# Blanchard & kahn conditions and rank condition is not verified

Hi everyone, Hi Professor @jpfeifer.
My model has error that there are less eigenvalue(s) larger than 1 in modulus for my forward-looking variable(s). Is there a timing error or is there a redundant equation in the model?
Thanks so much.
nek.mod (1.9 KB)

Yes, as model_diagnostics says:

Colinear equations
2     3    10    11


Take the four equations:

   lambda = (-sigma*c);
w =(eta*n)-lambda;
mc = w - mpl;
n*eta + sigma*c = mc + mpl;


The first three can be combined to

   mc = w - mpl = (eta*n)-lambda - mpl =(eta*n)-(-sigma*c)- mpl
`

which is the fourth one.

Thanks so much for the reply. So there aren’t timing error but there is a missing equation, right?

Not necessarily, there could be both, but there is definitely an equation missing.

I added a missing marginal cost equation, but the problem persists.
model.pdf (314.8 KB)
nek.mod (2.0 KB)

Now the problem is about eigenvalues, not a singularity. Maybe there is a mistake in the linearizations. Why did you use the linear model?

Unfortunately my thesis requires the passage of linearizations. I’ll check them again. Thank you for your help.
In case they were right, are there any other causes that create the problem? I exclude timing errors because I believe there are none.

Generally, it’s a mistake in the equations or a problem with the parameters. The most common mistakes are timing issues and wrong linearizations. The parameter issues may include wrong steady state values of the nonlinear model employed in a linearized model.
Have you tried starting from a simpler version of the model?

The model runs, the IRF are shown but they are theoretically wrong. Does this depend on the wrong parameters?
I attached the linearizations.
Linearization model.pdf (427.0 KB)

I still don’t get why you are not cross-checking your results with the IRFs from the nonlinear model.

Because there are linear model equations like those in yf and x (which I have linear by definition) of which I don’t know the corresponding non-linear equation.

You can combine linearized and nonlinear equations. So use the linear ones for yf and x and the nonlinear ones for the others.

Also in this case the model gives an error, so I start to think that I have made a mistake in defining some equation.

model.mod (1.5 KB)

I also want to learn this type model.

Linearization model
Defined: \frac{p_t^M}{p_t}=p_t^M;\frac{W_t}{P_t}=W_t;
\underline{FOC consumo}:
\vartheta_t=\beta^t C_t^{-\rho} \to \tilde{\vartheta}_t = -\sigma\tilde{c}_t

\underline{FOC labor}:
\beta^tN_t^\eta = \vartheta\frac{W_t}{P_t}\to \widetilde{W}_t=\eta\widetilde{\eta}_t-\widetilde\vartheta_t

@tulipsliu See e.g. DSGE_mod/Handout_RBC_model.pdf at master · JohannesPfeifer/DSGE_mod · GitHub
@anon23451153 The last file you posted does not properly use the nonlinear equations. There are many mistakes in linking the two.

Could you tell me why, with the monetary shock (ev), a reduction in the interest rate generates an increase in lambda and a reduction in inflation (dp)? conceptually it is wrong but I do not find the error.
nek.mod (2.1 KB)

Have a look at the economics. Y overall increases, but its composition changes, probably due to CE increasing.

Shouldn’t inflation also increase? I don’t get the results consistent with the theory because lambda increases, but it should decrease.

If consumption goes down, then marginal utility will go up. That is not per se problematic.

Thank you professor. So isn’t the reduction of inflation after the monetary shock a problem? this is what seems strange, because monetary policy is expansionary.