Comparison of elementary price indices

Abstract

Most countries use the Dutot, Jevons or Carli index for the calculation of their Consumer Price Index (CPI) at the lowest (elementary) level of aggregation. The choice of the elementary formula for inflation measurement does matter and the effect of the change of the index formula was estimated by the Bureau of Labor Statistics. It has been shown that difference between elementary indices can be explained in terms of changes in price dispersion. In this article, we extend these results comparing both population and sample elementary indices. We assume that prices from two compared time moments are log-normally distributed and correlated. Under the above-mentioned assumption, we provide formulas for biases and mean-squared errors of main elementary indices.