Mr. Shiller said the president has “legitimized” the mood that “the market might continue to go up and up.”
The peril for Mr. Trump is that market cycles invariably have downturns, too, sometimes significant ones, and claiming credit for the rise could also mean owning the fall.
“I liken him to Calvin Coolidge, a pro-business president who kept constantly trying to boost the stock market,” Mr. Shiller said. “He was president until 1929 and then it started to crumble.”
Mr. Trump inherited a strong economy from President Barack Obama. The unemployment rate was 4.8 percent in January when Mr. Trump took office and the nation had a solid record of adding private-sector jobs.
Stock markets have been rising essentially since March 2009, when the global financial crisis was near its worst. The stock markets are now in the second-longest bull run in history, trailing only the rally that lasted from 1987 until 2000.
“There is no doubt that the promise of a big corporate tax cut and rampant deregulation have had some effect on the markets,” said David Axelrod, a former senior adviser to Mr. Obama. “It’s also a fake measure of the rooster taking credit for the dawn, as the economy here and globally were steadily improving when he arrived.”
Wall Street and investors are emboldened by the tax cut proposal as well as Mr. Trump’s reversal of several major regulatory measures on environmental matters, financial services and the telecommunications industry. But analysts also attribute the robust market performance to strong corporate earnings.
Consumer confidence is also on the rise, which helps to add to an overall pro-market investment psychology.
“The market is not the economy,” said Dean Baker, director of the Center for Economic and Policy Research in Washington. “The market is a measure of future profitability.”
About half of the country has no money invested in the stock market, according to Federal Reserve data. But at rallies and speeches, the president often asks “how’s your 401(k) doing?”
That is a compelling statement — as long as the market climbs. But even the longest bull markets have eventually come to an end.
“If you want to say everything on a market going up is to your credit, it would seem to follow that if it goes down, it is to your blame,” Mr. Baker said. “I wouldn’t count on that in this case.”
President Bill Clinton also benefited from a stock market surge in the late 1990s, but within the White House, there was concern about aligning too closely with the gains.
Paul Begala, a former adviser to Mr. Clinton, said that the Treasury secretary, Robert Rubin, “used to tell me that the thing about stocks is that they go down as well as up, so he never wanted President Clinton to associate himself too closely to the stock market.”
“We felt like jobs and wages were what we should focus on, as well as the deficit,” he said.
“Trump, of course, breaks every rule,” Mr. Begala added. “He wants credit for the run-up, though he’s signed no meaningful economic policy into law. Not sure his strategy is working. Stocks are at an all-time high, and President Trump’s approval is at an all-time low.”
According to a CNN poll released on Tuesday, Mr. Trump’s overall approval rating was 35 percent.
The president’s rating hit that level “with a roaring stock market,” Mr. Begala said. “Where do you think he will be when there’s a correction?”
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