Eigenvalues of stable part of the DSGE model

In a typical DSGE model we have stable part and unstable part such as followes:

\rm X_{t}= \Gamma_{2}X_{t-1}+R1Z_{t}
\rm P_{t}= \Gamma_{3}X_{t-1}+\Gamma_{4}Z_{t}

\rm Y_{t}= \Gamma X_{t-1}+\Omega Z_{t}

y_{t} = y^{s} + A ( y_{t-1} -y^{s} ) +B u_{t} \ (Dynare \ \ notation)

y_{t} = y^{s} + A y_{t-1}^{h} +B u_{t} \ (Dynare \ \ notation)

We can derive \Gamma_{2} matrix such as followes :

gamma2_matrix = [oo_.dr.ghx(oo_.dr.order_var(6),:);
oo_.dr.ghx(oo_.dr.order_var(7), : )
oo_.dr.ghx(oo_.dr.order_var(8),: )
oo_.dr.ghx(oo_.dr.order_var(9),: )
oo_.dr.ghx(oo_.dr.order_var(10),: )
oo_.dr.ghx(oo_.dr.order_var(11),: )
oo_.dr.ghx(oo_.dr.order_var(12),: )

when we calculate \Gamma_{2} matrix eigenvalues ( stable part of the DSGE model ) and sort them two of eigenvalues are not the same with Dynare output results!!

we can sort eigenvalues of the \Gamma_{2} matrix with this command in MATLAB command line.


As we can see the first two eigenvalues of the stable part of the system are not the same with Dynare results.

ANEW_MODEL.mod (3.8 KB)