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BIS Working Papers
No 685
Why so low for so long?
A long-term view of real
interest rates
by Claudio Borio, Piti Disyatat, Mikael Juselius and
Phurichai Rungcharoenkitkul
Monetary and Economic Department
December 2017
JEL classification: E32, E40, E44, E50, E52.
Keywords: Real interest rate, natural interest rate,
saving, investment, inflation, monetary policy.
BIS Working Papers are written by members of the Monetary and Economic
Department of the Bank for International Settlements, and from time to time by other
economists, and are published by the Bank. The papers are on subjects of topical
interest and are technical in character. The views expressed in them are those of their
authors and not necessarily the views of the BIS.
This publication is available on the BIS website (www.bis.org).
© Bank for International Settlements 2017. All rights reserved. Brief excerpts may be
reproduced or translated provided the source is stated.
ISSN 1020-0959 (print)
ISSN 1682-7678 (online)
Why so low for so long?
A long-term view of real interest rates
Claudio Borio, Piti Disyatat, Mikael Juselius and Phurichai Rungcharoenkitkul†
2 December 2017
Abstract
Prevailing explanations of the decline in real interest rates since the early 1980s are premised
on the notion that real interest rates are driven by variations in desired saving and investment.
But based on data stretching back to 1870 for 19 countries, our systematic analysis casts doubt
on this view. The link between real interest rates and saving-investment determinants appears
tenuous. While it is possible to find some relationships consistent with the theory in some
periods, particularly over the last 30 years, they do not survive over the extended sample. This
holds both at the national and global level. By contrast, we find evidence that persistent shifts
in real interest rates coincide with changes in monetary regimes. Moreover, external influences
on countries’ real interest rates appear to reflect idiosyncratic variations in interest rates of
countries that dominate global monetary and financial conditions rather than common
movements in global saving and investment. All this points to an underrated role of monetary
policy in determining real interest rates over long horizons.
JEL classification: E32, E40, E44, E50, E52.
Keywords: Real interest rate, natural interest rate, saving, investment, inflation, monetary
policy.
We would like to thank Iñaki Aldasoro, Marco Buti and colleagues, Stijn Claessens, Andy Filardo, Marc Flandreau,
Joseph Gagnon, Gaston Gelos, Charles Goodhart, James Hamilton, Esa Jokivuolle, David Laidler, Enrique Martínez-
García, Luis Brandao Marques, Elmar Mertens, Emanuel Mönch, Francisco Nadal de Simone, Edward Nelson,
Lukasz Rachel, Umang Rawat, Daniel Rees, Larry Schembri, Hyun Song Shin, Nathan Sussman, Alan Taylor, Kostas
Tsatsaronis, Gregory Thwaites and BIS seminar participants for helpful comments and discussions. Amy Wood,
Diego Urbina and Giulio Cornelli provided excellent statistical assistance. All remaining errors are ours. The views
expressed are those of the authors and do not necessarily represent those of the Bank for International
Settlements, Bank of Finland or the Bank of Thailand.
†Rungcharoenkitkul (corresponding author), Senior Economist, Bank for International Settlements,
phurichai.rungcharoenkitkul@bis.org; Juselius: Senior Research Economist, Bank of Finland, mikael.juselius@bof.fi;
Borio: Head of Monetary and Economic Department, Bank for International Settlements, claudio.borio@bis.org;
Disyatat: Executive Director, Puey Ungphakorn Institute for Economic Research, Bank of Thailand, pitid@bot.or.th.
iv
Table of contents
Introduction ................................................................................................................................................................. 1
1. Real interest rate determination: an overview of approaches.................................................... 2
2. Real interest rate determination: the role of real factors ............................................................. 6
2.1 Essential elements of the empirical strategy ........................................................................ 6
2.2 Data and definition of variables ................................................................................................ 8
2.3 A first look at the data ............................................................................................................... 10
2.4 Tests and main results ................................................................................................................ 12
3. Real interest rate determination: the role of monetary factors .............................................. 21
3.1 Analytical considerations .......................................................................................................... 21
3.2 Previous work ................................................................................................................................ 25
3.3 New evidence on monetary policy regimes ...................................................................... 26
3.4 A monetary narrative of the evolution of real interest rates ...................................... 34
Conclusion ................................................................................................................................................................. 36
References ................................................................................................................................................................. 38
Annex A: Data and plots ...................................................................................................................................... 44
A.1 Data sources and coverage ...................................................................................................... 44
A.2 Data plots of real interest rates .............................................................................................. 46
A.3 Saving-investment factors for the United States and United Kingdom ................. 52
Annex B: Robustness results .............................................................................................................................. 53
B.1 Bivariate panel regression with time trends ...................................................................... 53
B.2 Average dependent and independent variables ............................................................. 54
B.3 Short-term market rates as the dependent variable ...................................................... 56
B.4 Excluding periods after the world wars ............................................................................... 60
B.5 Alternative expectations of inflation and GDP growth ................................................. 61
B.6 Savers’ ratio as an independent variable ............................................................................ 63
B.7 Time-varying retirement age interactions with demographic variables ................ 64
B.8 Productivity growth as an independent variable............................................................. 65
B.9 Risk premium as an independent variable ......................................................................... 66
WP685 Why so low for so long? A long view of real interest rate determination 1
Introduction
Global real (inflation-adjusted) interest rates, short and long, have been on a downward trend
throughout much of the past 30 years and have remained exceptionally low since the Great
Financial Crisis (GFC). This has triggered a debate about the reasons for the decline. Invariably,
the presumption is that the evolution of real interest rates reflects changes in underlying
saving-investment determinants. These are seen to govern variations in some notional
“equilibrium” or natural real rate, defined as the real interest rate that would prevail when
actual output equals potential output, towards which market rates gravitate.
The presumption that real interest rates are so anchored is evident in two broad analytical
strands.
The first focuses on observed real interest rates and relates them directly to the evolution
of the factors that underpin the economy’s saving-investment balance (eg IMF (2014), Bean et
al (2015), Council of Economic Advisers (2015)). One prominent variant is the hypothesis that
persistently weak demand for capital, a rising propensity to save and lower trend growth have
brought about an era of “secular stagnation” (Summers (2014, 2015)). Another variant argues
that a higher propensity to save in emerging market economies (EMEs), coupled with investors’
growing preference for safe assets, has boosted the supply of saving worldwide (Bernanke
(2005), Broadbent (2014), Caballero et al (2008)). Most recently, demographic changes have
been singled out (Carvalho et al (2016), Gagnon et al (2016), Rachel and Smith (2017)). This
strand typically does not consider inflation explicitly and links real interest rates directly to the
posited real-sector determinants. In effect, it assumes that over the relevant horizon the
observed (market) rate and the unobserved natural rate coincide.
The second strand focuses on the equilibrium or natural real rate, estimated as an
unobserved variable in a filtering system (eg Laubach and Williams (2015), Justiniano and
Primiceri (2010)). Typically, the natural rate is anchored to theory-prescribed variables, such as
potential growth and household preferences, which are themselves unobserved, and inflation
plays a critical role in pinning down the natural rate alongside the other latent system variables.
In Laubach and Williams (2003), for example, rising inflation indicates that output is above
potential and, correspondingly, that the actual interest rate is below the natural rate; falling
inflation indicates the reverse. These reflect the well known Phillips-curve and aggregate-
demand (IS) relationships that lie at the core of standard macroeconomic models.
Both strands share a couple of limitations. The bulk of the analysis examines the period
since the mid-1980s, when real interest rates have been declining. And neither tests directly
the hypotheses that the postulated saving-investment framework and/or the postulated
inflation determination process adequately characterise the data. These are regarded as
maintained hypotheses, be it in the underlying narrative and calibration of structural models
or in the filtering systems. There is little by way of direct estimation that tests the link between
observable variables, such as demographics, and real interest rates. Notable exceptions are
Hamilton et al (2015) and Lunsford and West (2017), who consider some such variables over
longer periods.
We aim to fill this gap by systematically examining the empirical link between real interest
rates and the posited determinants, not just since the 1980s but also back in history. Based on
data starting in the 19th century for 19 economies, we find only a tenuous link between real
interest rates and observable proxies for the main saving-investment determinants. Some
variables, notably demographics, do exhibit the expected relationship with real interest rates
2 WP685 Why so low for so long? A long view of real interest rate determination
in some subsamples, especially in the more recent one. But there is little evidence of a stable
relationship across subsamples. This applies to both domestic and global variables.
Going beyond the standard factors, we investigate whether monetary policy has persistent
effects on real interest rates. In our long sample, monetary policy regimes, such as the gold
standard, Bretton Woods and inflation targeting, go hand-in-hand with significant shifts in real
interest rates. At a global level, we find that the influence of external factors on countries’ real
interest rates reflects the importance of the financially dominant countries’ role as global
monetary anchors rather than common variations in global saving-investment determinants.
This suggests that co-movements in real interest rates across countries are more closely
related to the monetary policy of global anchor countries than to factors such as a global
saving glut.
Overall, our results raise questions about the prevailing paradigm of real interest rate
determination. The saving-investment framework may not serve as a reliable guide for
understanding real interest rate developments. And inflation may not be a sufficiently reliable
signal of where real interest rates are relative to some unobserved natural level. Monetary
policy, and financial factors more generally, may have an important bearing on persistent
movements in real interest rates.
The rest of the paper is organised as follows. Section 1 provides an overview of existing
approaches to explaining real interest rates, highlighting their limitations. Section 2 analyses
the relationship between real interest rates and a standard set of real-sector determinants for
a cross section of countries over a long time span. Section 3 explores the possible role of
monetary factors. The final section concludes. The Annexes provide detailed information about
the data and robustness tests.
1. Real interest rate determination: an overview of approaches
Prevailing approaches to explaining real interest rates are premised on the notion that the
desired (ex ante) supply of saving and the desired (ex ante) demand for investment determine
some notional equilibrium real interest rate consistent with full employment or output at
potential, also known as the “natural rate”. This notion takes root in the “loanable funds”
framework, where saving-investment determinants drive the demand for, and supply of, funds
that pin down the market-clearing interest rate (in equilibrium at the marginal product of
capital).1 The framework therefore focuses on the determinants of saving and investment.
On the saving side, the standard building block is grounded on households’ optimising
intertemporal consumption decisions, as captured by the Euler equation. The derived saving
function depends positively on unobserved intertemporal preferences and expected
consumption growth (or output growth in equilibrium). With household heterogeneity,
demographic variables and income distribution also come into play. A higher life expectancy
influences life-cycle decisions, raising desired saving and lowering the equilibrium real interest
rate. A higher dependency ratio lowers saving and raises the real interest rate as the working-
age population saves more than younger and older cohorts. Population growth influences
1 See Wicksell (1898) and Woodford (2003). As discussed in detail in Borio and Disyatat (2011, 2015), despite the
term, this market for funds is in fact a market for goods and bears no relationship to the flow of financing that
actually underpins economic activity. In fact, in contrast to current usage (eg Mankiw (2013)), even in the original
literature, “loanable funds” was not used as synonymous with “saving”, as credit also played a key role (eg
Robertson (1934) and Ohlin (1937)).
WP685 Why so low for so long? A long view of real interest rate determination 3
both the demographic dynamics and the capital-labour ratio, resulting in offsetting effects on
interest rates (Carvalho et el (2016)).2 Higher income inequality increases saving, as richer
households have a higher marginal propensity to save.
On the investment side, firm profit maximisation and the resulting demand function for
capital point to the relevance of factors such as the relative supply of labour and capital,
population growth, investment profitability, productivity growth and the relative price of
capital to that of output. Cheaper physical capital, eg from technological advances, means that
less investment is needed to maintain the same level of production. Provided this income
effect always dominates, as typically assumed, the relative price of capital should go hand-in-
hand with higher desired investment, and hence higher real interest rates.
If economies are financially integrated, the equivalent global variables matter as well. For
example, the saving glut hypothesis (Bernanke (2005)) posits that desired saving in emerging
markets has put downward pressure on real rates globally. Similarly, a greater demand for safe
assets (Caballero et al (2008, 2016)) may help explain declining risk-free rates. More generally,
a higher risk premium may lower desired investment and raise desired saving.3
The corresponding explanations for declining and persistently low real interest rates
follow essentially two approaches. The first, which focuses on observed real interest rates and
relates them directly to the evolution of the factors that underpin the economy’s saving-
investment balance, comes in two variants. One is largely narrative: it tells plausible stories
relating real interest rates to its determinants, typically based on informal inspection of the
behaviour of the relevant variables (eg IMF (2014), Bean et al (2014), Eichengreen (2015) and
Council of Economic Advisers (2015)). The other is calibration: this systematically uses theory
to identify factors behind shifts in real interest rate trends, and data to calibrate the
corresponding structural models (eg Gagnon et al (2016), Carvalho et al (2016), Eggertsson et
al (2017), Rachel and Smith (2017), Thwaites (2015), Vlieghe (2017)). In this variant of the first
approach, theory dictates the relationships and the data are only used to gauge their
quantitative importance conditional on the theory being true. The second approach is filtering:
this recovers equilibrium real interest rates statistically by anchoring them to some economic
relationships, notably the link between economic slack and inflation – the Phillips curve (eg
Laubach and Williams (2003, 2015), Holston et al (2016), Justiniano and Primiceri (2010), Del
Negro et al (2017) and Johannsen and Mertens (2016)). Table 1 provides a summary of selected
studies.
How far does the resulting empirical evidence support the hypothesis that saving-
investment imbalances have driven real interest rates to such low levels? Existing studies, in
our view, have provided estimates of the extent to which saving-investment determinants can
explain real interest rate movements conditional on the theory, but not convincing evidence
supporting the underlying theory itself. Too much of the theory has been embedded in
maintained hypotheses and thus its validity has not been subject to a test.
This conclusion is most obvious for the narrative variant of the first approach, which never
quite tests the saving-investment framework. Rather, it uses it to see what factors appear to
be more consistent with the downward trend in rates. And since it largely relies on informal
inspection of bilateral relationships graphically, it is not that hard to find some that appear to
2 Lower population growth raises the old-age dependency ratio, increasing the equilibrium real interest rates. But
it also raises the capital-to-labour ratio and lowers the marginal product of capital. The net effect on the
equilibrium real interest rate is a priori ambiguous.
3 The risk premium is defined as the difference between the cost of capital and the risk-free rate. Risk premium
shifts may originate from a repricing of risks (eg due to demand for safe assets, as in Gourinchas and Rey (2016)
and Del Negro et al (2017)) or changes in underlying risks (eg productivity growth uncertainty, as in Marx et al
(2017) or Vlieghe (2017)).
4 WP685 Why so low for so long? A long view of real interest rate determination
hold for at least part of the time. This type of analysis is best interpreted as a first look at the
data and as a basis for a more in-depth evaluation. Nor, in all fairness, does it pretend to be
more than that.
Calibration based on structural models – the second variant of the first approach – takes
the narrative approach much further. It quantifies the effect that specific saving and investment
factors would have within a fully specified theoretical model that is calibrated to fit the data
as closely as possible. Hence, it provides information about the relative importance of the
different factors in a general equilibrium setting, while at the same time addressing the
challenges raised by regime changes and expectations. Nevertheless, just as with the informal
approach, the validity of the underlying theory is not tested. Moreover, the models typically
include parameters that are poorly identified and have no clear benchmark values. The
resulting large number of degrees of freedom complicate the evaluation of the final results:
there is a risk that the importance of particular factors may be overstated or specific periods
“overfitted”.4
The filtering approach faces similar challenges. Here, the role of a priori restrictions on the
data is critical. In particular, one typical key maintained hypothesis is that inflation provides
the right signal to identify cyclical deviations of the market rate from the natural rate. All else
equal, if, say, inflation increases, it is inferred that output is above potential (Phillips curve),
which in turn implies that the market rate is below the natural rate (IS curve). And yet, the link
between economic slack and inflation has proved rather weak and elusive over the years,
making any firm inferences suspect (ie Forbes et al (2017), Stock and Watson (2007), Borio
(2017a)). Indeed, recent work has found that financial cycle proxies capture cyclical output
variations better than inflation (Borio et al (2017), Kiley (2015)), yielding natural interest rate
estimates that are somewhat higher and decline by less (Juselius et al (2017)). Moreover,
filtering approaches typically relate the unobserved natural rate to other unobservable
variables in the system, such as potential growth and preferences, giving rise to many degrees
of freedom when fitting the story. Thus, the maintained hypothesis ends up having a decisive
influence on the end-result (see Lubik and Matthes (2015) for a similar critique). And as with
calibration, the risk of “overfitting” in any given sample is material.
4 To be more precise, in calibration, the researcher choses values for both the structural parameters and unobserved
shock processes to mimic some key features of the data. These commonly include steady-state ratios between
variables, second moments of selected variables and so on. Yet the key features typically only constitute a small
subset of the model’s full implications for the data and there is less discipline in the remaining directions. This
gives the investigator considerable degrees of freedom when fitting the features of interest at the expense of
general model fit. Equally problematic is the high reliance on persistent shock processes or unobserved stochastic
trends. With sufficiently many such processes, the model can generate a perfect fit without an increase in
predictive power – a case of “overfitting”.
WP685 Why so low for so long? A long view of real interest rate determination 5
All this highlights the importance of confronting the hypothesis more directly with the
data, examining systematically the relationship between real interest rates and observable
variables. And yet, there are very few studies that do this. Much of this work examines an earlier
period – the surge of real interest rates in the early 1980s (Blanchard and Summers (1984),
Barro and Sala-i-Martin (1990), Orr et al (1995)). Hardly any have covered the more recent
phase of declining rates. An exception is Lunsford and West (2017), who focus on the United
States for the period 1890-2015 and evaluate the bivariate correlation between real interest
rates and a number of factors. The authors find weak evidence overall, particularly for variables
representing aggregate growth (GDP, consumption, total factor productivity (TFP)), though
they do find some support for demographic variables (for the weak explanatory power of
output growth, see also Hamilton et al (2015)). Our paper complements this work by
considering a wider set of countries, conducting joint-specification analysis to allow for
interactions between explanatory variables, and exploring the role of monetary policy.
A summary of selected studies on real interest rate determination Table 1
Study Methodology Coverage
Key factors
Growth & productivity
Demographics
Relative price of capital
Inequality
Global saving glut
Demand for safe assets
Risk premium
Others
IMF (2014) Narrative Global X X X X
Bean et al (2015) Narrative Global X X X X X
Eichengreen (2015) Narrative US X X X X
CEA (2015) Narrative Global X X X X X
Goodhart and Pradhan (2017) Narrative Global X
Gagnon et al (2016) Calibration US X
Carvalho et al (2016) Calibration Global X
Rachel and Smith (2017) Calibration Global X X X X X X
Thwaites (2015) Calibration Global X
Vlieghe (2017) Calibration UK X X
Marx et al (2017) Calibration Global X X X
Eggertsson et al (2017) Calibration US X X X X
Del Negro et al (2017) Filtering US X X
Laubach and Williams (2003) Filtering US X
Holston et al (2016) Filtering Four advanced X
Justiniano and Primiceri (2010) Filtering US X
Clarida (2017) Filtering Four advanced X
Gourinchas and Rey (2016) Predictive regression Four advanced Consumption
-to-wealth
Hamilton et al (2015) Long-run correlation Global X
Lunsford and West (2017) Long-run correlation US X X X X X X Money
growth
6 WP685 Why so low for so long? A long view of real interest rate determination
Indeed, a common premise of all the traditional approaches is that real interest rates over
long horizons are determined exclusively by real factors. Monetary policy exerts only a
transitory influence, which can be entirely ignored (narrative and calibration analysis) or
filtered out (filtering analysis). The maintained assumption is that monetary policy is neutral in
the long run. For example, Del Negro et al (2017, p 1) describe the natural rate as “… the
counterfactual rate that would be observed ‘in the absence’ of monetary policy”. Still, in our
view, the notion that in a complex monetary economy it is possible to cleanly delineate a
“monetary veil” from the underlying real drivers is an exceedingly strong presumption. This
presumption has not been sufficiently scrutinised. In Section 3 we explore its validity and
usefulness in the current context.
2. Real interest rate determination: the role of real factors
We next exploit long historical data and cross-country variation to test for long-term
relationships between real interest rates and the saving-investment determinants suggested
by theory. We impose no prior restrictions on these relationships and allow the data to speak
about their nature and stability. Before turning to the data and estimation, we outline the
essential elements of our empirical approach.
2.1 Essential elements of the empirical strategy
As noted, the standard saving-investment framework relies on the assumption that money is
neutral “in the long run”, so that only real factors drive real interest rates. Of course, strictly
speaking, the “long run” is an analytical concept. It is the result of a thought experiment: it
refers to a situation in which all the variables in the system, most notably prices, have been
allowed to adjust (a steady state). For the empirical analysis, that concept has to be translated
into calendar time.
Concretely, this can be done as follows:
=∗(;)+
(1)
where is the real interest rate, ∗ is the equilibrium real interest rate, which is a function of
saving-investment factors, , with parameters , and captures movements in the real
rates due to monetary policy. We assume that the ∗(∙) function is approximately linear, so
that ∗(;)=
. The more important assumption is that monetary policy does not have
lasting real effects on the real rate, which can be written formally as ~(0). We relax this
assumption in Section 3.
Given that monetary policy does not have lasting effects, Equation (1) implies that any
low-frequency movements or permanent changes in the real rate reflect solely saving-
investment factors.5 For instance, both the real interest rate and the saving-investment factors
display dynamics which are statistically hard to distinguish from a unit-root process over the
full sample. If (1) is true, this should in and of itself yield a lot of statistical power to estimate
. But if (1) is not true, it could also generate “spuriously” strong correlation between the real
interest rate and the saving-investment factors in specific subsamples.6 To the extent that such
5 Note that (1) is not a reduced form. The reduced form of , given (1) and the above assumptions, is a stationary
autoregressive representation around
∗ with steady-state =∗(;).
6 Under the unit-root assumption, estimates of would be super-consistent, ie they would converge at the rate of
. However, in this case, spurious correlation can also arise. Of course, unit-roots are best seen as convenient
WP685 Why so low for so long? A long view of real interest rate determination 7
correlations do not reflect a true structural relationship like (1), they are likely to be unstable
and strongly subsample-dependent.
We use several different approaches to correctly identify the parameters, .
The main part of the analysis is done based on long-term real interest rates, which should
be less influenced by cyclical factors and less contaminated by monetary policy. Here, we use
static panel regressions as well as dynamic ones, which identify explicitly the empirical steady
state.7 For robustness, we also estimate the correlations from five-year or 10-year non-
overlapping averages of all variables.8 We also employ different modelling strategies for
inflation expectations, as these are especially hard to measure over a 10-year horizon.9
Specifically, we use an autoregressive model in the baseline and an alternative one that
imposes a rational expectations assumption as robustness check – a model that is arguably
more consistent with the assumption of money neutrality.
We also carry out the analysis based on short-term rates. Here, it is more important to
tease out cyclical fluctuations and the influence of monetary policy. We do so by estimating
explicitly a short-term natural rate following a standard filter (Holston et al (2016)) on US and
UK data. For robustness, we also use raw short-term rates for a broader set of countries.
We rely on two statistical criteria to evaluate the results. First, we require the effects of
saving-investment factors to be statistically different from zero and have signs that accord
with theory. Moreover, the size of the effects should ideally also explain the bulk of the decline
in real rates. Second, we require the effects of the saving-investment factors, , to be
reasonably stable over different subsamples.10 Parameter instability would undermine the
framework’s predictive ability and be indicative of spurious correlation, possibly due to
coincidentally matching trends in specific subsamples or omitted persistent factors. This
possibility may be of particular concern given that the real interest rate and the saving-
investment factors display low-frequency trends that tend to co-move across countries and
are difficult to distinguish from unit-roots.11 For the purpose of checking parameter stability,
we split our sample into several subsamples. As additional robustness checks, we also run
rolling regressions with windows of 20, 30 and 40 years and examine backward- and forward-
expanding samples recursively. We exclude the two world wars throughout the analysis.
approximations to non-stationarity behaviour in and , but similar properties apply in general. For instance,
spurious correlation and structural breaks are notoriously difficult to tell apart. See Perron (2006) for an in-depth
discussion.
7 Again, under the unit-root assumption, estimates of can be obtained from a static specification due to super
consistency. Indeed, this was the idea behind the original Engle-Granger two-step procedure. Co-breaking has
similar properties.
8 Assuming that the business cycle does not exceed 10 years and that at least two full cycles are needed to identify
the relationship between the real rate and the saving-investment factors, we need at least 20 years of data for any
given sample.
9 For the measurement of the saving-investment factors themselves, we sidestep the thorny issue of measuring
expectations and simply use actual values.
10 More formally, we adopt the relatively weak requirement that 95% confidence intervals,
, of
and
where
and ′ index different subsamples, overlap, ie
, ∩
,≠0
11 In Annex B.1, we carry out a rudimentary assessment of the presence of spurious correlation due to global trends
by including linear time trends. If the parameters are sensitive to adding such a trend, either the results are
spurious or inference is fragile, as it is solely based on matching unidirectional trends. That is, any persistently
growing or declining series would yield significant results. We do indeed find that the estimates are sensitive to
the inclusion of time trends, casting further doubt on the existence of true underlying relationships.
8 WP685 Why so low for so long? A long view of real interest rate determination
One reasonable objection to our requirement of parameter stability is that true structural
breaks may have occurred as a result of fundamental changes in the economy. While this may
be so, it is not immediately apparent to us what observable drivers of such structural breaks
could be. We thus leave this possibility for further work, noting that if the supposed factors
are left unspecified or are intrinsically unobservable, the theory becomes untestable.
2.2 Data and definition of variables
The data are annual and cover 19 (currently) advanced economies over the period 1870-
2016.12 Table 2 summarises the key independent variables used, the predicted sign of their
influence on real rates, and our choice of proxies. Annex A provides details about data sources
and coverage.
The dependent variable is the ex ante real interest rate – a nominal rate minus expected
inflation, based on a CPI index. For the baseline, we use 10-year government bond yields (or
their closest proxies). We proxy expected inflation by recursively projecting an autoregressive
(AR) model, and compute its average over the relevant horizons. As in Hamilton et al (2015)
and Lunsford and West (2017), we use an AR(1) process estimated over a rolling 20-year
window to allow for time variation in inflation persistence.13 In Annex A2, we plot the time
series of interest rates and expected inflation.
12 Countries covered include Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan,
the Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, the United Kingdom and the United
States.
13 This procedure is a parsimonious way to allow for potential breaks in inflation dynamics. For an earlier discussion
of inflation process from historical perspective, see Friedman and Schwartz (1982). The 20-year estimation window
is shorter than the 30 years in Hamilton et al (2015) but the same as in Lunsford and West (2017). This choice does
not appear materially to affect the results. We measure expected inflation with at least 10 years of input data,
though the vast majority of countries have real interest rate series that start from 1870 (Annex A). We remove
inflation rates in excess of 25 per cent in absolute value from the estimation (an assumption that extreme inflation
rates are not useful for inferences about inflation dynamics). The autoregressive coefficient is capped at 0.9, to
limit the impact of extreme inflation (eg during the wars or hyperinflation episodes) on the long-term forecast.
With this assumption, the half-life for deviations between actual and expected inflation is at most 6.5 years. When
the cap is binding, the constant term is re-estimated.
WP685 Why so low for so long? A long view of real interest rate determination 9
Note that we capture any cross-border effects (à la global saving glut) to the extent that
the shifts in saving and investment can be traced back to the set of explanatory variables and
countries considered. We will investigate more specifically the role of global aggregates of
saving-investment factors in explaining individual countries’ real interest rates further below.
We do not attempt to account for the importance of the safe-asset-shortage channel or
(modern-day) emerging markets, however, owing to a lack of measures suitable for our long-
horizon analysis.14
14 Data on external positions for the United States and Germany are available only from 1950. Growing global
imbalances of net safe asset positions, with the United States and the euro area accounting for much of the net
asset supply, have been identified as a symptom of a safe-asset shortage, though not without controversy (eg
Cochrane (2016)).
Saving-investment determinants: definition and theoretical predictions
Table 2
Factor Expected relationship Variable definition
Marginal product of capital + Labour productivity (the ratio of GDP to hours worked) divided by
capital intensity (the ratio of the total capital stock to total hours
worked) times a constant capital share
Output growth + Annual real GDP growth
Productivity growth1 + Annual total factor productivity (TFP) growth
Dependency ratio2 +
Size of the dependent population (aged 65 or above and 19 or
under), divided by the size of the working-age population
Life expectancy3 – Life expectancy at birth
Population growth +/- Annual population growth
Relative price of capital + The capital price index divided by the consumption price index, and
since 1929, the gross private domestic investment deflator divided
by the personal consumption expenditures deflator
Inequality – Income share of the top 1% of the population
Risk premium4 – (i) Higher moments of annual GDP growth and inflation, as
measures of fundamental risks,5 (ii) US equity risk premium
1 Considered in robustness exercises. TFP growth is largely subsumed by GDP growth in the baseline analysis.
2 In robustness exercises (Annex B.6-B.7), we also consider the old-age dependency ratio (the size of population aged above 65 over its
working-age counterpart) and an alternative savers’ ratio (where the dependency ratio is redefined using 40-64 as the working-age bracket)
3 We use life expectancy at birth for its more complete coverage. Life expectancy at a higher age, say 20 years, shares a very similar trend over
our sample (eg the correlation between the two series is close to 90% even for the first 40 years of the sample, suggesting that child mortality
was not the dominant driver of the upward trend). In robustness exercises, we also control for time variation in the retirement age (itsel
f
negatively related to interest rates), using the labour force participation above age 65 as a proxy for it.
4 Considered in robustness exercises (Annex B.9). Note that some risk premium measures have not trended up over the last 30 years, hence
are not congruent with the decline in real interest rates. For instance, Cochrane (2016) has observed that the S&P 500 price-earnings ratio is
higher today than in 1980s. Gourinchas and Rey (2016) also find that the equity risk premium cannot explain secular movements in the
consumption-wealth ratio, which is their predictor of future real rates.
5 Skewness, measured as the third standardised moment, should have a positive relationship with real rates, as greater downside tailed ris
k
raises the risk premium.
10 WP685 Why so low for so long? A long view of real interest rate determination
2.3 A first look at the data
Real interest rates
In per cent Graph 1
Sources: Authors’ calculations.
Graph 1 shows the time series of global real interest rates, captured by the cross-country
median. We see that real rates of both long and short maturities tend to co-move closely,
although short-term rates are naturally more volatile. Excluding the World Wars, when real
rates drop, sometimes deeply into negative territory, one can discern four distinct phases. Up
to World War I – mostly the classical gold standard – real rates were comparatively high and
stable. In the interwar years, after recovering quickly from World War I, they started to fall
markedly in the wake of the Great Depression. Real rates then rose much more gradually
starting in the early 1950s and, after a new big dip during the Great Inflation, peaked in the
early to mid-1980s, reaching levels broadly similar to those seen in the early part of the sample.
Finally, real rates have been declining since then, to historically low levels, wars excepted.
Annex Graphs A.2 provide plots of real interest rates for individual countries.
Graph 2 plots the long-term real interest rates against the standard factors singled out as
potential drivers, all in terms of cross-country medians. Two observations stand out.
First, over the latest phase starting in the early 1980s, most of the standard factors are
correlated with the decline in real interest rates with signs that accord with the saving-
investment framework. This is confirmed in Table 3, which summarises the correlation between
median real interest rate and the median of each factor (correctly signed correlations are in
green). The median dependency ratio is the only exception – although a correct correlation
resurfaces if one takes into account the demographic dividends of large EMEs in recent
decades and looks at the dependency ratio based on a larger set of countries, including the
likes of China and India (broad dependency ratio).
Second, once we extend the sample to cover preceding periods, almost all of the
correctly-signed correlations disappear. Only life expectancy is consistently correlated with
real interest rates and with the right sign. Even then, Graph 2 suggests that this may reflect
strong correlations over certain subsamples, since life expectancy trends up throughout. Even
the marginal product of capital, which according to theory should be a summary statistic of
the net saving-investment balance, is hardly correlated with the real interest rate over the full
sample.
5
0
–5
–10
–15
201620061996198619761966195619461936192619161906189618861876
Short-term real rates Long-term real rates
WP685 Why so low for so long? A long view of real interest rate determination 11
Cross-country median of saving-investment determinants Graph 2
GDP and productivity Dependency ratios Life expectancy
Per cent Per cent Years
Inequality Relative price of capital Marginal product of capital
Per cent
Shaded area indicates the last 30 years.
Sources: Bergeuad et al (2016); Costa (1998); Eichengreen (2015); Roine and Waldenström (2015); Chartbook of Economic Inequality;
International Historical Statistics; World Wealth & Income Database; OECD; United Nations, Human Mortality Database; national data; authors’
calculations.
3
0
–3
–6
5
0
–5
–10
201619661916
Long-term real rates (lhs)
GDP growth (rhs)
TFP growth (rhs)
3
0
–3
–6
0.95
0.80
0.65
0.50
201619661916
Long-term real rates (lhs)
Dependency (rhs)
Global dependency (rhs)
3
0
–3
–6
75.0
62.5
50.0
37.5
201619661916
Long-term real rates (lhs)
Life expectancy (rhs)
3
0
–3
–6
20
15
10
5
201619661916
Long-term real rates (lhs)
Inequality (rhs)
3
0
–3
–6
1.20
1.05
0.90
0.75
201619661916
Long-term real rates (lhs)
Rpi (rhs)
3
0
–3
–6
0.11
0.10
0.09
0.08
201619661916
Long-term real rates (lhs)
Median MPK (rhs)
12 WP685 Why so low for so long? A long view of real interest rate determination
2.4 Tests and main results
To test more formally the relationship between real rates and their posited determinants, we
now estimate panel regressions to exploit also any cross-country heterogeneity for
identification. We start by estimating a bivariate fixed-effect panel specification
, =
+
, +
,, +,
where , is the 10-year real interest rate, and ,, is the saving-investment factor.15
In addition to considering the full sample, we also test the relationship in various
subsamples identified on the basis of the previous visual data inspection. These correspond to
the metallic standards (mostly the classical gold standard),16 interwar and postwar phases. We
further subdivide the postwar subsample into the pre- and post-Volcker-tightening eras. The
latter subsample has been extensively used in studies of the secular decline in interest rates.
The results confirm the indications of the simple correlation exercise (Table 4). For the last
30-year period (post-Volcker), the relationships appear to be more in line with the saving-
investment framework: most variables are significantly and correctly signed, except for the
marginal product of capital and the dependency ratio. For the full sample, however, only life
expectancy is significantly associated with real interest rates with the correct sign. And across
subsamples, there is clear parameter instability in all the variables, in both size and sign.
15 Unless otherwise stated, we apply the standard fixed-effects estimator here and below. While this estimator is
biased in dynamic specifications, the bias is likely to be small in samples with a large time dimension. All our
results are similar to those obtained by applying the Arellano and Bond (1991) estimator. Our results are also
similar if we treat some of the saving-investment factors as endogenous and use GMM instead. For instance, the
estimates where inflation expectations and GDP growth are endogenous are shown in Annex B5.
16 In what follows, we often use the shorthand “gold standard” or “classical gold standard” to refer to the metallic
standards more generally. This is because the classical gold standard covers most of the period and, in the
estimation, we do not distinguish the two types of regime. See Table 9 for details.
Correlation between median real interest rates and saving-investment factors1
Table 3
Factor Expected relationship 1985-2017 1870-2017
Marginal product of capital + 0.65 –0.20
GDP growth + 0.37 –0.28
TFP growth + 0.49 –0.29
Dependency ratio + –0.02 0.42
Broad dependency2 + 0.87 NA
Life expectancy – –0.87 –0.48
Relative price of capital + 0.36 –0.43
Inequality – –0.62 0.49
1 Correlation with signs consistent with saving-investment theory is shown in green, otherwise in red. War years are excluded.
2 Broad dependency ratio covers EMEs’ demographic information. Since the series is only available from 1960 onwards, only the correlation
over the recent sample is reported.
Sources: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 13
Thus, while the results in the most recent period may appear consistent with the standard
narrative, they clearly fail to survive once the sample is extended. This raises questions about
drawing strong inferences from the standard theoretical framework.
Moving to a multivariate framework confirms this conclusion. Complex interactions
among determining factors could introduce offsetting effects over time, making any bilateral
association (or lack thereof) between real rates and these factors unreliable. We thus estimate
a joint specification
, =
+
, +
, +,
where , now includes GDP growth, population growth, the dependency ratio, life
expectancy, the relative price of capital and income inequality. For parsimony, we leave out
TFP and the marginal product of capital, which should be redundant after the inclusion of GDP
growth and other saving-investment determinants (we will reconsider TFP and other
independent variables in robustness tests). Given that the different variables have different
coverage, the sample drops to 11 countries starting in 1870 at the earliest. This serves as our
baseline specification.
The results indicate even weaker evidence for the theory than the bivariate tests (Table
5). Not only is there little support in the full sample, but even for the most recent 30-year
window the only variable that significantly retains the expected sign is life expectancy. Again
there is substantial coefficient instability across subsamples in terms of both sign and size.
Bivariate panel regressions Table 4
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
Marginal product of
capital (+) 0.05 0.32*** –0.25 –0.33*** –0.57** 0.32
GDP growth (+) –0.09** 0.01 –0.08** –0.05 0.02 0.09*
TFP growth (+) –0.08 –0.01 –0.04 –0.04 0.11 0.24***
Population growth
(+/-) –0.12 0.10 0.10** –1.25*** –0.64*** –1.30**
Dependency ratio (+) 0.03*** –0.01 –0.12** –0.04** 0.13** 0.03
Life expectancy (-) –0.04*** –0.11*** 0.43*** 0.15*** 0.33* –0.35***
Relative price of
capital (+) 0.00 0.05 –0.12 –0.02** –0.07* 0.07***
Inequality (-) 0.03 –0.00 –0.46** –0.28** –0.61*** –0.33***
Robust standard errors in parentheses based on country clusters; ***/**/* denote results significant at the 1/5/10% level. Significant
coefficients with signs consistent with saving-investment theory are highlighted in green. Other significant coefficients are highlighted in red.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations
14 WP685 Why so low for so long? A long view of real interest rate determination
One likely reason for these results is that the strong subsample trends in the real interest
rate occasionally coincide with similar trends in the saving-investment factors, leading to
“spurious” subsample correlation. For instance, the steady decline in real interest rates in the
post-Volcker period is picked up by the steady increase in life expectancy over the entire
sample. In fact, any variable that trends over the same subsample will pick up the decline in
the real interest rate. In Table 4 above, the trends between any given pair generate significant
results. To test whether unidirectional trends within specific subsamples are the culprit, we add
a linear time trend in the bivariate specifications and check if the correlations survive. Indeed,
in this case, the factors typically lose significance or flip signs (see Annex B.1).
Another simple test of coefficient stability is to run a rolling regression. Graph 3 depicts
the time-varying estimates of the coefficients from a 20-year rolling window for the baseline
specification. In all cases, the estimates are very unstable.
Baseline specification Table 5
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
GDP growth (+) –0.09** –0.00 –0.07 0.08 0.07 0.03
(0.04) (0.02) (0.05) (0.07) (0.07) (0.05)
Population growth (+/–) –0.83* –0.50 0.25 –0.77** –0.00 –0.68
(0.39) (0.50) (0.36) (0.28) (0.28) (0.71)
Dependency ratio (+) 0.02 –0.03 –0.04 0.03 0.14*** –0.03
(0.02) (0.02) (0.09) (0.02) (0.02) (0.07)
Life expectancy (–) 0.04 –0.20*** 0.41 0.23** 0.47*** –0.32***
(0.03) (0.05) (0.24) (0.09) (0.13) (0.09)
Relative price of capital (+) 0.01 0.11** –0.06 –0.00 –0.06* 0.01
(0.02) (0.03) (0.05) (0.01) (0.03) (0.03)
Income inequality (–) 0.10* –0.01 0.00 –0.26*** –0.10 –0.10
(0.05) (0.05) (0.30) (0.05) (0.21) (0.15)
Constant –1.97 15.33*** –17.90 –14.27* –42.48*** 31.18***
(2.97) (2.61) (21.61) (7.79) (11.80) (7.95)
Adjusted R-squared 0.07 0.51 0.22 0.21 0.34 0.26
Number of observations 1102 202 205 643 303 340
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample, 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-
1979; post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations
WP685 Why so low for so long? A long view of real interest rate determination 15
Time-varying coefficients of the baseline regression Graph 3
GDP growth Dependency ratio
Life expectancy Relative price of capital
Inequality
Dashed lines indicate two-standard error bands and the shaded area in green the correct coefficient sign. Data during the two wars are
dropped from the estimation samples. Smaller subsamples around war periods are partly responsible for an increase in standard errors.
Source: Author’s calculations.
Given that movements in real interest rates are quite persistent, it is worth distinguishing
more formally between higher- and lower-frequency correlation. The static specification we
have used so far mixes up correlation at all frequencies, even though low-frequency correlation
tends to dominate asymptotically. To capture the low-frequency relationship between the
variables, we estimate a dynamic fixed-effects panel specification
∆, =
+
, +
∆,
+
∆,
−
, −
,+
0.30
0.15
0.00
–0.15
–0.30
–0.45
200319831963194319231903
0.6
0.4
0.2
0.0
–0.2
–0.4
200319831963194319231903
2.25
1.50
0.75
0.00
–0.75
–1.50
200319831963194319231903
0.2
0.1
0.0
–0.1
–0.2
–0.3
200319831963194319231903
2
1
0
–1
–2
200319831963194319231903
16 WP685 Why so low for so long? A long view of real interest rate determination
where , again consists of the same variables as before. The term in brackets captures any
long-run relationship between the real interest rate and these variables. Thus, the
coefficients are the dynamic-specification equivalents to in the static model. The short-run
adjustment parameter, , captures the speed with which changes in the real interest rate
correct deviations between the real interest rate and its determining factors in steady state.
Obtaining a short-run adjustment statistically different from zero requires that the steady-
state deviation in the parenthesis is approximately stationary: by construction, the change in
the real interest rate on the left-hand side is a stationary variable.
Dynamic fixed-effects panel specification Table 6
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
Long-run coefficients
GDP growth (+) –0.19*** 0.04 –0.15** –0.09 0.09 –0.25*
(0.07) (0.33) (0.08) (0.19) (0.14) (0.15)
Population growth (+/–) –0.67 –1.60*** –0.54 0.30 0.24 –0.53
(0.48) (0.58) (0.81) (0.73) (0.59) (0.95)
Dependency ratio (+) 0.03 –0.05 –0.13** 0.05* 0.24*** –0.06
(0.02) (0.04) (0.06) (0.03) (0.04) (0.10)
Life expectancy (–) –0.05** –0.27** 0.06 0.20** 0.54*** –0.38**
(0.02) (0.11) (0.08) (0.10) (0.20) (0.18)
Relative price of capital (+) –0.01 0.14*** –0.06* –0.01 –0.08** 0.04
(0.01) (0.02) (0.03) (0.02) (0.03) (0.02)
Income inequality (–) –0.08** 0.20*** 0.14 –0.22** 0.27 –0.05
(0.04) (0.07) (0.15) (0.10) (0.22) (0.21)
Short-run coefficients
Adjustment parameter –0.32*** –0.28*** –0.69*** –0.31*** –0.54*** –0.42***
(0.04) (0.08) (0.14) (0.05) (0.08) (0.04)
Constant 1.66 4.53 7.48 –4.44 –31.81*** 16.28***
(1.01) (3.19) (5.38) (2.88) (10.62) (6.04)
Adjusted R-squared 0.30 0.17 0.59 0.21 0.36 0.24
Number of observations 997 177 177 633 293 340
Country fixed effects yes yes yes yes yes yes
Differences yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Differences: lagged differences from t to t-2 of all variables included in the regressions.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 17
Estimates from the dynamic specification again fail to establish robust relationships
between real rates and saving-investment determinants (Table 6). For the full sample, life
expectancy and income inequality now have the correct sign and are statistically significant.
But these relationships, as well as those for the other variables, are not robust across
subsamples. For the post-Volcker period, again only life expectancy – the variable that trends
up throughout the sample – has a significant and correct sign.
Another, albeit crude, way of capturing the low-frequency correlation between the
variables is to use averages of the data in the regressions. In Annex B.2 we explore this method
with averages over non-overlapping samples for the baseline and bivariate regressions.17
Similar results obtain.
Next, given the high co-movement of interest rates across countries, many studies have
emphasised the role of global factors. This is most evident in the global saving glut and global
safe asset-shortage narratives, but can also arise if saving-investment factors have a common
component (eg Clarida (2017)). We explore this by constructing global counterparts to the
posited determinants and estimate their impact alongside the respective country-specific
variables, defined in terms of deviations from the global trend. The specification is the
following
, =
+
, +
+
(, −
)+,
where
is a measure of the global components in the determinants.18 We measure the global
components as the averages of each variable based on real GDP at purchasing power parity.
The main difference between this specification and the previous ones is that we allow for the
common global components to have different effects on real interest rates from the country-
specific ones.
For the most part, the global variables represent some improvement relative to the
domestic ones, but the instability generally persists (Table 7). The dependency ratio is
significant and correctly signed in subsamples prior to the most recent one, but is not
significant over the full sample. Inequality performs well over the full sample and the postwar
subsamples. However, in all other cases, the co-movements between the common trends in
real interest rates and the saving-investment variables are highly unstable. The coefficients on
the global components fluctuate over the different subsamples, sometimes changing signs or
losing statistical significance. This suggests that these relationships may be coincidental.
It might be argued that the global saving-investment factors exert uneven influence over
time, being stronger in periods of higher financial integration. We can readily use the
subsample estimates to test this proposition. Economic historians typically judge the gold
standard and the last 30 years or so as the two episodes of heightened financial globalisation
(eg Obstfeld and Taylor (2003), BIS (2017)). One should then expect the global saving-
investment determinants to be significant in both of these periods, and weaker otherwise. But
as Table 7 shows, this pattern hardly emerges.
17 The procedure is very closely related to that proposed by Lunsford and West (2017).
18 This parametrisation allows us to directly compare the size of
and
. For instance, if
=
, the global and
country-specific components have the same effect on the real interest rate. The connection between the coefficients
from this parametrisation and an alternative parametrisation given by , =
+
, +
+
, +, is
=
−
and
=
. Hence, in the alternative parametrisation,
reflects the difference in the real interest rate
response to changes in the global saving-investment components and those in their idiosyncratic counterparts. If, for
instance, the global and country-specific components have the same effect on the real interest rate, then
=0.
18 WP685 Why so low for so long? A long view of real interest rate determination
Lastly, we check whether the relationships remain as elusive if we use Holston-Laubach-
Williams filtered short-term natural rates in place of actual rates. This helps remove the
variation at business cycle frequencies. Recall that the methodology posits that the natural
interest rate ∗ consists of two components
Global versus country-specific determinants Table 7
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre–Volcker
(6)
Post–Volcker
Global component:
GDP growth (+) 0.01 –0.03 –0.13* 0.14*** 0.21*** 0.14*
(0.03) (0.02) (0.06) (0.04) (0.06) (0.07)
Population growth (+/–) –1.43*** –0.44 –2.45 0.56** 1.25*** 17.65**
(0.36) (1.14) (1.57) (0.18) (0.24) (7.60)
Dependency ratio (+) 0.05 0.40*** 0.83*** 0.08*** 0.24*** –0.06
(0.03) (0.09) (0.22) (0.02) (0.06) (0.16)
Life expectancy (–) –0.08 0.13 2.18*** 0.30** –0.50* 0.63
(0.05) (0.09) (0.58) (0.13) (0.25) (0.36)
Relative price of capital (+) –0.09*** 0.01 0.62** –0.14*** –0.08 0.03
(0.03) (0.02) (0.13) (0.04) (0.07) (0.07)
Income inequality (–) –0.15* –0.07 1.56** –1.02*** –2.96*** –0.95***
(0.08) (0.12) (0.66) (0.08) (0.54) (0.25)
Country specific component:
GDP growth (+) –0.08* –0.00 –0.11 0.02 0.01 –0.02
(0.04) (0.02) (0.07) (0.05) (0.05) (0.06)
Population growth (+/–) 0.02 –0.15 0.33 –0.18 –0.13 –0.20
(0.41) (0.14) (0.34) (0.22) (0.29) (0.64)
Dependency ratio (+) –0.00 –0.06*** 0.10 0.02 –0.01 0.04
(0.02) (0.02) (0.15) (0.02) (0.04) (0.07)
Life expectancy (–) 0.05 0.07 0.21 0.01 –0.50** 0.58
(0.07) (0.05) (0.12) (0.11) (0.19) (0.40)
Relative price of capital (+) 0.02 0.09*** –0.05 0.01 –0.04* 0.02
(0.01) (0.02) (0.03) (0.01) (0.02) (0.02)
Income inequality (–) 0.04 –0.04* –0.12 0.05 –0.10 0.13
(0.07) (0.02) (0.24) (0.08) (0.11) (0.13)
Constant 7.44 –38.44** –210.70*** –17.26* 41.77* –42.76
(6.09) (13.06) (59.31) (9.43) (21.87) (29.43)
Adjusted R-squared 0.17 0.75 0.30 0.45 0.53 0.39
Number of observations 1102 202 205 643 303 340
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016. Global components calculated as the averages of each variable based on real GDP at purchasing power
parity.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 19
∗=
+
where is the potential growth rate of the economy, and is the latent variable that captures
other unobserved determinants of the natural rate. We use the estimated models in Holston
et al (2016) to filter the natural rates and their components but start the exercise in 1861.19
Graph 4 shows these natural rate estimates for the United States and the United Kingdom. As
a preliminary observation, we note the interesting behaviour of the natural rate during the
gold (metallic) standard period (1870-1913). With inflation and nominal rates relatively stable,
the actual and estimated natural real rates are also relatively stable and track each other
closely. This contrasts with the substantial variation in underlying saving-investment
determinants during this period (Annex Graph A.3). We return to this point later.
The formal test of the relevance of saving-investment balances does not provide strong
support for the standard view once the role of maintained hypotheses is taken into account.
In Table 8, we report the estimated long-run relationships between ∗ (as well as its latent
component, ) and the set of saving-investment determinants from individual country
versions of the dynamic specification for the United States and the United Kingdom. True, over
the full sample, GDP growth now appears to be a significant determinant for both countries.
But this is so by construction: in this method, potential growth is assumed to be a major
determinant of the natural rate and GDP is an observed variable used to estimate it. Other
significant and correctly signed variables are life expectancy for the United States and the
19 We use their model as well as their estimated parameters. Thus, any differences between our natural rate estimates
and Holston et al (2016) stem essentially from different initial conditions for the latent variable, . Starting in
1961, Holston et al (2016) set the initial value of at zero. In our case, we filter the model from 1861, so our as
of 1961 is filtered using the historical data rather than assumed to be zero. As it turns out, the UK natural rate
estimates are very similar for the overlapping sample (Graph 4). For the United States, our natural rate estimate
fell significantly in the late 1940s (due to the decline in ), and subsequently remained persistently lower than
Holston et al (2016) estimates. We use policy interest rates where available, and replace them with short-term
rates as needed. In earlier samples for which only annual data are available, we interpolate all the series to
generate a quarterly time series before filtering. The filtered series are then aggregated up to the annual frequency
again for the dynamic fixed-effects regression.
Filtered natural interest rates based on Holston-Laubach-Williams model
In per cent Graph 4
United States United Kingdom
Sources: Holston et al (2016) and authors’ calculations.
5
0
–5
–10
20161996197619561936191618961876
Natural real interest rate
6
3
0
–3
20161996197619561936191618961876
HLW natural real interest rate
20 WP685 Why so low for so long? A long view of real interest rate determination
relative price of capital for the United Kingdom. But if we consider only the component of the
natural rate that is unrelated to potential growth, ie the latent variable, , then none of the
determinants has significant explanatory power. This suggests that it is hard to find much
support for saving-investment factors without hard-wiring the link a priori.
In addition to these specifications, we have conducted a wide range of robustness tests
(Annex B). These include: a replication of all key results using short-term interest rates; an
alternative treatment of inflation expectations; alternative independent variables and samples,
such as the exclusion of immediate postwar years; and the inclusion of risk premium proxies.
The broad conclusion remains the same. Moreover, it is also unlikely that an attenuation bias
due to possible measurement errors drives the results: this would just lead to statistically
insignificant results. Instead, most of the coefficients flip sign, for example from significantly
positive to significantly negative over different subsamples. Similarly, collinearity between the
saving-investment factors is probably not the culprit either, as the same conclusion emerges
from the bivariate specifications.
Filtered short-term natural rates and saving-investment determinants Table 8
United States United Kingdom
r* z r* z
Long-run coefficients
GDP growth (+) 0.39*** 0.32***
(0.05) (0.12)
Population growth (+/–) –1.28*** –2.07*** –0.13 0.01
(0.41) (0.71) (0.29) (0.17)
Dependency ratio (+) –0.08** –0.05 –0.00 –0.02*
(0.03) (0.05) (0.02) (0.01)
Life expectancy (–) –0.09* –0.07 0.04 –0.02
(0.05) (0.08) (0.06) (0.04)
Relative price of capital (+) –2.12 3.96 4.76* 2.02
(3.90) (6.48) (2.70) (1.62)
Income inequality (–) –0.09 0.21 0.08 0.06
(0.14) (0.24) (0.08) (0.05)
Short-run coefficients
Adjustment parameter –0.48*** –0.32*** –0.28*** –0.44***
(0.06) (0.06) (0.04) (0.06)
Constant 8.09 1.20 –1.89 0.15
(5.13) (5.16) (2.11) (1.99)
Adjusted R-squared 0.92 0.86 0.86 0.86
Number of observations 96 96 137 137
Differences yes yes yes yes
The specification is equivalent to the dynamic fixed-effects panel specification in 2.4, but without the country fixed-effects
term and the country index suppressed; ***/**/* denotes results significant at the 1/5/10% level.
Full sample, 1870-2016.
Differences: lagged differences from t to t-2 of all variables included in the regressions.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 21
Overall, the results point in the same direction: no single real factor, or combination of
such factors, can consistently explain the long-term evolution of real interest rates. This holds
at both the domestic and global levels. It suggests that the observed correlation between the
saving-investment factors and the real interest rate in the latest sample is largely coincidental,
mostly driven by temporary but unrelated trends in the variables.
3. Real interest rate determination: the role of monetary factors
In light of the weak empirical support for saving-investment proxies in explaining real interest
rate movements, is it possible to find a tighter relationship with other factors? Note that the
nominal long-term yields are currently at their unprecedented lows for most countries (Graph
5). Annex A.2.4 shows that the same is true for short-term nominal rates. Monetary policy
responses in the aftermath of the GFC clearly play an important role in driving down nominal
and, given relatively stable inflation, real interest rates. Could monetary policy play a more
important role than typically believed?
3.1 Analytical considerations
The previous analysis is based on the assumption that monetary policy is irrelevant for the
determination of real interest rates over the “relevant horizon”. This assumption, in turn, takes
root in the widespread view that monetary policy is neutral “in the long run” (eg Patinkin
(1956)).20
But could the role of monetary policy regimes be underestimated? There are at least two,
closely related reasons why this might be the case. The first is that market rates may fail to
track the unobserved theory-defined natural rate for very long periods. The second is that
standard models may ignore or play down the channels through which monetary policy
influences real rates over relevant horizons. Consider each in turn.
There is a broad consensus that market interest rates are determined by a combination
of central bank and market participants’ actions, given the supply of the underlying assets.
Central banks set the nominal short-term interest rate and influence the nominal long-term
interest rate through signals of future policy rates and asset purchases. Market participants
adjust their portfolios based on expectations of central bank policy, views about the other
factors driving long-term rates, attitudes towards risk and various balance-sheet constraints,
not least regulation. Given nominal rates, by construction, actual inflation – effectively
predetermined at a given point in time – determines ex post real rates, and expected inflation
determines ex ante real rates.
20 Of course, there is also a literature that questions money neutrality, going as far back as the 18th century (eg Law
(1705)) and stretching to the publication of the General Theory (Keynes (1936)). In the 1960s, the seminal
contributions of Mundell (1963) and Tobin (1965) postulated the failure of "super-neutrality", arguing for the
influence of variations in money growth on real variables, particularly the real rate of interest. More recently, the
notion of neutrality has been challenged in micro-founded monetary models (Weiss (1980), Espinosa-Vega and
Russell (1998), Bullard and Russell (2004), Reis (2007), Lioui and Poncet (2008), Williamson (2014)). Moreover,
when translating the analytical notion of “long run” into calendar time, Friedman (1968) noted that it could be as
long as two decades.
22 WP685 Why so low for so long? A long view of real interest rate determination
Nominal long-term rates
In per cent Graph 5
The shaded areas indicate the world wars, 1914-1918 and 1940-1945.
Sources: Global Financial Data; national data.
Thus, at any given point in time, interest rates necessarily reflect the interplay between the
central bank’s reaction function and private-sector beliefs and behaviour. And if this is true at
any given point in time, it must also be true at all points in time. Even if monetary policy is
neutral “in the long run”, one should expect it to influence real interest rates quite closely all
the time. Saving-investment imbalances do not directly influence market rates. At best, they
affect the natural rate.21 Their impact on the market interest rate is only indirect, through the
interaction between central bank and private sector agents’ decisions. By identifying the
evolution of real interest rates with saving and investment determinants, the implicit
assumption is that the central bank and financial market participants can roughly track the
evolution of the natural real rate over time.
But this is by no means straightforward. For central banks, measuring and tracking a given
definition of the equilibrium interest rate – an abstract concept – is a formidable challenge.
The corresponding estimates are highly uncertain, strongly model-dependent, and subject to
21 As argued elsewhere, the view that ex ante saving-investment balances directly influence the market rate results
from conflating saving and financing (Borio and Disyatat (2011)).
25
20
15
10
5
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201619911966194119161891
Australia
Canada
Austria Belgium
25
20
15
10
5
0
–5
201619911966194119161891
Denmark Finland France
25
20
15
10
5
0
–5
201619911966194119161891
Germany Italy Japan
25
20
15
10
5
0
–5
201619911966194119161891
Netherlands
Norway
New Zealand
25
20
15
10
5
0
–5
201619911966194119161891
Portugal Spain Sweden
25
20
15
10
5
0
–5
201619911966194119161891
Switzerland
United States
United Kingdom
WP685 Why so low for so long? A long view of real interest rate determination 23
large revisions.22 There is a material possibility that central banks may fail for prolonged
periods. The consequent impact on real interest rates can be persistent. For instance, even if
the standard model of inflation determination is correct, if the central bank keeps the interest
rate too low, inflation will increase over time.23 As Friedman (1968) noted, the presumption is
that such a reaction function is not sustainable: in the face of explosive inflation dynamics, the
central bank will be forced to abandon it. But over the intervening period, real interest rates
would reflect monetary rather than saving-investment determinants as such. This, in fact, is a
common reading of the Great Inflation of the 1970s.24 Actions by market participants
themselves may also contribute to persistent shifts in real interest rates, potentially
compounding any central bank “mistakes” and transmitting them through the yield curve.25
As regards the possibility that prevailing economic models may underestimate some key
channels through which monetary policy may exert persistent influence over real interest rates,
two examples spring to mind. The first concerns the inflation process; the second, the
interaction between monetary policy and the financial cycle.
The inflation process may be far less responsive to economic slack, and hence monetary
policy, than commonly presumed (eg Forbes et al (2017)).26 Imagine that inflation is below
target and that headwinds make it hard to generate the second-round effects whereby wages
chase prices.27 Then, easing policy would have a one-off impact on the price level, say through
currency depreciation, but only a temporary one on inflation. If the central bank continued to
try to push inflation up, nominal and hence real interest rates would trend downwards. In the
extreme, if inflation was entirely exogenous and trendless, the trend in the real interest rate
would simply depend on whether inflation was below or above target. For instance, the real
rate would tend to fall continuously if inflation started below target, as the central bank
repeatedly cut nominal interest rates in the vain attempt to boost it towards target.
Monetary policy may also have a long-lasting impact on the real economy, and hence
real interest rates, through the financial cycle.28 There is now a broad consensus that price
22 Borio et al (2014, 2017), for example, show that whereas typical output gap measures prior to the financial crisis
indicated that US output was close to potential, subsequent revisions indicate that the level of activity was
substantially above it.
23 Strictly speaking, of course, the inflation response depends on the expectations process. Adaptive expectations,
for instance, would result in a continuous increase, possibly at an accelerating rate (Fleming (1976)). In the case
of rational expectations, as typified by New Keynesian models, an interest-rate peg leads to indeterminacy in the
inflation path and the sign of the immediate response of inflation to monetary shocks also becomes indeterminate
(Cochrane (2017)). Such possibilities are therefore ruled out either outright or through equilibrium selection
mechanisms that imply these outcomes are not robust or learnable (García-Schmidt and Woodford (2015), Evans
and McGough (2015))
24 Lubik and Matthes (2016), for example, estimated a model of learning and argued that misperceptions about the
state of the economy on the part of the Federal Reserve led to sustained deviations from equilibrium real rates
during the Great Inflation of the 1970s.
25 This is quite apart from the impact of direct controls of interest rates. For instance, administered rates were quite
common in the postwar period, until the financial liberalisations of the late 1970s-early 1980s.
26 Indeed, there is a lot of evidence that the Phillips curve has been quite flat for a long time. See, for instance, Stock
and Watson (2007), Ball and Mazumder (2011), IMF (2013), Faust and Wright (2013), Faust and Leeper (2015), Kiley
(2015) and Blanchard (2017). See Borio (2017a) for a recent discussion.
27 As discussed elsewhere (eg Borio (2017a)), this could reflect a loss in labour’s “pricing” power as a result of much
greater competition from lower-cost producers or technology, ie the greater contestability of markets linked to
globalisation.
28 See Juselius et al (2017). In addition, a growing literature has documented the impact of monetary policy on risk
premia operating through a risk-taking channel. For a discussion of the risk-taking channel, see Borio and Zhu
24 WP685 Why so low for so long? A long view of real interest rate determination
stability is not sufficient for financial stability, as the GFC confirmed most recently. If, as long
as inflation is low and stable, central banks do not lean against the build-up of financial
imbalances but ease aggressively and persistently after the bust, this will tend to impart a
downward bias to nominal and real interest rates. Moreover, if, as a result, debt continued to
rise in relation to GDP or did not adjust sufficiently, a “debt trap” might even emerge: it would
become harder to raise interest rates without causing damage to the economy (Borio and
Disyatat (2014)). Seen through the standard framework lens, this would look like an exogenous
decline in the natural rate, whereas in fact it would simply reflect the path-dependent
interaction of monetary policy with the economy.
The gold standard regime provides prima facie evidence that the role of monetary factors
may well have been underestimated. During this regime, central banks did not target inflation
or output directly; rather, they targeted convertibility – internal and external (eg Wicksell
(1906)). As a first approximation, they kept policy rates roughly constant unless the
convertibility constraint came under threat, at which point they raised them (eg Flandreau
(2008)).29 In other words, gold acted only as a weak anchor for policy, and there was not much
systematic reaction to macroeconomic developments. The anchor worked only over long
periods, to the extent that convertibility was threatened, especially in the country at the centre
of the whole system.30 And yet, during this historical phase, inflation remained range-bound:
volatility aside, not least reflecting the high incidence of commodity and food prices in the CPI
index, underlying prices fell or rose gradually over long periods.
The tension with today’s prevailing paradigm is apparent. Seen through that lens, the
period of relative price stability would suggest that the market rate tracked the natural rate
quite closely (see below). And yet, not only would this have happened despite no explicit
central bank attempt to stabilise prices. The relative stability of the real rate also sits uneasily
with the concomitant high variability of the “usual suspects” expected to drive saving-
investment balances (Graph 2 and Annex Graph A.3). Indeed, it is not obvious why such drivers
should have been much more stable during that historical phase than postwar, as the data
confirm. Another possibility is that stable real rates largely reflected stable nominal rates
coupled with a weak link between the gap between the market and natural rate, as defined in
the traditional framework, on the one hand, and inflation, on the other. That is, the monetary
regime itself partly explains the evolution of real interest rates.
The recent experience with the effective lower bound may also be interpreted in a similar
way, although here the picture is fuzzier. One view stresses that monetary policy in the
traditional sense, as captured by the policy rate, was forced to be largely unresponsive to
economic developments, and yet this did not result in inflation spirals or signs of
indeterminacy (eg Cochrane (2017)). Another view focuses instead on the extraordinary easing
of financial conditions in the wake of unconventional measures – balance sheet policies,
(2012) and Adrian and Shin (2010); for a broader analysis of the financial cycle and the role of monetary policy,
see Borio (2014, 2017b).
29 This is the best description for advanced economies, especially the country at the core of the system (the United
Kingdom). In the periphery medium-term trends in interest rates were more common, as the currency pegs gained
credibility (see below). See Flandreau and Zumer (2004).
30 In his political economy lectures, Wicksell (1906) recognises this and discusses the related issues in some detail.
He notes, for instance, that the direct impact of increased gold supplies may be relatively small compared with
the indirect influence operating through interest rates and the convertibility constraint. He then postulates an
unobservable and time-varying natural rate to explain periods in which price declines coincide with falling interest
rates and contractions in gold production. This contrasts with economists more firmly rooted in the monetarist
tradition, who ascribe a bigger role to exogenous increases in gold in circulation in influencing the price level by
boosting expenditures (eg Fisher (1911) and, more recently, Bordo (1999)). For a discussion of these issues, and
of Wicksell’s shifting views, see Laidler (1991).
WP685 Why so low for so long? A long view of real interest rate determination 25
negative interest rates and forward guidance (eg Borio and Zabai (2016)) – which failed to
bring inflation back to target as expected. Hence central banks’ disappointment. This relative
unresponsiveness of inflation could be rationalised ex post through corresponding shifts in
unobserved natural rates. But it could also reflect other factors, such as the forces of
globalisation and possibly technology making the inflation process less sensitive to monetary
policy actions and exerting secular disinflationary pressures (eg Borio (2017b)). If so, repeated
attempts to push inflation towards target could lead to persistent declines in real interest rates.
Overall, therefore, there are good reasons to suspect that the role of the natural rate in
guiding the evolution of actual real rates could be much weaker than often presumed. Indeed,
the very concept of the natural rate has not gone unchallenged. It is well known, for instance,
that Keynes in his General Theory rejected it. He argued that there was no single natural rate
of interest that balanced the economy at full employment.31 In his liquidity preference theory,
in a way not very different from what was described above, the long-term interest rate was the
outcome of central bank and market participants’ decisions. Importantly, though, depending
on market participants’ expectations and willingness to take on risk, the interest rate could
persist at some arbitrary level for a long time. It is telling that both Wicksell’s conception of
the wedge between the market and the natural rate, and Keynes’ alternative framework of
interest rate determination, are premised on a capital market failure – agents fail to set rates
at the appropriate level. This contrasts with the now standard New Keynesian frameworks,
where the underlying “friction” is price (and possibly wage) stickiness.32
3.2 Previous work
We are not the first to explore the possibility that monetary factors may impart persistent
effects on real interest rates in the recent literature. In their survey of the well documented
persistence of real interest rates, Neely and Rapach (2008) conclude that existing theories have
not adequately explained its origin. They argue and provide supportive evidence that
monetary shocks contribute to persistent fluctuations in real interest rates – and by implication
that monetary policy is not neutral in the long run. A number of papers have also documented
the link between persistent real interest rate shifts and changes in monetary regimes. On a
sample of 13 industrialised countries, Rapach and Wohar (2005) find that most of the structural
breaks in mean real interest rates coincide with breaks in inflation, which they interpret as
suggestive of monetary policy’s influence. In related work, Caporale and Grier (2005) find that
the appointments of Federal Reserve Chairmen Paul Volcker in 1979 and Alan Greenspan in
1987 coincided with shifts in mean real interest rates even after controlling for changes in the
mean inflation rate.
More generally, various studies have found results consistent with monetary factors
having persistent effects on real interest rates. In a VAR framework, Galí (1992) found that
expansionary monetary shocks led to very persistent declines in real interest rates, with as
much as 60 per cent of the variation in the real rate explained by money supply shocks after 5
years. Similarly, King and Watson (1997) and Rapach (2003) find that an exogenous increase
31 Keynes rejected the notion that the rate of interest equilibrated the demand and supply for loanable funds
because, in his view, the generation of income and expenditure are causal and the rate of interest merely an effect:
“[the] novelty [of my theory] lies in my maintaining that it is not the rate of interest, but the level of incomes which
ensures equality between savings and investment.” (Keynes (1937), p 241). For an in-depth discussion, see
Leijonhufvud (1981) and for a more recent sceptical view of the natural rate, see Laidler (2011) and his review.
32 “It is only […] with sticky prices that one is able to introduce the crucial Wicksellian distinction between the actual
and the natural rate of interest, as the discrepancy between the two arises only as a consequence of a failure of
prices to adjust sufficiently rapidly" (Woodford (2003), p 238).
26 WP685 Why so low for so long? A long view of real interest rate determination
in the steady-state inflation rate, which they interpret as a change in the monetary regime,
decreases the steady-state real interest rate.
Finally, Gourinchas and Rey’s (2016) emphasis on the role of booms and busts in
explaining short-term real interest movements is consistent with the role of monetary policy.
To be sure, their interpretation focuses on the relative demand for safe assets in the aftermath
of a deleveraging shock. But the association between the consumption-to-wealth ratio and
subsequent short-term real risk-free interest rates could also be seen as reflecting the central
bank’s reaction function in boom and bust periods. That is, the abnormally low consumption-
to-wealth ratio following financial busts tends to coincide with periods of aggressive monetary
policy easing to support the economy, which in turn gives rise to the association with low
short-term risk-free rates in the subsequent period. Like us, they also find little support for a
role of productivity growth or demographics in explaining real rates over time.
3.3 New evidence on monetary policy regimes
We investigate the link between real interest rates and monetary factors in two ways. The first
examines whether various monetary regimes are associated with significant differences in the
levels of real interest rates in individual countries. If money is neutral over the relevant horizon,
then monetary regimes should not matter for real interest rates. The second takes a global
perspective and explores the relative importance of global saving-investment determinants
and global monetary factors. We consider each in turn.
To explore the effects of monetary regimes in individual countries, we follow the existing
literature and identify seven different monetary regimes outside of the wars.33 As Table 9
shows, regime dates are closely correlated across countries, though not perfectly. In Graph 6,
the top two panels display the UK and US real interest rates and their associated regime shift
dates as an example. One can already see that regime dates coincide with shifts in real rate
behaviour.
33 We mainly follow Benati (2008) and the Economic History Association (http://eh.net/) for the monetary regime
definition, though the classification elsewhere in the literature is largely similar. The latest regime encompasses
formal inflation targeting as well as the regime where inflation stabilisation is de facto a key objective. We do not
single out the zero-lower bound period as a distinct regime, and exclude wars from our analysis.
WP685 Why so low for so long? A long view of real interest rate determination 27
International monetary policy regimes
Table 9
Countries 1870s 1880s 1890s 1900s 1910s 1920s 1930s 1940s 1950s 1960s 1970s 1980s 1990s 2000s 2010s
Australia 1852
Austria 1892
Belgium 1878
Canada 1854
Denmark 1872
Finland 1877
France 1878
Germany 1871
Italy 1884
Japan 1897
Netherlands 1875
New Zealand 1821
Norway 1875
Portugal 1854
Spain
Sweden 1873
Switzerland 1878
United Kingdom 1821
United States 1879
Gold standard/silver/bimetallic1 Wars Interwar (between GS and BW) Post-Bretton Woods (between BW and IT)
No GS/paper Interwar gold standard Bretton Woods (between BW and IT) Inflation targeting/de facto/price stability
1 The table shows the year when a country joins the gold standard. In the empirical analysis, we do not distinguish between metallic standards. In the text, we use “gold standard” to refer to metallic standards.
Sources: Benati (2008); Meissner (2005); BIS; authors’ calculations.
28 WP685 Why so low for so long? A long view of real interest rate determination
Real long-term interest rates and monetary policy regimes
In per cent Graph 6
United Kingdom United States
Endogenous breaks: Time-varying constant Endogenous breaks: Time fixed effects
The shaded areas indicate the world wars: 1914-1918 and 1940-1945 for the United Kingdom; 1914-1919 and 1942-1945 for the United
States.
The vertical lines indicate the year corresponding to a monetary policy regime shift. For the United Kingdom: 1914, 1919, 1932, 1940, 1946,
1972 and 1992; for the United States: 1879, 1914, 1919, 1934, 1942, 1946, 1972 and 1984. For the lower panels, we use the regime dates of
global monetary anchor countries, namely the United Kingdom up to WWI and the United States thereafter.
Sources: Benati (2008); Meissner (2005); BIS; authors’ calculations.
The same result emerges controlling for the saving-investment factors. To test this, we
re-estimate the baseline specification on a 10-year rolling regression and allow for time
variation in the constant term as a simple way to detect endogenous breaks. Graph 6 (lower
left panel) shows that this estimated constant tends to change behaviour or reverse trend
around monetary policy regime shifts. The result seems inconsistent with the notion that
money is neutral and real interest rates could be explained by real factors alone.
We next examine the role of monetary policy more systematically by including regime
dummies in a panel estimation. We try a number of specifications.
The first is simply to regress the long-term real interest rate on regime dummies in a
panel fixed-effects specification. We define the dummies so that the coefficients indicate how
the level of the real interest rates changes relative to the previous regime, with the first regime
being the metallic-standard period.
5
0
–5
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–15
–20
20161986195619261896
5.0
2.5
0.0
–2.5
–5.0
–7.5
20161986195619261896
7.5
5.0
2.5
0.0
–2.5
–5.0
20161986195619261896
5.0
2.5
0.0
–2.5
–5.0
–7.5
20161986195619261896
WP685 Why so low for so long? A long view of real interest rate determination 29
The results are consistent with the relevance of monetary policy regimes. All but one of
the regime dummies are economically and statistically significant (Table 10, first column),
suggesting that monetary regime changes have material implications for the levels of real
Real long-term interest rates and monetary policy regimes Table 10
(1)
Regimes
(2)
Regimes
& base
(3)
Regimes
& base & time
Paper 1.74** 5.80*** 4.25***
(0.78) (0.45) (0.53)
Interwar gold standard –3.81*** –7.34*** –4.40*
(0.60) (1.71) (2.42)
Interwar non-GS 1.25 1.90** 0.29
(0.73) (0.62) (0.68)
Bretton Woods –2.07*** –3.74*** –1.55*
(0.69) (1.03) (0.81)
Post-Bretton Woods 2.08*** 1.83*** 6.03***
(0.54) (0.47) (1.59)
Inflation targeting –1.05*** –1.25*** –0.80
(0.42) (0.50) (0.55)
GDP growth –0.07* –0.06*
(0.03) (0.03)
Population growth –0.23 0.02
(0.33) (0.31)
Dependency ratio 0.05*** 0.03**
(0.01) (0.01)
Life expectancy 0.15* 0.06
(0.07) (0.06)
Relative capital price 0.00 0.02
(0.01) (0.01)
Income inequality 0.07 0.11
(0.05) (0.06)
Constant 3.76*** –10.17** –5.67
(0.33) (3.53) (3.65)
Adjusted R-squared 0.16 0.19 0.45
Number of observations 2339 1102 1102
Country fixed effects yes yes yes
Time fixed effects no no Yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Monetary policy regimes are country-specific, with regime dummies defined relative to the preceding regime in chronological order. The
two wars are excluded. Gold standard (strictly, any metallic standards) is used as the reference regime, followed by “paper” (adopted
concurrently by some countries in the earlier period), “interwar gold standard”, “interwar non-gold standard” (adopted after the gold
standard was abandoned and before WWII), “Bretton Woods” regime of fixed exchange rates, “Post-Bretton Woods”, where central banks
abandoned the pegs but did not generally focus on inflation as the nominal anchor, and “inflation targeting”, which also includes a de
facto focus on price stability. See details of regime classification in Table 9.
Source: Authors’ calculations.
30 WP685 Why so low for so long? A long view of real interest rate determination
rates. For example, countries that did not join the gold/metallic standard had a 1.74
percentage points higher real rate on average relative to those that did. Similarly, adopting an
inflation targeting regime lowers average real rates by 1.05 percentage points relative to the
post-Bretton Woods regime, and by 1.86 percentage points relative to the gold standard
regime (the sum of all regime dummies). Other dummies have an analogous interpretation.
Some might argue that regime changes occur endogenously in response to shifts in
equilibrium interest rates driven by real factors. To control for this possibility, we consider
monetary regime dummies jointly with the saving-investment determinants (Table 10, second
column). If anything, the effects of changes in monetary regimes on real rates are even larger
in this more general specification. All regime changes are now associated with statistically
significant changes in the level of real rates. In all but one regime change, the economic
significance is in fact higher after controlling for saving-investment factors.34
The last, and most stringent, exercise is to control for any unobserved global trends that
may have coincided with the regime dates. We do so by including time fixed effects (Table 10,
third column). The test is designed to exclude the possibility that unobserved global saving-
investment determinants drive the estimates. This stacks the cards against uncovering any
effect of monetary regimes: here we are exploiting only their cross-sectional variation, which
is rather small (Table 9). Despite this stringent criterion, we still find significant effects of many
regime changes. The role of monetary regimes is quite robust.
Inspecting the time fixed effects (Graph 6, lower right panel), one can also see an
association between monetary policy regimes and the trends of real interest rates, in addition
to average levels. Monetary-regime switch dates typically coincide with turning points of the
time fixed effect series. Unless there is an unobserved global real factor that accidentally
coincides with (or, even harder to imagine, endogenously prompts) monetary regime switches,
then the monetary regimes themselves seem to be dictating real rate behaviour.
Overall, our analysis suggests that monetary regimes are significantly associated with
shifts in the level of real interest rates. Indeed, our monetary regime dummies systematically
perform better than most of the saving-investment determinants. In addition, there appears
to be a relationship between monetary regimes and trends in real interest rates.
One interpretation of our results is that changes in monetary policy regimes may be
associated with changes in risk premia, in particular inflation risk premia, which have not been
purged from our measure of real rates. We explore this in a couple of ways. One is to use
short-term real rates, for which risk premia should be less of a factor, instead of long-term
ones. The results are robust to this (Table B.3.4 in the Annex). The second way is to include
rolling estimates of higher moments of output growth and inflation, which should be
correlated with movements in risk premia. Again, the results do not change much.35 Thus, while
34 One might also argue that some third factor could be driving both changes in monetary regime and real interest
rates. We find it generally hard to identify such factors, but oil price shocks could be one example. Our results,
however, do not lend much support for their role: both the post-Bretton Woods and inflation targeting regimes
were associated with rapid increases in oil prices, yet in the former the regime dummy is positive while in the
latter it is negative. If oil prices affected real rates, they should do so in the same direction across monetary
regimes.
35 In related work, Nakamura and Steinsson (2017) show that their substantial and persistent money non-neutrality
result is robust to changes in risk premia. For their part, Christensen and Rudebusch (2017) examine the inflation-
linked bond term structure and find that a falling short-term risk-free rate could explain about half of the decline
in long-term real yields over the last 20 years.
WP685 Why so low for so long? A long view of real interest rate determination 31
changes in risk premia may account for some of the correlation between monetary regime
changes and real interest rate movements, they do not seem to account for all of it.36
We next turn to the global perspective. The results in Section 2 have shown that there is
an important global component to real interest rates that is correlated with some of the global
saving-investment determinants. Here we extend the analysis to include also global monetary
factors and compare their importance with the global saving-investment determinants. Our
hypothesis is that in a financially integrated world, the role of anchor currencies is important
for the dynamics of world interest rates.
As extensively documented, the country acting as global monetary anchor has changed
over time. Up to World War I, under the classical gold standard, the United Kingdom played
the main anchor role (eg Bloomfield (1959) and De Cecco (1974)). After World War I the United
States started to play a similar role, given the abundance of its gold holdings and the United
Kingdom’s struggle to adhere to the old parity. The United States then consolidated its
unrivalled role in the post-World War II period, starting with the Bretton Woods agreement in
1944. We therefore focus on these two countries.
In addition, the degree of financial integration has evolved substantially over time. As
discussed earlier, our sample includes two waves of tighter financial and real integration – the
first starting in the latter half of the 19th century and the second starting from the early 1980s.
As expected, financial globalisation waves tend to coincide with a higher correlation of real
interest rates across countries (Graph 7).
We proceed in two steps. First, we construct a global monetary anchor variable, which
reflects the policy stance of the financially dominant country. Following the previous
discussion, we define the global monetary anchor as the UK policy rate up to World War I and
the US counterpart thereafter. We regress the US and UK short-term real interest rates on their
respective saving-investment determinants – both country-specific and global components.
We take the residuals from these regressions (ie the part of US and UK short-term real rates
that cannot be explained by saving-investment determinants) as a “clean” measure of US and
UK monetary policy, respectively. In the second step, we plug this clean measure into the
baseline panel regressions for the long-term real interest rates for all countries except the
United States and the United Kingdom, controlling for both country-specific and global
saving-investment determinants. This allows us to test whether the clean measure of monetary
policy retains explanatory power. We also conduct a purely global analysis by regressing the
GDP-weighted global real long-term interest rate (excluding the United States and United
Kingdom) on the global monetary anchor and global saving-investment determinants.
The results indicate that the anchor countries’ monetary policy matters for long-term real
interest rates in the full sample and all the subsamples with one exception – the (mostly)
classical gold standard (Table 11). This is the case both for the cross-country panel and time-
series global regressions. Meanwhile, most of the saving-investment determinants still
perform poorly, particularly in the cross-country panel: they have the wrong signs and/or
switch signs across subsamples.
36 More generally, to the extent that monetary regimes do affect risk premia, this is potentially another source of
money non-neutrality and consistent with the risk-taking channel of monetary transmission. For example, Bianchi
et al (2017) find episodes of persistently high asset valuation in the United States to be associated with persistently
low real fed funds rate and low equity risk premia.
32 WP685 Why so low for so long? A long view of real interest rate determination
The global monetary policy variable performs just as well in the global specification, but
among the saving-investment factors the global dependency ratio appears equally promising
(Table 12). To safeguard against the possibility that these results are driven by unidirectional
trends, we simply add a linear time trend to the regressions. As can be seen, while the results
for the global monetary policy variable are hardly affected, the dependency ratio loses
significance in the pre-WWII sample. This indicates that the results for the global dependency
ratio primarily reflect correlation between unidirectional trends in the two measures within this
specific subsample.
Financial globalisation and the cross-country real interest rate correlation Graph 7
The financial globalisation index is from Obstfeld and Taylor (2003), and is a stylised measure based on historical introspection. The index is
extrapolated from 2000 assuming an unchanged degree of financial globalisation.
Median beta is a time-varying measure of 10-year real interest rate correlation across countries. We first regress each country’s real rate on a
composite series made up of the UK real rate up to World War I and the US real rate thereafter, on a 10-year rolling sample. We then take a
cross-country median.
The vertical lines indicate the year corresponding to a monetary policy regime shift. For the United Kingdom: 1914; for the United States:
1919, 1934, 1942, 1946, 1972, 1984 and 2009.
Sources: Benati (2008); Meissner (2005); Obstfeld and Taylor (2003); BIS; authors’ calculations.
1
0
–1
–2
–3
201620061996198619761966195619461936192619161906189618861876
Financial globalisation Median beta
WP685 Why so low for so long? A long view of real interest rate determination 33
Global monetary policy and real long-term interest rates in the rest of the world Table 11
Dependent variable: individual countries’ real long-term interest rates
Full sample Gold standard Pre-WWII Post-WWII
Global monetary policy 0.29*** –0.08 0.39** 0.30***
(0.04) (0.07) (0.14) (0.06)
G: GDP growth 0.01 –0.05 –0.11** 0.04
(0.04) (0.03) (0.04) (0.08)
G: pop. growth –1.60** –2.03 –1.38 0.72
(0.58) (1.64) (1.61) (0.54)
G: dependency r. 0.03 0.21 –0.12 0.03
(0.04) (0.12) (0.19) (0.04)
G: life exp. –0.13* –0.12 0.04 0.21*
(0.05) (0.12) (0.28) (0.1)
G: capital price –0.10*** –0.07 –0.10 –0.16***
(0.02) (0.08) (0.07) (0.04)
G: inequality –0.19* 0.22 0.33 –1.07***
(0.10) (0.23) (0.31) (0.14)
C: GDP growth –0.08* –0.02 –0.13* –0.02
(0.04) (0.02) (0.07) (0.03)
C: pop. growth –0.15 –0.13 0.20 0.53
(0.61) (0.28) (0.52) (0.40)
C: dependency r. –0.03 0.06 0.05 0.02
(0.01) (0.07) (0.09) (0.02)
C: life exp. 0.03 0.11 0.19 0.32**
(0.07) (0.06) (0.17) (0.09)
C: capital price 0.02 0.09*** –0.03 0.02
(0.01) (0.01) (0.05) (0.01)
C: inequality 0.08 –0.06* –0.18 0.19**
(0.11) (0.03) (0.19) (0.07)
Constant 12.49 –14.93 6.03 –6.04
(6.94) (16.14) (31.66) (7.46)
Number of observations 889 159 324 556
Adjusted R-squared 0.21 0.79 0.21 0.48
Standard errors in parentheses; * p<0.1, ** p<0.05, *** p<0.01. Horse race between three potential determinants of real long-term interest
rates: (i) global monetary policy (set in the centre countries, the United States and United Kingdom); (ii) global aggregates of saving-
investment factors (denoted by G); and (iii) country-specific component of the saving-investment factors (denoted by C). Global saving-
investment factors calculated as the weighted cross-country averages of each factor based on real GDP at purchasing power parity.
34 WP685 Why so low for so long? A long view of real interest rate determination
Global monetary policy and global real long-term interest rates Table 12
Dependent variable: global real long-term interest rate excl US & UK
No linear trend Linear trend included
Full sample
Gold
standard Pre- WWII Post-
WWII
Full
sample
Gold
standard Pre-WWII Post
WWII
Global monetary policy 0.22*** 0.07 0.28*** 0.31*** 0.16** 0.08 0.39*** 0.31***
(0.06) (0.13) (0.10) (0.08) (0.06) (0.10) (0.08) (0.08)
G: GDP growth 0.12** –0.06 0.03 0.10 0.11** –0.05 0.04 0.06
(0.05) (0.04) (0.07) (0.07) (0.05) (0.03) (0.05) (0.07)
G: pop. growth –1.24*** 1.57*** –0.24 0.25 –1.53*** 3.10*** 0.59 0.28
(0.28) (0.55) (0.68) (0.33) (0.29) (0.51) (0.55) (0.33)
G: dependency r. 0.17*** 0.01 0.48*** 0.14*** 0.16*** –0.06 –0.13 0.15***
(0.03) (0.13) (0.15) (0.03) (0.03) (0.10) (0.15) (0.03)
G: life exp. 0.12*** –0.31* 0.72*** 0.26** 0.42*** 0.09 0.64*** 0.69**
(0.05) (0.13) (0.18) (0.10) (0.11) (0.13) (0.14) (0.10)
G: capital price –0.08*** 0.07* 0.02 –0.17*** –0.14*** 0.07** –0.17*** –0.20***
(0.03) (0.04) (0.06) (0.04) (0.03) (0.03) (0.06) (0.04)
G: inequality 0.20** –0.25*** 0.54*** –0.90*** 0.14 –0.58*** –0.14 –0.90***
(0.10) (0.09) (0.15) (0.12) (0.10) (0.09) (0.16) (0.12)
Constant –21.00*** 21.15 –86.04*** –20.04** –26.21*** 23.92* 5.35 –37.27**
(5.66) (18.00) (21.62) (8.72) (5.80) (13.69) (22.14) (15.30)
Trend –0.11*** –0.19*** –0.36*** –0.11
(0.04) (0.04) (0.06) (0.08)
Number of observations 139 42 66 65 139 42 66 65
Adjusted R-squared 0.46 0.73 0.45 0.80 0.49 0.84 0.67 0.81
Standard errors in parentheses; * p<0.1, ** p<0.05, *** p<0.01. Horse race between three potential determinants of global real long-term interest
rate: (i) global monetary policy (set in the centre countries, the United States and United Kingdom); (ii) global aggregates of saving-investment
factors (denoted by G); and (iii) country-specific component of the saving-investment factors (denoted by C). Global saving-investments factors
calculated as the weighted cross-country averages of each factor based on real GDP at purchasing power parity. The global real long-term interest
rate similarly constructed but we exclude the United States and the United Kingdom from the calculation.
3.4 A monetary narrative of the evolution of real interest rates
It may be useful to put together the various pieces of the jigsaw puzzle and provide a very
stylised narrative of the evolution of real interest rates in which monetary policy regimes play
a prominent role (Graph 8).37
37 For a more detailed discussion of the interaction between monetary, financial and real economy regimes over the
historical phase covered here, see Borio (2014).
WP685 Why so low for so long? A long view of real interest rate determination 35
Evolution of nominal and real long-term interest rates Graph 8
United Kingdom United States
Per cent (reversed) Per cent Per cent (reversed) Per cent
Dashed lines represent monetary policy regime dates of respective countries.
Shaded regions indicate World War I, 1914-1918 and World War II, 1940-1945 for GB and 1942-1945 for US.
Sources: Benati (2008); Meissner (2005); Global Financial Data; authors’ calculations.
During the classical gold standard, as already noted, central banks tended to keep
nominal interest rates rather constant, without responding much to macroeconomic
conditions or inflation. However, short-term volatility aside, this did not prevent inflation from
remaining relatively stable over longer horizons. As a result, also real interest rates were
generally rather stable throughout.
During World War I, just as during World War II, governments made sure interest rates
remained low and, with capital controls in place, increases in inflation drove them down,
reaching troughs.
In the 1920s, the United States took over as the global anchor, thanks to its growing
economic and financial might as well as plentiful gold supplies. As central banks began to
entertain macro stabilisation objectives, interest rates declined somewhat. Still, central banks’
comparatively passive behaviour combined with stable inflation meant that both nominal and
rates again remained relatively stable. In a way similar to the Great Moderation that preceded
the recent GFC, financial imbalances built up. The Great Depression, in part a financial boom
gone wrong (Eichengreen and Mitchener (2004), Rogoff (2015), Gourinchas and Rey (2016)),
induced central banks to cut rates drastically in an effort to support demand and push prices
up. In the years preceding World War II, conditions gradually normalised.
The postwar period saw monetary and financial repression: nominal rates were kept quite
low through a mixture of government intervention and controls, domestic and international.
As economies normalised and central banks gained further room for manoeuvre, rates
gradually edged up.38 But once inflation started to take hold in the 1960s and gained
momentum in the 1970s, real interest rates fell substantially.
The early 1980s ushered in both financial liberalisation and a much more determined anti-
inflation resolve, most evident in Volcker’s decision to allow interest rates to rise substantially.
38 The political will to tackle inflation played a role. In 1951, the Federal Reserve reached an agreement with the
Treasury, paving the way to pursue an independent disinflationary policy and raising the policy rate (Federal
Reserve Bank of Richmond (2011)). Similarly, the newly elected Conservative government in the United Kingdom
saw a higher Bank Rate as part of the policy package needed to address inflation (Ross (1992)).
20
10
0
–10 10
0
–10
–20
20161996197619561936191618961876
Expected inflationLhs:
20
10
0
–10 10
0
–10
–20
20161996197619561936191618961876
Nominal long-term rateRhs: Real long-term rate
36 WP685 Why so low for so long? A long view of real interest rate determination
Real interest rates naturally increased too and appeared very high compared with the previous
phase (eg G10 (1995)).
Since then, real interest rates have been declining following a combination of factors (eg
Borio (2017a)). A first factor, at work in the first sub-phase, is a natural normalisation from the
levels needed to fight the Great Inflation. Stickiness in inflation expectations, as market
participants had been burnt during the high inflation, no doubt slowed the process (eg Erceg
and Levin (2003)). A second factor, in part reminiscent of the interwar years, is the asymmetric
response to successive financial booms and busts, most notably those that culminated with
the banking strains in the early 1990s and then again, most spectacularly, the GFC. Central
banks focused on tight inflation objectives, as well as short-run macroeconomic stabilisation,
and did not respond to the build-up of financial imbalances (eg Borio (2014, 2017b). The third
factor, especially at play post-GFC, has been the central bank’s difficulty in pushing inflation
towards target post-crisis, not least as a result of the long-term headwinds induced by
globalisation and, possibly, technology (Borio (2017a)).
Conclusion
Nowadays the prevailing view among academics and policymakers is that the decline in real
interest rates since the early 1980s to historically low peacetime levels reflects a decline in the
natural (equilibrium) interest rate. In this view, changes in (ex ante) saving-investment balances
have pushed down the real interest rate consistent with full employment (output at potential).
The empirical evidence for this hypothesis has so far relied primarily on two approaches. One
approach assumes that observed real interest rates roughly track, on average and over long
periods, natural rates; it then links their observed decline to potential underlying determinants
of saving-investment balances, such as demographic factors or the relative price of capital,
mainly through informal inspection or calibrated models. Another approach filters out the
natural rate from market rates based on critical assumptions, including the hypothesis that
inflation responds stably and systematically to domestic economic slack and that the real
interest rate is a key factor influencing aggregate demand.
In this paper we have argued that the role of maintained hypotheses in this type of
evidence is uncomfortably strong. Accordingly, we have adopted a more data-driven
approach, which links observable proxies for the underlying determinants of saving-investment
balances to real interest rates, both market rates and traditional estimates of natural rates.
Importantly, we examine the corresponding relationships also beyond the standard recent
sample (from the early 1980s), in order to limit the risk of finding spurious relationships. To do
so, we go back in history, all the way to the late 1800s, for as many as 19 countries.
Our results cast doubt on the traditional interpretation. While there is a reasonable,
although by no means watertight, link between the posited underlying saving-investment
determinants and the real interest rate in the recent reference period, the link does not survive
beyond the standard sample. By contrast, we find robust evidence of the relevance of
monetary policy regimes, defined by the central banks’ interest rate-setting behaviour
(reaction function).
There are two ways in which this result, taken at face value, could be interpreted. One is
to suggest that the information content of the proxies for the saving-investment determinants
may have changed over time for structural reasons. We have not pursued this line of argument.
While no doubt possible, it is not immediately obvious to us why that should be the case.
Indeed, the unsystematic nature of the instability in the individual saving-investment
coefficients would suggest otherwise. Another interpretation is that the maintained
WP685 Why so low for so long? A long view of real interest rate determination 37
hypotheses deserve further investigation. For instance, the link between economic slack and
inflation has come under closer scrutiny for some time. And the problem would be
compounded if the link between real interest rates and aggregate demand was sometimes
unreliable (eg Borio and Hofmann (2017)). Taken together, these factors would raise questions
about the theoretical and, above all, practical usefulness of the concept of the natural interest
rate for policymaking. These issues clearly deserve further examination.
38 WP685 Why so low for so long? A long view of real interest rate determination
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44 WP685 Why so low for so long? A long view of real interest rate determination
Annex A: Data and plots
A.1 Data sources and coverage
39 Our long-term interest rate data are very similar to those in Mauro et al (2006).
Data sources Table A.1.1
Variables Series Data sources
Nominal interest rates
Policy interest rates (official policy interest
rates, or closest proxies)
BIS and Global Financial Data
Short-term interest rates (3-month
government bill yields, or closest proxies)
Global Financial Data, Jordà et al (2017), Bordo
et al (2001) and national authorities
Long-term interest rates (10-year
government bond yields or closest proxies)
Global Financial Data and national
authorities39
Macroeconomics
GDP annual growth
National authorities, Global Financial Data,
and the Maddison Project
(http://www.ggdc.net/maddison/maddison-
project/home.htm)
CPI annual growth
National authorities, Global Financial Data,
and Mitchell’s International Statistics
Productivity Total factor productivity, capital share, labour
productivity and capital density
Bergeuad et al (2016)
(http://www.longtermproductivity.com)
Demographics
Population sizes by age brackets
United Nations, Human Mortality Database
(http://www.mortality.org), and Mitchell’s
International Historical Statistics
Population growth and life expectancy at
birth
Human Mortality Database, Our World in Data
(https://ourworldindata.org/), The Human Life-
Table Database (http://lifetable.de)
Labour force participation above age 65 OECD, Costa (1998)
Relative price of capital Investment goods price index divided by
consumption price index
Eichengreen (2015)
Inequality Top 1% income share, or closest proxies
Roine and Waldenström (2015) and World
Wealth & Income Database
(http://wid.world/), supplemented by Lindert
(2000) and the Chartbook of Economic
Inequality
(https://www.chartbookofeconomicinequality.
com)
US equity risk premium Implied equity risk premium from a 2-stage
augmented dividend discount model
A Damodaran
(http://pages.stern.nyu.edu/~adamodar/)
Monetary policy regimes Dummy of policy regimes
BIS, Benati (2008), Meissner (2005), Eh.net
(https://eh.net/)
WP685 Why so low for so long? A long view of real interest rate determination 45
Data coverage Table A.1.2
Countries Policy
rate
Short
rate
Long
rate GDP CPI Productivity
Demographics:
Pop size by ages
Demographics:
Life expectancy
Relative price
of capital Inequality Population
growth
Labour force
participation (> 65)
Australia 1921- 1872- 1872- 1870- 1870- 1890- 1870- 1885- 1872- 1921- 1922- 1966-
Austria 1874- 1874- 1874- 1871- 1870- NA 1870- 1870- NA NA 1948- 1994-
Belgium 1881- 1881- 1881- 1870- 1871- 1890- 1870- 1870- NA NA 1870- 1983-
Canada 1935- 1934- 1881- 1871- 1871- 1890- 1870- 1870- 1872- 1920- 1922- 1976-
Denmark 1870- 1875- 1870- 1870- 1870- 1890- 1870- 1875- 1872- 1870- 1870- 1983-
Finland 1911- 1911- 1911- 1870- 1901- 1890- 1870- 1870- 1872- 1870- 1879- 1963-
France 1870- 1870- 1870- 1870- 1870- 1890- 1870- 1870- NA 1915- 1870- 1870-
Germany 1870- 1870- 1870- 1870- 1870- 1890- 1871- 1875- 1872- 1891- 1957- 1870-
Italy 1872- 1885- 1872- 1870- 1870- 1890- 1870- 1872- 1872- 1901- 1873- 1970-
Japan 1882- 1879- 1879- 1871- 1870- 1890- 1884- 1870- 1877- 1886- 1948- 1968-
Netherlands 1870- 1870- 1870- 1870- 1870- 1890- 1870- 1870- NA 1914- 1870- 1971-
New Zealand 1923- 1973- 1918- 1871- 1908- NA 1870- 1901- NA 1921- 1902- 1986-
Norway 1870- 1870- 1870- 1870- 1870- 1890- 1870- 1870- 1872- 1875- 1870- 1972-
Portugal 1941- 1941- 1941- 1870- 1931- 1890- 1870- 1940- NA 1976 1941- 1974-
Spain 1870- 1880- 1870- 1870- 1870- 1890- 1870- 1882- NA 1981- 1909- 1972-
Sweden 1870- 1870- 1870- 1870- 1870- 1890- 1870- 1870- 1872- 1903- 1870- 1963-
Switzerland 1870- 1870- 1893- 1870- 1870- 1890- 1870- 1876- NA 1933- 1877- 1991-
United Kingdom 1870- 1870- 1870- 1870- 1870- 1890- 1870- 1870- 1872- 1870- 1870- 1870-
United States 1914- 1870- 1870- 1870- 1870- 1890- 1870- 1880- 1872- 1913- 1934- 1870-
46 WP685 Why so low for so long? A long view of real interest rate determination
A.2 Data plots of real interest rates
Real policy rates
In per cent Graph A.2.1
The shaded areas indicate the world wars, 1914-1918 and 1940-1945.
Sources: Global Financial Data; national data.
5
0
–5
–10
201619911966194119161891
Australia
Canada
Austria Belgium
5
0
–5
–10
201619911966194119161891
Denmark Finland France
5
0
–5
–10
201619911966194119161891
Germany Italy Japan
5
0
–5
–10
201619911966194119161891
Netherlands
Norway
New Zealand
5
0
–5
–10
201619911966194119161891
Portugal Spain Sweden
5
0
–5
–10
201619911966194119161891
Switzerland
United States
United Kingdom
WP685 Why so low for so long? A long view of real interest rate determination 47
Real short-term rates
In per cent Graph A.2.2
The shaded areas indicate the world wars, 1914-1918 and 1940-1945.
Sources: Bordo et al (2001); Jordà et al (2017); Global Financial Data; national data.
5
0
–5
–10
201619911966194119161891
Australia
Canada
Austria Belgium
5
0
–5
–10
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Denmark Finland France
5
0
–5
–10
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Germany Italy Japan
5
0
–5
–10
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Netherlands
Norway
New Zealand
5
0
–5
–10
201619911966194119161891
Netherlands
Norway
New Zealand
5
0
–5
–10
201619911966194119161891
Switzerland
United States
United Kingdom
48 WP685 Why so low for so long? A long view of real interest rate determination
Real long-term rates
In per cent Graph A.2.3
The shaded areas indicate the world wars, 1914-1918 and 1940-1945.
Sources: Global Financial Data; national data.
5
0
–5
–10
201619911966194119161891
Australia
Canada
Austria Belgium
5
0
–5
–10
201619911966194119161891
Denmark Finland France
5
0
–5
–10
201619911966194119161891
Germany Italy Japan
5
0
–5
–10
201619911966194119161891
Netherlands
Norway
New Zealand
5
0
–5
–10
201619911966194119161891
Portugal Spain Sweden
5
0
–5
–10
201619911966194119161891
Switzerland
United States
United Kingdom
WP685 Why so low for so long? A long view of real interest rate determination 49
Nominal short-term rates
In per cent Graph A.2.4
The shaded areas indicate the world wars, 1914-1918 and 1940-1945.
Sources: Global Financial Data; national data.
20
15
10
5
0
–5
201619911966194119161891
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Canada
Austria Belgium
20
15
10
5
0
–5
201619911966194119161891
Denmark Finland France
20
15
10
5
0
–5
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Germany Italy Japan
20
15
10
5
0
–5
201619911966194119161891
Netherlands
Norway
New Zealand
20
15
10
5
0
–5
201619911966194119161891
Portugal Spain Sweden
20
15
10
5
0
–5
201619911966194119161891
Switzerland
United States
United Kingdom
50 WP685 Why so low for so long? A long view of real interest rate determination
Inflation and inflation expectations
In per cent Graph A.2.5
Australia Austria Belgium
Canada Denmark Finland
France Germany Italy
Japan Netherlands New Zealand
15
10
5
0
–5
–10
201619911966194119161891
15
10
5
0
–5
–10
201619911966194119161891
15
10
5
0
–5
–10
201619911966194119161891
15
10
5
0
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201619911966194119161891
15
10
5
0
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10
5
0
–5
–10
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10
5
0
–5
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10
5
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10
5
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10
5
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WP685 Why so low for so long? A long view of real interest rate determination 51
Inflation and inflation expectations (continued)
In per cent Graph A.2.5
Norway Portugal Spain
Sweden Switzerland United Kingdom
United States
The shaded areas indicate the world wars, 1914-1918 and 1940-1945.
Sources: Global Financial Data; national data.
15
10
5
0
–5
–10
201619911966194119161891
15
10
5
0
–5
–10
201619911966194119161891
15
10
5
0
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–10
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10
5
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10
5
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15
10
5
0
–5
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10
5
0
–5
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201619911966194119161891
Inflation
Short-term inflations expectations
Long-term inflation expectations
52 WP685 Why so low for so long? A long view of real interest rate determination
A.3 Saving-investment factors for the United States and United Kingdom
Saving-investment factors: United States and United Kingdom Graph A.3
GDP growth1 Dependency ratio Life expectancy
Per cent Per cent Years
Inequality Relative price of capital Marginal product of capital
Per cent
1 Five-year moving average.
Sources: Bergeuad et al (2016); Costa (1998); Eichengreen (2015); Roine and Waldenström (2015); Chartbook of Economic Inequality;
International Historical Statistics; World Wealth & Income Database; OECD; United Nations, Human Mortality Database; national data; authors’
calculations.
21
14
7
0
–7
–14
201619861956192618961866
United Kingdom United States
110
100
90
80
70
60
201519851955192518951865
75
60
45
30
15
0
201419841954192418941864
25
20
15
10
5
201119811951192118911861
1.4
1.2
1.0
0.8
0.6
201019851960193519101885
United Kingdom United States
0.165
0.130
0.095
0.060
0.025
200419841964194419241904
WP685 Why so low for so long? A long view of real interest rate determination 53
Annex B: Robustness results
B.1 Bivariate panel regression with time trends
This exercise checks for any spurious correlation between real interest rates and each of the
saving-investment factors due to the presence of global trends. We do so by including linear
time trends in each subsample. As the results below show, in comparison to Table 4, the
estimates are indeed sensitive to adding such a trend, suggesting that inference is fragile as it
is solely based on matching unidirectional trends.
Bivariate panel regressions with time trends Table B.1
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
Marginal product of
capital (+) 2.90 23.09*** –16.01 –17.94 –14.59 –18.36
GDP growth (+) –0.10*** 0.01 –0.07* 0.02 0.09* –0.01
TFP growth (+) –0.08* 0.02** –0.01 0.09** 0.18*** 0.05
Population growth
(+/–) –0.20 0.07 0.07** –0.98*** 0.07 –0.67
Dependency ratio (+) –0.01 –0.03 –0.00 0.00 0.08** –0.11**
Life expectancy (–) –0.12*** 0.11 0.36*** 0.00 –0.31 0.70**
Relative price of
capital (+) –0.00 0.06 –0.09 0.02** –0.05 –0.02
Inequality (–) 0.12*** –0.09 –0.21 –0.32*** 0.15 –0.03
Time trend Yes Yes Yes Yes Yes Yes
Robust standard errors in parentheses based on country clusters; ***/**/* denote results significant at the 1/5/10% level. Significant
coefficients with signs consistent with saving-investment theory are highlighted in green. Other significant coefficients are highlighted in red.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations
54 WP685 Why so low for so long? A long view of real interest rate determination
B.2 Average dependent and independent variables
In this robustness exercise, we re-estimate the baseline and bivariate specifications using
moving averages of all variables, in order to smooth out cyclical variations. Using both five-
year and 10-year moving averages, the results are very similar to those from the main
specifications. The two tables below report the results for five-year moving averages; the
inferences from those based on 10-year averages are similar.
Baseline specification using five-year averages Table B.2.1
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
GDP growth (+) –0.10 –0.13 –0.23 0.02 –0.07 –0.15
(0.08) (0.10) (0.25) (0.11) (0.05) (0.10)
Population growth (+/–) –1.20 –1.78 –0.90 –0.62 –0.15 –1.75*
(0.68) (1.50) (0.77) (0.64) (0.45) (0.89)
Dependency ratio (+) 0.02 –0.05* –0.00 0.01 0.07* –0.16***
(0.02) (0.02) (0.17) (0.02) (0.03) (0.04)
Life expectancy (–) 0.06 –0.16 0.56* 0.26** 0.62*** –0.30*
(0.05) (0.11) (0.26) (0.10) (0.07) (0.14)
Relative price of capital (+) 0.02 0.17*** 0.10 0.02 0.01 0.03
(0.02) (0.05) (0.11) (0.01) (0.03) (0.06)
Income inequality (–) 0.09 0.15 –0.27 –0.28*** –0.00 –0.05
(0.11) (0.11) (0.37) (0.07) (0.26) (0.25)
Constant –3.52 13.45* –24.67 –15.13* –46.94*** 39.11***
(4.76) (6.31) (18.96) (6.91) (9.31) (10.73)
Adjusted R-squared 0.05 0.59 0.45 0.39 0.76 0.23
Number of observations 247 36 42 149 62 87
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 55
Bivariate panel using five-year averages Table B.2.2
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
Marginal product of capital (+) 0.06 0.41*** –0.11 –0.37*** –0.20 0.17
(0.05) (0.03) (0.50) (0.08) (0.40) (0.25)
GDP growth (+) –0.13 0.08 0.05 –0.23** –0.11 0.25*
(0.08) (0.07) (0.15) (0.11) (0.12) (0.14)
TFP growth (+)
–0.09
(0.13)
–0.00
(0.07)
0.20
(0.23)
–0.11
(0.17)
0.03
(0.17)
0.52**
(0.23)
Population growth (+/–) –0.05 –0.15 0.20** –1.88*** –1.78*** –1.41*
(0.15) (0.17) (0.07) (0.40) (0.43) (0.68)
Dependency ratio (+) 0.03** –0.02 –0.21** –0.05** 0.06 –0.05
(0.01) (0.04) (0.09) (0.02) (0.09) (0.04)
Life expectancy (–) –0.03** –0.11** 0.41*** 0.20*** 0.48*** –0.14
(0.01) (0.05) (0.11) (0.05) (0.09) (0.10)
Relative price of capital (+) 0.01 0.05 –0.05 –0.04** –0.10* 0.04
(0.01) (0.04) (0.10) (0.02) (0.05) (0.02)
Income inequality (–) –0.00 –0.05 –0.62*** –0.33*** –0.73*** –0.16*
(0.04) (0.12) (0.18) (0.11) (0.18) (0.09)
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations.
56 WP685 Why so low for so long? A long view of real interest rate determination
B.3 Short-term market rates as the dependent variable
This set of tests replicates all our key specifications using short-term market interest rates
instead of long-term ones. As short-term real rates rely less on short-term inflation forecasts,
they should be more robust to any measurement errors in expected inflation. As the tables
below indicate, the results for the short-term rate are very similar in sign and size to those for
the long-term rate (Tables 5 and 6 in the main text). This is so in both the baseline and dynamic
fixed-effects panel specifications. For the global specification, the dependency ratio now loses
significance or flips sign in some samples. The relative price of capital fares slightly better than
in the long-term rate specification, but only at country-specific level. Overall, the lack of stable
relationships is still apparent. By contrast, monetary policy regime changes remain a significant
determinant of the average levels of short-term real rates.
Baseline specification using short-term interest rates Table B.3.1
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
GDP growth (+) –0.17** –0.19 –0.23** 0.11 0.07 0.04
(0.06) (0.15) (0.07) (0.11) (0.11) (0.06)
Population growth (+/–) –1.14** –0.27 1.03 –0.71 0.25 –1.36
(0.49) (0.67) (0.72) (0.50) (0.31) (1.30)
Dependency ratio (+) 0.03 –0.04 0.18 0.03 0.21*** –0.15
(0.02) (0.04) (0.10) (0.04) (0.04) (0.10)
Life expectancy (–) –0.05 –0.26** 0.51* 0.27* 0.24* –0.67***
(0.04) (0.10) (0.24) (0.14) (0.12) (0.13)
Relative price of capital (+) 0.01 0.15*** –0.06 0.01 –0.05* 0.04
(0.02) (0.04) (0.04) (0.02) (0.02) (0.05)
Income inequality (–) 0.04 –0.16 –0.25 –0.34*** –0.13 –0.01
(0.07) (0.21) (0.54) (0.10) (0.20) (0.22)
Constant 4.66 22.58** –36.88 –17.79 –33.23*** 65.67***
(4.62) (6.97) (24.87) (13.32) (9.61) (14.48)
Adjusted R-squared 0.11 0.28 0.22 0.14 0.21 0.37
Number of observations 1078 199 187 650 310 340
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 57
Short-term real rates in a dynamic fixed-effects panel specification Table B.3.2
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
Long-run coefficients
GDP growth (+) –0.28*** –0.12 –0.31*** 0.17 0.08 0.21
(0.08) (0.16) (0.12) (0.14) (0.11) (0.19)
Population growth (+/–) –1.31** –1.78*** –0.69 –1.07 –0.94 –2.69*
(0.56) (0.53) (0.89) (0.75) (0.92) (1.59)
Dependency ratio (+) 0.04 –0.08* 0.08 0.04 0.20*** –0.10
(0.03) (0.05) (0.06) (0.04) (0.06) (0.14)
Life expectancy (–) –0.14*** –0.34*** –0.08 0.27** 0.15 –0.34**
(0.04) (0.09) (0.15) (0.12) (0.22) (0.17)
Relative price of capital (+) 0.01 0.26*** –0.04 0.02 –0.08*** 0.16***
(0.02) (0.02) (0.03) (0.02) (0.03) (0.06)
Income inequality (–) –0.17*** 0.19 0.32 –0.47*** –0.00 0.01
(0.04) (0.13) (0.32) (0.12) (0.30) (0.20)
Short-run coefficients
Adjustment parameter –0.31*** –0.90*** –0.85*** –0.31*** –0.56*** –0.38***
(0.03) (0.19) (0.13) (0.02) (0.08) (0.05)
Constant 3.96** 21.31** 0.05 –5.18 –14.14 14.83*
(1.76) (10.61) (11.99) (3.45) (13.44) (7.57)
Adjusted R-squared 0.27 0.43 0.63 0.25 0.37 0.24
Number of observations 980 174 159 640 300 340
Country fixed effects yes yes yes yes yes yes
Differences yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Differences: lagged differences from t to t-2 of all variables included in the regressions.
Source: Authors’ calculations.
58 WP685 Why so low for so long? A long view of real interest rate determination
Global specification using short-term interest rates Table B.3.3
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
Global component:
GDP growth (+) –0.07 –0.21 –0.23** 0.22*** 0.32*** –0.05
(0.05) (0.12) (0.09) (0.05) (0.06) (0.11)
Population growth (+/–) –1.08** –1.22 0.17 0.51 1.99*** 1.36
(0.48) (1.90) (2.22) (0.32) (0.41) (6.62)
Dependency ratio (+) 0.02 0.14 1.12*** –0.02 0.49*** –1.05***
(0.03) (0.21) (0.30) (0.04) (0.07) (0.15)
Life expectancy (–) –0.29*** –0.14 2.09** 0.07 –0.36 –1.46**
(0.05) (0.16) (0.94) (0.11) (0.23) (0.49)
Relative price of capital (+) –0.18*** 0.04 0.15 –0.20*** 0.14* 0.24***
(0.04) (0.10) (0.27) (0.04) (0.07) (0.06)
Income inequality (–) –0.49*** –0.11 0.41 –1.22*** –2.99*** 0.41
(0.12) (0.12) (1.19) (0.09) (0.51) (0.25)
Country specific component:
GDP growth (+) –0.12* –0.20 –0.20* –0.00 0.01 –0.06
(0.06) (0.16) (0.10) (0.10) (0.09) (0.08)
Population growth (+/–) –0.15 –0.06 0.99 –0.52 –0.17 –0.36
(0.53) (0.29) (0.90) (0.50) (0.38) (1.01)
Dependency ratio (+) 0.04 –0.06 0.02 0.05 0.02 0.08
(0.02) (0.04) (0.17) (0.03) (0.05) (0.11)
Life expectancy (–) –0.01 0.13 0.38* –0.22 –0.82*** 0.57
(0.09) (0.12) (0.21) (0.14) (0.21) (0.55)
Relative price of capital (+) 0.04** 0.12*** –0.02 0.03** –0.03 0.08*
(0.02) (0.03) (0.04) (0.01) (0.02) (0.04)
Income inequality (–) –0.11* –0.18 –0.31 –0.01 –0.26 0.24
(0.06) (0.21) (0.54) (0.12) (0.28) (0.25)
Constant 26.76*** 1.18 –210.76** 8.27 7.98 184.56***
(5.22) (24.97) (92.95) (9.20) (18.77) (38.69)
Adjusted R-squared 0.23 0.33 0.27 0.36 0.38 0.53
Number of observations 1078 199 187 650 310 340
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016. Global components calculated as the averages of each variable based on real GDP at purchasing power
parity.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 59
Short-term interest rates and monetary policy regimes Table B.3.4
(1)
Regimes
(2)
Regimes
& base
(3)
Regimes
& base & time
Paper 2.91** 6.11*** 4.60***
(1.34) (1.66) (1.30)
Interwar gold standard –3.18** –6.11* –1.42
(1.31) (2.79) (3.03)
Interwar non-GS –1.79** –1.51 0.51
(0.74) (0.92) (1.20)
Bretton Woods –1.79** –3.87** –2.77**
(0.64) (1.43) (0.97)
Post-Bretton Woods 2.58*** 2.20*** 2.25
(0.50) (0.45) (2.59)
Inflation targeting –1.68*** –0.70 –1.20*
(0.44) (1.11) (0.64)
GDP growth –0.11* –0.07
(0.05) (0.05)
Population growth –0.31 –0.06
(0.52) (0.53)
Dependency ratio 0.06** 0.05**
(0.02) (0.02)
Life expectancy 0.12 0.04
(0.10) (0.08)
Relative capital price 0.02 0.04**
(0.02) (0.02)
Income inequality –0.05 0.01
(0.05) (0.05)
Constant 3.64*** 4.70*** 0.65
(0.17) (1.23) (1.43)
Adjusted R-squared 0.21 0.21 0.51
Number of observations 2219 1078 1078
Country fixed effects yes yes yes
Time fixed effects no no Yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Monetary policy regimes are country-specific, with regime dummies defined relative to the preceding regime in chronological order. The
two world wars are left out. Gold (metallic) standard is used as the reference regime, followed by “paper” (adopted concurrently by some
countries during the metallic standard), “interwar gold standard”, “interwar non-gold standard” (adopted after the gold standard was
abandoned and before WWII), “Bretton Woods” regime of fixed exchange rates, “post-Bretton Woods” where central banks have
abandoned the pegs but have not focused on inflation as the nominal anchor, and the final regime “inflation targeting” which also includes
de facto price stability focus. See details of regime classification in Table 9.
Source: Authors’ calculations.
60 WP685 Why so low for so long? A long view of real interest rate determination
B.4 Excluding periods after the world wars
Although we have excluded the wars from all our empirical analysis, it might be argued that
the reconstruction periods following the wars could unduly influence the results. In this
exercise, we drop five years immediately after both world wars from the estimation sample.
Doing so does not materially affect the conclusions for any of our previous results. The table
below shows only the baseline specification result.
Baseline specification, dropping five years after the world wars from sample Table B.4
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
GDP growth (+) –0.07** –0.00 –0.10*** 0.09 0.06 0.03
(0.03) (0.02) (0.02) (0.08) (0.09) (0.05)
Population growth (+/–) –1.52*** –0.50 –0.62** –1.39** –1.37** –0.68
(0.47) (0.50) (0.27) (0.49) (0.61) (0.71)
Dependency ratio (+) 0.01 –0.03 –0.14*** 0.04 0.15*** –0.03
(0.02) (0.02) (0.02) (0.03) (0.02) (0.07)
Life expectancy (–) –0.04 –0.20*** 0.13** 0.21** 0.37* –0.32***
(0.02) (0.05) (0.05) (0.08) (0.18) (0.09)
Relative price of capital (+) 0.01 0.11** –0.08** –0.00 –0.07* 0.01
(0.01) (0.03) (0.03) (0.01) (0.04) (0.03)
Income inequality (–) 0.02 –0.01 0.09 –0.24*** –0.09 0.10
(0.04) (0.05) (0.26) (0.06) (0.24) (0.15)
Constant 5.70* 15.33*** 6.97* –13.61 –34.95* 31.18***
(2.81) (2.61) (3.19) (7.91) (16.89) (7.95)
Adjusted R-squared 0.11 0.51 0.31 0.21 0.38 0.26
Number of observations 999 202 164 633 293 340
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1924-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening, 1980-2016.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 61
B.5 Alternative expectations of inflation and GDP growth
This robustness check considers an alternative approach to measuring inflation and growth
expectations. We allow for the possibility that agents might anticipate future average 10-year
inflation and GDP growth correctly, eg they might be able to foresee the protracted period of
slower growth associated with the Great Recession and revise expected inflation down. We
follow the approach by Gali and Gertler (1999), who impose the rational expectations
hypothesis through an orthogonality condition. In our context, the idea is to rewrite (1) as
=
,+,
+∗
;+
where is the nominal yield on government bonds, , and ,
are the average 10-
year ahead inflation and GDP growth rates, respectively, and
excludes the GDP growth rate.
Under rational expectations, errors in forecasting inflation are uncorrelated with information,
, dated or earlier. This gives the orthogonality condition
−
, −,
−∗
;−
=0
which can be used to estimate the parameters via GMM. With rational expectations, we would
expect to find =1.
Allowing for anticipated inflation with GMM estimation Table B.5
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
Average 10-year ahead inflation
(+, =1 if perfect foresight)
0.99***
(0.16)
0.38***
(0.07)
0.02
(0.34)
1.52***
(0.40)
–0.73
(0.55)
–0.88
(2.16)
GDP growth (+) –1.63***
(0.44)
–0.50
(0.63)
0.99
(0.65)
0.37
(1.22)
–3.65***
(1.00)
–4.37
(4.09)
Population growth (+/–) 0.15
(0.52)
0.04
(0.66)
–0.40**
(0.16)
–0.14
(0.56)
–0.73
(0.53)
0.80
(1.02)
Dependency ratio (+) 0.05 0.39*** 0.16 –0.18*** 0.34** 0.33
(0.04) (0.09) (0.11) (0.06) (0.14) (0.32)
Life expectancy (–) 0.01 –0.01 –0.18 0.41 –0.05 –3.21
(0.05) (0.02) (0.24) (0.42) (0.41) (2.27)
Relative price of capital (+) 0.01 0.01 –0.01 0.01 0.09** –0.06
(0.01) (0.02) (0.02) (0.04) (0.04) (0.06)
Income inequality (–) –0.03 0.20*** 0.30 –0.49*** –0.26 0.02
(0.09) (0.08) (0.21) (0.18) (0.31) (0.34)
Constant 3.96 –36.60*** –3.19 –14.30 4.62 252.69
(5.56) (9.33) (14.83) (33.67) (33.78) (175.80)
Adjusted R-squared NA 0.92 0.19 NA –0.03 0.32
Number of observations 727 39 65 589 303 295
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level. The set o
f
instruments include all variables in
, as well as the current and lagged values of the year-on-year inflation and GDP growth rates.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations.
62 WP685 Why so low for so long? A long view of real interest rate determination
Allowing for potentially rational expectations does not increase the relevance of the
saving-investment factors in explaining real interest rates. Again, the parameters for the
saving-investment factors often have the wrong sign, are statistically insignificant or vary
across samples. This suggests that any mismeasurement of inflation expectations due to a high
degree of agents’ foresight is unlikely to be the culprit. In fact, the results seem inconsistent
with the rational expectations hypothesis: is quite far from unity and statistically insignificant
in most subsamples. Less than fully rational inflation expectations may be one reason why
monetary policy seems to have effects that last beyond the normal business cycle.
Lastly, we also re-estimate the baseline regression computing real interest rates simply as
the difference between nominal rates and ex post inflation. The general pattern remains the
same: no saving-investment factor is systematically associated with real interest rates in the
way predicted by theory. Similar findings across various measures of expected inflation
suggest that our general conclusion is robust to mismeasurement problems.
WP685 Why so low for so long? A long view of real interest rate determination 63
B.6 Savers’ ratio as an independent variable
This robustness check evaluates alternative definitions of the dependency ratio. In particular,
we consider the “savers’ ratio”, used in Lunsford and West (2017), defined as the fraction of
the population aged between 40 and 64. This measure is inversely related to the dependency
ratio used in the baseline (and thus the expected sign should be negative). As reported in the
table below, this new variable is significant and correctly signed in the postwar subsamples,
but does not hold up in prior periods. We also experimented with the old-age dependency
ratio (namely dropping the youngest population from the calculation), and found very little
evidence of a systematic relationship (the result is not reported).
Baseline specification with savers’ ratio Table B.6
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
GDP growth (+) –0.10** –0.00 –0.07 0.06 0.06 0.03
(0.04) (0.02) (0.05) (0.06) (0.07) (0.05)
Population growth (+/–) –0.81* –0.27 0.29 –0.55** –0.21 –0.69
(0.41) (0.44) (0.43) (0.24) (0.23) (0.62)
Savers’ ratio (–) –0.18 0.41** 0.24 –0.46*** –0.57* –0.34**
(0.13) (0.16) (0.50) (0.09) (0.26) (0.14)
Life expectancy (–) 0.08 –0.17*** 0.40 0.36*** 0.29** –0.05
(0.05) (0.04) (0.26) (0.07) (0.11) (0.11)
Relative price of capital (+) 0.01 0.11*** –0.07 –0.03** –0.09*** –0.01
(0.02) (0.03) (0.04) (0.01) (0.02) (0.03)
Income inequality (–) 0.11* 0.00 –0.01 –0.17** –0.25 0.01
(0.05) (0.05) (0.30) (0.05) (0.22) (0.15)
Constant 1.72 2.11 –25.81** –9.83** –0.85 17.31**
(2.90) (3.80) (10.90) (3.68) (8.16) (6.21)
Adjusted R-squared 0.08 0.53 0.22 0.34 0.30 0.32
Number of observations 1102 202 205 643 303 340
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations.
64 WP685 Why so low for so long? A long view of real interest rate determination
B.7 Time-varying retirement age interactions with demographic variables
This exercise allows for the potential effects of a changing retirement age. We use the labour
force participation rate of 65-year olds as a proxy for the expected retirement age. The baseline
is then extended to include interaction terms between this proxy and the three demographic
variables, as well as between the dependency ratio and life expectancy. The main findings
survive. Neither specification delivers more stable relationships in any of the subsamples. The
interaction terms are also statistically insignificant in most subsamples.
Baseline specification with time-varying retirement age Table B.7
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
GDP growth (+) –0.10* –0.00 –0.07 0.10 0.06 0.04
(0.05) (0.03) (0.08) (0.06) (0.05) (0.05)
Population growth (PG) (+/–) –0.27 –2.04 –0.23 –1.72 –1.13 2.27
(1.26) (1.87) (7.26) (1.19) (2.51) (2.95)
Dependency ratio (DR) (+) –0.04 –0.33 –0.34 –0.45*** –2.19*** –2.10
(0.16) (0.52) (0.26) (0.14) (0.37) (1.62)
Life expectancy (LE) (–) 0.09 –0.73 1.68 0.18 –2.78*** –1.56
(0.24) (0.99) (2.23) (0.25) (0.75) (1.24)
Old-age participation (OP) (+) 22.39 327.35 –838.33 342.26** 314.90 252.97
(94.32) (413.54) (1070.12) (108.10) (261.82) (220.15)
PG x OP (+/–) –4.47 17.04 9.02 8.61 8.10 –9.51
(7.28) (12.60) (57.85) (7.80) (17.67) (11.88)
DR x OP (+) 0.40 –1.52 8.05* –0.72 –3.28** –0.13
(0.59) (2.44) (3.80) (0.43) (1.06) (1.07)
LE x OP –0.56 –4.11 1.50 –3.62** –0.56 –2.83
(0.72) (4.15) (16.62) (1.15) (3.27) (1.98)
DR x LE (+) –0.00 0.01 –0.01 0.01*** 0.04*** 0.03
(0.00) (0.01) (0.01) (0.00) (0.01) (0.02)
Relative price of capital (+) –0.01 0.06* –0.10* 0.01 –0.08** 0.03
(0.01) (0.03) (0.05) (0.02) (0.03) (0.03)
Income inequality (–) 0.10 0.02 –0.41 –0.10 –0.20 –0.09
(0.06) (0.03) (0.32) (0.08) (0.16) (0.16)
Constant –1.48 20.88 1.22 –27.26 146.48** 119.90
(14.85) (25.59) (123.14) (21.04) (52.77) (79.76)
Adjusted R-squared 0.11 0.41 0.32 0.28 0.42 0.29
Number of observations 965 117 160 643 303 340
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 65
B.8 Productivity growth as an independent variable
In this robustness check we replace GDP growth with total factor productivity growth in our
baseline specification. This reduces the sample size somewhat, as the productivity variable has
a smaller coverage. Again, the results are very similar to those already obtained with GDP
growth. In particular, we do not find any systematic correlation between TFP growth – or
indeed any of the other saving-investment factors – and real interest rates over time.
Baseline specification with productivity in place of GDP growth Table B.8
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
TFP growth (+) –0.07 –0.02 –0.03 0.21*** 0.23** 0.09*
(0.06) (0.01) (0.04) (0.05) (0.08) (0.05)
Population growth (+/–) –0.86* –0.59* 0.28 –0.76** –0.13 –0.59
(0.39) (0.30) (0.36) (0.27) (0.29) (0.69)
Dependency ratio (+) 0.02 0.10 –0.02 0.03 0.14*** –0.03
(0.01) (0.08) (0.09) (0.02) (0.02) (0.06)
Life expectancy (–) 0.05* –0.19*** 0.44 0.25*** 0.45*** –0.29***
(0.03) (0.02) (0.25) (0.07) (0.12) (0.08)
Relative price of capital (+) 0.00 0.12*** –0.06 0.00 –0.06* 0.01
(0.01) (0.02) (0.05) (0.01) (0.03) (0.03)
Income inequality (–) 0.10 –0.11 0.01 –0.25*** –0.12 –0.09
(0.06) (0.07) (0.30) (0.04) (0.20) (0.15)
Constant –2.86 4.04 –20.84 –16.27** –40.87*** 28.79***
(2.62) (7.32) (22.43) (6.65) (10.83) (7.38)
Adjusted R-squared 0.05 0.65 0.20 0.23 0.38 0.27
Number of observations 1043 143 205 643 303 340
Country fixed effects yes yes yes yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening, 1980-2016.
Source: Authors’ calculations.
66 WP685 Why so low for so long? A long view of real interest rate determination
B.9 Risk premium as an independent variable
We proxy the risk premium with measures of fundamental risks in the economy, namely
volatilities and higher moments of GDP growth and inflation, thereby also allowing for “tail
risks”, eg Vlieghe (2017). We compute 20-year rolling moments, and use the series as
additional saving-investment factors in the baseline. As shown in the table below, none of the
risk measures can explain real rate movements in the way predicted by theory.
Baseline specification augmented by fundamental risk measures Table B.9.1
(1)
Full sample
(2)
Gold standard
(3)
Interwar
(4)
Postwar
(5)
Pre-Volcker
(6)
Post-Volcker
GDP growth (+) –0.06 0.02* –0.12 0.09* 0.08 0.04
(0.04) (0.01) (0.07) (0.05) (0.05) (0.05)
Population growth (+/–) –1.04*** –0.55 0.85 –0.79* 0.25 –0.29
(0.30) (0.33) (0.51) (0.41) (0.23) (0.69)
Dependency ratio (+) 0.05*** 0.17** –0.06 0.08*** 0.17*** –0.03
(0.01) (0.06) (0.04) (0.02) (0.02) (0.07)
Life expectancy (–) 0.05* –0.13*** 0.25** 0.26** 0.32*** –0.28***
(0.03) (0.03) (0.09) (0.08) (0.09) (0.09)
Relative price of capital (+) –0.02 0.11*** 0.03 –0.02 –0.07*** –0.00
(0.01) (0.03) (0.03) (0.01) (0.02) (0.03)
Income inequality (–) 0.03 –0.07 –0.06 –0.25*** –0.33** –0.07
(0.07) (0.04) (0.24) (0.07) (0.12) (0.15)
GDP growth volatility (–) –0.44
(0.32)
–0.82***
(0.22)
–1.15
(0.78)
–0.26
(0.45)
0.14
(0.43)
0.74
(0.63)
Inflation volatility (–) 0.22
(0.13)
0.22
(0.12)
1.48***
(0.28)
0.09
(0.12)
–0.68***
(0.12)
0.05
(0.12)
GDP growth skewness (+) 0.15
(0.47)
–0.53**
(0.19)
2.82
(1.88)
0.25
(0.47)
0.27
(0.69)
0.66
(0.40)
Inflation skewness (+) –1.53***
(0.37)
–0.26
(0.27)
–2.20***
(0.61)
–1.69***
(0.39)
–1.25***
(0.18)
–0.38
(0.37)
GDP growth kurtosis (–) –0.15
(0.24)
–0.21
(0.15)
–0.26
(0.45)
0.00
(0.23)
–0.19
(0.34)
0.31**
(0.13)
Inflation kurtosis (–) 0.11
(0.20)
0.59**
(0.20)
0.42
(0.43)
0.36**
(0.15)
0.22
(0.13)
–0.06
(0.10)
Constant –2.56 –7.10 –10.84 –19.79** –29.46*** 25.02**
(2.94) (4.04) (10.33) (7.95) (6.86) (9.68)
Adjusted R-squared 0.18 0.77 0.56 0.32 0.56 0.29
Number of observations 983 147 173 630 290 340
Country fixed effects Yes Yes Yes Yes Yes Yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1870-2016; gold (metallic) standard: 1870-1913; interwar: 1920-1938; postwar: 1950-2016; pre-Volcker-tightening: 1950-1979;
post-Volcker-tightening: 1980-2016.
Source: Authors’ calculations.
WP685 Why so low for so long? A long view of real interest rate determination 67
As a second test, we also add a measure of the global equity risk premium. We use the
US equity risk premium as a proxy (left panel of Graph B.9.1), since the US is a major market
(also risk premium estimates for other countries are available for much shorter samples, if at
all). Given this global premium proxy, we focus on the specification that allows for its global
effects, namely an extension of Table 7 in the main text. The estimates are reported in Table
B.9.2, where we consider two subsamples to examine stability. While the risk premium has a
significant and correctly signed coefficient for the full sample, this is entirely driven by the
earlier part of the sample (the coefficient on the risk premium from a rolling regression is
shown in right-hand panel of Graph B.9.1). For the last 30 years, a higher risk premium actually
has a positive marginal impact on real rates once one controls for other saving-investment
factors. This contrasts with the narrative that emphasises the rise in the global risk premium
since the turn of the century as the cause of lower risk-free rates (eg as the right-hand panel
shows, the equity risk premium and median real rate are negatively correlated in the recent
period).
Equity risk premium and real interest rates Graph B.9.1
Equity risk premium Relationship between risk premium and real rates
Per cent
Dashed lines in the right hand panel indicate +/– two standard deviations.
Sources: A Damodaran, http://pages.stern.nyu.edu/~adamodar/; authors’ calculations.
6
5
4
3
2
201620061996198619761966
Equity risk premium
2
1
0
–1
–2
20162011200620011996199119861981
Coefficient from rolling panel regression
Bilateral correlation with median real rate
68 WP685 Why so low for so long? A long view of real interest rate determination
Global versus country-specific determinants with risk premium Table B.9.2
(1)
Full sample
(2)
1961-1979
(3)
1980-2016
Global component:
GDP growth (+) 0.15** 0.67*** 0.15**
(0.06) (0.11) (0.07)
Population growth (+/–) 1.17 –21.06*** 18.45**
(1.91) (4.89) (7.60)
Dependency ratio (+) –0.12 –0.02 –0.10
(0.08) (0.11) (0.16)
Life expectancy (–) 0.09 –1.33** 0.52
(0.20) (0.53) (0.34)
Relative price of capital (+) –0.03 0.43*** 0.02
(0.04) (0.08) (0.05)
Income inequality (–) –0.65*** 2.21* –0.94***
(0.17) (1.16) (0.24)
Risk premium (–) –0.25** –0.65** 0.19**
(0.09) (0.23) (0.08)
Country specific component:
GDP growth (+) 0.03 0.06 –0.02
(0.06) (0.09) (0.06)
Population growth (+/–) –0.04 –1.14 –0.33
(0.57) (0.76) (0.65)
Dependency ratio (+) 0.02 –0.00 0.03
(0.03) (0.06) (0.07)
Life expectancy (–) 0.18 –0.98** 0.58
(0.21) (0.40) (0.40)
Relative price of capital (+) 0.01 –0.06** 0.02
(0.02) (0.02) (0.02)
Income inequality (–) 0.09 –0.19* 0.13
(0.09) (0.09) (0.13)
Constant 10.45 97.91** –33.27
(18.39) (43.62) (28.72)
Adjusted R-squared 0.13 0.05 0.08
Number of observations 540 200 340
Country fixed effects yes yes yes
Robust standard errors in parentheses based on country clusters; ***/**/* denotes results significant at the 1/5/10% level.
Full sample: 1961-2016; global components calculated as the averages of each variable based on real GDP at purchasing
power parity.
Source: Authors’ calculations.
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