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University of Amsterdam Faculty of Economics and Business
Quantitative Easing and the yield curve. Has the ECB successfully lowered the yield curve?
Sebastiaan Hermanus Sollie
11157143
1st supervisor: prof. dr. S.J.G. van Wijnbergen
2nd
supervisor: dr. W.E. Romp
Abstract:
In the aftermath of the 2008 financial crisis and with Europe’s economy in a slump
the ECB had to take unconventional policy measures in order to push inflation back to
the targeted level. In line with other central banks all over the world, the ECB started
to conduct a Quantitative Easing policy. This paper explores the effect that the
Quantitative Easing policy has on the government yield curve. In order to estimate
this effect this paper employs a Nelson-Siegel model to estimate the level, slope and
curvature of the yield curve. After this a regression is used to distillate the effect that
Quantitative Easing had on the yield curve. A large group of control variables is
added in order to control for movements in the macro economy that influence the
yield curve over time. This paper finds that QE successfully lowered en flattened the
yield curve, aking it for now a successful unconventional policy tool.
2
Introduction ......................................................................................................................... 3
Section 1: Initial data exploration ................................................................................ 4
Section 2:Literature overview, channels via which QE influences the yield curve ........................................................................................................................................ 7
A “little” critique .......................................................................................................................... 9
Section 3: The model ...................................................................................................... 10 The Nelson-Siegel model .........................................................................................................10 Estimating the model ...............................................................................................................12
The regression .................................................................................................................. 13
Section 4: Data .................................................................................................................. 14 Variables determining the yield curve ..............................................................................15
Section 5: Results ............................................................................................................. 17 Robustness ...................................................................................................................................21 Different data ..............................................................................................................................21 Inflation expectations ..............................................................................................................23
Section 6: Conclusion ...................................................................................................... 25
Acknowledgments and future research References ........................................... 25
Appendix ............................................................................................................................. 29
3
Introduction
The 2008 financial crisis pushed the world economy in a recession from which it yet
has to recover. In the direct aftermath of the collapse of Lehman Brothers central
banks acted firmly by lowering their policy rates to virtually zero. By doing so they
expected to push the economy out of the negative spiral were it was in due to the
collapse of the financial system. However, these low interest rates were not sufficient
enough to push the economy out of the recession and back to full employment. Large
central banks from all over the world faced a feared scenario that is known as the
liquidity trap.
With policy rates at zero and inflation expectations decreasing the European
Central Bank (ECB) as well as the FED, BoE and the BoJ, was forced to look for
other policy measures that could increase economic activity. They took a wide variety
of measures from expending the lending facilities to buying bonds first solely
government bonds and later also corporate bonds. These purchases of bonds came to
be known as quantitative easing (QE), which is till today a highly controversial topic
in economics because the effectiveness and side effects of this policy is still
unexplored territory.
Krugman (2000) describes the importance of policy alternatives that can be
used when central banks face a liquidity trap. Quantitative easing and unconventional
market operations are the main policy alternatives according to Krugman. Those two
alternatives are used today by the large central banks all over the world. Both the FED
and the ECB use an asset purchase programme in order to expand the monetary base,
or to put it in the words of Krugman those central banks use unconventional market
operations to ensure quantitative easing. Krugman points to different channels via
which QE has an effect on the economy one of those is a decrease in interest rates
because of bond purchases by the central bank.
While the paper by Krugman was published fifteen years ago the topic of
quantitative easing is more relevant than ever. Since the outburst of the financial crisis
and the increased amount of unconventional monetary policy measures a large
amount of literature has been written on the topic. Kehmraj and Yu (2016) find that
the FEDs QE program was effective in reducing the corporate bond spread and
increased short-term investments. This contradicts the findings from Bowmand et.al.
(2015) that QE is not very effective in stimulating the economy. They used Japanese
bank data from the period 2000-2006 during which Japan had a QE program in place.
The researchers found that QE was not able to significantly increase bank lending and
therefor was unfit to stimulate the economy. Putnam (2013) presents a more nuanced
view on the topic he argues that QE was most effective when it was used to stabilize
the banking sector and less effective during the period after this. Putnam also points to
a new challenge that comes with QE namely an exit strategy, which can have negative
effects on the just recovered economy.
This paper adds to the literature by examining the effect of QE on the yield
curve. Central banks argue that by buying bonds they increase the price of these assets
that lowers the yield curve thereby stimulating investments. The hypothesis that is
tested in this paper is formulated as follows
Did the ECB Quantitative Easing program lower and flatten the yield curve?
4
The rest of this paper is structured as follows: section one explores some initial data
on the effectiveness of QE. Section two gives an overview of the current literature on
quantitative easing and the yield curve. In section three a model is presented that is
used to estimate the yield curve after that the model that is used to distillate the effect
of QE is presented. In section four the used data is presented. Section five shows the
results, acknowledgments and shortcomings. Finally section six concludes.
Section 1: Initial data exploration
On January 22, 2015 the ECB(2015) announced an extended asset purchasing
program to push the struggling Euro-area economy out of the financial crisis. By
buying large amounts of euro denoted government bonds the ECB aimed on lowering
interest rates and flattening the yield curve, since then the ECB bought a large amount
of euro denoted government debt. Figure 1 shows the amount of bonds bought under
the PSPP as a percentage of both total euro denoted government debt as well as all
euro denoted debt. At the end of March 2016 the ECB had bought almost 10% of the
total government debt in the Eurozone.
Note: Figure 1 shows the magnitude of the amount of bonds bought by the ECB under the QE-policy so far. While
total debt stayed more or less constant over the period, the percentage of purchased debt increased to 9% of all
euro denoted government bonds in march 2016. Source ECB, 2016a and 2016b.
Figure two displays the movement of the Euro-area yield curve since the
implementation of the PSPP. In order to avoid the suspicion of data selection I took
the yield curve data on the 20th
of every month or the closest available date. The
figure does not show all the yield curves from December 2014 up to May 2016
because some were virtually equal. The following yield curves were basically equal,
February 2015: March 2015
May 2015: June 2015
July 2015: August, September, October, November, December
January 2016: February, March, April
0
2
4
6
8
10
12
11950
12450
12950
13450
13950
14450
Apr/15 May/15 Jul/15 Aug/15 Oct/15 Dec/15 Jan/16 Mar/16
Pe
rce
nta
ge o
f d
eb
t
Euro
de
no
ted
de
bt
(x1
bill
ion
)
Figure 1: The QE policy takes a large part out of the total amount of debt
Total euro denoted debt (LHS)
PSPP holdings % of Total Gov debt (RHS)
PSPP Holdings % of Total € denoted debt (RHS)
5
Note: Every line represents a yield curve as published by the ECB for the 20th of the month or the nearest published day. For
some days the lines where virtually equal, those lines are combined and represented by the earliest curve. Source: ECB, 2016C
The December yield curve is the base reference line because this was exactly one
month before the Asset Purchase Programme (APP) was announced. The 15 year spot
rate was the highest in December ’15 and decreased over the rest of the sample
period. This decrease of the 15 year spot rate is a first tentative sign that the QE
program was effective in lowering the yield curve at longer maturities.
Two days before the announcement, on January the 20th
there was already a
lot of speculation in the market in anticipation of the ECBs board meeting. These
expectations lowered the yield curve in advance of the policies implementation. The
curve kept lowering over February and March hitting the lowest point in April. At that
point the assets purchasing program appeared to be very effective in lowering the
yield curve. However, in May 2015 the yield curve moved up again to levels
comparable to the situation in January. After that, in July the yield curve moved up
even further and remained at that level up to January 2016. During that time markets
expected the ECB to increase her asset purchase program, which she eventually did
on 10th
March 2016. (ECB, 2016e) On that day the ECB announced an expansion to
80 billion of her monthly bond purchases. In the months after that the yield curve
lowered to the level of May 2016.
Just observing the yield curve over time does not provide compelling evidence
on the effectiveness of the asset-purchasing program but also not for the
ineffectiveness. It is important to keep in mind, that the yield curve is influenced by a
wide variety of variables that change over time and that it would be shortsighted to
judge the effect of the program solely on the level of the yield curve.
-0.7
-0.2
0.3
0.8
1.3
1.8
2.3
0 20 40 60 80 100 120 140 160 180
Spo
t ra
te
Months till maturity
Figure 2: The movement of the yield curve during the QE-policy
19-Dec-14 20-Jan-15 20-Feb-1520-Apr-15 20-may-15 20-Jul-1520-Jan-16 20-may-16
6
Note: Figure 3 shows the movement of the expected future rate of inflation over the time period that the QE-policy
was active. The figure shows that especially short-term inflation expectations picked up over the period the policy is in place.
In order to assess the effectiveness of the program from a different perspective figure
3 shows the inflation expectations in the Euro area since the first of January 2015.
The program was implemented in a time when inflation expectations were at an all
time low, especially the one and five year inflation expectations have increase after
the introduction of QE. Both the decreased yield curve as the increased inflation
expectations show initial evidence on the effectiveness of the unconventional policy
measures.
In order to determine the effect of quantitative easing, section 3 describes a
regression model that employs a variety of variables that can be used to adjust for
changing macroeconomic variable. By adding a QE dummy this paper tries to filter
the effect that quantitative easing had out of yield curve data.
-1
-0.5
0
0.5
1
1.5
2
Jan/15 Apr/15 Jul/15 Oct/15 Feb/16 May/16Exp
ecte
d in
flat
ion
leve
l
Figure 3: Movement of inflation expectation over the QE period
1 year expectations
5 year expectations
10 year expectations
7
Section 2:Literature overview, channels via which QE influences the yield curve
The European Central Bank (ECB) did not start her QE program in the direct
aftermath of the 2007 financial crisis as the FED and BoE did. Despite this difference
in timing the channels via which the QE program influences the yield curve remain
the same. Altavilla, Carboni & Motto (2015) describe four different channels: the
signaling channel, asset scarcity channel, duration channel and credit premium
channel.
The signaling channel has an effect even before the actual policy is
implemented. Due to the forward looking nature of the yield curve agents incorporate
expectations of lower interest rates in the future into the current yield curve. Gern
et.al. (2015) state that via this channel a central bank can increase the power of her
forward guidance channel. If a central bank buys bonds of a longer maturity she
commits to keeping short-term interest rates low for a long period of time. If the
central bank decides to increase the short term interest rate while holding long term
bond the central bank suffers a lose due to a decrease in value of the long term bonds.
Eggertsson & Woodford (2003) elaborate on this effect. According to them both
inflation as well as real output are unaffected by QE. (Which is contradicted by the
latest literature.) However, they still emphasize the importance and effectiveness of an
asset purchase programme in case of deflation risk.
In order to lower the yield curve the central bank has to convince markets that
she is willing to keep interest rates low even if this by the Taylor rule is no longer
required. Only then markets lower the term structure thereby stimulating the
economy, which eventually boosts inflation. While in theory this sounds straight
forward in practice this more chanllanging, after all financial markets doubt and test
the commitment of the central bank to keep interest rates low. By purchasing long
term assets and therewith putting skin in the game the central bank can convince
financial markets that she is determined to keep interest low according to Eggertsson
& Woodford. The effect of this signaling channel is stronger for medium term bonds
than for long term bonds because interest rates are expected to increase in the future at
some point. Eggertsson & Woodford argue that the size and composition of QE does
not affect the yield curve, as the signaling channel is the only channel via which QE
can influence the yield curve, making it impossible to effect long maturity spot rates.
This confirmed by Bomfim (2003) who found that the medium length of the yield
curve changes almost one-for-one with the expectations on the future stance of
monetary policy. This is in line with the expectations expressed by Eggertsson &
Woodford.
The asset scarcity channel, assumes investors who have preferred habits.
Such a model with preferred habits was introduced by Modigliani & Sutch (1966) to
explain the behavior of the yield curve. They combine multiple theories into one more
realistic theory. The authors argue that the yield is influenced by three assumptions.
The first assumption is based on the existence of arbitrageurs whose actions create a
yield curve in which expected returns are equal over all maturities. The second
assumption is about the forward looking nature of the yield curve due to investors
who take into account future capital gains or losses due to changes in future interest
rates. The third assumption takes into account the personal preferences of investors.
Individual investors have their own objectives and might be only interested in an
investment that pays of after n-periods. When this is the case their payoffs are certain
if they invest in a n-period bond. Those investors would not have an incentive to
engage in a portfolio of different bonds in order to receive the same payoff. Only
when there are portfolio opportunities with a gain large enough to compensate for the
8
larger transaction costs as well as the increased risk, those investors would be tempted
to engage in such a portfolio. The existence of preferred habit investors creates
segregations between different maturities within the yield curve.
Altavilla, et.al.(2015) argue that if there are sufficient preferred habit investors
in the market and arbitrageurs are largely risk averse, the central bank has the
possibility to lower the longer term of the yield curve by buying bonds of longer
maturity. This is in line with the work of Greenwood & Vayanos (2014) who tested
the effect of the US government’s debt composition on the yield curve. Their results
were in line with a model in which different investors have different preferred habits
and therefor create a segregated yield curve. The authors argue that a central bank can
exploit this segregation by buying bonds of longer maturity and thereby lowering the
longer term of the yield curve.
The duration channel is in contradiction to the previous channel driven by
the arbitrageurs and preferred habit investors together. For the asset scarcity channel
arbitrageurs were assumed to be too risk averse which made them unable to integrate
the yield curve. However, in a model set up by Vayanos & Vila (2009) the yield curve
is determined by the interaction between arbitrageurs and preferred habit investors. In
this model, when a demand shock hits for a given maturity, arbitrageurs have the
ability to spread out the effect over the entire yield curve. So when the central bank
shocks demand by buying longer-term bonds this lowers the entire yield curve.
Altavilla, et.al.(2015) make use of this insight in formulating the duration channel.
When a central bank successfully lowers the maturity structure by buying longer-term
bonds, thereby lowering the total duration of the yield curve this reduces duration
risk. The reduction of the risk spreads out over the yield curve due to arbitrageurs.
The final channel described by Altavila et.al. (2015) is the Credit premium
channel. While the authors call this channel the credit premium channel, it is similar
(equal) to the portfolio rebalancing model described in the literature. The portfolio
rebalance model finds it origin in the work of Tobin (1969) in which he point out that
a change in the supply of an asset group does not only alter the yield of that asset
group but also the relative price towards other asset groups. This change in the
relative price forces investors to rebalance their portfolios. Not only Keynsian
economists like Tobin had a firm believe in the portfolio rebalance channel, also
monetarists like Friedman & Schwartz (1965) believed in this mechanism.
The main message of the portfolio rebalance model model is that a demand or
supply shocks to a group of bonds with a similar maturity influences the entire yield
curve. Christensen (2016) and Bernanke & Reinhart (2004) describe a reserve
induced effects of QE. They argues that when central banks buy government bonds
directly from non-banks this eventually effects the balance structure of banks, this
forces banks to rebalance their portfolios creating an upward pressure on asset prices
with different maturities. Some authors argue that the new reserves would stay on
banks balances sheets in the form of deposits (Herbst, Wu & Ho, 2014). This might
be true in the short run but is not in the medium run according to Bernanke &
Reinhart (2004)
The authors above focus on the financial intermediaries and how they are
affected by a central bank that buys government bonds. Joyce et.al. (2012) and
Bowdler & Radia (2012) address the portfolio rebalancing model from the perspective
of non-financial corporations and investors. When a central bank buys assets directly
from the public investors portfolio changes from one with long-term bonds to one
with short-term liquid bank deposits. So far QE does not influence the yield curve at
all. However, the authors argue that these investors care about the composition, both
9
for duration reasons as well ass for risk to return of their portfolio and thus start
buying longer-term assets in order to rebalance. This increased demand for longer-
term assets increases their prices, which in the case of bonds equals a lower yield.
Another channel often mentioned in the literature that is not specified by
Altavila et.al. (2015) is the liquidity channel. Kiyotaki & Moore (2012) describe a
model in which the central bank stimulates the economy via quantitative easing by
buying illiquid assets from the public. By replacing those assets with liquidity (cash)
the relief the liquidity constraint faced by the economy. According to the authors this
lowers the effect of a liquidity shock on output and consumption. This is why the
FED initially bought large amounts of MBSs in order to provide liquidity to a market
that was almost completely dried out. This liquidity was necessary in order to keep
the link between the FEDs policy rate and the market interest rate in place, in other
words to keep the short term interest rate low. In the Eurozone the ECB tried to
accomplish this via a different policy. The ECB (2015b) states that in order to
overcome a liquidity shortage, which banks all over the Eurozone faced, the ECB
decided to enhance her refinance facilities. The objective of the ECB after June 2014
was both to enhance the transmission mechanism and increase the accommodative
monetary policy stance.
A “little” critique
The channels mentioned above are the main channels according to a large part of
literature. However, Krishnamhurthy & Vissing-Jogrensen (2011) mention another
channel, namely the default risk channel. They argue that bonds with higher default
risk have higher prices. The default level of these riskier bonds will decrease after the
QE program is in place while this program stimulates the economy therewith
lowering the default risk. The described mechanism lowers the yield curve even
further. Despite the fact that Krishnamhurthy & Vissing-Jogrensen argue that this is
channel is important for the effectiveness of the QE program I object to the
importance of this channel. In their assessment of the default risk channel the authors
claim that the increased economic environment lowers default risk and thereby lowers
the default premium. I would like to emphasize that during a time of economic
recovery the economic environment enhances almost by definition and therefore the
default risk would decrease even without QE. In my opinion this channel shows the
willingness in the literature to find ways that explain why QE has to be a success.
While the papers are written by highly respected economists and published in
important journals it is important to point out that most of the researchers have to the
more or lesser extend a relationship with a central bank. This could make them a little
biased towards papers that applaud the effects of QE.
Martin & Milias (2012) address this problem. The authors point out that the
current literature is mainly based on highly frequency data, this makes it impossible to
include important macroeconomic variables such as inflation and output in the
equation. Besides the lack of longer periods of data also the period over which the
data is gathered is criticized by the authors. QE is a policy measurement that is only
undertaken in times of severe economic downturn, therefor there is only data
available gathered during crisis times. The lack of available data combined with the
lack of any counterfactual testing, that is not uncommon in economics, wories Martin
& Milias. Despite their critique on the economic research they could not deny that
QE probably has some positive impact on the economy.
10
Martin & Milias have some genuine concerns regarding the academic research on the
effects of QE. However, still most of the literature finds a positive effect of QE that
enhances economic recovery, via a lower yield curve, and helps to reach a sustainable
growth path. In the remaining part of this paper it is important to keep in mind that
this paper preforms research on the frontier of monetary policy in a non ideal
situation. Precisely because of this challenge researching the effect of QE is important
and necessary.
Section 3: The model
In order to assess the effectiveness of QE, this paper uses a model that estimates the
shape of the yield curve. After that a regression model is used in an attempt to
preform something as close as possible to a counterfactual. This section describes the
models used in order to estimate the effectiveness of the ECBs quantitative easing
policy. A model is presented that is used to estimate the shape, level, slope and
curvature of the yield curve. After that a regression model is presented that can be
used to estimate the effect of quantitative easing on the yield curve.
The Nelson-Siegel model
A good estimation of the yield curve is beneficial both for academics in order to
enhance their research as well for central banks who can employ the information
within the yield curve in order to assess the effectiveness of policy measures.
McCulloch(1979), Vasicek and Fong (1982) and Steeley (1991) are some authors
who tried to set up yield curve estimation model using a variety spline estimation
techniques. These models are often criticized for having parameters with no
straightforward economic value or intuition behind them and for being black boxes.
(Ioannides, 2003).
Svensson (1994) presents a much simpler filter that can extract a yield curve
out of data containing different spot rates. Svensonn builds on a similar model from
Nelson and Siegel (1987) this is why the model is often referred to as the Nelson-
Siegel-Svensson (NSS) model. While being slightly less accurate than the model by
McCulloch (1979) the NSS-model is often used because of its simplicity. A report
from the BIS (2005) confirms the popularity of the models, 8 out of 13 central banks
reporting to the BIS used either a NS-model or a NSS-model. The simple and
straightforward interpretation of the betas makes these models most useful for the
purpose of this paper.
In the Nelson and Siegel (1987) paper two models are presented, first a model
shown in equation (1) that connects forward rates over all maturities ().
𝑓(𝜏) = 𝛽
1+ 𝛽
2(𝑒
−𝜏
𝜆1) +𝛽3
(𝜏
𝜆1
𝑒−
𝜏
𝜆1)
(1)
Equation (2) shows the spot rate that is an average of all forward rates.
𝑦(𝜏) =
1
𝜏∫ 𝑓(𝜏)𝑑𝑥
𝜏
0
(2)
Inserting the equation (1) into equation (2) and solving the intergral gives the equation
as shown in equation (3). Appendix 2 shows the intermediate steps.
𝑦(𝜏) = 𝛽1
+ 𝛽2
(1 − 𝑒
−𝜏
𝜆1
𝜏
𝜆1
) +𝛽3
(1 − 𝑒
−𝜏
𝜆1
𝜏
𝜆1
− 𝑒−
𝜏
𝜆1)
(3)
11
In the Svensson (1994) paper a fourth variable is added to the model that enables to
model to fit the data even better. Equation (4) bellows shows the final Nelson-Siegel-
Svensson model (NSS-model)
𝑦(𝜏) = 𝛽1
+ 𝛽2
(1 − 𝑒
−𝜏
𝜆1
𝜏
𝜆1
) +𝛽3
(1 − 𝑒
−𝜏
𝜆1
𝜏
𝜆1
− 𝑒−
𝜏
𝜆1) +𝛽4
(1 − 𝑒
−𝜏
𝜆2
𝜏
𝜆2
− 𝑒−
𝜏
𝜆2)
(4)
The NSS-model as shown in equation (4) represents the spot rates at a given time τ. In
the equation y(τ) is the spot rate for a given maturity over τ periods in years. The two
lambdas have no direct informative value but are necessary to make the model fit the
data. The Betas nonetheless do have informative value regarding the shape and level
of the yield curve. The first beta is also called the level and is the asymptote to which
the yield curve converges. The second beta is the Slope of the yield curve and
determines the overall steepness of the curve. The third and fourth beta measure the
curvature of the yield curve and give it a hump-shape over the medium term.
Note: both figures show the effect of the different shape estimators according to the NSS-model for different days, as published
by the ECB (ECB, 2016c). A comparison between both graphs shows the large movement of both curvature parameters. This can
large movement make them less valuable in order to estimate the effect of QE. Therefore, in this paper the NS-model is used.
Figure four and five show two different yield curves as calculated by the ECB for the
Eurozone. It comes clear that the shape of the both curvature variable can vary over
time which enables the yield curve to take both an U-shape as well as an S-Shape
over the medium run. The slope is a more constant factor that mainly makes sure that
the longer term of the yield curve is higher than the shorter term. Morales (2010)
points out that first beta can be seen as an long term factor because it does not change
over time. The second beta on the other hand is a short-term factor that starts at one
but decays monotonically and quickly to zero. Both curvature betas are on the
medium side, they start at zero and in the limit will move back to zero.
12
Although the NSS-model has a better fit to the data than the Nelson-Siegel
model (NS-model) it also has one disadvantage regarding the curvature betas. The
first model has two curvature betas that can vary largely over time, making it more
flexible. These two betas make it at the same time more difficult to interpret the
meaning of the betas. The first curvature beta can go up while the other goes down,
thereby canceling each other out. The second model on the other hand fits the data a
little less but is more useful regarding the objective of this paper. The effect of QE on
the medium run is easier assessed if there is only one beta that describes the behavior
of the yield curve on the medium run. Figure 6 shows the shape the curvature beta can
take on depending on the level of lambda. In the graph the betas are shown for lambda
1, 2, 5 and 10 from the top to the bottom.
Note: Figure 6 shows the shape of the of the curvature beta for different values of lambda. The figure shows that the shape of the
curvature beta is sensitive for the value of lambda. This makes the yield curve sensitive to the value of lambda. It is important that the true value of lambda is estimated because a false value can bias the results by a lot.
Estimating the model
Before the betas can be estimated it is necessary to estimate the lambdas or shape
parameters. Nelson and Siegel (1987) estimate these shape parameters by estimating
the model for a range of lambdas and picking the lambda that has the best fit to the
data. In this paper the same technique is used. In order to determine the best fit, the
model is estimated for each date in the dataset and the R-Squared is calculated after
this the average R-Squared is calculated for each lambda after which the lambda with
the highest R-squared is picked. Figure 7 and Appendix 1 shows the average R-
squares for all values of lambda between 0,1 and 6,0 for both datasets of bond yield of
all governments and yield of triple-A rated bonds. The highest R-squared is reached
with a lambda of 2,2 for the triple-A bonds and at 3,48 for all government bonds.
These shape parameters are used for the estimation of the betas from the Nelson-
Siegel model. The parameters are used to estimate the model for each date in the
dataset. This gives a set of betas for each date in the dataset, these betas are then used
as depended variables in order to estimate the effect of quantitative easing on the
yield curve.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0 5 10 15 20 25 30
Effe
ct o
f th
e cu
rvat
ure
bet
a
Years to maturity
Figure 6: Shape of the Curvature beta
Lambda 1 Lambda 2 Lambda 5 Lambda 10
13
Note: Figure 7 shows the results of the grid search for the best fitting lambda parameter. For every set of yield a regression was
run for all lambda’s between 0 and 6 (interval 0.1) for all days the R-squared was calculated. After this the avcrage R-squared was calculated for every lambda. The highest average lambda for the dataset containing the triple-A bonds is at a lambda of 2.2.
The largest average R-squared for the data containing all bonds is lies at 3.48 however this is not a clear a maximum as for the
triple-A bonds. Making the estimated results more sensitive for measurement errors.
The same technique is used by Fabozzi. Martellini and Priaulet (2005) and Diebold,
Rudebusch and Aruoba (2006) those authors find a lambda of 3 and 1,37 respectively.
This implies that the maximum of the curvature parameters lie at 2,5 for the first and
5,4 years for the later, for this paper the maximum level of the curvature beta lie 3,95
year for the triple-A bonds and at 4,22 for all bonds.
The regression
The estimated level, slope and curvature parameter are used as depended variables in
the final regression. This regression is used to determine the effect of the ECBs QE
program, the regression adjust for changes in macroeconomic variables that influence
the yield curve. Equation (8) shows the regression.
𝐴𝑡𝑖 = 𝛽1𝑡
𝑖 + 𝛽2𝑡𝑖 𝑄𝐸𝐷𝑈𝑀𝑀𝑌𝑡 + 𝛽3𝑡
𝑖 𝑴𝑡 + 𝝐𝒕𝒊 (8)
For
𝐴𝑡𝑖 = (𝐿𝑡, 𝑆𝑡, 𝐶𝑡)
The variable of interest is the QE-dummy that measures the effect of the QE policy on
the yield curve. The matrix M (variables stated below) contains all the control
variables that influence the effect QE has on the yield curve.
Consumer Price index
Producer Price Index
Harmonized index of consumer prices
Unemployment
Employment growth
Output gap
Manufacturing utilized capacity
Production growth rate
Balance of Payments
ECB policy rate
FED policy rate
Risk aversion as computed by ECB
M1, M2 and M3 growth rate
EURONIA
EURIBOR 3months
Oil price
Exchange rates € to $ and the £
Inflation Swap Rates 1, 2, 5, 10, 15,
20, 25 and 30 years
0.98
0.985
0.99
0.995
1
0.985
0.986
0.987
0.988
0.989
0.990
0.991
0.992
0.993
0 1 2 3 4 5 6
Ave
rage
R-s
quar
ed fo
r al
l bon
ds
Ave
rage
R-s
quar
ed fo
r tr
iple
-A b
onds
Lambda
Figure 7: the average R-squared for a range of lambdas
Triple-A (LHS)
All bonds (RHS)
14
The data section below explores the foundation, as found in the literature, for using
this data. Further descriptions of the variables can be found in appendix 5 and the
online appendix.
The different estimations of the level, slope and curvature are used in order to
check for robustness of the findings. For all regressions robust standard deviations are
used in order to prevent hetroscedasticity from influencing the results. In total four
datasets are used namely, triple-A bonds and all government bonds combined with
both estimation techniques described above make four different sets of levels, slopes
and curvature betas.
Section 4: Data
This section describes the data used to estimate the yield curve as well as the data
used for the final regression. The data that is used to estimate the nelson-siegel model
are the daily yield curve estimations as published by the ECB (2016c) for the triple-A
bonds a maturity vector containing 1, 5, 10, 20 and 30 year spot rate is used, while for
the NS-model containing all bonds a maturity vector that contains the 1, 2, 5, 10, and
14,75 year spot rates is used.
The ECB uses bond data that is provided by Euro MTS ltd and the ratings as
published by Fitch Ratings. The ECB selects all bonds issued by central European
governments. After that all bonds with special features are excluded, so that only
fixed coupon bonds with finite maturity and zero coupon bonds remain in dataset.
Only government bonds that are actively traded and have a maximum spread of three
basis point between the bid and ask price are used in the calculation of the yield
curve. In order to make sure that the bonds are traded in markets with sufficient
market debt only bonds with a remaining maturity between 3 months and 30 years are
included. The remaining bonds then are used to calculate the spot rates for that day.
After the bond selection an outlier removal mechanism is applied to remove all bonds
with a yield that deviates more than two standard deviations from the mean. (ECB,
2016d)
When all bonds are included the euro-area yield curve is a weighted average
of the individual euro-area countries yield curves, weighted by the amount of
outstanding government bonds. Because of the restriction imposed on the used bonds,
it is likely that for the later time period no Greek bonds are included because those are
not traded actively and deviate from the mean. For the triple-A rated bonds this is
mainly the German yield curve in combination with a little influence of the
Netherlands and an even smaller influence of Luxembourg. Those are at this moment
the only three euro-area countries with a triple-A rating according to Fitch.
Table 1, Descriptive statistics of the spot rate data for triple-A rated bonds
1 Year 5 Years 10 Years 20 Years 30 Years
Mean 1,344395 2,089701 2,841297 3,366456 3,395890
Median 0,741502 2,422745 3,305643 3,723839 3,786511
Min -0,559712 -0,386434 0,097205 0,419161 0,527714
Max 4,539553 4,730363 4,776331 4,984930 5,175029
Count 3010 3010 3010 3010 3010 Note: the spot rate data that is used is an average over all triple-A rated euro-zone countries at the day of measurement. Source
ECB, 2016c
15
Table 2, Descriptive statistics of the spot rate data for all bonds
1 Year 2 Years 5 Years 10 Years 14,75 Years
Mean 1,671534 1,918389 2,570918 3,371678 3,749281
Median 1,368967 1,889895 2,803460 3,763688 4,081454
Min -0,365623 -0,319417 0,004168 0,700843 1,012885
Max 4,559675 4,769203 4,810006 5,068630 5,437936
Count 3010 3010 3010 3010 3010
Note: the spot rate data that is used is an average over all euro-zone countries. Source ECB, 2016c
Table one and two show the descriptive statistics of the triple-A and all bond yield
data respectively. The dataset consist out of a large variety of data with the one year
spot rate varying form 4.5 percent in September 2008 to -0.56 and -0.37 in June 2016.
It also appears that there is almost no difference in maximum values while there are
larger differences in minimum values between the two datasets. This difference can
be explained by the changing composition of both groups. The maximum values were
reached at times when almost all Eurozone countries rated triple-A while the
minimum values were reached in a time in which this was not the case. Currently only
Germany, the Netherlands and Luxembourg have a triple-A status at the three largest
rating agencies. (Trading economics, 2016)
Variables determining the yield curve
According to Ang and Piazzesi (2003) 85% of the variation in the yield curve is
explained by macroeconomic variables. This is good news regarding the objective of
this paper, that is to identify the effect of quantitative easing. When the right control
variables are added it is possible to distillate the effect of QE out of the regression.
Ang and Piazzesi use two categories of macro variables namely real activity variables
and inflation variables. Unemployment, growth rate of employment and the growth
rate of industrial production are part of the first and the CPI and PPI are part of the
later. The real activity variables are added while an increase in economic activity
increases demand for capital, this increases interest rates over all maturities. The
inflation variables are added because higher inflation means a higher depreciation
pressure for which capital owners want to be compensated.
Diebold, Rudebusch and Aruoba (2006) use the level of inflation, the central
bank’s policy rate and manufacturing utilization capacity in order to determine the
state of the economy. Paccagnini (2016) adds consumption to these variables in order
to determine the state of the economy. Both papers argue that the state of the
economy determines the level shape and curvature of the yield curve. Bernhardsen
(2000) emphasizes the importance of the variables mentioned above but for another
reason. Bernhardsen point out that according to the no arbitrage condition the yield
curve takes in account the future stance of monetary policy and the variables used by
Diebold et.al. (2006) are indicators on this future stance. Bernhardsen further adds
real income growth and inflation expectations ass indicators for the future stance of
monetary policy. Additionally Bernhardsen uses the debt-to-GDP ratio because the
higher the debt-to-GDP ratio the larger the risk premium on government bonds will
be, this pushes up the yield curve.
16
Chadha and Waters (2014) use 31 different variables divided over five categories, of
which inflation, real activity and policy variables are also used by the authors above.
The new categories introduced by Chada and Waters (2014) are foreign variables and
financial market variables. The foreign category includes exchange rates and policy
rates from the FED and the BoE while the financial category consist out of the
LIBOR rate, VIX volatility, gold- and oil-prices. The authors don’t provide real
economic intuition for their choice of these variables but test post-hoc if the variables
are of any significance.
The used dataset consists out of daily data on all days at which the ECB
published their yield curve data. For variables for which no daily data is available an
log interpolation technique is used in order to estimate the missing data. While this
data is used to complete the data set, the estimated variable are not used in the
conclusion and no explanatory value is attached to them. Appendix two and three
shows the descriptive statistics and the correlation matrix respectively.
Table 3 shows the correlation matrix for the interest rates that are used in the
paper of Chada and Waters (2014). It appears that there is a large correlation between
the different interest rates that apply on the Euro. This can be expected by the
connection all interest rates have to the ECB policy rate. All the interest rates below
are short term riskless rates, the large similarity and the conection to the policy rate
explain the large correlation shown in table 3. The table also shows the high
correlation between the policy rate of the FED, ECB and the BoE this can be
explained by an increasing globalized financial system. Because of the correlation and
in regard of the multicollinearity issue only the ECB policy rate is included in the
regression.
Table 3: correlation matrix of the different interest rates
ECB FED BoE EURONIA EURIBOR
ECB 1
FED 0,7701 1
BoE 0,8900 0,8955 1
EURONIA 0,9738 0,8444 0,9454 1
EURIBOR 0,9899 0,7742 0,8977 0,9823 1 Note: as can be expected there is a large correlation between the different interest rates. Therefor in the rest of this paper only the
most important interest rate, with regard on the effect of QE, the ECB policy rate is used.
The same multicollinearity problem arises for the inflation expectations data as shown
in table 4. Therefor each regression only uses one variable containing inflation
expectations. The expectation with the best fit according the regression is used.
Table 4: correlation matrix of the different inflation expectation maturities
1Year 2Year 5Year 10Year 15Year 20Year 25Year
1Year 1
2Year 0,9692 1
5Year 0,8548 0,9400 1
10Year 0,7572 0,8632 0,9691 1
15Year 0,7470 0,8420 0,9443 0,9782 1
20Year 0,7611 0,8477 0,9374 0,9629 0,9868 1
25Year 0,7733 0,8506 0,9249 0,9438 0,9738 0,9884 1
30Year 0,7947 0,8580 0,9104 0,9193 0,9555 0,9761 0,9892 Note: table 4 shows the correlation between the different time spans of inflation expectations. The largest correlation between the
different expectation variables is between those for who the maturity is close togheter. Because the variables for a large part contain the same information only the one with the best fit is included in the regression.
17
In an attempt to prevent a suspicion of data mining and because of the large
correlation between the variables CPI, PPI and HICP as well as between the variables
employment growth and unemployment and the variables utilized manufacturing
capacity, output gap and production growth rate, these variables are pooled in a
standardized variable. Respectively standardize inflation, standardized employment
and standardized output. The method used in order to pool these variables to one
single variable can be found in appendix 5.2.
Section 5: Results
This section describes the results from the regression in equation (8). Before the
regression output can be interpreted it is important to realize what the estimated betas
explain regarding the level, slope and curvature of the yield curve. The level is the
long term level towards which the yield curve converses and therefore the easiest to
interpret, when the QE variable lowers the level beta this means that the long term
interest rates decreases. The shape of the slope and curvature are determined by the
shape parameter lambda, figure 8 shows the shape of the shape and slope when the
lambda is fixed at the level calculated above.
Note: Figure 8 shows the shape of the slope and curvature beta for he estimated values of lambda. The both curves do not differ
much. The largest difference is between the both slope betas in the medium run.
The lines shown in figure 8 are flipped over the x-axes by making them
negative. This is because the slope and curvature are expected to have negative values
and therefor are flipped over the x-axes. While the shape of both curves are fixed over
time the regression only tests for a movement in the line.
Table 5 shows the regression output for the level parameter estimated with all
bond data using the NS-model. The first row shows the effect of QE on the level beta
and shows a significant decrease due to the QE policy, of about 2.5%. Unfortunately
for the ECB who would be happy with such a results, other variables needs to be
included that also influence the yield curve parameter and the interaction between the
parameter and the QE policy. First in regression (2) the policy rate is added to the
regression. The policy rate needs to be included fot two reasons, first the policy rate
determines at the short term the level of the interest rate and second in line with the
forward looking nature of the yield curve the curve takes in account all future levels
of the policy rate. In order to adjust for the stance of monetary policy more precisely
the growth rate of the monetary aggregate M1 is added. According to the quantity
theory of money Lucas (1980) a change in the growth rate of M1 increases the rate of
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0 5 10 15 20 25 30
Effe
ct o
n t
he
yie
ld c
urv
e
Years till maturity
Figure 8: The shape of the slope and curvature parameters
Slope All bonds
Curvature All bonds
Slope tripple-A bonds
Curvature tripple-A bonds
18
inflation by the same percentage. This gives to reasons for including the M1 growth
rate. For starters the M1 growth rate is expected to change long term inflation and
thereby it influences the longer term of the yield curve. Second as mentioned above it
gives a better view on the stance of monetary policy.
Regression (4) adds the standardized variables for inflation, employment and
production in order to correct for the stance of the economy, adding all these variables
lowers the effect of QE to a decrease of -0.845 of the level parameter. Finally
regression (5) corrects for the changed risk aversion. Regression output column (4)
and (5) combined show that the estimated effect of the QE policy on the level beta
lies between 0.845 and 0.786 for this dataset. Further on in this section the effect of
the QE-policy on the slope and curvature is assessed after that figure 9 and 10 give
more insight in the movement of the entire yield curve.
Table 5 (β1) – Regression results for all bonds
(β1) (1) (β1) (2) (β1) (3) (β1) (4) (β1) (5)
QE dummy -1.943*** -2.080*** -1.829*** -0.641*** -0.769***
(0.0293) (0.0340) (0.0381) (0.0389) (0.0457)
ECB policy rate
-0.0796*** -0.0928*** 0.0392*** -0.00739
(0.00910) (0.00839) (0.00790) (0.00941)
M1 growth rate
-0.0554*** -0.0475*** -0.0437***
(0.00211) (0.00162) (0.00160)
Std. inflation
0.302***
(0.0108) (0.0118)
Std. employment
-0.535***
(0.00786) (0.00997)
Std. production
(0.00654)
Risk aversion
0.0313***
(0.00480)
Constant 5.174*** 5.315*** 5.740*** 5.333*** 5.395***
(0.0115) (0.0210) (0.0236) (0.0179) (0.0205)
N 3010 3010 3010 3010 3008
adj. R-sq 0.532 0.544 0.609 0.818 0.821 Note: Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001, The table shows the effect that the
independent variables have on the level beta (β1) all bonds NS-model. All variables but the QE dummy are
control variables and no explanatory value can be attached to the estimated betas. The description of the
variables can be found in appendix 5.
The signs of the standardized employment and the standardized production are
different as expected. For the unemployment variable this means that an increase in
unemployment or a decrease in the employment growth increases the long-term
interest rate were a decrease is expected. Lower employment growth or increased
unemployment equals lower economic activity and therefor a decrease in the interest
rate is expected. The same applies for the standardized production variable for which
the output gap, the utilized production capacity and the industrial production growth
are the base variables. Appendix 7 contains a regression table that shows the different
base variables for the standardized variables. The table shows a consequent picture in
which higher activity and a lower interest rate go hand in hand. Therewith it is not
said that higher activity leads to a lower interest rate but for this dataset this is the
case regardless the chosen variables and more important the estimated effect of QE is
similar among the different base variables.
19
The variables proposed by Chada and Waters (2014) are not used in the
regression because of multicollinearity problems. As described above are most of the
interest rates highly correlated. Appendix 8 contains all the VIF values of the reported
regressions. The variables Euro/Dollar exchange rate and the oil price are used as
robustness test variable further on the in this section. Euro/Dollar exchange rate is
added because the US is the largest trade partner of Eurozone. (ECB, 2016f)
Table 6 (β2) - Regression results for all bonds
(β2) (1) (β2) (2) (β2) (3) (β2) (4) (β2) (5)
QE dummy 0.179*** 2.200*** 0.161*** 0.0350 0.608***
(0.0446) (0.0417) (0.0466) (0.0475) (0.0546)
ECB policy rate
1.170*** 0.731*** 0.709*** 0.885***
(0.0145) (0.0130) (0.0122) (0.0114)
Std. inflation
-0.269*** -0.140***
(0.0133) (0.0133) (0.0151)
Std. employment
0.968*** 0.967***
(0.0128) (0.0114) (0.0140)
Std. production
0.162*** 0.112***
(0.0131) (0.0129) (0.0100)
M1 growth rate
0.0565***
(0.00220)
Risk aversion
-0.130***
(0.00528)
Constant -3.576*** -5.647*** -4.720*** -5.115*** -5.029***
(0.0336) (0.0301) (0.0226) (0.0223) (0.0244)
N 3010 3010 3010 3010 3008
adj. R-sq 0.001 0.712 0.899 0.915 0.916 Note: Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001, The table shows the effect that the
independent variables have on the level beta (β2) all bonds NS-model . All variables but the QE dummy are
control variables and no explanatory value can be attached to the estimated betas. The description of the
variables can be found in appendix 5.
Table 6 shows the regression results with depended variable B2. The same intuition is
used as for B1 however, for B2 the standardized production variable is no longer
significant. This might be because production is stickier than inflation and
employment, therefor it has no influence on the effect that QE has on the short-term
interest rate. This final added regression does not change the QE variable by much..
Also when regressions that are not reported are estimated containing oil prices or the
Euro/Pound exchange rate, the QE beta remain close to 0.3. While this is good news
from an econometrics point of view this is not from a policy point of view. If 0.3 is
the true value of the beta, quantitative easing increases the short-term interest rate and
thereby has the opposite effect than was intended by the ECB. However, the slightly
positive value can be misleading due to the monopoly that the ECB has over the
short-term interest rate. The ECB decreased the interest rate from 4.25% in October
2008 to 1% in May 2009. This decreased the short-term side of the interest rate
already even before the QE program was in place. Since the slope parameter is most
active on the short term, this affects the estimated effect of the QE policy. It is also
important to take in account the effect on the level, slope and curvature beta
combined.
20
Table 7 (β3) - Regression results for all bonds
(β3) (1) (β3 (2) (β3 (3) (β3 (4) (β3 (5)
QE dummy -2.452*** -1.912*** 0.394*** 0.202* 0.369***
(0.0452) (0.0688) (0.101) (0.0924) (0.108)
ECB policy rate
0.313*** 0.817*** 0.785*** 0.841***
(0.0259) (0.0348) (0.0339) (0.0364)
Standardized inflation
0.349*** 0.547*** 0.559***
(0.0410) (0.0377) (0.0378)
Standardized employment
-1.053*** -1.055***
(0.0279) (0.0251) (0.0288)
Standardized production
-0.286*** -0.363***
(0.0265) (0.0271) (0.0273)
M1 growth rate
0.0864*** 0.0796***
(0.00556) (0.00608)
Risk aversion
-0.0453**
(0.0140)
Constant -1.335*** -1.888*** -2.949*** -3.553*** -3.613***
(0.0311) (0.0614) (0.0651) (0.0804) (0.0805)
N 3010 3010 3010 3010 3008
adj. R-sq 0.211 0.258 0.472 0.506 0.507 Note: Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001, The table shows the effect that the
independent variables have on the level beta (β3) all bonds NS-model. All variables but the QE dummy are
control variables and no explanatory value can be attached to the estimated betas. The description of the
variables can be found in appendix 5.
Table 7 states the regression output for the curvature beta In order to do so an
“average”1 yield curve is calculated using the average value of the variables used in
the regressions in table 5, 6 and 7. Figure 9 and 10 show these “average” yield curves,
figure 9 shows the estimated yield curves without the risk aversion variable while
figure 10 shows the curves with the risk aversion variable included.
Note: Figure 9 and 10 show the “average” yield curve with and without the QE policy. The dotted lines show the difference
between both yield curves. The increasing shape of the difference curve proves the flattening effect that QE has on the yield curve.
Both figures also show a line that describes the difference between both curves. This
is to test if the ECB succeeded in her objective to flatten the yield curve. When the
risk aversion variable is included it seems that the ECB was successful in flattening
the yield curve, however, when the risk aversion variable is not included this is not
the case. In a model without risk aversion, the difference between both yield curves
decreases over time so the yield curve becomes steeper and not flatter only for 30 year
maturity bonds the difference is larger than for short term bonds.
1 The average of all the included variables are calculated and used to plot the yield curve.
21
Robustness
In order to prove the robustness of the findings this section uses the variables euro-
dollar exchange rate and the oil price to show the sensitivity of the QE variable.
Table 8 – Robustness test of the estimated effect of QE, all bonds
β1 (1) β1 (2) β2 (3) β2 (4) β3 (5) β3 (6)
QE dummy -0.678*** -0.704*** 0.460*** 0.522*** 0.103 0.0652
(0.0360) (0.0375) (0.0532) (0.0526) (0.0851) (0.0853)
ECB policy rate 0.491*** 0.276*** 0.454*** 0.729*** 0.920*** 0.607***
(0.0109) (0.0126) (0.0132) (0.0171) (0.0366) (0.0460)
Std. inflation 0.052*** 0.0222***
0.035*** -0.007
(0.00187) (0.00201)
(0.00711) (0.00733)
Std. employment 0.198*** 0.381*** -0.308*** -0.536*** 0.069 0.336***
(0.0110) (0.0120) (0.0153) (0.0146) (0.0356) (0.0421)
Std. production -0.404*** -0.387*** 1.007*** 0.933*** -0.887*** -0.861***
(0.0102) (0.0104) (0.0121) (0.0136) (0.0324) (0.0309)
M1 growth rate -0.0265** -0.0265** 0.136*** 0.146***
(0.00883) (0.00865) (0.0118) (0.0109)
Risk aversion 0.00139 -0.017*** -0.097*** -0.099*** -0.0172 -0.044***
(0.00428) (0.00398) (0.00528) (0.00478) (0.0131) (0.0122)
€/$ exchange 1.955*** 3.952*** 0.499*** -2.284*** -2.846*** 0.0664
(0.112) (0.112) (0.115) (0.131) (0.416) (0.488)
Oil price
-0.015***
0.0142***
-0.021***
(0.00054)
(0.00053)
(0.0016)
Constant 0.181 -0.733*** -4.060*** -1.956*** -0.281 -1.614**
(0.151) (0.129) (0.153) (0.142) (0.550) (0.554)
N 3008 3008 3008 3008 3008 3008
adj. R-sq 0.878 0.913 0.892 0.913 0.437 0.476 Note: Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001, The table checks for robustness of the QE-dummy
by adding the Exchange rate and the oil dollar price (β1,2 and 3) all bonds NS-model . All variables but the QE dummy
are control variables and no explanatory value can be attached to the estimated betas. The description of the variables can
be found in appendix 5.
Table 8 shows the estimated parameters when those variables are included. The
added variables give an insight in the robustness of the model, the estimated betas for
QE are similar to the estimated column (5) betas for QE in table 5, 6 and 7 column
(5). This proves that the model is robust and can be assumed to estimate the value of
the QE beta with a fair degree of certainty.
Different data
The section above explored the effect of QE on the yield curve parameters using the
NS-model and Euro-area spot rate data containing bonds of all ratings. In this section
the data on triple-A bonds is used as well as the estimated level, slope and curvature
parameters that are estimated using the model that adjusts for multicollinearity. In this
section only the regressions from column (4) and (5) are reported because the section
above provides sufficient evidence on the validity of the model. Appendix 9 reports
the robustness test using the same variables as above.
22
Table 9 - Regression results for triple-A rated bonds
Table 9 β1 (1) β1 (2) β2 (3) β2 (4) β3 (5) β3 (6)
QE dummy -0.843*** -0.800*** 0.0436 0.400*** 0.277*** 0.243**
(0.0321) (0.0349) (0.0418) (0.0483) (0.0750) (0.0833)
ECB policy rate 0.576*** 0.588*** 0.353*** 0.472*** 0.769*** 0.760***
(0.00947) (0.00758) (0.0138) (0.0132) (0.0278) (0.0270)
Std. inflation 0.152*** 0.150*** -0.337*** -0.307*** 0.124*** 0.125***
(0.0115) (0.0117) (0.0131) (0.0154) (0.0329) (0.0329)
Std. employment -0.492*** -0.505*** 1.081*** 0.986*** -0.744*** -0.736***
(0.00791) (0.00855) (0.0101) (0.0124) (0.0203) (0.0217)
Std. production -0.00401
0.207*** 0.137***
(0.00816)
(0.0143) (0.0121)
M1 growth rate 0.028*** 0.0253*** 0.0118***
0.0712*** 0.073***
(0.00151) (0.00147) (0.00197)
(0.00463) (0.00505)
Risk aversion
-0.0125**
-0.0961***
0.00905
(0.00441)
(0.00521)
(0.0130)
Constant 2.813*** 2.808*** -3.294*** -3.436*** -4.073*** -4.068***
(0.0197) (0.0179) (0.0233) (0.0244) (0.0599) (0.0588)
N 3010 3008 3010 3008 3010 3008
adj. R-sq 0.867 0.866 0.879 0.891 0.426 0.425 Note: Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001, The table shows the effect that the independent
variables have on the level beta (β1, 2 and 3)triple-A bonds NS-model . All variables but the QE dummy are control
variables and no explanatory value can be attached to the estimated betas. The description of the variables can be found in
appendix 5.
Table 9 shows the regression output for the estimated NS-parameters using the
dataset containing triple-A bond data. The results are similar to the output for the data
containing all bonds. The largest difference is the significance of third beta parameter,
this parameter is insignificant for the previous data but is significant when the triple-A
bonds are used.
Note: Figure 11 and 12 the “average” yield curve with and without the QE policy. The dotted lines show the difference between
both yield curves. The increasing shape of the difference curve proves the flattening effect that QE has on the yield curve.
Figure 11 and 12 show the effect that QE has on the yield curve. The changes in both
yield curves are larger for the triple-A bonds than for all bonds in figure 9 and 10. For
these types of bonds the QE policy has a flattening effect on the yield curve. These
larger effects can be explained by taking a look at the targeted bonds of the QE
program. Before June 2016 the ECB only bought government bonds that had a triple-
A rating and thereby they targeted the yield curve for triple-A bonds directly. The
23
results in the figures 9 and 10 are smaller because they also consist out of non-
targeted bonds that are issued by Euro-area peripheral countries. While the
differences are small, the largest difference comes from the regression without risk
aversion for a ten-year maturity and is only about 0.3%. The asymmetric effect over
the euro area can create new imbalances in the currency area, that make it harder for
the ECB to reach her targets in a currency area without a fiscal transfer system. While
a difference of 0.3% appears small it is important to keep in mind that this is only a
part of the real difference. Considering that the dataset containing all bonds also
includes triple-A rated bonds making the 0.3% an underestimation of the real
difference in effect between targeted and peripheral countries.
The area inside the little dashed box is shown in appendix 6 in order to assess
the 95% confidence interval of both yield curves. Because of the small values of the
standard errors those confidence intervals are not visible in figure 11.
Inflation expectations
The signaling channel described in the literature overview assumes forward looking
investors that take the future stance of monetary policy into account as well as the
future level of inflation. The future level of inflation can also help to predict the future
stance of monetary policy. When the central bank conducts monetary policy via a
Taylor rule (Taylor, 1993) an investor can estimate the future stance of monetary
policy using his or her expectations on future inflation. Chun (2011) shows evidence
for the sensitivity of the yield curve to changes in expectations on both future
inflation as well as the future output level. By a lack of reliable data on expectations
on the future output level this section only assesses the effect of inflation
expectations. Because of the lack of reliable inflation expectations data from before
2008, this section uses employs a dataset that contains data from July 22 2008.
The section above already proves that the different datasets give similar results
regarding the effect of QE. In order to prevent an information overload this section
only shows the effect from inflation expectation on the effectiveness of QE for the
estimated NS-parameters for all bonds data. The regression output table can be found
in appendix 10. The variable M1 growth is omitted because of multicollinearity
issues. Figure 13 and 14 show the effects of QE without and with inflation
expectations.
Note: Figure 18 and 19 show the “average” yield curve with and without the QE policy. The dotted lines show the difference
between both yield curves. The increasing shape of the difference curve proves the flattening effect that QE has on the yield curve.
24
The biggest difference between graphs 13 and 14 in comparison with other similar
graphs above is the lack in impact on the short run from the QE policy. This can be
explained by the employed dataset, where the sections above employs a datasets that
runs from 2004-2016 the dataset used to assess the effect of inflation expectations
only runs from 2008-2016. During this period ECB interest rates where equal or
below 1%. Considering the monopoly power that the ECB has over the short-term
interest rate it seems logical that the lower end of the yield curve did not change much
over this sample period.
The effect that QE has on the yield curve does not change much when the
regression incorporates an inflation expectation variable, the difference is about 0.1%
over each maturity. The lack of impact from the inflation expectation can be
explained by the way the ECB conducts monetary policy. The ECB actively targets
inflation expectations, therefore, the inflation expectation variable is not independent
from the ECB policy rate as well as the QE dummy. This relation had an effect on the
influence of the inflation expectations variable.
25
Section 6: Conclusion
Acknowledgments and future research
26
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Appendix
1. Average R-squared over a series of lambdas.
For Triple-A rated bonds Lambda R-squard Lambda R-squared Lambda R-squared
0,1 0,985672763 2,1 0,992163074 4,1 0,989460322
0,2 0,985672763 2,2 0,992184084 4,2 0,989342996
0,3 0,985673033 2,3 0,992157516 4,3 0,98923377
0,4 0,98567996 2,4 0,992091094 4,4 0,989132481
0,5 0,985722791 2,5 0,991992069 4,5 0,989038913
0,6 0,98585034 2,6 0,991867072 4,6 0,988952807
0,7 0,986102262 2,7 0,991722039 4,7 0,988873872
0,8 0,986490241 2,8 0,991562191 4,8 0,988801794
0,9 0,986998768 2,9 0,991392052 4,9 0,988736246
1 0,987595213 3 0,991215483 5 0,98867689
1,1 0,988240363 3,1 0,991035735 5,1 0,988623383
1,2 0,98889606 3,2 0,990855514 5,2 0,988575385
1,3 0,98952964 3,3 0,990677035 5,3 0,988532558
1,4 0,990115877 3,4 0,990502084 5,4 0,98849457
1,5 0,990637274 3,5 0,990332077 5,5 0,988461098
1,6 0,99108339 3,6 0,990168109 5,6 0,988431828
1,7 0,991449698 3,7 0,990011002 5,7 0,988406456
1,8 0,991736293 3,8 0,989861349 5,8 0,988384694
1,9 0,991946652 3,9 0,989719549 5,9 0,988366262
2 0,992086533 4 0,989585838 6 0,988350895
For all bonds Lambda R-squared Lambda R-squared Lambda R-squared
0,1 0,88585995 2,1 0,991874718 4,1 0,994670625
0,2 0,886931886 2,2 0,992514882 4,2 0,994634148
0,3 0,891735002 2,3 0,993031563 4,3 0,994595681
0,4 0,900027472 2,4 0,993447422 4,4 0,99455573
0,5 0,910419126 2,5 0,99378071 4,5 0,99451472
0,6 0,9216786 2,6 0,994046202 4,6 0,994473002
0,7 0,932845406 2,7 0,994255911 4,7 0,99443087
0,8 0,943242058 2,8 0,994419646 4,8 0,994388566
0,9 0,952472092 2,9 0,994545448 4,9 0,994346289
1 0,960380423 3 0,994639928 5 0,994304204
1,1 0,96698558 3,1 0,994708539 5,1 0,994262446
1,2 0,9724079 3,2 0,994755791 5,2 0,994221124
1,3 0,976811672 3,3 0,99478542 5,3 0,994180325
1,4 0,980367269 3,4 0,994800532 5,4 0,994140119
1,5 0,983230883 3,5 0,994803707 5,5 0,994100561
1,6 0,985536365 3,6 0,994797097 5,6 0,994061693
1,7 0,987394045 3,7 0,994782494 5,7 0,994023547
1,8 0,988892867 3,8 0,994761394 5,8 0,993986145
1,9 0,990103713 3,9 0,994735049 5,9 0,993949503
2 0,991082805 4 0,994704501 6 0,993913628
30
Appendix 2
Equation (A2.1) and (A2.2) are equal to equation (1) and (2)
𝑓(𝜏) = 𝛽
1+ 𝛽
2(𝑒
−𝜏
𝜆1) +𝛽3
(𝜏
𝜆1
𝑒−
𝜏
𝜆1)
(A2.1)
𝑦(𝜏) =
1
𝜏∫ 𝑓(𝑥)𝑑𝑥
𝜏
0
(A2.2)
In order to find the NS-model equation (A2.3) needs to be solved.
𝑦(𝜏) =
1
𝜏∫ 𝛽
1+ 𝛽
2(𝑒
−𝜏
𝜆1) +𝛽3
(𝜏
𝜆1
𝑒−
𝜏
𝜆1) 𝑑𝑥
𝜏
0
(A2.3)
𝑦(𝜏) =
1
𝜏[ 𝛽
1𝜏 + 𝛽
2(−𝜆𝑒
−𝜏
𝜆) + 𝛽3
(−𝜆𝑒−
𝜏
𝜆(𝜏 + 𝜆))}0
𝜏
(A2.4)
𝑦(𝜏) =
1
𝜏{[ 𝛽
1𝜏 + 𝛽
2(−𝜆𝑒
−𝜏
𝜆) + 𝛽3
(−𝜆𝑒−
𝜏
𝜆(𝜏 + 𝜆))] − [𝛽2(−𝜆) + 𝛽
3(−𝜆)]}
(A2.5)
𝑦(𝜏) =
1
𝜏[ 𝛽
1𝜏 + 𝛽
2(𝜆 − 𝜆𝑒
−𝜏
𝜆) + 𝛽3
(𝜆 − 𝜆𝑒−
𝜏
𝜆(𝜏 + 𝜆))]
(A2.6)
𝑦(𝜏) = 𝛽
1+ 𝛽
2(𝜆
𝜏+
𝜆
𝜏𝑒
−𝜏
𝜆)+𝛽3(𝜆
𝜏+
𝜆
𝜏𝑒
−𝜏
𝜆 − 𝑒−
𝜏
𝜆)
(A2.7)
𝑦(𝜏) = 𝛽1
+ 𝛽2
(1 + 𝑒
−𝜏
𝜆
𝜏
𝜆
)+𝛽3
(1 − 𝑒
𝜏
𝜆
𝜏
𝜆
− 𝑒−
𝜏
𝜆)
(A2.8)
Where equation (A2.8) equals the equation (3).
31
Appendix 3 CPI PPI HICP Standardized
Inflation
Unemployment Employment
Growth Standardized
Employment
PPI 0.936807 1
HICP 0.691805 0.479109 1
Standardized
Inflation
0.995105 0.952875 0.702443 1
Unemployment -0.21104 -0.20587 -0.49127 -0.26403 1
Employment
Growth
-0.0063 0.147372 -0.05618 0.043192 -0.1094 1
Standardized
Employment
-0.04312 0.112054 -0.14206 -0.00268 0.064544 0.984864 1
Output Gap 0.074529 -0.09658 0.481818 0.075693 -0.67053 -0.4497 -0.56839
Utalized
Capacity
0.28358 0.456345 -0.07222 0.313612 0.119397 0.859826 0.884034
Production
Growth
0.2188 0.45455 -0.48348 0.216986 0.28832 0.225547 0.276712
Standardized
Production
0.325431 0.482045 -0.21952 0.324202 -0.16401 -0.06839 -0.09726
ECB POLICY 0.607034 0.514524 0.784479 0.63771 -0.76811 -0.04794 -0.18207
FED POLICY 0.342782 0.313591 0.424251 0.365926 -0.62064 0.32455 0.217605
BoE POLICY 0.368648 0.337753 0.54048 0.406159 -0.69098 0.262322 0.142865
QE Dummy -0.51391 -0.41319 -0.409 -0.49386 0.005093 0.596789 0.600028
M1 Growth -0.81506 -0.78285 -0.58 -0.82064 0.096617 -0.14606 -0.12979
M2 Growth -0.13494 -0.19892 0.378805 -0.09158 -0.53634 0.42495 0.3331
M3 GROWTH -0.03246 -0.0867 0.395008 0.008364 -0.46276 0.592804 0.514446
BOP -0.58979 -0.49665 -0.67008 -0.60478 0.693157 0.409691 0.532174
Risk aversion 0.26868 0.24151 0.556313 0.318264 -0.68291 0.152001 0.033517
EURONIA 0.539567 0.506671 0.654251 0.578861 -0.76288 0.115874 -0.0167
EURIBOR 0.571556 0.51929 0.724075 0.611271 -0.80095 0.068459 -0.07094
LIBOR 0.553795 0.504342 0.715337 0.594751 -0.80935 0.080635 -0.06018
DOLLAR EUR 0.418648 0.317628 0.371366 0.400885 -0.21584 -0.5763 -0.61621
POUND EUR 0.299514 0.18154 0.363421 0.284208 -0.2191 -0.6757 -0.71657
YENN EUR -0.54369 -0.48049 -0.38034 -0.5309 -0.09115 0.152789 0.137497
YUAN EUR 0.370517 0.268555 0.444763 0.367259 -0.51847 -0.59617 -0.68893
OIL PRICE 0.646125 0.582104 0.246381 0.6047 0.397183 -0.25867 -0.19043
Inflation 1 Year 0.789982 0.694238 0.473578 0.758272 -0.05336 -0.31602 -0.32657
Inflation 2 Years 0.771804 0.649218 0.545141 0.742176 -0.1734 -0.41335 -0.44521
Inflation 5 Years 0.684263 0.525819 0.616718 0.659153 -0.28728 -0.53832 -0.59053
Inflation 10
Years
0.620983 0.442386 0.633495 0.596124 -0.30296 -0.62316 -0.67845
Inflation 15
Years
0.608422 0.42481 0.583218 0.57532 -0.18465 -0.64114 -0.67586
Inflation 20
Years
0.615594 0.442838 0.543783 0.580115 -0.13864 -0.63527 -0.66195
Inflation 25
Years
0.617552 0.4564 0.496832 0.579301 -0.08988 -0.63491 -0.65309
Inflation 30
Years
0.634612 0.48271 0.463369 0.593442 -0.02598 -0.62741 -0.63441
Output Gap Utilized
Capacity
Production
Growth
Standardized
Production
ECB
POLICY
FED
POLICY
BoE
POLICY
QE Dummy M1 Growth M2 Growth M3
GROWTH
Risk aversion EURONIA
Output Gap 1
Utilized Capacity -0.63249 1
Production Growth -0.57709 0.551044 1
Standardized
Production
0.063613 0.188721 0.778312 1
ECB POLICY 0.650707 -0.06468 -0.3403 0.085422 1
FED POLICY 0.383929 0.270373 -0.10369 0.169876 0.730087 1
BoE POLICY 0.487595 0.197508 -0.25027 0.070511 0.86131 0.91753 1
QE Dummy -0.26388 0.365582 0.165875 0.000397 -0.42901 -0.00101 -0.12356 1
M1 Growth 0.108965 -0.39066 -0.08236 -0.0178 -0.50974 -0.28897 -0.33817 0.608199 1
M2 Growth 0.382033 0.089527 -0.56405 -0.39429 0.472769 0.600794 0.683637 0.365891 0.146638 1
M3 GROWTH 0.24209 0.293649 -0.45055 -0.36286 0.43267 0.639927 0.681651 0.416367 0.022927 0.962876 1
Risk aversion 0.476764 0.003565 -0.34368 -0.05247 0.691815 0.390413 0.571437 -0.08665 -0.23207 0.494781 0.437162 1
EURONIA 0.527928 0.100156 -0.23278 0.12265 0.945319 0.827943 0.916589 -0.33239 -0.50727 0.507821 0.487638 0.616398 1
EURIBOR 0.57481 0.039251 -0.28597 0.093618 0.974576 0.770793 0.88514 -0.37362 -0.52915 0.481141 0.452716 0.691352 0.975493
LIBOR 0.576786 0.041093 -0.29257 0.087095 0.971346 0.775256 0.88951 -0.3573 -0.51539 0.495865 0.465813 0.695626 0.976322
DOLLAR EUR 0.35782 -0.40284 -0.18442 0.049194 0.481696 0.150401 0.204202 -0.81225 -0.50266 -0.28968 -0.36342 0.042574 0.45392
POUND EUR 0.442332 -0.5781 -0.28745 -0.01205 0.384246 -0.14979 -0.01974 -0.73751 -0.349 -0.29586 -0.42033 0.212026 0.237092
OIL PRICE -0.24511 0.138603 0.245436 0.111341 0.100271 -0.03068 -0.06575 -0.65491 -0.69828 -0.53625 -0.44534 -0.31927 0.098348
Inflation 1 Year 0.083184 -0.02666 0.211077 0.32175 0.335395 0.107436 0.043125 -0.50704 -0.57426 -0.37361 -0.31801 -0.09339 0.260056
Inflation 2 Years 0.247352 -0.16566 0.079687 0.287334 0.44504 0.160847 0.118301 -0.56569 -0.54169 -0.30027 -0.28401 -0.00782 0.353855
Inflation 5 Years 0.456255 -0.3568 -0.15295 0.163578 0.567794 0.187951 0.215059 -0.65701 -0.48938 -0.18417 -0.22455 0.107619 0.459425
Inflation 10 Years 0.556385 -0.46346 -0.27238 0.094541 0.613642 0.18284 0.257279 -0.73198 -0.4595 -0.13614 -0.20822 0.162813 0.485582
Inflation 15 Years 0.496444 -0.4388 -0.24596 0.080705 0.553793 0.158416 0.229854 -0.75958 -0.46762 -0.18218 -0.24589 0.082257 0.434542
Inflation 20 Years 0.455235 -0.40771 -0.18426 0.124413 0.515715 0.148656 0.204116 -0.76358 -0.47467 -0.23896 -0.29011 0.032309 0.405175
Inflation 25 Years 0.406856 -0.38015 -0.11747 0.168787 0.471531 0.13353 0.172052 -0.7572 -0.469 -0.28936 -0.33231 -0.02008 0.369382
Inflation 30 Years 0.340719 -0.34413 -0.05291 0.196802 0.41982 0.095911 0.121574 -0.75099 -0.47981 -0.34383 -0.37408 -0.07094 0.318415
33
EURIBOR LIBOR DOLLAR
EUR
POUND
EUR
OIL
PRICE
Inflation 1
Year
Inflation 2
Years
Inflation 5
Years
Inflation
10 Years
Inflation
15 Years
Inflation
20 Years
Inflation
25 Years
EURIBOR 0.999635 1
LIBOR 0.468073 0.457888 1
DOLLAR EUR 0.3034 0.292677 0.781003 1
POUND EUR 0.060585 0.078009 0.037554 -0.23073
YENN EUR 0.600866 0.593975 0.922012 0.794951
YUAN EUR 0.089438 0.070321 0.595883 0.302122 1
OIL PRICE 0.29507 0.276974 0.546403 0.394528 0.729541 1
Inflation 1 Year 0.397534 0.380455 0.641753 0.495889 0.678474 0.969246 1
Inflation 2
Years
0.510234 0.495429 0.765006 0.634289 0.599521 0.855079 0.94004 1
Inflation 5
Years
0.542876 0.528662 0.800343 0.701517 0.554084 0.757588 0.863342 0.969117 1
Inflation 10
Years
0.480346 0.464874 0.796716 0.669386 0.626689 0.747425 0.842147 0.944193 0.978111 1
Inflation 15
Years
0.447649 0.431458 0.789236 0.633713 0.66679 0.761604 0.847869 0.937299 0.962723 0.986754 1
Inflation 20
Years
0.406795 0.389837 0.775596 0.604045 0.69722 0.773772 0.850808 0.924806 0.943634 0.973713 0.988398 1
Inflation 25
Years
0.353134 0.334948 0.74965 0.579687 0.732338 0.795252 0.858196 0.910205 0.918991 0.955321 0.975991 0.98916
Appendix 4
CPI PPI HICP
Standardized
Inflation Unemployment
Employment
Growth
Standardized
Employment
Mean 1.65628 1.66191 1.32393 0.00000 9.85970 0.38834 0.00000
Median 1.90000 2.55441 1.36233 0.36745 10.10000 0.64665 0.30553
Minimum -0.60000 -8.14949 0.62577 -2.07542 7.20000 -2.23211 -2.65477
Maximum 4.00000 8.89510 2.02860 2.03217 12.10000 1.99944 1.28378
Skewness -0.20612 -0.50045 -0.02412 -0.29121 -0.23741 -0.49997 -0.87406
Kurtosis 2.14024 2.39261 1.81207 2.00112 1.91729 2.50912 3.18402
Count 3010 3010 3010 3010 3010 3010 3010
Output Gap
Utilized
Capacity
Production
Growth
Standardized
Production
ECB
POLICY
FED
POLICY
BoE
POLICY
Mean -0.17732 80.14210 0.37198 0.00000 1.56874 1.51944 2.14045
Median -0.84753 81.12376 1.38806 -0.11544 1.00000 0.25000 0.50000
Minimum -2.86100 69.50000 -21.53364 -2.75859 0.00000 0.25000 0.50000
Maximum 3.10700 85.10000 9.27343 2.52300 4.25000 5.25000 5.75000
Skewness 0.42891 -1.32138 -1.79501 0.16639 0.70721 1.07101 0.58947
Kurtosis 1.56675 4.57377 6.61541 2.95927 2.28918 2.49769 1.42842
Count 3010 3010 3010 3010 3010 3010 3010
QE
Dummy M1 Growth M2 Growth M3 Growth
Risk
aversion EURONIA EURIBOR
Mean 0.11661 7.83628 5.75721 4.88872 -0.10999 1.25395 1.63340
Median 0.00000 7.00673 5.46439 4.51914 -0.59000 0.40730 1.05700
Minimum 0.00000 0.22843 1.29433 -0.40000 -3.27000 -0.60000 -0.26400
Maximum 1.00000 17.84141 11.79348 12.50000 10.74000 4.46190 5.39300
Skewness 2.38904 0.45409 0.27321 0.43584 1.61570 0.75500 0.78871
Kurtosis 6.70750 2.49205 1.67321 2.00796 6.37121 2.06437 2.36941
Count 3010 3010 3010 3010 3008 3010 3010
LIBOR
DOLLAR
EUR
POUND
EUR
OIL
PRICE
Inflation 1
Year
Inflation 2
Years
Mean 1.60542 1.31026 0.78393 77.40917 1.20238 1.31721
Median 1.00000 1.31330 0.79508 73.45000 1.25900 1.42500
Minimum -0.28186 1.05215 0.65565 22.48000 -0.75750 -0.15250
Maximum 5.39125 1.59785 0.98030 140.73000 2.99000 2.79000
Skewness 0.78896 -0.05141 -0.08356 0.07133 -0.27119 -0.25569
Kurtosis 2.34676 2.98954 1.67651 1.74842 2.60128 2.40188
Count 3010 3010 3010 3010 2017 2017
Inflation 5
Years
Inflation 10
Years
Inflation 15
Years
Inflation 20
Years
Inflation 25
Years
Inflation 30
Years
Mean 1.58042 1.89117 2.05909 2.11991 2.16139 2.22004
Median 1.67000 1.98000 2.15000 2.19000 2.23500 2.29600
Minimum 0.43750 0.96500 1.22565 1.35313 1.42625 1.49565
Maximum 2.78500 2.68900 2.71400 2.73500 2.76500 2.82500
Skewness -0.33207 -0.56997 -0.66908 -0.62861 -0.58688 -0.58091
Kurtosis 2.31466 2.35486 2.51296 2.52404 2.45572 2.34746
Count 2021 2017 2017 2017 2017 2017
35
Appendix 5.
Variable Description Source CPI Inflation of consumer prices Datastream PPI Inflation of producer prices Datastream
HICP Harmonized indices of consumer prices Eurostat Standardized
Inflation Uses CPI, PPI and HICP to calculate a standardized variable
2 Computed
Unemployment The unemployment rate as percentage of the labor force not working
hours adjusted
Datastream
Employment
Growth Growth rate of employed not working day adjusted Datastream
Standardized
Employment Uses Unemployment and Employment growth to calculate a
standardized variable
Computed
Output Gap Difference between actual output and potential output in percentage IMF Utilized
Capacity Percentage of production goods currently utilized Datastream
Production
Growth Growth rate of the industrial production excluding construction Datastream
Standardized
Production Uses the Output gap, utilized capacity and production growth to
calculate a standardized variable
Computed
ECB POLICY The policy rate of the European Central Bank ECB FED POLICY The policy rate of the Federal Reserve Datastream BoE POLICY The policy rate of the Bank of England Datastream QE Dummy A dummy which is 1 at times in which the QE policy was in place ECB
M3 GROWTH Growth rate of the monetary aggregate M3 ECB BOP Balance of payment for the Euro area in percentage Datastream
Risk aversion A measure of risk aversion calculated by the ECB ECB EURONIA A short term interest reference rate Datastream EURIBOR A short term interest reference rate Datastream
LIBOR A short term interest reference rate Datastream DOLLAR EUR The exchange rate between the US dollar and the Euro Datastream
POUND EUR The exchange rate between the British pound and the Euro Datastream YENN EUR The exchange rate between the Japanese Yenn and the Euro Datastream YUAN EUR The exchange rate between the Chinese Yuan and the Euro Datastream OIL PRICE The price of a barrel of Oil in dollars Datastream
Inflation 1 Year Expected inflation in one year Datastream Inflation 2
Years Expected inflation in two years Datastream
Inflation 5
Years Expected inflation in five years Datastream
Inflation 10
Years Expected inflation in ten years Datastream
Inflation 15
Years Expected inflation in fifteen years Datastream
Inflation 20
Years Expected inflation in twenty years Datastream
Inflation 25
Years Expected inflation in twenty-five years Datastream
Inflation 30
Years Expected inflation in thirty years Datastream
2 The appendix 5.2 shows the procedure to standardize variables.
36
Appendix 5.2: Standardized variables
This appendix uses the Standardized inflation variable as an example for how the
standardized variables (µ) are calculated. First the base variable (underlying
macroeconomic variables for example CPI and PPI) are selected. For each base
variable the average over the sample period is calculated. As shown in equation
(A4.1) in which αit is the value for an individual variable at data point t ∈(1, T).
�̃�𝑖 =
1
𝑇∑ 𝛼𝑖,𝑡𝑑𝑡
𝑇
𝑡=0
(A4.1)
After the average is calculated a new variable is created (δ) that consist out of all the
variable of interest in the case of the standardized inflation variable those are CPI, PPI
and HICP.
𝛿𝑖,𝑡 =𝛼𝑖,𝑡
𝛼�̃�+
𝛼𝑖+1,𝑡
𝛼𝑖+1̃+
𝛼𝑖+2,𝑡
𝛼𝑖+2̃ (A4.2)
For this new variable, δ the average and the standard deviation are calculated as
shown in equation (A4.3) and (A4.4) respectively.
�̃�𝑖 =
1
𝑇∑ 𝛿𝑖,𝑡𝑑𝑡
𝑇
𝑡=1
(A4.3)
𝛿𝑆�̃�𝑖 = √1
𝑇∑ (𝛿𝑖,𝑡 − �̃�
𝑖)
2𝑇
𝑡=1
(A4.4)
These variables are used to calculate the final standardized variable as is shown in
equation (A4.5).
𝜇𝑖,𝑡 =
𝛿𝑖,𝑡 − �̃�𝑖
𝛿𝑆𝐷�̃�
(A4.5)
This procedure is used to give an equal weight to each base variable and to end up
with a standardized variable with zero mean and standard deviation of one.
Appendix 6
Note: The graph above provides proof that the QE significantly lowers the yield curve at 95% level because both confidence
intervals do not overlap.
-1.5
-1
-0.5
0
0.5
1
1.5
2
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Spo
t R
ate
Years till maturity
Differnces in short-end of the yield curve including 95% confidence interval.
Without QE
With QE
37
Appendix 7
β1 (1) β1 (2) β1 (3) β1 (4) β1 (5)
QE dummy -0.640*** -0.555*** -0.521*** -0.511*** -0.680***
(0.0455) (0.0412) (0.0414) (0.0424) (0.0528)
ECB policy rate 0.266*** 0.379*** 0.415*** 0.420*** 0.646***
(0.0221) (0.0154) (0.0145) (0.0196) (0.0287)
M3 growth rate -0.122*** -0.132*** -0.149*** -0.137*** -0.257***
(0.00591) (0.00594) (0.00698) (0.00726) (0.00544)
Standardized inflation 0.321*** 0.324*** 0.305*** 0.291*** 0.155***
(0.0117) (0.0131) (0.0105) (0.0104) (0.0116)
Standardized employment -0.359*** -0.269*** -0.343***
(0.0184) (0.0280) (0.0168)
Output gap 0.0642***
(0.00717)
Utilized Capacity
-0.0424***
(0.00576)
Production Growth
-0.0167***
(0.00148)
Standardized production
-0.0741*** -0.137***
(0.00880) (0.0108)
Employment Growth
-0.346***
(0.0125)
Unemployment
0.0339*
(0.0152)
Constant 5.213*** 8.464*** 5.091*** 5.155*** 4.947***
(0.0378) (0.479) (0.0249) (0.0159) (0.182)
N 3010 3010 3010 3010 3010
adj. R-sq 0.801 0.800 0.804 0.801 0.763
Note: Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001, The table shows the effect that different
base variables have (β1) all bonds NS-model . All variables but the QE dummy are control variables and no
explanatory value can be attached to the estimated betas. The description of the variables can be found in appendix
5.
Appendix 8
VIF table (5) (2) (3) (4) (5)
QE dummy 1.22 1.35 2.51 3.10
ECB policy rate 1.22 1.23 3.85 5.43
M1 growth rate 1.17 1.37 1.52
Standardized inflation 3.00 3.01
Standardized employment 2.98 3.50
Standardized production 1.66 1.84
Risk aversion 1.67
Mean VIF 1.22 1.25 2.56 2.87
VIF table(6) (2) (3) (4) (5)
QE dummy 1.22 2.49 2.48 2.95
ECB policy rate 1.22 3.85 3.64 4.74
Standardized inflation
2.58 2.79 2.79
Standardized employment
2.96 2.97 3.49
Standardized production
1.61
M1 growth rate
1.32 1.51
Risk aversion
1.51
Mean VIF 1.22 2.70 2.64 2.83
VIF table(7) (2) (3) (4) (5)
QE dummy 1.22 2.49 2.51 3.10
ECB policy rate 1.22 3.85 3.85 5.43
Standardized inflation
2.58 3.00 3.01
Standardized employment
2.96 2.98 3.50
Standardized production
1.61 1.66 1.84
M1 growth rate
1.37 1.52
Risk aversion
1.67
Mean VIF 1.22 2.70 2.56 2.87
According to Hair et.al. (1995) state that a VIF value below 10 is an indication that
multicollinearity problem can be ignored and does not influence the results
38
Appendix 9
β1 (1) β1 (2) β2 (3) β2 (4) β3 (5) β3 (6)
QE dummy -0.705*** -0.731*** 0.460*** 0.522*** 0.103 0.0652
(0.0350) (0.0360) (0.0532) (0.0526) (0.0851) (0.0853)
ECB policy rate 0.480*** 0.266*** 0.454*** 0.729*** 0.920*** 0.607***
(0.00920) (0.0115) (0.0132) (0.0171) (0.0366) (0.0460)
Standardized inflation 0.188*** 0.371*** -0.308*** -0.536*** 0.0686 0.336***
(0.0113) (0.0120) (0.0153) (0.0146) (0.0356) (0.0421)
Standardized
employment -0.402*** -0.385*** 1.007*** 0.933*** -0.887*** -0.861***
(0.0101) (0.0104) (0.0121) (0.0136) (0.0324) (0.0309)
Standardized
production
0.136*** 0.146***
(0.0118) (0.0109)
M1 growth rate 0.0508*** 0.0215***
0.0353*** -0.00743
(0.00186) (0.00204)
(0.00711) (0.00733)
Risk aversion 0.00524 -0.0131*** -0.0971*** -0.0992*** -0.0172 -0.0440***
(0.00412) (0.00384) (0.00528) (0.00478) (0.0131) (0.0122)
Euro/Dollar exchange 1.928*** 3.924*** 0.499*** -2.284*** -2.846*** 0.0664
(0.113) (0.110) (0.115) (0.131) (0.416) (0.488)
Oil price
-0.0147***
0.0142***
-0.0214***
(0.000535)
(0.000529)
(0.00160)
Constant 0.243 -0.671*** -4.069*** -1.965*** -0.281 -1.614**
(0.152) (0.126) (0.153) (0.141) (0.550) (0.554)
N 3008 3008 3008 3008 3008 3008
adj. R-sq 0.877 0.913 0.892 0.913 0.437 0.476
Note: Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001, The table checks for robustness of the QE-
dummy by adding the Exchange rate and the oil dollar price (β1,2 and 3) Triple-A bonds NS-model . All variables
but the QE dummy are control variables and no explanatory value can be attached to the estimated betas. The
description of the variables can be found in appendix 5
Appendix 10
β1 (1) β1 (2) β2 (3) β2 (4) β3 (5) β3 (6)
QE dummy -0.946*** -0.983*** 0.716*** 0.726*** 1.702*** 1.219***
(0.0501) (0.0471) (0.0621) (0.0610) (0.0752) (0.0873)
ECB policy rate -0.138*** -0.240*** 0.842*** 0.848*** 0.163** -0.145*
(0.0141) (0.0170) (0.0206) (0.0214) (0.0595) (0.0710)
Standardized inflation 0.448*** 0.316*** -0.174*** -0.159*** 0.945*** 0.253***
(0.0174) (0.0188) (0.0210) (0.0253) (0.0479) (0.0596)
Standardized employment -0.494*** -0.320*** 0.778*** 0.764*** -1.693*** -1.024***
(0.0141) (0.0191) (0.0188) (0.0236) (0.0281) (0.0602)
Standardized production -0.0294*** 0.0217* 0.0588*** 0.0549*** -0.569*** -0.385***
(0.00831) (0.00874) (0.0127) (0.0130) (0.0270) (0.0316)
Risk aversion 0.0447*** 0.0735*** -0.0922*** -0.0950*** 0.202*** 0.336***
(0.00532) (0.00567) (0.00708) (0.00707) (0.0190) (0.0211)
INFLATIONSWAP5Y
-0.0436
2.081***
(0.0512)
(0.166)
INFLATIONSWAP10Y
0.642***
(0.0587)
_cons 5.243*** 4.166*** -5.047*** -4.987*** -2.904*** -5.747***
(0.0212) (0.102) (0.0263) (0.0786) (0.0710) (0.223)
N 2015 2015 2015 2015 2015 2015
adj. R-sq 0.850 0.858 0.810 0.810 0.656 0.696
Note: Standard errors in parentheses * p<0.05, ** p<0.01, *** p<0.001, The table checks for robustness of the QE-
dummy by adding the Exchange rate and the oil dollar price (β1,2 and 3) all bonds NS-model . All variables but the
QE dummy are control variables and no explanatory value can be attached to the estimated betas. The description of
the variables can be found in appendix 5
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