Honestly efiled?

Congress is pushing the IRS to drive up efiling (to save expenses) and drive down the "tax gap" to collect more taxes. The tax gap is the gap between what we all owe in taxes (if we followed the law) and what the IRS collects.
I listened to a great presentation on Fora.TV:
Dan Arierly: Predictably Irrational
I part of his presentation discusses how honesty changes depending on whether students sign their answer sheet and even the differences based on whether they sign at the top or bottom of the page. It struck me that taxpayers who sign do not have to physically sign their return are going to be less honest. I wonder if the IRS has done testing to see how much in taxes when taxpayers are electronically separately from the signing.