Observable, global identification of likelihood, multi modal

Dear Johannes,
First thank you for your helpful guidance last time in the forum.
I have a question about the functional format of observables and global identification of likelihood, when the observed variables have none of nonlinear forms such as square root, square, cubic and so on, does it mean the likelihood function is less likely to suffer from global identification problem such as multi modality problem?
Best,
Jesse

Dear Jesse,

The likelihood is the density of the sample conditional on the parameters. For inference purpose we maximise this object with respect to the parameters, meaning that, from this point of view, it has to be understood as a function of the parameters. The shape of the likelihood with respect to the observed endogenous variables is not the main issue. If the model is approximated at first order, the reduced form is linear with respect to the variables but a potentially highly non linear function of the parameters we want to estimate. The mapping from the deep parameters to the reduced form parameters goes through a generalized eigenvalue problem.

Best,
St├ęphane

Dear St├ęphane
Thank you very much for your helpful reply.
Best wishes,
Jesse