First thank you very much for your previous guidance, I am grateful.
I have a question about relationship between steady state inflation and inflation target when monetary policy rule is inflation targeted and inflation target is nonzero (e.g. most central banks have inflation target 2%),
I think theoretically, in the steady state, inflation rate is zero, in my DSGE model, inflation is PAI=ln(Price/Price(-1)), hence, in steady state, Price=Price(-1), inflation=0.
However, I have used Taylor type interest rate feedback rule for monetary policy
R-steady_state( R )=rho * (R(-1)-steady_state( R ))+(1-rho) * thetay * (Y-steady_state(Y))+(1-rho) * thetapai * (PAI-Inflation_target)+(1-rho) * thetasg * (Stock_Growth-steady_state(Stock_Growth))+epsR
R is interest rate, Y is output, PAI is inflation, epsR is monetary policy shock, I treat inflation_target as a parameter to be estimated using Bayesian method. Initial value and prior mean of inflation_target is 2%.
I find a problem about what should steady state inflation be when inflation target is 2%?
Scenario 1, if I put steady state inflation PAI to 0 and inflation_target is nonzero,e.g.2%, then I find Taylor type interest feedback rule becomes inequality, and the program broke down.
Scenario 2. if I put steady state inflation PAI to 2%. then I find Taylor type interest feedback rule is satisfied. however, inflation is PAI=ln(Price/Price(-1)=0.02, it means that Price does not have a steady state,
Thank you very much and look forward to hearing from you.