What do tests of the relationship between employment and technical progress hide?

The debate about whether technical progress causes technological unemployment, as the Luddites argued in the early 19th century, has recently resurfaced in the context of new technologies and automation and the so-called Fourth Industrial Revolution. We review the main issues and then consider in detail the studies of Autor and Salomons (2017, 2018). They find that after both direct and indirect effects are accounted for, technical change is, on the aggregate, employment-augmenting. They find no evidence that technical change (proxied by the growth of productivity) reduces employment growth. We demonstrate that the regressions they estimate are problematic because they approximate an accounting identity. One or two variables in the identity (output growth or both output growth and capital growth) are omitted, which implies that the coefficient of productivity growth suffers from omitted-variable bias. As the omitted variable is known, we can have a good idea of what the statistical results must be. We conclude that, unfortunately, their work does not shed light on the question they address.