The tax credit system was established in 2003 and makes payments to people based on their circumstances for the full tax year. In the first three years of the system £5.8 billion overpayments have been made.
In today's report, the PAC warns that although HM Revenue and Customs (HMRC) always seeks to recover these payments, it "cannot always do so and has so far written off over £500 million".
"It is unlikely to recover a further £1.4 billion of debt," the report states.
"The recovery of these debts can cause hardship to claimants and places an administrative burden on [HMRC]."
The PAC acknowledges that changes have been made in an attempt to improve the scheme, but argues that HMRC has "still not developed an adequate response to the unacceptable levels of error and fraud in the scheme".
Commenting on the report, PAC chairman Edward Leigh said: "This is the fourth time that this committee has had to examine the current tax credits system – and it will not be the last.
"Changes have been made to the system but who will be confident that they will make any difference? HMRC itself is uncertain how effective they will be. Nor does it have up to date information on the amount of public money lost through claimant error and fraud. It is quite extraordinary that [HMRC] doesn't routinely estimate this and or set targets for reducing levels.
"What we do know is that tax credits suffer from the highest rates of error and fraud in government. And HMRC seems incapable of mounting a credible and effective response to the flood of money being wasted in this way," Mr Leigh added.
The Liberal Democrats have seized on the report as being a "terrible indictment" of a system "burdened with the very worst administration".
Liberal Democrat work and pensions spokesman David Laws said: "Levels of fraud and error in tax credit payments remain unacceptably high, creating huge waste and often placing families in real distress and financial hardship.
"The tax credit system was meant to help the poorest families in society, but due to systemic failures and administrative incompetence it has become a system which many of the most vulnerable are scared to enter."
In response to the report, an HMRC spokesperson said: "Tax credits provide support to six million families including ten million children, and take-up is higher than any previous system of income-related financial support for in-work families.
"Overpayments fell by a fifth between 2003-04 and 2004-05. Accuracy in calculating and processing tax credit awards has risen to over 97 per cent and HMRC are making good progress in implementing the package of measures announced in the 2005 pre-Budget report, which has increased the flexibility of tax credits and improved certainty for families; once these measures are fully implemented they are expected to reduce overpayments by a further third."
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