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

of goods index, or COGI) as for example the well known Laspeyres price in-
dex. The COLI is the ratio of minimum costs c required to attain the same
utility level U under two “price regimes” given by the price vectors p_t and p₀
respectively, that is

_pκ∕         / ʌ -ʌ ^c (Pi^,u)                       z_n

^Pot ⁽Po, Pi, и ⁽q⁾ , ^u) = —----—^{,                     (1)}

c (Po,u)

The COLI thus compares the expenditures required for attaining the same
level of utility (well-being) rather than those required for buying the same
quantities of goods. In the COGI approach quantities q₀ and q_t are regarded
as exogenous (i.e. independent of prices) and given, as e.g. in the Laspeyres
price index

or the Paasche price index

whereas in the COLI context, q-vectors are said to be determined or
“explained” by (rational) consumer behaviour as conventionally assumed in
microeconomic theory and therefore endogenous. For this reason the COLI
claims to possess a theoretical (microeconomic) foundation of an index func-
tion of a CPI. It is assumed that households are engaged in utility maximi-
sation subject to the restriction of a given total expenditure (or income) M
and a given vector p of prices. The COLI allows for substitutions among
the same goods in response to varying relative prices, while the COGI keeps
everything constant except prices. Therefore the COLI will in general display
lower inflation rates, which not infrequently may be welcomed (politically),
and the difference P_fL — P^f > 0 is called “substitution bias” (of P_fL).

Those who advocate the COLI use to emphasise that the COLI enjoys
a theoretical justification or “theoretical underpinning” (in contrast to the
COGI which “only” may be justified by representing a weighted average of
price relatives and by the “principle of pure price comparison” according
to which the index is reflective of price changes only). Note, however, that
(1) only defines the COLI P^ but it does not give any hints about how to
compile this index in practice because the c-function (and the utility function

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