Nested CES production in RBC model

Steady state
1

I am trying to run a simple RBC model with a nested CES function where

Y_t = (mu*K_t^nu + (1-mu)*L_t^nu)^(1/nu)

, where L_t is an aggregate labor services given by another ces function aggregating traditional and green-skilled labor: L_t = (alpha*L_t^theta + (1-alpha)*L_t^theta)^(1/theta). However, the attached .mod file gives an error: Any suggestion will be greatly appreciated.

Error using print_info (line 32)
Impossible to find the steady state (the sum of square residuals of the static equations
is 0.0004). Either the model doesn’t have a steady state, there are an infinity of steady
states, or the guess values are too far from the solution

Error in steady (line 102)
print_info(info,options_.noprint, options_);

Error in basic02.driver (line 263)
steady;

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

basic02.mod (4.1 KB)

2

CES functions often introduce rather strong nonlinearities that may cause numerical problems for mode finders. You should try to work with an analytical steady state.

3

fsolve_ln_lg_k02.m (3.5 KB)

I wrote the following analytical code where in the standard cobb-douglas production function, the aggregate labor services aggregates a continum of tasks between 0 and 1 that can be done by type-g and type-t labor with endogeneous task allocation threshold J. I get the following steady state values but I am not sure how to check if they make sense. Also, should L^n+L^g=L in ss?
Steady ss values:
J: 0.923238
Y: 0.230148
K: 2.163723
L_n: 0.402499
L_g: 0.034943
C: 0.176055
W_g: 0.312954
W_n: 0.312954
L: 0.076326
W: 2.020270
R: 0.035101

4

You could try modeling that special case first and only then move to the more general CES case.