ESTIMATING THE NATURAL RATE OF INTEREST BASED ON THE SVAR
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ESTIMATING THE NATURAL RATE OF INTEREST BASED ON THE SVAR THE CASE OF BELGIUM Word count: 15 818 Ayoub Elomari Student number : 01402069 Jonas Van Oost Student number : 01402123 Supervisor: Prof. dr. Selien De Schryder Master’s Dissertation submitted to obtain the degree of: Master of Science in Business Administration – Finance and Risk Management Academic year: 2017 – 2018
Transcript of ESTIMATING THE NATURAL RATE OF INTEREST BASED ON THE SVAR
ESTIMATING THE NATURAL RATE OF
INTEREST BASED ON THE SVAR THE CASE OF BELGIUM
Word count: 15 818
Ayoub Elomari Student number : 01402069
Jonas Van Oost Student number : 01402123
Supervisor: Prof. dr. Selien De Schryder
Master’s Dissertation submitted to obtain the degree of:
Master of Science in Business Administration – Finance and Risk Management
Academic year: 2017 – 2018
ESTIMATING THE NATURAL RATE OF
INTEREST BASED ON THE SVAR THE CASE OF BELGIUM
Aantal woorden: 15 818
Ayoub Elomari Stamnummer : 01402069
Jonas Van Oost Stamnummer : 01402123
Promotor: Prof. dr. Selien De Schryder
Masterproef voorgedragen tot het bekomen van de graad van:
Master of Science in de Handelswetenschappen – Finance en risicomanagement
Academiejaar: 2017 – 2018
VERTROUWELIJKHEIDSCLAUSULE/ CONFIDENTIALITY AGREEMENT
PERMISSION
Ondergetekende verklaart dat de inhoud van deze masterproef mag geraadpleegd en/of gereproduceerd worden, mits bronvermelding.
I declare that the content of this Master’s Dissertation may be consulted and/or reproduced, provided that the source is referenced.
Naam studenten/name students: Ayoub Elomari en Jonas Van Oost
Handtekening/signature
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Nederlandstalige samenvatting – Dutch summary
Meerdere studies, zoals deze van Laubach en Williams (2015), wijzen op een dalende trend
in de neutrale intrestvoet sinds de financiële crisis. Deze masterproef zal de neutrale rente
uitleggen aan de hand van bestaande literatuur. Zo zal er eveneens een overzicht gegeven
worden van de drijvende factoren van deze neutrale rente. Daarnaast worden de factoren die
leidden tot de dalende trend aangehaald. Vervolgens wordt een snelle blik geworpen op de
schattingsmethoden om tot de neutrale intrestvoet te komen. Daarnaast zal het belang voor
het monetaire beleid van deze maatstaf gemotiveerd worden. Hierbij zal er ook aandacht
geschonken worden aan de verschillende problemen, die het schatten van deze variabele met
zich meebrengt.
De evolutie in de neutrale intrestvoeten van de grootmachten, zoals de Verenigde Staten en
de Europese Unie, zijn reeds uitvoerig beschreven. Voor België was dit echter niet het geval.
Aangezien dit volgens ons van wetenschappelijk belang is, heeft dit ons ertoe bewogen om
zelf een schatting te maken van de neutrale intrestvoet voor België van 1995 tot 2018. Het
wetenschappelijk belang uit zich in de belangrijkheid van de neutrale rente. De vergelijking
tussen de geobserveerde reële rente en de geschatte neutrale rente toont ons hoe de
economie fluctueert rond zijn evenwicht. De onderzoeksvraag van onze econometrische studie
luidde als volgt: “Is er een neerwaartse trend waarneembaar in de neutrale intrestvoet voor
België in de laatste jaren?”
De neutrale intrestvoet werd geschat aan de hand van een SVAR. Deze schatting wordt
vervolgens vergeleken met de geobserveerde reële intrestvoet en vergeleken met schattingen
van de Verenigde Staten en de Eurozone. Om dit gestructureerd te kunnen uitvoeren, werden
drie vragen vooropgesteld:
1) Kennen de geobserveerde reële rente en de geschatte neutrale rente een gelijkaardig
verloop?
2) Hoe ziet het verloop van de neutrale rente eruit in vergelijking met de Verenigde Staten
en de Eurozone?
3) Is onze schatting van de neutrale rente in de Verenigde Staten, die gebaseerd is op de
SVAR, gelijkaardig aan deze van Holston, Laubach en Williams (2016)?
Deze vragen werden in de thesis beantwoord aan de hand van grafieken. Daarnaast werden
de resultaten ook teruggekoppeld aan de literatuur.
Tot slot werden er enkele kritische bevindingen geformuleerd met betrekking tot onze
resultaten en de onenigheid over een uniforme definitie van de neutrale rente in de literatuur.
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Preface
We have chosen to write our Master’s Dissertation about the natural rate of interest, as we are
strongly interested in the monetary policy and the way the economy works. Writing a Master’s
Dissertation is required to obtain the Master degree of Business Administration in Finance and
Risk Management.
The rest of the preface will be used to give a word of appreciation to the people that helped
realizing this thesis.
First, we want to thank Prof. dr. Selien De Schryder, our promoter, for the guidance and
meetings through the academic year. We also want to thank her for offering this subject.
Besides this, we want to thank Frederic Opitz, Ph.D. assistant of Prof. dr. Selien De Schryder.
Mister Opitz helped us with estimating the natural rate of interest in EVIEWS.
Furthermore, we want to thank every other person involved. This includes friends and family,
who motivated and supported us during this process. Besides them, we also want to thank all
the other lecturers, who taught us the important economic insights through our education.
Finally, our last expression of gratitude goes to each other for the efficient and productive
collaboration. We proudly present our Master’s Dissertation.
We hope you enjoy reading this thesis.
Ayoub Elomari and Jonas Van Oost
Ghent, August 2018.
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Table of Contents Nederlandstalige samenvatting – Dutch summary .................................................................................. i
Preface ......................................................................................................................................................ii
List with used abbreviations ..................................................................................................................... v
List with used figures and tables ............................................................................................................. vi
1. Introduction ......................................................................................................................................... 1
2. Literature review ................................................................................................................................. 3
2.1 What is the natural rate of interest? ............................................................................................. 3
2.2 Importance of the natural rate of interest .................................................................................... 4
2.3 The main driving factors of the natural rate of interest................................................................ 7
2.3.1 Trend growth rate of output .................................................................................................. 7
2.3.2 Preferences for savings .......................................................................................................... 9
2.3.3 Government spending .......................................................................................................... 10
2.3.4 Capital flows ......................................................................................................................... 10
2.3.5 Global factors ....................................................................................................................... 10
2.4 The declining trend of the natural rate of interest ..................................................................... 11
2.4.1 The United States of America ............................................................................................... 11
2.4.2 The United Kingdom ............................................................................................................. 13
2.4.3 The Euro Area ....................................................................................................................... 14
2.4.4 Will the low level of the natural rate of interest persist? .................................................... 14
2.4.5 Problems of the low level of the natural rate of interest..................................................... 15
2.4.6 Possible solutions ................................................................................................................. 16
2.5 Measuring the natural rate of interest ........................................................................................ 17
2.5.1 Laubach-Williams model ...................................................................................................... 17
2.5.2 Adjusted Laubach-Williams model ....................................................................................... 18
2.5.3 Laubach-Williams model using real-time data ..................................................................... 19
2.5.4 Alternative way to estimate the natural rate of interest: the SVAR .................................... 20
2.6 Problems with the natural rate of interest ................................................................................. 20
3. Econometric study ............................................................................................................................. 21
3.1 The study of Brzoza-Brzezina (2003): background ...................................................................... 22
3.2 Methodology ............................................................................................................................... 23
3.3 Data description .......................................................................................................................... 26
3.4 Descriptive statistics .................................................................................................................... 27
3.5 Estimation results ........................................................................................................................ 29
3.6 Analysis of the natural rate of interest for Belgium .................................................................... 31
3.6.1 The natural rate of interest .................................................................................................. 31
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3.6.2 The natural rate of interest and the real interest rate ......................................................... 34
3.7 Belgium compared to other economies ...................................................................................... 35
3.7.1 Belgium versus the U.S. ........................................................................................................ 36
3.7.2 Belgium versus the Euro Area .............................................................................................. 37
3.8 The SVAR model compared to the LW model ............................................................................. 38
4. Conclusion ......................................................................................................................................... 39
5. Bibliography ....................................................................................................................................... 42
6. Appendices ........................................................................................................................................ 47
6.1 Descriptive statistics .................................................................................................................... 47
6.1.1 Belgium ................................................................................................................................. 47
6.1.2 U.S......................................................................................................................................... 47
6.1.3 Euro Area .............................................................................................................................. 47
6.2 Augmented Dickey-Fuller test ..................................................................................................... 47
6.3 The real interest rate (1960-2017) .............................................................................................. 48
6.4 VAR lag selection test .................................................................................................................. 48
6.5 VAR output: EVIEWS .................................................................................................................... 49
6.6 SVAR coefficients: EVIEWS .......................................................................................................... 51
6.7 GDP growth for Belgium .............................................................................................................. 51
6.8 Correlations ................................................................................................................................. 51
6.8.1 Natural rate of interest Belgium and the real interest rate ................................................. 51
6.8.2 Natural rate of interest Belgium and U.S. ............................................................................ 52
6.8.3 Natural rate of interest Belgium and Euro Area ................................................................... 52
6.8.4 SVAR model and Laubach-Williams model ........................................................................... 52
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List with used abbreviations
ADF: Augmented Dickey-Fuller
CPI: Consumer Price Index
ECB: European Central Bank
E.g.: For example
FRBSF: Federal Reserve Bank of San Francisco
FRED: Federal Reserve Economic Data
GDP: Gross Domestic Product
GRETL: Gnu Regression Econometrics and Time-series Library
HP: Hodrick-Prescott
IS: Investment and Savings
LW: Laubach and Williams
NBB: National Bank of Belgium
NRI: Natural rate of interest
SVAR: Structural Vector Autoregression
U.K.: United Kingdom
U.S.: United States
VAR: Vector Autoregression
VMA: Vector Moving Average
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List with used figures and tables
Figure 1: Money supply, money demand and the interest rate. ............................................................ 6
Figure 2: GDP growth and its trend growth rate for Belgium (NBB). ...................................................... 8
Figure 3: The natural rate of interest for the U.S. - updated dataset (Holston et al., 2016) ................ 11
Figure 4: The natural rate of interest for the U.K. - updated dataset (Holston et al., 2016) ................ 13
Figure 5: The natural rate of interest for the Euro Area - updated dataset (Holston et al., 2016) ....... 14
Figure 6: Determination of the natural rate of interest (Laubach & Williams, 2015). .......................... 18
Figure 7: The inflation rate - Belgium .................................................................................................... 28
Figure 8: The real interest rate from January 1992 to June 2018. ........................................................ 30
Figure 9: The natural rate of interest for Belgium from January 1995 to June 2018. ........................... 31
Figure 10: The natural rate of interest and the real interest rate for Belgium. .................................... 34
Figure 11: The interest rate gap for Belgium. ....................................................................................... 35
Figure 12: Belgium compared to the U.S. ............................................................................................. 36
Figure 13: Belgium compared to the Euro Area from January 1999 to June 2018. .............................. 37
Figure 14: The natural rate of interest based on the SVAR compared to the LW model. .................... 38
Table 1: Descriptive statistics: inflation rate and the real interest rate. ............................................... 27
Table 2: Summarized ADF-test .............................................................................................................. 29
1
1. Introduction Economic theory indicates that there is a long-run equilibrium at which economic variables,
such as inflation and output, are at a level where resources are fully employed. This long-run
equilibrium is called the natural rate of interest (Franco, 2017). This concept is mostly ascribed
to Wicksell (1898), who defines the natural rate of interest as follows: “There is a certain rate
of interest on loans which is neutral in respect to commodity prices and tends neither to raise
nor to lower them”.
The natural rate of interest is important for monetary policymakers, as it is a benchmark. This
allows policymakers to assess the current situation of monetary policy. It indicates whether the
real interest rate is expansionary or contractionary. For example, if the real interest rate is
below the natural rate of interest, thus a negative interest rate gap, the output gap gets higher
(stimulating the economy), leading to a higher level of inflation (Weber, Wolfgang & Worms,
2007). Besides this, the natural rate of interest is the real interest rate that balances savings
and investments at full employment. For this reason, monetary policymakers try to set the
nominal policy rate relative to the natural rate of interest in order to close the output gap and
obtain price stability.
Moreover, the natural rate of interest has caught more attention in recent years (Deutsche
Bundesbank, 2017). Several studies demonstrate the decreasing trend of the natural rate of
interest in the past decade. This downfall began at the start of the Great Recession and is still
going on (Laubach & Williams, 2015).
Due to the importance and the lower level of the natural rate of interest, we take a closer look
at the driving factors (of the decline) of the natural rate of interest. These driving factors will
allow us to understand the fluctuations of the natural rate of interest over time.
The decreasing trend is already examined by several studies across numerous countries.
However, Belgium is not included in these studies. The natural rate of interest is unobservable
and must be estimated (Wilhelmsen & Garnier, 2005). A well-known model for the estimation
of the natural rate of interest is the Laubach-Williams model (2003). However, this is not the
only method to estimate the natural rate of interest. The variety in definitions and estimation
methods could cause some problems, as this leads to different results. Nevertheless, it still
must be estimated. Therefore, we estimate the natural rate of interest for Belgium.
Our research question is formulated as follows: “Does the level of the natural rate of interest
in Belgium have a decreasing trend over the recent years?”. To answer this question, we
estimate the natural rate of interest for Belgium from 1995 to 2018 based on the methodology
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of Brzoza-Brzezina (2003), by using monthly data. The 12-month treasury bills rate of Belgium
was used as a proxy for the nominal interest rate and the inflation rate was calculated by using
the Consumer Price Index (CPI) that included all goods and services.
Next to estimating the dynamics of the natural rate of interest for Belgium, it might also be
interesting to see how close or far Belgium was to reaching the natural rate of interest, as
monetary policy decisions are made by the European Central Bank (ECB). We further also
estimate the natural rate of interest for the U.S. and the Euro Area to compare the estimates
to one another and to see whether our estimation of the natural rate of interest for the U.S. is
similar to the well-known estimates in Holston, Laubach and Williams (2016).
Our results show that the natural rate of interest has a decreasing trend in Belgium, which was
probably caused by a lower trend growth rate of output, global factors, an increase of the risk
aversion after the financial crisis and an increase in savings. Besides this, the course of the
natural rate of interest for Belgium has a lot of similarities to those of the U.S. and the Euro
Area. The comparison between the SVAR model estimates and the Holston et al. (2016)
estimates follow a similar path at a different level. However, the decreasing trend is more
visible in the Holston et al. (2016) estimation. Perhaps, this is the case because Holston et al.
(2016) use a more extensive model.
The rest of this Master’s Dissertation is structured as follows. Chapter two discusses the
literature regarding the variety in definitions of the natural rate of interest and its importance.
In this section, the natural rate of interest is linked to the monetary policy, inflation and the
money supply and demand. Besides this, and more importantly, the driving factors of the
natural rate of interest and its declining trend are discussed. Additionally, we will elaborate on
the consequences of the low level of the natural rate of interest and the solutions for this
situation. Furthermore, the most well-known estimation methods of the natural rate of interest
are briefly discussed. To conclude the literature review, the problems that come along with the
natural rate of interest are put forward.
Chapter three includes the econometric part, where the used method and data will be
described to estimate the natural rate of interest for Belgium. This estimation will then be
compared to the real interest rate and to an estimation for the U.S. and the Euro Area.
Moreover, the estimation based on the SVAR will be compared to the Holston et al. (2016)
estimation, which is based on the Laubach-Williams (2003) model. Finally, a conclusion is
formulated, as well as some critical remarks.
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2. Literature review
2.1 What is the natural rate of interest? There is no clear-cut definition of the natural rate of interest. This leads to a wide variety in
definitions of the natural rate of interest in the literature (Boeckx, Cordemans & Dossche,
2013). Therefore, we will first formulate a general explanation of the concept, after which we
will provide an overview of different definitions.
The natural rate of interest is the interest rate that occurs in case that the economy achieves
optimal production (full employment) and stable inflation (Constâncio, 2016). This means that
at this rate, the real Gross Domestic Product (GDP) is equal to potential GDP. In other words,
the natural rate of interest is the rate compatible with sustainable economic growth and stable
inflation in the long run. This is seen as the generally accepted explanation of the natural rate
of interest (Boeckx et al., 2013; Pettinger, 2016). Furthermore, the natural rate of interest is
also known as the neutral interest rate, equilibrium interest rate or simply represented by r*.
However, some authors tried to give an own definition of this concept. Below, an overview is
given of some of the definitions found in the literature. The definitions could be divided in two
groups. The first group emphasizes the stabilization of the output gap and prices, while the
second group focuses on the benchmark role of the natural rate of interest. Below, we will start
with the first group.
The first definition was phrased by Wicksell in 1898. He described the natural rate of interest
as follows: “There is a certain rate of interest on loans which is neutral in respect to commodity
prices and tends neither to raise nor to lower them”.
Another commonly used definition of the natural rate of interest is the one of Bomfim (1997):
“The interest rate consistent with output converging to potential, where potential is the level of
output consistent with stable inflation". This definition is similar to the general definition (ut
supra). This explanation is used by several other authors, such as Laubach and Williams
(2003) and Manrique and Marqués (2004). Cavalcanti de Araùjo and Gomes da Silva (2014)
simplified this definition and define the natural rate of interest as the rate that maintains inflation
stability and targets a sustainable economic growth.
Moreover, Brzoza-Brzezina (2003) provided the following definition: “The natural rate of
interest is defined as the level of the real interest rate which leads to a neutral monetary policy
and consequently, to a stabilized inflation rate”. This definition stresses the importance of the
natural rate of interest for monetary policy reasons and emphasizes the stabilized prices.
According to this definition, the economy is stabilized if the real interest rate is equal to the
natural rate of interest. This definition could be placed in both groups and is a good transition
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to the second group, which puts the focus on the benchmark role. The following definitions
belong to this second group.
Öğünç and Batmaz (2011) define the natural rate of interest as follows: “Monetary policy
authorities, in setting the interest rates, commonly need a benchmark to assess whether the
level of the interest rate is stimulative or contractionary for the economic activity. This
benchmark is generally called the neutral real interest rate”. This definition stresses the value
of the natural rate of interest for monetary policy decisions. Monetary policymakers should use
the natural rate of interest as a benchmark to set their interest rate targets.
Moreover, the natural rate of interest is defined as the level of real interest rate that is neither
expansionary nor contractionary. This definition was given by Richardson and Williams (2015).
In other words, if the natural rate of interest is achieved, there is no overheating or recession
of the economy (Pettinger, 2016).
The benchmark role of the natural rate of interest is also linked to the investment and savings
relationship. More detailed, the natural rate of interest is the intersection of the IS curve and
the level of potential GDP (ut infra). At this point, the real interest rate is equal to the natural
rate of interest (Laubach & Williams, 2015). More specifically, Summers (2018) defines the
natural rate of interest as “the interest rate at which savings and investments would balance
without a major acceleration of deceleration in growth”.
These different definitions have some similarities and could all be linked to the general
explanation. Furthermore, we could conclude that the natural rate of interest is the real interest
rate that would occur if all economic variables, such as output and employment, are in
equilibrium. The natural rate of interest is about balancing the economy. However, this variety
of definitions leads to different estimation methods, which results in a lot of variation in the
outcomes. Therefore, the estimation of the natural rate of interest could be uncertain (Crespo
Cuaresma, Gnan & Ritzberger-Grünwald, 2005).
2.2 Importance of the natural rate of interest Given that the natural rate of interest is so uncertain, why would this concept be so important?
Pursuing the natural rate of interest is very crucial for conducting monetary policy. The natural
rate of interest is assumed to provide the best possible outcome for the economy in terms of
growth and stable inflation (Pettinger, 2016).
Weber et al. (2007) put the natural rate of interest forward as an important factor for monetary
policy, as it contains information about the current state of the economy. It specifies a
benchmark to set the interest rate targets.
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Wilhelmsen and Garnier (2005) confirm this statement and explain the benchmark role as
follows: if the real interest rates are above the natural rate of interest, then inflation is expected
to decrease. But, if the real interest rate is below the natural rate of interest, the inflation will
reach a higher level. The natural rate of interest namely is the rate at which all resources are
optimally utilized in the economy and at which the inflation growth is stable. Furthermore, Ichiue
and Ueno (2007) also state that the natural rate of interest is an important concept for monetary
policymakers and that they should aim for this rate in the long run.
Carlstrom and Fuerst (2016) explain the functioning and importance of the natural rate of
interest for monetary policy through the Taylor rule. Consider this the Taylor rule:
It = r* + 𝜋* + α x ( 𝜋 - 𝜋*) + β x (𝐺𝐷𝑃 - 𝐺𝐷𝑃*),
with It the policy rate. This is the short-term interest rate which the central bank targets.
Furthermore, r* represents the natural rate of interest, which occurs when the difference
between the current inflation and the inflation target and the difference between the current
GDP and potential GDP are zero. 𝜋 indicates the current inflation and 𝜋* the inflation target.
Finally, GDP is the current GDP, while GDP* indicates the potential GDP.
According to Carlstrom and Fuerst (2016), the natural rate of interest is essential in determining
the short-term nominal interest rate. Besides this, the Taylor rule is also used for inflation
control. As the natural rate of interest is an important determinant of this equation, it contributes
to the inflation control. The natural rate of interest is seen as a benchmark, as this would be
the interest rate if inflation is constant.
Besides this, it is important to track the natural rate of interest, especially when the real interest
rate deviates from its steady state. This can be measured by the interest rate gap. The
economy is stable when the real interest rate is equal to the natural rate of interest (gap equals
zero). But if this is not the case, policymakers know that the economy is unbalanced. Therefore,
the natural rate of interest should be tracked to adapt the real interest rate targets (Canzoneri,
Cumby & Diba, 2015).
As mentioned above, the natural rate of interest is useful to adjust the monetary policy
decisions in the long run (Weber et al., 2007). More specifically, policymakers could decide to
conduct an expansionary or contractionary monetary policy. Monetary policy is conducted
mostly through open market operations. This means that the central bank will purchase and
sell securities in the open market. This way, the central bank tries to influence the short-term
nominal interest rate to stimulate or restrict the economy (Board of Governors of the Federal
Reserve System, 2018).
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The relationship between money demand and supply and the interest rate is illustrated by
figure 1 (ut infra).1 Expansionary means that the central bank tries to stimulate the economy.
So, the central bank prints money and buys bonds. This way, the money supply increases.
Graphically, this would mean that the money supply shifts to the right (Ms’-curve). By
increasing the money supply, lower nominal interest rates are achieved (i’). Because of this,
people are stimulated to increase their consumption, as it is cheaper to borrow money. This
leads to an increase of the money demand.
Contractionary means that the central bank wants to slow down the economy and prevent high
inflation. This is the opposite of expansionary monetary policy. The central bank sells treasury
notes, leading to a lower supply of money and a decreased inflation. The inflation is
decreasing, due to the lower consumption, as people are less inclined to borrow money if the
nominal interest rates are at a high level. Contractionary policy leads to a shift of the money
supply to the left (Ms”-curve), as there is less money in circulation. This pushes the nominal
interest rate to a higher level (i”).
Figure 1: Money supply, money demand and the interest rate.
Mostly, the real interest rate is compared to the natural rate of interest. The difference between
these two concepts is also known as the interest rate gap. On the one hand, If the real interest
rate is bigger than the natural rate of interest, then the economy is growing less/shrinking.
More detailed, this means that higher real interest rates (higher than the natural rate of interest)
are discouraging people to borrow money for their consumption. This leads to a lower demand
of money and a lower level of production (Weber et al., 2007). This is ultimately reflected by
lower inflation. In this situation, the monetary policy of the central bank was too contractionary.
As a reaction, the central bank wants to stimulate the economy. Therefore, they will apply
expansionary measures to make sure the economy gets stimulated.
1 Figure 1 is manually drafted based on the course of Macro-Economics.
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On the other hand, if the real interest rate is below the natural rate of interest, the economy is
growing and stimulated, leading to higher inflation (Weber et al., 2007). More detailed, the
effects of a negative interest rate gap are an expansion of the consumption, more investments
by enterprises, production above potential and thus a stimulated economy. This will then lead
to an increase of market prices and there will eventually be an increase in the inflation rate
(Deutsche Bundesbank, 2017).
In the case that the central bank wants to prevent overheating of the economy and inflation
growth, it will apply contractionary measures. So, for monetary policymakers it is very important
to know the level of the natural rate of interest. The central banks can indirectly affect the short-
term real interest rate based on the level of the natural rate of interest. This can be done by
changing the short-term nominal interest rate, which will eventually have an impact on the real
economy and inflation (Deutsche Bundesbank, 2017).
This all shows the importance of tracking the natural rate of interest as accurately as possible.
Otherwise, a measure to stabilize the economy could become destabilizing (Weber et al.,
2007). Besides this, Woodford (2001) states that the natural rate of interest varies over time
and is not constant. Therefore, he points out the need for policymakers to take the changes of
the natural rate of interest into account. These changes can affect their targets concerning the
macro-economic stability. More specifically, the price stability.
2.3 The main driving factors of the natural rate of interest
The natural rate of interest is affected by multiple determinants. These influences could be
difficult to map. However, it is important to know these forces, as they cause the natural rate
of interest to fluctuate and to vary over time. The main driving factors, found in the literature,
are the trend growth rate of output, preferences for savings, government spending, capital
flows and global factors. These factors are described one by one below.
2.3.1 Trend growth rate of output
The trend growth rate of output is an important determinant for the level of the natural rate of
interest. This can be explained as follows. A lower productivity level, lower than its potential,
will lead to lower incomes, as there are less goods and services available to be sold. Lower
incomes push people to save more money. More savings increase the supply of money, as
people hold more funds in their banking accounts. This results in a lower natural rate of interest,
which is obliged to stabilize the investment and savings plans and to maintain economic growth
and stable inflation. Lower rates lead to a higher demand of money, due to the attractiveness
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to borrow money at a cheaper borrowing cost. This leads to more investments, which increases
the productivity in the future (McDermott, 2013).
From another point of view, this becomes: if an economy experiences a higher trend growth
rate of output, a higher future demand is expected. This leads to an investment opportunity for
firms. On the other hand, the expected income growth diminishes the tendency of market
players to save money. These two factors have an upward pressure on the natural rate of
interest (McCririck & Rees, 2017).
So, a decline (increase) in the trend growth rate of output leads to a decline (increase) in the
natural rate of interest (Mésonnier & Renne, 2004; Pescatori & Turunen, 2015; Holston et al.,
2016).
Figure 2 displays the trend growth rate of output for Belgium, calculated by using the HP filter.2
The trend growth rate of output is calculated over 21 years (from 1996 to 2017) relative to the
actual output growth rate. The actual growth rate is illustrated by the yearly changes in real
GDP, which is retrieved from the National Bank of Belgium (NBB).
Figure 2: GDP growth and its trend growth rate for Belgium (NBB).
In figure 2, the blue line represents the GDP growth for Belgium, while the orange dotted line
illustrates the trend growth rate of output. For Belgium, we see that the trend is decreasing,
due to a lower GDP growth since the financial crisis. This decline in the trend growth rate of
output for Belgium could lead to a decrease of the natural rate of interest.3 Moreover, if the
actual growth rate is above (below) the trend growth rate of output, the economy is booming
(in a recession). In this case, there is a positive (negative) output gap. The real GDP is higher
(lower) than its potential.
2 The Hodrick-Prescott (HP) filter is used to eliminate the short-term fluctuations to visualize the long-term trend. The GDP data was imported in Excel and transformed with the HP filter add-in. 3 In the econometric study, we will verify if there is a decline in the natural rate of interest for Belgium.
9
It might be interesting to discuss the factors that have an impact on the trend growth rate of
output, as these indirectly affect the natural rate of interest. The main drivers of the trend
growth rate of output are briefly listed below (Pettinger, 2017):
- Technological development: improvements in technology could lead to higher
productivity, which leads to a higher trend growth rate of output.
- Productivity per worker: better education and training lead to an increase of the output
per worker. This leads to an increase of the trend growth rate of output.
- Accessibility to resources: economic growth can be stimulated through easier access
to resources.
- Quality of infrastructure and transport: Better infrastructure leads to more efficiency,
which leads to more (qualitative) production.
- Entrepreneurial environment: if people are more motivated to start a new business, the
GDP will increase. This leads to a higher trend growth rate of output.
- Demographics: the population growth has an impact on the productivity of a country. If
the population grows faster, the labor force will be higher. This leads to more
productivity (Summers, 2014).
2.3.2 Preferences for savings If households are more inclined to save money and invest or consume less, a lower interest
rate is needed to balance savings and investments. An increase (decrease) in savings will lead
to a drop (increase) of the natural rate of interest (McDermott, 2013). The preference for
savings is determined by several factors, such as risk aversion, demographics and income
expectations. These factors are discussed below.
The level of risk aversion has a significant influence on the savings behavior. If households
are more risk averse, e.g. due to uncertainty about the future, they will increase their savings.
On the contrary, if households are observing good prospects about the future, they will
decrease their savings and will invest more. Risk aversion could also show itself in the choice
for safer assets when investing. This means that risk averse investors will avoid unnecessary
risks and will always choose for the investment with the lowest risk, even if the return is lower
(Karni, 1982).
Besides this, the composition of demographics is a very important determinant of the
preference for savings. The change in the composition of the population itself could lead to a
higher or lower amount of savings (Schultz, 2004). For instance, people are getting older
nowadays in developed countries. The ageing of the population leads to serious concerns with
respect to the pension scheme, as the retired people will outnumber the active population. This
causes the people to save more, as they fear losing their pension payment or not getting one
10
at all (Eggertsson, Mehrotra, Singh & Summers, 2016). Moreover, old people typically save
more than the younger part of the population. If most of the country’s population are older
people, then the country automatically saves more (Demirgüc-Kunt, Klapper & Panos, 2016).
Finally, future income expectations also affect the preference for savings. According to the
income expectation hypothesis, a lower income expectation leads to a higher saving rate of
households. For example, if people expect to lose their job, they will save more money to be
able to survive (Arent, 2012).
2.3.3 Government spending
The amount spent by the government is another determinant for the level of the natural rate of
interest. Higher government debt leads directly to a higher natural rate of interest. This can be
explained as follows. An increase of government debt needs to be financed by higher tax
income. These taxes are paid by the citizens and lower their disposable income. Consequently,
the consumers have less money in excess, which leads to lower savings (Winter, 2016;
Canzoneri et al., 2015). As mentioned above, a decrease in savings leads to an increase of
the natural rate of interest.
2.3.4 Capital flows
Capital flows can also affect the level of the natural rate of interest. An increase (decrease) of
capital inflows in a certain country leads to a decrease (increase) in the natural rate of interest
in that country (Eggertsson et al., 2016). Moreover, international capital flows have a large
impact on long-term interest rates.
For example, a large amount of foreign purchases of U.S. bonds leads to a decrease of the
U.S. interest rates. These foreign purchases of U.S. bonds lead to an increase of the circulating
money in the U.S. Money becomes less valuable, as there is a bigger money supply.
Therefore, the interest rates drop. This leads to a lower borrowing cost (Warnock & Warnock,
2005).
2.3.5 Global factors
Due to the higher globalization, determinants of one economy influence the other economies.
More specifically, domestic interest rates in an open economy can be affected by interest rates
in other countries. Consequently, the trend growth rate of output, demographics and the level
of risk aversion of foreign countries may influence the domestic natural rate of interest
(McCririck & Rees, 2017).
11
For example, if the level of risk aversion in country A rises, people will save more. In an open
economy, this will lead to lower investments of country A in country B. This leads to a lower
capital inflow to country B, which will impact the natural rate of interest in country B. Thus, a
change in the level of risk aversion in country A does affect the natural rate of interest in both
country A and country B (Karni, 1982; McDermott, 2013).
2.4 The declining trend of the natural rate of interest
Several studies, such as the study of Laubach and Williams (2015), observe a decreasing
trend of the natural rate of interest in the U.S. in the past decade. The authors state that this
decrease began at the start of the Great Recession and that the natural rate of interest is at a
historically low level.
Holston, Laubach and Williams (2016) provided another study about the measurement of the
natural rate of interest. Unlike the study back in 2015, which only focused on the U.S., this
paper estimated the natural rate of interest for multiple advanced economies (United States,
Canada, the Euro Area and the United Kingdom). The graphs below display these estimates
for the different economies from 1990 onwards.4 The findings of this research confirm the
earlier results from Laubach and Williams (2015) with respect to the U.S.
2.4.1 The United States of America
Figure 3: The natural rate of interest for the U.S. - updated dataset (Holston et al., 2016)
Figure 3 illustrates the estimated natural rate of interest for the U.S. Holston et al. (2016) state
that there is a clear decreasing trend of the natural rate of interest since 2007. Moreover, the
level of the natural rate of interest remains close to zero in recent years. This decline is also in
4 The sample data in Holston, Laubach and Williams (2016) runs from 1961 until 2015 for three of the four economies. Only for the Euro Area, the data started in 1972. However, we depict an updated dataset of the Holston, Laubach and Williams estimates until January 2018 (FRBSF, 2018). The figures only start in 1990, as we want to discuss the trend of the level of the natural rate of interest over the more recent years.
12
line with other studies, such as the study from Laubach and Williams (2015), Wynne and Zhang
(2017) et cetera.
According to Holston et al. (2016), the decrease of the natural rate of interest since 2007 was
caused by the decline in the trend growth rate of output because of the financial crisis. This
means that there was lower productivity, which led to a lower return on capital investments,
resulting in lower demand for investment funds. This caused a downward pressure on the
natural rate of interest (Carlstrom & Fuerst, 2016). Besides this, there are other determinants
that have an influence on the natural rate of interest, which were not further discussed by
Holston et al. (2016). Several other authors have mentioned these other determinants more
detailed.
For instance, Pescatori and Turunen (2015) ascribe the decline in the natural rate of interest
since the financial crisis, next to the trend growth rate of potential output, to the higher risk
aversion and the preference for safer assets. As seen above, higher risk aversion leads to
more savings. This results in a decline in the natural rate of interest. Moreover, this risk shock
is also the reason why there is a slow recovery, as the level of risk aversion stays high (Barsky,
Justiniano & Melosi, 2014).
Another study, from Eggertsson et al. (2016), also explained the decrease since the Great
Recession for the U.S. This study states that the increase in capital inflows to the U.S. also led
to the lower natural rate of interest. The investments of other countries in the U.S. treasuries
put downward pressure on the natural rate of interest.
Moreover, the declining trend over the recent years might also be caused by a slower
population growth and higher life expectancy. This affects the saving and consumption
behavior of the market players. The higher life expectancy increases the retirement period of
each individual. Therefore, people will save more during their lives. This saving incentive gets
even stronger if the government cannot assure that current public pension systems have
enough funds to provide a decent pension. This causes a downward pressure on the natural
rate of interest (Carvalho, Ferrero & Nechio, 2017).
Finally, Laubach and Williams (2015) state that the economy has almost fully recovered, but
the natural rate of interest did not go up. The expected evolution of the natural rate of interest
is discussed in subsection 2.4.4.
The declining natural rate of interest, however, does not only apply to the U.S. Interestingly,
other advanced economies also experience a decrease in the natural rate of interest. This
means that this decline is an international phenomenon. Below we discuss the estimates for
the United Kingdom and the Euro Area.
13
2.4.2 The United Kingdom
Figure 4: The natural rate of interest for the U.K. - updated dataset (Holston et al., 2016)
The decline of the natural rate of interest since the Great Recession is also visible for the
United Kingdom, albeit less severe than in the U.S. The natural rate of interest recovered in
2010 but dropped again due to the Euro crisis. The estimates of the natural rate of interest in
the United Kingdom remain at a level of approximately 1.5 % in recent years. This contrasts
with the estimates of the U.S., where the natural rate of interest is close to zero (ut supra).
According to Holston et al. (2016), the decline of the natural rate of interest in the United
Kingdom is, as in the U.S., due to the decline in trend growth rate of output in the United
Kingdom and some other factors. These other factors are described below.
According to Goldby, Laureys and Reinold (2015), the fact that people are saving more money,
due to higher risk aversion during and after the financial crisis, is a reason for this decline.
Moreover, the increase in demand for safer assets and the decline in investment rates since
the Great Recession put downward pressure on the natural rate of interest in the United
Kingdom.
Besides this, global events also had an influence on the natural rate of interest in the United
Kingdom, as the United Kingdom is a small open economy. This means that, for instance, a
decline of the interest rates in the U.S. could also have caused a decline of the interest rates
in the United Kingdom (Goldby et al., 2015).
The United Kingdom also experiences a lower population growth and a higher life expectancy.
This leads to a downward pressure on the natural rate of interest over recent years, consistent
with the U.S (Carvalho et al., 2017).
14
2.4.3 The Euro Area
Figure 5: The natural rate of interest for the Euro Area - updated dataset (Holston et al., 2016)
The decline of the natural rate of interest in the Euro Area since the Great Recession is clearly
visible in figure 5. Just like the United Kingdom, the natural rate of interest in the Euro Area
recovered in 2010, but experienced another decline caused by the Euro crisis. The estimates
then even got negative, which was not the case for the U.S. and the United Kingdom (ut supra).
Holston et al. (2016) ascribed the decline in the Euro Area partly to the decline of the trend
growth rate of output. However, Haavio, Juillard and Matheron (2017) put two other important
reasons forward, next to the trend growth rate of output, as the main drivers for the declining
trend in the Euro Area during and after the financial crisis.
According to Haavio et al. (2017), an enormous risk shock caused the market players to
increase their precautionary savings and decrease their investments, as they are less willing
to hold risk. The risk aversion persisted even after the financial crisis, due to the high
uncertainty. Besides this, the natural rate of interest fell and remained at low levels due to
weakened growth prospects, which also led to higher savings or investments in riskless assets.
Finally, the demographics (lower population growth and higher life expectancy) also affected
the natural rate of interest in the Euro Area, consistent with the U.S. and the United Kingdom
(Carvalho et al., 2017).
2.4.4 Will the low level of the natural rate of interest persist?
The determinants that caused the decrease of the natural rate of interest are expected to stay
the same, according to Williams (2016). This means that the level of the natural rate of interest
is believed to stay low for a long time. This is because the underlying factors are of a structural
nature.
15
The structural factors that impacted the savings and investment relationship are the changing
demographics, the increase of savings in developed economies, the slowdown of innovation
and a lower government spending. However, the impact of the structural factors is
strengthened by cyclical factors, such as the financial crisis. This crisis led to a higher level of
risk aversion, which led to more savings, and a setback in productivity. These factors all cause
the decrease of the natural rate of interest to persist in the medium run. To bring the natural
rate of interest back to a higher level, structural changes are required (De Backer & Wauters,
2017).
Most economists believe that this low level will persist. However, some authors believe that a
sudden upward movement of the natural rate of interest is possible. For instance, Del Negro,
Giannoni, Giannone and Tambalotti (2017) mention that the natural rate of interest will
probably stay at a lower level, but that this is not certain. Sudden changes in the market
structure, perceptions of the investors, the degree of risk aversion, regulation and many more
could cause a shock that will push the natural rate of interest in any direction.
2.4.5 Problems of the low level of the natural rate of interest
The low level of the natural rate of interest is a big challenge for policymakers, as conventional
monetary policy becomes more difficult. With these low interest rates, there is not much room
to stimulate the economy during a recession due to the zero lower bound. The zero lower
bound appears when the short-term nominal interest rates are reduced to zero or close to zero
(Williams, 2016; Eggertsson et al., 2016).
If the nominal interest rates are at the zero lower bound, the monetary policy suffers from the
liquidity trap. This means that the monetary policy cannot lower the nominal short-term interest
rate to stimulate the economy. At this point, consumers may prefer holding cash instead of
investing. Besides this, nominal interest rates at the zero lower bound come along with low
inflation and lower growth of production, as consumption falls back due to the preference for
holding cash. Moreover, economic downturns will recover more slowly in this situation.
These side effects make it hard for policymakers to achieve price stability and a balanced
economy. As monetary policy is ineffective in this situation, other methods to stimulate the
economy are required (Eggertsson, 2010; Williams, 2016). Possible alternatives to increase
the level of the natural rate of interest are described in the next section.
16
2.4.6 Possible solutions
Conventional monetary policy is ineffective if nominal interest rates are at the zero lower
bound. Therefore, unconventional methods must be implemented. Forward guidance, large-
scale asset purchases, fiscal policy and a negative policy rate are examples of such methods.
Forward guidance means that the central bank announces the path of current and future
monetary policy tools, with the objective to retain price stability. A statement about the
upcoming monetary policy objectives gives the banks and other participants of the economy a
good insight of the future borrowing costs. For instance, when we are at the zero lower bound,
the ECB should make a statement that they will maintain the nominal interest rates at a low
level. This way, the commercial banks can set lower nominal interest rates for long-term loans.
Commercial banks are aware that there will be an opportunity to borrow money from the central
bank at low nominal interest rates in the future. This provides cheaper loans for the consumers,
which encourages spending and investments. This leads to a stimulated economy. Moreover,
forward guidance reduces risk in the market, as uncertainty of future policy rates is removed.
This decreases false predictions of the market players (European Central Bank, 2017;
Ryczkowski, 2017).
Besides this, large-scale asset purchasing is another solution to conduct monetary policy in a
situation of the zero lower bound. If the central bank announces to purchase a big amount of
assets (e.g. bonds) from the banks, then the prices of the assets will fall. This also has a
stimulating effect on the economy. If the central bank eventually buys these assets, the banks
are receiving additional money to provide more loans to households and firms (Delivorias,
2015).
Furthermore, fiscal policy could be one solution to get out of the zero lower bound. Fiscal policy
is conducted through government spending (public debt) and taxes. Fiscal policymakers could
increase the public debt, which will be funded by higher taxes, to stimulate the economy
(Eggertsson et al., 2016). The increase in taxes results in a lower disposable income, which
will lead to lower savings of the citizens. As mentioned above, this will have an upward
pressure on the natural rate of interest (Winter, 2016).
Finally, the negative interest rate policy (NIRP) is another possible solution to stimulate the
economy in the face of the zero lower bound. In this policy, the nominal interest rates are
targeted below the zero lower bound by the ECB. The negative interest rate has a double
effect. On the one hand, the ECB will charge commercial banks a negative interest rate on
deposits. This means that saving money in a deposit account is no longer interesting, as the
principal amount will decrease over time. On the other hand, banks now also have cheaper
17
access to money from the ECB. Due to competition, they will translate this cost reduction in
lower lending rates for their clients. With this measure, the policymakers aim at more
investments to stimulate the economy and eventually increase inflation. Thus, this method tries
to soothe the zero lower bound and target a higher inflation. This policy has already been
implemented in the Euro Area by the ECB (IMF, 2017; Blanchard, Dell’Ariccia & Mauro, 2010;
Ball, 2014).
2.5 Measuring the natural rate of interest
The biggest obstacle for policymakers is, however, that the natural rate of interest is
unobservable. Consequently, the natural rate of interest should be estimated (Wilhelmsen &
Garnier, 2005). Below, we briefly describe different estimation methods.
2.5.1 Laubach-Williams model
Laubach and Williams (2003) created the most well-known estimation method for the natural
rate of interest. The researchers applied the so-called Kalman filter. The Kalman filter can be
compared to the least-squares method, as it also tries to find the best fitting line through a
number of points. But, in contrast to the least squares method, the Kalman filter does not
require all the values to be known in advance. Therefore, it is suitable to be used in real-time,
with the result always being “the most appropriate” approach (Welch & Bishop, 2001).
Laubach and Williams (2003) estimated the natural rate of interest within a state-space model,
containing inflation, output and real interest rates. This model became a huge revelation, as it
is regarded as the basis of estimating the natural rate of interest. Later studies applied this
model to measure the effect in their own countries. Besides this, other authors (ut infra) used
this model as a starting point to develop an even more extensive model.
The main conclusion of the Laubach-Williams (2003) study is that the natural rate of interest
shows significant variation over the examined period (1960-2000) in the U.S. Besides this,
variation in the trend growth rate of output seems to be an important determinant for the
fluctuations in the natural rate of interest (ut supra). Furthermore, it might be necessary to
nuance the results of this study, as they are only valid for closed economies. More specifically,
the study was based on the U.S. but did not take effects from other countries into account.
This seems to be an important missing factor. Seeing the U.S. as a closed economy is not
realistic, as the U.S. is highly active and connected in the international economy.
In a later study of Laubach and Williams (2015), the natural rate of interest in the U.S. is
estimated with the Laubach-Williams model (LW model) (2003). In this more recent study, they
additionally use the IS curve (investment and savings relationship), as shown in figure 6 (ut
18
infra). The IS curve shows all combinations between income and nominal interest rates, where
the market for goods is in equilibrium. A low interest rate leads to a bigger demand for
consumption and investments, which leads to an increase of production. Figure 6 illustrates
the negative relationship between aggregate spending and the real interest rate. It is a
downward-sloping line, because if the real interest rate increases, the demand for goods
decreases. Besides this, there is also a vertical line, which shows the level of potential GDP.
This is a vertical line, because the authors (Laubach & Williams, 2015) assumed that the
potential GDP is independent to the level of the real interest rate. At the intersection of the IS
curve and the level of potential GDP, the real interest rate is equal to the natural rate of interest.
Figure 6: Determination of the natural rate of interest (Laubach & Williams, 2015).
The natural rate of interest can change over time. Laubach (2009) demonstrated this
assumption by showing that increases in long-run projections of the federal government budget
deficits are related to increases in long-term real interest rates. In that case, the IS curve will
move to the right, which leads to an increase of the natural rate of interest.
2.5.2 Adjusted Laubach-Williams model
Where Laubach and Williams (2003) focused on estimating the natural rate of interest in a
closed economy, Wynne and Zhang (2017) used the same model from Laubach and Williams
(2003) and expanded it to a two-country setting. This way, they estimated the natural rate of
interest in an open economy. In addition, they assumed the domestic natural rate of interest to
be related to the trend growth rate of output in the home country and the foreign country. In
the study from Wynne and Zhang (2017), the U.S. is seen as the home country and Japan as
the foreign country.
As this study takes the trend growth rate of output from the other country into account, the
model of Wynne and Zhang (2017) differs from the initial Laubach-Williams (2003) study. The
results of the study from Wynne and Zhang (2017) led to the important insight that the natural
19
rate of interest of the home country and the foreign country were indeed influenced by the
other country’s trend growth rate of output and not only by their own trend growth rate.
Another study (Duca & Wu, 2009) modified the LW model (2003) by changing the IS
relationship and the inflation equation. Duca and Wu (2009) added two variables to the LW
model (2003): Regulation Q (Reg Q) and wage-price control dummies. They added Req Q to
track the extra effect of the imposed boundaries for nominal interest rates on the investment
and savings relation. The wage-price dummies were added, as the authors believe that this
has an important effect on inflation. Reg Q was added to the IS relation, while the control
dummies were added to the equation of inflation. Reg Q is the difference between the market
interest rate and the deposit rate on small deposits.
Results show that Reg Q is statistically significant with a negative effect, while the wage-price
control dummies are statistically significant with a positive effect. This means that excluding
these variables could lead to omitted variable bias. Excluding Reg Q could lead to an
overestimation of the impact of real interest rates and excluding the dummy variables gives a
misleading prediction of how price pressures are affected by the output gap. This modified LW
model was found to be statistically more significant than the original LW model (2003). This
means that the estimates of the modified LW model are more reliable and that excluding the
variables indeed leads to omitted variable bias.
2.5.3 Laubach-Williams model using real-time data
Earlier studies have already estimated the natural rate of interest. However, these estimates
are based on data available today and are historical time series. Clark and Kozicki (2005) tried
to expose the difficulties of estimating the natural rate of interest in real time. Real-time data is
data delivered and processed immediately after collection. More specifically, it is the data
accessible to policymakers at the time decisions were made (Cimadomo, 2011). To achieve
this, Clark and Kozicki (2005) used a range of small simple models and 22 years of real-time
data of the U.S. The authors estimated various basic models provided by Laubach and
Williams (2003) and Kozicki (2004), using real-time data.
The main findings of this study are that the estimates of the natural rate of interest could be
different if the data is revised. The results of Laubach and Williams (2003), based on the
newest data, show that real rate estimates were highly imprecise in real-time. So, data
revisions may cause large fluctuations over time in given historical estimates of the natural rate
of interest. The authors (Clark & Kozicki, 2005) state that the real-time estimation problems
make it very hard to make policy decisions based on the estimates of the natural rate of
interest.
20
2.5.4 Alternative way to estimate the natural rate of interest: the SVAR
In a study of Brzoza-Brzezina (2003), the natural rate of interest is estimated in the U.S. using
the Structural Vector Autoregression (SVAR). The work of Blanchard and Quah (1989) is a
seminal paper in the SVAR literature in which the authors imposed long-run restrictions to
estimate potential output. The methodology of the study of Brzoza-Brzezina (2003) is similar
to that of Blanchard and Quah (1989). The major difference is that Brzoza-Brzezina (2003)
also applies a short-run restriction in the SVAR model for the shocks.
This estimation method will be explained into more detail in the next chapter, as this method
is used for the econometric part. Brzoza-Brzezina (2006) proved that the SVAR is a good
substitute for the LW model (2003). More specifically, the author found a high correlation level
(0.88) between the results using the LW model (2003) and the SVAR.
2.6 Problems with the natural rate of interest Although the natural rate of interest is an important concept for monetary policy, several
authors mention some important problems that come along with it.
The first problem of the natural rate of interest is related to the description of the concept.
There are multiple definitions for the natural rate of interest. This variety in definitions has led
to several models and different estimation methods. It is not clear which model is the best one
to estimate the natural rate of interest (Crespo Cuaresma et al., 2005).
Secondly, the natural rate of interest is a very difficult concept to estimate and it is impossible
to know for sure if the estimate is accurate (Blinder, 1998). If the natural rate of interest is not
correctly estimated, then estimation errors could become policy errors and, in this case,
stabilization policy might become destabilizing. Besides this, a wrong measurement of the
trend growth rate of output leads to a wrong estimate of the output gap and this eventually
leads to an incorrect estimate of the natural rate of interest. This can cause a lot of uncertainty
for the natural rate estimates (Orphanides & Williams, 2002; Laubach & Williams, 2003).
On the other side, the natural rate of interest contains key information about the factors that
drive inflation. Therefore, policymakers are nearly obliged to take this concept into account
(Weber et al., 2007). However, Blinder (1998) concludes that the natural rate of interest should
be seen mostly as a concept instead of a basis for regulation. It should merely be regarded as
a way of thinking for policymakers.
21
3. Econometric study
After explaining the concept of the natural rate of interest, identifying its driving factors and
elaborating on the decreasing trend in different economies, we estimate the natural rate of
interest for Belgium to see if there is a sign of this decreasing trend. Belgium is a small open
economy, where monetary policy is conducted by the ECB. It might be interesting to see how
close or far Belgium was to reaching the natural rate of interest. Besides this, the estimation
could be useful, as this was not done before for Belgium. Therefore, this econometric study
might be relevant for the Belgian government and economy. Moreover, we also estimate the
natural rate of interest for the U.S. and the Euro Area to compare the estimations to one
another. Finally, our estimates for the U.S. are also compared to the estimates in Holston et
al. (2016).
The estimation is based on the SVAR from Brzoza-Brzezina (2003). This method was chosen
because of its feasibility. Other models, such as the Laubach and Williams model (2003),
exceed the scope of a Master’s Dissertation. The estimation based on the SVAR should
provide good estimates, as the results of the SVAR model are highly correlated (0.88) with the
results based on the LW model (Brzoza-Brzezina, 2006).
In this section, the level of the natural rate of interest in Belgium will be examined. As stated in
chapter 1, the research question of this thesis is to verify whether the level of the natural rate
of interest in Belgium shows a decreasing trend over the recent years. Moreover, we will
attempt to give an answer to several questions related to the natural rate of interest. These
questions are phrased and motivated below.
1. Do the observed real interest rate and the estimated natural rate of interest follow a
similar course over time in Belgium?
2. How does the estimated natural rate of interest for Belgium relate to the estimations for
the U.S. and the Euro Area?
3. Is our estimation of the natural rate of interest for the U.S. based on the SVAR similar
to the estimates in Holston et al. (2016)?
Question one is derived from the model that we used to estimate the natural rate of interest.
Brzoza-Brzezina (2003) starts his model by defining the interest rate gap as the difference
between the observed real interest rate and the unobservable natural rate of interest. In the
SVAR model, the real interest rate is, along with the change in inflation, used to retrieve the
natural rate of interest.
22
Logically, this means that the real interest rate and the natural rate of interest are supposed to
follow a similar path. This can easily be verified by comparing the estimates of the natural rate
of interest to the real interest rate. The two series will be made graphically visible. Besides this,
the correlation matrix is another indicator, which will show whether they follow a similar path
over time.
Question two is linked to the statement of Holston et al. (2016), who described the decreasing
trend as an international phenomenon. Therefore, we will compare the estimation of the natural
rate of interest for Belgium with the estimates for the U.S. and the Euro Area. This way we can
check for evidence of the decreasing trend in other economies and if these estimates follow a
similar course.
The third question is formulated to see whether the estimation based on the SVAR differs
substantially from the estimation based on the LW model. A big difference in the results could
indicate that the SVAR model is not as accurate as Brzoza-Brzezina (2003) describes it.
The graphs used in our econometric study were computed in GRETL.
3.1 The study of Brzoza-Brzezina (2003): background
This study defines the natural rate of interest as the level of the real interest rate, which leads
to a neutral monetary policy and consequently, to a stabilized inflation rate. This definition
shows that estimating the natural rate of interest can be very important for monetary policy (ut
supra).
Brzoza-Brzezina (2003) estimated the natural rate of interest in the U.S. over the period 1960
until 2003, using the Structural Vector Autoregression (SVAR). The model consists of two
variables: the real interest rate and the change in inflation.5
A requirement for using the SVAR model is that all variables should be stationary. If this
restriction is fulfilled, the VAR model can be estimated. Then, Brzoza-Brzezina (2003)
combines long-run restrictions and short-run restrictions to define the SVAR model. These
restrictions are discussed in the methodology section (ut infra).
Brzoza-Brzezina (2003) found that there was a lot of variability for the natural rate of interest
over the period 1960-2002. Besides this, he found that an increase in the productivity growth
has led to an increase of the natural rate of interest. This is in line with the literature, where
productivity growth is described as a driving factor of the natural rate of interest.
5 The change in inflation is not being tracked by economic or financial institutions. Brzoza-Brzezina (2003) defines this as the first difference of inflation.
23
3.2 Methodology
Brzoza-Brzezina (2003) explains that SVAR models are mostly used to obtain historical time
series of unobservable variables. Therefore, he used the SVAR to estimate the natural rate of
interest for the U.S. We based the estimations of the natural rate of interest for Belgium, the
U.S. and the Euro Area on his methodology. Below, we will describe the procedure from
Brzoza-Brzezina (2003) to estimate the natural rate of interest based on the SVAR model.
Brzoza-Brzezina (2003) starts with defining the interest rate gap (GAP) as follows:
(1) GAP ≡ r – r*.
Thus, the interest rate gap, which is a statistical relationship, is the difference between the
observed real interest rate (r) and the unobservable natural rate of interest (r*). This
unobservable variable needs to be estimated in order to identify the interest rate gap.
Formulated in another way, this becomes:
(2) r = r* + GAP.
In the SVAR model, all variables are required to be stationary. This leads to the following
equations:
(3) rt* = ϕ1 (L). r*t-1 + u1,t = Ξ1 (L)u1,t
(4) GAPt = ϕ2 (L). GAPt-1 + u2,t = Ξ2 (L)u2,t .
Equations (3) and (4) are assumptions on how the natural rate of interest and the interest rate
gap are generated and develop over time. ϕ(L) and Ξ(L) are polynomials in the lag operator,
where Ξ(L) equals (I - ϕ(L).L)-1. With equations (3) and (4), Brzoza-Brzezina (2003) assumes
that the natural rate of interest and the interest rate gap are driven by a series of shocks. These
structural shocks are unobservable. Therefore, the real interest rate is influenced by two
structural shocks, namely u1,t and u2,t.. Equation (5) equals equation (2) with the assumptions
(3) and (4) implemented.
(5) r = Ξ1 (L)u1,t + Ξ2 (L)u2,t..
Then, according to the definition of the natural rate of interest:
(6) Δ 𝜋 = Ψ (r - r *) = Ψ GAP = Ψ Ξ2 (L)u2,t Ψ < 0.
24
The Δ indicates the change in the inflation rate (𝜋). Equation (6) is based on theory, which
represents a definition of the change in inflation. For example, Weber et al. (2007) found that
a negative interest rate gap leads to a positive output gap, which leads to higher inflation in the
long run.
This equation says that a change in inflation equals the deviation of the real interest rate from
its equilibrium rate. If the real interest rate equals its equilibrium, then the change in inflation
should be zero. Besides this, the following relation could be derived from this equation: if the
interest rate gap is positive, then inflation needs to decrease to keep the equation balanced.
This is the case, as Ψ is assumed to be negative. Moreover, This equation shows us that the
u2,t shock also influences the inflation rate, as this shock is assumed to drive the interest rate
gap in equation (4).
Now, both the real interest rate and the difference in inflation can be regarded as a distributed
lag of all structural shocks (current and past):
(7) |Δπ𝑡
𝑟𝑡| = |
𝑆11(𝐿) 𝑆12(𝐿)𝑆21(𝐿) 𝑆22(𝐿)
| |u1,𝑡
𝑢2,𝑡|,
Si,j(L) is a polynomial in the lag operator. Equation (7) is the matrix notation of equations (5)
and (6). Unfortunately, this matrix is unfeasible to estimate, as the structural model is unknown.
This makes it difficult to get the u-vector. A better way is explained below. Equation (8) is the
reduced form VAR in equational form, which is feasible to estimate. We are interested in the
reduced form shocks. These are the residuals from the following regressions.
Δπt =∑ 𝑎1,1(𝑙) Δπ𝑡−1 + ∑ 𝑎1,2(𝑙) r𝑡−1 + Ԑ1,𝑡 𝐾2
𝑙=1
𝐾1
𝑙=1,
(8)
rt =∑ 𝑎2,1(𝑙) Δπ𝑡−1 + ∑ 𝑎2,2(𝑙) r𝑡−1 + Ԑ2,𝑡 𝐾4
𝑙=1
𝐾3
𝑙=1,
Equation (9) is the matrix form of the reduced form VAR (8). This is the output of the VAR we
get in EVIEWS.6
(9) |Δπ𝑡
𝑟𝑡| = |
𝐴11(𝐿) 𝐴12(𝐿)𝐴21(𝐿) 𝐴22(𝐿)
| |Δπ𝑡−1
𝑟𝑡−1| + |
Ԑ1,𝑡
Ԑ2,𝑡|,
This time, the polynomial in the lag operator is Ai,j(L).
6 The VAR output of EVIEWS can be found in appendix (6.5).
25
Equation (10) is then the Vector Moving Average (VMA) representation of the VAR estimates
of equation (9).7 This is presented as:
(10) |Δπ𝑡
𝑟𝑡| = |
𝐶11(𝐿) 𝐶12(𝐿)𝐶21(𝐿) 𝐶22(𝐿)
| |Ԑ1,𝑡
Ԑ2,𝑡|,
Furthermore, equation (11) is the relationship between equations (9) and (10). Equation (11)
displays the calculation to go from (9) to (10). This calculation is done, as we will need the C-
matrix later in the methodology:
(11) C(L) = (I – A(L)L)-1.
The residuals Ԑ in equation (12) have the following relationship with the innovations u:
(12) |Ԑ1,𝑡
Ԑ2,𝑡| = |
𝑠11(0) 𝑠12(0)𝑠21(0) 𝑠22(0)
| |u1,𝑡
u2,𝑡|.
This means that the structural shocks could be calculated with the VAR residuals, if Si,j(0) were
known. However, this matrix is unknown. To achieve identification, four restrictions are
imposed on equation (7). These restrictions, along with the assumptions of equations (3) and
(4), will allow us to extract the unobservable parts, namely r* and GAP, out of the observable
real interest rate. First, the shocks are normalized by assuming that the variance of the
structural shocks is 1, which gives us two restrictions.
Furthermore, equation (6) learns us that u1,t does not affect Δ 𝜋. As equation (6) represents
the long-run relations, the shock of the natural rate of interest is required to have no impact on
Δ 𝜋 in the long run. Here, Brzoza-Brzezina (2003) prevents the shock u1,t to have a permanent
effect on inflation. To achieve this, restriction (13) is imposed on equation (7).
(13) S1,1(1) = 0.
Equation (14) is the fourth restriction, which is based on economic insights. Brzoza-Brzezina
(2003) states “as monetary transmission works only with a substantial lag, we can safely
restrict the innovations to the interest rate gap”. Here, he assumes that changes in the interest
rate gap will not affect the inflation rate in the short-term. Therefore, he assumes the shock u2,t
to have no impact in the short run. For example, if the real interest rate is set too high (positive
interest rate gap), there will not be an impact on inflation in the short-term. Monetary policy
actions need time to have an impact. Therefore, equation (14) eliminates the influence of u2,t
on inflation in the present month:
(14) s1,2(0) = 0.
7 The VAR was transformed to a VMA in Matlab.
26
At this moment, a shock of the natural rate of interest only has a partial effect on the real
interest rate. This is because Brzoza-Brzezina (2003) did not introduce the standard identifying
restriction of orthogonality of the shocks (u1,t and u2,t). This way, the rest of the effect will be
regarded as a change of the interest rate gap.
If the imposed restrictions are taken into account, the following calculations can lead to the
missing elements of the S(0) matrix:
(15) s1,1(0) = +−
√𝑣𝑎𝑟(Ԑ1,𝑡),
(16) s2,1(0) = −+ [
𝐶1,1(1)
𝐶1,2(1)] . √𝑣𝑎𝑟(Ԑ1,𝑡) ,
(17) s2,2(0) = √−2𝑠2,1(0)
𝑠1,1(0). 𝑐𝑜𝑣(Ԑ1,𝑡, Ԑ2,𝑡) + 𝑆2,1
2 (0) + 𝑣𝑎𝑟(Ԑ2,𝑡).
After this, the natural rate of interest can be calculated by setting all S2,2(L) = 0 in equation (7).
This comes from equation (3), which states that r* is not affected by u2,t. On the contrary, u1,t
does influence the natural rate of interest.
(18) rt* = S2,1(L)u1,t .
The s2,1(l) coefficients can be derived from the following equation, which is the result of the
substitution of equations (7) and (10) into (12):
(19) S(L) = C(L).S(0)
3.3 Data description
To estimate the natural rate of interest, reliable data is required. Therefore, monthly data was
retrieved from the National Bank of Belgium (NBB) for the Belgian estimation.8 For the U.S.,
data was retrieved from the Federal Bank of St. Louis (FRED) and Eurostat data was used for
the Euro Area. Monthly data was chosen, as this is consistent with Brzoza-Brzezina (2003).
Besides this, the monthly frequency is necessary to make assumption (14) plausible.
Moreover, monthly data provides more observations than annual or quarterly data. The dataset
covers a period from January 1992 until June 2018.9
8 All data was seasonally adjusted in EVIEWS by using the X-12 function. This was done to eliminate spurious regression that is caused by seasonal effects. 9 Only for the Euro Area, the data started in January 1997.
27
As mentioned above, the estimation of the natural rate of interest based on the SVAR only
requires two variables, namely the real interest rate and the change in inflation. The real
interest rate could not be retrieved directly. Therefore, a proxy was used for the nominal
interest rate. For Belgium, we used the 12-month treasury bills rate, as this is also used by
Brzoza-Brzezina (2003). Besides this, the 3-month treasury bills rate was used as a proxy for
the nominal interest rate in the U.S.10 Finally, we used the 12-month money market rates for
the Euro Area. We chose the money market rates as a proxy for the Euro Area, as the Euro
Area does not issue treasury bills. This money market rate consists of short-term securities
and loans up to 12 months, such as treasury bills and federal funds rates. The money market
rate for the Euro Area is a weighted average of its members’ rates.
Furthermore, the Consumer Price Index (CPI) that included all goods and services was chosen
for all three economies. The inflation rate was then manually calculated in Excel by using year-
on-year growth rates of the CPI. The change in inflation could simply be calculated by taking
the first difference of the inflation rate. Finally, the real interest rate was calculated by using
the Fisher equation, which is the difference between the nominal interest rate and the inflation
rate.
3.4 Descriptive statistics
Minimum (%) Maximum (%) Mean (%)
Inflation rate -1.61 5.96 1.94
Real interest rate -3.60 7.49 0.80
Table 1: Descriptive statistics: inflation rate and the real interest rate.
Table 1 illustrates the summary statistics of the implemented variables for Belgium. We only
discuss the descriptive statistics for this country, as the focus is laid on the Belgian natural rate
of interest.11 The results show some interesting findings. The inflation rate has an average of
1.94 % between January 1992 and June 2018. Compared to the inflation target for price
stability of the ECB, which is set at 2 %, the average inflation rate over this period is very close
to this target. However, the inflation rate was not always near the 2 % target.
More specifically, the inflation rate in Belgium peaked in July 2008 at 5.96 %. During the
financial crisis, real estate prices were thought to keep increasing. This rise of real estate prices
was fueled by a high demand. The construction sector expanded, as extra houses were built
to meet the demand. More construction leads to a higher demand for commodities and energy
10 We did not use the 12-month treasury bills rate for the U.S., as data was lacking in the series. This 3-month rate causes the real interest to be lower than it would be with the 12-month rate. 11 However, the descriptive statistics of the U.S. and the Euro Area can be found in the appendix (6.1)
28
sources, which reflects itself in higher prices. This eventually led to an increase of the inflation
rate (NBB, 2008).
Besides this, the inflation rate hit rock bottom in July 2009 with a level of -1.61 %. This fall is
caused by the collapse of commodity and real estate prices mid-2008, because of the financial
crisis. Moreover, productivity in the construction sector (and many other sectors) fell back, due
to a lower demand (Silver & Zieschang, 2009). Commodity prices are an important driving
factor of inflation. For example, oil is an important resource in the economy, it gives an
indication of the state of the economy. When oil prices rise, inflation follows the same path.
During the financial crisis, the prices of oil plummeted, due to a lower demand. This led to a
decrease of the inflation rate (Langager, 2018).
Figure 7 shows that the inflation rate mostly fluctuates around 2 %. Moreover, the peak
moments, which are discussed above, are clearly visible on the graph. Besides this, the
inflation rate shows a high level of variation after the financial crisis.
Figure 7: The inflation rate - Belgium
Table 1 shows that the average real interest rate is 0.8 %, which is very low. Besides this, the
real interest rate reached its lowest level in February 2017 (-3.60 %). This is due to the low
nominal interest rates at the zero lower bound and the high inflation rate (± 3 %). As the real
interest rate is the difference between the nominal interest rate and the inflation rate, it is
normal that the real interest rate reaches this low level in this period. The highest level is
reached in August 1992 (7.49 %). This is due to the high level of nominal interest rate in that
period (± 9 %).
29
3.5 Estimation results
The first step undertaken was the stationarity test. As stated above, the SVAR model has a
condition that all variables must be stationary. The test can be done in GRETL by using the
Augmented Dickey-Fuller test.12 Stationarity means that the process of the variable fluctuates
around a constant mean. On the contrary, non-stationarity means the variable proceeds in a
trend (Koop, 2006). If the t-test is more negative than its critical value (-2.89), we can conclude
that the variable is stationary and compatible with the SVAR. Below, the tests are summarized
in table 2.
Inflation rate Change in inflation Real interest rate
T-value -3.43 -8.43 -1.68
Table 2: Summarized ADF-test
Table 2 shows that the inflation rate is stationary, as its t-value is more negative than the critical
value. However, to calculate the natural rate of interest based on the SVAR, the change in
inflation is used. This variable is computed by taking the first difference of the inflation rate,
which also leads to a stationary variable.
Table 2 also illustrates that the hypothesis of non-stationarity cannot be rejected for the real
interest rate, as its t-value is not more negative than the critical value. Therefore, we analyzed
the course of the real interest rate through time, which is presented in figure 8 (ut infra). On
the x-axis, the time is presented, while the real interest rate is shown on the y-axis. Non-
stationarity implies that the variable shows a trend (Koop, 2006). As the graph demonstrates,
this is not completely the case. The real interest rate varies over time. It could be argued that
the real interest rate is decreasing systematically over this period, but there is still a high level
of variation.
Moreover, if we would look at the real interest rate over a longer period, it becomes clearer
that this downward movement is part of a fluctuation over time.13 Furthermore, Lanne (2002)
argues in his study that the real interest rate follows a stationary process. Besides this, it is
more practical to interpret the results with the real interest rate, rather than using the first
difference of this variable. Therefore, we will perform the estimation with the real interest rate,
as it is prescribed by Brzoza-Brzezina (2003).
12 The results of this test can be found in the appendix (6.2). 13 The real interest rate from 1960 to 2017 can be found in the appendix (6.3)
30
Figure 8: The real interest rate from January 1992 to June 2018.
Now that we checked for the stationarity tests, we can continue with our VAR model. In order
to know how many lags we should implement, we performed the lag selection test in GRETL.
The VAR lag selection test indicated that the model should be estimated with twelve lags. This
is common with monthly data. The output of this test can be found in the appendix (6.4).
Consequently, we get the VAR model with twelve lags.14 The estimation output of this VAR is
attached to the appendix (6.5). Now, we can move over to the SVAR, as the structural
coefficients and the error terms from the VAR are required to estimate the natural rate of
interest. This can be done by following the steps (10) to (12) explained in the methodology.
Equation (12) allows us to get the reduced form error terms of the VAR |Ԑ1,𝑡
Ԑ2,𝑡|. However, the
structural errors u1,t and u2,t are required to estimate the natural rate of interest. Therefore, the
S(0) matrix has to be identified. But, as explained in the methodology, some restrictions should
be imposed to achieve identification.
After imposing these restrictions, we can identify the S(0) matrix, using equations (15) to (17).
Nevertheless, these steps can be automatically executed by EVIEWS. These results can be
found in the appendix (6.6). The results provide us the following S(0) matrix:
S(0) = |0.282444 0
−0.58748352 0.392390|.
To complete the formula to estimate the natural rate of interest, only the shocks are missing.
This could be extracted from the VAR using EVIEWS. More specifically, by multiplying the S(0)
matrix with the C(L) matrix, we obtain the S(L) matrix, which illustrates the effect of the
14 We also checked for autocorrelation and heteroskedasticity. However, we are only interested in the point estimate. Therefore, the outcome of these tests is irrelevant.
31
residuals on the natural rate of interest.15 We chose to implement all lags of the residuals in
our estimation to get an as accurate estimation as possible. However, the further we go back
in time, the less significant the effect of the next lagged residuals is on the natural rate of
interest. Finally, equation (18) identifies the natural rate of interest as the u1,t shock multiplied
by the effect of the residuals on the natural rate of interest.
EVIEWS and Matlab provided us the series to calculate the natural rate of interest. This was
then imported and calculated in Excel.
3.6 Analysis of the natural rate of interest for Belgium
3.6.1 The natural rate of interest
Now that we have estimated the natural rate of interest for Belgium, we can analyze its course
through time.
Figure 9: The natural rate of interest for Belgium from January 1995 to June 2018.
Figure 9 shows the estimated natural rate of interest over time for Belgium and its trend.16 On
the x-axis the time is shown, expressed in years. The data begins in January 1995 and ends
in June 2018. We chose to present the natural rate of interest starting from 1995, because
from this point, we can see the impact of different crises (ut infra). Moreover, we faced the
starting point problem, as we did not have enough observations to provide an accurate
estimation of the natural rate of interest before 1995. Besides this, we only want to focus on
15 This step represents equation (19). 16 The trend was calculated by using the HP filter in Excel.
32
the more recent years. The y-axis illustrates the natural rate of interest in percent. The graph
demonstrates that the natural rate of interest varies between -1.47 % and 1.45 %.
On the one hand, the minimum of the natural rate of interest was observed in July 2008. At
this time, the Belgian economy was hit by the financial crisis. The subprime mortgages and the
fall of Lehman Brothers affected the Belgian banking market. Many banks who invested in
these subprime mortgages lost a lot of money. Several banks came into difficulties, such as
Dexia and Fortis. This led to a lack of confidence among the banks. This expressed itself in a
decrease of the interbank loans and higher LIBOR-rates (Matthews & Thompson, 2014).
Besides this, the banks also were less inclined to lend money to consumers, which led to a
credit crunch. This resulted in a decrease of investments. Moreover, the risk aversion of the
consumers increased in these uncertain times. Consumers started to save more money and
invested less. As seen in the literature review, an increase of the savings and a decrease of
the investments will lead to a decrease of the natural rate of interest. This could explain the
sudden fall in this period (Michielsen, 2017).
On the other hand, the maximum of the natural rate of interest was reached in June 2009.
However, this maximum was temporary, as the natural rate of interest decreased right after
this event. The reason behind this increase can be found in the real estate prices. During the
financial crisis, the real estate prices dropped due to the lower demand. This caused the
inflation to decrease. The lower level of inflation caused the real interest rate to increase. As
the estimation of the natural rate of interest is derived from the level of the real interest rate in
the SVAR model, this explains the increase of our estimation in this period (Hennesey, Holtz-
Eakin, & Thomas, 2011). This is due to the assumptions made in the methodology and the
construction of the model.17 In reality, the natural rate of interest should be independent from
monetary policy decisions, as the central bank acts after the natural rate of interest moved.
Next to the financial crisis, the dotcom crisis and the Euro crisis also led to a decline of the
natural rate of interest. The impact of the dotcom crisis, which took place in the late 1990s until
2001, was less severe than the other crises. This is thus less noticeable on the graph. This
could indicate that a crisis leads to a decrease of the natural rate of interest (Del Negro et al.,
2017). This can be linked to the fact that a crisis comes along with an increase of the risk
aversion.
17 r = r* + GAP. Our model relies on this assumption. This causes the real interest rate to influence the
natural rate of interest, as the real interest contains information about the natural rate of interest.
33
But more importantly, figure 9 gives a clear answer on the research question (ut supra). Since
1998, there is a decreasing trend of the natural rate of interest in Belgium. This was temporarily
interrupted by the financial crisis and the Euro crisis. After these events, the natural rate of
interest started decreasing again. These findings are in line with Laubach and Williams (2015),
who stated that the natural rate of interest still has a decreasing trend since the Great
Recession. Remarkably, the estimation of the natural rate of interest remains negative since
2015. Perhaps, this is due to the structural nature of the underlying factors, which was
discussed in the literature review.
The increase of risk aversion since the financial crisis and global factors, such as the Lehman
Brothers bankruptcy, have proven to be driving factors of the declining trend in the natural rate
of interest in Belgium. Besides these determinants, there are several other factors that could
explain this decreasing trend.
One important factor is related to the demographics. The Belgian population is ageing over
time, because of the higher life expectancy (Moens, 2018). This causes people to save more,
as they will need more money to survive. Moreover, the savings increase because there is a
concern that the pension scheme will not be able to provide a pension payment in the future.
As mentioned in the literature review, an increase in savings leads to a decrease of the natural
rate of interest.
The slower growth of the GDP in Belgium after the financial crisis could be another factor of
the decreasing trend (NBB, 2018).18 A decline of the trend growth rate of output, due to a
slower growth of production, is proven to lead to a decline in the natural rate of interest.
Besides this, Mario Draghi announced in May 2009 that the policy rates would decrease. This
led to a decrease of the nominal interest rate in the following years, which on his turn caused
the decrease of the real interest rate (Michielsen, 2017). Draghi had to cut the nominal interest
rate because the real interest rate was higher than the natural rate of interest at that time.19
The economy cooled down, which led to disinflation. The nominal interest rates did not
decrease immediately, as monetary policy measures need time to have an impact. As
mentioned above, the estimation of the natural rate of interest depends on the level of the real
interest rate in our model. This partly explains the decrease of the natural rate of interest since
2009.
18 The growth of GDP for Belgium can be consulted in the appendix (6.7). 19 This can be seen in figure 10.
34
3.6.2 The natural rate of interest and the real interest rate
Figure 10: The natural rate of interest and the real interest rate for Belgium.
Figure 10 demonstrates the course of the real interest rate compared to the course of our
estimated natural rate of interest for Belgium. On the x-axis the time is shown, expressed in
years. The data begins in January 1995 and ends in June 2018. The y-axis illustrates the rates
in percent.
Question one is whether the natural rate of interest and the real interest rate follow a similar
course over time (ut supra). The graph positively answers the question, as both series do move
in the same direction. Moreover, the correlation matrix of these two series indicates a high
correlation of 0.69.20 This proves that both series follow a similar path. This finding is not
surprising, as the real interest rate is used to derive the natural rate of interest in the SVAR
model. Furthermore, monetary policymakers will try to reach the natural rate of interest,
because the economy is stabilized at this rate.
We can divide figure 10 in three periods in function of how the real interest rate fluctuates
around the natural rate of interest. To facilitate the interpretations, we could make use of the
interest rate gap. This is illustrated by figure 11.
20 The correlation matrix can be found in the appendix (6.8.1).
35
Figure 11: The interest rate gap for Belgium.
The first period is the period before 2003, where the real interest rate is constantly above the
natural rate of interest. This means that there was a positive interest rate gap, which indicates
that the monetary policy was too contractionary in that period. The second period is the period
between 2003 and 2010. Here, a positive and negative interest rate gap alternate. This means
that the real interest rate fluctuated around the natural rate of interest. The third period is the
period from 2010 until now. During this period, the real interest rate is permanently below the
natural rate of interest. This negative interest rate gap is meant to stimulate the economy.
However, the real interest rate is noticeably lower than the natural rate of interest in recent
years, which could indicate that the monetary policy of the ECB is too loose for Belgium.
3.7 Belgium compared to other economies
After estimating the natural rate of interest for Belgium, we followed the same procedure to
estimate the natural rate of interest for the U.S. and the Euro Area to compare this to the
estimation for Belgium. This will give an answer on the second question: “How does the
estimated natural rate of interest for Belgium relate to the estimations for the U.S. and the Euro
Area?” This comparison might be interesting, as we will be able to verify whether this
decreasing trend is an international phenomenon or not.
This section will focus more on the courses of the different natural rates of interest and on how
the rates relate to each other. Later, we will also compare our estimates for the U.S. to the
estimates in Holston et al. (2016).
36
3.7.1 Belgium versus the U.S.
Figure 12: Belgium compared to the U.S.
Figure 12 shows the natural rate of interest for Belgium compared to the natural rate of interest
for the U.S from January 1995 to June 2018.21 As the graph demonstrates, both series follow
a similar path. In most cases, both series fluctuate in the same directions over time. This is
also confirmed by the correlation matrix, which shows a correlation level of 0.69.22 Besides
that, both series have a decreasing trend. This confirms the statement from Holston et al.
(2016) that this decreasing trend is an international phenomenon.
Just like the estimation for Belgium, the dotcom crisis and the financial crisis are visible in the
natural rate of interest for the U.S. This is characterized by a drop in the estimation. However,
a decline is not always caused by a crisis. More specifically, a slower trend growth rate of
output puts downward pressure on the natural rate of interest. The decline in investments due
to persistent risk aversion and the ageing population also have a negative effect on the natural
rate of interest. These factors make a recovery of the natural rate of interest more complex
(Fischer, 2017).
21 As mentioned above, we used different proxies for the nominal interest rate. For Belgium the 12-month treasury bills rate was used, while the 3-month was used for the U.S. 22 The correlation matrix can be found in the appendix (6.8.2)
37
3.7.2 Belgium versus the Euro Area
Figure 13: Belgium compared to the Euro Area from January 1999 to June 2018.
Figure 13 shows the estimate of the natural rate of interest for Belgium compared to the
estimate for the Euro Area. Both estimates follow a similar course, which can also be confirmed
by the correlation matrix. Here, the correlation level is 0.76.23 This is even higher than the
correlation between the Belgian estimate and the estimate of the U.S. Besides this, there is a
lot more fluctuation in the estimate of the natural rate of interest for Belgium than for the Euro
Area. As mentioned above, the data for the Euro Area is a weighted average of its countries.
This could explain why the estimation for the Euro Area shows less fluctuation than Belgium,
which is a member of the Euro Area. Besides this, most rates are quite synchronized among
the countries in the Euro Area (Franks, Barkbu, Blavy, Oman & Schoelermann, 2018).
Furthermore, the decreasing trend in the Euro Area is less visible than the other estimates
based on the SVAR model. However, this decline in the Euro Area was also caused by a
decline in the trend growth rate of output, higher risk aversion and changing demographics.
Both series experienced a sharp decline of the natural rate of interest during the financial crisis
and the Euro crisis. After the Euro crisis, the natural rate of interest in the Euro Area stayed
relatively low. This is due to the decrease in the trend growth rate of output in this period
(Holston et al., 2016). However, there is a slight recovery of the natural rate of interest since
2017. This is caused by the increase of the trend growth rate of output in 2017. This was the
first increase in the trend growth rate of output since 2007 (Constâncio, 2017).
23 The correlation matrix can be found in appendix (6.8.3)
38
3.8 The SVAR model compared to the LW model
Figure 14: The natural rate of interest based on the SVAR compared to the LW model.
By comparing our estimates with the estimates in Holston et al. (2016), we can answer
question three: “Is our estimation of the natural rate of interest for the U.S. based on the SVAR
similar to the estimates in Holston et al. (2016)?” This question rose due to the diverging results
in the literature and the disagreement about which model is the most suitable for estimating
the natural rate of interest.
Figure 14 demonstrates our estimation of the natural rate of interest for the U.S. compared to
the estimation of Holston et al. (2016). The blue line is the estimation based on the SVAR,
while the red line is based on the LW model. This graph indicates that there is a big difference
between the results, as our estimation is a lot lower than the more complex Holston, Laubach
and Williams estimates. Nevertheless, both series indicate a decreasing trend in the natural
rate of interest, but this is more visible in the estimation based on the LW model.
Besides this, our estimation shows a lot of variation through time, while the LW model seems
to decrease steadily. Moreover, the estimations follow a similar path, albeit at a different level.
Therefore, it might be more interesting to examine the evolution of the natural rate of interest
instead of its level. Finally, the estimations diverge at the end, as the SVAR estimates go down
and the LW estimates go up.
The results could differ from each other because we used another proxy for the nominal
interest rate and inflation. We used the 3-month treasury bills rate, while Holston et al. (2016)
used the federal funds rate. Besides this, we chose the CPI that included all goods and
services. On the contrary, Holston et al. (2016) used the CPI excluding food and energy.
Consequently, there are many natural rates of interest for each maturity and market.
39
Finally, our estimation of the natural rate of interest is mostly more negative compared to the
LW model. Perhaps our estimation of the natural rate of interest could be underestimated,
which could be caused by a lack of variables in the model or by the chosen data. This is also
motivated by Laubach and Williams (2003), who indicated that other estimation methods, other
than their LW model (2003), could over- or underestimate the natural rate of interest. Besides
this, we think that our estimation is less accurate than the LW model, as the SVAR model only
relies on the real interest rate and the change in inflation. The LW model takes a lot more
variables into account, which leads to a better representation of the economy in this model.
Although Brzoza-Brzezina (2006) found a high correlation between the SVAR and the LW
model (2003), we believe that the estimates of the natural rate of interest would be more
precise if the estimation was done with the LW model (2003). This can be motivated by the
correlation matrix. Brzoza-Brzezina found a correlation of 0.88 between his SVAR estimates
and the LW model (2003), while our estimates only show a correlation level of 0.28.24
Unfortunately, the LW method exceeds the scope of our Master’s Dissertation.
4. Conclusion
The natural rate of interest is the rate which leads the economy to optimal production (full
employment) and stable inflation in the long run (Constâncio, 2016). The natural rate of interest
is very important for policymakers, as it contains information about the state of the economy
(Weber et al., 2007). This concept is seen as a benchmark for monetary policy.
Monetary policymakers try to steer the real interest rate towards the natural rate of interest, as
this closes the output gap, stabilizes inflation and balances the investment and savings
relation. However, if the inflation rate is below its target and the output gap is negative,
monetary policymakers will try to set the real interest rate lower than the natural rate of interest
(negative interest rate gap). This way, the output gap gets higher, which stimulates the
economy. This leads to a higher level of inflation (De Backer & Wauters, 2017).
Several studies, such as Holston et al. (2016), pointed out that there is a declining trend of the
natural rate of interest over the recent years. The declining trend in the U.S., the United
Kingdom and the Euro Area was caused by mostly the same factors, namely the decline in the
trend growth rate of output, slower population growth, higher life expectancy, more savings
and higher risk aversion. This natural rate of interest is expected to stay low, as most of these
factors are of structural nature. The impact of the structural factors is also strengthened by
cyclical factors, which makes it difficult for the natural rate of interest to recover.
24 The correlation matrix can be found in appendix (6.8.4).
40
The natural rate of interest is unobservable and should be estimated. Laubach and Williams
(2003) estimated the natural rate of interest within a model, containing inflation, output and real
interest rates. The SVAR is however proven to offer a good substitute for measuring the natural
rate of interest (Brzoza-Brzezina, 2006).
Therefore, we made an estimation of the natural rate of interest for Belgium based on this
methodology. This study was conducted due to the absence of information about the natural
rate of interest for Belgium. The econometric study struck a light on the natural rate of interest
for Belgium and how it relates to other economies. More specifically, the natural rate of interest
does have a decreasing trend over the recent years in Belgium. Therefore, our research
question is answered.
The main factors of this decreasing trend in Belgium could be the changing demographics, the
higher level of risk aversion caused by the financial crisis and the slower growth of GDP. More
detailed, the changing demographics and higher risk aversion led to more savings, which leads
to a decline in the natural rate of interest. This decline is necessary to balance the investment
and savings relationship. Besides this, the slower growth of GDP indicated a drop in
production, which led to a decline of the trend growth rate of output. This could also explain
the decline in the natural rate of interest for Belgium.
Furthermore, the real interest rate and the natural rate of interest for Belgium follow a similar
path. However, we see that the interest rate gap in Belgium changes from positive to negative
over time. The interest rate gap was positive from 1995 to 2003, which means that the
monetary policy was too contractionary. Between 2003 and 2010, a positive and negative
interest rate gap alternate. Finally, the interest rate gap is permanently negative since 2010.
This indicates that monetary policymakers try to stimulate the economy in recent years.
Besides this, the estimation of the natural rate of interest for Belgium compared to the
estimates for the U.S and the Euro Area resulted in the following conclusions. First, all three
estimations show a decreasing trend of the natural rate of interest, but this was less noticeable
for the Euro Area. This indicates that the decrease of the natural rate of interest is an
international phenomenon, which is consistent with Holston et al. (2016). Moreover, all three
estimations showed a drop of the natural rate of interest in times of crises, which can be
explained by higher risk aversion, more savings and a decline in the trend growth rate of output.
Finally, we have some critical remarks. Our estimation of the natural rate of interest could be
underestimated due to a lack of variables. Laubach and Williams (2003) indicated that other
estimation methods, other than their LW model (2003), could over- or underestimate the
natural rate of interest. We think that this statement is correct, as our estimates for the U.S.
are in general lower than the estimates in Holston et al. (2016).
41
Although the correlation between the SVAR and the LW model (2003) is high (Brzoza-
Brzezina, 2006), we believe that the estimates of the natural rate of interest would be more
precise if the estimation was done with the LW model (2003). The LW model (2003) is more
extensive and takes more variables into account, such as the output gap. Unfortunately, this
method exceeds the scope of our Master’s Dissertation.
Besides this, there are various definitions available for the natural rate of interest. This could
cause a lot of variation in the estimation results for different models. This makes the natural
rate of interest less reliable. There is currently no one best way to estimate the natural rate of
interest. Further research in Belgium is required to verify whether our results are accurate or
not. Perhaps, future estimations could use other proxies for the nominal interest rate and the
inflation rate, as this could lead to different results. However, we were still able to identify the
decreasing trend and discuss the driving factors that affected the natural rate of interest.
Although there are some issues regarding the natural rate of interest, the concept should
definitely be used as a way of thinking. It provides important insights for the economy and
should therefore be implemented in the decision making of monetary policy as a
complementary tool (Blinder, 1998).
42
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6. Appendices
6.1 Descriptive statistics
6.1.1 Belgium
Summary Statistics, using the observations 1992:01 - 2018:06
Variable Mean Median S.D. Min Max
Inflationrate 1,94 1,95 1,08 -1,61 5,96
Realinterestrate 0,798 0,875 2,33 -3,60 7,49
6.1.2 U.S.
Summary Statistics, using the observations 1992:01 - 2018:06
Variable Mean Median S.D. Min Max
Inflationrate 2,30 2,41 1,12 -1,96 5,50
Realinterestrate 0,160 0,0367 1,86 -4,01 3,64
6.1.3 Euro Area
Summary Statistics, using the observations 1997:01 - 2018:06
Variable Mean Median S.D. Min Max
Inflationrate 1,71 1,88 0,918 -0,588 4,18
Realinterestrate 0,644 0,380 1,38 -2,16 3,15
6.2 Augmented Dickey-Fuller test ADF:inflation rate Belgium Augmented Dickey-Fuller test for Inflationrate_SA testing down from 12 lags, criterion AIC sample size 305 unit-root null hypothesis: a = 1 test with constant including 12 lags of (1-L)Inflationrate_SA model: (1-L)y = b0 + (a-1)*y(-1) + ... + e estimated value of (a - 1): -0,0755966 test statistic: tau_c(1) = -3,42816 asymptotic p-value 0,01007 1st-order autocorrelation coeff. for e: 0,014 lagged differences: F(12, 291) = 16,079 [0,0000]
ADF Real interest rate Belgium Augmented Dickey-Fuller test for Realinterestrate testing down from 12 lags, criterion AIC sample size 305 unit-root null hypothesis: a = 1 test with constant including 12 lags of (1-L)Realinterestrate model: (1-L)y = b0 + (a-1)*y(-1) + ... + e estimated value of (a - 1): -0,015718 test statistic: tau_c(1) = -1,67663 asymptotic p-value 0,4432 1st-order autocorrelation coeff. for e: -0,031 lagged differences: F(12, 291) = 7,496 [0,0000]
48
ADF: Change in inflation Belgium Augmented Dickey-Fuller test for Changeininflation testing down from 12 lags, criterion AIC sample size 305 unit-root null hypothesis: a = 1 test with constant including 11 lags of (1-L)Changeininflation model: (1-L)y = b0 + (a-1)*y(-1) + ... + e estimated value of (a - 1): -1,00393 test statistic: tau_c(1) = -8,42664 asymptotic p-value 2,699e-014 1st-order autocorrelation coeff. for e: -0,007 lagged differences: F(11, 292) = 15,885 [0,0000]
6.3 The real interest rate (1960-2017)
6.4 VAR lag selection test VAR system, maximum lag order 12 The asterisks below indicate the best (that is, minimized) values of the respective information criteria, AIC = Akaike criterion, BIC = Schwarz Bayesian criterion and HQC = Hannan-Quinn criterion. lags loglik p(LR) AIC BIC HQC 1 -52,97830 0,386743 0,459929* 0,416016 2 -46,63198 0,01288 0,371357 0,493335 0,420146 3 -44,48995 0,36893 0,383541 0,554309 0,451844 4 -43,12208 0,60298 0,400801 0,620360 0,488620 5 -41,19387 0,42579 0,414386 0,682736 0,521721 6 -39,08214 0,37661 0,426768 0,743909 0,553618 7 -35,88524 0,17161 0,432034 0,797967 0,578400 8 -33,07338 0,22907 0,439825 0,854549 0,605706 9 -31,55548 0,55185 0,456101 0,919616 0,641497 10 -30,67778 0,78063 0,476576 0,988881 0,681487 11 -26,57864 0,08458 0,475925 1,037022 0,700352 12 34,92698 0,00000 0,098840* 0,708727 0,342782*
49
6.5 VAR output: EVIEWS
Vector Autoregression Estimates
Date: 07/29/18 Time: 11:24
Sample (adjusted): 1993M02 2018M06
Included observations: 305 after adjustments
Standard errors in ( ) & t-statistics in [ ] CHANGE_IN_INFLATION REAL_INTEREST_RATE CHANGE_IN_INFLATION1 0.230794 -0.051388
(0.08828) (0.10069)
[ 2.61442] [-0.51036]
CHANGE_IN_INFLATION2 0.063074 0.101374
(0.08929) (0.10185)
[ 0.70637] [ 0.99534]
CHANGE_IN_INFLATION3 0.088212 -0.126588
(0.09006) (0.10272)
[ 0.97953] [-1.23238]
CHANGE_IN_INFLATION4 0.041725 0.008574
(0.08858) (0.10104)
[ 0.47102] [ 0.08486]
CHANGE_IN_INFLATION5 -0.003401 0.057280
(0.08839) (0.10082)
[-0.03848] [ 0.56812]
CHANGE_IN_INFLATION6 0.119703 -0.149272
(0.08825) (0.10066)
[ 1.35646] [-1.48300]
CHANGE_IN_INFLATION7 -0.073160 0.074326
(0.08840) (0.10083)
[-0.82761] [ 0.73715]
CHANGE_IN_INFLATION8 0.038482 -0.053523
(0.08818) (0.10057)
[ 0.43643] [-0.53218]
CHANGE_IN_INFLATION9 0.100326 -0.019325
(0.08810) (0.10049)
[ 1.13878] [-0.19231]
CHANGE_IN_INFLATION
10 -0.078124 0.038560
(0.08825) (0.10066)
[-0.88525] [ 0.38307]
CHANGE_IN_INFLATION
11 0.254379 -0.269139
(0.08665) (0.09883)
[ 2.93575] [-2.72317]
CHANGE_IN_INFLATION
12 -0.575625 0.491593
(0.04892) (0.05579)
[-11.7676] [ 8.81075]
REAL_INTEREST_RATE1 0.017329 1.095561
(0.08351) (0.09526)
50
[ 0.20750] [ 11.5010]
REAL_INTEREST_RATE2 -0.006480 -0.002934
(0.12482) (0.14237)
[-0.05191] [-0.02061]
REAL_INTEREST_RATE3 0.075757 -0.227856
(0.12438) (0.14187)
[ 0.60910] [-1.60614]
REAL_INTEREST_RATE4 -0.055061 0.188504
(0.12350) (0.14086)
[-0.44584] [ 1.33819]
REAL_INTEREST_RATE5 0.024579 -0.069200
(0.12360) (0.14098)
[ 0.19885] [-0.49084]
REAL_INTEREST_RATE6 -0.007520 -0.041201
(0.12169) (0.13880)
[-0.06180] [-0.29683]
REAL_INTEREST_RATE7 -0.171215 0.215717
(0.12106) (0.13808)
[-1.41430] [ 1.56222]
REAL_INTEREST_RATE8 0.206655 -0.295627
(0.12112) (0.13815)
[ 1.70620] [-2.13988]
REAL_INTEREST_RATE9 -0.023812 0.138274
(0.12158) (0.13868)
[-0.19586] [ 0.99709]
REAL_INTEREST_RATE
10 -0.129700 0.006230
(0.12127) (0.13833)
[-1.06949] [ 0.04504]
REAL_INTEREST_RATE
11 0.169838 -0.125161
(0.12167) (0.13878)
[ 1.39588] [-0.90187]
REAL_INTEREST_RATE
12 -0.093292 0.102952
(0.07953) (0.09071)
[-1.17308] [ 1.13495]
C -3.75E-05 -0.011960
(0.01785) (0.02036)
[-0.00210] [-0.58747] R-squared 0.407476 0.977344
Adj. R-squared 0.356688 0.975402
Sum sq. resids 22.33684 29.06031
S.E. equation 0.282444 0.322160
F-statistic 8.023116 503.2878
Log likelihood -34.12990 -74.25816
51
6.6 SVAR coefficients: EVIEWS
6.7 GDP growth for Belgium Source: NBB
6.8 Correlations
6.8.1 Natural rate of interest Belgium and the real interest rate
Correlation coefficients, using the observations 1993:02 - 2018:06
5% critical value (two-tailed) = 0,1123 for n = 305
NRI305L Realinterest
Rate
1,0000 0,6854 NRI305L
Structural VAR EstimatesDate: 07/29/18 Time: 11:32Sample (adjusted): 1993M02 2018M06Included observations: 305 after adjustmentsEstimation method: Maximum likelihood via Newton-Raphson (analytic derivatives)Convergence achieved after 10 iterationsStructural VAR is over-identified
Model: e = Su where E[uu']=IS =
C(1) 0-2.08 * C(1) C(2)
including the restriction(s)@S(1,2)=0@F(1,1)=0
Coefficient Std. Error z-Statistic Prob.
C(1) 0.282444 0.011436 24.69817 0.0000C(2) 0.392390 0.015887 24.69817 0.0000
Log likelihood -194.6211
52
1,0000 Realinterest
Rate
6.8.2 Natural rate of interest Belgium and U.S.
Correlation coefficients, using the observations 1993:02 - 2018:06
5% critical value (two-tailed) = 0,1123 for n = 305
NRIUS NRIBE
1,0000 0,6932 NRIUS
1,0000 NRIBE
6.8.3 Natural rate of interest Belgium and Euro Area
Correlation coefficients, using the observations 1998:02 - 2018:06
5% critical value (two-tailed) = 0,1254 for n = 245
NRIBE EU
1,0000 0,7565 NRIBE
1,0000 EU
6.8.4 SVAR model and Laubach-Williams model
Correlation coefficients, using the observations 1994:1 - 2018:1
5% critical value (two-tailed) = 0,1996 for n = 97
NRIUS NRIHolstone
tal
1,0000 0,2808 NRIUS
1,0000 NRIHolstone
tal
