I hope someone is able to shed some light on an issue that’s been bothering me for quite some time now. I’m simulating a two-equation deterministic new-Keynesian model. It’s very simple - one equation for the output gap (x) and one for inflation (pi):
x = x(t+1) - sigma*(i(t) - pi(t+1))
pi = Bpi(t+1) + kx
Where sigma =1, k = 0.2, and B = 0.97. I rendered interest rate (i) exogenous since I want that to be equal to 0 for all periods up to t=0, where it jumps to 1.
I have followed the paper (Cochrane, 2015) that simulates this model in deriving the model solutions manually and have graphed those in Matlab, producing the same output as in the paper (I have attached my Matlab code). However, if I put this model in Dynare (.mod file attached) - as far as I know including all correct blocks and commands etc. - the output is different: inflation and output both, when graphed, show much steeper and faster dynamics than when they are graphed in Matlab from the solutions. This strikes me as odd as the graphs should be the same! After all, solving the model manually versus having Dynare solve it should not make a difference. The steady state values derived are correct, it’s only the dynamics in the graphs that are not correct.
Any ideas what might be going wrong here?
Note: please only focus on the dotted lines in the matlab graph, for the unexpected case (solid lines is expected), as this is the one I’m also modelling in Dynare.