Is wage compression a necessary condition for firm-financed general training?

In recent contributions, Acemoglu and Pischke argue that wage compression induces firms to invest in general training. However, they consider only absolute wage compression. We extend their approach to consider relative wage compression and argue that wage compression as generally understood in the literature is of the latter type. We show that factors associated with an increase in the absolute difference between output and wages might have no effect on the ratio of output and wages (e.g., if the output and wage of every worker doubles, there is absolute wage compression but not relative wage compression). Importantly, we show that, although relative wage compression is not a necessary condition for firms' willingness to pay for general training, it does increase firms' incentives to pay for workers' general training. We show that the departure from the competitive framework highlighted in Acemoglu and Pischke is much more general than implied by their analysis.