Depends on the employee, and why they moved. 1. If you really value the employee, and might lose them if you don't give them a raise, then give them a raise.

Depends on the employee, and why they moved. 1. If you really value the employee, and might lose them if you don't give them a raise, then give them a raise. 2. If the move was to a certain degree out of their hands (moving with a partner, etc), this would make me more likely to give them a raise. 3. If they moved of their own accord, then after committing to the move they ask for a raise because of living costs, this would leave a sour taste in my mouth - I don't like being painted into a corner.