Proponents of an increase in New York’s minimum wage argue that no full-time worker — especially a head of household raising children — should have to live on $7.25 an hour, or $15,000 a year.

But here’s the thing: No one has to live in such poverty.

Low- and modest-income workers in New York receive more than $4.6 billion annually in wage supplements from the federal, state and New York City provision for an Earned Income Tax Credit. The credit is now claimed by more than 1.6 million working households in the state — one out of every five income tax filers — yet is often ignored in debates over the minimum wage, welfare reform and the perceived fairness of New York’s tax system.

A single mother raising two children in New York and working full time at the minimum wage can claim a total of $6,646 from the federal and state EITC, increasing her annual income to $21,726. This is the equivalent of a job effectively paying $10.44 an hour, rather than the nominal minimum wage of $7.25 an hour.

The EITC is based on income tax returns, so it is a benefit available only to people who work. And, the credit is refundable, meaning that if it exceeds the amount of taxes owed, the difference becomes a refund. As a result, it puts money directly into people’s pockets, effectively acting as a negative income tax. In fact, more than 85 percent of EITC benefits are refunded.

Estimates by the Internal Revenue Service and others show that 75 percent to 80 percent of all eligible EITC households receive the benefit. The federal EITC is a major anti-poverty tool, lifting 6.3 million people including 3.3 million children out of poverty in 2010. The state EITC, set at 30 percent of the federal credit, adds an additional anti-poverty effect for working households.

Unlike a minimum wage increase, the EITC provides income support only to workers who really need it — without leading to job loss, deterring hiring or raising the cost of labor across the board.

By contrast, based on a comprehensive analysis of minimum wage studies, economists David Neumark of the University of California at Irvine and William Wascher of the Federal Reserve Board concluded that a higher minimum wage “neither helps low-income families or reduces poverty.” They found that the EITC “subsidizes earnings for low-income working families and creates incentives for employment among families with no workers — pursuing much the same goals as suggested by the rhetoric, if not the reality of minimum wages.”

Few minimum wage earners are the primary source of household income. A 2007 study by economists Richard Burkhauser of Cornell and Joseph Sabia of the University of Georgia found that only 13 percent of workers earning a wage of $7.25 or less were the primary earner in a household, while 46 percent were in families with incomes at or above three times the poverty level. The study concluded: The majority of low wage workers are not household heads … and an even greater share are not poor household heads.”

In another study, particular to New York, the same researchers concluded that an increase in the state minimum wage from the then $7.15 to $8.25 hourly would result in the loss of 29,000 jobs.

The state EITC increases tax progressivity, making New York the most generous state in the nation when it comes to taxing poor workers. Among the 42 states with income taxes, New York has the highest tax thresholds in the nation — the income at which earners begin to pay state income taxes — at $34,600 for a family of three and $40,300 for a family of four.

Debates will continue about adequate wages, whether New York taxes are fair and what more can be done to alleviate poverty. But in the interest of full disclosure, it’s time for decision makers to stop ignoring the existing EITC and the $4.6 billion it provides to New York’s low-income earners annually.