**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 MartínezGarcía, 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.

**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 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.

**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 both the demographic dynamics and the capital-labour ratio, resulting in offsetting effects on interest rates (Carvalho et el (2016)). 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.

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 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".

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.

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.

**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:

where *r _{t}* is the real interest rate,

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.^{[1]} 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 *p.* 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.^{[2]} To the extent that such 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, *p.*

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.^{[3]} For robustness, we also estimate the correlations from five-year or 10-year nonoverlapping averages of all variables.^{[4]} We also employ different modelling strategies for inflation expectations, as these are especially hard to measure over a 10-year horizon.^{[5]} 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, *p,* to be reasonably stable over different subsamples.^{[6]} 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.^{[7]} 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.

**2.2 Data and definition of variables**

The data are annual and cover 19 (currently) advanced economies over the period 18702016.^{[8]} 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.[9] In Annex A2, we plot the time series of interest rates and expected inflation.

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.

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.

**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

and *X _{f i t}* is the

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),^{[2]} 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.

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 *X _{it}* 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.

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.

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

where *X _{i t}__{s}* 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

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.^{[1]} 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 *Xt* is a measure of the global components in the determinants.^{[1]} 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.

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 rt* consists of two components

where *g _{t}* is the potential growth rate of the economy, and

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.

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)).^{[1]}

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.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. 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 large revisions. 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. 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. 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.

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)). Imagine that inflation is below target and that headwinds make it hard to generate the second-round effects whereby wages chase prices. 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.There is now a broad consensus that price 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)). 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. 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, 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.

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.*

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, Gall (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 in the steady-state inflation rate, which they interpret as a change in the monetary regime, decreases the steady-state real interest rate.

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.[13] 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.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.

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

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.

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. Thus, while 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.

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.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.

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).

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. 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 antiinflation resolve, most evident in Volcker's decision to allow interest rates to rise substantially.

Real interest rates naturally increased too and appeared very high compared with the previous phase (eg G10 (1995)).

**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).

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