Index-Number Tests and the Common-Scaling Social Cost-of-Living Index

David Donaldson and Krishna Pendakur

Economics working papers from Vancouver School of Economics

Abstract: For a change in prices, the common-scaling social cost-of-living index is the equal scaling of every individual's expenditure level needed to restore the level of social welfare to its pre-change value. This index does not, in general, satisfy two standard index-number tests. The reversal test requires the index value for the reverse change to be the reciprocal of the original index. And the circular test requires the product of index values for successive price changes to be equal to the index value for the whole change. We show that both tests are satisfied if and only if the Bergson-Samuelson indirect social-welfare function is homothetic in prices, a condition which does not require individual preferences to be homothetic. If individual preferences are homothetic, however, stronger conditions on the Bergson-Samuelson indirect must be satisfied. Given these results, we ask whether the restrictions are empirically reasonable and find, in the case that individual preferences are not homothetic, that the restrictions make little difference to estimates of the index.

Keywords: social cost of living; aggregation; welfare economics (search for similar items in EconPapers)
JEL-codes: C43 D63 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2010-02-04, Revised 2010-02-04
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Journal Article: Index-number tests and the common-scaling social cost-of-living index (2012)
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Persistent link: https://EconPapers.repec.org/RePEc:ubc:bricol:david_donaldson-2010-4

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