Shock to mean of tax process

In a simple RBC setup, I have a tax process described by the following AR(1) process:
t = c + 0.9*t(-1) + u
where c is a constant and u is a normally distributed shock with mean 0 and variance sigma. I am trying to model a change in the tax regime that is unanticipated by agents.

  1. Is it possible to change the mean of the process i.e. change c to c1 at some future date?
  2. Alternatively, can dynare handle a markov switching process for the tax rate?

Depends on what your are trying to achieve. For IRFS, you can have permanent shocks to the mean. This does not work for simulations or estimation. Markov-switching DSGE models are not possible yet.

Thanks. I am simulating the model. If the change in regime were anticipated, then could I use varexo_det and specify in which period the mean changes?

Out of curiosity, how would you specify a permanent shock to the mean (unanticipated) for IRFs?

Yes, under perfect foresight, you could do this.

A permanent shock simply means you define c to be a unit root process

A shock eps_permanent will permanently move c. You can do this for IRFs, but not for simulations, because due to the unit root your system will move arbitrarily far away from the old steady state/approximation point and thus become very inaccurate.