A useful feature of the conditional logit model with a specification including a full set of alternative specific constants is that:

where s_j is the proportion of times in the data that alternative j is selected, and the right-hand side is the average predicted probability for alternative j. Using the log-likelihood function in (16.13) and the specification v_ij=δ_j+βX_ij for j=1,..,J−1 and viJ=βXiJ for j=J, show that the first order conditions with respect to δ₁,…,δ_J−1 for maximum likelihood estimation lead to (*) for all alternatives.

Eq 16.13

Transcribed Image Text:

exp(vj) Lexp(v.) h=] j = 1,..., J,