Sounds like there are no grand theories on connections between unemployment and productivity (at least in the long run).
The article states 2 ways in which technology improvements can cause permanent changes to the natural unemployment rate:
1. Job search technology speeds up the process of finding the right employer for the unemployed worker. The natural unemployment rate is ‘natural’ because all workers spend some time in between jobs. If this in-between time is shorter than fewer people will be unemployed at any one time.
2. Productivity growth increases profit (more output per unit of labor) which encourages firms to want to produce more by hiring more workers.
There’s one ‘it depends’ model presented that shows that examines the fact that some technical progress may destroy more jobs than it creates. The determining factor is the cost of upgrading jobs as capital becomes obsolete. If it costs a lot to upgrade an existing job as the capital used in that job becomes obsolete, that job will be abandoned. The problem with this model is that the relationship between unemployment and productivity depends on the type of job and the technology. In other words, it says nothing of the relationship between the two in aggregate.
Too bad, this last model has appeal. I wonder if we can talk about productivity in terms of its relationship to unemployment by examine its decreasing and increasing components… change in employment equals change in leveraged productivity (technical progress that improves existing jobs) minus change in replicative productivity (technical progress that replaces existing jobs). How would you measure aggregate productivity broken into its leveraged and replicative components? I’m sure I could find out more here, but I’m going to pass on paying $30 to see the article… Berkeley has it, and I guess you can access the article via ScienceDirect if your inside Berkeley’s network.