The interpretation of Gerali et al(2010)

Hi. I’m working on the model by Gerali et al. (2010) and try to figure out how they estimate/calibrate the parameters in the first part. I cannot understand how the capital utilization cost parameter in the line 246 is derived: "eksi_2 = 0.1*r_k_ss; " I can see that “eski_1= r_k_ss” from the F.O.C of capital utilization rate at the steady state where “exp(u) =1”, but why the relative elasticity of capital rental rate(“exp(r_k)”) with resptct to capital utilization(“exp(u)”) at the steady state is 0.1? It seems this parameter is given in advance but I cannot figure it out from the model by myself.

Your kindly help is much appreciated.
EA_GNSS10.mod (38.3 KB)

It follows directly from the calibration in Table 1. The parameter you mean is equal to the ratio of xi_2/xi_1, which is 0.1.

Thanks for replying, and I found the formal explanation in their previous working paper as well, saying that they set this ratio 0.1 as to limit the non-linearity of the model.

Hi Mr.Chan, I’m currently having trouble dealing with the steady state of this model (Gerali et al., 2010), would you be so kind to show me a demonstration of how to analytically calculate the steady state with pencil and paper? Thank you very much sir!

Hi magnolia,

for models of this family it is not really possible to derive the steady state analytically, thus you have to go the direction of doing it numerically. That is also why in the file above, there are initial values given to help Dynare deriving it.

Dear DoubleBass,

thank you for your help! I noticed that the initial value of this model happens to be the steady state, so there must be a solution(whether analytically or numerically, numerically most likely) to the steady state outside the mod file.

If it is a numerical solution, there must be some way to simplify the equations in the model that enables matlab to use fsolve or other function to get the steady state, do you know how to simplify it?

Thank you for your reply sir!

As Prof.jpfeifer mentioned in other post, the setting of initial value in a complicated model is rather tricky, any slight change to the value of parameters may cause a failure. Therefore I think it’s best to solve the steady state without using initial value :smiley:

Yes, in general, not using initial values is to be preferred if it is possible. This, however, does not apply to this case and so you would have to go with a second best option and so either use a steady state file or compute it outside of Dynare and fill it in via initial values.
The approach in both cases is similar, like you mentioned, reduce the model as far as possible and then use a numerical solver to find the steady state. The way I do this is by trying to solve it analytically on paper and then reduce the system of equations until no longer possible. By then the size should be reduced, as for some variables it is indeed possible to find their steady states, and you should be able to use either fsolve in Matlab or the steady state file integration in Dynare.