Doraszelski and Jaumandreu (2018) estimate a CES production function with two forms of productivity shocks (1) labor augmenting and (2) Hicks neutral. They claim that the increase in labor augmenting productivity is the reason that the labor share of income is falling. In their figure 1 they show the increase in labor augmenting productivity by industry and in figure 2 they show that in a hypothetical scenario without labor augmenting productivity that labor share would be higher.
My intuition would be that labor augmenting productivity should increase the income share to laborers, but clearly that is wrong.
Is there an intuitive explanation for the conclusion of this paper?