I’ve read most posts regarding how Dynare implements an implicit conditional expectations operator and when we may need to add an auxiliary variable. For example,

[Expectation of function,vs,function of expectations)

[Expected value of a power)

However, the following message from model_diagnostic does confuse me.

model_diagnostic: the Jacobian of the static model is singular

there is 1 colinear relationships between the variables and the equations

Colinear variables:

y

c

ca

cn

h

ha

hn

gs

qs

s

g

wr

br

dr

ndr

tr

tra

tb

Colinear equations

5 6 8

Here are equation 5, 6 , and 8 in my model:

```
1 = beta*rf*(qs(+1)/qs/pistar(+1))*((ca(+1)/ca)^(-rho));
1 = beta*r*(gs/gs(+1)/pih(+1))*((ca(+1)/ca)^(-rho));
rf = r*(qs*gs*pistar(+1)/(qs(+1)*gs(+1)*pih(+1)));
```

I understand we can ignor the Jensen’s inequality if we consider the log-linearized model, and then the equation 5 and 6 imply the equation 8. However, I don’t understand why these three equations still have the conlinear relationship when we’ve considered the second order approximation of model. Does Dynare still not take into account the Jensen inequality when I simulate the model at order 2?

I’d appreciate any idea. Thank you.