As the New York City Police Department scaled back its controversial stop-and-frisk initiative over the last several years, gun seizures plummeted and the share of killings involving guns rose.

The issue took center stage nationally this week when Republican Donald Trump and Democrat Hillary Clinton argued over the initiative’s merits during the first presidential debate Monday. Trump said Mayor Bill de Blasio’s decision to shut it down in the face of a legal challenge is partially to blame for an increase in murders in the city from 2014 to 2015.

“How many people were’t carrying firearms because they were deterred from carrying firearms?”

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Clinton objected on two grounds. The first — it is unfair to blacks and Hispanics, who were the targets of a disproportionate share of the stops — is debatable, given that blacks and Hispanics also commit a disproportionate share of crimes and tend to live in high-crime neighborhoods where police concentrate a larger share of resources.

But it is Clinton’s second claim — that the program was ineffective — that is more peculiar. The Democratic nominee is a tireless advocate for “commonsense gun safety laws” — not because she wants to disarm law-abiding citizens, she insists — but because she wants to make sure the bad guys don’t have them.

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This is how she put it during her acceptance speech at the Democratic National Convention: “I’m not here to take away your guns. I just don’t want you to be shot by someone who shouldn’t have a gun in the first place.”

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Under Clinton’s own rationale, she should support a program that gives police the ability to remove guns from people who are not authorized to have them. And there is little doubt that stop-and-frisk did that. Officers seized 7,778 guns during stop-and-frisk searches from 2003 through 2013, according to department data collected by the New York Civil Liberties Union.

Those guns could have been used by criminals to wreak a lot of havoc — precisely the type of people Clinton said during the convention that she wants to disarm.

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The objection raised by Clinton and the New York Civil Liberties Union is that police found guns during a minute fraction of the stops.

But Michael Cutler, a former federal immigration officer who worked on a drug task force during the heyday of the stop-and-frisk program, said the heavy enforcement had a positive impact in ways that statistics cannot measure.

“How many people were’t carrying firearms because they were deterred from carrying firearms?” he asked. “With all the talk and all the rhetoric about guns … If you’re that concerned about getting guns off the street, you ought to be concerned about getting guns away from the people who should not have them.”

Cutler added, “Stop-and-frisk goes a long way toward that.”

David Weisburd, a criminologist who has studied stop-and-frisk policies, said his research focused the effect of stops on “micro-geographic areas,” a few hundred feet, and seven-day time periods.

“They seemed to deter crime over small distances and short time periods,” said Weisburd, director of the Center for Evidence-Based Crime Policy at George Mason University.

Concentrating enforcement on small crime “hotspots” makes sense, he said, because 1 percent of the city’s intersections are responsible for 25 percent of the crime, and 5 percent produce half of the crime.

Weisburd cautioned, though, that the resentment caused by stop-and-frisk programs may outweigh the benefits. Perhaps there are other ways to achieve the same result — for instance, by having a highly visible police presence, where officers tell people there have been a string of crimes in the area and that they will be there in force.

“There’s a place for it,” he said. “I don’t think it’s something that can be applied in an extremely broad matter.”

Rep. David Cicilline, a Rhode Island Democrat and gun control advocate, tried to get FBI Director James Comey during a congressional hearing Wednesday to blast Trump and stop-and-frisk policies, but the FBI chief would not oblige. He declined to comment on Trump but said stopping a suspect and patting him down “is a very important tool” in certain situations.

“To my mind, its effectiveness depends upon the conversation that occurs after the stop,” Comey said. “When it’s done well, someone is stopped and they are told, ‘I stopped you because … ‘”

Comey disavowed indiscriminate stops and said overuse could poison a police department’s relationship with the community.

“It’s an important tool when used right, and what makes the difference between right and wrong is what’s the nature of the conversation with the person you stop,” he said.

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Police told the New York Daily News last summer that 72 percent of the city’s murder victims at that point in the year had been shot; normally, it is about 57 percent.

Eugene O’Donnell, a professor at John Jay College and a former police officer, told Newsday last year that reducing stops begets fewer gun seizures — which leads to more violence.

“If you do more stops, you will get more guns,” he said, later adding, “When you get one less gun [confiscated] chances are one possible life will be lost.”