# New Keynesian model with capital requires absolute variables and log-deviations - singularity

Hi all,

I am currently trying to model a very simple New Keynesian model with endogenous capital accumulation as laid out in ‘On the Mechanics of New Keynesian Models’ by Peter Rupert and Roman Sustek.
Contrary to the basic New Keynesian model without capital which consists entirely of variables denoting log-deviations from steady state, this model requires both the processes y, c, k etc as well as the log-deviations from steady state y_hat, c_hat, k_hat.
Dynare does not calculate the steady-state but rather returns any initial values provided for the absolute variables as the steady state (given that the initial values for the log-deviations are 0). However, all variables, absolute and deviations converge to 0 following a monetary shock, and diagnostics tell me that there is a unit root.
I’m inclined to think that the singularity is due to the above log-linearized capital-dynamics equation: In steady state, y_hat, c_hat and i_hat are 0, leaving both sides of the equation 0 and steadystate(c), steadystate(k) and steadystate(i) undetermined. Could this be the reason? If so, how would I go about solving this?

Model diagnostics returns:
MODEL_DIAGNOSTICS: The Jacobian of the static model is singular
MODEL_DIAGNOSTICS: there is 4 colinear relationships between the variables and the equations
Relation 1
Colinear variables:
y
c
k
r
Relation 2
Colinear variables:
y
c
k
r
Relation 3
Colinear variables:
y
c
k
r
Relation 4
Colinear variables:
y
c
k
r
Relation 1
Colinear equations
1 2 3 4 5 6 7 8 9 10 11 12 13 14

Relation 2
Colinear equations
1 2 3 4 5 6 7 8 9 10 11 12 13 14

Relation 3
Colinear equations
1 2 3 4 5 6 7 8 9 10 11 12 13 14

Relation 4
Colinear equations
1 2 3 4 5 6 7 8 9 10 11 12 13 14

MODEL_DIAGNOSTICS: The presence of a singularity problem typically indicates that there is one
MODEL_DIAGNOSTICS: redundant equation entered in the model block, while another non-redundant equation
MODEL_DIAGNOSTICS: is missing. The problem often derives from Walras Law.

I am very new to Dynare, so please forgive me if I have missed something obvious.

From what I can see, nothing in your model determines the actual steady states of the level variables. That should explain the message. Any initial value for `c, y, l , r` is acceptable.