Labor productivity at the nation's businesses other than farms rose a healthy 3.1 percent in 1984, the Labor Department reported yesterday, but some economists said the figures raised a question of whether such strong gains will be repeated in 1985 and later years.

Future productivity growth is a key to how fast the economy can expand without eventually encountering shortages of labor and production capacity and generating new inflationary pressures. A few economists and politicians have urged the Reagan administration to seek rapid economic growth on the grounds that the tax cuts, business deregulation and other policy changes of the last four years have put productivity back on a fast growth track, such as occurred in the 1960s.

Some analysts, while making no such policy recommendations, believe that productivity growth prospects have improved substantially, if not back to the more than 3 percent pace of much of the '60s. But other productivity experts think that the 3.1 percent rise in 1984 and the 3.5 percent increase the year before were primarily the result of cyclical forces associated with the economic recovery rather than a more fundamental change, and they warn that the big gains likely will not continue.

One economist who earlier had been in the more optimistic group, Martin Neal Baily of the Brookings Institution, said the year-over-year gain of 3.1 percent "is respectable for this point in the recovery, but it is not indicative of any big change" in the underlying trend of productivity growth.

"Within 1984, the quarterly numbers do not look so good. The jury is still out," but it is beginning to look as if the pattern of much weaker productivity growth in the later stages of a recovery may be repeating itself, he said.

After rising at a 3.2 percent annual rate in the first half of the year, output per hour worked increased at only a 1.1 percent rate in the second half as the overall pace of the economic expansion slowed, the department's report said. Preliminary estimates show productivity grew at a 1.7 percent rate in the fourth quarter following a revised decline at a 1.1 percent rate in the third quarter.

Even though the increase for the whole year was also somewhat smaller than the 3.5 percent rise in 1983 -- the first year of the recovery following the deep 1981-82 recession -- last year's 3.1 percent gain was nevertheless the second best figure since 1976.

The substantial increase in labor productivity offset most of a 4.6 percent increase in compensation paid per hour by nonfarm businesses, so that labor costs per unit of production rose only 1.5 percent during 1984. That was almost the same as 1983's 1.4 percent increase in unit labor costs and was a major factor in holding down inflation, analysts said.

Since labor costs constitute up to three-fourths of all costs in many industries, their change has a powerful effect on the rate of inflation.

"We've really locked in low inflation," commented Edward Yardeni, chief economist for Prudential-Bache Securities. "Business has come to terms with labor to slow down the rate of increase" in unit labor costs, he added.

Economists have never managed to explain by direct statistical methods more than about one-fourth to one-half of the slowdown in productivity growth that occurred in the latter half of the 1970s. However, a number of potential reasons -- such as soaring energy prices, an increase in the proportion of women and younger workers in the labor force, and increasing regulation of business -- generally are being reversed or at least stabilized. This reversal and some other economic developments have convinced some productivity experts such as John Kendrick of George Washington University that trend growth of productivity has improved. Kendrick, for example, expects output per hour to rise at about a 2.5 percent annual rate over the remainder of the decade.

He noted in a recent article that a 2.5 percent productivity growth rate "is below the 1948-66 rate which was boosted by special forces of recovery from depression and war, but it is near the 50-year trend. Combined with projected increase in labor force, employment (assuming 6 percent unemployment in 1990), and total hours worked, it spells a 4 percent overall real growth rate in gross national product . . . far stronger than the 2.2 percent growth rate from 1973 to 1981."

Contrary to Kendrick's analysis, economist Robert J. Gordon of Northwestern University recently wrote that the relatively rapid productivity growth since the bottom of the recession "was a normal cyclical phenomenon, the counterpart of the rapid output growth that occurred in the same period . The cessation of productivity growth in the third quarter of 1984 , the counterpart of relatively slow output growth in that quarter, supports the pessimistic assessment . . . "

Gordon, in a paper published in the Brookings Papers on Economic Activity last month, concluded "the nonfarm private productivity trend has not revived when 1979-84 is compared with 1974-79."