DEMAND FOR MEAT AND FISH PRODUCTS IN KOREA

The first-differentiated Stone's index, ∆ logP* may be decomposed into three components:

n  nn

(9)           ∆ log P * = ∑ w. ∙∆ log pj + ∑ ∆ w ■ log p_j - ∑ ∆ w ∙∆ log p_j .

j =1j =1j =1

The second and third term are likely to be quite small since, in the context of time-series data,
shares usually do not change much from one observation to the next (Alston and Chalfant).

Substituting the first term of ∆ logP * from Equation (9) into the first-differentiated LA/AIDS in

Equation (8) yields

(10)           ∆w_i≈∑ⁿ γ_ij∆logp_j+β_i[∆logX-∑ⁿ w_j∆logp_j].

j =1j =1

Equation (10) is similar to the Rotterdam model. Any difference is in the specification of the
income term. Theil and Clements (1987) refer to DQ in Equation (1) as a finite change version of
the Divisia volume index (Alston and Chalfant). It is approximately equal to

(11)          DQ* =∆ log X -∆ log P ° ,

n

where ∆ log P ° = ∑ w_j ■ ∆ log p_j, which is similar to the first-differentiated Stone’s price index
j=1

in Equation (9). Substituting DQ* for DQ, the Rotterdam model is re-specified as follows

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