This hit and run claim would normally be put through your collision coverage since neither the at-fault party nor vehicle was found. You would need to get specifics about your insurance company's rating system from your auto insurance agent, however since you were not at-fault usually in Louisiana you would not have your rates raised due to a claim to fix your car.
The Louisiana Department of Insurance consumer guide notes that your driving record can be considered by your insurance provider as a rating factor. When they look at your record, a clean record usually allows you to have a good driver discount while tickets and at-fault accidents can mean higher premiums.
Insurance companies must act within Louisiana law and Department of Insurance regulations when raising your rates. An insurance carrier must place on file with the LA Department of Insurance their rating system and list under what certain circumstances they will increase rates.
In general, each LA auto insurance carrier has a plan for how much additional money they will charge if you have one or more accidents that are your fault.
As in most states insurance companies are regulated by the state. When deciding whether to raise your rates or how much to raise them, the companies have to follow a set procedure. They cannot just arbitrarily choose an additional amount of money to charge you and then charge the next person in the same circumstances a different amount. However, the exact formula or rating system will vary greatly from company to company.
To find out about your insurance company's specific rating system that they have filed with the state you should be able to ask your agent and / or contact the Louisiana Department of Insurance. Just speaking to your agent about their rating system and the possibility of making a claim to fix the damages from the hit and run accident should not affect your rates in any way.
If you want to get information on Louisiana insurance laws or need consumer advice about auto insurance you can contact the Louisiana Department of Insurance at 1-800-259-5300 or 225-342-5900 in Baton Rouge.