Violation of Jensen's Inequality?

Dynare help (legacy posts)
1

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.

2

model_diagnostics only checks the Jacobian (i.e. first order derivative) and this of the static model (i.e. ignoring the different timing). I am not aware that this has direct implications for the second order terms resulting from Jensen’s Inequality. It is just a useful diagnostic check that can help to detect errors.
You can make sure that the Jensen’s terms are not ignored by looking at the oo_.dr.gs2 terms that store the uncertainty correction.