Timing of capital in two sector model

Stochastic simulations
1

I saw Timing of capital in two sector economy before , but I still have some quetsion on it.

Case1:
k(-1)=kT+kN
yT=AT * NT^(1-a) * kT^(a)
yN=AH * NH^(1-b) * kN^(b)

Case2:
k=kT+kN
yT=AT * NT^(1-a) * kT(-1)^(a)
yN=AH * NH^(1-b) * kN(-1)^(b)

Would it produce the same output ?

2

No, it would not. In case 1, at time t when you produce, you can still decide how to split the capital stocks for production. In case 2, you use the capital stock split that was decided at t-1.

3

Thanks for response, and I think Case1 is reasonalbe than Case2.

4

Hi,

I am trying to solve a similar model (total capital is predetermined, its allocation is not).

I therefore use the timing of the above Case 1 for production and aggregation, but how should I treat capital timing in the two agents (entrepreneur and household in my case) budget constraints?

I use

c^h_t + q^k_tk^h_t=w_t^hl^h_t+q^k_t(1-\delta)k^h_{t-1}+f(k^h_t)
and
c^e_t + q^k_tk^e_t+w_t^hl^{d}_t=q^k_t(1-\delta)k^e_{t-1}+f(k^e_t,l_t^{d})

but I have 14 eigenvalues larger than 1 for 12 forward looking variables.

Any suggestion would be really much appreciated.

Thanks,

Aldo

5

The timing for the two individual capital shocks needs to be shifted by one period to the future relative to what you have in your equations.

6

Thank you Professor, I will try it.