Explaining Recent Declines in Labor's Share in US Income

Op-ed on VOX

October 15, 2015

The US debate over income inequality in the 1980s and 1990s focused on the growing disparity between the earnings of skilled and unskilled workers and the earnings of the super rich. Since 2000 and especially after 2007, however, the decline in labor's share of national income (See figure 1) has been added to these concerns.

There are several plausible reasons for this development—globalization, automation, weak bargaining power of labor, political capture, higher markups—but the natural starting point for explaining factor income shares is the theory of the functional distribution of income enumerated by John Hicks (1963) and Joan Robinson (1932) in the 1930s. This theory, which emphasizes the ease with which capital and labor can be substituted, points to a combination of weak investment and technical change that has made workers more productive as the explanation for recent declines in labor's share in income.

Figure 1 Share of labor compensation in US national income 1969-2014

Figure 1

Source: BEA National Income Accounts Table 1.12.

Capital's income equals the rate of return on capital (r) times the quantity of capital (K). Similarly, labor's income equals the wage rate (w) times the amount of labor employed (L). Thus the ratio of factor incomes, (rK / wl), can be expressed as the product of relative factor prices (r/w) and relative factor quantities (K/L).

Relative factor prices (r/w) and relative factor quantities (K/L) will generally move in opposite directions. More expensive capital—a rise in r/w for example—will induce firms to produce with lower capital-labor ratios. Thus the changes in the ratio or shares of income that accrue to capital and labor will depend upon how relative quantities and relative prices change. If two goods are close substitutes, a small change in their relative prices will give rise to large changes in the relative quantities that will be demanded. Similarly, if capital and labor are easily substituted, a large change in the relative supplies of capital and labor will need relatively small changes in their relative prices for demand to adjust:

  • If substitution is easy, a given percentage increase in the quantity of capital relative to labor (K/L) will raise capital's income share because it will be offset by a relatively small percentage decline in capital's relative price (r/w);
  • If substitution is difficult, however, small changes in the relative supplies of capital and labor will give rise to large changes in their relative prices.

In this case, a percentage increase in the quantity of capital relative to labor will be more than offset by the percentage decline in the relative price of capital, and capital's income share will fall.

The ease with which capital and labor can be substituted can be defined more precisely with a measure known as the elasticity of substitution—depicted by σ. This indicates the percentage change in K/L when r/w changes by 1 percent. Since relative prices and quantities will move in opposite directions, σ is defined negatively. When σ = 1, relative prices and quantities move in opposite directions by similar percentages and factor income shares are unchanged. However if σ is greater than one, capital's share will rise when its price falls since the percentage change in the relative capital-labor ratio will exceed the decline in the relative price of capital. If σ is less than one, however, capital's share will fall when its relative price falls since the percentage decline in prices will exceed the percentage increase in the relative supply of capital.

Based on the assumption that substitution possibilities are considerable and σ is greater than one, several leading recent authors have claimed that a rise in the quantity of capital relative to the quantity of labor (capital deepening) is responsible for the decline in labor's share in US income. This view is reflected in papers by Elsby et al. (2013) and Neiman and Karabarbounis (2014), and most famously in the book, Capital in the Twenty-First Century, by Thomas Piketty (2014). The explanations for capital deepening offered by these authors differ, but all three imply that since capital and labor are highly substitutable, the increased relative supply of capital has been met with a less than proportional decline in its relative price. Specifically, Elsby et al. claim the reason is an increase in capital intensity due to the offshoring of more labor intensive production, Neiman and Karabarbounis claim that the declining price of investment goods has raised the capital-labor ratio, and Piketty claims capital deepening has taken place due to a decline in the growth rate in the face of a constant saving rate.

But this line of explanation suffers from two basic flaws. First, it is at odds with the preponderance of studies (see surveys by Chirinko 2008, Rognlie 2014, and Lawrence 2015) that have found that the substitution possibilities between capital and labor are relatively low and σ < 1. In this case capital deepening would actually increase rather than reduce labor's share.

A second problem is that these explanations ignore the possibility of technical change that makes labor more productive—so-called labor augmenting technical change. This second oversight is also serious, because studies of the direction of technical change have concluded it is net labor augmenting (Antras 2004, Wei 2014, and Young 2010). In the face of powerful labor augmenting technical change, even if the physical ratio of labor to capital might have fallen, therefore, once technical change is taken into account, the effective supply of labor relative to capital might actually have risen.

A new view

Correcting these two flaws provides an alternative line of explanation for the decline in labor's share:

  • Limited substitution possibilities between capital and labor (σ < 1) combined with acceleration in the pace of labor augmenting technical change, which raises the effective labor-capital ratio.

In recent work (Lawrence 2015), I present empirical support for this alternative explanation.

Using regressions that produce estimates of both the elasticity of substitution between capital and labor and the magnitude of capital and labor augmenting technical change, I find that the elasticity of substitution is generally less than one in many US industries as well as the US economy as a whole. The estimates also imply the effective capital-ratio has actually fallen in many industries because the measured rise in the (physical) capital-labor has been more than offset by an acceleration in the pace of labor augmenting technical change.

In combination, these estimates of low substitution elasticities and declines in the effective capital-labor allow me to account for much of the decline in labor's share in the US sectors and industries (such as manufacturing, mining, and information technology) that are responsible for most of the decline in labor's share in income.

Important differences in policy implications

The policy implications of this alternative explanation are profoundly different from those advocated by Piketty. Piketty advocates taxing capital. But if σ is < 1, increasing taxes on capital could lead to further reductions in labor's share. Paradoxically, with σ < 1, policies that increase investment and the supply of capital could achieve more equal distributions of income. Accordingly lower taxes on capital and a progressive consumption tax could be the most effective approach to boosting investment and reducing US income inequality.

References

Antras, P. 2004. Is the US Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution. B. E. Journal of Macroeconomics 4(1).

Chirinko, R. S. 2008. The Long and Short of It. Journal of Macroeconomics 30: 671–86.

Elsby, M. W. L., B. Hobjin, and A. Sahin. 2013. The Decline of the U.S. Labor Share. Brookings Papers on Economic Activity. Washington: Brookings Institution.

Hicks, J. R. 1963. The Theory of Wages 1932, 2nd ed. London: MacMillan.

Karabarbounis, L., and B. Nieman. 2014. The Global Decline of the Labor Share. Quarterly Journal of Economics 129(1): 61–103.

Lawrence, R. Z. 2015. Recent Declines in Labor's Share in US Income: A Preliminary Neoclassical Account. PIIE Working Paper 15-10. Washington: Peterson Institute for International Economics.

Piketty, T. 2014. Capital in the Twenty-First Century. Cambridge, MA: Belknap.

Robinson, J. 1932. Economics of Imperfect Competition. London: MacMillan.

Rognlie, M. 2014. A Note on Piketty and Diminishing Returns to Capital. MIT Working Paper. Cambridge, MA: MIT.

Wei, T. 2014. Estimates of Substitution Elasticities and factor-Augmented Technical Changes. Oslo, Norway: Center for International Climate and Environmental Research (CICERO).

Young, A. T. 2010. US Elasticities of Substitution and Factor-Augmentation at the Industry Level. Working Paper. College of Business and Economics, West Virginia University.

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Robert Z. Lawrence Senior Research Staff

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