I run into a problem in replicating Dedola, Karadi and Lombardo 2013, which is a two-country extension based on Gertler and Karadi 2011.
The code works well (I made some simplifications from their original code). My question is when I solve the model by hand, the model seems to have multiple steady states since the asset holding allocations are indeterminate between the two counties while Dynare can find a unique steady state. This is very confusing to me and I’ve been thinking about this for quite a while and still could not figure out why.
I attached the code and the model description pdf file. This is very important to me and really appreciate if anyone could help out!
Hi, Dynare uses a Newton like nonlinear solver to compute a steady state. So even if the model has more than one steady state, Dynare will report at most one steady state (the one identified by the solver if he finds a solution). And there is no way for Dynare to determine the number of steady states. Depending on the initial condition provided to the solver, Dynare will find different steady states (if there is more than one). In your case you have a continuum of steady states.
Dear Stéphane,
Thank you so much for your reply! I tried different initial guesses of the indeterminate variables and Dynare still works well but returns different steady states. I used to think that Dynare will only work if the model has a unique steady state. Did not know that Dynare will also work if the steady states are indeterminate. I learned. Thanks!!!
There are indeterminate steady states, but any initial value you give for the indeterminate variable is a steady state. In this case, solving for the steady state works, because the initial value is already correct and all other variables can be found, conditional on this value.
There are indeterminate steady states, but the initial value is not yet a steady state. In this case, it will not work. The problem is that the indeterminacy of the steady state prevents the Newton solver from finding the direction in which the residuals decrease. Thus, generally when you have unit roots, you need to provide the steady state analytically.