Why are interest rates so low today? Many believe that the worldwide abundance of savings is due to the retirement of OECD baby-boomers and the Chinese one-child policy. Can these factors explain the fall in long-term real interest rates, from around 4.5% in 1990 to around 0% since 2015? By contrast, the return on capital, defined as profits over the stock of capital, if anything, increased from 1990 to 2000 and remained stable at around 10% until 2015. Why do investors accept such low returns on bonds while, at the same time, the return on physical capital has remained stable?


Our model features all the potential causes for the decline in real interest rates: demography, trend productivity and risk. In it, generations can save either by lending to the younger generation or by purchasing firms that produce goods and generate profits. The return on stocks is risky because firms' productivity can vary over time. The model is calibrated to simulate the long-term evolution of interest rates, the return on capital, economic growth and the level of debt in the United States, the euro area and the world economy for the last 50 years. It lets us identify and quantify the factors that led to the decline in real interest rates.


Only one factor can explain why both risk premia and debt levels have increased. This is a change in risk perception, which in the model takes the form of uncertainty about the growth rate of productivity. We show that even a moderate increase in the standard deviation of the year-on-year growth rate of productivity, say, from 0.08% to 0.1%, can explain why the difference between return-on-capital and the real interest rate has increased from 3.5% in 1990 to 10% today.

For an average long-term growth rate in productivity of 2%, a growth rate that fluctuates somewhere between 1.8% and 2.2% leads investors to hold a much larger proportion of "safe asset/debt" in their portfolio than if this growth rate were to fluctuate between 1.84% and 2.16%. While these changes seem small, their effects on growth rates can be large when cumulated over an entire generation.

Interestingly, once the effect of rising uncertainty on growth is taken into account, the equilibrium interest rate falls even without any deleveraging. Indeed, according to our model, explaining a 3% fall in real interest rates only by deleveraging would require that debt has been halved since 1990. This is in sharp contrast with the data, since debts as a share of GDP have actually increased since 1990. Finally, ageing and the decline in productivity since 1990 account for only a small proportion of the decline in real interest rates.


Risk-free rates have been falling since the 1980s while the return on capital has not. We analyse these trends in a calibrated overlapping-generations model with recursive preferences, designed to encompass many of the "usual suspects" cited in the debate on secular stagnation. Deleveraging cannot account for the joint decline in the risk free rate and increase in the risk premium, and declining labour force and productivity growth imply only a limited decline in real interest rates. If we allow for a change in the (perceived) risk to productivity growth to fit the data, we find that the decline in the risk-free rate requires an increase in the borrowing capacity of the indebted agents in the model, consistent with the increase in the sum of public and private debt since the crisis.

JEL classification: E00, E40

Keywords: secular stagnation, interest rates, risk, return on capital

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