Non-Linear Solver for Parameters


I am quite familiar with using external steady state files when simulating non-linear models. They are very handy when the steady state of one or more variables does not have a closed-form solution and instead must be solved numerically.

Today I have encountered a situation in which the model boils down very nicely if two ``change-of-variable” principals are applied. NB I’m working with a basic non-linear small open economy model. First, I restrict the labour disutility parameter, which allows me to calibrate hours of labour to, say, 1/3 — bog standard. Second, I restrict the constant, which appears in the international consumption risk sharing relationship, since I do not want to impose symmetry in NIIP. This allows me to calibrate the real effective exchange rate to, say, unity, in which case absolute PPP holds.

The problem is, the model structure is such that both of these restrictions depend on one another in a non-linear way. This means that I need to apply a non-linear solver to these parameters first before proceeding to the model and steady state sections. Alternatively, I could proceed without imposing these restrictions. However, there are good economic reasons for doing so and the remaining steady state computations boil down incredibly neatly.

I can easily write a separate .m file, much like the external steady state file, but I was wondering if there is an easy way to call such files inside the "parameter” segment (i.e. before typing up the ``model” section)? If so, could you please let me know the relevant command?

The other option is to compute these parameters separately and copy-in the resulting values manually, but this is a little tedious and not flexible when changing parameter values if, for instance, you are trying to estimate the unrestricted structural parameters of the model. Is there a workaround to this?

Thanks a lot in advance!

This is a classic case of parameter dependence. If you cannot do this in closed form, you should code this in a steady state file. is an example