Revisiting Capital-Skill Complementarity, Inequality, and Labor Share
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Analysis by @LeeOhanian finds rising inequality btw higher & lower-skilled workers driven by substitutability btw capital & lower-skilled workers, alongside capital-skill complementarity.
Lee Ohanian, Musa Orak and Shihan Shen, "Revisiting Capital-Skill Complementarity, Inequality, and Labor Share," National Bureau Of Economic Research, April 2021, https://www.nber.org/papers/w28747
Takeaway, “…. Our main finding is that the....model continues to fit the data quite well, with high substitutability between unskilled labor and capital, and relative complementarity between skilled labor and capital... The estimation thus chooses a somewhat smaller, though still highly significant, complementarity between skilled labor and equipment capital to attenuate this increase: 0.76 when gross labor share is used, and 0.72 for net labor share, compared to 0.67 in....(gross labor share).... We find that capital-skill complementarity continues to be a critical determinant of U.S. wage inequality, irrespective of which definition of income is used to measure labor’s share. Labor’s share of income does influence the degree of estimated complementarity between equipment and skilled labor, but it does not have a sizeable effect on the model’s ability to account for the skill premium. The findings indicate that capital-skill complementarity remains a quantitatively important determinant of U.S. wage inequality…”
New from Lee Ohanian supports the view that talent is the limiting constraint, finds the rise in inequality btw skilled and lower-skilled workers has been driven by synergies between capital and high skilled workers and substitutability between capital and the lower skilled workers
Core results, "... We find that capital-skill complementarity continues to be a critical determinant of U.S. wage inequality, irrespective of which definition of income is used to measure labor’s share. Labor’s share of income does influence the degree of estimated complementarity between equipment and skilled labor, but it does not have a sizeable effect on the model’s ability to account for the skill premium. The findings indicate that capital-skill complementarity remains a quantitatively important determinant of U.S. wage inequality...."
They look at labors share of gross income and net of depreciation, "...Regarding labor share, we analyze the modelusing both labor share of gross income, which is the measure that has declined, and labor share of income net of depreciation, which has not declined as much, and which is now being analyzed widely within the literature. only considered gross labor share since there were no large changes in depreciation during the years they studied, and thus there was no need to consider both…”
Ed Comment:We should add this but I don’t fully understand it. I think you have to measure labor’s share net of depreciation. Depreciation as a share of GDFP is growing because IT-related assets grow obsolete faster. So do other intangible assets. If obsolescence is accelerating, I would think the value of skilled labor is growing more important too. Somebody is obsoleting assets/designing more competitive replacements. I also think labor’s share is increasingly mismeasured as professional services and self-employed income grow. That share is flowing to the highest skilled. I also think the assets are riskier (and harder to replace), and so produce higher returns. My guess is that the GDP share changes are largely fully explainable for logical economic reasons.
Ben Comment:They’re assuming perfect competition, a 0-profit condition. I think this is a real flaw in their analysis because the labor share is falling - and profits are the part of capital share that are increasing. Using BEA data they way they are makes it impossible to tease these apart. They also make strong assumptions about the risk premium (that it’s 0). The data work is very model dependent and (as noted above) the model has some limitations I’m really interested in their Figure 5.3 (attached). They’re saying that if they freeze labor inputs (green line), the labor share explodes. This makes sense to me - freezing labor but allowing capital to grow means labor because the limiting factor and the price goes way up. In this light, how do we interpret solid red and dashed black lines (real data and constant capital growth with growing labor inputs, respectively). The implication I’m drawing is that labor is not the limiting factor in the economy at the moment - but capital is. I think this fits with Ed’s argument that equity capital (or risk underwriting capital) is more limited in today’s economy than anything. That said, it’s hard to draw any real implications like that from this paper because they ignore profits and equity.