Ireland (2003) and Non-stationarity

Hi all,

I’m trying to get a slightly modified version of the Ireland (2003) ’ “Endogenous Money or Sticky Prices” to work. I depart from his paper is three ways: first I simplify the monetary authority’s response function to only inflation, second I rewrite the model in either ‘inflation’ where as he had the ratio of prices, and third I use a stochastic labour augmenting technology: X.t, where X.t/X.t+1 = exp(1+growth), whereas Ireland used a deterministic trend: growth^t. Therefore I’m using the trend_var and deflator options.

I’ve attached the mod file. Here are a link to two PDF files. The first one is the list of equations from the model I have derived. The second is the latex output from Dynare.

My first problem would be getting the steady state! I’ve’ tried using Matlabs fsolve but it’s highly sensitive to the initial guess. But more importantly:

My second problem, was that even after I just guessed from numbers in the initval block I got the following error message:
“trends not compatible with balanced growth path; the second-order cross partial of equation 2 w.r.t. trend variable X and endogenous variable Phi is not null”
This seems to be caused by the equation being nonlinear.

Any suggestions or tips?
v1.mod (2.49 KB)
v1_dynamic.pdf (105 KB)
my_equations.pdf (111 KB)

I may be missing something, but the equations still seem to be wrong:

w = (Phi*C^(1/gamma)*eta)/(a*(1-H));
If w and Phi have trend X, the trend cancels on both sides. That still leaves the trend in C in this equation. I don’t see how this is consistent with a BGP.