Bruce writes a bit about it here. The main thrust is that since the cost of ID theft is borne by individuals and not creditors, creditors have no incentive to verify that the person applying for credit is on the level. The solution is to put the cost on lenders:
Either give victims the ability to sue lenders who issue credit in their names to identity thieves, or pass a law with penalties if lenders do this.
Brad in the comments has the best idea:
Better than allowing the victim to sue: put the burden of proof on the lender to collect.
Eva impersonates Alice, and Bob issues credit to Eva. If Bob tries to collect from Alice, all Alice should have to do is say “that’s not me” and that should be the end of the conversation. If Bob believes that Alice is trying to defraud him, he can take her to court and convince a judge or a jury that he is owed money. This will dramatically tighten lending practices, but it will also massively curtail identity theft.