Linear vs nonlinear: same shape but different magnitude

Hi, I solved a model using the nonlinear method in dynare, then log-linearized the same model by hand and solved it using the linear method in dynare. Given the same parameter values, the shapes of the irfs are the same, but the magnitudes are different.

Attached is the model setup, codes and figures. The irfs generated by two methods are proportional, but the proportions for different variables are different.

Why is there such discrepancy and which method is reliable? Thanks! (34 KB)

Your nonlinear version results in IRFs as linear deviation from steady state. Your “linear” model in contrast is not “linear” but actually “loglinear”, i.e. in percentage deviations. The difference is that in the loglinear one the IRFs are basically scaled with the respective steady state values (Jacobian transformation). This explains the different scale, but same shape. You would get exactly the same if you used an exp() substitution in the nonlinear model. For details, see Pfeifer(2013): “A Guide to Specifying Observation Equations for the Estimation of DSGE Models” … ations.pdf.

Thank you, professor. Your paper helps a lot. Actually, the irfs will be the same if we add ``loglinear’’ option in the stoch_simul command in the nonlinear model.

I have another question asked in the topic ``steady state: solution of multi-nonlinear-equation system ‘’, hope your could have a look. Thanks!