Gov. Andrew Cuomo’s campaign for a statewide $15-an-hour minimum wage is based on the assertion that “no one who works a full-time job should be forced to live in poverty.”

Few would disagree. But here’s the thing: No one who works a full-time job in New York has to live in poverty — thanks largely to a program pioneered at the state level by the governor’s father.

That policy is the Earned Income Tax Credit, or EITC, a wage supplement claimed by nearly one of every five New York households last year. The combined federal, state and city tax credit in New York averages nearly $3,000, but it can range from just a few dollars to as much as $8,427 in cash, depending on income, marital status and family size.

As its name implies, the EITC isn’t a welfare entitlement, but can only be “earned” by people who work and file income tax returns. Crucially, it is “refundable,” which means that when the credit exceeds the amount of taxes owed, the difference becomes a net payment to eligible tax filers. As a result, it puts money directly into the pockets of eligible workers, effectively acting as a negative income tax.

If Cuomo was fairly portraying reality, he would recognize, as bipartisan policymakers suggest it should, that New York’s $9 an hour minimum wage already works in conjunction with the EITC, other tax credits and benefits to raise the effective hourly wage for a household of three earning $9 an hour to $16.67 without causing job loss. And, he would look to raise the state EITC to a higher level.

The EITC has enjoyed strong bipartisan backing since its federal inception in the mid-1970s. New York’s EITC, now pegged at 30 percent of the federal credit, was initiated in 1994 by Gov. Mario Cuomo, a Democrat, and significantly expanded under Republican Gov. George Pataki.

Consider, for example, a single mother supporting two children in New York while working full-time at the minimum wage of $9 an hour, an annual income of $18,720. By itself, that’s below the official federal poverty line of $20,090 for a family of three — but the combined federal and state EITC brings her annual cash income to $25,887, which is 29 percent above the threshold.

Additional refundable federal and state child tax credits for the same worker come to $2,660, on top of which she typically will be eligible for a cash-like Supplemental Nutritional Assistance Program benefit totaling $6,132.

These supplements bring the worker’s total income to $34,679 — equivalent to a full-time wage of $16.67 an hour.

Senior Cuomo administration officials have touted the benefits of the EITC.Samuel D. Roberts, commissioner of the state Office of Temporary and Disability Assistance, has called it “the most effective tool we have in helping middle- and low-income families escape poverty and achieve increased economic security.”

The EITC is more effectively targeted than a minimum wage to raise incomes for lower-wage households. By contrast, a $15-an-hour minimum wage would deliver higher incomes to millions of households that are not poor.

Consider again our single mother of two working full time for $9 an hour. Because the EITC and other cash wage supplements become smaller with higher incomes, her net gain from Cuomo’s proposed $15 minimum would come to just $2.80 an hour, not the nominal $6 an hour.

Meanwhile, another minimum-wage working mom ineligible for the EITC — because her husband brings home a higher salary — will pocket the full additional $6 an hour. In either case, the employer will incur the full amount of the raise, plus added payroll tax and unemployment insurance. Those higher wages won’t come out of thin air.

If Cuomo wants to help low-wage workers in particular, he should be looking for ways to boost the EITC to at least 35 percent of the federal level, as proposed by Assemblyman Robin Schimminger of upstate Kenmore.

Above all, when he talks about state policies to help the working poor, the governor should stop ignoring the EITC — and start recognizing that it works.

Russell Sykes was deputy commissioner of the state Office of Temporary and Disability Assistance from 2004 to 2011. He recently co-wrote the paper, “Making Work Pay: How New York State’s EITC Boosts Pay for Low-Income Workers,” for the Empire Center on Public Policy.