Collinearity among inflations and relative price level

General DSGE Modeling
1

I have a complicated log-linearized model with about 80 equations. It has 1 collinear relationship. How can I eliminate collinearity among these equations:

pi_str = rho_pi_str * pi_str(-1) + e_pi_str;
pi_o = rho_pi_o * pi_o(-1) + e_pi_o;
p_o_str = pi_o - pi_str + p_o_str(-1);

pi_str: the world inflation
pi_o: the oil price inflation
p_o_str: the world price level divided by the oil price level.

Thanks in advance.

2

edit:
p_o_str: the oil price level divided by the world price level.

3

is a unit root process. That of course creates collinearity.

4

So, How can I fix the singularity problem?

MODEL_DIAGNOSTICS: The singularity seems to be (partly) caused by the presence of a unit root
MODEL_DIAGNOSTICS: as the absolute value of one eigenvalue is in the range of ±1e-6 to 1.
MODEL_DIAGNOSTICS: If the model is actually supposed to feature unit root behavior, such a warning is expected,
MODEL_DIAGNOSTICS: but you should nevertheless check whether there is an additional singularity problem.
MODEL_DIAGNOSTICS: The presence of a singularity problem typically indicates that there is one
MODEL_DIAGNOSTICS: redundant equation entered in the model block, while another non-redundant equation
MODEL_DIAGNOSTICS: is missing. The problem often derives from Walras Law.

5

Obviously, you need to modify your model, i.e. get rid of the unit root process.