Washington ? One of every five children who gets free or discounted meals at school may be ineligible because the family’s income is too high, a government-commissioned study says.

The Agriculture Department, which runs the lunch program, says billions of dollars in education aid, including grants for computer hookups, are divvied up on the basis of the lunch numbers, encouraging school officials to push the figures higher.

Young boys and girls stand in line to receive their lunches at Jefferson Middle School cafeteria in Long Beach, Calif. One of every five children who gets free or discounted meals at school may be ineligible for them because their family income is too high, according to a government study.

Some 13 million children received free meals last year, and an additional 2.6 million paid a discounted price, a maximum of 40 cents per meal.

“I don’t want to decrease the number of kids that participate if they are eligible to receive it … (or) deter eligible children from receiving these benefits,” said Eric Bost, Agriculture’s undersecretary for food and nutrition programs.

But Bost also said millions of ineligible children reaping a benefit their families don’t qualify for is a problem that demands a solution.

Schools rely upon parents to report their income properly and check the financial records of no more than 3 percent of families to verify eligibility. Some schools even provide incentives to parents, including free raffle tickets, to get them to apply for free or discounted meals for their children.

Studies for the department by Mathematica Policy Research, an independent research firm, indicate that the error rate grew rapidly in the 1990s. In 1999, the latest year for which data were available, the lunch rolls were 27 percent higher than they should have been, based on an analysis of census data. That’s up from 23 percent in 1998 and just 5 percent in 1994.

The issue has divided school officials. The American School Food Service Assn., which represents school nutritionists, says there’s obviously a problem.

“While there is room to argue the size … it is very likely that there may be children approved who should not be,” said Marcia Smith, the group’s president and school food director in Polk County, Fla.

But Bruce Hunter, associate executive director of public policy for the American Association of School Administrators, said the Bush administration is just looking for a way to cut school spending. “For every child who is enrolled who ought not to be there is a child who is not enrolled who should be,” he said.

Bost, who briefed a congressional committee recently on the problem, said in an interview he is working with the Education Department to find a way to correct the numbers without requiring a lot of new paperwork. That could include asking for new congressional authority to tighten the scrutiny of the applications, he said.

In Texas and California alone, about $4 billion in federal and state education money is distributed to districts and schools based on the school lunch numbers.

Teachers who work in schools with high participation in the lunch program can get college loans forgiven, according to the Education Department.

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Because so much money is at stake, “this has resulted in some schools allowing ineligible students to enroll in the program,” Bost said.

Education officials had no comment on the issue.

A family of four with an annual income of up to $22,945 can qualify this year for free school meals. The cutoff for the discount rate is $32,653. The income limits are higher in Alaska and Hawaii.

The Agriculture Department started experimenting two years ago, during the final months of the Clinton administration, with new methods of checking eligibility.

Twenty-two school districts are involved in the project. In some cases, parents are being required to provide documentation of their income, such as pay stubs, when they turn in the application. In other cases, districts are selecting small numbers of applications to check for problems. Where error rates are high, the schools are supposed to check a much larger number of applications.