# Colinarty problem in the DSGE model

Hi.

I have a Colinarty problem in a DSGE model between two variables namely B and T. Bonds and Tax revenue.I think that I did not include an important equation in the model and I have a redundant equation in the model.When I employ model_diagonistics dynare shows there are collinarity problem between B and T and in some of the equations in the model. I attached dynare codes for more information.

Government budget constraint is:

T_{t}+\frac{B_{t}}{P_{t}}+\frac{M_{t}-M_{t-1}}{P_{t}} = \frac{R_{t-1}^{ n}B_{t-1}}{P_{t}}+G_{t}

\overline T =(\frac{1}{\beta}-1)\overline B +\overline G

I want to define Fiscal policy rule and Tax revenue equasions. I have four new questions but only two new variables in the model and therefore I can not run the model.

T_{t}=\phi_{T}Y_{t}\varepsilon_{t}^{T}

G_{t}=\phi_{G}Y_{t}\varepsilon_{t}^{G}

\varepsilon_{t}^{T} and \varepsilon_{t}^{G} are two AR(1) processes and show Tax revenue shock and government spending shock in the model.

\phi_{G} and \phi_{T} are government spending to GDP ratio and the ratio of tax revenue to GDP. I defined B_{t}=\phi_{b}Y_{t}.In steady state situation we have

\overline B=\phi_{b}\overline Y
\overline G=\phi_{G}\overline Y

I did not include tax revenue equasion in the model.I don’t know what is the main reason of Colinarty problem in dynare ? Unit root ? removing a non-redundant equasion ?

I attached dynare codes.NEWNKDSGE.mod (3.8 KB)

This seems like a consequence of Ricardian equivalence. Bonds and taxes are perfect substitutes.

Therefore can I set this situation :

\overline T=\overline B

No, you can drop one of the variables by setting them to 0.

Oki. Do you mean \overline B=0 or \overline T=0

I set \overline B=0 but in this situation there is Colinarty problem for variable T.

In the second step I set \overline T=0 but there is the same problem.

I want to know in these situations in DSGE models how researchers work with B and T or government budget constraint.I saw the the above mentioned government budget constraint in many DSGE models but there was not any Colinarty problem in solving the model.

NEWNKDSGE.mod (3.8 KB)

NKDSGE.mod (4.4 KB)

I have another DSGE model with 24 different equasions. I can run it in dynare despite of Colinarty. This file 's name is : NKDSGE.mod and the results are acceptable to some extent.

But in the first DSGE file or NEWNKDSGE.mod I set \overline B=0 and I can not run the model due to the Colinarty problem.

According to the dynare proabably I did not include an important equation in the model.

Your variable B does not appear anywhere in the model anywhere.

In government budget constraint equation in the model there is variable B and B(-1) and Bss.

I set Bss=0 therefore Gss=Tss according to the government budget constraint.

Gss=\phi_{G}Yss

but there is Colinarty problem too.

Because of the 0 premultiplying the B, it drops out from the model. Thus, it will not be determined.

Do you mean I should remove government budget constraint equation from the model ?

No, I am saying that one of your variables is not determined in your model, implying a singularity. Thus, there must be a redundant equation as well. I don’t know which one it is.

I think that I have a redundant equation in the model, for example:
government budget constraint.
But in some DSGE models I saw this equation in the model.Can I remove this equation from my model ? Although in many DSGE models we do not enter household’s budget constraint in the model but I am not sure about the government budget constraint equation.

In equilibrium I set Bss=0 but I can not get rid of the model problem. In other DSGE models researchers set Bss=0 or not ?

I have Colinarty between B and T. I added other variables and equations to the model, but I can not get rid of Colinarty problem between B and T. I think the problem is in log-linear form of the government budget constraint equation.

It all depends on your model. You need to step back and think about what is going on in your model. If Ricardian equivalence holds, then only one of the two is residually determined. You can set the other one to 0. At the same time, you need as many equations as variables.