Identification and Parameter Dependence

Problem and Question
Dynare says a parameter used to calibrate a structural parameter within an external steady-state file is not identified, while the structural parameter itself is.

I am wondering if this is expected behavior for the identification command as related to this sort of nesting of parameters.

I am working with a model which incorporates variable capacity utilization with an endogenous depreciation function \delta(u_{t}). The elasticity of \delta'\left(u_{t}\right) with respect to u_{t} evaluated at steady state is \varepsilon=\frac{\delta_{2}}{\delta_{1}} . \delta_{1} is calibrated to pin down the value for u_{t}, so one can choose either \delta_{2} or \varepsilon as the free parameter. I would like to treat \varepsilon as the free parameter to be estimated and solve for \delta_{2}=\varepsilon\delta_{1}.

I declared both \delta_{2} and \varepsilon as parameters in the .mod file (is this the issue?) and then solve for \delta_{2} as above in an external steady state file. I have used the identification command when only \delta_{2} or \epsilon are to be estimated (not both), and it identifies the former (which enters directly into the model block) but not the latter (which indirectly enters the model block by changing the value of \delta_{2} from the steady state calculation.

The identification command should be able to pick up the colinearity between the parameters even if you have an external steady state file, it should switch to numerical derivatives in this case. Which version of Dynare are you using? I am just asking as there used to be a bug with external steady state files we recently fixed (or maybe not :wink: )

Anyways, how do you treat \delta_1, do you also declare this as a parameter? Note that it is better practice to declare \delta_2 as a model local variable in the model block, see Model declaration in the manual.

I could have a deeper look if you’d be willing to share your mod file either in this topic or (if you need confidentiality) via PM or email (

I wouldn’t mind sharing my .mod file, but I have it broken into many smaller .mod files so it might be a headache to share; if I need to I can probably make a MWE instead and send it along.

\delta_{1} is used to calibrate the steady state utilization rate to 1 and is a function of a few steady state creatures, which is why I have \delta_{2} being set in the steady state file instead of as a model-local.

I am using Dynare version 4.5.7, so I guess I am a few versions behind. I will update it and see if the problem persists.

Thank you very much @wmutschl; updating to 4.6.3 seems to have solved the problem.

It also seems noticeably faster, and I love the changes to the output for identification. Lots of neat stuff in here to explore!