## Timing of capital in two sector economy

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### 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 such in the code, however I am not very sure how kT and kN should be treated. As predetermined, or as normal ones?

Thanks a lot!

Kyriacos
kyri82

Posts: 141
Joined: Thu Feb 10, 2011 6:14 pm
Location: Toulouse - France

### Re: Timing of capital in two sector economy

In this case, only the total capital stock k is predetermined. Hence, you have to use a law of motion for capital
Code: Select all
`k = (1-delta)*k(-1) + i`

The total capital stock in the economy k(-1), which was decided by investment in the period before (hence the (-1) timing), can be freely divided between the individual sectors. Hence, kT and kN are determined at time t and not predetermined (normal variables). The corresponding resource constraint thus reads
Code: Select all
`k(-1) = kT + kN`
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Johannes Pfeifer
University of Cologne
jpfeifer

Posts: 6940
Joined: Sun Feb 21, 2010 4:02 pm
Location: Cologne, Germany

### Re: Timing of capital in two sector economy

Dear all,

I have a similar model; two country two sector model with capital. I assume that investment can only be done by using the output of traded sector but capital can be used in the production of both sectors. Even though I changed the timing of the resource constraint as you suggested, there are some issues with the results. The model solves however the results dont make any sense.

I would really appreciate any help regarding my model.

Best,
Ayse
ayse yilmaz

Posts: 1
Joined: Tue Nov 26, 2013 5:36 pm

### Re: Timing of capital in two sector economy

You need to be more specific what the problem is.
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Johannes Pfeifer
University of Cologne
jpfeifer

Posts: 6940
Joined: Sun Feb 21, 2010 4:02 pm
Location: Cologne, Germany

### Re: Timing of capital in two sector economy

Hi,
I am working on Smets and Wouters model and have introduced informal sector. I have achieved the steady state already. But the Blanchard-Kahn condition is not satisfied.
Could anyone help me out.thank you.
eab

Posts: 7
Joined: Wed Dec 07, 2016 5:45 am

### Re: Timing of capital in two sector economy

Have you checked whether the problem outlined here affects your model?
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Johannes Pfeifer
University of Cologne
jpfeifer

Posts: 6940
Joined: Sun Feb 21, 2010 4:02 pm
Location: Cologne, Germany

### Re: Timing of capital in two sector economy

Hi,
Yes I do have capital in my model too but it's determined by the utilisation rate in both sectors. So I have.....
k_t=u_t*k_bar_t-1 and
k_bar_t is determined by the standard capital utilisation equation.
Does the timing condition also affect it?
eab

Posts: 7
Joined: Wed Dec 07, 2016 5:45 am

### Re: Timing of capital in two sector economy

You need to sort out how the timing works in this case for both sectors.
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Johannes Pfeifer
University of Cologne
jpfeifer

Posts: 6940
Joined: Sun Feb 21, 2010 4:02 pm
Location: Cologne, Germany

### Re: Timing of capital in two sector economy

Hi,
Thank you very much. Its working perfectly.
eab

Posts: 7
Joined: Wed Dec 07, 2016 5:45 am