# 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),: )
oo_.dr.ghx(oo_.dr.order_var(13),:)];

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.

vpa(sort(eig(gamma2_matrix)),4)

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)