The rise in reported hate crimes across the United States over the past several years has been accompanied by the revival of a polarizing debate: How many of those crimes are real?

The arguments of some conservative commentators that most or all of those incidents are fake have grown louder, especially since President Trump’s 2016 election.

Some on the left have also made dubious claims, citing misleading statistics that hate crimes rose dramatically in areas where Trump held campaign rallies.

But beneath the partisan spin, the evidence points to some firm conclusions — as well as ongoing scholarly disagreement.

No serious researcher believes the majority of hate crime reports are false. Even Wilfred Reilly, a political scientist at Kentucky State University and author of “Hate Crime Hoax: How the Left is Selling a Fake Race War,” believes that fewer than 2 out of 10 reported hate crimes are fabricated. Where academics disagree is on just how many hoaxes take place.

Reilly estimates that as much as 15 percent of the hate crimes reported to the Federal Bureau of Investigation are falsified. Another researcher who has closely examined the subject — Brian Levin of the Center for the Study of Hate and Extremism at California State University at San Bernardino — puts the hoax rate much lower, at less than half of 1 percent.

What accounts for the difference? Levin and Reilly diverge on what should be classified as a hoax. Levin, a criminologist, counts hate crimes that are reported to authorities — such as the police or college campus officials — and later are shown to be deliberately falsified.

Reilly casts a wider net, including in his database various noncriminal incidents that initially generated speculation about hateful motives. He counted cases where there was no hoaxer, such as the toppling of tombstones in a Jewish cemetery outside Philadelphia because of age and recent landscaping, or the discovery of a “noose” on a D.C. construction site that police determined was merely a rope used to move equipment.

He said his 15 percent figure is an estimate based on extrapolating from the dozens of hoaxes he has identified per year and inferring that many less-publicized hate crimes must also be hoaxes that were never revealed.

Reilly acknowledged that there are cases in his database — which also includes alleged incidents of racial profiling by police — that might be seen by some as questionable.

But Reilly, who is black and teaches at a historically black university, defended his expansive criteria in an interview with The Washington Post, saying one goal of his research is to hold the news media to account for embracing questionable stories of bigotry.

“No one’s denying that there are real hate crimes. I think the focus for me is on media coverage,” he said. “I think my focus is on the media’s intentional creation of this narrative of ethnic conflict. Both the left and the right do this.”

Levin said a stricter definition is needed to separate deliberately falsified reports of hate crimes from more ambiguous events.

“A hate crime is more than a folkloric, cultural label,” he said. “It’s actually a legal and statutory one as well. And that’s the one that I study.”

But Levin’s criteria exclude some incidents that others might classify as hoaxes. For instance, he does not count a wave of telephoned threats to Jewish community centers and institutions in the United States in 2017 that were later found to be the work of a Jewish, Israeli American man. Levin argued that case is not a hoax, noting that the victims were selected because of their religion — and because most bomb threats, even if they never materialize, still terrorize people.

Levin acknowledged the damage done by bogus hate allegations, even if they are few in number. Hoaxes call into question the credibility of all victims, he said, and can inflame existing tensions around race, gender, religion and sexual orientation.

“It’s really terrible, what these false reporters are doing,” he said.

The uproar one person can cause through a hate hoax has been seen again and again. In the fall of 2017, a car at Kansas State University was covered in racist graffiti, prompting the university’s president to suspend classes and hold a campuswide rally to denounce hatred.

When the car’s owner admitted that he was responsible for the graffiti, police opted not to press charges. The campus Black Student Union denounced that decision, saying that “the fact that an African American man committed this act should not undermine its effect on K-State students” and “does not negate the current racist and discriminatory actions that continue to occur on our campus and in our community, state and nation.”

Almost a year to the day later, in November 2018, a second hate hoax hit the university. This time, a student posted a photo of a racist sign he claimed to have found on his apartment door. He later admitted to campus police that he created the sign himself.

Such clusters of staged incidents periodically pop up, perhaps because one hoax inspires another. Twice in July 2018, servers at Texas restaurants said they received racist notes scrawled on receipts by customers, claims that circulated widely on social media. In both cases, the servers confessed to having written the slurs themselves.

Some hoaxers have also sought to exploit political divisions exacerbated by Trump’s election. The week before voters went to the polls in 2016, a historically black church burned down in Greenville, Miss. The words “Vote Trump” were spray-painted on the building’s brick exterior, drawing national media coverage.

In Mississippi, with its bitter history of slavery, segregation and lynchings, the attack on an African American church was especially ominous. But authorities soon discovered that it was committed by Andrew McClinton, one of the church’s black parishioners, over a dispute within the congregation.

“I’m an old man. I’ve been around a long time. You have a church fire in Mississippi, you better be on it, investigating it, to make sure it’s not racially motivated,” said Mike Chaney, the state fire marshal and insurance commissioner.

“The problem you run into is the perception,” he added. “Once it gets on the news as racially motivated, and then they do a retraction three days later in small print — nobody notices that.”

But while hate hoaxes may seize the national imagination, they are all but absent from the day-to-day work of many on the ground who investigate and prosecute hate crimes. Detective Orlando Martinez, hate crimes coordinator for the Los Angeles Police Department, estimated that five of his unit’s approximately 1,500 cases over the past five years have involved deliberate false reports.

Hoaxes, he said, “are not something that we have to worry about.”

Far bigger challenges, he said, stem from the difficulty in solving hate crimes — which often involve stranger-on-stranger attacks, vandalism or other offenses that leave few clues for police — and victims’ reluctance to come forward in the first place.

In five years tracking hate crimes in the country’s second-largest city, Martinezhasseen few hoaxes.But he does worry that many real hate crimes have never come to light.

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