When I code a log-linearised model in Dynare and set the AR(1) coefficient of a shock to 1, the following error message appears:
dynare_estimation_init:: The steady state at the initial parameters cannot be computed.
I have often got the same error message when I defined an equation for the level of a nominal variable say, price = inflation + price(-1).
I remember from many years ago, in the dynare code for the first Smets-Wouters Euro-area model (SW2003), the inflation target shock in the monetary policy was ‘proper’ unit root and not merely very persistent. The earlier versions of Dynare were able to handle the unit roots without any problems - if I remember correctly.
What surprises me is that when I deal with open-economy models with debt accumulation - which are non-stationary in the absence of quick-fixes like endogenous risk premia or adjustment costs - newer versions of Dynare can still ‘solve’ the model and produce impulse response functions. It is just that the model being non-stationary, the IRFs of several real variables will not return to steady-state. So with the command ‘check’, I can observe that one eigenvalue is exactly unity…which disappears when I introduce the stationarity-inducing model features.
How is it that dynare offers a model solution for one type of model exhibiting a unit root while it does not do so for other types?