WASHINGTON — From tax cuts to relaxed regulations to tariffs, each of President Trump’s economic initiatives is based on a promise: to set off a wave of investment and bring back jobs that the president says the United States has lost to foreign countries.

“We have the greatest companies anywhere in the world,” Mr. Trump said at the White House recently. “They’re all coming back now. They’re coming back to the United States.”

Mr. Trump’s tax cuts unquestionably stimulated the American economy in 2018, helping to push economic growth to 2.5 percent for the year and fueling an increase in manufacturing jobs. But statistics from the government and other sources do not support Mr. Trump’s claim about his policies’ effectiveness in drawing investment and jobs from abroad.

Foreign investment in the United States grew at a slower annual pace in the first two years of Mr. Trump’s tenure than during Barack Obama’s presidency, according to Commerce Department data released in July. Growth in business investment from all sources, foreign and domestic, accelerated briefly after Mr. Trump signed a $1.5 trillion tax-cut package in late 2017 but then slowed. Investment growth turned negative this spring, providing a drag on economic output.