Deterministic time varying parameters

Estimation
1

Dear friends,

Is Dynare capable of handling deterministic time varying parameters?
For example, my model (linear) have an equation of the following type,
X(t) = alpha(t)*y(t)+beta(t)*z(t),
Where x, y, and z are variables and alpha and beta are known parameters (known even for the future).
One way would be treat the parameters as variables, but, in this case the model wouldn’t be linear anymore. Besides that, in order to forecasting, all forecasts would have to be conditional on these parameters.
I looked in the reference but I didn’t found, is there an automatic way to dealing with problems of this kind?

Thanks!
Rodrigo

2

That very much depends on the context you are working in. Which command do you want to use? For perfect foresight simulations, you can easily define them as exogenous variables.

3

Thank you for your replay!

Actually, I want to estimate and forecast the model.
I think I could have described the model better.

The “whole” model is like:

x(t) = alpha_1(t)*y_1(t) + alpha_2(t)*y_2(t) +u(t)
u(t) = rho * u(t-1) + e(t)
y_i(t) = c_i + eta_i * v_i(t) + u_i(t)
u_i(t) = rho_i * u_i(t-1) + e_i(t), i in {1,2}

where x and v_i are observables variables, y_i, u, and u_i are non-observables ones, alpha_i are known parameters (like weights), and rho, c_i, eta_, and rho_i are parameters to be estimated.
My goal is to forecast x and y_i conditioned in the path of v_i, without lose the linearity of the model (the model has a lot more variables).

Thanks!
Rodrigo

4

I see. This will make the model definitely nonlinear and make estimation hard. Have you checked whether you could linearize these now nonlinear equations? Are your parameters to be estimated stochastic? If not, everything is still conditionally linear. You could then estimate the model with the Kalman filter, although that may not be doable with Dynare in a straightforward way.

6

You should @rodrigo here.