Explicitly Modeled Expectational Errors


I am attempting to replicate (and extend with usual frictions) the Cochrane (2021) model found here: https://static1.squarespace.com/static/5e6033a4ea02d801f37e15bb/t/60cf6474f779756d877f92ce/1624204407753/ftmp_surplus.pdf

Generally, this is quite straightforward as all linearized equilibrium equations are presented (see p. 12). I am having difficulty only with equation 31 that specifies an explicit enforced relationship between the inflation expectation error and the model errors. Obviously, if I include this equation as is, I have one more equation than endogenous variables. Could you please advise on how to do this? Would the results look any different if this equation were omitted altogether? I do not recall any other time I have seen calibrated coefficients for the dependency of expectational errors on model shocks.

My Dynare mod file is attached.

Thanks for your help!

cochrane_2022_model.mod (4.3 KB)

According to the appendix, you only need equations (8)-(20). Expectational errors are using in some solution techniques, e.g. gensys.

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Thanks for the reply! Eqn. 16 within the 8-20 range is still the explicitly modeled expectational errors but as per your comment I will simply disregard this equation.