How to handle factorial or factorial-alike form?

Dynare help (legacy posts)
1

I wonder how a factorial or a factorial-alike form could be handled with Dynare.

Just for simplicity, an example is as follows.

y(t)=y(t-1)+x(t)
x(t)=(1+1/1)(1+1/2)…* (1+1/t)

I have attempted to transform the factorial into

logx(t)=log(1+1/1)+log(1+1/2)…+log(1+1/t)

In recursive form: log(x(t))=log(x(t-1))+log(1+1/t)

In Dynare

y=y(-1)+x;
log(x)=log(x(-1))+log(1+1/t);
t=t(-1)+1

However, log(1+1/t) is a bit problematic, as t is introduced as a new variable and denotes the same time period to which y and x refer. Besides, I don’t know how to assign an initial/a steady state value to the new variable t. How to deal with the scale of t is also a issue.

Thank you for your advance and tips!

2

I am not sure, Dynare can handle such a setup. Dynare uses local solutions by approximation the decision rules around a well-defined steady state. In your case, I am not even sure such a steady state exists due to the trend in t.