When you entered your W-2 from the hospital, in box 12 you must have entered a "G" which is elective deferrals to a 457(b) plan. 457(b) plans are offered by state and local governments and some nonprofits. Since you are working for a hospital, a non-profit, you would answer "No" to the question regarding working for a state or local government.
Saving for your retirement is a good idea with your contributions growing tax deferred. Plus some employers match the amount you contribute and depending on your income level, you may be eligible for a Retirement Savers Credit from the IRS.
Click HERE for more information on the Retirement Savers Tax Credit.
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