Advanced Econometrics Takeshi Amemiya

Multivariate Nested Logit Model

The model to be discussed in this subsection is identical to the nested logit model discussed in Section 9.3.5. We shall merely give an example of its use in a multivariate situation. We noted earlier that the nested logit model is useful whenever a set of alternatives can be classified into classes each of which contains similar alternatives. It is useful in a multivariate situation because the alternatives can be naturally classified according to the outcome of one of the variables. For example, in a 2 X 2 case such as in Table 9.1, the four alterna­tives can be classified according to whether у, = 1 or y, = 0. Using a parame­terization similar to Example 9.3.5, we can specialize the nested logit model to a 2 X 2 multivariate model as follows:

Р(Уі = 1) - ві exp (z',y)[exp (pj'x'nP) + exp (рГ'хіoP)Y' (9-4.5)

-і - (flj exp (z',y)[exp (pj'x'nP) + exp (pT'x’M'

+ a0 exp (4y)[exp (Po'xitP) + exp (Po'xooP)]^),

______ exp (pT'x'uP)______

exp (pj'x'uP) + exp (pT'x'ioPY

and

The two-step estimation method discussed in Section 9.3.5 can be applied to this model.