x(t+1) = Ax(t) + b, (x is forward-looking)

x(t) = Ax(t-1) + b. (x is predetermined)

The difference between "forward-looking variables" vs. "predetermined variables" has to do with conditional expectations. In the example above, x(t+1) = Ax(t) + b, (x is forward-looking) as E_t x(t+1) = Ax(t) + b.

In contrast, in x(t) = Ax(t-1) + b. (x is predetermined), you could also add an conditional expectation at time t, but it would be redundant. Due to this conditional expectations operator, both statements are not (!) the same

seems to be the same in Dynare. You can read the help files of Dynare or BK(1983) to find some help.

最好引用一下，这是 jpfeifer 的解释。