Timing of capital in two-sector RANK model

Stochastic simulations
1

Hi everyone,

I am currently working on a closed-economy, two-sector RANK model. The only error I have left when simulating the model is:

There are 35 eigenvalue(s) larger than 1 in modulus for 34 forward-looking variable(s)
The rank condition ISN'T verified!

Error using print_info
Blanchard & Kahn conditions are not satisfied: no stable equilibrium."

I suspect a few things that may be causing this issue, but I think the problem is probably related to the timing of capital in my equations, as is usually the case when this error pops up. I’ve seen some other topics on this issue in two-sector models on the forum, but I did not yet see a topic where my model setup is used. The setup is as follows:

I have a ‘c’ sector and a ‘v’ sector. I have two separate capital accumulation equations for these sectors as in Katayama & Kim (2018), to ensure that sectoral capital is immobile across sectors upon impact of shocks. These equations are of the following form:

1) K_ct = (1-cdelta)*K_ct(-1) + I_ct - cxi/2*((I_ct/K_ct(-1))-cdelta)^2 * K_ct(-1);
2) K_vt = (1-cdelta)*K_vt(-1) + I_vt - cxi/2*((I_vt/K_vt(-1))-cdelta)^2 * K_vt(-1).

In all other equations of the model, I apply the same timing. In the production function of both sectors, e.g., I also write K_ct(-1) and K_vt(-1). That is how I usually added capital to my one-sector models, and it worked fine.
The only extra equation that I have now in the two-sector setup, is the aggregation of this capital, which I include as: K_t = K_ct + K_vt.
I wonder if there is anything wrong with the timing of my variables as such.

If this would be correct, I also suspect something else which may be causing the issue. Specifically, I also have bonds in my model, which for now are only present in the budget constraint of households. Hence, I am not explicitly adding the fact that b_t = 0 in my mod.file, I only do this in the steady-state file. I don’t know if this is allowed, or whether I need to explicitly put b_t = 0 in the mod.file as well. However, that would require me to remove another redundant equation, while I do not think there are any redundant equations in the model now.

Thanks in advance!

2

The timing you describe is correct if you want to separate, immobile capital stocks. You basically duplicate the sectors.

The bond part may be an issue. The error message shows that your model is explosive. Bonds exploding may cause the message.

3

Hi Johannes,

Thanks a lot for the response! The issue was indeed related to not explicitly adding b_t = 0 to the mod.file. To simulate the model, therefore, I had to remove a redundant equation.

I had the following market clearing conditions:

  1. Y_ct = C_t + I_ct
  2. Y_vt = V_t + I_vt
  3. Y_t = Y_ct + Y_vt

Removing the first one from the system of equations, and adding b_t = 0, solved the problem. This seemed a bit strange to me, as I ought this to be a necessary equation to have in the model. However, as Y_ct is already specified later for the production function of the ‘c’ sector, maybe this makes sense.

Thanks again!

Kind regards, Alec