One of the main macroeconomic facts of the last decades in the US is the steady decline of safe real interest rates (e.g. Bernanke 2005, Caballero et al. 2008, Summers 2015, Williams 2017). The blue line in Figure 1 shows that the real safe return dropped by about 6% from 1980 to 2016. Less noticed, but perhaps as remarkable, is the fact that the real return on productive capital remained stable over the same period of time (red line), at around 6.5%. The result is a growing gap between the safe real interest rate and the rate of return on productive capital, especially since the early 2000s.
Figure 1 Real safe return and real return to capita in the US
Notes: The safe real return is constructed as the ex-ante real yield on 90-day US Treasuries, using median expected price changes from the University of Michigan’s Survey of Consumers.
Source: FRED. The real return to capital is constructed as the real after-tax return to US business capital, computed by Gomme et al. (2011) and adjusted for the share of intangibles in total capital from Koh et al. (2016). The real after-tax return to capital is constructed as total after-tax capital income, net of depreciation divided by the previous period’s value of capital. Business capital includes non-residential fixed capital (structures, equipment, and intellectual property) and inventories.
In parallel, during the second part of the period since the early 2000s, the division of national income between labour and capital has been dramatically altered, as the share of labour has declined by 4%.
In a recent paper, we argue that these secular divergent macroeconomic trends are deeply intertwined (Caballero et al. 2017). Using a simple accounting method coupled with conventional first-order conditions for monopolistically competitive firms hiring labour and investing in risky capital, we argue that these twin divergences between rates of return and factor payments arise from a combination of a rise in the capital risk premium, an increase in monopoly rents from mark-ups, and capital-biased technical change.
On the one hand, the growing gap between the safe real interest rate and the rate of return on productive capital must reflect a combination of an increase in the capital risk premium – consistent with the view that there is a growing shortage of safe assets – and of an increase in monopoly rents from mark-ups – perhaps arising from increasing barriers to entry and returns to scale. On the other hand, the decline in the labour share originates from a combination of an increase in monopoly rents from mark-ups and capital-biased technical change – perhaps from the progress of automation technologies.1 The connection between these two macroeconomic trends is that they both bear the signature of rising mark-ups.
The difficulty, of course, is that neither the capital risk premium, nor mark-ups, nor capital-biased technical change are directly observable from available data. With two macro facts and three potential explanations, the most one can do is to provide some decompositions under alternative scenarios. We consider two such (polar) cases: without changes in technology in scenario A, and without changes in mark-ups in scenario B.
Because scenario A ascribes the entire decline in the labour share to an increase in mark-ups (as in the recent work of De Loecker and Eeckhout 2017 or Barkai 2016), it provides a lower bound on the increase in capital risk-premium. Conversely, because scenario B assumes mark-ups are constant, it ascribes the entire increase in the gap between safe real interest rates and the rate of return to productive capital to an increase in the capital risk premium. The truth must lie somewhere in the middle.
Under both scenarios we find a significant increase in the capital risk premium since 2000, and especially since 2008. This is true even under the extreme assumption that the decline in the labour share is entirely caused by rising mark-ups (scenario A). The associated rise in mark-ups is simply not big enough to fully account for the increasing gap between the safe real interest rate and the rate of return on productive capital.
A key parameter underlying this inference is the elasticity of substitution between capital and labour. This parameter determines the required change in mark-ups (scenario A) or in capital-biased technical change (scenario B) required to rationalise the decline in the labour share in an environment of declining relative price of investment goods. This is because the impact of the decline in the relative price of investment goods on the labour share depends on the elasticity of substitution between capital and labour. It increases the labour share if the elasticity of substitution is less than one, and increases it otherwise. This implies, for example, that under scenario A, the required increase in mark-ups is larger when the elasticity of substitution is lower.
A natural benchmark with a unit elasticity of substitution conveys the main message. The dominant factor, but not the exclusive one, is a steady and sharp rise in the capital risk premium. Scenario A generates a moderate rise in the mark-up factor (price over variable costs) from 1.017 before 2000 to 1.064 after 2008, and a significant rise in the capital risk premium from 1.28% to 6.63% over the same period. Scenario B reallocates the mark-up adjustment to capital-biased technical change and an even larger capital-risk premium rise from 1.94% to 8.93%.
When we reduce this elasticity to 0.8, the mark-up rises significantly from 1.04 to 1.12, while the capital risk premium change compresses but it is still large, from 0.47% to 4.85%. When we increase the elasticity of substitution to 1.25, then the mark-up change vanishes in Scenario A but the capital risk premium now rises from 1.98% to 8.34%. There is a symmetric result for Scenario B, with mark-up changes replaced by degrees of capital-biased technical change, but in this case, the capital risk premium is unaffected.
Our simple macroeconomic framework therefore delivers a consistent message. Regardless of the underlying assumptions, the estimates suggest a substantial increase in the capital risk premium since 2000 and, especially since 2008.
These estimates of the capital risk premium can be converted into estimates of the equity risk premium by applying the appropriate leverage ratio. For example, with a debt-to-equity ratio of 0.5, the equity risk premium is 1.5 times the capital risk premium. The evolution of the equity risk premium is a scaled-up version of that of the capital risk premium.
These macro-based results are broadly in line with more sophisticated finance-based estimates. Figure 2 reports the first principal component estimated across 20 models of the equity risk premium, using different methods ranging from time-series VAR models that seek to estimate expected dividend growth in the spirit of the simple Gordon dividend growth model, to cross-sectional models that seek to estimate the market price of risk.
Figure 2 US equity risk premium
Notes: One-year Treasury yield from Federal Reserve H.15; Equity risk premia (ERP) from Duarte and Rosa (2015)
While these estimates are based on more sophisticated econometric methods, a simple back-of-the-envelope calculation based on the earnings yield on the S&P500 is also useful. Figure 3 displays the behaviour of the S&P500 earnings yield. Abstracting from the large swings around the time of the Global Crisis, we observe two distinct phases: a significant decline in the earnings yield between the early 1980s and the early 2000s from 14% to 2%, followed by a modest rebound and a stabilisation around 5%. Under the classic Gordon model, we can convert the earnings yield into a rough measure of the equity risk premium, given assumptions about the share of earnings reinvested and the growth rate of dividends. Taking the expected growth rate of dividends to be equal to its realised value, and using a share of reinvested earning of 20%, we find an increase in the capital risk premium over the period, from 2.08% to 4.87%. This is broadly in line with our macro estimates.2
Figure 3 Inverse of the S&P 500 price-earnings ratio
Notes: computed using the price index divided by 12-months trailing reported earnings, and real ex-ante return on 10-year real Treasury Securities constructed using median expected price change from the University of Michigan’s Survey of Consumers.
Source: Global Financial Database and FRED.
Finally, we offer a narrative centred on the secular evolutions of safe and risky expected rates of return as depicted in Figure 2. Very broadly, we identify three phases, which we analyse in our papers.3
- The first phase occurs from 1980-2000, in which the expected rate of return on equities declines in tandem with safe real rates, the former falling more than the latter.
- In the second phase, from 2000-2008, the expected rate of return on equities is more or less stable (with some ups and downs), but risk-free rates keep falling. The equity risk premium is increasing.
- In the third and final phase, from 2008 to now, the expected rate of return on equities is more or less stable (with some ups and downs), and the risk-free rate declines to the zero lower bound. The equity risk premium is increasing.
In phase one, the decline in interest rates is driven by general supply and demand factors affecting all assets (safe and risky). In phases two and three, the decline in the risk-free rate is driven in large part by specific supply and demand factors affecting safe assets. The stable expected return on equities in phases two and three is consistent with the stable return on productive capital over that period.
Phase two corresponds to the intensification of the ‘global savings glut’, China coming online, and the rise in international reserve accumulation across emerging markets in the aftermath of the Asian financial crisis. It seems that a substantial share of the desired demand for assets was for safe assets, explaining the divergence between safe and risky returns.
The safe asset shortage intensifies in phase three through a combination of factors, including increased global risk aversion after the financial crisis, regulatory changes for banks and insurance companies at a global level, and declines in the supply of safe assets (sovereign debt crisis, collapse in private supply).
What can we say about the near future from these facts? The secular trends in mark-ups, capital-biased technical change, and risk premia seem unlikely to reverse anytime soon. We are therefore likely to live in a prolonged era of low interest rates, high capital risk premia, and low labour share.
Acemoglu, D, and P Restrepo (2016), “The Race Between Machine and Man: Implications of Technology for Growth, Factor Shares and Employment”, NBER Working Paper 22252.
Autor, D, D Dorn, L F Katz, C Patterson, and J Van Reenen (2017), “The Fall of the Labor Share and the Rise of Superstar Firms”, NBER Working Paper 23396.
Barkai, S (2016), “Declining labor and capital shares”, Stigler Center for the Study of the Economy and the State, New Working Paper Series 2.
Bernanke, B (2005), “The Global Saving Glut and the U.S. Current Account Deficit”, Sandridge Lecture, Virginia Association of Economics, Richmond, VA.
Caballero, R J, E Farhi, and P-O Gourinchas (2008), “An Equilibrium Model of ‘Global Imbalances’ and Low Interest Rates”, American Economic Review 98 (1), 358–93.
Caballero, R J, E Farhi, and P-O Gourinchas (2015), “Global Imbalances and Currency Wars at the ZLB”, NBER Working Paper 21670.
Caballero, R J, E Farhi, and P-O Gourinchas (2016), “Safe Asset Scarcity and Aggregate Demand”, American Economic Review 106 (5), 513–18.
Caballero, R J, E Farhi and P-O Gourinchas (2017), “Rents, Technical Change, and Risk Premia Accounting for Secular Trends in Interest Rates, Returns on Capital, Earning Yields, and Factor Shares”, American Economic Review 107 (5), 614-620
De Loecker, J, and J Eeckhout (2017), “The rise of market power and the macroeconomic implications”, NBER Working Paper 23687.
Duarte, F M, and C Rosa (2015), “The Equity Risk Premium: A Review of Models”, Federal Reserve Bank of New York Staff Report 714.
Gaggl, P, and M Eden (2016), “On the Welfare Implications of Automation”, mimeo, Brandeis.
Gomme, P, B Ravikumar, and P Rupert (2011), “The Return to Capital and the Business Cycle”, Review of Economic Dynamics 14 (2), 262–78.
Gutiérrez, G (2017), “Investigating Global Labour and Profit Shares”, mimeo, NYU.
Grossman, G M, E Helpman, E Oberfield, and T Sampson (2017), “The Productivity Slowdown and the Declining Labor Share: A Neoclassical Exploration”, NBER Working Paper 23853.
Karabarbounis, L, and B Neiman (2014), “The Global Decline of the Labor Share", Quarterly Journal of Economics, 129 (1), 61-103.
Koh, D, R Santaeulàlia-Llopis, and Y Zheng (2016), “Labor Share Decline and Intellectual Property Products Capital”, Barcelona Graduate School of Economics Working Paper 927.
López-Salido, D, J C Stein, and E Zakrajšek (2017), “Credit-Market Sentiment and the Business Cycle”, Quarterly Journal of Economics, 132 (3), 1373-1426.
Rognlie, M (2015), “Deciphering the Fall and Rise in Net Capital Share: Accumulation or Scarcity”, Brookings Papers on Economic Activity, 46 (11), 1-69.
Summers, L H (2015), “Have we entered an age of secular stagnation?”, IMF Fourteenth Annual Research Conference in Honor of Stanley Fischer, Washington DC, IMF Economic Review, 63 (1), 277-280.
Williams, J C (2017), “Three Questions on R-star”, FRBSF Economic Letter, February, 2017-05.
 Different authors have investigated the possibility that the decline in the labour share is due to some form of capital-biased technical change, exploring different variants of that hypothesis: a decline in the relative price of investment goods (Karabarbounis and Neiman (2014)); capital-biased technical change and automation within firms (Koh et al. (2016), Acemoglu and Restrepo (2016), Gaggl and Eden (2016), Grossman et al. (2017)); a composition effect across firms via the the reallocation of market-share to more capital-intensive “superstar” firms (Autor et al. (2017), Kehrig and Vincent (2017)); a composition effect across sectors with a reallocation of value-added to the more capital intensive housing sector (Rognlie 2015). Other authors have tried to link the decline in the labour share to the rise of mark-ups (Barkai (2016), Gutierrez (2017)).
 An important caveat is that some risk premia exhibit different patterns from those that we have inferred. Most prominently, the credit spread between corporate bonds of various ratings and U.S. Treasury bonds of the corresponding maturity have remained strikingly stable over time except during the financial crisis. The different behaviours of these different risk premia could arise either because different factors are priced in these different markets, or because these markets are significantly segmented with more pervasive ``reach for yield'' within the fixed income space in response to the aggressive QE policies followed by all major central banks in the aftermath of the global financial crisis. López-Salido et al (2017) offers evidence of segmentation between credit markets and stock markets by showing that empirical predictors of returns in one market have essentially no predictive power for the other.
 Caballero et al. (2008) focused on general asset market factors behind the decline in interest rates in phase (1). Caballero and Farhi (2017), Caballero et al. (2015), and Caballero et al. (2016) analyse both general asset market factors and factors specific to safe asset markets to account for phases (2) and (3).