, where T_0 is the unusual part, it contains terms, that only depend on gaps in t=0. t.i.p are terms independent of monetary policy. T_0 depends on parameters and endogenous variables, it’s a huge term but is of the form:
From what I understand, normally a second order expansion of the welfare function (of the form: W = \sum \beta^t [ln(C_t) - N_t]), leads to a simple welfare function in quadratic gaps, but in the model I’m trying to replicate (this one), the steady-state is inefficient, which leads to extra terms depending linear on the output gap.
In order to circumvent this problem, the objective function is derived under timeless commitment, following Beningno and Woodford, 2005. The term T_0 is supposedly set at time zero, but I lack the theoretical understanding behind it and I don’t really understand what that means.
I was hoping I could still replicate the results in Dynare, given that I have the full quadratic gaps equation, but maybe it is not that easy.
When I try to use the nonlinear model and equation (26), I get an error, that the static model contains NaNs.
I thought this would happen, because the model has a distorted steady-state and I would need to readjust the steady-state model block somehow for this work. I was hoping I could circumvent the problem using the linear model and the quadratic gaps equation.
Is the steady-state not an issue? Hansen2020_NotLinearized_Ramsey.mod (4.2 KB)