Problem on Capital Accumulation and BK condition

I am trying to combine a Heterogeneous firm model and a Energy part.
However I met BK condition problem, here’s my bafflement:

  1. If I use the regular convention of K=(1-DELTA)*K(-1)+I, and the capital market divided into 2 parts, Ks and Kp, how would I express K_t = K_s,t + K_p,t in model.
    K(-1)=Ks+Kp; ys=F(Ks),ys=F(Kp);
    is this a correct method?
  2. The model met BK condition when I used such convention by having 2 forwl_var by 3 explosive root. But, If I use
    it works well. What is the difference between
    (a) K=(1-DELTA)*K(-1)+I,
    (b) K(+1)=(1-DELTA)*K+I,
    (c) K(+1)=(1-DELTA)*K+I(+1)
  3. How is the difference of ‘Forward-Looking Variable’ and others in the Dynare process. If I use (b) or (c) and get a answer, what is that? How can it be explained?
  4. Or the problem is not in the using of ‘K’, but I cannot see where could the mistakes be. Here’s my ‘codezip’, and I been struggled on working on the BK condition problem, the reference of ‘Energy’ is in the pack.

Thanks a lot in advance! (879.4 KB)

Ys = f(Ks);
Yp = f(Kp);
K(-1) = Ks + Kp;
K = (1-delta)*K(-1) + I;

K = (1-delta)*K(-1) + Imeanscapital_tomorrow = (1-delta)*capital_today + investment today;
K = capital tomorrow (which must be decided today)
K(-1) = capital used today (which was decided yesterday)
I = New investment today.

K(+1) = capital used next two periods if we are in period t today
I(+1) = investment next period if we are in period t today

If we are in period t (i.e., today), then use K = (1-delta)*K(-1) + I because you can only decide K(+1) when we are in period t+1. But we are not in period t+1, we are in period t.



Thanks a lot! That’s exactly the problem I met.

Thanks a lot!