Knowledge that Transforms

I am glad to be able to state, right from the beginning, that I fully agree with Dr. Preinreich as concerns the relativity of depreciation technique. I never had the intention of stating that there is a true method of depreciation, so much the less, as I do not accept any true capital value. This, I hope, will be clear from the following addition to my paper. In my study of depreciation schemes, I have tried to introduce great simplifications. But I do not think this has veiled fundamental difficulties of the problem, as Dr. Preinreich seems to suspect. I should also like to emphasize that my introduction of the distribution, which I may denote by (,u, s) and which is characterized by a slight constant mortality during s years followed by a catastrophical mortality after this time of all buildings left, is something more than the well-known annuity method of depreciation, although it may be interpreted formally in such a way. To replace the vague risk margin in the valuation rate of interest by ,i seems to be a theoretical improvement of the scheme. For with it, depreciation insurance is introduced in practice. But the advantages of the scheme are perhaps more easily grasped when the method is applied to numerical work, and I shall permit myself to come back to this question at a later occasion with the support of practical examples. The simplifications I have introduced (or the restrictions as to generalizations that I have found it advisable to impose on my theory) are evidently, as I have already stated in my paper, a matter of taste, and de gustibus non est disputandum. But in choosing these first approximations, I tried of course to profit by a long experience of practical mathematics. Personally, I am convinced that the choice will prove itself to have been happy, but such statements can be demonstrated only by practical work. I also have the impression that the double line of thought which is illustrated by my two approximations one ad-

STATISTICIANS are familiar with the moving average. For example, when monthly prices are given, it may be desirable to eliminate the seasonal variation. The average of the monthly prices for a calendar year may be found, then the average of the prices from the February of this year to the January of the next, then from March to February, and so on. Each average thus formed involves just once each of the twelve months; and such averaging would seem a good method for eliminating the effects of the seasonal cycle. A question, however, arises: When we take out one cycle, such as the twelve-month cycle, are we likely to put in another cycle, with substantial waves? Under certain conditions, the answer is: Yes. But to understand why such an unwelcome cycle intrudes itself, some explanation is required. As a basis for studying cycles, it is often assumed that data contain an additive chance constituent. That is, it is assumed that the rth measurement Ur may be analyzed thus:

for this country in a period of 70 years of rapid urbanization. The statistical procedure is based on the following considerations: Expenditure on house room minus the running costs of providing it determine the composite value of a combination of building and land, called dwelling. In this combination, for the purpose of determining the shares of this composite value attributable to building and site respectively, building is treated as the factor which can be reproduced at a certain cost. Its value, therefore, cannot, except for a very short time, exceed its cost of reproduction.4 The site is the specific factor.5 Its value is equal to the value of the combination minus the value of the cost factor.6 Schedule A of income tax contains figures on

THE PURPOSE of this paper is to provide a diagrammatic approach to the theory of interest determination, with special emphasis on the supply side of the problem. In Figure 1 the elements which determine the of a particular asset are depicted. On the Y-axis is measured the percentage of of an asset which the individual thinks he can get. Where the asset has no actual value, the term will be used to denote the intrinsic or maximum value which the individual attaches to the assetwhat he thinks it is ultimately worth on the market if he takes to find the most enthusiastic buyer. For the analysis of liquidity as such, we assume that no change in the market value of the asset is expected other than those due to the individual's own action. On the X-axis is the time, measured from the present moment, which the individual thinks it will take to realize the corresponding percentage of face value. The extent to which it pays him to shop around for highbidding buyers depends upon the perfection of his knowledge of the market, which will in turn depend upon the degree of perfection in the market itself. As an individual shops around, his knowledge of the market, and so its perfection, increases. It will be readily seen that assets typically regarded as liquid, such as equities, are assets for which a highly competitive, perfect-knowledge market exists. He is not absolutely certain, however, as to the percentage of face value he can get within a given period, particularly as the begins to get fairly long. Accordingly, we do not have a single cent of face for each point of time, but a probability distribution for each point of time. Probability is measured by the area between two ordinates of the distribution curves, situated in planes parallel to the YZ plane, the total area under each curve being equal to unity. The individual knows exactly what the immediate market value is, so for the x = 0, the height of the probability curve approaches infinity while the width approaches zero. As the shopping period is increased, his estimates become more vague and his degree of certainty diminishes. The dispersion of the probability distribution increases as we move out along the time axis; the curves become lower, flatter, and wider. To each distribution corresponds a single value which can be used to express it: some single value which the individual regards as a situation equivalent to that represented by the distribution, and which could be determined through choice. For example, a certain 75 per cent of face

(1) MR. HAAVELMO' contends that the variate difference method is not applicable to certain dynamic economic schemes, as, e.g., the cobweb theorem. It never has been claimed that this is the case, and the author has pointed out very carefully in his monograph2 that the variate difference method deals only with superimposed random variation. A more extensive discussion of the general problem of the role of errors in economics is to be found in a short article published in the Quarterly Journal.3 The view is put forward there that some types of errors have a deep-rooted influence on economic developments, and this is in agreement with Mr. Haavelmo's statements. Dynamic schemes, like the one of Frisch and the ideas indicated in Haavelmo's article have to be dealt with by other methods. These problems are probably closely related to a study of serial correlation. The author has indicated some possible methods of analysis in an appendix of his monograph4 and even put forward tentatively an exact test of significance for serial correlation based upon the method of selection. (2) The author has indicated5 that he does not consider the method of selection an entirely satisfactory test of significance for the equality of the variances of two consecutive series of differences. It is of course very true that the test is not efficient since it utilizes only a certain percentage of the total data available. The fundamental hypothesis tested is the equality of the variances of two consecutive difference series. The case that the variance of the higher difference series is larger and not smaller than the variance of the lower difference series can arise (a) because they are really equal and appear different because of chance fluctuations, (b) because the variances form an increasing instead of a decreasing series and the whole method is not applicable. For this reason it seems that we have to consider not only the upper but also the lower tail of the distribution in testing the hypothesis that the variances of two consecutive difference series are equal and appear different only because of random fluctuations.