Dear All,

I have a question about perhaps using Dynare for a task it was not built for.

I have a nonlinear deterministic system, X_t = G(X_(t-1)) , where X_t is a 2X1 vector and G is a nonlinear function. I want to determine the stability of this system at a particular steady state. The way I would usually do this would be to linearize the system around the steady state, so that X_t = A*X_{t-1}, where A is a 2X2 matrix, and then calculate the eigenvalues of A. I suspect a particular steady state to a saddle path, so I should find one eigenvalue less than one in absolute value, and one greater than one in absolute value.

However, I was wondering if Dynare would be able to automate this task, since Dynare can do its own linearizations, and also do some stability analysis. However, when the check command is used in dynare, I’m not sure exactly what matrix the eigenvalues are calculated for.

So my question is: is it possible to use dynare to check for the stability of deterministic systems? If so how? See attached my sample mod file. This solves a deterministic system, then simulates a path for the variables. The initial conditions selected are such that the economy is on the saddle path – I estimate these initial conditions in another file.

All the best,

Jake

nonlin_old.mod (3.8 KB)