Knowledge that Transforms

IN reply ' to the present writers' appraisal of his method of estimating the size distribution of a given aggregate income,2 David Durand attempts to justify the validity and practical usefulness of his method.3 In the process, however, he has shifted the emphasis from the issues we raised to other matters. Dr. Durand's initial method necessitated graphic interpolation from a cumulative frequency curve. Given an income distribution at one level of aggregate income, it yielded a distribution of a new aggregate, with the same relative inequality as measured by the Lorenz curve, and with income size classes having the same limits. He suggested that this method was useful in investigating the effect of income variations on demand, savings, tax yields, etc. In working with Durand's derived distribution, we discovered that average incomes within the income size classes, as calculated from the table in his initial article, differed sharply from the corresponding average incomes in the original NRC distribution. Noting these discrepancies, we pointed out that it was impossible for theoretical reasons to maintain simultaneously the same Lorenz curve, class limits, and average incomes in the derived as in the original distribution. Durand admits the theoretical validity of this point, but claims that it lacks significance because most problems involving income distributions . . . do not require great precision. 4 We disagree with Durand in this matter. The originator of a statistical technique cannot foretell all the uses to which it may be put or the degree of accuracy which may be expected of the results. In describing the technique, therefore, he should indicate its shortcomings, and the degree of accuracy of the results it yields. Durand did not mention in his initial article, that the published table representing his derived distribution yielded average incomes substantially different from the original NRC averages, and that in four of the seventeen size classes the indicated averages were outside the limits of their respective classes. Durand did not even mention the possibility that results of this character might be produced by his method. In his later article, Durand demonstrates that by numerical interpolation he can derive a new distribution with averages that come much closer to those in the original NRC distribution, although small differences still exist. This modified method does not possess the advantage of simplicity which he claimed for his initial method. We are more seriously concerned, however, that the main points made in our original article shall not be lost sight of in what is essentially a discussion of highly refined techniques of numerical interpolation. Our criticism was concerned with the basic issue of the consistency of graphic (or other) methods for estimating the size distribution of different aggregate incomes with the objectives for which those methods are used. Most persons engaged in statistical estimation presumably would consider that consistency with its objectives is one of the prime requisites of an acceptable and useful method, even when the underlying data are rough. We pointed out that there are two fundamental approaches to this problem of statistical estimation. The approach presented by Durand results in a distribution retaining the original income size classes and Lorenz curve. With this method it is impossible to retain the same average income within the original 1 David Durand, An of the Errors Involved in Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXX (1948), pp. 63-68. 2 Eugene Clark and Leo Fishman, Appraisal of Methods for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, XXIX (I947), PP. 43-46. 'David Durand, A Simple Method for Estimating the Size Distribution of a Given Aggregate Income, this REVIEW, xxV (I943), Pp. 227-30. 4 David Durand, An of the Errors .. op. cit., p. 63.

C ONSIDERABLE attention has been given of recent years to changes in the pattern of wage relationships within and between industries. Among the more recent observations in this area is that of David R. Roberts.' Mr. Roberts, on the basis of measurements of changes in straight-time hourly earnings between major industry groups concludes, regulation of wages led to a narrowing of wage differentials between industries, between firms in the same industry, and between different classes of work in the same plant. Such effects have been more than temporary. Developments since V-J Day indicate that much of this wartime heritage has become a permanent ingredient of our economy. While the rate of reduction in differentials has been considerably slowed down, the trend in that direction still persists. 2 These observations are consistent with the general view. However, a study of distributions of wage earners within manufacturing industry by straight-time earnings, rather than comparisons of changes in distributions of averages between industry groups, leads to the conclusion that the trend toward lesser dispersion has not been substantially slowed down since the War. Table i presents the available distributions from January I94I to July I947.3 Exact statistical comparisons of the distributions are difficult because of the fact that all of them are open-end distributions, and arithmetic means are neither available nor calculable. Published data on average straight-time hourly earnings are not particularly useful since the samples are different. Several rough measures of the changes in the shape of the distributions have, however, been

ONE of the outstanding developments in collective bargaining in I948 was the General Motors contract with the United Automobile Workers.' Two phases of this contract led to considerable discussion: (a) the cost of living adjustment clause and (b) the annual improvement factor for each of the two years for which the contract was drawn. Cost of living clauses are not unique in labor contracts.2 The inclusion of an annual improvement factor in the collective bargaining contract, however, did represent a significant departure from past practice. Under the General Motors' formula, provision was made for an annual improvement factor of 3 cents an hour in I948 and an increase of the same amount in May I949, in addition to adjustments required to meet changes in living costs. Since at the time the contract was signed, the average hourly rate for General Motors was about $1.50, the rate of improvement provided was about 2 per cent a year. The General Motors' rate of increase apparently was based on the long-term national average increases in output per man-hour.

JN a I948 issue of this REVIEW, Professor Ragnar Frisch detailed an ingenious plan which would, it was hoped, rescue international from the existing chaos of bilateralism and restore it to a truly multilateral basis.2 Few economists will disagree with his ultimate aim of restoring multilateralism, but it appears to the present writer that Frisch's particular policy proposals are thoroughly infected with the cardinal marginal utility heresy, and are consequently of questionable merit. By using the more orthodox notion of an ordinal welfare index, however, it seems quite feasible to attack the multilateral problem, and, at least in principle, solve it. Because of space limitations, it is hardly possible to do justice to Professor Frisch, and to reproduce his entire discussion. What follows is the barest skeleton of his remarks. He points out that the prevalent system of conducting international on an essentially bilateral basis primitive barter is a quite inefficient method of organizing the international division of labor. In place of this patchwork, some comprehensive multilateral arrangement must be set up. Apparently, Frisch envisages a condition of repressed inflation 3 within each trading country, i.e., a condition in which money prices are meaningless as transformation ratios.4 Consequently, each participating nation must group all import and export goods into perhaps ten categories (0,1,2, . . . 9), such that, within each category at the given domestic prices, the same marginal social valuation is put on a (or whatever the local currency unit may be) of one good as on a of any other good. Furthermore, a crown's worth of goods in category 3 is preferred to a crown's worth of goods in category 2, but is in turn inferior to a crown's worth of goods in category 4. Next, an international authority is to ascertain the categories into which its members place various quantities of import and export goods. It is then claimed that there will exist a unique allocation of trade, given two conditions: (i) the requirement that, in terms of any currency unit, the aggregate value of imports of any one nation from all other nations within the system must, within rather close limits, equal the aggregate value of exports of that nation to all other nations within the system; and (2) the condition that the global from trade be maximized. The crucial objection to the Frisch plan arises from the fact that the notion of global gains is not unambiguous.