Inflation and steady state solution

Dear all,

I’m trying to find a steady state for Christiano, Lawrence J. & Trabandt, Mathias & Walentin, Karl, 2010. “DSGE Models for Monetary Policy Analysis,” Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 7, pages 285-367. There is a curious phenomenon that if I set steady state inflation PIbar equals to 1, we can calculate the steady state normally, if we set PIbar equals to 1.01, there is an error:

There are 2 eigenvalue(s) larger than 1 in modulus
for 4 forward-looking variable(s)
The rank condition ISN’T verified!

And if we set PIbar equals to 1.03, the error is:

Equation number 1 : 0.34095 : FOC consumption
Equation number 2 : 0 : FOC labor hours
Equation number 3 : 0 : Euler equation
Equation number 4 : 0 : FOC of H and I
Equation number 5 : 0.039136 : marginal cost
Equation number 6 : 0.47773 : X1
Equation number 7 : 0.31079 : X2
Equation number 8 : 0 : ptilt
Equation number 9 : 0.14434 : 9
Equation number 10 : 0.33369 : pstar
Equation number 11 : -0.026537 : y
Equation number 12 : 0 : 12
Equation number 13 : 0 : 13
Equation number 14 : 0 : Taylor Rule
Error using print_info (line 32)
The steady state is complex (the sum of square residuals of imaginary parts of the steady state is 59.6188)

After many checks, I temporarily believe that there is no error in the model part and the equation solved in the steady state m file. The question I want to ask is, what is the relationship between inflation and steady-state error reporting? What ideas can I use to solve such problems?

Thank you in advance!!
nk_baseline_steadystate.m (3.2 KB)
nk_baseline.mod (3.8 KB)

It seems that you implement trend inflation in that case without perfect indexing. It is well-known that trend inflation in that case can affect determinacy properties. For example, price dispersion is not 1 in steady state.

I see. Thank you!