# Single collinear equation

Dear all!

I am trying to replicate a New-Keynesian DSGE model. I use equations from the Appendix of the paper, where the Taylor rule is defined by authors as follows:
r_{f,t} = \rho_r r_{f, t-1} + (1-\rho_r) \left[ r_f^{ss} + \alpha_{\pi}log(\pi/\bar{\pi}) + \alpha_Ylog(Y/Y(-1) \right] ,
where Y stands for output, r_{f,t} is the net policy rate and \pi is inflation rate. There is no issue with the steady state.

However, when I try to simulate a model I have the issue.
When I try this:

r_f = rho_r*r_f(-1) + (1-rho_r)*( steady_state(r_f) + alpha_pie*log(pie/steady_state(pie))
+ alpha_Y*log(Y/Y(-1)) );


I run into the issue:

MODEL_DIAGNOSTICS:  The Jacobian of the static model is singular
MODEL_DIAGNOSTICS:  there is 1 colinear relationships between the variables and the equations
...*list of variables*...
Colinear equations
58
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.


What surprise me is the fact that Dynare point only at single equations 58, which is my Taylor rule.

I adjust the equation, for example, by using specific values for steady state:

(1+r_f) = (1+r_f(-1))^rho_r * (1 + 0.0121325)^(1-rho_r) * ( (pie/1.005)^alpha_pie * (Y/Y(-1))^alpha_Y )^(1-rho_r) ;


Then I get:

MODEL_DIAGNOSTICS:  No obvious problems with this mod-file were detected.
Error using print_info
Blanchard & Kahn conditions are not satisfied: no stable equilibrium.


Any help would be highly appreciated. I am using Dynare 5.4 and MATLAB_R2023b (Intel architect).

See

Dear Professor,

Thank you for your response. I have looked through the forum and implemented this idea of pinning down steady state value of inflation, but the error (as I have pointed above) is still as follows:

MODEL_DIAGNOSTICS:  No obvious problems with this mod-file were detected.
Error using print_info
Blanchard & Kahn conditions are not satisfied: no stable equilibrium.


Might it be a timing error or anything else? Any hint would be highly appreciated!