Exercise 14.2 in Koop, Poirier and Tobias's book (i.e. Bayesian econometric methods) talks about the case that in probit model, the regression and scale parameter are not jointly identified.

I wonder, in general, is there any rules or heuristics that can help us to judge when regression coefficients and scale parameter can be jointly identifiable and when not?

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    $\begingroup$ Please add self-study since this is related with an exercise from a textbook. $\endgroup$ – Xi'an Jul 21 '17 at 8:30

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