Parameter transformation

[irish]

Dear all,

I am trying to estimate a dsge model using bayesian techniques, with transformed parameters. Specifically, I need the tranformation only for the minimization process, while in the metropolis hasting the original parameters must be considered.
1) Is it enough to declair the transformation using the pound operator and to define the whole model in terms of the transfomred variables, while in the estimation block to declair the original paramteres ones? As for example

parameters ..alpha.. ;

model(linear);
..
#alpha_bound=log(alpha/(1-alpha));
..
y=alpha_bound*x;
..
end;

estimated_params;
..
alpha, .., ..
...
end;

2) Does the computation of the jacobian and of the hessian automatically account for this tranformation? That is, when computing the jacobian of alpha it should use exp(alpha)/(1+exp(alpha))^2 instead of just alpha.

Thank you very much,
irish.

[jpfeifer]

Why exactly do you need this transformation, i.e. what are you trying to achieve?

[irish]

Dear Mr Johannes,
Thank you very much for your kind reply.
This kind of transformation is used in a paper I am trying to replicate.
Actually, I'm not sure why the authors have implemented it. The model is
very close to be indeterminate, so may be this could be a reason.

Thanks a lot,
irish

[jpfeifer]

If it is a purely numerical reason, you should try to work without this transformation. My guess is that is has to do with the Jacobian. What is the source you are referring to?