Problem on Capital Accumulation and BK condition

[Nakatuma]

Hello!
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
   K(+1)=(1-DELTA)*K+I(+1),
   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!
codezip.zip (879.4 KB)

[kofiemma]

@Nakatuma

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?

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

“K = (1-delta)*K(-1) + I” means “capital_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.

[jpfeifer]

See

BK condition not satisfied...i'm crazy

This simply means that there is most probably still a timing error. Remember: there is one unique timing of variables in your model. By arbitrarily changing the timing of some variable, you change the eigenvalues and make the model run. But the results will be wrong, because the timing is still not correct. (there is also the slight chance that it is a matter of the parameter values being wrong, but that is quite rare according to my experience). The standard recommendation is: start with a sim…

and

Timing of capital in two sector economy

Hello all, I am building a two-sectoral model, and I have a question about the timing of sectoral-capital variables: In my model, T and N are sectors, hence kT is capital in sector T and kN is capital in sector N. Then, I assume that the economy’s aggregate capital is simply: k = kT + kN. However, I assume only one law of motion for aggregate capital such that: k = (1-delta)*k(-1) + i - written in Dynare language. It is clear to me that k is a predetermined variable and should be treated as su…

[Nakatuma]

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

[Nakatuma]

Thanks a lot!