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Divisia Index

In: Price Index Numbers

Author

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  • Naohito Abe

    (Hitotsubashi University)

Abstract

The Divisia index, introduced by François Divisia in 1925, is a unique economic index that treats time as a continuous variable, contrasting with standard indices which rely on discrete-time points. It defines price and quantity indices through logarithmic differentiation, enabling integration over time, which enables us to conduct various economic analysis easily. Key properties include transitivity, factor reversal, aggregation consistency, and homogeneity of degree one, making it particularly relevant for productivity analysis under continuous-time models. Despite its theoretical strengths, practical application of the Divisia index faces difficulties due to the discrete nature of real-world data, necessitating approximations that often lose desirable properties. Chain indices, such as the chain Törnqvist index, serve as discrete approximations but are less accurate with high-frequency data, often displaying unrealistic trends. The Divisia index also encounters issues with path dependency and fails to satisfy identity and monotonicity without assumptions of homothetic preferences or linear homogegneous production technology.

Suggested Citation

  • Naohito Abe, 2025. "Divisia Index," Springer Texts in Business and Economics, in: Price Index Numbers, chapter 0, pages 153-165, Springer.
    • Handle: RePEc:spr:sptchp:978-981-97-6305-4_7
    DOI: 10.1007/978-981-97-6305-4_7
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