Axel A Weber: The role of interest rates in theory and practice - how useful is
the concept of the natural real rate of interest for monetary policy?
Text of the G.L.S. Shackle Biennial Memorial Lecture 2006, by Mr Axel A Weber, President of the
Deutsche Bundesbank, at St. Edmund's College, Cambridge, 9 March 2006.
The references for the lecture can be found on the Deutsche Bundesbank's website.
* * *
1 Introduction
It is obvious that interest rates play a key role in monetary policy today. On the one hand, the
instrument of most central banks is a short-term interest rate. On the other, interest rates contain
important information on the current state of the economy, and the extent to which past monetary
policy measures have already started to take effect. Put it differently, interest rates are important as
both an input into and an output of monetary policy decisions - they are instrument variables as well
as indicator variables.
Of course, there is no such thing as 'the' interest rate. Rather, there is a wide variety of them.
Neglecting other relevant features, we have to distinguish interest rates at least with respect to their
time to maturity and with respect to whether they are expressed in nominal or in real terms. Interest
rates that matter for consumption and investment decisions are likely to be of longer maturity.
Moreover, since economic agents ultimately benefit from the consumption of real goods, it will be real
rates rather than nominal rates that they are mainly interested in.
Monetary policy directly controls nominal and very short-term rates. However, since - according to the
expectation theory of the term structure - longer-term rates depend on expected future short-term
rates, a central bank does have the ability to affect them by influencing private agents' expectations. A
similar argument holds for real rates. Given the level of nominal rates, real interest rates depend on
expected future inflation rates. To a large extent, these depend on the degree to which the public
believes monetary policy will be able to ensure price stability. Besides expected short-term interest
rates and expected inflation, longer-term real rates also depend on several types of risk premia, for
example inflation risk. These constitute an additional channel through which monetary policy may
influence long-term real rates. Thus, monetary policy exerts both a direct effect on short-term nominal
rates and an indirect but important effect on long-term real rates.
Understanding how current economic variables - such as economic activity and policy variables -
interact with expected future variables is a challenge that has been featuring prominently in both
academic discussion and monetary policy practice in recent years. Accordingly, the book by Michael
Woodford "Interest and Prices", which is cited frequently nowadays, characterizes the practice of
central banking mainly as the management of expectations. This is an aspect of which G.L.S. Shackle
was already well aware, as we shall see later.
Having said that monetary policy does have an influence on a variety of interest rates it is not clear a
priori whether certain levels of these rates are 'adequate' in the sense that they represent prudent
monetary policy. This brings me to my second point, the information content of interest rates. Inferring
the current monetary policy stance from prevailing interest rates requires some sort of benchmark.
Ideally, this would be a reference level - depending on current economic conditions - with which some
particular interest rate could be compared, the difference between the two then measuring how loose
or tight monetary policy is. For such a benchmark to be useful for the monetary policy decision-making
process, it should satisfy certain criteria, including the following three.
• theoretical
First, that benchmark rate should be based on sound foundations. This would allow
a meaningful interpretation of its behaviour and the driving forces behind it.
•
Second, the difference between some particular interest rate and this benchmark rate should
ideally be a summary variable reflecting the overall pressure on inflation. If this is not possible,
it should, at least, contain some predictive power for future inflation.
• Third, the benchmark should be readily computable from observable economic data. Ideally,
this criterion includes the requirement that these data should be available with sufficient
precision at the time they are needed.
Actually, there is an economic variable which is often claimed to provide such a benchmark role: the
natural real rate of interest on which I will focus in this talk. I will start with Wicksell's notion of the
natural rate, followed by a presentation of its definition and role in today's monetary macroeconomics.
After that, I will focus on approaches to measuring the natural real rate of interest (NRI) and its
usefulness for the practice of monetary policy. At the end of my remarks, I will try to judge whether the
natural rate is able to satisfy all or some of the criteria I have listed.
2 Wicksell's concept of the natural rate of interest
The concept of a natural rate of interest goes back to Wicksell. He defined it as the level of the real
interest rate at which prices have no tendency to move either upward or downward. The starting point
of his analysis is the assumption that any movement in the price of a single good must have been
caused by a mismatch between the demand for and the supply of this particular good. Accordingly, the
movement of the aggregate price level must have been caused by a mismatch between aggregate
demand and aggregate supply. Wicksell therefore stressed that any theory which intends to explain
the overall rate of inflation must therefore be able to explain the underlying aggregate demand and
supply movements.
A second important aspect of Wicksell's theory is related to the role of money and credit. He did not
doubt that money growth is a necessary condition for inflation, but his approach is based on the
endogeneity of money - in other words, money is not exogenous. Here, the banking system plays the
crucial role: By extending credit to firms and households it determines the growth rate of money and
thereby aggregate demand.
Key to the understanding of this connection is Wicksell's 'cumulative process'. Banks setting 'too low'
an interest rate trigger a high credit demand from investors because, given the relatively low interest
rate costs, they have a high expected return. Owing to the prevailing very large degree of flexibility in
the banking sector, banks can satisfy this higher loan demand, which results in an increase in money
growth and a higher demand for investment goods. This tends to increase the price level of investment
goods and the competitive wages in the investment goods sector, causing expenditures and the
overall price level to rise. This is how Shackle describes the next steps in Wicksell's cumulative
"The cost of production per physical unit of goods will be rising month by month, but the price
process:
of goods per unit will be rising as fast, will be keeping ahead, and the persisting gap per unit will invite
an ever-larger output".1 The cumulative process of strong money creation by a highly flexible banking
system and a higher aggregate price level does not end until the banks have raised the interest rate
sufficiently. Here, 'sufficiently' means that the interest rate - which is set by the banks - should be
raised to the level at which the overall demand for goods equals their supply - that is, the interest rate
at which prices remain constant. Wicksell referred to this interest rate level as the 'natural rate of
interest'.
Shackle was certainly right when in the foreword to the English translation by Stephen Frowen of
Wicksell's "Value, Capital and Rent" in 1953 he compared the contribution to economic theory made
by Wicksell's concept of a natural rate of interest to that made by the steam locomotive in the built-up
of modern societies.2 But, with the benefit of hindsight, we now know that Shackle was a little too
pessimistic when he predicted that the natural rate could become as obsolete as the steam
locomotive. Modern monetary theory - as embodied in the latest generation of New-Keynesian
macroeconomic models, for example - proves that the opposite is true. It is not by accident that
Michael Woodford's textbook - which became sort of a standard work in modern monetary theory -
'Geldzins
carries the title "Interest and Prices" - the English translation of the title of Wicksell's book
und Güterpreise'.
3 The natural rate of interest in modern macroeconomic theory
In order to highlight the key role of the natural interest rate concept in modern monetary theory, it is
useful to recapitulate briefly the core structure of New-Keynesian models which form the workhorse of
today's monetary policy analysis.3 Basically, such models add various forms of nominal rigidities to the
features of the real-business-cycle paradigm which is based on the notion of dynamically optimising
agents in a world characterised by stochastic shocks. One of the key elements is the assumption of
rational expectations: Agents fully take into account the specifics of the model world they inhabit and
the consequences of today's actions for the future. In particular, they bear in mind how the monetary
authority is likely to react to macroeconomic developments, and this, in turn, influences their own
actions in the here and now.
Models in this micro-based paradigm render it possible to analyse the outcomes of policy changes
without running into the Lucas critique. Moreover, such models can highlight and quantify the ability of
monetary policy to influence private sector expectations which are key to a proper understanding of
the effects of monetary policy. Based on this view, as I mentioned before the practice of modern
central banking has frequently been described as being, to a large extent, the management of private
expectations. This is an aspect of monetary policy which was already stressed by Shackle in his 1949
article on "The nature of interest rates." Describing a situation in which the central bank tries to bring
interest rates down he states that [p. 115] "a consensus of market opinion can be swung, by words
and deeds of the monetary authority or its
masters".
The structure of the basic New-Keynesian model can be easily represented by three equations
characterising the dynamics of the interest rate, output and inflation. The first equation can be related
to the supply side, the second to aggregate demand, and the third specifies monetary policy
behaviour. The equation representing aggregate supply captures the price-setting behaviour of firms,
resulting from profit-maximisation under the obstacle of some sort of nominal price rigidity. Owing to
this rigidity, firms have to take into account the expected development of prices in the next period
when setting their prices today. In its most basic form, this equation is known as the "New-Keynesian
Phillips curve" which expresses current inflation as a function of currently expected inflation for the
πt
4
next period Et(πt+1) and the current output gap xt:
πt = β·Et(πt+1) + κ· xt. (1)
The latter stands for the amount of slack in the goods market and is defined as the difference between
actual output and its natural level, that is, the production level which would prevail in the hypothetical
situation of fully flexible prices.
The demand equation ('IS curve') is based on the assumption that households optimise their whole
consumption stream over the present and the future. This leads to an expression relating the current
output gap to the currently expected output gap of the next period Et(xt+1) and an interest rate gap:
-1
σ
xt = Et(xt+1) - ·(it - Et(πt+1) - rt *) (2)
The natural real rate of interest comes in at this stage: the interest rate gap is the difference between
the actual ex ante real interest rate it - Et(πt+1) and the natural real rate of interest rt *. This variable
turns out to be a key variable for the design of monetary policy in this class of models. Within the
NewKeynesian paradigm it is defined as the one-period equilibrium real rate of return that would prevail in
the hypothetical equilibrium with completely flexible prices, that is, in the absence of nominal price
rigidities. As is evident from the demand equation the situation where current and expected output is at
its flexible-price level is accompanied by the actual real interest rate being equal to its natural
counterpart and thus by a closed interest rate gap.
The natural rate of interest is influenced solely by real factors such as productivity growth, movements
in government expenditure, the growth of the workforce, the tax structure, and the time preference of
households. As a consequence, the natural rate is not constant over time but mirrors the dynamics of
all those driving forces. Accordingly, it is subject to short- and long-run fluctuations.5 As for the
absolute level of the natural real rate, one cannot state that a high or low level does per se represent a
state of the economy which is desirable or not. It simply reflects its driving forces which themselves
could, in principle, be gauged as being favourable or not. For instance, an increase in the natural rate
may be induced by a rise in productivity growth but may also be rooted in the need to finance larger
social security deficits.6
For monetary policy purposes, the indicator quality of the natural rate for inflation is of special interest.
To this end, what matters is the level of the actual real interest rate compared with the natural rate of
interest. Again, this is illustrated most clearly within the baseline New-Keynesian model. An actual real
interest rate below the natural level - that is, a negative interest rate gap - implies a positive value of
the output gap which tends to increase inflation. If, for instance, an expected permanent future
increase in productivity induces agents to expect higher income in the future, they will try to smooth
consumption by already raising their consumption level in the present. In a flexible price equilibrium,
the natural real interest rate would rise, increasing current desired savings in order to equate the
current consumption level and current natural output again. However, if the actual real interest rate
does not rise sufficiently, there will be a negative interest rate gap, which increases the current output
gap - that is, stimulates the economy too much - which in turn leads to inflationary pressure.7
Interestingly, in these models the current inflation rate can be expressed solely as a sum of current
and expected future interest rate gaps. In this sense, the sequence of interest gaps is a sufficient
statistic for the determinants of inflation. This is close to the story told by Wicksell. Indeed, it may be
interpreted as a forward-looking variant of the Wicksellian analysis outlined above.8 However, at this
point the New-Keynesian paradigm also differs from Wicksell's theory in one crucial aspect: while
Wicksell viewed inflation as being a disequilibrium phenomenon, inflation in the New-Keynesian model
is an equilibrium phenomenon. In the latter case, all markets clear each period and all variables are
consistent with the optimality conditions of forward-looking households and firms.
4 Monetary policy and the natural rate of interest in theory
Since there is no trade-off between output and inflation stabilisation in the theoretical model presented
so far, the prescription for stability-oriented monetary policy is straightforward: measure the currently
prevailing natural real rate of interest, and equate the one-period interest rate - which is the monetary
policy instrument - with that number. If an inflation rate different from zero is viewed as desirable, the
resulting interest rate should simply be increased by that amount. For expositional clarity, I will assume
a zero inflation objective in the following theoretical remarks.9
The key role which the natural rate plays with regard to the inflation process in the described basic
New-Keynesian model thus renders monetary policy a simple task: Although there are a variety of real
shocks that influence inflation, the central bank only has to care about the movements in the natural
rate through which the shocks are channelled. However, in this benchmark New-Keynesian model,
consistent
too, the described policy would have the problem that it is merely with the equilibrium
outcome of price stability but does not necessarily create it. The problem is that it permits the
occurrence of other less desirable equilibria with fluctuating inflation and output gaps. This is why
monetary policy must also commit to react sufficiently strongly to endogenous variables such as the
deviations of the output gap and inflation from their target values. Thus - assuming a zero inflation
objective - the monetary policy reaction function in this theoretical model would set the short-term
interest rate as
*
it = rt + g1· xt + g2·πt, (3)
*
where denotes the natural real rate of interest. If the monetary policy authority credibly commits to
rt
follow the natural rate and to react to unfavourable situations, these situations will never occur at all.
Thus, following the above rule not only supports the equilibrium of full stabilisation but pins it down as
the only possible one.
We should further note that a simple Taylor rule of the form
it = c + g1· xt + g2 ·πt, (4)
which does not follow the variations in the natural rate of interest would generally not be able to
generate full stabilisation. To illustrate this, assume for the moment that monetary policy can
nevertheless commit to (4) and at the same time completely stabilize output and inflation. In this case,
the nominal interest rate and expected inflation would be constant over time. However, since the
natural real rate of interest moves due to exogenous factors, the resulting interest rate gap varies. But
according to demand equation (2) this would be incompatible with the assumed complete stabilisation
of the output gap. This line of reasoning shows that the simple policy rule (4) is not capable of
implementing complete stabilisation unless the natural rate is constant.
Unlike in the simple model considered so far, monetary policy will in general not be able to guarantee
full stabilisation at all times. One important factor that generates a trade-off between output and
inflation stabilisation is the presence of cost-push shocks. These appear as an additional disturbance
term in the Phillips curve,
= β· + κ· + (1a)
πt Et(πt+1) xt et.
Thus, a cost-push shock constitutes an additional driving force to inflation beyond those effects that
operate via the output gap. The presence of such shocks can arise from time-varying market power of
firms, from time-varying distortionary consumption or wage taxation, or from time-varying
wage-markups in imperfectly competitive labour markets.10 In contrast to the earlier example, where all
inflationary pressures had been due to real shocks - manifested in movements of the natural rate -
the central bank will now face a trade-off between output-gap and inflation stabilisation. If a cost push
shock arises, the monetary authority may raise the interest rate to counterbalance the effect on
inflation. This, however, now comes at the cost of generating a negative output gap. In this case, the
weights that the central bank attaches to both targets come into play. In theory, this is typically
represented by a loss function that increases in squared deviations of the output level and inflation
from target.11
The policymaker seeks to minimize this loss function, taking the functioning of the economy as a
constraint. In the presence of cost-push shocks, it is immediately evident that - contrary to the model
without cost-push shocks - a vanished interest rate gap does not imply price stability. What the
optimal policy looks like in this case depends, in particular, on whether or not the policymaker can
credibly commit to future actions or - in the language of the "time inconsistency" literature - whether
monetary policy is conducted under discretion or commitment. In any case, given the existence of
cost-push shocks, a policy that merely traces the path of the natural rate is not optimal. Rather,
optimal policy will have to take into account both: movements in the natural rate and the nature of
additional cost-push shocks which are not manifested in the natural rate.
5 Monetary policy and the natural rate of interest in practice
In light of the discussed theoretical considerations, the natural rate of interest could in principle play an
important role in the conduct of monetary policy. And at least conceptually its measurement would be
straightforward: identify its real driving forces, get to know in what way the NRI is affected by each of
them, and finally measure their values. Obviously, all of these three steps imply considerable
obstacles. Step one requires an exhaustive enumeration of all those real factors that are potentially
important. Step two requires a precise knowledge of how these factors affect the real rate, thus
requiring some sort of a very exact economic model. Finally, step three requires a measurement of
variables which are themselves partly unobservable, such as the time discounting rate of private
households. Therefore, the natural rate has to be estimated indirectly based on current and past
observations of directly observable economic data, making use of a more or less detailed model
prescribing the interactions of the NRI with these variables.
However, policymakers intending to make use of the natural rate are in an even less comfortable
position than econometricians conducting ex post analyses for estimating the NRI at a given point in
history. Econometricians can use current, past, and future observations to make inferences about the
NRI, while policymakers have only past and current data at their disposal. Moreover, past and current
data may also be affected by data revisions, this so-called 'real-time data problem' being, in itself, a
significant obstacle to monetary policy analysis on its own.
5.1 Estimating the natural rate of interest
For estimating the NRI, a number of different methods have been established in the literature.
Unfortunately, they lead to a wide range of different results.12 Such variability across estimation
methods poses an additional problem besides the one of uncertainty surrounding any statistical
estimate. As we shall see below, dealing with these uncertainties in an appropriate manner is a real
challenge for monetary policy - a challenge which is both discussed in the current academic literature
and debated in the context of policymaking in practice. The various approaches to estimating the NRI
in the literature can be grouped into the following three categories: (1) univariate filtering approaches,
(2) structural econometric models with the NRI as a latent variable, and (3) fully-fledged equilibrium
models with microeconomic foundations. In my following remarks, I will sketch the nature of these
methods and comment on their advantages and drawbacks.
One approach to estimating the NRI is based on simply using realised real rates. The idea supporting
this modus operandi, is that in the long run - that is, after all shocks have washed out - the actual real
rate should have converged to its natural counterpart. If moving averages of actual real rates are taken
over the typical length of a business cycle, the resulting number may be interpreted as being close to
the natural rate. Since the method uses actual real rates it already inherits the arbitrariness of
measuring them: one has to decide between ex ante and ex post measures of inflation and on the
type of price index used. Additionally, one has to decide the window width over which the sequence of
means is computed. Since all these choices will have an influence on the level of the estimated natural
real rate, different variants of this approach can result in quite different point estimates of the NRI.
The NRIs resulting from such moving average estimations typically constitute a fairly smooth time
series. However, this stands in contrast to the characterising features of the 'true' natural rate outlined
above, because - theoretically - it can in fact exhibit strong variations corresponding to the size and
dynamics of the real shocks it depends on. In general, methods based on averaging will by their very
nature translate a de facto abrupt persistent upward change in the NRI into a smooth phase of
transition. This drawback remains even if the averaging method is refined, as is the case, for example,
in methods that filter out low-frequent components from the real rate.13
Alternatively, the literature also employs econometric models which explicitly specify the dynamics of
the natural rate as an exogenous stochastic process. This approach is - on the one hand - based on
exogenous shocks and - on the other - on the assumption about certain structural relations between
observable variables and the NRI.14 These structural equations may contain quite general
formulations of inflation and output dynamics based on economic theory. Typically, they nest a variety
of specifications from both specific theories and ad hoc assumptions. For instance, an inflation
equation may nest a forward-looking Phillips curve that would result from particular assumptions of a
micro-founded equilibrium model - as mentioned above - but would also contain lagged inflation and
real activity in order to take account of some degree of backward-lookingness that is present in the
data. Here, the key idea is that the NRI - which, by its very nature, is unobservable - may be filtered
out from observable data on the basis of the model's implications for the interaction between the NRI
and these observable variables. This filtering technique is more efficient if it is two-sided, that is, if it
uses not just past and current data, but also future data. However, since policymakers are confined to
one-sided filtering, this real-time problem tends to reduce the usefulness of this method.
The aforementioned econometric approaches specify a fairly general structure of the dynamics of key
economic variables that interact with the NRI. Alternatively, one may use more specific general
equilibrium models of the economy, which are usually based on explicit microeconomic foundations.
For the euro area, the model by Smets and Wouters (2003), for instance, has gained some popularity
as a tool for monetary policy analysis. Such a model makes it possible to emulate the hypothetical
flexible-price path of the economy, that is, the sequence of equilibria in which all real variables are at
their natural levels. This counterfactual exercise allows us to derive the natural rate of interest. Usage
of an estimated equilibrium model also makes it possible to track and interpret the very sources of its
variation, such as shocks to technology, government spending, or a change in the tax system.15
Moreover, structural equilibrium models direct attention to the role that specific key variables may play
in identifying the relative natural rate movements. As outlined above, inflation may be represented by
the sum of future expected natural real interest rates. But an immediate proxy for the expected natural
real interest rate is even less available than it is for the current natural real rate. However, exploiting
the logic of forward-looking models, these important future developments may be inferred from
observations available in real time. For instance, in variants of the New-Keynesian model, presented in
Andres, Lopez-Salido and Nelson (2004), portfolio adjustment costs lead to a forward-looking
specification of money demand. This, in turn, implies that current real balances are linked not only to
current income and interest rates but also to the sum of expected future values of the NRI and interest
rate gaps. In other words, if their model is true, money contains valuable information on future natural
real rates. For policymakers, this a crucial point: Given the real-time data problems with which they are
confronted, looking at monetary developments may be useful for learning about the current (and
future) state of the economy even in the New-Keynesian world which, at first sight, has no such role
for money to offer. And this point is to some extent also related to Wicksell's theory, where an interest
rate gap has direct implications for credit and money growth. I will come back later to the issue of
monetary indicators' usefulness.
However, deriving the natural rate of interest from structural models is accompanied by the risk that
the underlying narrow view of economic interactions may not be an adequate representation of reality.
Basing estimates of the NRI on a distorted picture of real-world interactions would then lead to a
distorted estimate of the NRI. Obviously, this shows that the use of the concept of the natural rate of
interest for policymaking comes with the problems of model and data uncertainty.
5.2 Monetary policy guided by estimates of the natural rate of interest
From the foregoing remarks it should come as no surprise that point estimates of the natural rate of
interest vary immensely across methods. Again, it is important to note that this variation across
estimation approaches prevails in addition to the statistical uncertainty surrounding every point
estimate for any given model on which it is based. For the euro area since 1999, a synopsis in a paper
by Crespo Cuaresma, Gnan, and Ritzberger-Grünwald (2005) shows that estimated paths of the NRI
differ considerably in terms of their levels, the range that they cover over time, and their smoothness.
Therefore, the natural question arises as to whether the concept of the NRI can be useful to monetary
policymakers in practice. For illustration, let us consider again the most basic New-Keynesian model
without any output/inflation trade-offs. Here, policymakers can completely stabilise the path of inflation
and output: they set the nominal interest rate equal to the natural real rate of interest plus their inflation
objective. They commit to react to inflation and output gap fluctuations, but these would never occur in
equilibrium. However, if the natural rate is not measured precisely and is simply replaced by its
estimate in the above rule, then "estimation error becomes policy error, and stabilization policy
becomes
destabilizing".16
One therefore has to explore what the optimal monetary policy looks like in the presence of
measurement uncertainties concerning the natural rate. This is one instance of the general question of
how monetary policy should act in presence of uncertainty about the state of the economy and this
issue currently constitutes a very active research area. Under specific assumptions the apparently
comfortable principle of 'certainty equivalence' prevails: optimal policy should react to its best estimate
of a state variable in exactly the same way as it should react if this variable were precisely observable.
It is immediately clear that even in this 'straightforward' case, every policy that comes in the form of a
'simple rule' loses that property of simplicity: reacting to the 'best estimate' of any state variable
usually implies conducting a one-sided filtering exercise, yielding a state estimate which is a function
of all current and past observables. Moreover, this approach is conditional on two crucial
requirements: first, the central banker has to know the structure of the data-generating process for the
NRI in order to come up with the best estimate. And second, this best estimate will typically depend on
the degree of mismeasurement of the NRI which, in general, is not precisely known either. Thus, in
trying to react appropriately to state uncertainty, uncertainty kicks in on another level, posing an even
greater challenge.
If model uncertainty or uncertainty about the degree of mismeasurement prevails, policymakers are
well advised to go for a strategy that is robust to misconceptions of the true economic mechanism or
the degree of NRI mismeasurement. That is, a policy that performs acceptably under a variety of
possible model structures should be preferred to one that is optimal in one specific environment but
would lead to disastrous outcomes if another setting prevailed. One way to tackle this issue is the
Bayesian approach, where the policymaker has to assign a subjective probability distribution over the
a prior