Help with addressing indeterminacy problem

[Carol]

I am simulating a NK model which has capital in it. Since capital is predetermined, I took the capital equation one period backward. Taking the capital equation one period backward, I get: k=(iss/kss)*i(-1)+(1-delta)*k(-1). But the model does not solve since I am getting indeterminacy when I run it.

However, if I also take the return on capital equation ,rk, one period backward the model solves. When I take the rk equation backward, I get:
rk=((ilss*ibss)/rkss)*(ib(-1)+il(-1)-pi+theta_k*(k-k(-1)))-(ilss/rkss)*((1-delta)*il+theta_k*(k(+1)-k));

Why is it that I get indeterminancy when I run the model as is (only taking the capital equation one period backward), but when I take both the capital and return on capital (rk) equations one period backward, the model solves?

Can anyone please tell me why? Also, is this strategy for getting a solution correct?

[jpfeifer]

What do you mean with taking the rk equation backward? Your timing need to be consistent. If you have

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k=(1-delta)*k(-1)+i

and

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rk=alpha*k(-1)^(alpha-1)*l^(1-alpha)

the Euler equation must be something like

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1/c=beta*1/c(+1)*(1-delta)+rk(+1))

[Carol]

Thanks for replying jpfeifer,

The original rk equation is:
rk(+1)=((ilss*ibss)/rkss)*(ib+il-pi(+1)+theta_k*(k(+1)-k))-(ilss/rkss)*((1-delta)*il(+1)+theta_k*(k(+2)-k(+1))); (1)

If I take the above equation one period backward, I get:
rk=((ilss*ibss)/rkss)*(ib(-1)+il(-1)-pi+theta_k*(k-k(-1)))-(ilss/rkss)*((1-delta)*il+theta_k*(k(+1)-k)); (2)

When I run the model with rk one period backward using equation (2), it solves.

My euler equation is coded in dynare as:
c(+1)=c+sigma*(ib-pi(+1)).

Should the rk equation (1) or (2) be used and is my overall timing consistent? Please let me know. Thanks.

[jpfeifer]

Sorry, but I do not get, why rk only appears in expectations. Usually, only the second equation should appear.

[Carol]

Thanks jpfeifer. In my model, the expected rental rate of capital depends on the current and expected loan rate, inflation and the bond rate.
I have tried entering rk as stated in (1) and using the 'predetermined_variables k;' notation and the model solved. Is this ok? Thanks again.

[jpfeifer]

Considering your confusion with the timing, it is best to use the predetermined_variables command (which by the way does nothing else than shift the timing of capital by one in all equations) together with the usual begin of period-notation that is regularly used in papers.

[Carol]

Okay, thanks jpfeifer.