No, only for very small shocks should the two coincide. After all, a nonlinear model should be close to linear near the approximation point.
@jpfeifer I run the code NK_baseline.mod with orders 1 and 2 using exp(x), resulting in IRFs are not identical. There are small differences in responses. I would like to confirm the reason behind it.
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First, according to the Dynare manual, the difference bc of the shift effect of variance of future shocks and other interaction terms, as highlighted below. Is it correct?
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You also mentioned here in the forum that in the second order, Dynare produces GIRFs where other shocks averaged out. Is it done by default? Would comparing the IRFs from first and second order approximation be correct?
Thanks!
- Yes that is correct. Obviously, it makes a difference whether you are trying to approximate a nonlinear function with a linear or quadratic function.
- At first order, the GIRF would result in exactly the same IRF computed at first order. Thus, the comparison is typically correct. But in the end it depends on what you are trying to do.
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