Was there a steep drop in productivity at the nation's private businesses other than farms in the second quarter of this year?

A few weeks ago the Labor Department reported that productivity, as measured by output per hour worked, fell at an annual rate of 5.7 percent, the greatest one-quarter decline since it began keeping the numbers in 1947. Yesterday, following some revisions in GNP figures on output, the Labor Department revised the number to a smaller 4.3 percent rate of decline.

But that revision by no means wipes out the puzzle some economists see in the productivity estimates. They believe that further revisions are in store for the GNP numbers, and that the reported decline in productivity -- which has major implications for further rates of inflation -- will be trimmed further, perhaps even erased altogether.

The Labor Department also reported a separate set of productivity estimates for manufacturing based on the output figures in the Federal Reserve Board's Index of Industrial Production rather than Commerce's GNP numbers.

Manufacturing productivity in the second quarter rose at a 2.8 percent annual rate, compared to the 4.3 percent rate of decline reported for all non-farm private business.

Together, those estimates imply a whopping decline in productivity in just non-manufacturing businesses, a decline so unlikely that economist Alan Greenspan of Townsend-Greenspan & Co. called it "virtually meaningless."

"Productivity could not have possibly behaved the way the numbers indicate during the second quarter," Greenspan said.

And that leaves the puzzle. The most likely solution is an upward revision in real output as shown in the GNP accounts for the second quarter, Greenspan believes. The first revision reduced a reported 3.3 percent drop at an annual rate to a 2.4 percent rate of decline.

Meanwhile, the Labor Department must go ahead and make its productivity calculations using the current available output data.

The new second-quarter data for non-farm private business shows output dropping at a 3.8 percent rate while hours were going up at a 0.5 percent rate, giving the 4.3 percent decline in productivity.

The comparable data for the manufacturing sector, based on the Fed's output figures, shows a 1.1 percent rate of decline in output but a fall at a greater 3.8 percent rate in the number of hours worked. That combination left the reported 2.8 percent increase in manufacturing productivity.

Hourly compensation for workers in non-farm business rose at an annual rate of 7.8 percent in the second quarter, the department said. Adding that to the 4.3 percent rate of decline in productivity meant until labor costs were rising at a swift 12.7 percent rate.

Since changes in unit labor costs usually are reflected in later inflation rates, the productivity drop -- if correct -- could have serious consequences on the price front.