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

to this criterion of a sufficiently wide “domain of applicability” there are
some other properties that ought to be considered, such as “flexibility”⁴⁰ or
“computational facility” and “factual conformity”⁴¹. As regards the crite-
ria for functional forms mentioned above the Almost Ideal Demand System
(abbreviated by the nowadays unfortunate acronym AIDS) of Deaton and
Muellbauer (1980) and the more general system QUAIDS (quadratic AIDS)
of [2]Banks et al. (1997) represent a fair compromise.

3.1 Almost Ideal Demand System

The starting-point of [11]Deaton and Muellbauers (1980) AlDS is a cost
function of the price independent generalized logarithmic (PIGLOG) class
of preferences:

In c (p,u) = (1 — и) In a (p) + и In b (p),                (24)

where the utility level и generally lies between 0 (subsistence level) and
1 (bliss point) and where

N      ι NN

In a (p) = α₀ +    a_i Inp_i + -        ⁷0’ ɪnPi ɪnPi         (25)

i=l            i i=l j=l

and

N

ɪn ^{b (}p⁾ = ɪn ^{α (}p⁾⁺ fio Π pf^l ∙                   ⁽²⁶⁾

i=l

Filling in equations (25) and (26) in (24) results in the AIDS cost function

⁴⁰Diewert defines flexibility in his Lecture Notes (ch. 4) as follows: it is a function
f(q) that “can provide a second order approximation to an arbitrary function f* around
any (strictly positive) point q* in the class of the linearly homogenous functions.” And by
second order approximation is meant: “A twice differentiable function f(q) .. . can provide
a second order approximation to another such function f*(q) around the point q* if the
level and all of the first and second order partial derivatives of the two functions coincide
at q*.”

⁴¹According to [22]Lau (1986) this is not met if for example the system can only yield
linear Engel-curves (which e.g. applies to AIDS as opposed to QUAIDS). Also Lau had
shown that it is not possible to reconcile the above mentioned criteria so that a compromise
is called for.

22

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