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Mr. Hudak said one factor in recent decline could be the fact that ATF has been without a permanent director for six years. In January, Mr. Obama nominated acting agency director B. Todd Jones to become its permanent head, but Mr. Jones is still awaiting Senate confirmation.

“The lack of leadership has its effects on priorities,” Mr. Hudak said. “And the ATF has such a diverse area of law enforcement that they have to make choices about what they prosecute.”

In the wake of last year’s shooting rampage at Sandy Hook Elementary School, gun-rights groups have argued the solution is more prosecutions of gun crimes, not more restrictions on law-abiding firearms owners.

“Prosecuting criminals who misuse firearms works,” NRA CEO Wayne LaPierre testified to Congress earlier this year. “Unfortunately, we’ve seen a dramatic collapse in federal gun prosecutions in recent years That means violent felons, gang members and the mentally ill who possess firearms are not being prosecuted. And that’s unacceptable.”

Attorney General Eric. H. Holder Jr. told the Senate Judiciary Committee earlier this year that prosecuting gun crimes is part of the answer and can serve as a deterrent, but that preventing people who acquire guns to commit crimes from getting them in the first place is crucial as well.

“We have limited resources and we have to try to figure out where we want to use those limited resources, and one has to look at why the gun was denied, and then make a determination whether or not we should use those limited resources to bring a prosecution against that person,” Mr. Holder said, referring to people who have been denied firearms because of the FBI’s National Instant Criminal Check System (NICS).

Mr. Chipman acknowledged that with different administrations’ ideologies result in different priorities, which could affect the numbers, but he cautioned that drawing conclusions about causes and effects can be risky.

“You can’t possibly know what those numbers mean until you layer the political environments at the time and the cases being pursued,” he said.

Both Mr. Hudak and Mr. Chipman discounted one potential reason for the spike in prosecutions — the 1994 enactment of a ban on military-style semiautomatic rifles. That ban ran from 1994 until its expiration in 2004, and those latter years coincide with the recent peak, which started in 1998.

But the analysts said that was likely unrelated.

“The assault weapons ban was a shell of what the original writers intended it to be,” Mr. Hudak said. “I can’t imagine there would be a four-year lag in the effect of the assault weapons ban on prosecutions.”