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.

摘要

各国使用 Dutot、Carli 或 Jevons 指数来计算最低汇总水平的消费者价格指数 (CPI)。在本文中，我们在假设价格由几何布朗运动 (GBM) 描述的情况下，比较了样本基本指数的预期值和方差。我们考虑两种情况，即只有一个同质产品组的情况和由同质子组组成的异质产品组的情况。我们为它们的偏差、方差和均方误差提供了公式。我们通过模拟研究证实了所提出的连续时间方法的实用性。