I'm going to be in agreement with going after the kid to get the money. Most of the time these idiots don't care about a ticket, etc. What they do care about is if you take away his lunch money.
Case in point: ages ago I was sideswiped by a wise *** kid in a Firebird. He cut me off at a redlight when he suddenly came into my lane. I had to stop short to keep from ***-ending him. Light changed green he flew to the shoulder of the road and I went by him. Just as soon as I cleared him he came back out on me, crossed the double yellow into on coming traffic, and had to swerve back in to keep from getting hit head on. He hit me as he came back in to my lane. He took off, blowing another redlight, making a left hand turn and forcing a bunch of cars smoke some brakes as he did so. I had his license number and headed to the local cop shop.
Half an hour later they came hauling his *** in. The cop inspected the damaged to both vehicles and you could see the paint from his car on mine and vice versa.
After talking with the cop and writing a brief estimate (I'm a licensed body estimator in NYS) I asked the kid if he had the money for the damages to my car. We settled for $500 right there with the cop as witness, with the kid muttering that he had saved that up for the prom. Was going to give his girl a special night, with the limo, blah blah blah. Guess he wasn't going to take her out to anywhere but McDonalds and in his rusty Firechicken afterall. He didn't get charged with hit and run, but did get a couple of tickets for reckless driving. Seems one of the cars he cut off in his getaway had gotten a license plate and called it in, too. He wound up getting hit in pocketbook a couple of times. My settlement right then and there, the tickets, and the increased insurance.