The bare minimum to be at the Cobb Stage II, an aftermarket downpipe is required. The exhaust is optional, but will not get the best performance results.  The 2007 STI's are known for boost spikes when running a catless downpipe.

In order to avoid this, a Helix catted downpipe was installed. The downpipe has a bellmouth opening and flows much better than the stock downpipe.

The stock downpipe is very restrictive as it is flat where the internal wastegate vents into the downpipe. This causes alot of exhaust flow collisions, slowing flow.