Collinearity created by prices in an open economy

Stochastic simulations
1

Hello everyone,
I have designed an open economy DSGE model, and I am encountering an issue with collinearity. The collinearity arises from the various types of inflation and prices in the model. I present the equations that are collinear below. Thank you in advance for any guidance or suggestion.
// (9) Domestic price dynamics
p_d_real = pi_d - pi + p_d_real(-1);

// (11) Non-domestic price dynamics
p_n_real = pi_n - pi + p_n_real(-1);

// (12) Overall inflation
pi =alphac*( p_d_real_ss ^(1-thetac))pi_d+(1-alphac)( p_n_real_ss ^(1-thetac))*pi_n;

// (40) Domestic price dynamics for government
p_d_g_real = pi_d - pi_g + p_d_g_real(-1);

// (42) Non-domestic price dynamics for government
p_n_g_real = pi_n - pi_g + p_n_g_real(-1);

// (43) Government inflation
pi_g =alphag*( p_d_g_real_ss ^(1-thetacg))pi_d+(1-alphac)( p_n_g_real_ss ^(1-thetag))*pi_n;

// (47) Foreign inflation
pi_star = rho_pi_star*pi_star(-1) + e_pi_star;

OPEN-COLL.mod.mod (10.6 KB)

Error:

Colinear equations
9 11 12 40 42 43

Relation 2
Colinear equations
9 11 12 25 26 40 42 43 47

Relation 3
Colinear equations
9 11 12 25 26 40 42 43 47

2

Your model has unit roots that explain the collinearity message. I would not worry about them too much for now. The immediate issue is that your model does not satisfy the Blanchard Kahn conditions. Often that is caused by a timing error or another mistake in the model. Fixing that may also remove the unit roots.