U.S. President Donald Trump admitted to making up information when he told Prime Minister Justin Trudeau the United States has a trade deficit with Canada − even though he had no idea if that was true.

Then, he claimed to have subsequently discovered his fib was correct and the United States has a “$17-billion” deficit with its neighbour to the north.

To top it all off, Mr. Trump suggested the United States doesn’t bother to include either oil or lumber in its trade balance calculations for an unexplained reason.

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We do have a Trade Deficit with Canada, as we do with almost all countries (some of them massive). P.M. Justin Trudeau of Canada, a very good guy, doesn’t like saying that Canada has a Surplus vs. the U.S.(negotiating), but they do...they almost all do...and that’s how I know! — Donald J. Trump (@realDonaldTrump) March 15, 2018

It all came in a rambling anecdote told by the President at the end of a fundraising speech, a tape of which was leaked to The Washington Post.

At a private St. Louis fundraiser for Senate candidate Josh Hawley on Wednesday, Mr. Trump recounted an argument he had with Mr. Trudeau on the subject.

“Trudeau came to see me. He’s a good guy, Justin. He said ‘No, no, we have no trade deficit with you. We have none. Donald, please.’ Nice guy, good-looking, comes in ‘Donald, we have no trade deficit.’ He was very proud, because everybody else, you know, we’re getting killed,” Mr. Trump said, according to a transcript of the tape published on the Post’s website.

“I said, ‘Wrong, Justin, you do.’ I didn’t even know. Josh, I had no idea. I just said, ‘You’re wrong.’ You know why? Because we’re so stupid [at negotiating trade deals.] And I thought they [the Canadians] were smart,” Mr. Trump said.

The President said he had one of his aides check the numbers.

“’Well, sir, you’re actually right. We have no deficit, but that doesn’t include energy and timber. But when you do, we lose $17-billion a year,’” Mr. Trump quoted the aide as telling him.

At issue is the balance of trade, the difference between how much in goods and services a country imports and exports. Mr. Trump believes the United States’ trade deficit is a sign that his country is being cheated by its trading partners. Most economists, and the Canadian government, argue the figure is largely inconsequential in determining whether a trading relationship is healthy.

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The United States, Canada and Mexico are renegotiating the North American free-trade agreement at Mr. Trump’s behest, as he seeks to tip the balance of trade in the United States’ favour.

The U.S. Bureau of Economic Analysis says the United States actually has a trade surplus of US$7.7-billion with Canada. The Office of the United States Trade Representative (USTR) – the agency charged with renegotiating NAFTA – calculates the United States’ advantage as being even greater, at US$12.5-billion. According to the USTR, Canada runs a surplus in the trade of goods but the United States more than makes up for it with a surplus in the services sector.

It was not clear why the President seemed to believe “energy and timber” were excluded from the U.S. government’s calculations. Oil is a major Canadian export to the United States, and the two countries are currently locked in a trade dispute over Canadian exports of softwood lumber, but both goods are counted in trade-balance calculations.

On Thursday, Mr. Trump doubled down on his claim.

“We do have a Trade Deficit with Canada, as we do with almost all countries (some of them massive). P.M. Justin Trudeau of Canada, a very good guy, doesn’t like saying that Canada has a Surplus vs. the U.S.(negotiating), but they do…they almost all do…and that’s how I know!” he tweeted.

U.S. President Donald Trump on Thursday wrote on Twitter that 'We do have a Trade Deficit with Canada,' despite data on from his own trade representative showing the opposite, and a day after he bragged to donors that he had insisted on the wrong assumption in a meeting with Canada's prime minister. Reuters

Mr. Trudeau, who is currently on holiday in Florida, did not comment on Mr. Trump’s remarks on Thursday. “Canada and the United States have a balanced and mutually beneficial trading relationship. According to their own statistics, the U.S. runs a trade surplus with Canada,” said Adam Austen, a spokesman for Foreign Affairs Minister Chrystia Freeland.

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A senior Canadian government source said they don’t know what exact meeting Mr. Trump was alluding to in his remarks on Wednesday, as the trade deficit talk comes up almost every time the two leaders speak.

The President has long been the focus of fact-checkers – a tally by the Washington Post found more than 2,000 false statements since he took office – but it is rare for him to admit that he does it. His book The Art of the Deal memorably described lying as “truthful hyperbole.”

“It’s an embarrassment to the United States for the President to be lying to other countries. There are a lot of issues where the United States has made commitments to other countries; if they can’t have confidence in the word of the President, they can’t have confidence in those commitments,” said Jordan Tama, a foreign-policy expert at American University in Washington.

Mr. Trump is preparing for sensitive talks with North Korean dictator Kim Jong-un – a high-stakes gambit aimed at avoiding a nuclear confrontation.

Roland Paris, Mr. Trudeau’s former foreign-policy adviser and now a professor of public and international affairs at the University of Ottawa, said world leaders learned a while ago to be careful when interpreting what Mr. Trump says and not to engage in a public spat with him.

“Trump’s language is a mish-mash of selective facts, contradictions and fabrications, but his actions are a lot more important than his words,” Prof. Paris said. “I think that the Prime Minister has been handling the Canada-U.S. file very adroitly and it has involved not publicly provoking a thin-skinned President.”

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Mr. Trudeau’s shrewdness is, at least, one thing on which the President would agree. In the fundraising speech, he expressed some grudging admiration for Canada’s firmness at the NAFTA table, where Ottawa is fighting back against Mr. Trump’s protectionist demands.

“Canada,” Mr. Trump said, “they negotiate tougher than Mexico.”