Dear all,

I am dealing with a model embedded with a signal extraction problem. As seen in Patrick Hurtgen’s paper (http://www.sciencedirect.com/science/article/pii/S0165188914000177), one should first solve the full-information model in order to get the linear policy coefficients.

Firstly, I noticed that Dynare gives us the model solution in the following state-space form:

Y(t) = H*s(t-1) + G*e(t), where “s” stands for the state variable vector and “e” the shock vector.

As explained in (https://www3.nd.edu/~esims1/using_dynare_sp15.pdf, page 7), this formulation comes from the following state-space representation:

s(t) = A*s(t-1) + B*e(t)

x(t) = F*s(t), where “x” stands for the control variable vector.

Substituting the s(t) equation in the x(t) one, we get:

s(t) = A*s(t-1) + B*e(t)

x(t) = C*s(t-1) + D*e(t), where C = FA and D = FB

Stacking them we arrive at the Y(t) “Dynare” formulation.

However, in Hurtgen’s article (p.283) the state-space form is written differently as (using the notation above):

x(t) = F*s(t-1)
s(t) = A*s(t-1) + B*e(t)

I cannot seem to find out how to convert the Dynare output into the above representation. What am I missing here?

Thank you all in advance.