Taxman Audits puts mathematical quirk to work in spotting fudged returns

Thursday, April 30th, 2009

Numbers start with 1 more often than with other digits

Glen Mcgregor

Canadians tempted to get creative with their income-tax returns might want to familiarize themselves with the work of Frank Benford before the Thursday night tax-filing deadline.

The Canada Revenue Agency is using a little-known statistical phenomenon named after the late American physicist to help identify which tax returns to examine more closely.

Benford’s “law” holds that in a series of naturally occurring numbers, the number 1 will appear as the first digit more often than other numbers. Whether the figures are street addresses, expense reports or tax deductions, the “loneliest number” leads off about 30 per cent of the time.

The number two occurs as the leading digit substantially less often, in about 18 per cent of real-life numbers.

Figures starting with a nine account for only five per cent of a typical data set.

A bank statement, for example, should contain far more entries for numbers like $1.70, $10.55 or $1,082 than those beginning with larger numbers, such as $6.50, $800 or $98.60.

The pattern may seem counter-intuitive but that’s what makes it a powerful tool for spotting expense-account fudgers and tax cheats. Someone who fabricates numbers tends to distribute them randomly, with an equal share of leading digits from one to nine.

When these kinds of numbers are crunched by a computer, sets that don’t conform to the leading-digit pattern can be easily spotted and singled out for closer examination.

Benford, who worked as engineer for General Electric, first tripped over this phenomenon in 1938, reportedly when he noticed certain logarithm tables in a textbook were more worn than others.

But only in recent years has the value of the pattern as an auditing tool been recognized by forensic accountants, in part because faster and cheaper computers allow first-digit analysis to be performed easily on large amounts of data.

The CRA says it is now using the first-digit rule in certain circumstances to combat what it politely calls “non-compliance” in tax returns.

Benford’s law is a useful initial risk-assessment tool. However, it is never used in reassessments or in support of reassessments, which are done based on facts and tax law,” said spokesman Philippe Brideau.

While the CRA won’t say exactly how it employs Benford’s law, the agency has shown interest in using it to analyze corporate tax returns, says Mark Nigrini, a professor at the College of New Jersey and the leading expert on Benford-based tax auditing.

Two years ago, Nigrini spoke to CRA’s research division about his research and encouraged them to put the simple, but effective, technique to use in the field.

“They need to use all the new tools at their disposal,” he says. “It should be one of your tests, of many.”

Benford’s law is most effective at determining what sort of tax information is more prone to errors or fraud and how best to deploy auditors.

Nigrini says analysis of U.S. tax returns shows deductions for mortgage payments tend to follow Benford’s law closely, but claims for charitable contributions tend to be “very messy” when sorted by their leading digits.

“When people invent fraudulent numbers, they tend to avoid numbers that two of the same digit following each other – for example 155 or 773,” says Nigrini, who helps Ottawa-based CaseWare IDEA develops statistics software based in part on Benford’s law.

Benford’s law could be particularly useful as more Canadians file their tax returns electronically, without having to submit paper receipts to back up claims for childcare expenses, political donations and charitable contributions, among others.

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