Short answer
Yes. When your loans come due, servicers link to your tax return to verify income. A return showing no income speeds things up and can set you up for a $0 payment in your PGY1 year. Without one, they may ask for a pay stub, which will show income.
A short clip from his webinar for residents and fellows, with captions.
Watch the full webinar from 2:59Why file with no income
When you engage your loans, the student loan servicers link up your tax return to verify your income. As a fourth-year medical student you likely have no income. Filing speeds the process along, and it will likely set the stage for a $0 payment for your PGY1 year.
What happens if you don't
If you don't file, they may require a pay stub or some other financial verification. A pay stub will naturally show some income, which may create a situation where you have a payment as a PGY1. So do your taxes, even if you don't have any income as a fourth-year.
Where Jay covers this
Jump to each moment in his webinars.