The Mayekawa Lecture:
Fiscal Policy under Low Rates:
Taking Stockby Olivier J. Blanchard

I. Introduction
Let me first thank the Bank of Japan (BOJ) for inviting me to the conference. I am
honored to deliver the Mayekawa Lecture. The topic of my talk is fiscal policy under
low rates, which is an issue that I have thought about for a few years. In this lecture I
hope to present my current but evolving thoughts on this topic.
For the past few decades, advanced economies, including Japan, the U.S., and most
European countries, have faced low nominal and real interest rates, and this is thestarting point of my talk. Low interest rates have two important but distinct dimensions.
The first dimension has come to be known as “secular stagnation,” although thisterm may be not the best. I would define this as a situation in which the neutral interest
rate r∗ — the real interest rate consistent with aggregate demand suﬃcient to achieve alevel of output equal to the potential level of output — is less than the growth rate of
the economy g.
The second dimension is the zero lower bound (ZLB) of nominal interest rates,
meaning that nominal interest rates cannot be strongly negative. Although we havelearned that the nominal rate can decrease a little below zero, the ZLB still puts a lower
bound on the real interest rate, which is equal to the nominal rate minus the inflationrate.
We may have secular stagnation without the ZLB, but we have had both in many
countries for the last 10–20 years. Given the prolonged duration, this is a good time totake stock of the situation. As mentioned by Governor Kuroda in his opening remarks,
these two dimensions have serious implications for the way we think about fiscal andmonetary policies.
I focus on three issues that have been discussed at length in Japan but are still highly
relevant. The first issue is what will happen to interest rates in the future. Are we likely
to face both secular stagnation and the ZLB in the future? If interest rates increase tomuch higher levels, we could return to the old way of doing business. The second issue
is how we should assess debt sustainability in the low interest rate environment. It isclear that the old rules regarding levels of debt or debt-to-GDP ratios are just not the................................
The author is Robert M. Solow Professor Economics Emeritus at Massachusetts Institute of Technology, and
C. Fred Bergsten Senior Fellow at the Peterson Institute for International Economics. Transcribed from the
Mayekawa Lecture at the 2021 BOJ-IMES Conference held online by the Institute for Monetary and Economic
Studies of the Bank of Japan on May 24–25, 2021. The views expressed in this lecture are those of the author anddo not necessarily reflect the oﬃcial views of the Bank of Japan.

MONETARY AND ECONOMIC STUDIES / NOVEMBER 2021
DO NOT REPRINT OR REPRODUCE WITHOUT PERMISSION

23

Figure 1 Real 10-year Rates

Sources: Private communication, ECB.

appropriate ones for assessing debt sustainability. Finally, the third and most diﬃcultissue is how we should conduct fiscal policy in this environment. I am going to review
both the theory — the way we have thought about the issue in academia — and thepractical implications for policymakers. I feel slightly awkward in giving this lecture
in Japan because Japanese policymakers have been ahead of the game; they are aheadin taking decisions. In general, they have taken the right decisions and have played amajor role in what has happened and in determining how we think about fiscal policy.

II. Interest Rates Now and in the Future
Let me start with the first question on interest rates now and in the future. There has
been an enormous amount of empirical work on this issue. I would like to focus on threegraphs. The first graph, Figure 1, shows the evolution of 10-year real interest rates in
the U.S., the Eurozone, and Japan. This graph is striking in that it shows interest rates
have been steadily decreasing. It is also clear that the decline in interest rates has beensteady, not just a temporary decline due to the financial crisis or the COVID-19 crisis.
However, Figure 1 is somewhat misleading. Figure 2 shows a longer series, 10year real interest rates for the U.S., going back to 1950 (updating a series constructedby Robert Shiller). If we look at the graph starting in 1985, the decline is absolutely
striking. But, if we take a longer view, it is not obvious that there has been a majordecline. More importantly, it is the 70s and the 80s that look exceptional. In the 70s,
inflation was high, but the nominal rate did not increase accordingly, and thus the real
rate became strongly negative. In the 80s, the Volcker and the Thatcher disinflation led
to a sharp increase in interest rates. This suggests that these two decades are actually the
exceptions, and that we should take out the period between 1970 and 1990 to explore
whether there has still been a decline in interest rates. Figure 2 shows that, while there

24 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2021

The Mayekawa Lecture: Fiscal Policy under Low Rates: Taking Stock

Figure 2 USA Real 10-year Rate

Source: Shiller (2015), updated using Federal Reserve Bank of St. Louis FRED data set.

Figure 3 Real Safe Interest Rate (Global Measure)

Source: Schmelzing (2020).

has indeed still been a decline, it is less dramatic than the decline shown in Figure 1.
To examine the decline further, I am going to show you a third graph, Figure 3,
which was created by Paul Schmelzing of Harvard University, who has made an extremely valuable contribution by finding a series of proxies for the safe interest rate
starting in the 1300s. Based on his work, safe interest rates in various places are shownin Figure 3. At the beginning, they are basically interest rates for Venice borrowing
from the rest of the world. At the end, they are mostly U.S. treasury interest rates. The
decline in interest rates is striking: a decline of about 2–3 basis points a year on aver-25

Table 1 Probability that the nominal interest rate is less than some threshold, 5 or
10 years out
Currency
USD
EUR
GBP
USD
EUR
GBP

Expiry
5y
5y
5y
10y
10y
10y

< 0%
12%
54%
24%
15%
37%
26%

< 1%
29%
81%
53%
25%
61%
44%

< 2%
60%
92%
78%
44%
78%
66%

< 3%
81%
96%
90%
65%
88%
81%

< 4%
90%
98%
95%
80%
93%
89%

Source: Private communication.

age for more than 700 years. Figure 3 indicates therefore that the decline is really anunderlying trend and suggests that it is likely to continue. This is my interpretation ofthis graph and my own assessment of what is likely to happen to interest rates.
The downtrend in interest rates suggests that there are low frequency fundamental
factors at work. While studies of the decline in interest rates have pointed to a range
of factors, two of them seem plausible here. The first factor is that as income has
increased, savings have likewise increased more than in proportion: Poor people andpoor countries save little. In addition, as life expectancy has increased, people havestarted saving for retirement, which has also increased savings. The second factor isan increase in the liquidity of these safe assets. If you had a claim on Venice in the
1300s, it may have been safe but not easy to exchange to get cash. On the other hand, if
you now have treasury bills, you can sell them in the market, and liquidity is no issue.
These could be the two main factors underlying the decline in interest rates and, if so,
the implication is that these low rates are there to remain.
However, there might be bumps in the rates, and I would not be surprised if interest
rates exceeded growth rates occasionally. For example, President Biden’s stimulus program may be too strong, forcing the Fed to increase the interest rate to a level higher
than the growth rate, and this may be the case for a few years. However, what mattershere is not such temporary deviations but the steady state. I think we can assume that
we are going to be with high probability in a regime of secular stagnation for sometime. But not with 100% probability: While we have convincing plausible explanations for past declines in interest rates, we are not sure exactly what factors lie behindthese declines and how powerful a role they will play. If I were a policy maker, I would
therefore work under the assumption that the neutral interest rate r∗ is going to be likely
less than the growth rate g but I would not assume that this will happen with probability
one.
What do investors think? Options traded on sovereign bonds allow us to computethe implied probability of interest rates reaching certain levels in the future. As shownin the first row of Table 1, investors in the U.S. implicitly put the probability at 90%
that the short rate will be less than 4% in 5 years. This is an interesting number because
it is roughly what we expect the nominal growth to be; 2% for the real growth rate and
2% for the inflation rate. Accordingly, they put very high probability on real interest
rates being less than the growth rate 5 years on. The probability goes to 98% for Europe
and a still high 93% 10 years on. Investors clearly expect to be in a low interest rate

26 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2021

The Mayekawa Lecture: Fiscal Policy under Low Rates: Taking Stockenvironment for some time.
Turning to the ZLB, I also think that we are going to be in a regime in which the
ZLB remains relevant for policymakers. While nominal rates will likely be a bit higher
than today, say 2% or 3%, they will still reduce the room that monetary policy has
to maintain output at potential and inflation at the target level in the face of adverse
shocks. This is the world that we should be expecting for the next decade or so.

III. Debt Sustainability
A. Basic Dynamics of Debt-to-GDP Ratios
Let me now move on to the issues surrounding fiscal policy. The first issue is debt sustainability. We now understand that there is no magic number for debt-to-GDP ratios.
Japan has convinced the world that it can sustain a 250% for the ratio of gross debt to
GDP without a debt crisis. The reason is clear. The sustainable level of debt-to-GDP
ratios depends on the safe interest rate, and what matters to a first approximation is the
product of debt-to-GDP ratio and the interest rate.
Let me start from the basic dynamics of debt-to-GDP ratios. I would like to introduce some notations. Let us take d to denote a debt-to-GDP ratio, r the real interest
rate, g the growth rate, and s the primary balance, which is positive if there is a surplus
and negative if there is a deficit. Then, the basic dynamics of debt-to-GDP ratios aredescribed asd=(1 + r)d (−1) − s.
(1 + g)(1)

The primary balance that stabilizes the debt-to-GDP ratio can be computed by equating
the current debt-to-GDP ratio d and the debt-to-GDP ratio last year d(−1) in (1) as toget:s=(r − g)d.
(1 + g)(2)Then, (2) implies, if r − g is negative, that the right-hand side is also negative, whichmeans that the government can stabilize the debt-to-GDP ratio with a negative primarybalance, that is, with a primary deficit.
The implications from (2) can be stated in three ways. First, as I have just shown,
the government can run a primary deficit to keep the debt-to-GDP ratio constant. Second, even if the government runs an even larger primary deficit, the debt-to-GDP ratio
will converge to a higher value, but it will not explode. In other words, when r − g isnegative, debt can increase to high levels, but it does not spiral out of control in theway that it would if r − g were positive. Third, maybe even more strikingly, it implies
that the government can issue more debt without having to raise taxes later to pay for
it. The reason is that issuing more debt raises the debt-to-GDP ratio, but, from then,the debt ratio will slowly decrease over time as r − g is negative in equation (1). Whois paying for the higher debt, if not the taxpayers? Implicitly, it is the investors who areaccepting such a low rate.

27

If we were in a world in which r − g was negative forever with probability 1, all these
conclusions would be the right ones, and there would be no issue of debt sustainability.
However, this is much too strong a statement, and there are two reasons why wemust be careful about debt sustainability. The first reason is uncertainty. As I mentioned, while the probability that r will be greater than g is small, it is positive andone must take this probability into account. Debt sustainability could be an issue if wehave a high level of debt and there is a change in the environment. If the debt-to-GDP
ratio is very large, as in Japan, the impact of a change in r − g becomes magnified. Insuch a case, you may find yourself having to generate a much greater primary surplus
if circumstances go against you.
The second reason is the eﬀect of debt itself on the real interest rate r throughcrowding out. In a closed economy, when government debt increases, capital is
crowded out and the marginal product of capital increases. Then, at a suﬃciently highlevel of debt, r will eventually exceed g. Hence, there is a limit on debt sustainability.
In an open economy, since what matters, if financial markets are integrated, is moreglobal than national debt, an individual country has more room to issue debt, but thereis eventually also a limit to the level of global debt.
B. How to Assess Debt Sustainability
Having provided general considerations, I want to move on to how to assess debt sustainability. First, “debt sustainability” needs to be defined. Let me oﬀer a definition.
Debt is sustainable if the probability that a country will be able to generate a suﬃcient
primary balance to cover interest payments over the next 5–10 years (longer horizons
that have just too much uncertainty) is very high. This is an operational definition,
which is clear and implementable:
The probability of debt sustainability depends not just on the level of debt, but also
on several other factors. The first factor is the distribution of r − g, which I have alreadydiscussed. Both the expected path of r − g (the first moment) and how much r − g
can fluctuate (the second moment), and in particular the probability that r − g turns
positive, matter. Second, it is also important to take into account implicit liabilities.
Pension systems and social insurance may have to be partly financed from the budget
in the future. Third, the path of a primary balance must be taken into consideration, including both the first and the second moments. Fourth, the initial tax level is important,because the higher the initial tax rate, the less the room there is to generate a primary
surplus by increasing taxes. For example, my country, France, is perhaps close to thelimit of increasing taxes. Fifth, the nature of the government also matters. If a large
adjustment is needed to shift from, say, a primary deficit to a primary surplus, it will bepolitically costly. It therefore makes a diﬀerence whether, for example, the governmentis a coalition or a single party government. The ability to implement large adjustments
depends on the political circumstances. Finally, debt maturity is important, because, if
r − g changes, the dynamic eﬀects on debt payments will depend on the maturity ofthe debt. If the maturity of the debt is long, it gives more time for the government toadjust. If the maturity of debt is 10 years, for example, the fiscal authority has roughly
10 years to move from a primary deficit to a primary surplus. On the other hand, if thematurity of debt is just one year, the fiscal authority is likely to be in serious trouble.

28 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2021

The Mayekawa Lecture: Fiscal Policy under Low Rates: Taking Stock

A general rule that captured all these elements and ensured debt sustainability justcannot be written ex ante. This is the problem for example with European Union fiscal rules: they cannot fit all situations. This is an assessment that can only be done
at one time in one place, each year, in each country. The right tool exists. It is calledstochastic debt sustainability analysis (SDSA), and it can be used to compute, basedon existing policies and commitments, the distribution of outcomes 5 or 10 years on. It
allows one to assess the probability that, based on existing policies and commitments,
the government will fail to either cover the interest payments on the debt, and debt will
increase. It then allows an examination of what the government needs to do to avoid
that outcome. I have seen this method used a number of times when I was at the IMF,
and although a full SDSA depends on many assumptions and does not give definitive
answers, I have found that it does allow for a very useful discussion. It requires thecontribution of an independent expert authority to ensure the plausibility and the reliability of results. And if that expert authority, for example a fiscal council, concludes
that there is an issue regarding debt sustainability, there must be a process throughwhich the government explains how it will modify its policies, and a monitoring process of how the issue evolves over time. I believe a process along these lines is the way
to assess debt sustainability.
C. Multiple Equilibria and the Role of Central Banks
Sometimes, interest rates increase suddenly. One of the reasons is that sovereign bondmarkets are prone to multiple equilibria, a phenomenon we call “sudden stops.” Even if
there is no change in fundamentals, if investors start becoming anxious and anticipate
some probability of default, they will ask for a higher spread. Unfortunately, thesehigher rates may well make their worries self-fulfilling by making it harder for thegovernment to control debt, and thus there can be a large range of equilibria. We haveplenty of models in which this happens, and there are a plenty of cases where this has
in fact happened. Emerging market economies are particularly prone to this danger, but
it is not irrelevant even for advanced economies.
The question then is, what should be done when this happens? One response would
be to ensure a level of debt so low that these worries about default cannot become
self-fulfilling. If debt is very small, even a larger spread will not lead to much larger
interest payments. However, this response is misguided, because the range of multiple
equilibria where we can have both a normal equilibrium or a bad one can be very large.
Hence, fiscal austerity that reduces the debt-to-GDP ratio from 100% to 90% does not
eliminate multiple equilibria. So, this does not provide a good argument for trying to
reduce debt, because it would be necessary to reduce debt-to-GDP ratios to 40% say,which is not possible over only a decade or so.
Central banks have a role to play here. If investors start worrying about debt sustainability without any change in fundamentals, central banks with deep pockets canplay the role of a large stable investor to prevent self-fulfilling non-fundamental runs
on government debt. This is what the BOJ has been doing. In this case, investors haveno reason to fear and do not run. This has worked so far.
However, I feel a warning is warranted here. When investors’ concerns partly reflect
adverse changes in fundamentals and a higher risk of default, it is not certain that29

central banks’ interventions will succeed. Central bank interventions basically swap
two assets. That is, when a central bank intervenes, it buys government bonds andissues central bank reserves — which typically pay an interest rate close to that on
short term government bonds. This swap of government debt for bank reserves is justa change in the composition of the liabilities of the consolidated government (central
government plus central bank), but the total liabilities of the consolidated government
have not changed. Thus, this swap does not reduce overall default risk, and the spreadon government bonds may not come down despite the central bank intervention. So far,
BOJ and other central banks interventions have been successful in reducing spreads.
So my concerns may be overblown, but I still worry that central banks’ interventions
may not work if investors get worried about an increase in fundamental risk. This is an
issue I think warrants careful consideration.

IV. Optimal Debt Policy
A. Dynamic Ineﬃciency
Let me now move on to the final topic, optimal debt policy. This is diﬀerent from debt
sustainability: we may be able to sustain debt at a 150% of GDP, but that does notmean that such a level of debt would be the right level to aim at.
In considering optimal debt policy in terms of welfare, a major question is whether
low rates are a sign of what is called “dynamic ineﬃciency.” Dynamic ineﬃciency
means that there is too much capital and the marginal product of capital is too low,which is reflected in safe interest rates as well as other rates. To explore this issue, Peter
Diamond, more than 50 years ago, developed an overlapping generation model andshowed that, when r was less than g, this was a sign of excess capital accumulation1. In
this case, he showed, issuing more debt would be welfare-improving. All generations
would benefit from the government issuing debt until additional crowding out of capitalmade the interest rate equal to the growth rate. By the government issuing debt andusing the funds to distribute goods to those currently alive, those currently alive would
be better oﬀ. Capital would be crowded out and future generations would have lesscapital, but this would be beneficial because capital was just not very productive in thefirst place.
When I was teaching at MIT, I used to say that this was an important theoreticalpossibility, but it would probably never happen. I am not so sure today.
The question is what rates should we be looking at in assessing dynamic ineﬃciency? Should we be looking at the safe rate, which is less than g, or at the averagemarginal product of capital, which is higher than g? I started considering these questions three years ago in my AEA Presidential Lecture2 . I found that indeed, there was astrong presumption for the safe rate, i.e. the risk adjusted marginal product of capital,
to be the right rate to compare to the growth rate, suggesting that we were indeed in a
regime of dynamic ineﬃciency. But I showed that potential general equilibrium eﬀects
implied that the right rate was close to but was not quite the safe rate. Basically, it................................
1. For details, see Diamond (1965).
2. For details, see Blanchard (2019).

30 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2021

The Mayekawa Lecture: Fiscal Policy under Low Rates: Taking Stockwas a weighted average of the safe rate and the average marginal product of capital.
Turning to the data, this implied that the condition for dynamic ineﬃciency may not besatisfied, that the welfare cost of debt might be positive, but quite small.
The safe rate may not the appropriate rate to be looking at for at least two other reasons. The first reason is the equity premium puzzle, which is one of the major unsolved
puzzles in macroeconomics. Investors ask for a large premium on risky assets. Putanother way, they accept very low safe rates given the average rate of return on risky
assets. It is hard to reconcile this behavior with what we think are reasonable degrees
of risk aversion. Until we can explain the equity premium, we should be careful to takethe safe rate as a good indicator of what the correctly risk-adjusted marginal productof capital. The second reason is known as “financial repression,” which has happened
many times in history. Under financial repression, the treasury forces central banks or
private banks to hold sovereign bonds at low rates. Although we no longer observe, in
advanced economies, this kind of explicit financial repression, we have something similar in the macro prudential liquidity requirements, though these are perfectly justified
in terms of financial stability. Liquidity requirements force banks to hold more safe assets than they would want, with the result that safe rates are depressed relative to what
they would otherwise be. This eﬀect should also be taken into account in considering
the appropriate rate for assessing dynamic ineﬃciency.
My bottom line guess is that we are probably not in the dynamic ineﬃciency region,
but that debt is not so costly from a welfare viewpoint, because private capital is justnot highly productive. While debt crowds out capital, the cost of issuing debt may not
be very large in terms of welfare. In the current environment, if governments have gooduses for debt, they should issue more.
B. Practical Advice for Policymakers
Finally, I want to translate the above discussion into practical advice for policymakers.
I proceed in two steps.
In the first step, I ignore the ZLB and assume that monetary policy can choose theappropriate interest rate to maintain output at potential. In this case, we do not haveto worry about the adverse eﬀect of fiscal austerity on demand and in turn on output:
monetary policy can undo those adverse eﬀects. Then it is probably better to slowly
decrease debt-to-GDP ratios, for two reasons. First, a decrease in debt-to-GDP ratios
enhances debt sustainability, albeit very slowly. Realistically, the process must be slow:
an annual decrease in debt-to-GDP ratios of 1% or 2% at most. The limit is given bywhat monetary policy can oﬀset. Any faster decrease might be too much to be oﬀset
by monetary policy. Second, if we believe that the economy is dynamically eﬃcient,a slow decrease in debt-to-GDP ratios improves the welfare of future generations. Increasing debt may however be justified if it is used for investment to improve the future,such as investing in measures to limit global warming.
The world considered in the first step is not however the world we are likely to be inin the next decade or so. As I discussed before, the ZLB will be relevant in the following
sense: Although the ZLB may not be strictly binding, the low nominal interest rateenvironment will continue, and this will reduce the room central banks have to oﬀset
the adverse eﬀects of fiscal austerity on output. The first step ignored the ZLB. Now

31

in the second step, let me begin by assuming that the ZLB is strictly binding, so that
central banks cannot maintain output at potential even absent adverse shocks, which isthe situation in many countries at this point. In this case, it is obvious that fiscal policy
is needed to keep output at potential. The fiscal authority must run a deficit suﬃcient
to increase demand and get the economy back to full employment. There is a trade-oﬀ:
running a deficit gets output closer to potential, but it entails a slightly higher future costand a slightly lower probability of debt sustainability. If the probability of sustainability
remains high however, there is no question about the desirability of running deficits inthis case. This is what the Japanese authorities have concluded and decided to do, andI totally agree with that decision. Even if the ZLB is not strictly binding and nominalinterest rates are, say, 2% or 3%, there may still be limited room for monetary policy
to react to adverse shocks, in which case governments will again need to be ready touse expansionary fiscal policy. The implication of this line of arguments is that, withlow rates, fiscal policy has become much more important than it used be. With respect
to adverse shocks, we must design much stronger and better automatic stabilizers.
COVID-19-related spending is an example of appropriate policies that have given
protection to firms and people and increased aggregate demand. “Whatever it takes,”
even if the COVID-19-related fiscal spending increased deficits and debt, was the rightpolicy principle.
With respect to public investment, two things are worth mentioning. First, weshould make sure that all public investment that has a risk adjusted social rate of return higher than the safe rate is done. In what areas could such investments be madein Japan? Although Japan may have no great need for traditional infrastructure investment, such as in roads and bridges, there are many other dimensions to public
investment. Some of these have been triggered by COVID-19, and this is clearly an
area in which public investment is possible. So is the need for public (and private)
green investment. Second, whether such spending is financed by debt or taxes should
depend on the state of the economy. If private demand is too weak to achieve potential
output, spending should be financed by debt, which is more expansionary. On the other
hand, if private demand is strong enough, spending should be financed by taxes. Thisis a very simple financing rule, which depends on the state of the economy.
Let me take on a last issue. What if we remain in an environment in which the
ZLB keeps binding and the fiscal deficits required to boost aggregate demand are large
enough to lead to a steady increase in debt ratios? Again, this resonates with Japanbecause Japan has been in such a situation for a long time. Suppose that that situation
lasts for another ten or twenty years. Other ways to stimulate demand will have to beconsidered, because at some stage the debt levels will become too high. What can be
done?
Theoretically, there are two ways to stimulate demand: reduce saving or increase
investment. On the saving side: I do not know how much room there is in Japan toreduce precautionary saving, but, in the U.S. for example, having a good health insurance system such as Medicare for all would make a considerable diﬀerence. It would
be good on its own, and most likely decrease precautionary saving. On the investment
side: During the COVID-19 pandemic we have realized that there is a number of potential public investment projects which are very much needed, many in the form of

32 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2021

The Mayekawa Lecture: Fiscal Policy under Low Rates: Taking Stock

R&D, with respect to both public health and global warming issues. There is also someevidence that the spillover eﬀects of public green investment on private green investment can be quite strong. If we did either one or both of these measures, we could
maintain output at potential without having to run large deficits and increase debt. Thissounds worth exploring.
Although there is much more to be done, this summarizes my thoughts at this point.
Thank you very much.

33

References
Blanchard, Olivier, “Public Debt and Low Interest Rates,” American Economic Review, 109(4), 2019,
pp. 1197–1229.
Diamond, Peter A., “National Debt in a Neoclassical Growth Model,” American Economic Review,
55(5), 1965, pp. 1126–1150.
Schmelzing, Paul, “Eight Centuries of Global Real Interest Rates, R-G, and the ‘Suprasecular’ Decline, 1311–2018,” Bank of England Staﬀ Working Paper No. 845, Bank of England, 2020.
Shiller, Robert J., Irrational Exuberance: Revised and Expanded Third Edition, Princeton, NJ:
Princeton University Press, 2015.

34 MONETARY AND ECONOMIC STUDIES / NOVEMBER 2021