• HomoTopy

Homotopy

Here is the syntax for a future homotopy mechanism for steady state computation

Two new ptions in steady command:

• homotopy_mode = 1,2 or 3 (see below)
• homotopy_steps = Integer (sets the number of steps used in the homotopy procedure)

Parameters or exogenous variables (in deterministic models) for which we need to change values are declared in a homotopy_setup block.

Each line of this block has the form

name , expresssion 1, expression 2

• expression 1 must return the initial value (for which it is easy to compute the steady state)

• expression 2 must return the desired value for the parameter or exogenous variables.

Example

steady(homotopy_mode=1,homotopy_steps=3);

homotopy_setup;
alpha, 0.3, 0.3^2;
psi, 0.05, 2*0.5;
end;

Homotopy mode 1

In this mode, the distance between the boudaries for each parameter are divided in as many intervals as there are steps and the problem is solved as many time

Homotopy mode 2

Same as above, but only one parameter is changed at a time. The problem is solved nbr of parameters time nbr of steps times

Homotopy mode 3

Dynare tries first the most extreme values, if it fails to compute the steady state, the interval between initial and desired values is divided by two for each parameters. Every time, that it is impossible to find a steady state, the previous interval is divided by two. When one succeed to find an steady state, the previous interval is multiplied by two. In that last case homotopy_steps contains the maximum number of computations attempted before giving up.