# Jacobian matrix and static model

Dear all,

This post is about the Jacobian matrix, the static model and why it is important for log-linearized models.

I have written a model with two different agents with Calvo pricing and a Taylor Rule that I have log-linearized. So, at the steady state, each variable equals zero. In this model, the agents holds bonds and money, and log-linearized equation caracterizing the bonds holding writes itself:

``sigm*c1 + ii = sigm*c1(+1) + pii(+1)``

with sigma the risk aversion, ii, pii and c1 the interest rate on bonds, the inflation rate and the consumption for agent 1. In the static model, since the sigma*c1 drops out, this equation is collinear with the Taylor Rule:

``ii = psi*pii(+1)``

So I rightly get the following error message:

[quote]model_diagnostic: the Jacobian of the static model is singular
there is 1 colinear relationships between the variables and the equations
Colinear variables:
b
Colinear equations
8 13[/quote]

My Dynare question is : why Dynare needs to compute this Jacobian matrix, even if the model is already linear? Why is the static model needed? I understand that it would need the steady state values of variables to perform linearization, but I do not understand why it needs the static model.

I join my .mod file and my _steadystate.m file to this post, if you feel that there might be something strange within.

model.mod (1.93 KB)

Dear all,

I have not been able to solve my problem yet, I am guessing that it comes from a bad economic modelization, but I can’t figure out why. I will try to ask somebody in my Department, but if one of you come with an idea, please be my guest!

Anyway, talking about Dynare, I do not understand yet why the software needs to compute the static model. I went back to my computational economics lectures, and can’t understand what Dynare is doing by computing such a ``static" model. Any enlightment would be very much appreciated, the better I understand the software, the easiest it is to use.