Virtually half of the assistant secretary jobs at the Department of Housing and Urban Development (HUD) are vacant. So are one-third of those at the Energy Department and 11 of the 38 at the Defense Department, according to Cabinet departments and the Office of Personnel Management.

White House Personnel Office statistics show that 22 percent of executive-level jobs in Cabinet departments are vacant or filled temporarily by acting appointees, as members of the Reagan administration begin to filter back into private life in the waning months of the president's term.

"I think the number may be the highest we've had in modern times," said G. Calvin Mackenzie, director of the National Academy of Public Administration's authoritative presidential-appointee project.

"Who's deciding the budget questions? Who's determining the legislative agenda? Who's setting the priorities for giving out grants?" he asked.

Robert H. Tuttle, director of White House personnel, vehemently defended his staffing record. "There is no brain drain," he said. "There are no more vacancies than there have ever been."

Tuttle said only 18 of 284 top jobs are actually vacant. Nominees for 12 others are pending before Congress, 23 other appointees have been selected by the president but are undergoing clearance, four have been announced but not nominated and six jobs are held on an acting basis.

"That's a nice way to count it, but it flies in the face of common sense," Mackenzie said. "If a job doesn't have somebody in it who has gone through the background checks and been confirmed by the Senate, it is vacant."

Leonard Weiss, staff director of the Senate Governmental Affairs Committee, called Tuttle's reasoning "sort of ridiculous. In the midst of the process, something can easily go wrong."

Mackenzie added that "it's hard to recruit right now. If I were asked to uproot my family, take a leave of absence from my job, divest myself of stock and resign from boards of directors for 11 months of an administration -- almost no one wants to do it."

Tuttle contended that he is having little trouble filling jobs. "A lot of quality people want to come in," he said.

The jobs in question are among the administration's plums. They pay $77,500 a year and make policy affecting billions of dollars in spending, millions of workers and thousands of state and local governments.

Current vacancies include general counsel of the Energy Department, assistant secretary of mine safety and health at the Labor Department and assistant secretary for territorial and international affairs at Interior.

The Pentagon has no assistant secretary of defense for research and technology, no assistant secretary for production and logistics and no assistant secretary for international security policy.

The only overall statistics available outside the White House Personnel Office come from the Office of Personnel Management, which uses a smaller total. OPM reported that 61 of 274, or about 22 percent, of executive-level jobs in all Cabinet departments were vacant at the end of December. A year earlier, the figure was 16 percent.

No comparable figures could be obtained last week for the end of the Carter administration. Charles H. Levine, distinguished professor of government and public administration at American University, said, "The Democrats tended to hang on until the end."

Vacancy rates vary from department to department. The Education Department is fully staffed at top levels, according to its spokesman, Loye Miller, after confirmation last year of new assistant secretaries for elementary and secondary education, vocational education and civil rights.

But at HUD, almost half of such posts are vacant. The job of assistant secretary for public affairs became vacant Oct. 6, 1982, but Tuttle dismissed the importance of filling it because "it has an acting" assistant secretary.

HUD has lacked an assistant secretary for community planning and development since Oct. 28, 1986. The White House has twice nominated Deborah Gore Dean to the post, which has authority over about $3.7 billion, more than 40 percent of HUD's annual budget.

The Senate has twice returned her nomination to the White House, and Tuttle said no decision has been made about a third try.

HUD has been without a president of Ginnie Mae, the Government National Mortgage Association, since last February and without an assistant secretary for public and Indian housing since March. Tuttle said persons have been selected and are "in clearance."

The HUD assistant secretary for legislation and congressional relations left in January, and Tuttle said he is searching for a replacement. He counts this as the department's only genuine vacancy.

The number of vacancies is not as astonishing as it might be in private industry, where executive turnover is normally rare. Executive jobs in every administration since 1964 have turned over rapidly, approximately every 24 months, according to the National Academy study, the most extensive on the topic.

Tuttle said the Reagan administration has reversed the pattern, increasing the average length of service of presidential appointees who require Senate confirmation to 31 months.

Mackenzie said the Reagan administration tended to "carry more vacancies than previously," according to his 1984 study. "A lot of people stayed until the end of the Carter administration," he said.

James Pfiffner, professor of government and politics at George Mason University, said the vacancies pose less of a problem now than at the beginning of an administration. "The main programs of the administration have been established, and they are usually carried out dutifully by the departmental staff," he said.