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Separability and AggregationThe Collected Works of W. M. Gorman, Volume I$
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W. M. Gorman, C. Blackorby, and A. F. Shorrocks

Print publication date: 1996

Print ISBN-13: 9780198285212

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198285213.001.0001

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Klein Aggregates and Conventional Index Numbers

Klein Aggregates and Conventional Index Numbers

Chapter:
(p.257) 16 Klein Aggregates and Conventional Index Numbers
Source:
Separability and Aggregation
Author(s):

W. M. Gorman (Contributor Webpage)

, C. Blackorby, A. F. Shorrocks
Publisher:
Oxford University Press
DOI:10.1093/0198285213.003.0016

This paper was presented at the European Meeting of the Econometric Society in Innsbruck in 1953; it has never been published, survives in several drafts, and was the first attempt to try to put together the issues raised by aggregation and equilibrium conditions. Klein (1946) posed the problem of aggregating inputs and outputs in an economy's production function when there are no equilibrium conditions restricting the allocation of commodities. This problem was solved by Nataf (1948) who derived the general forms of the aggregates and the economy technologies that are consistent with the Klein aggregation problem. Gorman here analyses the usefulness of the aggregates that solve the Klein problem, arguing that these Klein aggregates are not useful for many purposes in their general form, and proposing additional requirements that useful Klein aggregates should satisfy. For several of these additional requirements, Gorman derives the circumstances in which such aggregates exist.

Keywords:   aggregation, conventional index numbers, equilibrium, Klein aggregates, production functions

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