Estimation of a parameter that determines the steady state

Hello everyone,
I am trying to estimate a non-linear model and I want to estimate three parameters that determine the steady state that is, for example:

model;
\widetilde{C}_{t} = C_t + \varpi Y_t^P
end;

steady_state_model;
\widetilde{C}_{t} = C_t + \varpi Y_t^P
end;

estimated_params;
varpi, 0.000, , , normal_pdf, 0.000, 1.000;
end;

The problem is that if I put it this way, the initial value of the parameter does not change with the estimate, that is, the mode is equal to the initial value and with zero variance. I tried using init_val instead of steady_state_model and the estimate manages to move to a new mode, but if I try to restart the mode calculation to get the parameters to converge, it gives me several WARNINGS for example that the model has different steady state values.

How could I estimate these kinds of parameters? that is, parameters that define the first moments of the variables (or the steady state), since with the parameters that determine the second moments I have no problems.