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Minister of Defence Peter MacKay responds to a question during question period in the House of Commons on Parliament Hill in Ottawa on Wednesday, April 24, 2013.Sean Kilpatrick/The Canadian Press

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Not even the highest levels of the federal public service can make sense of the government's own spending reports.

In recent days the government has been on the defensive after Auditor-General Michael Ferguson said Ottawa can't explain why departments approved $12.9-billion in anti-terrorism spending between 2001 and 2009, yet only reported spending $9.8-billion.

The government offered some possible explanations. Perhaps the money lapsed without being spent. Maybe it was spent on programs not related the anti-terrorism initiative. Opposition parties offered their own theories.

The real answer is not known. However, the Globe recently discovered another case involving about $2-billion and it serves as a reminder that confusion over Ottawa's archaic accounting system is a constant headache – even for those in charge.

Michael Horgan and Robert Fonberg are two of the most senior and influential government officials in Ottawa. Mr. Horgan is the deputy minister of Finance and Mr. Fonberg is currently deputy minister of National Defence. He moves to a senior position at the Privy Council Office May 13.

Every month, Mr. Horgan's department releases a report called the Fiscal Monitor, which tracks government spending throughout the fiscal year. The report shows the year-to-date size of the surplus or deficit and also tracks some specific spending areas, including defence.

When the March 2012 report was published showing results at the end of the 2011-12 fiscal year, it listed defence spending for that year as $22.5-billion – up from $19.7-billion – which would be an increase of 14 per cent during a period when National Defence was supposed to be cutting back. The defence spending number attracted media attention and it was noted that the Department of National Defence could not fully explain the figure.

The amount simply wasn't accurate. Mr. Fonberg and Defence Minister Peter MacKay were steamed. Mr. Fonberg fired off a strongly worded letter to Finance, accusing them of publishing "misleading and inexplicable" information about defence spending.

"There was no prior consultation with my officials before publishing the Fiscal Monitor," Mr. Fonberg wrote to Mr. Horgan on July 16, 2012, in a letter obtained by the Globe under Access to Information. "As a result, neither DND officials nor Minister MacKay were in a position to respond to questions from the media or in the House of Commons. The embarrassment to Minister MacKay and to the department was compounded by the fact that, apparently, [Department of Finance] officials would not respond to media questions on the DND data, and a complete explanation of the derivation of the data was not provided to DND officials until Friday, June 22, 2012." Mr. Fonberg's note indicates DND waited over a month before receiving an explanation from Finance.

When official year-end figures were reported in the Public Accounts in the fall of 2012, they proved Mr. Fonberg right. Spending was $20.5-billion that year, up from $20.3-billion in the previous year's Public Accounts – an increase of about 1 per cent, not 14 per cent.

(Update: A Finance Canada official disputes the reference to the above Public Accounts figures as they are reported on a cash basis of accounting rather than accrual and includes some categories that the Finance figure does not. Finance points to another section of the Public Accounts that reports DND spending on an accrual basis, showing it rose from $21.6-billion in 2010-11 to $23-billion in 2011-12. Still, that works out to an increase of less than seven per cent, not the 14 per cent that Finance had reported in its Fiscal Monitor report.)

The difference is largely explained by year-end accounting changes. Mr. Horgan wrote to Mr. Fonberg explaining that year-end changes include making sure that money shifting between departments during the year are properly sorted out for government-wide revenue and expenses in the final Public Accounts.

Officials at Finance and National Defence said the two departments have since sorted out their differences. The March 2013 fiscal monitor will be released later this month.

Both the Auditor-General's report and the dispute between DND and Finance underscore the importance of a current push to reform the way Ottawa reports spending.

That work continues May 21 when MPs on the Government Operations and Estimates Committee will hear from Bill Matthews, who heads the Treasury Board's expenditure management sector. By many accounts, he is one of the only people in government who fully understands what happens to taxpayer money in Ottawa.

Bill Curry covers finance in the Ottawa bureau.

Editor's note: an earlier version of this story in correctly said Bill Matthews would be questioned by committee on May 7. In fact, he is scheduled to appear on May 21.