Skip to main content# Chapter 3| The evolution of interest rates, past and future

## 3.1 The evolution of the safe rate

## The dramatic decline in $(r-g)$

## Potential factors behind the decline in safe rates

## 3.2 Interest rates and growth rates.

## 3.3 The role of demographics

## 3.4 Conclusions

The chapter looks at the evolution of interest rates, and is organized in six sections.

Published onMar 30, 2022

Chapter 3| The evolution of interest rates, past and future

The chapter looks at the evolution of interest rates, and is organized in six sections.

Section 1 looks at the evolution of safe real rates over time. It shows that, even ignoring the high real rates of the mid-1980s which were largely due to disinflationary policies followed by central banks, safe real rates have steadily declined across advanced economies, the United States, the euro zone, and Japan, over the last 30 years. Their decline is due neither to the Global Financial Crisis of the late 2000s, nor to the current Covid crisis, but to more persistent factors.

Section 2 shows that this decrease has led to an increasing gap between growth rates and safe rates, and thus to an increasingly negative value of $(r-g)$. While potential growth has slightly declined, the decrease in interest rates has been much sharper. While there have been periods of negative $(r-g)$ in the past, this one looks different, neither due to wars, nor to bursts of inflation under low nominal rates, nor to financial repression.

Section 3 looks at the potential factors behind the decline in safe rates. Different factors have different effects on saving/investment, and on riskless/risky rates: Saving/investment factors affect all rates roughly in the same way. Risk/liquidity factors lead to lower safe rates and higher risky rates. The evidence is that both sets of factors have been at play. Within each set, the list of suspects is long, but their specific role is hard to pin down.

The last two sections look more closely at two of the potential factors, where I have found the discussion to be misleading in the first case and confused in the second case.

Section 4 looks at the relation between growth rates and interest rates. There is a wide belief that the two are tightly linked. Indeed, some of the research has been based on a relation known as the “Euler equation”, a relation between *individual* consumption growth and the interest rate derived from utility maximization, which implies a close link between the two. I argue that this relation however has no implication for the relation between *aggregate* consumption growth (or output growth) and the interest rate. Indeed, perhaps surprisingly, the empirical relation between the two is typically weak, and often nonexistent. Lower potential growth is not the main cause of lower rates.

Section 5 looks at the role of changing demographics. Three major demographic evolutions have been at work in advanced economies, namely: a decrease in fertility, an increase in life expectancy, and the passing effect of the baby boom. Some researchers have made the argument that these evolutions are partly behind low rates but will reverse as we look forward, leading to higher rates in the future. I argue that the future is likely to be dominated by the increase in life expectancy, and this is likely to further decrease rather than increase interest rates.

Section 6 concludes. The overall evidence suggests that the long decline in safe interest rates is due to deep underlying factors, which do not appear likely to reverse any time soon. Investors in bond markets share this conclusion. The conclusion must however be qualified in two ways. The first is that we do not have a precise enough sense of the factors behind the decline to be sure, and that fiscal policy must therefore be designed under the assumption of a small but positive probability of a reversal. The second is that the future path of interest rates is not exogenous and depends very much on fiscal policy itself. For example, the 2021 Biden stimulus may well increase aggregate demand, and by implication, lead to higher $r^*$ and $r$ for a few years. As I shall discuss in later chapters, fiscal policy should indeed be designed so as to achieve a value of $r^*$ which allows central banks no longer to be tightly constrained by the ELB. If such a fiscal policy were to be implemented, it would imply a floor on future values of $r^*$, and by implication on future values of $r$ itself.

Figure 3.1 shows the evolution of 10-year real interest rates on sovereign bonds, constructed as the difference between 10-year nominal rates and 10-year forecasts of inflation, since 1992, in the US, the euro zone, and Japan.

Why look at these bonds? Because they are largely considered safe from default, so they are a good measure of the safe rate. Why 10-year rates? Because they are close to the average maturity of public debt, and thus a good indicator of the average interest rate on public debt; the average maturity of debt is 7 years for the advanced country members of the G20, 7.8 years for France, 14.8 years for the UK, 5.8 years for the US.1

Why start in 1992 and not earlier? Real rates were even higher in the early 1980s, and peaked around 1985 in most advanced economies. Thus, the figure would be more even more striking if it started in 1985. It would however be misleading. To see why, one must go back to what happened in the 1970s. During that decade, increases in the price of oil and other commodities led to increasing inflation. Central banks increased nominal rates, but by less than inflation, leading to very low real rates, and continuing high inflation. It took until the early 1980s for Paul Volcker, the chairman of the Fed in the United States and for other central bankers around the world, to decide to decrease inflation and to embark on tight monetary policies, resulting in very high real rates for a while. Thus, the high rates of the mid-1980s were not reflecting high neutral rates, but actual rates much above neutral rates. By the early 1990s, inflation was now lower and stable, and the real rates were close to neutral rates. This explains the choice of the date.

*Source: US: 10-year nominal rate on government bonds minus 10-year inflation forecasts from the Survey of Professional Forecasters. Euro: From Isabel Schnabel 2021 *[1]*. Japan rate: Nominal 10-year rate minus 10-year inflation forecast, constructed from Adachi and Hiraki 2021 *[2]*, Figure 8.*

Note that for some of the period, starting in Japan in the late 1990s, in the Euro zone in the late 2000s, and in the US in the late 2000s (with a period of higher rates in the late 2010s), the ELB was binding, so that the actual rate would have been even lower in the absence of the ELB constraint.2 In terms of the discussion in the previous chapter, the neutral rate $r^*$ was lower than $r$. If we were to construct series for $r^*$, the decline would be even more pronounced.

Figure 3.1 yields two major conclusions:

While the decline started earlier in Japan (and for some time, it was seen as a Japan idiosyncratic evolution, until it caught up with the US and the euro zone), it has been largely common to all three economies. This suggests either that the same forces were operating in all countries, or that financial markets are largely integrated, or, more likely, a combination of the two.

The decline has been steady, and is not due either to the Great Financial Crisis or to the Covid-19 crisis. It started long before, and while the two crises led to lower neutral rates, only partly reflected in actual rates because of the ELB, they are hardly visible in the figure.

How historically unusual are such a steady decline and sustained low levels of real rates? Going back further in time, the lack of measures of inflation expectations makes it harder or impossible to construct ex-ante real rates, i.e. nominal rates minus expected inflation; real time forecasts do not exist, and econometric constructs are not as reliable. One can however easily compute ex-post real rates, i.e. nominal rates minus realized inflation. Looking at the United States over the 20th century, doing so shows that there indeed have been periods of low or negative ex-post real rates. This was for example the case during WWII and its aftermath. In 1942, the Fed agreed to peg the Treasury bill rate at a very low level (3/8%) to allow the Treasury to finance war spending at low cost, a case of “fiscal dominance” of monetary policy. After the war, the economy boomed and inflation steadily increased, reaching 20% in February 1951, leading to extremely low real rates; at that point, the Fed and the Treasury agreed to stop the peg, and real rates recovered from 1952 on. As I mentioned earlier, this was also the case in the 1970s when central banks kept rates too low in the face of higher inflation; this is now generally seen as a policy mistake which had to be undone through disinflation policies in the early 1980s. The current situation is very different from these episodes. In both earlier cases, the evidence suggests that, for different reasons in the two cases, the actual rate $r$ was substantially lower than the neutral rate $r^*$. This is not the case today: If anything, the fact that the ELB is binding implies that $r$ is higher than $r^*$. Low rates are not due to fiscal dominance or policy mistakes, but to very low neutral rates.

*Source: Schmelzing. Centered moving average over 20 years.*

It is useful to take an even longer view, and for this, I shall rely on the work of Schmelzing 2018 [3], who has constructed series for the safe real rate over seven centuries, starting with borrowing by Venice in the 1300s, to borrowing by the US treasury today.3

Figure 3.2 again shows a striking picture, with the safe rate decreasing from 10-15% in the 1300s to close to 0% today.4 It suggests a strong underlying negative trend, of about 1.2 basis point per year5, and thus deep, low frequency, forces at work (the estimated negative trend since 1992 is much stronger, about 15 bp per year in the US, 20 bp in Japan, 18 bp in the euro zone).

My conclusions from the evidence in this first section are twofold:

The longer historical evidence suggests deep low frequency underlying forces at work.

Something has happened in the last 30 years, which is different from the past—even if one ignores the abnormally high rates of the mid-1980s.

As we saw in the previous chapter, what is important for fiscal policy and debt dynamics is not so much $r$, but $(r-g)$. Figure 3.3 shows the evolution of the US 10-year real rate (the same series as in Figure 3.1) and the forecast 10-year real output growth rate, from the Survey of Professional Forecasters, since 1992.6 7

*Source: 10-year nominal yields minus SPF forecasts of 10 year inflation, and SPF forecasts of 10 year real growth rates.*

The figure is again quite striking. Forecast US real growth went up in the 1990s, from 2.6% in 1992 to 3.3% in 2001, but has come down since then, and stands at 2.3% in 2021, thus just a bit lower than in 1992. The safe real rate, as we have seen earlier, has decreased substantially, and since 2000, $(r-g)$ has turned negative, and increasingly so. At the start of 2021 (the latest date for which there are forecasts), 10-year $(r-g)$ was equal to -3.2%.8 Markets thus expected $r$ to be substantially lower than $g$ for the next 10 years; in fact they expected it to hold for much longer. At the start of 2021, the rate on 30-year TIPS (that is indexed bonds) was -0.4%. A reasonable forecast of real growth over the next 30 years might be 2%, implying a value of $(r-g)$ over the next 30 years of -2.4%.

This increasing gap is unusual. Can we learn more from looking at the potential factors behind these evolutions?

The decline in rates has triggered a large amount of empirical research, many of them looking at the last 30-50 years, some of them at longer periods, some focusing on the United States, others on the world as a whole, some using econometric methods from correlations to vector autoregressions, others using calibrated models.9

Among the factors that may have shifted saving or investment, researchers have looked at the role of growth on both saving and investment; the role of demographic evolutions, from the baby boom to higher longevity and to lower fertility, on saving; the role of the accumulation of international reserves by emerging market countries on saving; the role of increasing within-country inequality on saving; the role of decreases in the price of capital goods on investment; the role of decreases in technological progress (the initial Alvin Hansen worry) on investment; and, importantly, the role of fiscal policy. On this point, Rachel and Summers 2019 [4] in particular have emphasized that fiscal policy, in particular the substantial increase in debt ratios over the period (that we saw in Table 1 earlier) probably led, other things equal, to an *increase* in $r^*$ during that period. Put another way, absent fiscal policy, the decline in $r^*$ would have been even larger than it has been. This is an important point, both historically and prospectively: Forecasts of $r^*$ must depend on what fiscal policies will be in the future.

Among the factors that may have shifted risk premia or liquidity discounts, researchers have looked at the role of increases in investors’ risk aversion (often called “market risk aversion” to reflect the fact that it may depend on more than individual risk preferences); the role of increases in risk itself coming from more complex processes of production; the role of increases in risk coming from a higher proportion of intrinsically more risky intangibles in investment; the role of increases in the demand for safe assets by emerging markets; the role of increases in the demand for safe and liquid assets coming from liquidity regulations in the wake of the Great Financial Crisis; the reassessment of what assets are truly safe, in the light of the Global Financial Crisis; the role of aging as older individuals, in particular retirees, tend to want safer portfolios.

The role of each of these factors, and whether their evolution might be different in the future than in the past, deserves a full discussion, but would go beyond what I can do here. My reading of this line of research is that, while some of these factors are indeed plausible suspects, their quantitative role is hard to pin down. Empirical work faces many challenges:

To state the first obvious difficulty, the variable we are trying to explain, $r^*$, is not directly observable, and the ELB, which cuts the link between $r$ and $r^*$, complicates matters.

Then, there is the issue of what period one should look at. Rachel and Summers for example look at the period 1970 to 2017, but the decrease in safe rates really only happened from the mid-1980s on and, as argued earlier, movements in $r$ in the 1970s and early 1980s largely reflected deviations of $r$ from $r^*$, negative in the 1970s, positive in the 1980s.

Yet another issue is the role of national versus global factors. When looking for example at saving as a determinant of $r^*$ in a particular country, should one look at shifts in country saving or in world saving? The answer is a mix of the two, depending on the size of the country, the degree of international financial integration, and the permanent or temporary nature of the shifts. It is likely for example that the high saving rates and the resulting sustained large current account surpluses that China ran over the period increased world saving and led, other things equal, to a lower $r^*$ for the rest of the world.10 In contrast, a temporary expansion of demand, such as that triggered by the Biden stimulus, even if it leads to an increase in $r^*$ in the United States (an issue to which I shall return in Chapter 6) may not lead to a similar increase in $r^*$ in other countries. They may decide to deviate from the US $r^*$ and let their exchange rate move accordingly.11

In short, identifying the role of both domestic and global factors on saving, investment, risk, and risk perceptions is not easy. Reading the papers that have had the courage to try, one has a feeling of an abundance of riches, of too many explanatory variables and too few observations. Indeed, when the sample is extended, as done for example by Schmelzing, few of the correlations between rates and potential explanatory variables appear robust. Thus, while the papers point to the right set of suspects, few of them can be indicted, and their specific quantitative contributions must be taken with a grain of salt.12

I think one can however reach a few conclusions, in particular on the relative role of saving/investment shifts versus the role of safety/liquidity factors. The discussion and the figures in Chapter 2 give a way of looking at the data. A positive shift in saving should lead to higher saving and investment and a decrease in all rates, safe and risky.13 An adverse shift in investment should lead to lower saving and investment, and a decrease in all rates, safe and risky. An increase in risk or risk aversion, or a higher demand for liquidity, should lead to a decrease in the safe rate but an increase in risky or less liquid rates. This suggests looking at what has happened to saving/investment rates and to risk premia.

*Source: World Bank open data, gross savings.*

Figure 3.4 shows the evolution of the gross saving rate for the world as a whole, as well as for high income and upper middle income countries (roughly corresponding to emerging markets), since 1992.

The figure shows three important evolutions. First, the increase in the saving rate in middle income countries (reflecting largely the high Chinese saving rate) from 2000 to 2008, which led to a focus on China’s reserve accumulation and talk of a “global savings glut”, but was followed by a decrease from then on. Second, the stable saving rate of high income countries, except for a dip during the Great Financial Crisis. Third, as a result of the first two (low income and lower-middle countries account for little of world saving), no obvious trend and a fairly stable saving rate for the world as a whole. This suggests that, to the extent that there were positive saving shifts, they were accompanied by adverse investment shifts, both resulting in a roughly unchanged saving rate, but both contributing to a decrease in $r^*$.

Turning to risk and liquidity factors, the discussion above suggests looking at what has happened to safe versus risky rates. Thus, Figure 3.5 shows, for the US, the evolution of the safe real rate, measured as in Figure 3.1, and a measure of the expected rate of return on holding the S&P 500, since 1992.14 The expected rate of return on stocks is constructed using an extension of Gordon’s formula, which states that the expected rate of return can be expressed approximately as the sum of the dividend price ratio plus a weighted average of the future growth rates of dividends.15 Given that there is no available time series for real time forecasts of future dividends, I approximate them by forecasts of output growth over the following 10 years, taking a simple unweighted average of forecast US output growth over the 10 years.16

*Source: Safe rate: 10-year nominal rate minus 10-year forecast of inflation, from Survey of Professional Forecasters. Dividend-Price ratio: Case-Shiller. Forecast 10-year growth of output: Survey of Professional Forecasters.*

The figure sends again a clear message. It shows that the expected rate of return on stocks has decreased, but much less than the real rate of return on bonds (about 2% over the period, compared to 4% for the safe rate). The difference between the two, i.e. the equity premium, has substantially increased.17 This suggests that part of the decrease in the real safe rate reflects a higher demand for safety, or/and a higher demand for liquidity on the part of financial investors.18 More has been at work than just shifts in saving and investment.

Before moving to conclusions and potential implications for fiscal policy, I want to take up two issues, namely the relation between interest rates and growth rates, and the role of demographics in the determination of $r^*$. The reason is that I find some of the discussion of the first misleading, and discussion of the second confusing.

There is a widely shared belief that the decrease in interest rates reflects in large part a decrease in growth rates. Indeed, a large part of the research on the causes of low interest rates starts from a theoretical relation between interest rates and growth, known as the Euler equation. Its logic is straightforward.19

Ignoring uncertainty, standard utility maximization suggests that individuals form consumption plans according to the following relation:

$g_c = \sigma (r-\theta)$(1)

where $g_c$ is the rate of growth of individual consumption, $\sigma$ is the elasticity of substitution between consumption across time, and $\theta$ is the individual’s subjective discount rate. The relation, which is known as the *Euler equation* is intuitive. Suppose that the interest rate is equal to the subjective discount rate, so $r-\theta=0$: In this case, $g_c = 0$ and people will want to plan so as to have flat consumption over their life. If $r > \theta$, then it becomes attractive to defer consumption, and to plan on an increasing consumption path, so $g_c>0$. How much to twist the path in response to the interest rate depends on the elasticity of substitution $\sigma$. If it is low, people are not willing to trade off consumption much across periods, and the effect of $(r-\theta)$ on the slope of the path is small. If it is high, the effect is larger.

Assuming that this holds, at least approximately, for an individual, what does this imply about aggregate consumption? If all people are identical and live forever, what holds for one individual holds in the aggregate, and thus holds for the economy as a whole. If the economy is in approximate steady state, the growth rate of consumption is equal to the growth of output, which is itself equal to the growth rate of potential output. The interest rate must then be such as to induce consumers to choose a consumption path consistent with the growth rate of potential output. So we can invert the relation above, to get a causal relation from output growth to the interest rate:

$r = \theta + g/\sigma$(2)

where $g$ is the growth rate of potential output.

This suggests a tight relation between the interest rate and the growth rate. For example, a slowdown in productivity growth, which decreases the growth rate of potential output, leads to a decrease in the interest rate, with an effect which depends on the size of $\sigma$.20 This has led various researchers to use this equation (or a generalization of it to allow for richer specifications of utility, and for uncertainty) to organize their examination of the data.

Where does this approach go wrong? One may argue that standard utility maximization does not describe individual decisions accurately; and there is plenty of evidence that this is indeed the case. But the main issue is elsewhere. The actual economy is composed of finitely lived individuals. Even if each of us were to plan consumption according to his/her Euler equation, and decided for example to have an upward sloping consumption path (if $r>\theta$), this has no implication at all for the relation between the interest rate and the aggregate growth rate. This is shown very simply in Figure 3.6.

Assume people live for two periods (think 30 years for each period). The same number of people are born each period.21 There is no population growth, nor technological progress, so all individuals face the same budget constraint when they are born, and choose the same consumption path. If $r>\theta$, they all choose an upward sloping path, so each individual consumption path slopes up. But aggregate consumption, which in each period is the sum of the consumption of the young and the consumption of the old, is obviously flat, whatever the slope of individual paths, thus whatever value of the interest rate.

In other words, if people have finite lives (which they do), *no matter how long they live*, there is no reason to expect the Euler relation to hold for aggregate consumption.22

This does not exclude an effect of growth on the interest rate in more appropriate models. Higher income growth may lead consumers to spend more today in anticipation of higher income in the future, leading to lower saving. Higher output growth may lead firms to anticipate higher demand in the future, leading to higher investment. Together, lower saving and higher investment can combine to increase the neutral rate. Symmetrically, and more relevant to the present situation, lower growth may lead to higher saving and lower investment, leading to a lower $r^*$.

Empirically, however, the relation appears surprisingly weak. First, in the current context, world growth, which is the relevant variable to look at if financial markets are largely integrated, has barely budged over the last 30 years. Based on World Bank data, average world real growth was 2.7% in the 1990s, 2.8% in the 2000s, 2.9% in the 2010s.23 Thus, it seems hard to blame lower growth for lower rates. More generally, and perhaps surprisingly, the data however do not show a strong relation (let alone causality) between growth rates and interest rates. For example, using the long Schmelzing sample, and 7-year centered moving averages, the correlation is actually strongly negative (Schmelzing 2018 [3], Figure 16), and is unstable across major historical episodes. Similarly, Borio et al. [5] (Table 1), looking at correlations since the beginning of the 20th century, shows the correlation to be slightly negative, and unstable across time.

With respect to the underlying long-term evolutions, I suspect that the *level* of output rather than its growth rate may be the more relevant variable, as argued for example by Von Weizsacker and Kramer 2021 [6]. Poor people do hardly save as their income is just enough to sustain their consumption. The same is true of poor countries. As people become richer, as countries become richer, saving increases, leading to a decrease in the neutral interest rate. Indeed, based on World Bank data, the saving rate in low income countries is much lower than in richer countries, averaging 12% from 1994 to 2007 (the period for which the data exist), compared to about 25% for the world as a whole24

Can demographic evolutions explain some of the decrease in the interest rate? The literature is confusing. Some argue that demographic evolutions have indeed led to a decrease in $r^*$, but they will lead in the future to a major decrease in saving, and thus a higher $r^*$ (Goodhart and Pradhan 2020 [7]). Others argue the opposite and forecast further declines in the interest rate (Auclert et al. 2021 [8]). Yet others, such as Platzer and Peruffo 2021 [9] conclude that demographics explains much of the decrease in $r^*$ but, looking forward, forecast $r^*$ to be about flat from now on.25

There are three major demographic evolutions at play around the world:

The first is the decrease in fertility rates (the average number of children per woman), more pronounced in emerging markets and developing economies, but present nearly everywhere. The global fertility rate has decreased from 5 in 1950 to 2.5 today; looking forward, it is forecast to decrease further, but at a much lower pace, reaching 2.3 in 2045-2050. 26

The second is the increase in life expectancy, which again has happened everywhere. Global life expectancy has increased from 45 years in 1950 to 72 years today. Forecasts are that this will continue at roughly the same pace in the future, except in very rich countries, where the increase will be more limited.27

The third, which was most pronounced in advanced economies, is what is known as the “baby boom,” a major but temporary bump in births after WWII. As baby boomers age, the effect of this bump will fade over time.

To think about the effects of each of these three factors, it is useful to use a simple diagram, based again on a simple overlapping generation structure:

Suppose that people live for two periods, working during the first and receiving an income of 1, retiring in the second and thus consuming out of their saving; suppose that the interest rate and the discount rate are both equal to zero, so people want flat consumption paths. The diagram on the left of Figure 3.7 shows the evolution of the wealth for one consumer throughout his/her life: Wealth increases from 0 to 1/2 at retirement age, and then declines from 1/2 back to zero during retirement. Assuming that population is constant, the cross section of wealth is also given by Figure 3.7 and total wealth in the economy is given by the area of the triangle, thus 1/4 + 1/4 = 1/2.

Now suppose that there is an increase in longevity and that people live for three periods, again working in the first and receiving an income of 1, but now being retired for two periods. The diagram on the right of the figure shows the evolution of wealth for one consumer throughout his/her life. To keep consumption constant throughout life, the consumer now needs to save 2/3 of his/her income when working. Wealth increases from 0 to 2/3 at retirement age, and then declines back to zero over the two retirement periods. Looking at the new steady state, assuming that population is constant, total assets in the economy are given by the area of the triangle, thus 1/3 + 2/3=1, thus twice as much as before.

The assumptions underlying the figure are simplistic, the change in life expectancy obviously too extreme. The dynamic adjustment which takes place when longevity increases is ignored. The age of retirement is assumed fixed; if it increased in proportion to the increase in life, namely by 1/2, the saving rate would remain constant (historically, the retirement age has increased however less than proportionately). The presence of pay-as-you go social security reduces the effect on saving. People save for other reasons than life cycle reasons. People leave bequests. But the basic conclusion is robust, and is a clear and important one: Longer life expectancy is likely to lead to an increase in saving, and thus a decrease in the interest rate.28

Similar exercises can be done to think about the effects of lower fertility, and of the baby boom. I leave computations to the reader, who can use the same diagrammatic approach. A lower proportion of workers relative to retirees decreases overall saving, but decreases income by proportionately more, so the saving rate (which is the ratio of the two) again goes up. The baby boom leads to an increase in the saving rate when the boomers work, and a decrease in the saving rate when they retire, an effect which is relevant today but will fade in the future. The dominant factor however, looking forward, will be longer life expectancy, and this suggests continuing downward pressure on the interest rate.

What about the future?

Investors appear confident that this will remain the case for some time. This can be inferred from deriving risk neutral probabilities from option prices on Treasury bonds of different maturities. The results, as of the time of writing (January 2022), for the United States, are shown in Table 3.1.

Currency | Expiration | $<0\%$ | $<1\%$ | $<2\%$ | $<3\%$ | $<4\%$ |

USD | 5y | 11% | 27% | 54% | 77% | 88% |

USD | 10y | 16% | 29% | 50% | 71% | 84% |

EUR | 5y | 50% | 76% | 88% | 93% | 96% |

EUR | 10y | 38% | 60% | 77% | 86% | 92% |

UK | 5y | 25% | 51% | 74% | 87% | 93% |

UK | 10y | 32% | 52% | 70% | 83% | 90% |

*Source: Private communication.*

Investors give, for example, a probability of 12% to the short US nominal interest rate exceeding 4% in 5 years, a probability of 16% to it exceeding 4% in 10 years; the corresponding probabilities are 4% and 8% for the euro zone, and 7% and 10% for the UK. Probabilities that the nominal rate exceeds 4% are particularly interesting, as this is a plausible forecast of what nominal GDP growth may be over the next 5 to 10 years (2% real and 2% inflation).29

Are they right? I believe they roughly are, both about the fact that the probability is high that safe interest rates remain lower than growth rates for a decade or more, and about the fact that the probability is however less than one.

I read the steady decline in rates as evidence of deep underlying factors at work: Real interest rates have steadily declined in all major economies for more than three decades. This decline has not been due to the Global Financial Crisis or the Covid crisis. In most advanced economies, 10-year real rates are now typically 3% lower than 10-year real growth forecasts.

Large negative values of $(r-g)$ have happened in the past and the sign of $(r-g)$ eventually and sometimes quickly reversed. But these episodes were typically due to unexpected inflation, or to financial repression, to $r$ being less than $r^*$. This is not the case today. If anything, the fact that the ELB is binding indicates that the opposite is true, that $r^*$ is less than $r$.

I wish we had a better sense of exactly which factors have contributed to the decline. The list of suspects is long, but their individual role is not well established. My reading of the evidence leads me to put more weight on shifts in saving, due to demographics and to higher income, and on increases in the demand for liquid and safe assets. In general, looking at the longer list of potential factors, I see no obvious reason why their effect should change sign any time soon.

Some may however. Of the non policy factors, there is, for example, a non negligible probability of a pick-up in the rate of technological progress, associated for example with green investment. This might lead to higher growth (although the effect may be more on the nature of growth than the rate of growth), and thus even more negative $r^*-g$. But it would also lead to a large increase in investment. Estimates are that green investment might increase overall investment by 2.0% of GDP for a decade or more. This would lead to sustained higher aggregate demand and thus an increase in $r^*$.3031

And, coming back to the main theme of the book, the main policy factor, i.e. fiscal policy is likely to matter very much:

A sharp temporary increase in public spending may lead for some time to a sharp increase in $r^*$, forcing central banks to increase $r$ to avoid overheating. At the time of writing, there is a worry that the Biden stimulus of 2021 may indeed lead to overheating, increasing inflation, and the need for the Fed to increase rates substantially32 The effect should however eventually disappear as the effects of the stimulus on demand fade over time.

Pushing the argument further, a sustained sequence of large deficits could increase debt ratios, and by implication increase $r^*$ permanently, increasing $r^*-g$, and even possibly changing the sign of the inequality. Estimates of the effect of debt on the neutral rate in the literature (which are unfortunately not much better than back of the envelope computations; more on this in Chapter 5) suggest that a 1% increase in the debt ratio leads to an increase in the neutral interest rate of 2-4bps. Thus, were (world?) public debt ratios to increase by another 50% of GDP, say, this might lead to an increase in $r^*-g$ of 1 to 2%, substantially narrowing the difference between $r^*$ and $g$. Such a debt outcome is unlikely, but the computation makes the point that the more fiscal policy is used, the higher $r^*$ will be relative to $g$.

Indeed, one of the main conclusions of this book will be that the goal of fiscal policy should be to maintain $r^*$ high enough that the ELB condition is not strictly binding, and possibly higher. If such a fiscal policy is implemented, this would put a floor on how low $r^*$ can be.