Elementary price indices under the GBM price model

Jacek Białek

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 5, 1232-1251

Abstract: Countries use either the Dutot, Carli or Jevons indices for the calculation of their Consumer Price Index (CPI) at the lowest level of aggregation. In this paper, we compare expected values and variances of sample elementary indices under the assumption that prices are described by a geometric Brownian motion (GBM). We consider two situations, i.e., the case with only one homogeneous product group and the case with a heterogeneous group of products consisting of homogeneous subgroups. We provide formulas for their biases, variances and mean-squared errors. We confirm the utility of the presented continuous time approach via a simulation study.

Date: 2022
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DOI: 10.1080/03610926.2021.1938127

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