I will come back to refine this answer later - running up against the end of lunch break

Since you don't sem to have any explicit forward-looking / rational expectations elements in your system (the equation for `Pie` depends only on lags), I don't know why you are expressing your time subscripts as $T+2$ rather than $t$, $t-1$, $t-2$ (note: it's always better to use lower-case letters for single-letter variable names, to avoid conflicts with built-in Mathematica symbols).

Your system is essentially linear, so I would suggest that you define your system as a vector state variable with a matrix of coefficients, which you can then update to simulate a time series using `NestList`. If you also had stochastic elements, which the above equations don't seem to do, then you would use `FoldList`. Because you have two lags of variables on the right-hand side of the equations, the first lag is also a state variable, which you need to track as part of the state vector.

Once you do that, you will realise that you have not specified equations for some of your variables, including $R$ (I'm guessing interest rates) and $YNlev$ (I'm guessing nominal GDP). You need to do this to have a complete system. In the latter case, it is presumably just the identity that $YNlev = Ylev * Pi$.

The other functionality that might be useful to you is [`RSolve`](http://reference.wolfram.com/mathematica/ref/RSolve.html).