## International Statistical Review

- Internat. Statist. Rev.
- Volume 74, Number 2 (2006), 235-270.

### Stochastic Index Numbers: A Review

Kenneth W. Clements, Izan H.Y. Izan, and E. Antony Selvanathan

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#### Abstract

The stochastic approach is a new way of viewing index numbers in which uncertainty and statistical ideas play a central role. Rather than just providing a single number for the rate of inflation, the stochastic approach provides the whole probability distribution of inflation. This paper reviews the key elements of the approach and then discusses its early history, including some previously overlooked links with Fisher's work contained in his book *The Making of Index Numbers*. We then consider some more recent developments, including Diewert's well-known critique of the stochastic approach, and provide responses to his criticisms. We also provide a review of Theil's work on the stochastic approach, and present and extend Diewert's work on this topic within the context of the Country Product Dummy method which measures price levels internationally. The paper also contains some recent material on the value of information from the perspective of the stochastic approach, as well as illustrative applications.

#### Article information

**Source**

Internat. Statist. Rev., Volume 74, Number 2 (2006), 235-270.

**Dates**

First available in Project Euclid: 24 July 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.isr/1153748795

**Keywords**

Index numbers Stochastic approach Measurement of inflation

#### Citation

Clements, Kenneth W.; Izan, Izan H.Y.; Antony Selvanathan, E. Stochastic Index Numbers: A Review. Internat. Statist. Rev. 74 (2006), no. 2, 235--270. https://projecteuclid.org/euclid.isr/1153748795

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