I agree w/Steve on this. Usually, a 1/2" 'ribbon board' is installed in the 'empty gap' all the way around. Then, the 4" of 'missing' drywall is installed.
You can save yourself some $$$ by getting some 4" or even 3" boards at the Home Center. Cut them, lengthwise, to 'fit in the gap'. Leave about 1/4" at the corners and where 2 boards meet (for expansion and contraction.) Then, have your drywall Contractor put in the drywall and the FIRST coat of spackle. Watch what he does with the spackle and talk to him about what he's doing. Then, ask him about how to sand and put on the next coating of spackle. THe most important coat is the 1st coat as well as the LAST coat (but the last coat can be continually 'fixed' yourself until you're satisfied with the smooooooth results.) Use a 220 grit sandpaper and ALWAYS put on thin layers of spackle. Be prepared for lots of dust!
THen, when you're all done, apply PRIMER/SEALER (2 coats) to the new spackel and drywall. Then, 2 topcoats of paint. Use GOOD quality paint from your local Paint Retailer (found in the YELLOW PAGES under PAINT - RETAIL.) Be SURE to let each coat of EVERYTHING dry overnight. If you have more ?'s on this, post back or e-mail me directly.
My best to ya and hope this helps.
Jay J -Moderator
PS: The contractor's work should be that expensive based on what I have described you having him do ...