 # Shocks in stochastic simulations

#1

Dear Prof Pfeifer,

I have a couple of questions relating to stochastic simulations.

1. I have a model with a positive government spending (gc) shock financed by lump sum taxes. Given this, following the gc shock, the labour income tax rate (tauW) should be constant at 0. Its percentage deviation from steady state goes from 0 to -3e^-17, which is also approximately zero. However, this issue does not happen with the capital income tax shock (tauK), which stays at 0 following the shock. I just want to confirm that there is no issue, i.e., that the value of tauW is actually staying at its steady state value even though its percentage deviation from steady state is going to -3e^-17?

Please run the run.m file, which in turn runs cycle_irf.mod to show the results for the gc shock.

1. Secondly, if I model a tax process as follows:

tauW = (1 - rhoW)tauW_SS + rhoWtauW(-1) + (1 - rhoW)gammaN(D/GDP - D_SS) + epsW;

If I want to write this equation in exp(logs), do I express the steady state values of the tax rate (tauW_SS) and debt (D_SS) as the exponent of their steady state values exp(tauW_SS) and exp(D_SS), respectively, or just simply as their steady state values? It is not clear to me how to treat steady state values in this context.