Assessing Interest-Rate Risk from the Rate’s Constituent
Components
by Frank Browne and Mary Everett1
ABSTRACT
Any increase in interest rates will have implications for the Irish economy, and more specifically for the stability and soundness of
the Irish financial system. The overall impact of an interest-rate rise will depend on the factors behind the increase. This paper
examines some of the likely causes and consequences of an interest-rate hike. In order to understand how the nominal interest
rate might evolve over the short and medium term, we decompose the nominal interest rate into its constituent components, the
most important of these being the equilibrium real rate of interest. Analysis of various models of the equilibrium real rate of interest
for the euro area shows that in the short-run, there does not appear to be a likelihood of a substantial increase in the nominal
interest rate stemming from a significant shift in the underlying equilibrium real rate of interest, or from the other components of
the nominal interest rate. Over the medium-term horizon (chronologically approximately three to seven years), however it is likely
that the euro area economy will revive and will see a much higher equilibrium real rate of interest. A steady state growth rate of
3 per cent, combined with an inflation rate of about 2 per cent (consistent with the ECB’s inflation objective) and a risk premium
of 1 per cent would add up to an equilibrium mortgage rate of approximately 6 per cent. With the typical variable mortgage rate
of interest being around 3 per cent now (October 2005), an increase in interest rates to this putative equilibrium level would
double the repayments burden. For highly indebted borrowers, this would be an intolerable burden and would almost certainly
mean a sharp increase in the ratio of non-performing loans.
1. Introduction
This paper looks at the issue of interest-rate risk now
facing the Irish economy and how its realisation might
impact on financial stability in Ireland. It starts from the
proposition that all increases in the headline nominal rate
are not the same in their impact on financial stability.
The effect depends on the factors behind the increase.
At the moment, short-term rates in the euro area are at
an all-time low as is the whole term structure of nominal
interest rates. It would appear, therefore, that the risk is
all on the upside. The issue, therefore, is not whether
interest rates will rise but rather by how much.
The aim of the article is to examine the range of possible
causes for a hike in interest rates. The variety of driving
forces for an increase in rates have to be scrutinised
because the effect on the economy and financial
stability, via its effects on households, non-financial firms
and banks, depends on which driving force(s) are behind
the increase in rates. Our treatment of interest-rate risk
in our previous Financial Stability Reports was partial and
did not examine some of the likely causes and
implications of an interest-rate rise. The central message
of this background paper is that the implications of an
interest-rate rise for the Irish economy generally, but
more specifically for the stability and soundness of the
Irish financial system, depends on the reason for the
rise.
2. Disentangling the Components of the
Nominal Interest Rate
In last year’s Financial Stability Report, the Irish
equilibrium nominal mortgage rate of interest was put at
approximately 6 per cent2. The equilibrium interest rate,
which is defined in Box 1 and elaborated on within
Section 3, is the rate to which the economy tends to in
the medium to long run. It was concluded that an
increase in the standard variable mortgage rate to this
level would be a cause for concern for financial stability
given the very large proportion of mortgage borrowers
who are partaking in variable-rate contracts. However,
such an increase in the rate was not in itself considered
to be systemically threatening. Nevertheless, it was
concluded that it might be a realistic threat if
accompanied by what was deemed to be the other
major potential shock to the economy in the form of a
substantial increase in the rate of unemployment.
The financial stability implications arising from an
increase in the mortgage rate must be qualified further.
First, it has to be acknowledged that, for the most part,
1
The authors are respectively, Head of Monetary Policy & Financial Stability and an economist in the Statistics Department. The views expressed in
this article are the personal responsibility of the authors and are not necessarily those held by the CBFSAI or the ESCB. The authors would like to
thank Anne-Marie McKiernan for helpful comments.
2
An estimate of 6 per cent for the Irish equilibrium mortgage rate is comprised of an ECB estimated equilibrium real rate of 3 per cent , an inflation
target of 2 per cent, plus a 1 per cent risk premium (i.e., an estimate of banks’ margin). For further detail see Box 6, Financial Stability Report 2004,
September, CBFSAI.
Financial Stability Report 2005
123
Box 1: Definitions of Equilibrium, Nominal and Real Interest Rates
Equilibrium Interest Rate
This rate is variously known as the natural rate or the neutral rate or the Wicksellian rate after Wicksell (1936)1, who first identified
it as an important economic concept. Wicksell described the natural rate as ‘a certain rate of interest on loans which is neutral in
respect to commodity prices and tends neither to raise nor to lower them’. It is defined as the rate that would be obtained when
all prices are fully flexible. It is the rate that would prevail in general equilibrium and according, in Wicksellian terminology, the
rate that equates the ex-ante supply of savings (by households) with the ex-ante demand for investment (by firms).
Nominal Interest Rate
The short-term nominal interest rate is the de facto instrument of monetary policy. It is the cost of using money over a period of
time, which does not take the effects of inflation into consideration.
Real Interest Rate
The real interest rate is the nominal interest rate adjusted for inflation effects. It is the difference between the nominal interest rate
and the inflation rate.
——————
1
Wicksell, K., (1936), ‘‘Interest and Prices’’ (translation of the 1898 edition by R.F. Kahn), London: Macmillian.
if the mortgage rate does rise significantly in the coming
years, it will most likely do so on account of factors
which are predominantly exogenous to the Irish
economy. Secondly, and the main point we want to
make in this background paper, is that the effects on the
Irish economy, but more especially on the Irish mortgage
and housing markets, depends on which of these
reasons might be driving any increase in the mortgage
rate.
The danger posed for financial stability in Ireland
depends on how any such exogenously driven increase
in interest rates would also be likely to precipitate a
simultaneous and substantial increase in Irish
unemployment. This is really the type of double effect to
which the Irish economy is currently vulnerable because
of the combination of the rapid rate of increase of
household indebtedness over the past decade and the
very high proportion of adjustable-rate mortgages in the
total outstanding stock of mortgages. The likelihood that
an increase in the interest rate would also precipitate an
increase in unemployment depends on the reason for
the increase in the interest rate.
If, for example, an increase in the exogenouslydetermined headline nominal mortgage rate were to
occur because of upward pressure on the equilibrium
real interest rate, i.e., the natural or real equilibrium rate,
which is a component of the headline nominal rate, then
the consequences for the stability of the financial system
would be different in significant ways than it would be
in the case of an increase arising from, say, an increase
in expected inflation. This is because, in the former case,
the increase in the equilibrium rate would be likely to
have its origin in an increase in the trend growth rate of
the euro area economy. While this would, of course,
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Financial Stability Report 2005
drive up nominal interest rates in general and
consequently the nominal mortgage rate in Ireland,
which could possibly lead to an increase in loan arrears
and defaults, the improved performance of the euro area
economy would undoubtedly also be good for the
overall performance of the Irish economy. The increase
in the mortgage rate, due to the rise in the equilibrium
real interest rate, would, therefore, be unlikely to be
accompanied by a simultaneous increase in the
unemployment rate. Indeed, given the weight of the
euro area in Irish exports, it is not inconceivable that
unemployment might even fall on balance. Although the
burden of servicing mortgages for Irish households
would of course increase and could be accompanied by
an increase in loan arrears and defaults, this would by
itself be very unlikely to pose any systemic threat to the
financial system in a situation in which there is no
simultaneous deterioration in overall economic
performance or in unemployment.
However, in the latter instance of an inflation scare, the
increase in nominal rates would be unequivocally
deleterious to the economy and to its financial stability. It
would drive up nominal interest rates without this being
accompanied by any benign countervailing force coming
from an enduring improvement in the overall
performance in the euro area economy, in the form of an
increase in the potential growth rate. Instead, the overall
performance of the euro area economy would almost
certainly deteriorate. Maintaining the ECB’s price stability
objective would require a tightening of monetary policy,
putting further upward pressure on both real and
nominal interest rates, and slowing the euro area
economy in the process. Chart 1 illustrates in a simplified
format the potential consequences of an increase in the
nominal interest rate in these two cases.
Diagram 1: Causes and Consequences of a Mortgage Interest Rate Change
Mortgage loan
debt servicing
Loan arrears
Loan defaults
On
balance,
little threat
to financial
stability in
Ireland
Nominal interest
rate
Equilibrium rate
component of the
nominal rate arising
from an increase in
potential growth of the
euro area economy
Mortgage loan debt
servicing
Improved
performance of the
Irish economy
Loan arrears
No adverse
implications for
Irish unemployment
Loan defaults
Combination
could be a
threat to
financial
stability in
Ireland
Nominal interest rate
Inflation expectations
component of nominal
interest rate in the euro
area
Tightening of
monetary conditions
via the bond market or
monetary policy
resulting in a
deterioration of the
euro area economy
Adverse
implications for
Irish unemployment
Financial Stability Report 2005
125
These considerations suggest that an increase in the
headline nominal rate of interest should not necessarily
be seen as a negative for the economy because it may
be driven by an increase in the natural rate which is itself,
in turn, driven by an acceleration in the underlying
growth rate of the euro area economy. Nor can a fall in
the nominal rate necessarily be seen as a positive for
the economy since it might merely be symptomatic of
deterioration in the long-run potential of the euro area
economy to produce goods and services. It is clear,
therefore, that it is important to know the factors driving
the nominal rate so as to be able to make an assessment
of the likely implications for financial stability.
Since the late 1960s or early 1970s, until the mid 1980s,
Chart 1 reveals that the bulk of the variation in the
nominal rate of interest was attributable to factors of the
less benign type such as inflation premia and inflation
risk premia for most of the industrialised countries. The
variation in the natural rate tended to be overwhelmed
by the explosion of nominal values driven by inflation
(see Chart 1).
Chart 1: Nominal Rates of Interest for a Sample
of Industrialised Countries
per cent
US
Australia
UK
Japan
25
Canada
Euro area
20
15
10
5
0
1960
Q1
64
68
72
76
80
84
88
92
96
00
05
Q2
The low inflation environment prevailing in industrialised
economies since the early 1990s should mean that
variation in the equilibrium or natural rate should now
play a proportionately larger role in variation in the
nominal rate. This effect should also be reinforced by
the improved allocation of resources promoted by price
stability which should, other things being equal, have
helped to improve the potential growth rates of these
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Financial Stability Report 2005
economies. In order to clarify the issues involved, the
headline nominal interest rate, therefore, has to be
decomposed into its theoretical sub-components. We do
not know what the reaction of an economy will be to a
change in the headline rate unless we know to which of
these components, or subset of these components, the
change is due. These sub-components are not directly
observed and, therefore, have to be estimated. The
deconstruction into separate components depends on
the model used to explain movements in the headline
rate of interest.
This type of decomposition for the euro area allows us
to look at the separate influences of cyclical factors and
longer-term structural factors bearing on the nominal
rate of interest. This more detailed analysis allows us, in
turn, to make a more thorough assessment of the
likelihood of an interest-rate increase and to infer
whether such an increase will be more or less deleterious
for the stability of the financial system in Ireland. In order
to effect this decomposition of the nominal rate of
interest we look at a number of different models of the
equilibrium real rate of interest in this background paper.
3. Micro Foundations of the Equilibrium
Real Rate of Interest
A key sub-component of the nominal rate of interest is
the real equilibrium interest rate, as defined in Box 1. In
a world devoid of risk or uncertainty, any change in the
nominal rate of interest has to come from one of two
sources, i.e., a change in the real rate of interest or a
change in expected inflation. If the rate of return on a
debt security is known with certainty over the time
horizon to the maturity of the security then this nominal
rate of return can be written as the sum of the real rate
of return and the inflation rate that is expected to prevail
over this period. Since bond holders can only be
persuaded to hold the bond if the nominal rate of return
compensates for the loss of purchasing power, nominal
bond yields are often used as indicators of future
inflation.
The ex-ante real interest rate is the difference between
the nominal interest rate and the expected inflation rate.
The expected inflation rate is not observed but it can be
estimated and also allows for the estimation of ex-ante
real rate. When there is no inflation and output is
growing at its potential rate in the steady state then this
ex-ante real interest rate becomes the natural or
equilibrium real rate of interest. This natural interest rate
can best be understood at a micro level by being placed
in the context of the behaviour of the individual
representative consumer and producer.
Figure 1: The Production Opportunity Set
C1
consumption tomorrow. It is the marginal rate of
transformation (MRT) available with the existing
production infrastructure. At the point of equilibrium in
the figure (A), the MRS is equal to the MRT. This is a
Robinson Crusoe economy without capital markets
and therefore lacking a capability of transferring
consumption across time [implying that consumption (C)
and income (Y) have to be the same in both periods, i.e.,
Y0 = C0 and Y1 = C1].
A
Y 1 =C 1
C0
Y 0 =C 0
In steady state equilibrium, the rate at which consumers
substitute consumption over time at the margin (the socalled marginal rate of intertemporal substitution, MRS),
should be equal to the rate at which resources not
consumed today are transformed into future output at
the
margin
(known
as
the
rate
of
technical
transformation in production, MRT). And both of these
should equal the equilibrium or natural real rate of
In such a Robinson Crusoe economy with only one
individual there is opportunity to exchange consumption
between individuals across time. Figure 2 shows that two
individuals (as consumers cum investors) can both enjoy
higher levels of utility by being able to move along the
capital market line (i.e., w1ABw0 in the figure) than they
could in the complete absence of financial markets. For
our purposes here, the main thing to note is that the
slope of the capital market line is the equilibrium real
rate of interest. In equilibrium, this capital market line is
tangent to both the production opportunity set of the
economy and the indifference curves of all (but, in the
diagram, only two) investors. This means that, in
equilibrium, the MRS for all investors between current
and future consumption, is equal to the equilibrium real
rate of interest, which, in turn, is equal to the MRT
according to which firms transform current output into
(higher) future output. In symbols, we have that:
interest. This can be understood better in the context
of the accompanying Figure 1. The two axes represent
consumption now (C0) and consumption tomorrow
MRSi = MRSj = −(1+R*) = MRT
(C1).3 The curved convex line represents an indifference
curve in the sense that the consumer is indifferent
Figure 2: The Investment Decision
between the consumption bundles at any point along
the curve. The slope of the tangent at any point on the
C1
curve indicates the rate at which the consumer is willing
to trade off consumption today for consumption
tomorrow, i.e., it reveals the consumer’s subjective rate
w1
of time preference. The subjective rate of time
A
preference can be conceived as being the rate of interest
Investor 2
a consumer must receive in order to transfer present
consumption to the future and maintain total utility. The
P1
B
concave curve represents productive opportunities that
allow any given value of resources to be converted into
Investor 1
a higher level of future consumption. The slope of the
tangent to the curve indicates the rate at which a euro’s
C0
P0
w0
worth of consumption foregone today is transformed by
the productive process into more than a euro’s worth of
3
See Copeland, T. and J. Weston, (1988), ‘‘Financial Theory and Corporate Policy’’, Massachusetts: Addison Wesley for a more complete discussion.
Financial Stability Report 2005
127
To approximate the equilibrium rate, R*, it is clear from
this that we can tackle it either from the side of the
producer via the production-based-capital asset pricing
model (PCAPM), or from the side of the consumer which
we do by employing the consumption-based-capital
asset pricing model (CCAPM). The most important
breakdown of the components of the headline nominal
rate for the purposes of the present exercise is the twoway breakdown between the equilibrium real rate and
all the remaining components of the nominal rate. This
is because, as mentioned previously, an increase in the
nominal mortgage rate in Ireland, which is driven by an
increase in the equilibrium real rate in the euro area,
would be much less damaging to financial stability in
Ireland than would a corresponding increase in the
nominal rate coming from any of the latter’s many other
components. Indeed, it could be on balance beneficial
to overall financial stability in the long run. This is why in
the following a lot of attention is devoted to isolating the
equilibrium real rate.
4. Empirical Models of the Equilibrium Real
Rate of Interest
A number of ways have been proposed in the literature
for approximating the equilibrium real interest rate. They
can usefully be seen as falling into the following
categories:
●
simple averages of the actual real rate over long
periods of time;
●
long-dated yields on inflation indexed bonds;
●
‘‘Golden rule of growth’’ model;
●
‘‘Taylor rule’’ methodology; and
●
capital asset pricing (CAPM) models, whether
consumption-based or production-based.
We briefly examine each of these in turn below.
However, we give most attention to the method in the
last bullet point, which we consider to be the most
comprehensive. This is because it permits the headline
rate to be decomposed into a number of separate
components of which the equilibrium rate is just one.
4.1 Simple Averages of the Actual Real Rate for
Periods of Low Inflation
This simple method approximates the equilibrium rate by
taking averages of the actual real rate (i.e., the difference
between the actual nominal rate and the actual inflation
rate) over long time periods. This approach relies on the
logic that an average over a long enough time period
would wash out short-run deviations between the actual
real rate and the natural real rate, thereby yielding an
estimate of the natural rate. Table 1 reports a number
of estimations of the natural rate of interest for various
countries using this simple average approach.
The variations in the natural rates of interest across the
countries and sub-periods listed in the table could be
explained by a number of factors. The type of monetary
policy regime in operation, the stability of inflation, fiscal
conditions and various historical experiences all
contribute to explaining the differences in the natural
interest rates. In general, it would be expected that the
natural rates would vary across nations, as interest rates
are country specific and are subject to economic
conditions relevant to that country. This is particularly
true for the full period for which the calculations are
made. However, as financial markets become more
liberalised and integrated, the natural rates across
countries should converge more. The estimates for the
most recent sub-period (1999Q1-2005Q1) from Table 1
are, with the possible exception of that for the UK,
implausibly low.
Table 1: Simple Averages of the Short-Term Real Interest Rate, 1981Q1-2005Q1
Short-term real interest rate
Euro area
United States
United Kingdom
Japan
Australia
Canada
Average inflation
1981Q12005Q1
19811989
19901998
19992005Q1
1981Q12005Q1
19811989
19901998
19992005Q1
3.85
2.21
3.94
2.08
4.15
3.78
4.82
3.86
4.92
3.62
4.94
5.12
4.72
1.78
4.09
1.63
4.84
4.14
1.20
0.44
2.30
0.51
2.02
1.32
3.72
3.53
4.40
1.11
4.81
3.70
5.76
4.67
6.27
1.95
8.22
6.11
2.89
3.10
3.95
1.38
2.61
2.25
1.98
2.51
2.34
−0.48
3.05
2.30
Sources: ECB, US Federal Reserve and IMF International Financial Statistics.
Note: Albeit, the breakdown of the simple averages of the short-term real interest rate and inflation into sub-periods undermines the principles of
long-run averages, these breakdowns are none-the-less informative.
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Financial Stability Report 2005
Although a worthwhile approach as a way of conveying
the broad benchmark for the natural rate, these
averaging methods suffer from the disadvantage that the
estimated equilibrium rate is a single number and,
therefore, constant over the period for which it is
calculated. Although one would expect the equilibrium
rate not to be too erratic since it is anchored in the
steady state characteristics of the real economy, and,
therefore, less variable than the actual real rate, it is
nevertheless unlikely to be a constant over time. It is
related to a number of factors that are likely to
experience some volatility in the short run and to change
with the passage of time even if only slowly, arising, for
example, from structural change in both the real
economy and in financial markets.
4.2 Long-dated Yields on Inflation Indexed Bonds
An intuitively appealing approach that does not involve
the specification and estimation of a model is to
approximate the equilibrium rate using long-dated
inflation-index-linked bonds. The rationale for this
approach is, first, that the difference between yields on
indexed and non-indexed government bonds of identical
maturity can be used as a measure of expected inflation
and, secondly, that the long-dated yield reflects
expectations at long horizons providing, in principle, a
closer measure of the steady state.
Chart 2: Real Bond Yields in the Euro Area and
France Derived from French Inflation-Linked Bonds
per cent per annum
Chart 2 displays real bond yields in the euro area (since
early 2002) and in France (since early 1999)4. The most
salient feature of the graph is the downward trend in the
estimate of the equilibrium rate from almost 4 per cent
in March 2000 to less than 1.5 per cent in March 2004.
However, this seems like too big a movement over such
a short space of time to be a plausible estimate of an
equilibrium rate. There are a number of shortcomings to
using this method. The yields on inflation-indexed bonds
may suffer from distortions arising from thin markets, tax
arrangements and time varying risk premia. A more
practical shortcoming is that long time series on indexlinked bonds are not in general available.
4.3 ‘‘Golden Rule of Growth’’ Model
The above methods are fairly ad hoc in that they do not
invoke any theory to motivate the approach used in the
estimation of the equilibrium rate. Given the discussion
above on the definition of the equilibrium real interest
rate, one would expect the rate to be related to a
number of deep parameters in the economy relating to
the long-run potential growth rate of the economy, the
preference of households for consumption now relative
to consumption in the future, and demographic
developments. The precise nature of the relationship
between these variables and the equilibrium rate is
crystallised in the neo-classical growth model (i.e., the
Golden rule growth model) as described, for example, by
Laubach and Williams (2001) in the following equation:
5
r* =
1
q + + n,
4
where:
r* is the equilibrium real rate of interest,
3
q is the rate of technological progress,
is the coefficient of relative risk aversion,
France
Euro area
2
n is the population growth rate, and
is the discount rate.
1
0
May-99
00
01
02
03
04
05
Aug
Source: French Treasury, Reuters and the ECB
Note: French index-linked bond linked to the French CPI is
maturing in 2009. The French index-linked bond linked to the
euro area HICP is maturing in 2012. Monthly averages.
4
An acceleration in the rate of technological progress (q)
increases total factor productivity and the return to
investment. The ensuing increased demand for
investment funds drives up the equilibrium real rate of
interest for a given level of savings. An increase in the
population growth rate (n) enhances the labour
endowment in the economy and leads to an increase in
the potential growth rate whose funding requirements
These are derived respectively from French government bonds linked to the French CPI and from French government bonds linked to the euro
area HICP.
Financial Stability Report 2005
129
drives up the equilibrium real rate of interest for a given
supply of loanable funds. An increase in the discount
rate (), or a fall in the rate of time preference, would
see a proportion of consumption being brought forward
from the future to the present. This reduces the level
of current savings and drives up the equilibrium rate of
interest. The equilibrium real rate also varies inversely
with the consumer’s attitude to risk (where denotes
the coefficient of relative risk aversion), with an increase
(decrease) in the degree of relative risk aversion causing
the consumer to save (dissave) more leading to a fall
(increase) in the equilibrium rate.
Recall again that the equilibrium rate is the rate that
would prevail in general equilibrium and accordingly also
the rate that equates the ex-ante supply of savings (by
households) with the ex-ante demand for investment
funding (by firms). An advantage of this approach is that
it allows the equilibrium rate to vary over time and can
also offer an explanation as to why it changed by relating
it back to fundamental driving forces. Employing the
Golden rule growth model to calculate the equilibrium
real interest rate for the period 1971 to 2003 yields an
average equilibrium rate of 2.48 per cent5. Estimations
from this model in various sub-decades move around the
overall average rate, there was an average rate of 3.16
per cent in the 1970s, 2.45 per cent in the 1980s, 2.34
per cent in the 1990s, and an average rate of 1.56 per
cent in the period since the start of EMU until 2003. It is
notable that, as with the method outlined in Section 4.2,
the estimate of the equilibrium rate that emerges for the
last sub-period seems to be on the small side.
4.4 ‘Taylor Rule’ Methodology
This approach is based on the belief that monetary
authorities’ interest-rate decisions are based on the
observed behaviour of the economy, i.e., the behaviour
of inflation and the output gap. It proposes that the
central bank adjusts the nominal rate of interest
according to the following rule:
r(t) = r* + ((t) − *) + (x(t) − x*)
where r and r* are the actual and equilibrium real rates
of interest, and * are the actual rate of inflation and
the rate of inflation being targeted by the central bank
respectively, x and x* symbolise actual and potential
output growth rates, and their difference, the output gap.
It is clear from this specification of central bank
behaviour that if inflation is equal to its target, and output
is growing at potential then the actual real rate of interest
5
is equal to the equilibrium rate. Whenever inflation is in
excess of target or the output gap is non-zero, the central
bank will maintain the actual real rate above or below
the equilibrium rate as appropriate in order to correct
these deviations from the central bank’s objectives.
Given the central bank’s inflation target (*) and an
estimate of the economy’s potential output growth rate
(x*) along with the corresponding actual values of these
variables ((t) and x(t)), and the actual rate of interest r(t)
as well as estimates of and , an estimate of the natural
rate r* can be derived from the last equation. Using this
approach for the US economy, when (*) is taken to be
2 per cent, Reifschneider and Williams (2000) report a
value of about 2.5 per cent for the equilibrium rate of
interest. They also state that lower inflation targets yield
higher equilibrium real interest rates. They report an
equilibrium real rate of 3.5 per cent for an inflation target
in the region of 0 per cent to 1 per cent.
Estimates of r* for the euro area, synthetic pre-1999 and
actual post-1999, from 1985 to 2002, produced by
Gerdesmeier and Roffia (2003), place estimates of the
natural rate in the region of 2.1 per cent to 3.2 per cent.
However, in the shorter sample period starting in 1995,
Gerdesmeier and Roffia (2003) estimate lower rates for
r* in the region of 2.22 per cent, and 1.78 per cent for
the period 1999 to 2002. This suggests that the
equilibrium real rate for the euro area may have fallen
over time. A fairly persuasive set of rationales has been
put forward as to why the equilibrium real rate fell in the
group of countries that currently comprise the euro area.
Section 4.6 provides a summary of the factors, which
may conceivably have contributed to this fall.
4.5 Consumption-Based
Capital
(CCAPM) Model Approach
Financial Stability Report 2005
Pricing
Another way of looking at the natural rate of interest is
as the rate that would prevail if the economy behaved
as in the classical model, i.e., free of nominal frictions
and informational asymmetries. In such a world,
households would be able to exchange consumption
across time as desired (in accordance with the behaviour
depicted in Figure 2 above), with the only constraint
being the cost (to the borrower) or benefit (to the lender)
of doing so, which is the natural rate of interest. The
consumption-based capital asset pricing model
(CCAPM), which we use here to decompose the
headline nominal rate, is founded on this observation. In
this approach, therefore, the natural rate is being inferred
from the intertemporal portfolio behaviour of the private
The values imputed into the ‘‘Golden rule of growth’’ equation for q, n, σ and θ are explained respectively in the Annex.
130
Asset
sector of the economy. The CCAPM places
intertemporal consumption and saving behaviour in a
stochastic setting, and in doing so, provides additional
risk-based determinants of the headline nominal rate of
interest.
to save will, other things being equal, drive down the
risk-free real rate of interest and hence the headline
nominal rate also. Uncertainty about future consumption
is measured by the variance of the one period ahead
forecast for consumption.
The theoretical components of the nominal interest rate
are dictated by the elements that enter into the
theoretical CCAPM pricing model. If the data suggest
that the model is a good representation of household
consumption and saving behaviour then the relative
magnitudes of the various components of the nominal
interest rate, and how they have changed over time, can
be inferred from the estimated model. The theoretical
model is the following:
The fourth component listed (E(Δp)) is expected inflation.
This is the standard variable used to test for the validity
of the Fisher hypothesis as to whether nominal interest
rates contain a full inflation premium. However, what
bondholders are concerned about is the expected
change in the purchasing power of money (i.e., E(Pt/Pt+1))
over the holding period of the bond and not the
expected inflation rate over this period (i.e., E(Pt+1/Pt))6.
In a world of uncertainty, according to Jensen’s
inequality, the expected value of one is not the inverse
of the expected value of the other. According to Jensen’s
inequality, a mean-preserving spread in the inflation rate
(Var(Δp)) results in an increase in the expected
purchasing power of money. Other things being equal,
this results in an increase in the demand for bonds
driving up bond prices and depressing bond yields. The
relationship between the expected inflation and
expected future purchasing power in a world of
uncertainty can be written as follows:
i = + E(Δc) − (1/2)Var(Δc) + E(Δp) − (1/2)Var(Δp) −
Cov(Δc,Δp)
(i)
The first component of the headline nominal rate of
interest (i) is the discount rate (). It reflects the fact that
the more heavily individuals discount the future (i.e., the
higher is the discount rate), the greater is current
consumption and the lower is current savings. This
reduces the supply of loanable funds and, other things
being equal, drives up the real, and accordingly the
nominal, rate of interest.
The second component is expected aggregate real
consumption ((E(Δc)). For a given discount rate, the
higher the expected growth rate of consumption, the
higher is future consumption relative to current
consumption and the higher the interest rate has to be
to prevent people transferring future consumption to the
present, where consumption goods are in fixed supply.
There is a natural corollary of this — when there is an
incipient excess supply of current consumption goods,
the higher current consumption needs to be relative to
future consumption to encourage people to consume
more now and less in the future and, therefore, the lower
the interest rate needs to be. Expected consumption is
captured by the one-period (one period is equal to a
quarter) ahead forecast of consumption.
The third component captures uncertainty about future
consumption (Var(Δc)). The more uncertain risk-averse
individuals are about future consumption the more they
will want to save now to insure themselves against the
realisation of this uncertainty. Their increased preference
6
7
E(Pt/Pt+1) = exp[−Et(ΔPt+1) + 1/2Vart(ΔPt+1)]
(ii)
The first term on the right hand side reflects the fact that
bondholding households7 expect to be compensated for
any inflation, which they expect to occur over the
holding period of the bond. If the current yield does not
reward them for the inflation they expect to occur over
the holding period of the bond, then they will sell off
their bond holdings. This will have the effect of driving
down the price of bonds and boosting the yield.
Therefore, either an increase in expected inflation or a
fall in the variance of future prices implies a decline in
expected future purchasing power. This spills over into a
reduction in demand for bonds, which inflates bond
yields, which accounts for the positive and negative signs
on these respective variables in equation (ii) above8.
The final component (Cov(Δc,Δp)) is less familiar. It is
another risk term, called the covariance risk. It captures
the risk to portfolios arising from the correlation between
the business cycle and interest rates. It is assumed that
households would prefer to hold assets that would
enable them to smooth consumption over time. They
This is a key distinction made by Evans and Wachtel (1992) whose model provides the core theoretical framework for this paper.
The introduction of collective investment schemes, in particular money market, bond and equity mutual funds, enabled retail investors to gain
effective access to the securities’ markets.
Financial Stability Report 2005
131
would accordingly want to hold assets that would yield
a high return when income (and, therefore, consumption)
is subject to cyclical downturn. This implies that they would
want to hold assets that would co-vary negatively with
consumption, i.e., Cov(Δc,Δr) < 0. Since the expected real
rate varies negatively with the price level, households
would want to hold assets such that Cov(Δc,Δp) > 0. If,
in fact, the asset is such that the first of these covariances
is positive and the second negative, then households
would expect to be compensated for this and, to be
persuaded to hold the asset, would have to be rewarded
with a risk premium (i.e., a covariance risk premium).
This would then be build into the observed nominal rate
of interest. Detailed empirical results for the euro area
are reported in Browne and Everett (2004).
If financial markets are relatively liquid, following a
loosening of the stance of monetary policy, then the
nominal rate of interest will be low relative to its
fundamental determinants as represented by the
CCAPM. The model must, therefore, be adjusted to
capture this well-known Keynesian liquidity effect of
monetary policy. The background to this adjustment
follows the work of Fuerst (1992) and is explained in
more detail in Browne and Everett (2003). This model
suggests that it is expected money growth that impacts
on the nominal interest rate. However, it could be
argued that changes in money, whether anticipated or
not, will, by relaxing the liquidity constraints noted
already, have a dampening effect on the nominal and,
other things being equal, the real interest rate. The sign
of the effect is unambiguously negative. Chart 3 depicts
our estimate of the equilibrium rate of interest along with
the actual real rate for the euro area.
Chart 3: Actual and Equilibrium Real Interest Rates
for the Euro Area
per cent
Equilibrium real
rate of interest
8
7
Actual real rate
of interest
6
5
4
3
2
1
0
1982 Q2
85
90
95
00
05 Q1
Note: Data are moving averages (window = 6 quarters).
As can be seen from Table 2, evaluations of the
equilibrium real rate of interest vary across the different
methods of estimation. Variations in the estimations may
be the result of a number of factors. Most obviously, the
models employed are comprised of different
components, and the periods of estimation also differ.
4.6 Factors Contributing to the Trend Decline in the
Equilibrium Rate
All the time-varying estimated equilibrium rates for the
euro area seem to display a common feature: a
downward trend. Chart 4a shows our estimate of the
equilibrium rate for the euro area from the early 1980s
Table 2: Summary of Equilibrium Real Interest Rate Estimates for the Euro Area
Model
Rate - %
Period of estimation
4.1 Simple averages of the actual rate
3.85
1981-2005
4.2 Long dated yields on inflation indexed bonds
4
1.5
March 2000
March 2004
4.3 Golden rule of growth model
2.48
1971-2003
4.4 Taylor rule
2.1-3.2
2.22
1.78
1985-2002
1995-2002
1999-2002
4.5 CCAPM
CCAPM including liquidity constraints
2.17
2.51
1981Q1-2005Q1
1981Q1-2005Q1
8
There have been other interpretations of the Var(ΔPt+1) term. Friedman for example argued that inflation uncertainty erodes the efficiency of the
market mechanism in allocating resources decreasing real output and shifting the aggregates supply curve to the left necessitating an increase in
the real interest rate. This would suggest a positive sign on this variable. Others have argued that uncertainty about inflation reduces demand for
investment and puts downward pressure on the real interest rate.
132
Financial Stability Report 2005
to the first quarter of 2005. The rate fell from a peak of
about 4 per cent in 1988 to about 2 per cent in 2004.
A leading candidate to account for this trend decline is
productivity.
Chart 4a: Equilibrium Real Interest Rate for the
Euro Area
per cent
5
Total factor productivity growth, displayed in Chart 4b,
demonstrates a fairly strong declining trend since the late
1980s. Changes in expected total factor productivity
growth tend to affect the equilibrium rate via
households’ current and future consumption and saving
preferences. If a dampening of expectations in total
factor productivity growth occurs, households’
expectations of their future income will decline and,
therefore, they will choose to save more in the current
period. The equilibrium rate of interest must decrease in
order to encourage households to save less today and
to stimulate current consumption.
Demographic developments can also have an effect on
savings patterns. As Chart 4c demonstrates, the overall
trend of total population growth is downward9. This
downward trend in population growth feeds into the
equilibrium interest-rate calculations, which can be seen
most directly via the ‘‘Golden rule of growth’’ model,
discussed in Section 4.3. The declining working-age
population and the corresponding drop in the available
workforce, means that less capital will be required to
equip workers. Therefore, a fall in the equilibrium rate
of interest will be necessary to encourage investment in
capital. This implies that reduced population growth
since the 1960s may have contributed to the fall in the
equilibrium interest rate during this time.
Other structural changes and fundamental components
of the economy may also have been instrumental in the
decline of the equilibrium rate. The introduction of the
euro in January 1999, has led to the elimination of intra
euro area exchange-rate risk premia leading to a
permanent fall in the real cost of borrowing. Current
inflation rates in the euro area are more predictable than
those in previous decades due to the ECB’s increasingly
credible commitment to price stability10. This has
resulted in a reduction of inflation risk premia in the euro
area. The constraints of the requirements imposed on
euro area Member States by the Maastricht Treaty has
created lower national government deficits, which, in
turn, has led to increased investor confidence and
reduced national inflationary pressures. All of these
factors were likely to have been influential in the trend
decline of the equilibrium real interest rate over the last
number of years.
4
3
2
1
0
1982
85
88
91
94
97
00
03
05
Q1
Note: Data are moving averages (window = 6 quarters).
Chart 4b: Trend Total-factor Productivity Growth
per cent per annum
(based on quarterly data)
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
1981
84
87
90
93
96
99
02 03
9
The slight upward trend in the total population growth rate since 1999 is due to euro area immigration however, the euro area’s natural population
growth rate continues to decline.
10
Price stability is defined as a year-on-year increase in the Harmonised Index of Consumer Prices (HICP) for the euro area of below 2 per cent.
Financial Stability Report 2005
133
ongoing downward trend in the volatility of consumption
growth over at least the last 25 years11. So this also
seems highly unlikely.
Chart 4c: Rate of Increase of the Total
Population (Crude Rate)
per cent
1.2
Chart 5: Volatility of Consumption Growth
1.0
per cent
2.0
1.8
0.8
1.6
0.6
1.4
1.2
0.4
1.0
0.8
0.2
0.6
0.0
1960
65
70
75
80
85
90
95
00
0.4
03
0.2
0.0
5. Assessment of the likely Sources of
Upward Pressure on the Nominal
(Mortgage) Rate of Interest
Any increase in the headline nominal mortgage rate of
interest will put some pressure on heavily indebted
households. But some increases may be less threatening
to their financial health than others. A situation in which
an increase in the headline nominal rate of interest is
driven by an increase in the equilibrium real rate is
probably the least unfavourable development for the
vulnerable household sector in Ireland. An examination
of some of the models of the equilibrium rate discussed
above, and the factors they suggest are behind
movements in the equilibrium rate, may help to infer
what are the chances of a sharp increase in the nominal
mortgage rate arising from a similarly sharp increase in
the equilibrium rate. In this respect, the decomposition
suggested by the consumption-based capital asset
pricing model, i.e., the model discussed in Section 4.5, is
probably the most instructive. Assuming that the rate at
which agents discount the future does not change, a
sharp increase in the equilibrium rate would only occur
if there was an expectation that consumption would
increase substantially or if the variance of consumption
growth were to rise significantly. Mainstream forecasts
do not envisage any such acceleration in consumption
growth. For the variance of consumption growth to
suddenly start increasing would mean the reversal of an
11
1982
Q2
85
88
Financial Stability Report 2005
94
97
00
03
05
Q2
Looked at from the production side of the economy, the
strong correlation between the equilibrium real interest
rate (as estimated from the CCAPM model) and trend
total factor productivity growth (see Chart 4b) would
suggest that the equilibrium rate would only rebound if
the downward trend in total factor productivity growth
since about the early 1990s were to be reversed which
seems unlikely at least over the near-term horizon of the
next few years. If anything, recent discussion on the low
potential output growth rate for the euro area tended to
be focused on a downward revision of the growth
potential. The positive correlation between population
growth and the equilibrium rate is more obvious over
longer periods than that shown in Charts 4a and 4c,
where, over this shorter time period, there is no notable
relationship. So it would look as if the least unfavourable
event, an increase in the equilibrium real interest rate,
has quite a low probability of happening over the next
few years.
Of course, the lower the equilibrium rate the less upside
potential there is to any particular value for the headline
nominal rate of interest. One of the reasons why the
current structure of nominal interest rates is so low in
the euro area by historical comparisons is because the
A steeper downward trend has existed in the volatility of consumption growth since the mid-1990s.
134
91
equilibrium rate has been subject to a downward trend
noted since at least the early 1980s.
So what about a sharp increase in the nominal mortgage
rate arising from much more unfavourable events
stemming from developments that would affect the
‘‘nominal’’ component (i.e., an expected loss of
purchasing power by bondholders) and/or the risk
component (i.e., consumption covariance risk) of the
nominal rate? With respect to the former, there is
nothing to doubt the ECB’s determination to keep
inflation at its target of close to, but below, 2 per cent.
For more recent time periods, consumption covariance
risk does not feature as a significant phenomenon. There
was a drop in the estimated covariance in 2002Q1, after
which it remained at this low level close to zero. This
may be largely attributable to an increasing capability
of households to smooth consumption across time. Any
increase in this covariance from this low level is highly
improbable since the developments most likely
responsible for consumption smoothing (i.e., financial
market deregulation and financial innovation) are most
unlikely to experience any reversal of the recent trend
towards more liberalisation. Therefore, the upside risk to
the nominal mortgage rate from either of these two
factors seems fairly small from the current perspective.
Despite this, a short-term burst of inflation stemming,
say, from strong cost-push factors such as oil prices could
become embedded via second round effects unless
countered by the central bank. Such an inflation scare
could lead to substantially higher interest rates, which
would no doubt spill over into mortgage rates in Ireland,
the bulk of which are variable rates. This would pose
problems for mortgage holders particularly those who
are already highly geared. A sudden bunching of nonperforming loans could, in turn, erode the quality of
mortgage lenders’ loan books.
Over the medium-term horizon (chronologically
approximately three to seven years), it is likely that the
euro area economy will revive and will see a much
higher equilibrium real rate of interest. As noted already
in footnote 1 above, a steady state growth rate of 3 per
cent, combined with an inflation rate of about 2 per cent
(consistent with the ECB’s inflation objective) and a risk
premium of 1 per cent would add up to an equilibrium
mortgage rate of approximately 6 per cent. With the
typical variable mortgage rate of interest being around 3
per cent now (October 2005), an increase in interest
rates to this putative equilibrium level would double the
repayments burden. For highly indebted borrowers, this
would be an intolerable burden and would almost
certainly mean a sharp increase in the ratio of nonperforming loans.
There is, however, a silver lining in this medium-term
scenario. This arises from the fact that the event most
likely to drive the mortgage rate to this level is a
corresponding increase in the equilibrium rate, which
would only happen if the potential growth rate (and the
consumption growth rate) in the euro area economy
were to accelerate from the current low rate in the
region of 1.5 per cent to 3 per cent, provided peoples’
time preferences do not shift and provided there is no
increase in the volatility of overall growth (or
consumption growth) which seems reasonable. Such
acceleration in the growth rate of Ireland’s main trading
region would undoubtedly be beneficial to the
conjunctural performance of the economy. It would
probably mean that any depressing effect on the
economy coming from the housing and bank loan
markets would tend to be offset by an improved
international trade position.
The less favourable events impacting on the actual
mortgage rate (i.e., the probability that any increase in
the headline nominal mortgage rate being driven by
events that are unfavourable to the overall euro area
economy, namely, an increase in expected inflation or
an increase in consumption covariance risk) are deemed
to be less long lasting in their effects than those affecting
the equilibrium rate. Not only is the first of these
unfavourable, it would almost certainly evoke a
tightening of monetary policy which would, in turn,
almost certainly slow the euro area economy with
adverse implications for the Irish economy and financial
stability in Ireland.
6. Conclusions
The overall impact of any interest-rate increase on the
financial stability of the Irish banking system is likely to
depend on the reasons why the rate increased. There are
a number of important long-term developments currently
influencing the euro area economy, which are probably
now having a determining effect on the level of nominal
and real interest rates. Decomposing the headline
nominal interest rate into its constituent components
(where the number and nature of these components
depend on the model of the interest rate used) can be
helpful in endeavouring to understand how the nominal
interest rate might evolve over the near- and mediumterm future.
Financial Stability Report 2005
135
None of the components in the two more
comprehensive models examined12 would suggest that
there is currently much danger of a substantial increase
in the nominal interest rate stemming from a significant
shift in the underlying equilibrium real rate of interest.
The likelihood of either a turnaround in the recent trend
in total factor productivity, or population growth (the
Golden rule of growth model), or a burst on household
consumption expenditure or a reversal of the downward
trend in the variance of consumption growth (the
consumption-based capital asset pricing model) seem
remote, especially given the prospects for the euro area
conjuncture. Inflation also seems set to remain in the
region of the ECB’s target, while upward pressure on the
nominal rate coming from risk factors seems low, the
scope for nominal interest rates to rise substantially
seems limited.
There are a number of longer-term institutional and
structural factors moulding this picture for the nominal
interest rate. First, there appears to be little dispute about
the fact that structural rigidities are constraining total
factor productivity in the euro area. Although there has
been some structural reform, it is moving at a very slow
pace. It is unlikely then to have the effect of relaxing the
binding constraint on productivity growth in the short to
medium term. Sluggish consumption growth is also tied
up with the poor performance of the euro area economy
reinforced by an aging population and probably also
precautionary saving arising from the reforms that have
been announced. The low volatility of consumption
growth following a long trend decline over the last 30
years or so is probably attributable to financial market
reforms and financial innovation and is, therefore, almost
certainly here to stay. Another important institutional
reform has come in the shape of an independent central
bank (the ECB) mandated to achieve price stability in the
euro area, a task in which it has so far largely succeeded,
a performance set to persist into the future. There are,
therefore, many factors, which would suggest that the
current low interest rate regime could endure for some
time.
An event, which could upset this scene in the near term,
is a sudden burst in inflation probably driven by some
combination of a supply shock and cost push such as a
(further) substantial oil price hike. To prevent this from
becoming embedded in overall inflation and in inflation
expectations, the ECB might have to raise interest rates
quite sharply.
12
These are the ‘‘Golden rule of growth’’ and the capital asset pricing models.
136
Financial Stability Report 2005
Focusing on the longer-term horizon a quite different
picture could emerge. The structural reforms that are
currently being undertaken could be intensified. The new
technologies that have raised productivity growth
permanently in the US may come to be embraced more
enthusiastically by European firms resulting in a similar
increase in overall potential growth rate for the euro
area. If this were to happen, then the equilibrium interest
rate and the nominal mortgage rate would also increase
towards the 6 per cent benchmark rate we have
identified or maybe even higher.
The danger posed for financial stability in Ireland by an
increase in the nominal rate of this size would depend
on whether any such increase would also be
accompanied by a simultaneous and substantial increase
in Irish unemployment. This is really the type of double
effect to which the Irish economy is currently vulnerable
because of the combination of the rapid rate of increase
of household indebtedness over the past decade and the
very high proportion of adjustable rate mortgages in the
total outstanding stock of mortgages. The likelihood that
an increase in the interest rate would also precipitate an
increase in unemployment depends on the reason for
the increase in the interest rate.
Unfavourable increases in the nominal mortgage rate are
more likely in the short to medium term (arising from an
inflation scare for example). However, given the
credibility of the ECB’s commitment to price stability, any
such increase would hardly be long lasting. The less
unfavourable type of increase (coming from an increase
in the equilibrium rate) is more likely to be something
that would happen over a longer time frame (probably
3 to 7 years from now). Although it would probably see
nominal variable-rate mortgages double in size, it would
be accompanied by an improvement in the potential
growth rate of the euro area economy which would
benefit the Irish economy. Any damage done to the
systemic health of the Irish financial system would tend
to be contained by the fact that unemployment would
be unlikely to rise at the same time as the increase in
interest rates.
References
Browne, F. and M. Everett, (2003), ‘‘The Real Interest
Rate Spread as a Monetary Policy Indicator’’,
Monetary Policy Discussion Paper, No. 3., Monetary
Policy and Financial Stability Department, CBFSAI.
Browne, F. and M. Everett, (2004), ‘‘The Real Interest
Rate Spread for the Euro Area’’, mimeo.
Central Bank & Financial Services Authority of Ireland,
(2004), ‘‘Financial Stability Report’’, Central Bank &
Financial Services Authority of Ireland.
Copeland, T. and J. Weston, (1988), Financial Theory and
Corporate Policy, Massachusetts: Addison Wesley.
European Central Bank, (2004), Monthly Bulletin,
European Central Bank, May.
Evans, M. and P. Wachtel, (1992), ‘‘Interpreting the
Movements in Short-Term Interest Rates’’, Journal of
Business, Vol. 65, No. 3.
Fagan, G., J. Henry and R. Mestre, (2001), ‘‘An AreaWide Model (AWM) for the Euro Area’’, ECB Working
Paper, No. 42, ECB.
Fuerst, T.S., (1992), ‘‘Liquidity, Loanable Funds and Real
Activity’’, Journal of Monetary Economics, Vol. 29,
pp3-24
Gerdesmeir, D. and B. Roffia, (2003), ‘‘Empirical
Estimates of Reaction Functions for the Euro Area’’,
ECB Working Paper, No. 206, ECB.
Laubach, T. and J. Williams, (2001), ‘‘Measuring the
Natural Rate of Interest’’, Finance and Economics
Discussion Series 2001-56, Board of Governors of the
Federal Reserve System (U.S.)
Lucas, R. E., (1990), ‘‘Liquidity and Interest Rates’’,
Journal of Economic Theory, Vol. 50, pp237-264.
Reifschneider, D. and J. Williams, (2000), ‘‘Three Lessons
for Monetary Policy in a Low-Inflation Era’’, Journal of
Money, Credit and Banking, Vol. 32, No. 4.
Wicksell, K., (1936), ‘‘Interest and Prices’’ (translation of
the 1898 edition by R.F. Kahn), London: Macmillian.
Annex: Data Sources and Methods
Data used to calculate simple averages of the actual real
interest rate are sourced from the ECB, US Federal
Reserve and the IFS, August 2004. The long-dated yields
13
on inflation-indexed bonds in the euro area and France
are extracted from the ECB’s Monthly Bulletin, May
2004.
Trend total factor productivity growth is used as a proxy
for the rate of technological progress, a component of
the neo-classical growth model, and is sourced from the
Area Wide Model13 database. The population growth
rate is sourced from Eurostat’s New Cronos database.
The coefficient associated with expected consumption
calculated via the CCAPM approach, is used as a
measure of the constant relative risk aversion coefficient.
The rate of time preference is assumed to be the inverse
of the discount rate variable in the CCAPM framework,
outlined in Section 4.5.
Estimates of the equilibrium real rate of interest
calculated via the Taylor rule are sourced from
Reifschneider and Williams (2000), and Gerdesmeier
and Roffia (2003).
The performance of the CCAPM approach is assessed
using quarterly data for the period 1980 to 2004. All data
are sourced from the Area Wide Model database, ECB
monthly bulletins and the IFS. ECB data post-1999 is
linked with AWM data prior to this date, in order to
ensure consistency across all data sequences. A similar
method is employed (by the ECB) for the re-scaling of
the AWM database to ECB monthly bulletin data.
The chosen measure of the nominal interest rate is the
short-term interest rate and the three-month money
market rate sourced from the AWM and ECB,
respectively. The consumption data are the AWM
databases’ and ECB’s nominal private sector
consumption data deflated to constant prices. The
measure of inflation is derived from the Harmonised
Index of Consumer Prices (HICP) based in the year,
1996. The data series for real money stock, i.e., the
liquidity variable, is compiled from German total reserves
minus gold, sourced from the IFS, August 2004 and the
ECB.
Fagan. G, Henry. J and Mestre. R (2001). ‘An Area-Wide Model (AWM) for the euro area’. ECB Working Paper No. 42.
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