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Accounting for macro-finance trends

Most developed economies have experienced large declines in risk-free interest rates and lacklustre investment over the past 30 years, while the profitability of private capital has increased slightly. Using an extension of the neoclassical growth model, this column identifies what accounts for these developments. It finds that rising market power, rising unmeasured intangibles, and rising risk premia play a crucial role, over and above the traditional culprits of increasing savings supply and technological growth slowdown.

Real interest rates on safe assets such as government bonds have declined persistently since the 1980s. This price change signals that the demand for safe assets outstrips the supply, and it has significant implications for investors and policymakers. For instance, low real interest rates affect government debt sustainability or the ability of monetary policy to stimulate the economy in a downturn. What drives this decline? Does it simply reflect rising savings, due to ageing in advanced economies and precautionary savings by emerging markets? And why is investment not increasing in light of these higher savings?

Our starting point is the observation that, remarkably, not all rates of return are falling. In particular, the profitability of private capital has, if anything, increased slightly. This leads us to ask – what is driving the wedge between these two rates of returns?

Potential drivers of the return spread

In theory, one would expect businesses to expand investment to the point where the marginal return equals the interest rate, and hence to drive down the profitability to equal the risk-free rate. We see three main potential reasons why this mechanism may break down.

First, if competition is limited, firms may under-invest as they prefer to raise prices and produce less. We call this the rents story. It has received significant support from different studies recently (among many others, see Furman and Orszag 2015, Barkai 2017, Gutierrez and Philippon 2017, De Locker and Eeckout 2017, Eggertsson et al. 2018).

Second, the required extra compensation for investing in risky private capital rather than safe assets may have increased, either because investors now perceive a higher risk or because they are effectively more risk averse. We call this the risk premium story (e.g. Caballero and Farhi 2018, Caballero et al. 2017, Del Negro et al. 2018, Marx et al. 2017).1

Third, technological change may affect the profitability of capital – for instance, changes in the price of capital, in physical depreciation, or in the ‘production function’ (for instance, capital-biased or skill-biased technical change). We call this the technology story. Of particular interest is the shifting nature of capital assets. Historically, the majority of capital was made up of physical assets such as plant and equipment used for production. These physical assets are rather well measured. But there has been a growing shift towards ‘intangible’ forms of capital, such as software, patents, brands and customer base, or firm-specific human capital, which are less well measured. 

Underestimating the quantity of capital (if one does not properly measure the intangible one) leads naturally to overestimate the profitability of private capital. In this case, the true profitability of capital is low (since we underestimate the quantity of capital that needs to be compensated) and there may be no wedge in reality between private return on capital and the risk-free rate. We call this the intangible story (e.g. Crouzet and Eberly 2018).

Using the neoclassical model as an accounting framework

In a recent paper (Farhi and Gourio 2018), we propose a simple accounting framework to empirically distinguish between these different stories. Our framework builds on the standard neoclassical growth model, the backbone of modern macroeconomics. This framework is often used to understand quantitatively the behaviour of the ‘big ratios’ emphasised since Kaldor – the investment-output and capital-output ratios or the labour share. Our main innovation is to introduce risk in a tractable way, which allows us to analyse financial variables such as the price-dividend ratio, Tobin’s Q, or the risk-free rate. This innovation is, of course, also required to entertain the risk premium story. 

The core of our approach can be described (with a slight simplification) in three steps. First, we use the standard Gordon growth formula, which holds in our model, to infer the risk premium on private capital. The Gordon growth formula states that the dividend yield equals the expected return less the growth rate of the economy. The expected return is, in turn, the sum of the risk-free rate and a risk premium. Since we can observe the dividend yield, the growth rate and the risk-free rate, we can infer the risk premium.

Second, given this risk premium and the observed depreciation and investment prices, we can construct the user cost of capital. If there were no market power, this user cost would equal the return on private capital. We can deduce the mark-up necessary to be consistent with the observed return on capital. Finally, in a third step we infer the change in the bias of technology required to match the labour share. Our approach hence uses macroeconomic and financial data jointly to disentangle the market power, risk premia and technology stories.

Finally, we also incorporate other factors that are important to understand the evolution of the economy – the increase in savings supply, change in productivity growth, investment prices, depreciation, population and employment. Even though these factors have little effect on the spread between the return on private capital and the risk-free rate, they affect the other quantities we must look at (such as the labour share or the profitability of capital) to study the spread.

Decomposing the spread

Our main finding is summarised in Figure 1 and in Table 1. The top panel depicts the spread between the rate of return (or profitability) on private capital and the risk-free rate. The bottom panel depicts the three components of the spread, corresponding to rents, risk premia, and technology. The key finding is that the technology component is stable and hence does not account for the increase observed during this period. But both the risk premia and rents play a significant, and roughly equal, role in accounting for the increase in the spread during the past 30 years.

Figure 1 Spread between the private return on capital and the risk-free rate 

Note: Each data point reflects an estimation on a centred 11-year rolling window. For instance, the last point is 2011, estimated using data from 2006 to 2016.

Table 1 Changes in macro-finance moments


Source: Authors’ analysis.

Why do we reach this conclusion? As we explained, the risk premium on private capital is inferred from the Gordon model. The dividend yield equals the risk free-rate plus the equity premium less the growth rate of the economy. In the data, the risk-free rate fell considerably more than the growth rate, while the dividend yield has only fallen modestly. Hence, the equity premium must have risen. This increase in the risk premium only accounts for about half of the measured increase in the profitability of capital, and so the rest must be explained by an increase in market power. This increase in mark-ups is roughly consistent with the decline in the labour share, leaving little role for biased technical change.

While this method may seem exceptionally simple or even naïve, we show in our paper that its results are consistent with a broad set of models that also find that the equity risk premium has increased (e.g. Duarte and Rosa 2015). At the same time, we acknowledge that this increase in the risk premium needs ultimately to be explained and understood better – we will discuss this below.

On the other hand, if we had abstracted from risk, like many authors before us, we would have reached some unsettling conclusions. First, without an increase in risk, the increase in market power needed to match the observed behaviour of the return on capital is about twice as large – something that may seem implausible. Second, this increase in market power leads, by itself, to a huge decline in the labour share, so the model requires technology to become more labour-biased to match the moderate decline in the labour share. This seems counterintuitive in light of the many studies that emphasise that technical progress has been capital-biased or, at worst, high skill-biased. In our paper, we show that the role of market power is even lower once we take into account the intangible story.

Implications for other variables

Our model shows that rising market power and risk premia help explain a variety of other facts – low investment growth, the decline in the risk-free rate, and the behaviour of Tobin’s Q and other valuation ratios. Table 2 provides a decomposition of the evolution of these variables into the main drivers. For instance, the investment-output ratio has been held back by higher market power and higher risk premia, despite the boost from the higher savings supply.

Table 2 Decomposition of changes in macro-finance moments

Source: Authors’ analysis.

Conclusion and future research

Our approach provides some important cues regarding which forces explain the main macro-finance trends of the past 30 years.

One important question left open for future research is why risk premia have risen. Indeed, it is not obvious that risk has risen – for instance, there is little trend in implied or realised stock market volatility during this period. We conjecture that several factors might be at play. Some of these factors increased perceived risk, while others increased the willingness to bear risk (i.e. effective risk aversion). Perceived risk is likely higher following the sequences of financial crises in emerging markets in the 1990s and in developed markets in the 2000s. Effective risk aversion may be also higher due to an ageing population, heightened precautionary behaviour of emerging market investors, or changes in regulation.


Barkai, S (2017), “Declining labor and capital shares”, London Business School working paper.

Caballero, R J and E Farhi (2018), “The safety trap”, Review of Economic Studies 85(1): 223-274.

Caballero, R J, E Farhi and P-O Gourinchas (2017), “Rents, technical change, and risk premia”, American Economic Review 107(5): 614-620.

Carvalho, C, A Ferrero and F Nechio (2016), “Demographics and real interest rates: Inspecting the mechanism”, European Economic Review 88: 208-226.

Crouzet, N and J Eberly (2018), “Understanding weak capital investment: The role of market concentration and intangibles”, Jackson Hole Economic Policy Symposium, Federal Reserve Bank of Kansas City.

De Loecker, J and J Eeckhout (2017), “The rise of market power and the macroeconomic implications”, NBER working paper 23687.

Del Negro, M, D Giannone, M Giannoni and A Tambalotti (2017), “Safety, liquidity, and the natural rate of interest”, Brookings Papers on Economic Activity, Spring: 235-294.

Duarte, F and C Rosa (2015), “The equity risk premium: A review of models”, Federal Reserve Bank of New York Staff Report 714.

Eggertsson, Gauti, Jacob A. Robbins, Ella Getz Wold, 2018. “Kaldor and Piketty's Facts: The Rise of Monopoly Power in the United States”, NBER Working paper 24287.

Farhi, E and F Gourio (2018), “Accounting for macro-finance trends: Market power, intangibles, and risk premia”, Federal Reserve Board of Chicago working paper WP-2018-19. 

Furman, J and P Orszag (2015), “A firm-level perspective on the role of rents in the rise in inequality”, working paper. 

Gutierrez, G and T Philippon (2018), “Declining competition and investment in the US”, NBER working paper 23583.

Marx, M, B Mojon and F Velde (2017), “Why have interest rates fallen far below the return on capital”, Federal Reserve Bank of Chicago working paper.


[1] Relatedly, the compensation for the special liquidity of government bonds may also have increased. However, the quantitative magnitude of this increase is likely limited. We infer this from the limited increase in the spread between government bonds and other safe, but less liquid assets such as highly rated corporate bonds.

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