All that means is that in industries (construction, especially) where employers were reluctant, or unable, to cut wages in the recession, there was higher unemployment as well as slower recovery of employment in the recovery, than in more flexible industries (finance, insurance, real estate).... we consider whether industries with higher or lower degrees of wage flexibility have seen different evolutions of wage growth and unemployment. Our findings suggest that industries with the most downwardly rigid wage structures before the recession have seen the slowest wage growth during the recovery, conditional on changes in unemployment. In contrast, industries with fairly flexible wage structures have seen unemployment and wage growth move more closely together. These findings provide cross-industry evidence that downward nominal wage rigidities have played an important role in the modest recovery of wages in recent years.
Just basic economics; surplus and shortage are resolved, in a market economy, through the price mechanism. It shouldn't even be questioned, given the thousands of previous examples we have.
Unfortunately, some have exceptionally thick heads. Unless there's some other explanation for a devotion to, say, the belief that legally mandated minimum wages won't affect employment levels.