Mark Thoma says something very smart:
Mark Thoma: Economist's View: The EITC versus The Minimum Wage: They are complements, not substitutes.
And he quotes Arin Dube in 2013:
7) The best evidence suggests that minimum wage increases lead to moderate reductions in the poverty rate, especially together with the Earned Income Tax Credit. There are strong theoretical rationales—and empirical confirmation—that minimum wages and EITC are complementary policies when it comes to helping low-income families. A high minimum wage prevents wage reductions that can result from an EITC. Since the EITC is indexed to the CPI, minimum wage indexation will prevent erosion of EITC benefits for minimum wage workers.
And he quotes me:
Brad DeLong in 2004:
... I like the EITC. Come the Day of Wrath, my best pleading will be the role I played in 1993 in the Clinton administration in expanding the EITC. But the EITC is a program that uses the IRS to write lots of relatively small checks to tens of millions of relatively poor people who satisfy picky eligibility rules. This is not the IRS's comparative advantage. The IRS's comparative advantage is using random terror to elicit voluntary compliance with the tax code on the part of relatively rich people. The EITC is a good program, but it a costly program to administer, and it is administered imperfectly to say the least.
The minimum wage, on the other hand, is nearly self-enforcing: its administrative costs are nearly nil, for workers (legal workers, at least) have a very strong incentive to drop a dime on bosses who violate it. From a government-administrative and error-rate perspective, it's a very cost-effective program.
The right solution, of course, is balance: use the minimum wage as one part of your program of boosting the incomes of the working poor, and use the EITC as the other part. Try not to push either one to the point where its drawbacks (disemployment on the one hand, and administrative error on the other) grow large. Balance things at the margin.