Forward looking vs. predetermined variables

General DSGE Modeling
2
  1. The way you set up the first equation, n_t will be predetermined. You can see that the variables on the right that determine it are all dated t-1. If you use that stock at the end of period timing timing, you do not need to define n as a predetermined_variables. If you were to use this, the timing would be shifted by Dynare, which is not what you want.
  2. You may also want to have a look at End of period convention and decision lag
  3. No, the second formulation is not identical as the left hand side is now E_t(n_{t+1}), which is not the same as n_{t+1} in a stochastic model.