In the US, most things are based on credit and not on actual money you have. If your credit is bad you can't do basic things like get a car, a house or a loan. If your identity is stolen someone else can do things in your name, and for example not pay back a loan. This causes your credit rating to sink, on top of the other problems (like people coming to your house because you didn't pay them).
If you check out http://money.visualcapitalist.com/all-of-the-worlds-money-an... you can see the derivatives and debt are a huge chunk of the not-actual-money part of the economy, which one way or the other is based on credit, credit ratings or ratings in general.
While this probably doesn't scale back to 1 person's identity, it does show that having someone mess with your credit is a whole lot worse than someone just stealing some money.