Need help for car accident settlement

Here is the story. I was driving the car and stopped for red light. The van behind me failed to stop and crashed my rear bumper. The police came but the other driver claim that he left the insurance policy at home. He gave me the policy number by writing but I found out it's not valid later on.

I called the other driver so many times but he didn't pick up the phone. My guess is that he probably doesn't have insurance and he's trying to ignore me. It happened in New York and the other driver's license plate is from Mississippi. The damage cost around $2000. I try to avoid small claim court because that cost time and doesn't guarantee that he will pay the money even if I win. Is there anyway I can make him to pay? I do have his plate#, driver license information. At least I want to find a way to make his license suspend because of driving without insurance!

Thanks in advance