Forward-looking equation problem

[jpfeifer]

No, that is model is special. See

Autocorrelation correlation coefficient

To be more precise, the Gali model is purely forward-looking. There is no endogenous propagation via endogenous state variables. Hence, the endogenous variables all inherit the persistence from the exogenous shocks. As you only have a single shock, all variables are just a function of that shock and have exactly the same autocorrelation.