(12) w.∖ logqi = ∑ Yijδ logPj + βiDQ *
j=1
= ∑ Yi, ∆ log Pj + βi [∆ log X - ∑ W ∙ A log Pj ].
j =1j =1
On the right-hand side, the real income terms in the first-differentiated LA/AIDS in
Equation (10) differs from the Rotterdam model. The differences is the use of Wj instead of wj
in the Rotterdam model in Equation (12).
Equation (10) and (12) can be combined as
n
(13) (1- φ)Δw.log(qi) + (φ∖wi = ∑Yijδ log(p,) + βiDQ*, i = 1,2,...,n .
j=1
Equation (13) is a linear combination of the LA/AIDS and the Rotterdam model. If φ = 0,
Equation (13) reduces to the Rotterdam model; if φ = 1 , Equation (13) reduces to the first-
differentiated LA/AIDS. A test of the hypothesis that φ = 0 can be interpreted as a test of the
hypothesis that the Rotterdam model is the correct specification.
The LA/AIDS can be tested directly as well. In the alternative compound model,
n
(14) (1 — λ )∆Wi + λ∆Wi log(qi ) = ∑ Yij∆ log(p, ) + β.∆ log(X / P *)
j=1
λ = 0 implies that the LA/AIDS is correct while λ near 1 is evidence against the LA/AIDS in
the direction of the Rotterdam model.