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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?

Michael Gmeiner
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I'm not a macroeconomist (so definitely not used to looking at those types of equations in that setting), but I think the intuition is that the estimated substitutability of labor and materials is <1 (see page 1048). As labor becomes more productive, you need relatively fewer units of it and shift resources towards the other (non-augmented) inputs.

Effectively, it's easier to think of it more as halfway in between a Leontief and Cobb Douglas function. In a CDPF, you're right--you'd want resource shares to remain constant, and the increase in labor productivity would lead to increased output (and hence higher wages per unit of labor). However, in a Leontief world, if labor became twice as productive half of your labor stock would become redundant. Reducing the labor used would reduce wages (if labor markets were somewhat competitive). Any "gains" from labor being more productive go into purchasing more capital, not raising wages.

Let me know if that wasn't clear. (Obviously I also defer completely to any macroeconomist who interprets the cause differently!)

AndrewC
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  • I was curious if their estimate of $\sigma$ implying a more Leontief production function was the explanation, which is essentially what you said.

    Am I correct in interpreting that wages increase to laborers that remain but total wage bill declines?

     – Michael Gmeiner Jul 21 '21 at 13:27