Niiice, good stuff. Lemme make sure I’m getting this right:

\epsilon_{scb} is a shock

p_{scb} are the parameters we’re sampling, and the eqs at the top of page 2 show us how to go from p_{scb} to \epsilon_{scb}. It looks like there’s just a scalar transformation for every p_{scb}/\epsilon_{scb} pair.

q_{scb} are quantities. Any chance p_{scb} are prices?

It looks like \epsilon_{scb} = V_{scb}.

What’s bugging me is that I expected to find a distribution on the shocks, \epsilon_{scb}, and the right hand side of the eq looks like it is something like that (if V_{scb} = \epsilon_{scb}). The left hand side, however, says this distribution is p(q_1, q_2, ..., q_K)? Is there a relation between q_{scb} and \epsilon_{scb} that I’m missing? I see how the \Psi_\epsilon term produces the e^{\epsilon_{scb}} s.

Also the Jacobian adjustments are written as if the transform we care about is from q_{scb} to \epsilon_{scb}, and, as far as I can tell, we have a transform from p_{scb} to \epsilon_{scb} (but this is probly just another variant of what I’m not understanding above).

Why doesn’t u^{T} B u fall out of the Lagrangian?

And why does \Psi_{scb} multiply the derivative of u^{T} B u in the optimality conditions? It looks like it’s just dotted with q in the original Lagrangian.

Hopefully this snail’s pace check is useful for you haha. Maybe it’ll eventually turn into insight into your problem rather than just me askin’ questions.