Problems of operationalizing the concept of a cost-of-living index

might be questioned when u_t > u_q just like is being criticised for its constant
basket which is constantly becoming unrepresentative and irrelevant with the
passage of time. Other vexing problems with the COLI theory are problems
involved in

• proceeding from the single household case to the multiple household
case³⁸, and

• in justifying the usual multistage index compilation of official statis-
tics, not only in terms of aggregation properties of index functions³⁹ in
terms of sub-utility maximisation as it would be required in the COLI
framework.

However this would go beyond the topic of this paper.

3 Demand Systems

After having analysed Diewerfs Superlative Index Approach, we will now
turn to the Demand Systems Approach to approximate the COLI. There is
more than one demand system in accordance with the usual assumptions of
the utility maximising household. Hence a choice has to be made among a
number of functional forms, each of which renders specific functions for the
indirect utility function or the cost function and above all for the budget
shares. This choice may be oriented at various desirable properties of the
respective functional forms. The specific regression functions may for ex-
ample comply with the (microeconomic) “regularity requirements” of utility
and demand functions only within a more or less wide range of possible val-
ues for the parameters of the function rather than “globally”. In addition

following argument against the Laspeyres price index P^l ([27]Triplett (2001), p. 324):Any
index different from the COLI means that the utility level is not constant such that “sta-
bilising the Laspeyres” by the monetary authorities “implies diminishing living standard”.
However P^l traces the cost of buying the same basket of goods which of course involves
the same level и given a constant utility function. It is only the cost c(p_t, uq) which will
by definition be smaller than po^q_t.

³⁸The question which of the two weighting schemes (plutocratic or democratic) is prefer-
able is still not resolved.

³⁹For example Diewert discussed this type of considerations only in [14]Diewert (2000),
p. 63ff.

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