## Why Elementary Price Index Number Formulas Differ: Price Dispersion and Product Heterogeneity

_IMF Working Papers, July 1, 2006_

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## Bibliographic details
- Authors: Mick Silver, Saeed Heravi
- Published: July 1, 2006
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781451864342.001

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### Summary
- Authors: Mick Silver, Saeed Heravi
- Date: July 1, 2006
- Core purpose: Develop elementary-level aggregation theory to inform users and compilers of Consumer Price Index (CPI) aggregation formulas promulgated by the Consumer Price Index Manual (2004) and used in IMF training and technical assistance.
- Main finding summary: Differences between commonly used elementary index formulas—primarily the Dutot and Jevons formulas—can be explained by changes in price dispersion that arise from product heterogeneity. The paper uses a sample-estimator approach and an illustration based on scanner data to demonstrate these mechanisms.
- Policy relevance: Choice of elementary index formula matters for CPI compilation; the paper discusses implications for formula selection.

### Methods and Data
- Theoretical approach: Elementary-level aggregation theory using an approach based on sample estimators.
- Empirical illustration: Scanner data used to show how price dispersion and product heterogeneity drive differences between Dutot and Jevons formulas.

### Key findings
- Most countries use either the Dutot or Jevons index formula.
- The Dutot and Jevons formulas generally give different results.
- Differences between these formulas can be explained by:
  - Changes in price dispersion, and
  - Product heterogeneity, which affects observed price dispersion.
- Advice on the choice of formula therefore matters for CPI compilers and users.

### Implications for choice of formula
- The analysis implies that CPI compilers should consider:
  - The extent of price dispersion in the sampled products,
  - The degree of product heterogeneity in elementary aggregates,
  - How sample estimation interacts with aggregation formula properties.
- Practical guidance: Choice between Dutot and Jevons should be informed by observed dispersion patterns and heterogeneity; the paper examines these implications in detail.

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_Source: https://www.imf.org/en/publications/wp/issues/2016/12/31/why-elementary-price-index-number-formulas-differ-price-dispersion-and-product-heterogeneity-19328_