Formulas for Consumer Price Index at the elementary aggregate - A new proposal from the economic point of view

The price level in the aggregate economy and, more concretely, controlling its changes, has become one of the high-priority objectives within the framework of the regional macroeconomic analysis. Its different evolution could modify the interregional capital and commercial flows, being able to cause strong shocks, and of asymmetric nature, in each economy. The first step to reach this objective is obtaining a trustworthy and comparable measurement of the inflation in the different regions to be compared. The Index Number Theory is then used to calculate Consumer Price Indexes (CPI) the regional level. The calculation of CPI is made, at least, in two phases. In the first one, Elementary Price Index is considered (EPI). In the second and later phases, these EPI are combined, along with weighting information based on household’s expenditure, to obtain CPI for different aggregation levels to the country level. As previous step to the calculation of the IPE and CPI, the set of goods and services has to be defined based on households’ consumption behaviour. These sets are grouped in layers, named elementary aggregates, based on their homogeneity of satisfying consumer’s necessities. The COICOP (Classification Of Individual Consumption by Purpose) has important implications at the time of analyzing the behaviour of the consumer within each elementary aggregate, because of a high possibility of substitution between products. Nevertheless, this possibility diminishes and can get to be null when the goods and services satisfy necessities with very different nature. Whether what is wanted it is to calculate an EPI that correctly reflects the consumer behaviour, the described homogenous character cannot be forgotten, especially if, in addition, we take into account that National Statistics Agencies have no expenditure information available for weighting purposes, only data of prices to calculate EPI. This paper is focussed on analysis of the formula used to obtain the IPE, with the limitations of available information just commented. The election of the formula for the IPE has not been widely studied in the economic literature, being the proposal by Carli in 1764 and Dutot in 1738 [ extracted Reference of OIT (2003), chapter 20, pages 12-13 ] the most often used for practical purposes. Nevertheless, Fisher (1922) had already recommended not using the Carli’s formula because of the bias to the rise that it introduces [Fisher (1922), pages 29-30]. Throughout the 20th century different authors has continued looking for the ideal formula extending possible approaches to the subject: the approach of Divisia, the stochastic approach, the economic approach and the axiomatic approach. The final summary of these studies can be synthesized in "Toward to Dwells Accurate Measure of The Cost of Living” by the Advisory Commission To The Study The Consumer Price Index presented in 1996. This report, also known as Boskin’s Report, suggests the use of geometric mean price indices at the elementary aggregate for the EPI, this formula is attributed to Jevons in 1983 [OIT (2003), chapter 20, pages 12-13 ]. In the present paper, we demonstrate that all usually formulas for the calculation of the IPE are incoherent with the theory of consumer behaviour, in an aggregate characterized by the high level of substitution caused by homogeneity in the consumption purpose. In addition, the formula proposed by Rodriguez, González and Rodriguez (2004), is not only superior from the axiomatic point of view, but also from the economic approach, is the only one that is able to reflect the expected consumer behaviour.