The Claims: "We've put more money in people's pockets by cutting taxes for the middle class and raising them on the wealthiest one per cent."

-- Justin Trudeau, speaking to the media after the election call on Sept. 11

"Justin Trudeau promised to help the middle class. But once he took office, he increased taxes [for] 80 per cent [of] the middle class."

-- Andrew Scheer, speaking to supporters in Trois-Rivières, Que., later that same day

The Facts:

The promise of a middle-class tax cut was central to the 2015 Liberal campaign. And the party fulfilled it shortly after taking office by dropping the tax rate on earnings between $45,282 and $90,563 to 20.5 per cent from 22 per cent. That was paid for by creating a new tax bracket for earnings above $200,000 with a marginal rate of 33 per cent, up from the old top rate of 29 per cent.

The Department of Finance calculates that the 1.5 per cent "middle-class" reduction has benefited more than nine million people, saving singles among them an average of $330 a year and couples an average of $540 a year.

The Conservatives' counterclaim is based on a 2017 study from the Fraser Institute, a B.C. think-tank that favours lower taxes and less government spending. That paper attempted to measure the net overall effect of a broader range of Liberal changes to the tax system, including the elimination of credits for public transit passes and children's sports activities and income-splitting for couples with young children — all of which were brought in under the previous Tory government.

The Fraser Institute paper calculated that those additional changes by Ottawa turned a gain into a loss for most families with children, with 60 per cent across all income brackets paying more tax as a result. And in the case of middle-class families (defined as earning between $77,000 and $107,000 annually) the study claimed that 81 per cent of them now pay higher taxes — $840 on average — a figure that Scheer has been citing in his campaign stump speech.

However, as a number of economists have since pointed out, the Fraser Institute's paper failed to include the effects of what replaced those cancelled tax credits — the new Canada Child Benefit (CCB) enacted by the Liberals. A rather large omission, given that those payments are now worth a maximum of $6,639 a year per child under age six, and $5,602 for each kid between six and 17.

For example, according to the Department of Finance, a couple with two children making a total of $110,000 in 2019 will see a $186 tax reduction from the "middle class" cut, a loss of $270 from the eliminated tax credits and receive CCB payments totalling $2,085, for a net gain of $2,001.

Why the Fraser Institute study chose to exclude the CCB from its pocketbook calculations isn't entirely clear. CBC News reached out to two of the paper's authors but had not received a response by publication time.

But in a recent op-ed in the Globe and Mail, one of them — Milagros Palacios, a Fraser Institute taxation expert — suggested that it was largely on philosophical grounds because the CCB is a transfer, not a tax cut.

"Tax cuts allow Canadians to keep more of their own income and strengthen the incentives for work effort, investing in training and education and entrepreneurship," she wrote. "Conversely, increasing the value or volume of government transfers makes Canadians more dependent on government and other people's money."

Lindsay Tedds, an associate professor of economics at the University of Calgary, doesn't buy that argument.

"You can't ignore that kind of income transfer," she says. "And if you do, it's not a genuine analysis."

Still, in this tax debate, both sides are playing for political advantage, employing different definitions of "middle class" and cherry-picking numbers from the same source — Statistics Canada's Social Policy Simulation Database and Model — to arrive at drastically different conclusions.

"In these sound bites, they're playing with the semantics of words," says Tedds. "They're finding the answers they want to find."

The Verdict: It's complicated. But the Liberals' numbers seem to offer a more complete picture of the net effect on the wallets of the middle class.