Earned Income Tax Credit Improvement and Simplification Act 2013 - Amends the Internal Revenue Code, with respect to the earned income tax credit, to: (1) make permanent the increase in the rate of such credit for taxpayers with three or more qualifying children and the reduction in the amount of the marriage penalty for such credit; (2) allow such credit for an individual with no qualifying children who has attained the age of 21 but not 25 and is not a full-time student, and whose qualifying children do not have valid social security numbers; (3) revise eligibility rules relating to married individuals living apart and qualifying children claimed by another family member; and (4) repeal the denial of such credit for taxpayers with excess investment income.