Suppose an individual $i$'s utility from alternative $j$ is given by:
$U_{ij} = \alpha_j +v_j'\omega+\epsilon_{ij}$
where the joint density of $\epsilon_{i}$ is type 1 extreme value.
The choice probability of alternative $j$ is then given by multinomial logit as:

$Pr(y_i=j|v)=\frac{e^{\alpha_j +v_j'\omega}}{\sum^J_{k=1}\alpha_k +v_k'\omega}$

According to my lecture notes, we are unable to separately identify $\alpha_j$ from $\omega$.
Can someone explain why?

I was given an explanation analogous to fixed effects where demeaning the regression removes any time invariant constants but I'm not clear on how that links to this.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.