If you don't mind me asking, why doesn't birthday money "count"?
Because my husband and I agree that earning the money indicates that the youngster is willing to do something besides just "veg" in front of the box. Call it an earned privilege, I guess.
We also subscribe to the "no money, no license" theory of teenage driver school. Son-&-heir was shocked to find out that no, neither one of us would take him over to take his driving test on his 16th birthday, even though a car was waiting for his use in our driveway. I told him to pay me a month's worth of insurance costs first. He had a fast food job two days later, got his first paycheck three weeks after that, paid the money, and went to take (and pass) his test. We had to drive him to/from the job for those three weeks, but he hasn't been wheel-less or job-less since. (He had two short "jobless" stints in high school while wrestling season and a couple of theatre productions kept him from having a decent work schedule, but we helped cover those - school things are important, too.)
Lady Niniane