RBC with public capital

Stochastic simulations
1

Hello I constructed a simple social planner model with public capital, following Baxter and King (1993). For simplicity, labor is endowed (fixed). The production function is Cobb-Douglas, but includes both private and public capitals. The utility is set as log of consumption.

When I constructed a model in the first place, technology was a standard form, like A*k^(theta1)*kg^(theta2), but this did not work well. I moved technology shocks to private and public investments as separate two shocks. Still not working well. The steady state was calculated well, but the simulation was not with the following error message… Can you please have a look? Many thanks in advance!

Error using print_info
The generalized Schur (QZ) decomposition failed. For more information, see the documentation for Lapack function
dgges: info=30, n=6. You can also run model_diagnostics to get more information on what may cause this problem.

Error in stoch_simul (line 120)
    print_info(info, options_.noprint, options_);

Error in Planner0826.driver (line 200)
[info, oo_, options_, M_] = stoch_simul(M_, options_, oo_, var_list_);

Error in dynare (line 281)
    evalin('base',[fname '.driver']);

After punching in model_diagnostics:

MODEL_DIAGNOSTICS:  The Jacobian of the static model is singular
MODEL_DIAGNOSTICS:  there is 2 colinear relationships between the variables and the equations
Relation 1
Colinear variables:
y
c
k
kg
i
ig
Relation 2
Colinear variables:
y
c
k
kg
i
ig
Relation 1
Colinear equations
     2

Relation 2
Colinear equations
     1

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.

Planner0826.mod (2.0 KB)

2

This looks like a numerical issue caused by the massive size differences in steady states:

STEADY-STATE RESULTS:

y  		 85681.3
c  		 38990.2
k  		 1.99252e+06
kg 		 171017
i  		 39850.4
ig 		 6840.69
A  		 1
Ag 		 1
3

Dear Professor Pfeifer,

Many thanks for your comment. The steady states were analytically solved based on the following parameters in the code, which are rather standard. I tried different values, but still the problem persists. Could you please advice on a possible way forward? Thank you very much for your help once again.

+++++
// 4. Numerical settings for parameters
betta = 0.99; // Discount factor
rho = 0.9; // Persistence of tecnhology
theta1 = 0.7; // Private capital share
theta2 = 0.1; // Public capital share
delt = 0.02; // Depreciation rate
delt_g = 0.04; // Public depreciation rate

4

It works with

theta1    =  0.2;  % Private capital share 
theta2    =  0.2;  % Public capital share

but at some point you run into numerical issues.

5

Many thanks, Professor! Yes seemingly once theta 1 and theta 2 become, big the problem appears again.