Risk premium in a non-linear model

[AnaGr]

Hello everyone

I have a doubt related to the risk premium in an open economy model, to model it I followed Adolfson et al (2007), who assume that the premium is:

Φ=exp⁡(-ϕ_a (A_t-A)+ϕ_t)

with ϕ_t as a risk premium shock, however, I am adapting the model (with some differences) in its non-linear form, but I have doubts about how to introduce the risk premium and the value of the parameters. Unlike the authors, I am not including the risk premium shock, the way I entered the risk premium in the nonlinear model is:

Φ_t=exp⁡(-ϕ_a (A_t-A))

I set the parameter ϕ_a=0.01, but that value gives me very strange IRFs (like rising inflation after a monetary policy shock, or lower output after a technology shock), the IRFs only make sense when I set ϕ_a to something like 0.0001, does that value make sense? I guess I’m confused with the magnitude of the ϕ_a parameter in a non linear model. Lastly, in the model that I’m trying to estimate I haven’t done yet the exp substitution, so I don’t know if the way I entered the risk premium equation is correct, and I don’t know how it would change when I do the exp substitution.

Greetings and thanks
Ana.

[jpfeifer]

Originally, closing conditions like that were use to induce stationarity by putting in a small risk premium. Schmitt-Grohe/Uribe (2003) showed this to not matter too much for linearized models with small parameter values. That may be different for nonlinear models, see https://www.bankofcanada.ca/wp-content/uploads/2017/06/swp2017-21.pdf

Finally, don’t do a full exp()-substitution. Append auxiliary variables. See

Question about understanding irfs in dynare

To be more precise: it depends on how the variables in your model are measured. As @stepan-a says, Dynare conducts a linearization. If you for example have a nonlinear model and your model variable is simply the level of output, the IRF will measure the difference between the variable and its steady state (or its mean at higher order). This is the case with https://github.com/DynareTeam/dynare/blob/master/examples/example1.mod In contrast, if your model variable already measures percentage…

[AnaGr]

Thanks professor, the paper is very interesting. One last question, a risk premium shock like the one shown in the first equation ( \Phi = exp(-\phi(A_t-A)+\phi_t) ), in the literature is usually considered as an inefficient shock, am I correct?

Greetings
Ana

[jpfeifer]

That depends on the interpretation you attach to it. But most of the time, this risk premium does not result from efficient considerations like technology or preferences.