Federal officials sought to lay the groundwork Thursday for a key argument in its historic antitrust case against AT&T and Time Warner, attempting to show how the $85 billion megamerger could lead to sharp subscriber declines among AT&T's rivals in the TV business.

Cable companies and other TV providers could lose roughly 12 percent of their customer base in the event of a protracted, hypothetical programming dispute with an AT&T-owned Time Warner, said John Hauser, a marketing professor at the Massachusetts Institute of Technology, who appeared in federal court Thursday as the Justice Department's expert witness.

Hauser's results are based on a series of online surveys of 1,600 people using established research methods developed in the 1960s, he said. The study is critical to the Justice Department's case, because its findings plug directly into the agency's economic models showing that the AT&T merger would lead to higher prices for consumers.

But under questioning by AT&T, Hauser conceded that he had not analyzed any real-world programming disputes, where actual subscriber losses have sometimes been far less substantial.

When cable companies and content companies fail to agree on a price or other terms for TV programming, it can lead to a “blackout” of channels in which the programming disappears from the service. Some companies have been known to use blackouts — or the threat of blackouts — to pressure the other side into making concessions in negotiations. The Justice Department alleges that AT&T-Time Warner could use the tactic to either extract higher programming fees from its rivals or entice customers to switch to AT&T's own TV service, DirecTV.

Hauser's study divided respondents into several groups of 400 individuals. One group was asked questions about its TV consumption habits and little else. The other groups were asked to consider a scenario in which Time Warner's content — which includes channels such as TNT or Cartoon Network — had been taken off the air for differing amounts of time, such as one week, one month or indefinitely. Then the members of each group were asked how likely they were to switch TV providers.

Nearly 29 percent of those who contemplated a permanent blackout said they would switch, according to Hauser, compared with a baseline likelihood of 16 percent among those who were not asked to consider any blackout.

“People who get the blackout scenario, they're going to be more likely to switch,” Hauser told Judge Richard Leon.

Defending that higher “departure rate” will be vital to the government's case. But AT&T and Time Warner have sought to cast doubt on the study, taking aim at what their lawyers have called a “preposterous” estimate by Hauser that does not reflect reality.

Peter Barbur, an attorney representing Time Warner, ticked off several past contract disputes involving cable companies and the producers of cable content. For example, he said, a one-month blackout involving Dish Network and Turner Broadcasting — whose properties include CNN and TBS and which is owned by Time Warner — led to a loss of 30,000 subscribers in 2014, or about 0.25 percent of Dish's customer base at the time. Another dispute involving Viacom and Cable One, said Barbur, also led to losses of less than 1 percent.

“I'm not going to say it can't be reconciled,” said Hauser, when asked to compare his double-digit estimate with real-world results. “I believe my numbers are accurate.”

Hauser said that each blackout scenario was unique, involving different channels going off the air or different blackout durations. Within Hauser's own study, there is a wide disparity between groups that considered longer or shorter blackouts. About 8 percent of respondents who were asked to consider a one-month blackout said they would switch providers, a sharp drop from the roughly 29 percent who contemplated a permanent blackout.

AT&T has said it is not interested in permanently withholding Time Warner's content from other TV providers, because it benefits the company to have the content widely distributed. It has also claimed that wide distribution increases each channel's advertising revenue and relieves pressure on the channels to earn money from viewer fees.

Gregory Rigdon, Justice's next witness and a Comcast executive who has negotiated programming contracts with Turner, said he believed Hauser's estimates were high. Asked by Leon for his opinion, Rigdon told Leon that one of Hauser's figures, the 8 percent loss rate for a one-month blackout, “seems like a big number.”

Rigdon added that in his career, he has not seen a blackout involving a major network group that has lasted for more than a year.