A New Approach to the Construction of Index Numbers

Abstract

T HE importance of fluctuations in index numbers as guides to the formulation of economic policy decisions hardly requires emphasis. Changes in Federal Reserve policy, for example, are based, at least in part, upon price level variations, as measured either by the BLS consumer price index or by the index of wholesale prices. Similarly, many of the economic time series used by the Council of Economic Advisers as indicators of the state of the economy or of fundamental trends within the system are index numbers. And, to an ever increasing extent, the incomes of significant portions of our economy are adjusted periodically in response to movements in price indexes. spite of this situation, these indexes, which underlie so much of our economic life, are basically inadequate as quantitative measures of change. For, first of all, the solution to the problem of correct weighting of the members of the sample is not at all obvious.' But, in addition, the construction of an index number is normally associated with the selection, on an a priori basis, of the sample of commodities which is to be utilized in the evaluation of the index.2 use of such a judgment sample precludes the determination of the extent to which an observed difference in two indexes can be ascribed to sampling errors, rather than to real causes. This defect is extremely important, since index numbers are generally employed for intertemporal, interregional, or intersectoral comparisons, where differences are often quite small, and their significance correspondingly uncertain. Furthermore, the use of an arbitrary fixed sample permits neither changes in product quality nor the introduction or disappearance of consumer products readily to be incorporated into the standard type of index. Any attempt to take such effects into account must of necessity impair the continuity of the index through time. At present, the author knows of no method in use which will allow the realistic evaluation of the statistical errors associated with an index number. view of the practical significance of this problem, it is suggested in this paper that the items used in the computation of an index be chosen in a statistical manner. use of a probabilistic sample would, in principle at least, remove all the above mentioned deficiencies inherent in the normal method of sample selection. And, while the proposed procedure would not solve the problem of appropriate weighting, it would have the further advantage of being in conformity with the modern statistical trend towards the replacement of judgment samples by probability samples. order to test whether the use of a sampling procedure governed by the laws of chance would lead to unforeseen practical complications, it seemed advantageous to apply the method suggested, on a small scale, to a more or less realistic situation. Among other information which could be gained from a preliminary investigation of this nature would be an estimate of the magnitude of the sampling variance, as well as hints regarding the difficulties and problems which might arise in full-scale application. * author is indebted for valuable comments to Professors W. L. Crum, R. Dorfman, E. H. Huntington, and G. Kuznetz. Bureau of Business and Economic Research, University of California, Berkeley, kindly financed the study, and Mr. Kenneth J. Oberman aided in the research. 1 For a discussion of this problem see R. Frisch, Some Basic Principles of Price of Living Measurements, Econometrica, xxii (October I954), 505 f.; and M. J. Ulmer, Economic Theory of Cost of Living Index Numbers (New York, I949). 2 Thus, in describing the procedure employed for the selection of the list of goods included in the index, the BLS writes: In I950 and I95I the Bureau priced and studied the price changes of hundreds of items. Using this information and extensive price records of the past, the Bureau selected about 300 items, which together can be used to estimate the average change in prices of all items in the 'market basket.' U.S. Bureau of Labor Statistics, The Consumer Price Index as revised, I953, Bulletin II40 ('953), 3.