Aside from falsely insisting that he did not lose the 2020 election, former President Donald J. Trump has peddled a related set of theories centered on one question: What would the world have looked like had he stayed in office?

Mr. Trump, in rallies and interviews, has repeatedly asserted — more than a dozen times since December, by one rough count — that three distinct events, both in the United States and abroad, are a product of the 2020 election.

“There wouldn’t have been an attack on Israel. There wouldn’t have been an attack on Ukraine. And we wouldn’t have had any inflation,” he declared during a rally in January in Las Vegas. The next month in South Carolina, he baselessly claimed that Democrats had admitted as much.

Politicians routinely entertain what-ifs, which are impossible to prove or rebut with certainty. But Mr. Trump’s suppositions underscore the ways in which he often airs questionable claims without explanation and which might not be supported by the broader context.

And unlike simply attacking an opponent’s record or making a campaign promise, such alternative realities enjoy the benefit of being untestable.

“People already grapple with how to hold elected officials accountable,” said Tabitha Bonilla, an associate professor of political science at Northwestern University who has researched campaign promises and accountability. “And what is super interesting here is that there’s no way to hold someone accountable at all, because there’s no way to measure any of this.”

Here’s a closer look at his assertions.

WHAT WAS SAID

“I will have the horrible war between Russia and Ukraine settled before I even take office. Got to be settled. It never would have happened. And even the Democrats admit that if Trump were president, that would have — Putin would have listened to me 100 percent.”
— during a January rally in New Hampshire

Mr. Trump’s speculative notion that he could have simply dissuaded President Vladimir V. Putin of Russia from invading Ukraine is not necessarily borne out by history.

The conditions precipitating the decision by Mr. Putin to invade Ukraine in February 2022 date back many years. Mr. Putin has maintained that Ukraine is fundamentally part of Russia, ignoring evidence to the contrary — including the views of most Ukrainians. And he has long taken issue with the expansion of NATO, including the addition of former Soviet republics, as well as the prospect of Ukraine one day joining.

Asked to elaborate on Mr. Trump’s argument, his campaign simply referred to a 2022 poll in which 62 percent of respondents answered “no” when asked whether they believed that Mr. Putin would move against Ukraine if Mr. Trump were president.

Still, experts do not see a realistic scenario in which Mr. Trump would have stopped Mr. Putin from advancing on Ukraine.

“There was no appreciable shift in Russian policy because Trump was making nice to Putin,” said Charles A. Kupchan, a senior fellow at the Council on Foreign Relations.

Mr. Kupchan said he could envision a situation in which Mr. Trump would have encouraged Ukraine to capitulate to Mr. Putin — and reverse its drift toward Western influence — as a means of de-escalation. But he noted that lawmakers and allies would have almost certainly resisted such a position.

Juliet Kaarbo, a foreign policy professor at the University of Edinburgh, expressed similar skepticism. “Trump’s claim does not rest on solid assumptions,” she said. “He (or others) have not provided a reasonable causal chain that links him being in the presidency to an alternative outcome.”

In a recent journal article, Ms. Kaarbo and colleagues in part dismiss the theory, concluding that “it is reasonable to assert that Trump’s re-election would not have prevented Russia’s invasion of Ukraine.”

Instead, they argue why Mr. Trump’s remaining in power would have probably made the West’s united response to the invasion “implausible” and could have possibly contributed to an early Russian victory. They cite his cynical attitude toward NATO and his request that Ukraine’s president help investigate Joseph R. Biden Jr., his political rival, before the 2020 election.

“Although Trump’s record on Russia and Putin was mixed (his administration did, after all, continue some sanctions against Russia and send some military weaponry to Ukraine), Trump himself opposed some of these policies at times and was very positive toward Putin and very negative toward Ukraine,” Ms. Kaarbo said in an email.

A former national security adviser to Mr. Trump, John R. Bolton, offered a similar view in a 2022 interview after the invasion.

“We did impose sanctions on Russian oligarchs and several others because of their sales of S400 antiaircraft systems to other countries,” said Mr. Bolton, who has become a critic of his former boss. “But in almost every case, the sanctions were imposed with Trump complaining about it and saying we were being too hard. The fact is that he barely knew where Ukraine was.”

He added, “It’s just not accurate that Trump’s behavior somehow deterred the Russians.”

WHAT WAS SAID

“The horrifying attack on Israel would never have happened. They wouldn’t even have thought of doing such a thing if President Trump was behind the Resolute Desk in the Oval Office.”
— during a rally this month in Virginia

There is no clear Trump-era policy that would have prevented Hamas from carrying out its Oct. 7 attack on Israel, experts say. His campaign did not elaborate on his theory, and apart from his effort to blame his successor, he has said very little about the conflict.

At best, Mr. Trump can contend that there was a sense of calm in the Middle East during his presidency, though that argument has its flaws.

“What we can say that might support Trump’s claim is that we did not see significant conflict between Israel and Hamas during his time in office,” said Jonathan Schanzer, senior vice president for research at the Foundation for Defense of Democracies, an organization that has been critical of Hamas. He added that the unpredictability of Mr. Trump’s foreign policy could have theoretically worked to deter adversaries in the Middle East from stoking conflict.

But, Mr. Schanzer said, that calm was deceiving: Hamas was building up its military infrastructure during that time.

Others are more adamant that Mr. Trump’s argument lacks merit.

“In the case of the Hamas attack, there is nothing that his administration could or would have done differently from the Biden administration,” said Natan Sachs, the director of the Center for Middle East Policy at the Brookings Institution.

He noted that the Trump administration facilitated the Abraham Accords, under which Israel normalized relations with several Arab countries. “But the downside of the Abraham Accords was also the marginalization of the Palestinian issue,” Mr. Sachs said.

Mr. Trump sometimes makes his assertion while maintaining that Iran, which has supported Hamas over the years, had less access to money as a result of sanctions put in place during his administration. But that is not proof that Hamas could not, or would not, have carried out the attack as a result.

While the Trump-era sanctions did leave Iran with fewer resources, “that does not mean that they stopped funding Hamas,” said Mr. Schanzer, a former terrorism finance analyst at the Treasury Department.

Iran’s support “certainly is relevant to Hamas from the ability to carry out this attack,” Mr. Sachs said. But he said the attack was not an expensive operation that necessarily required real-time funding by Iran.

“There is nothing that Trump or Biden or anyone else could have done to deter Hamas specifically from carrying out the attack,” he said.

WHAT WAS SAID

“When you think of it, inflation wouldn’t have happened.”
— during a rally in Georgia this month

Mr. Trump’s claim ignores the reality that the coronavirus pandemic undoubtedly helped drive up prices — meaning inflation was all but inevitable regardless of who won the 2020 election — and he has not explained in detail how he would have averted inflation. The surge began in early 2021 and peaked in mid-2022.

“The pandemic of 2020-2022 caused massive disruption to supply chains around the world and made it harder to produce and ship goods for an extended period of time,” said Tarek Hassan, an economics professor at Boston University. “This led to what we call cost-push inflation in all major economies, with the prices of goods jumping up as a result. Neither the outgoing President Trump in 2020 nor President Biden had much influence on this outcome.”

But analysts have attributed many factors to the uptick, including government policies. Research indicates that pandemic relief packages signed by both Mr. Trump and Mr. Biden played a role by driving up consumption.

Three notable developments before January 2021 helped drive inflation, said Campbell R. Harvey, a professor of finance at Duke University.

In 2020, as the pandemic took root, the Federal Reserve began buying mortgage bonds and government debt in large quantities — or what is known as quantitative easing. Its balance sheet that year jumped to more than $7 trillion in assets from $4 trillion. At the same time, lawmakers and Mr. Trump were spending trillions to respond to Covid and its economic effects, causing the federal deficit to spike. And housing costs and rents began to rise. (The median price of homes sold nationally jumped 14.6 percent from the second quarter of 2020 to the first quarter of 2021.)

“You put that together and it is challenging to make the case that there would be no inflation,” Mr. Harvey said. “But again, we just don’t know the counterfactual.”

Mr. Trump has suggested that, if elected this year, he would lower inflation, though economists say some of his proposals — including tariffs on imported goods and his calls for enormous deportations — could potentially have the opposite effect.