In normal circumstances, yes, when it comes about from capital deepening (ie businesses investing in equipment rather than taking profits) or a more educated workforce. But productivity will also raise when unemployment goes up, because unemployment is rising.
The least productive jobs usually disappear first when businesses close and cut back. Overall output falls but the amount of work done falls even more, so productivity (output divided by hours of work) climbs. That’s not a good thing – everyone is worse off.
That will be worth remembering when New Zealand’s productivity stats come out in March, and they show a big leap in productivity. It would be embarassing for anyone to foolishly claim that increase is somehow a result of Key sitting around and smiling for the cameras, when it’s really a result of tens of thousands of Kiwis losing their jobs.