Finding steady states with infinite sums of habit

Steady state
1

Hi all

I am attempting to run the single sector small open economy model of Schmitt-Grohe and Uribe (2003) with the habit persistence in consumption and labour in Khorunzhina (2015). The difficulty is that utility depends on all past consumption and all past labour supply. I have simplified by considering only the previous 100 periods so I am dealing with a finite sum in the FOCs.

I am having alot of trouble calculating the steady state. Is the specification I have used for the steady state correct (particularly the use of the for loop)?

Am I likely to run into further problems because of the size of the FOC’s?

Thanks in advance for your help.

Kind Regards

Niall

SGU_2003.mod (4.8 KB)

2

Usually, in steady state such infinite sums boil down to a simple geometric series, whose limit can be computed analytically.

3

Thanks Johannes,

I’ve done that now, I had worked out the SS for the FOC for consumption analytically and now have done the same for the FOC wrt labour.

I think i’m dealing with a wider issue that my SS is not specified correctly.

Thanks again.