I’ve been going through the excellent replication codes by Johannes Pfeifer for Gali 2015.

In Gali (2015) Chapter 5, a cost push shock is motivated as a time-varying discrepancy between the natural level of output y^n_t, and the efficient level of output y^e_t. On page 128 in Gali’s book, it says u_t = \kappa(y_t^e - y_t^n).

Assuming that natural output is a function of technology, y_t^n = \psi^n_{ya}a_t, then it seems as if fluctuations in u_t are associated with fluctuations in y^e_t, and by extension, fluctuations in r_t^e.

Yet, in the codes for Chapter 5 by Johannes Pfeifer, y_t^e and r_t^e don’t fluctuate, in response to cost push shocks. In the codes, I found the definiton y^e_t=\psi^n_{ya}a_t, which is not in the book. Since y^e_t doesn’t move, r^e_t doesn’t move either.

My question is: is it possible that y^e_t was not correctly defined in the codes? (It should not matter for the remaining results, since it is only the definition for y^e_t which would be incorrect, other equations would be unaffected.)

I might have found a solution. Willi Mutschler has in his Chapter 5 codes (Optimal policy in the New Keynesian Baseline model with Dynare | Willi Mutschler), the definition for the efficient level of output as y^e_t=\psi^{YA}*a_t, but importantly, he backs out the natural level of output from this definition u_t = \kappa*(y^e_t-y^n_t), I think this is correct, since it introduces the wedge in between natural and efficient output which seems absent in Johannes Pfeifers codes for Ch. 5. But it would be great to see if others agree with that.