A Taste-Dependent True Index of the Cost of Living - Phlips, Louis; Sanz-Ferrer, Ricardo (The Review of Economics and Statistics, 1975)
THE pathbreaking introduction of the linear expenditure model by Klein and Rubin (1947-1948) opened the way to an econometric implementation of the theory of the true cost-of-living index. The hypothesis of a given static utility function, however, raises doubts about its relevance to a world of changing preferences. This paper aims at developing an econometric application of the theory of the true cost-of-living index for the case of taste changes. It is our hope that we will thus contribute to the improvement of the official indices measuring the cost of living. In a static context, the relevant indifference class is mostly chosen with reference to a price income vector. (For example, prices and income may be those prevailing during the base period or those prevailing during the period of comparison.) But the indifference class can also be made subject to the choice of a commodity vector, there being a one-to-one correspondence between the two vectors. In a dynamic world with continuous and systematic taste changes, on the contrary, the two vectors will not lead to the identification of the same indifference class, as was pointed out by de Souza (1974). Furthermore, the indifference class chosen is indicated by a corresponding utility level in a static model, while the utility function is time dependent in a dynamic model. A reference year is then needed to fix the time dependent parameters of the dynamic utility function. This opens the way to using the utility level not only as an indicator representative of an indifference class but also as determining of itself a level of satisfaction in a cardinalist sense. A correspondence has then to be established between indifference curves of one map at one moment of time and those of a map at another moment (i.e., after a change in tastes). And this correspondence has to be interpreted as representing equal welfare. In this paper, we develop an algorithm for the computation of two dynamic indexes. One index implements the theory developed by Fisher and Shell (F-S for short) in their wellknown 1969 paper on taste and quality change in the pure theory of the true cost-of-living index and is called the (ordinal) F-S index. This index belongs to the class of simultaneous indices, the comparison being based on current tastes while the indifference class is chosen with reference to the base period price-income vector. The other index, called the index, belongs to the class of temporal indices. It takes the base year utility level as a reference point and determines the income that together with comparison period prices and tastes will allow the consumer to attain the base-year utility level. The base period utility level is obtained by maximizing the base period utility function subject to the base period price-income vector constraint. Before proceeding, it is worth noticing that the adjective characterizes the choice of the base-year utility level as the reference point. As a result, the cardinal index is invariant only under monotonic transformations of the utility function that are not time dependent. In particular, this index is based on the assumption that there is no change over time in the of the consumer as a pleasure machine. (This assumption corresponds to the hypothesis of the absence of neutral technical progress in the theory of production.) A change in efficiency does not affect the preference ordering nor the demand functions, but does affect the utility level and therefore the index.' Received for publication May 10, 1973. Revision accepted for publication August 1, 1974.