Is a higher growth rate of total factor productivity (TFP) associated with a lower unemployment rate? Theory does not help much here, as it depends whether new technology can be capitalized in existing jobs or not. If it is, then any improvement in technology improves the marginal return of labor, and more workers are hired. If it is not, labor and technology are essentially substitutes, and workers are displaced as new technology is adopted. Finally, unemployment is also impacted by how much technology is embedded in new jobs. Distinguishing between all these effects becomes an empirical matter.
Christopher Pissarides and Giovanna Vallanti show that the first story dominates: TFP growth reduces unemployment. They develop a growth model à la Mortensen-Pissarides with capital, different types of technologies (disembodied, embodied), and different wage equations. The vintage of jobs is important, as only new ones can benefit from one type of technology progress. A calibration exercise with extensive robustness analysis then gives a clear result.
This analysis is done at the aggregate level. There is no doubt that some technology improvements have led to some firings. A prime example is how typographers disappeared from printing plants within a few years of the adoption of desktop publishing. But this allowed to hire others, hopefully reconverted typographers.