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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.

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