In smaller companies where decision makers are usually more empathetic towards the employee, there are various other ways you can get them to move without having to use an external offer as leverage. At bigger companies that are more restricted by process, they do this for a reason and ultimately data speaks louder than words. Assuming you've exhausted the usual strategy of establishing your value that is not fully compensated and they're just not moving, if you have a competing offer for $20k more, they now have no choice but to increase the urgency with how they approach you up the chain.
