# Steady state & residuals + colinear relationships

Hi!

I’m trying to implement the model from “TECHNOLOGY INNOVATION AND DIFFUSION AS SOURCES OF OUTPUT AND
ASSET PRICE FLUCTUATIONS” by Comin, Gertler and Santacreu. In the steady state I get non-zero residuals in 2 equations. I know what it means. Obviously, there is a mistake in my steady-state, but I can’t find it. Remark: some parameters are chosen in an another way than in the paper. I ask you to look at the mod-file and I would be very thankful if you could tell, whether there is and where is the mistake. Thanks in advance!!!
cgs.mod (6.5 KB)
w15029.pdf (539 KB)

Are you sure the shock processes are correct?

```% stochastic processes log(chi) = rho*log(chi(-1)) + eps; %31 log(x) = eta*log(x(-1)) + sigma; %32 log(g) = nu*log(g(-1)) + varrho; %33 log(p_k_st) = rho_st*log(p_k_st(-1)) + eps_st; %34 ```
means they will all have steady state 0. That is not what you use for x and g.

Thanks a lot! Setting the four parameters to 1, or, equivalently, using

``````% stochastic processes
log(chi) = log(chi(-1)) + eps; %31
log(x) = log(x(-1)) + sigma; %32
log(g) = log(g(-1)) + varrho; %33
log(p_k_st) = log(p_k_st(-1)) + eps_st; %34``````

makes all the residuals = 0.

I finally could derive the steady state equations to get all the residuals = 0. I’m getting 8 eigenvalues greater than one for 12 jump variables. So I use the `model_diagnostics` command. And I get the following output:

```model_diagnostic: the Jacobian of the static model is singular there is 7 colinear relationships between the variables and the equations Relation 1 Colinear variables: y c g p_k j i z_k z_y v_k v_y n_y a_k a_y h_k h_y x k l o_k o_y pi_k pi_y p_k_et n_k j_y j_k i_s i_e lambda_y lambda_k p_k_bar Relation 2 Colinear variables: c g p_k j z_k z_y v_k v_y n_y a_k a_y h_k h_y x k l o_k o_y pi_k pi_y p_k_st p_k_et n_k j_y j_k lambda_y lambda_k p_k_bar Relation 3 Colinear variables: c g p_k j z_k z_y v_k v_y n_y a_k a_y h_k h_y x k l o_k o_y pi_k pi_y p_k_st p_k_et n_k j_y j_k lambda_y lambda_k p_k_bar Relation 4 Colinear variables: c g p_k j z_k z_y v_k v_y n_y a_k a_y h_k h_y x k l o_k o_y pi_k pi_y p_k_st p_k_et n_k j_y j_k lambda_y lambda_k p_k_bar Relation 5 Colinear variables: c g p_k j z_k z_y v_k v_y n_y a_k a_y h_k h_y x k l o_k o_y pi_k pi_y p_k_st p_k_et n_k j_y j_k lambda_y lambda_k p_k_bar Relation 6 Colinear variables: c g p_k j z_k z_y v_k v_y n_y a_k a_y h_k h_y x k l o_k o_y pi_k pi_y p_k_st p_k_et n_k j_y j_k lambda_y lambda_k p_k_bar Relation 7 Colinear variables: c g p_k j z_k z_y v_k v_y n_y a_k a_y h_k h_y x k l o_k o_y pi_k pi_y p_k_st p_k_et n_k j_y j_k lambda_y lambda_k p_k_bar Relation 1 Colinear equations 6 7 9 10 12 13 14 Relation 2 Colinear equations 6 7 9 10 12 13 14 Relation 3 Colinear equations 31 Relation 4 Colinear equations 32 Relation 5 Colinear equations 33 Relation 6 Colinear equations 34 Relation 7 Colinear equations 6 7 9 10 12 13 14 The presence of a singularity problem typically indicates that there is one redundant equation entered in the model block, while another non-redundant equation is missing. The problem often derives from Walras Law.```

What does this colinearity mean? How could it be, that only one equation at a time (No. 31 - 34, stochastic processes) is colinear? Is the eigenvalues problem arising from the steady state or does it depend on the starting values for k, lambdas and other? Varying this I get from 5 to 8 eigenvalues > 1, bot not more.
cgs.mod (6.53 KB)

Your exogenous processes specify unit roots. That’s why there is collinearity in these equations. Given the many missing explosive eigenvalues, I would think that you are having a systematic timing issue in your model.

I rewrote three of four exogenous processes, such that they are sorting with the paper now. But in the paper one process looks like

``log(X_t) = log(X_t-1) + sigma; %31``

Can it be a problem?

Furthermore I get 3 colinear equations (number 6,7 and 30). In order to have the equation

``log(Chi_t) = rho*log(Chi_t-1) + eps; %30``

fulfilled in the steady state I choose Chi = 1. But then the equations 6 and 7

```z_y(+1) = (chi_y_bar*(chi^ksi_y) + phi)*z_y; %6 z_k(+1) = (chi_k_bar*(chi^ksi_k) + phi)*z_k; %7```
imply that in the steady state chi_k_bar + phi = 1 and chi_y_bar + phi = 1. But that contradicts the calibration of the model (chi_k_bar = 0.0304, chi_y_bar = 0.0202, phi = 0.99). What is the right way? Thanks in advance!