Your waste and fraud quiz question of the week: in which program is the federal government losing $10 million a day?

Answer: its debt collection effort.

The government's ability to collect on the $25 billion citizens owe in overdue taxes and loans is costing $10 million a day in interest alone.

Now the Reagan administration is beginning a push to increase the debt collection effort of all federal agencies. David A. Stockman, director of the Office of Management and Budget, has told Congress that the administration expects to add $3.3 billion to government revenues over the next three years from the new effort.

The OMB has directed each agency to establish plans and targets for collecting its debts by Sept. 30, and is pushing legislation that would make it easier for the government to go after debtors.

The problem is staggering. An OMB study last year showed that Americans and foreign governments owe the federal government $175 billion and that $25 billion is past due. About $13 billion of the overdue amount is delinquent taxes, the rest mostly overdue student or housing loans.

For years federal program managers simply shoveled money out the door with little thought or attention to collecting benefit or loan overpayments. College student loans were a prime example.

Nat Coluzzi, chief of the guaranteed student loan branch at the Department of Education, said his agency has more than 600,000 delinquent accounts, but did not have enough staff to collect on them until about 1978. "We were late getting started. It's the nature of government," he said. "You have to have the problem before you deal with it."

Lately, the department has been working hard on the backlog. At Tysons Corner, computers spew out thousands of dunning letters to delinquent federal college loanholders. At regional offices around the country, workers use telephone banks to sweet-talk more debtors. As recently as March, more than 1,000 temporary employes worked on collections.

And for the past 2 1/2 years, two private collection agencies have joined the effort, running down 100,000 hard-to-collect education loan accounts.Through Mach, they had picked up $4.6 million, and after taking about a third of that as a fee, left $3 million for the Treasury.

The Education Department's debt collection program is noteworthy because, with more than $700 million in overdue loans, it has been among the worst government agencies in collecting. It also has been the first to turn to outside collection agencies for help.

Now to help the rest of the government, the Senate is moving legislation that would:

Allow agencies to authroize private credit agencies to tell individuals that they have overdue government debts, giving them incentive to pay and clear their records.

Require applicants for federal credit to provide Social Security numbers so agencies can more easily find delinquent debtors, and allow agencies to screen applicants against Internal Revenue Service lists of delinquent taxpayers.

Permit a federal employe's salary to be offset to pay off existing federal debts. Recent studies found that 18,000 federal employers had defaulted on student loans and 66,000 more owed money to the Veterans' Administration.

Allow agencies to disclose to private collection agencies the IRS's addresses of delinquent debtors. This is perhaps the most controversial of the bill's provisions, and is opposed by civil liberties groups who fear collection companies would abuse the debtors' right to privacy.

Increase the interest rate on overdue debts to reflect prime rates and adjust it yearly so debtors have more of an incentive to pay off the government from the start.

The bill, sponsored by Sen. Charles H. Percy (R-Ill.), has been reported by the Government Affairs Committee and is pending in the Finance Committee. A narrower bill, covering only disclosure of debtor information to credit bureaus, has passed the House.

The administration, meanwhile, is working on a package of actions that agencies can take on their own without congressional help.

"Targets for 24 agencies will force program managers to take note," one OMB official said. "We're going to measure their collections against those targets. We're serious about this."