The AIDS developed by Deaton and Muellbauer is specified as
n
(3) Wi = αi + ∑ Yij log Pj + βilog( E / P ), i = 1,2,..., n,
j=1
where wi is the budget share of the ith good, E is the total expenditure on the group of goods,
and logP is the price index for the group defined as
1nn
(4) log P=ai+bilog pi+⅛∑∑ cjlog pi log pj.
2 i=1 j=1
This price index makes the system nonlinear. To make the model linear in parameters,
Deaton and Muellbauer suggested using Stone’s price index defined as
n
(5) logP*= ∑ wi,tlogpi,t.
i=1
The model which uses Stone’s price index is the Linear Approximate AIDS (LA/AIDS)
as follows
n
(6) wi = αi + ∑ Yij log Pj + βlog( e / P *), i = 1,2,...,n.
j=1
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