Unstable linear model singularity

Hi, I want to replicate The Macroeconomic Consequences of Natural Rate Shocks: An Empirical Investigation (nber.org)

To obtain the parameter delta and the natural rate.

Using the specifications on the paper for the calibration outputs a singularity. When changing the parameters, the problem does not seem to change. As the model is small and linear, I dont know what to do to start estimating.

naturalrate.mod (6.3 KB)

Whenever there is a unit root, there will be a singularity in the static Jacobian. That warning message is expected for this type of model.