Friend hit our car help!!

Ok ladies my husband and I have been stressing over this since it happened on Friday. Our friend came over and ran into the back of our 2011 ford taurus. We want to go threw insurance to ensure our vehicle gets fixed asap. He however says he can't go threw his insurance because he already pays too much. He wants us to file a hit and run which for one is illegal because we would have to lie... he won't give us his insurance info but like I said he is a friend (or so we thought) so we know his name and everything. What would you guys do??? Lie and file the hit and run or go to police and give them his name so we can get his insurance info?? As a result he may get charged for not cooperating... I am so torn. Damage is over 3000$ and we don't have extra cash to pay ourselves and I also feel we shouldn't have to.

*****update*****

We sent a copy of the estimate to our friend which is 3700$ he has agreed to pay out of pocket instead of going through insurance. My husband and I have drawn up a contract that states he has 2 months to come up with the money so we can get the car fixed and if he doesn't have the funds at that time then we can file a claim. We are all going to sign it and have a witness sign as well and we have also saved all the texts from him that show he admits to the accident being his fault. Thanks for all your information. As much as I want to go through insurance I am willing to let him at least try to pay for it.