A few states, e.g. Massachusetts, set the rates rules and forms and there are fewer options or ways to reduce cost. Talk with your agent about the rules in your state. Your agent will often have excellent ideas on how you can cut costs. Enroll your child in driver training. Driver training can be expensive, but you will save hundreds of dollars in insurance cost each year.
Many companies give significant premium discounts for good students.
But - don't rely completely on the driving schools. Test your child in regard to passing, parallel parking, looking all ways when making a turn, Y or U-turns, speed, traffic law understanding, general attitude and respect for the power of the automobile. Don't convert the learners permit into a license until your teen passes YOUR driving test. Even after your child is licensed, test your child's abilities in rain and snow before you permit the child to drive alone in adverse weather. In the wrong hands, cars are lethal weapons.