Completely linear? We don't do that.
Our daughter has a fixed allowance, and we expect a certain amount of help around the house as being part of the family. We don't make any explicit ties between the two, and we don't seem to have any problems.
We bought an eBay lot of Polly Pockets and divided them up into $5 bags. (This is a better deal that what we could get in the store new.) Her allowance isn't enough that she can "buy" one every week.
After sensing her frustration we gave her the opportunity to earn some more money by doing extra work. It happened to be cleaning up after our dogs in the back yard, a chore we had neglected for quite a while. She stuck with the job, and truly earned that money. (She'll be six in January.) What's more, it was a good deal for me. It needed to be done, and I didn't really want to do it. :)
So, for now this seems like a fair balance. It prevents her from getting the idea that she won't work unless she gets paid, but she also knows that working harder does have its rewards.
We still have time to teach her the idea of working smarter.
(This isn't a formal study. It's just my experience.)