This is an enormous task and I cannot within the compass of this study do more than formulate some generally-worded observations. I shall not question the mathematical validity of statistical methods used, but shall limit myself to questioning the economic meaning of the results of certain statistical calculations and computations. But before proceeding to do this I want to emphasize the importance that I attach to the use of statistics along with deductive thinking as instruments of economic research. My preference is, however, for statistical information illustrating the real economic processes, not to hypothetical constructions.1 Such information is essential both in formulating problems and in testing the results of deductive reasoning; and it is hardly necessary to say that it is theoretical analysis in turn which formulates questions for the economic statistician to answer. It is, however, quite another matter when the statistician starts to calculate secondary series on the basis of the direct or raw data, and when, by applying to the primary data the different methods proper to mathematical statistics, he tries to draw conclusions regarding the functioning of the economic system.2 Here doubts are permissible and I shall endeavour to make clear some of them.

In the first place, as regards the rationality of the methods employed, it is important not to forget that mathematical calculations should be applied only within homogeneous groups.3 This is evident, but how often forgotten! Now a price is not a number of money units but a number of money units per unit of the good in question; therefore a collection of prices of different goods is not a homogeneous collection. Thus one can calculate the average price of bread on the basis of a collection of prices of bread quoted in different localities or on different days (I leave aside, for the time being, the economic meaning of such an average), but it is not rational—even though mathematically correct—to calculate an average of prices of different commodities and call it their average price. One may try to overcome the difficulty by calculating the price-changes of each of the different commodities and by computing from the index-numbers thus obtained the variations in the average prices of this group of commodities. But this is hardly more rational a procedure though it is even less open than the former to mathematical criticism. If the price of bread rose by 10 per cent from one year to the next, and the price of coal by 5 per cent, the numbers 10 and 5 represent for an economist variations in the price of bread and in that of coal respectively. One cannot obtain a significant result by calculating an average of these figures. This does not exclude the possibility of making any statistical calculations on the basis of prices of individual commodities—but it restricts considerably the scope of such calculations.4

This application of the principle of homogeneity is even more striking in the case of more elaborate calculations such as indices of the general trend of business, or of economic development. Many such indices have been calculated in the recent years.5 These indices are weighted or unweighted averages of other index-numbers representing changes in various economic phenomena.6 They may be wholesale and retail prices, carloads, production of certain important commodities (iron, wheat, etc.), totals of bank clearings, averages of stock-exchange quotations.7 Some of the series used are in themselves violations of the “principle of homogeneity”. One moment of sober reflection should make it clear that it is vain to wish to represent by one single series of figures, by one single curve, changes that occur in a complex collection of heterogeneous phenomena. And it is surprising how the quest for simplicity has thus far triumphed over the realization that heterogeneity and complexity may be irreducible to homogeneity and simplicity. It is easier to deal with one curve than to deal with ten or twenty curves “behaving” differently; nevertheless it may not be possible to reduce the ten or twenty curves to a single one and still have a significant result. What makes the computation rationally impossible (though it may be mathematically easy to make) is the fact that the phenomena covered by the ten or twenty or more curves are heterogeneous.

One can compare the variations shown by the individual curves, but one cannot compute them into a single curve. Every one of such figures or curves represents changes that occurred in some concrete phenomenon; and just as one cannot add tons of coal to sums of bank clearings and to baskets of wheat, one cannot reasonably calculate averages summing up changes that occur in each of the series. If one persists in making such calculations, the results obtained are void of any significance.8 It is good to keep this in mind in an epoch when our knowledge of the happenings in the real world is rapidly becoming an index-number knowledge, and when people appraise all too often the changing economic situations on the basis of such “indices of general business conditions” or “indices of the general trend of economic development” and accordingly determine their own behaviour. In consequence such statistical constructions are not only meaningless but may become positively dangerous.

Let us now return to index-numbers of prices. We have seen that averages of prices or of price changes are not significant constructions if the prices in question are prices of heterogeneous commodities. To overcome the difficulty the notion of “composite commodities” has been introduced, which are “made up of the various individual goods and services in proportions corresponding to their importance as objects of expenditure”.9 But there are no “composite commodities” in the real world and it is vain to speak of a price of something that does not exist. Furthermore in constructing such “composite commodities” or weighted index-numbers one necessarily introduces important arbitrary elements. Unweighted index-numbers have often been rightly criticized on account of neglecting the relative importance of the various commodities.10

There is however a way out of the difficulty. There exist certain aggregates of commodities, which are linked organically, and can be larger or smaller and more or less diversified according to their significance. Such are, for example: total production in a period of time; total sales in a period of time, either in a whole economy or in a group of enterprises (e.g. mail-order houses in the United States); the aggregate of different factors of production needed for manufacturing a certain quantity of a commodity; the aggregate of commodities and services consumed in a certain period of time by an individual or a family living on a determined standard; and so forth. Now what we can calculate is the cost of such an aggregate; and we can compare the costs of that aggregate at different moments of time; changes in them reflect (but do not measure) the changes that occurred in prices of the various commodities and services entering into the aggregate. One must not, however, compute changes that took place in the costs of different aggregates into one average! Changes in the costs of such aggregates are what one usually tries to calculate with the help of weighted averages of prices; but while the latter method contains a large element of arbitrariness the former is free from it in view of the organic character of the aggregates.

It is important to devote some more attention to the calculations based on the most general aggregates of goods, such as the total volume of production, or the total volume of transactions. Changes observed are due to changes that have taken place in the volume structure of the aggregate and to changes that occurred in the prices of the different components of the aggregate. If one could isolate one sort of changes, and then the other, one might obtain an indication of the extent to which changes in the value of the aggregate were due to its changing volume and structure, and of the extent to which they were due to changing prices. There are well-developed statistical methods that make such calculations possible.11 They consist, roughly speaking, in assuming alternatively a constant volume and structure of the aggregate with variable prices, and constant prices with a variable structure and volume of the aggregate. In the former case the constant aggregate is that of a base year and prices are taken such as they have been in reality at the different time-moments (or, for each component of the aggregate, average prices over a period of time). In the latter case the reverse procedure is used: prices of a base year are used together with aggregates that have been really observed in successive periods of time. It will be observed that in either case we get aggregate money values, which we can compare with one another. In one case we obtain a variable series of money values, variations in which are due to changes in individual prices. It is the nearest we can legitimately come to a general price index, considering that there is not, in the real world, such a thing as a “general price level”. The other method gives us a series of values, variations in which represent changes in the volume and structure of the aggregate. Considering that it is impossible to represent by one series of numbers changes in total physical volumes of heterogeneous aggregates, this is the only method of ascertaining how changes in the quantities of different components affect the value of the aggregate. The results of such calculations are sometimes called “indices of the physical volume of production” (or of trade); the reader will easily see why the term is misleading. Some “indices of physical volume” are however calculated by much more doubtful methods.

Thus we see that the application of index-numbers to price changes is of a limited scope, though may be useful and enlightening within that scope! There is one further limitation which we must consider at present.

The assumption that quantities composing the aggregate remain constant while prices change, or reciprocally, is only approximately correct and that only under certain circumstances. That prices and quantities are interdependent in their variations is a fundamental economic truth. To assume that variations of the one are not associated with the variations of the other is possible only for very short periods of time and only for periods of economic stability. Otherwise there is no ground for supposing that the prices actually observed are the same as they would have been had quantities really remained stable—and vice versa. Therefore the use of index-numbers of the variety described is possible only in certain circumstances, and otherwise may lead to more or less serious errors.

It follows that comparisons of indices for years which are far removed from one another cannot yield significant results. Where aggregates have changed considerably, no calculations which rest on the assumption that they remained stable can give correct results. And if, on the other hand, one allows for changes of both physical aggregates and the prices of their components, the results obtained cannot be used as price-indices.

Conclusions reached in the preceding pages may appear to be mostly negative and the reader may well ask: if most statistical calculations, discussed here, are meaningless or misleading, what else do you suggest? I am not certain that I do suggest anything else. New and different methods might very usefully be worked out, particularly methods which would enable us to deal with changing structures. This is a type of analysis for which, I think, we lack adequate statistical instruments. But as regards methods I have discussed and criticized in this Appendix12 I doubt whether anything should be put in their place at all. The human mind is always in search for unity and simplicity. In that search and in the particular field of economic phenomena, statistics seemed to provide a comfortable way out of the perplexing multiplicity and heterogeneity presented by the economic world and the processes that are taking place therein. Hence certain methods referred to above gained wide acceptability. But the multiplicity does exist and by ignoring it one falls into erroneous or meaningless statements about the world and about economic processes. Averages more often conceal reality than reveal it and have to be used cautiously, even in homogeneous collections; but they are simply without meaning in collections that are not homogeneous. There is no such thing in the real economic world as the “general price level”; but what exists are prices, and it is the movements of prices and the changes in the structure of money values (including prices, incomes, debts) that are of real interest and of intense importance for the understanding of economic phenomena. As we have seen in the preceding pages, money is purchasing power, that is, power to buy; but there is no such thing as a general purchasing power of money. Purchasing power is a right, not a dimension. The monetary unit is the unit of economic value; but the unit of value has no value. The process of valuation is different in economics from the process of measurement in the physical world; its theory is the same as the theory of price formation. Why should we speak of “stable value of money”, when we mean “stable prices”? Prices are the direct datum of the economic process. Only by finding out how they are established and what are the mechanism and the dynamics of their change shall we get any insight into the question of what we really mean by “stable prices” and how to proceed to obtain them. To calculate averages of doubtful significance, to call their reciprocal “purchasing power of money” and to set out to keep this “purchasing power” stable, increases rather than diminishes the distances that separate us from the solution of our problems.

In conclusion, one more general, methodological observation. Whether legitimate or not, statistical constructions are always calculated results, not data given by the economic process. Therefore changes in these constructions cannot be used to explain economic changes, but merely to describe them. I have already had the opportunity of pointing this out in discussing the concept of “gold prices”, but applications of this reservation are manifold. It is important to give much care to the use one makes of statistical constructions, as here also the past record of economic statistics is far from clear. I am convinced that econometrics will play a greater part in the future development of economic science than it has in the past; this is precisely why I am anxious to see its methods properly applied—for then only will the value of the results obtained correspond to the amount of labour put into working them out.

• 1There is much difference between the views that are widely held in this matter in Great Britain and the United States, and views that are commonly accepted on the Continent. This explains the emphasis laid on that issue. Vide infra, pp. 68 and 69.
• 2The reader may find it useful in this context to contrast the United States’ unified monetary system, now embodying a Federal Reserve System, with what would have existed had each of the 48 States of the Union sovereign powers over its particular monetary system.
• 3The word “international” is used, of course, with utter disregard of its etymological significance; but this usage is universally recognized.
• 4F. A. von Hayek, Monetary Nationalism and International Stability, London, 1937.
• 5loc. cit., p. 4.
• 6Except when a World State exists.
• 7i.e., “real” factors of production (goods), monetary factors (capital) and, thirdly, labour.
• 8“In the last analysis . . . it is the political factor which gives rise to the economic problem of international monetary transfer. If historical accident had not created independent sovereign states . . . no such ‘problem’ would have arisen”. Lionel Robbins, Economic Planning and International Order, London, 1937, pp. 279–80.
• 9To change the weight of a coin (“debasement”) is analogous to the modern forms of devaluation. While, as we shall see presently, the expression “changes in the gold contents of a currency unit” is open to criticism, it shows at least clearly the analogy in question. But what Sovereign Prince of the days gone by would have accepted an international undertaking never to debase the currency? And even if he did accept it, this would be an analogous matter to the type of international monetary convention mentioned in an earlier part of this chapter. The Latin Union was to some extent an example of a limited convention of this kind. But it all goes to show that not even a general limitation of monetary circulation to precious metals would automatically insure a system which would work internationally in the same manner as a monetary system works within a country in regulating the supply of money in the different regions.
• 10loc. cit., pp. 270–80.
• 11Cf. my “Monetary Internationalism and its Crisis”, a chapter in The World Crisis, London, 1938, pp. 348 et seq.
• 12I expect to discuss it at considerable length in my book on the Theory of Banking which is in the course of preparation.