Using Git is good for more then just tracking code changes. If you train your coders to use it in the right way, it can be used to track time as well as productivity.
The most important part of the commit is the message. I like to have developers under me write their commit messages in the following format:
fixed regex on validator #13 @0.5 hours
This tells me not only what they did, but also what issue in the ticket tracker it was related to and also how long it took them to fix it.