Perfect foresight model with occasionally binding constraint

Perfect foresight simulations
1

Dear all

I am in trouble with how to deal with occasionally constraint.

If I think about ZLB and following max function, I understant that I need to use “lmmcp” option and “mcp” to bind the interest rate as non-negative.
i=max(A,0)

However, if I want to think about max function such like following with U,U_p,U_t are all determined as endogenously, I am not sure how to define in dynare code.

U=max{U_p,U_t}

If there is shock, we do not know how U_p and U_t will move. I think I cannot bind them by “mcp” because I am not sure which variable will be larger after shock comes.

Like that, if I want to define max function whose both of elements are determined as endogenously, how to deal with this??

Is using “expanded_path” command only way to come over this issue??

I thought following slide p.41 may be the answer to this, but I cannot find original code of this. The latest version of this slide seems to use “mcp” option instead.
(https://sebastien.villemot.name/pdf/talks/2015/deterministic.pdf)

It would be much appreciated if you could give me some hints about this.

Thank you.

2

The problem with max()-operators is that they make many solvers rather unstable in their performance. But sometimes it still works. Have you tried with the max-operator?

3

Hi,

there is a more recent version of the slides. https://sebastien.villemot.name/pdf/talks/2019/deterministic.pdf

Maybe it could be useful to tag your equations like this?

[ mcp = 'U_p > U_t' ]
U = U_p
[ mcp = 'U_p < U_t' ]
U = U_t
4

Dear Prof

Thank you for reply

It did work if I set
“perfect_foresight_solver(lmmcp);”
without any setting about “mcp”.
If I did not input “lmmcp”, it did not work.

But, is it acceptable that I set just “lmmcp” without setting any specific constraint by “mcp”?
It looks a little bit weird as far as I see dynare manual.

Best regards

5

Can you please provide me with the example?

6

This attached file is code.
Please try do_file, because I initially solve steady-state by matlab before running dynare code.

Code.zip (5.4 KB)