A HIGHER federal minimum wage is a key plank of President Obama’s anti-

inequality platform, and he is likely to repeat that popular proposal in his State of the Union address. Phasing in a raise from $7.25 per hour, the current level, to $10.10, as Mr. Obama suggests, would help many hard-pressed low-income Americans.

But it’s easy to overstate the impact. First, there’s the risk a higher minimum would reduce employment in some low-wage industries, albeit marginally. Second, a federal increase would be partially redundant in the 21 states and the District where the minimum is already higher than $7.25; these jurisdictions account for more than half of the nation’s population. The largest state, California, will have a $10.00 minimum by Jan. 1, 2016. Third, 80 percent of the beneficiaries would not be poor, according to a recent report by Isabel Sawhill and Quentin Karpilow of the Brookings Institution. Indeed, 30 percent of them live in households earning above $60,000.

If Mr. Obama and Congress want to maximize the benefits to struggling working people, they’ll pair action on the minimum wage with reforms to the government’s largest benefit program targeting the working poor: the Earned Income Tax Credit (EITC). The EITC provides an annual wage supplement to workers based on their earnings, their marital status and how many children they have. Over the years, it has proven highly successful at boosting work effort and reducing poverty. But it remains incomplete; the most salient defect is the EITC’s treatment of single, childless workers, who remain eligible for at most $487 per year. By contrast, the maximum benefit for a family with three children is just over $6,000 per year.

It won’t be cheap to boost the EITC, whose total cost at present is over $60 billion per year. But, as Ms. Sawhill and Mr. Karpilow pointed out, a higher minimum wage would save the government money because of recipients’ reduced need for federal benefits, and some of those savings could be applied to the EITC. They also argue for better targeting of the EITC by nearly quadrupling the maximum benefit to single, childless workers and by shifting resources to workers with younger families as opposed to those with more, older children. The boost to young singles would come at the slight expense of those over 39. They would also eliminate marriage penalties in the current law. Overall, the Sawhill-Karpilow proposal would reduce the poverty rate by 1.1 percentage points without any additional cost to the government.

Not everyone agrees with the plan’s trade-offs — it shifts resources within EITC recipient groups as opposed to just boosting the overall program’s cost and finding offsetting tax increases or spending cuts elsewhere. Still, it’s a politically realistic attempt to tackle several big issues — incomes, work effort and family formation — at once. Most important, the plan reminds voters that employers can’t do the entire job of fighting poverty. That’s a burden government must share.