However, using Stone’s price index causes a simultaneity problem since the dependent
variable wi appears on the right-hand side of the LA/AIDS. To avoid the simultaneity problem,
n
the lagged share has been used for P*, as log P* = ∑ wi,t-1 log pi,t (Eales and Unnevehr).
i
Equation (6) implies that the budget shares of various commodities are linearly related to the
logarithm of the real total expenditure and relative prices.
The general demand restrictions of adding-up, homogeneity, and symmetry are satisfied
by the following parametric restrictions on the AIDS.
|
(7) Adding-up: |
nnn ∑αi=1, ∑γij=0, ∑βi=0. i = 1 i = 1 i = 1 |
|
Homogeneity: |
n ∑γij = 0. |
Symmetry: γij = γji .
A test procedure developed by Alston and Chalfant (1993) is used to choose between the
AIDS and the Rotterdam model. The right-hand side of a first-differentiated version of the
LA/AIDS is virtually identical to that of the Rotterdam model, even though the dependent
variables differ. In several studies, the LA/AIDS has been estimated in the first-differentiated
form (e.g., Deaton and Muellbauer, Eales and Unnevehr, Moschini and Meilke, Alston and
Chalfant). In the first-differentiated form, the LA/AIDS becomes
n
(8) ∆ wi = ∑ Yij∆ logPj + βi∆ log(E / P*).
j=1