The economy is recovering, yet the Labor market is still in the doldrums (we will see just how bad tomorrow morning). In other words, output is up, yet the number of hours of work to create that output is down. This, by definition, means that output per hour — otherwise known as productivity — is going up.

Today we found out by just how much. Non-farm business productivity grew at a seasonally adjusted annual rate of 9.5% in the third quarter, the highest rate since the third quarter of 2003 when it hit 9.7%. Output grew at a 4.0% rate, while hours worked fell at a 5.0% rate in the third quarter. On a year-over-year basis, productivity grew 4.3% as output fell by 3.5% while hours worked fell by a staggering 7.5%. That was an all-time record (since the government started keeping track back in 1948).

To put these numbers in perspective, for all of 2008, productivity grew only 1.8%, and from 2001 through 2007 (the last business cycle) productivity grew at an average rate of 2.6%. The vast majority of that productivity is accruing to capital, rather than labor.

Unit labor costs fell at a 5.2% annual rate in the third quarter and are down 3.6% year over year, also an all-time record. Things were also good down on the farm, since overall business productivity grew at an even higher 9.8% in the quarter, with unit labor costs falling 5.1%. The non-farm productivity gains are coming on top of a 6.9% increase in the second quarter. In the second quarter, unit labor costs fell at a 6.1% annual rate.

Manufacturing productivity was even better, soaring at an astounding 13.6% rate, as output jumped 7.7% while hours worked fell at an annual rate of 5.2%. On a year-over-year basis, productivity increased 3.1% as output plunged 10.8%, but hours worked dropped 13.5%. For all of 2008, manufacturing productivity grew 0.8%, and it averaged growth of 2.3% during the last expansion.

The surge was especially strong among the manufacturers of durable goods, with a 21.2% productivity increase. Output surged 12.4% even as hours fell 7.2%. This is just a snap back from late last year when employers were slow to react to the freefall in the economy. Even with that astounding increase for the quarter, on a year-over-year basis, durable goods manufacturing productivity is still down 0.9% year over year, with output down 16.9% and hours worked down “only” 16.1%.

Productivity is a very important number, since it is the ultimate source of gains in the standard of living. If GDP is going up only because the population is growing, then each person is not going to be any better off on average. After all, even under Chairman Mao, when millions of Chinese were starving, the People’s Republic had a higher total GDP than did Sweden, even though the Swedes were living very well at the time.

However, increases in productivity do the most good for living standards when the benefits are shared. If it is just a case of better machines producing the same amount of stuff with fewer workers, and those laid off workers cannot find other jobs, they don’t see much of a benefit.

These numbers go a long way in explaining why so many companies have reported better-than-expected earnings in the third quarter. Their revenues are shrinking a lot slower than their costs are, since for most businesses, labor is one of the largest expense items.

The huge jump in productivity, especially in durable manufacturing, is the key to understanding why so many very cyclical companies like Caterpillar (CAT) and Ford (F) were able to simply blow away expectations in the third quarter. This is very good news for the stock market, and it is the reason that so many stocks are up so much today.

While there is no way that we will be able to continue growing productivity at this sort of rate, if the reason productivity growth slows over the next few quarters is that hours worked start to increase, it will be a very good thing.

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