# Risk premium in a non-linear model

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.

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

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

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.