Income for taxes, yes. Income for EIC, maybe. If it meets the rules below, then your income goes below zero and you don't qualify for EIC. The EIC chart shows $384 for $5,000 income for MFJ with no kids. No EIC for no income.
Chart page 31, Publication 596, Earned Income Credit:
Wages. Earned income includes the amount from line 1, Form 1040, reduced by:
•Scholarship or fellowship grants not reported on Form W-2.
•Amounts received for work performed while an inmate in a penal institution.
•Amount received as a pension or annuity from a nonqualified deferred compensation plan or a nongovernmental IRC section 457 plan
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