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

the official German Family Budget Surveys EVS). To our knowledge there
are no studies of demand systems of a comparable broad scope (comparing
various systems) to be found in the literature to date.

2 The superlative index approach: assump-
tions and problems

2.1 Setting the stage

Given the immense problems with the Demand Systems Approach (DSA)
DiewerFs Superlative Index Approach (SIA) was well accepted and hailed
everywhere on the part of the price statisticians as it promised to have solved
finally a seemingly insurmountable measurement problem. The SIA is gen-
erally seen as the first and possibly (to this day at least) only method that
allows the unobservable COLI (or an approximation of it) to be compiled
validly in practice using observable price and quantity vectors only. The
message of the SIA is usually understood as follows: Diewert was able to
show that certain well known price indices P were “exact” for a specific cost
function (and correspondingly quantity indices Q exact for a specific utility
function). This means that if preferences of a household are following a cer-
tain utility function (or cost function derived from it) the COLI takes the
form of a certain index (like Fisher P^f, Tbrnqvist P^τ or Walsh P^w), which
then is said to be “exact” for this particular type of utility or cost function.
If this function is “flexible” in a sense to be defined later, the corresponding
index is called “superlative” by Diewert. In fact P^f, P^τ and P^w are the
most prominent representatives of this family of “superlative” price indices.

In this part we try to show that this remarkable result of the SIA has
its price in that it requires some restrictive assumptions which are unlikely
to be met in reality and that its relevance notoriously seems to be greatly
exaggerated. Before going into detail of explicit and implicit assumptions
made in developing the SIA it seems to be pertinent to state right at the
outset how (we believe that) the message of “superlative indices” probably
is understood by the ordinary price statistician. It seems to us that in his
view the following five statements are true

1. There are only small number of index function proved to be superlative

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