Dynamic calibration of time-varying parameters using minimum distance estimation

Dear all,

I have a simple dynamic model that boils down to 4 constraints to identify 4 endogenous variables, H, Y, hbar and m. I wish to dynamically calibrate 3 parameters (A, v and B) so as to minimize the squared distance of the 3 (out of 4) simulated variables with the data. I have the data for Y, m and H. However, I’m having a hard time solving the issue as I don’t know whether it is possible to deal with parameters as if they were time-varying. I could also treat them as variables, yet declaring them as parameters seems to me way simpler. In any case, I should define an objective function equal to the squared deviation between the simulated and observed variables. I don’t know how to construct this function as it should have as an argument the vectors of values of the 3 parameters, to then use fminsearch to minimize it.

Is there a way to define an objective function that:

  • receives as an input 3 vectors (or unique longer vector) for the 3 shocks I wish to calibrate
  • Simulates deterministically the model over 21 periods
  • Returns a scalar which equals the sum of the squared deviations between the 3 simulated endogenous variables and the data I have?

I hereby attached the .mod file with the baseline model treating my 3 shocks/time-varying parameter as standard (invariant over time) parameters.

model3.log (1.7 KB)

Thank you in advance.

model3.txt (944 Bytes)
If you don’t manage to open the former file try with this file in .txt

I think the rough outline in

should work.