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Lambert here: Thinking purely politically, this analysis squares a lot of circles.

By Robert Z. Lawrence, Professor of International Trade and Investment, John F Kennedy School of Government Harvard University, Senior Fellow, Peter G. Peterson Institute for International Economics, and a former member of of the President’s Council of Economic Advisors under President Clinton. Originally published by VoxEU.

The US debate over income inequality in the 1980s and 1990s focused on the growing disparity between the earnings of the skilled, the unskilled and the super-rich. After the global crash, the decline in labour’s share of national income has been added to these concerns. This column presents an alternative explanation for this decline, arguing that limited substitution possibilities between capital and labour combined with the acceleration in the pace of labour-augmenting technical change raises the effective labour-capital ratio. The policy implications of this alternative explanation are profoundly different from those currently circulating.

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 labour’s share of national income (See Fig 1) has been added to these concerns.

There are several plausible reasons for this development — globalisation, automation, weak bargaining power of labour, 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 emphasises the ease with which capital and labour 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 labour’s share in income.

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

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, labour’s income equals the wage rate (w) times the amount of labour 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-labour ratios. Thus the changes in the ratio or shares of income that accrue to capital and labour 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 labour are easily substituted, a large change in the relative supplies of capital and labour 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 labour (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 labour will give rise to large changes in their relative prices.

In this case, a percentage increase in the quantity of capital relative to labour 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 labour 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%. 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-labour ratio will exceed the decline 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 labour (capital deepening) is responsible for the decline in labour’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 labour 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 or more labour intensive production, Neiman and Karabarbounis claim that the declining price of investment goods has raised the capital-labour 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 labour are relatively low and σ < 1. In this case capital deepening would actually increase rather than reduce labour’s share.

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

A New View

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

Limited substitution possibilities between capital and labour (σ < 1) combined with acceleration in the pace of labour augmenting technical change, which raises the effective labour-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 labour and the magnitude of capital and labour 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-labour has been more than offset by an acceleration in the pace of labour augmenting technical change.

In combination, these estimates of low substitution elasticities and declines in the effective capital-labour allow me to account for much of the decline in labour’s share in the US sectors and industries (such as manufacturing, mining, and information technology) that are responsible for most of the decline in labour’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 labour’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: 671-686.

Elsby, M W L, B Hobjin, and A Sahin (2013), “The Decline of the U.S. Labour Share”, Brookings Papers on Economic Activity, Washington, September.

Hicks, J R (1963), The Theory of Wages 1932, reprinted as 2nd edition, London, UK: MacMillan.

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

Lawrence, R Z (2015), “Recent Declines in Labour’s Share in US Income: A Neoclassical Account”, NBER Working Paper 21296 and WP 15 – 10, The 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.

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

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.