Download A Simple Way to Overcome the Zero Lower Bound of Interest Rates

A Simple Way to Overcome the Zero Lower Bound of Interest Rates for
Central Banks – Evidence from the Fed and the ECB within the Financial
Crisis
by
Jens Klose
(University of Duisburg-Essen)
Abstract
In this paper we investigate how Fed and ECB monetary policy changed within the financial
crisis of 2007-2010. We argue that due to the very low interest rates classical monetary policy
rules like e.g. the Taylor rule could lead to false conclusions. We propose a new way of
conducting monetary policy when the zero lower bound becomes binding via shaping the
inflation expectations. Our results indicate that using this modified Taylor rule shows similar
tendencies in the reaction coefficients as the standard Taylor rule at least if no interest
smoothing term is included.
JEL code: E43, E52, E58
Keywords: Financial Crisis, Federal Reserve, European Central Bank, Quantitative Easing,
Inflation Expectations, Taylor Rule
Corresponding author:
Jens Klose
University of Duisburg-Essen
Universitätsstr. 12,
D-45117 Essen, Germany
Phone: +49 201 183 3218
E-mail: [email protected]
-1-
1. Introduction
Within the ongoing financial crisis, starting in 2007, central banks all over the world
have cut interest rates at a rapid pace. So a lot of them soon faced the problem of the zero
lower bound of interest rates which ultimately makes traditional monetary policy, which
tackles the nominal interest rate, no longer applicable. However, traditional monetary policy
rules like the Taylor rule would predict that nominal interest rates should be negative.1
Several authors have proposed ways to achieve a negative nominal interest rate. These
suggestions rely mainly on taxing money holdings (Goodfriend 2004) since holding cash is
the opportunity cost of leaving it at the bank account. Since holding cash is costless if it is not
taxed, the nominal interest cannot be lower than zero. However, with a tax it could. But we do
not observe that governments tax money holdings within the current crisis, so this seems not
to be the way monetary policy is conducted in these times.
But how do central banks conduct monetary policy under these circumstances?
Another strand of literature has suggested that shaping inflation expectations and by this
influencing the real interest rate in this situation is an opportunity for central banks.2 In fact,
central banks have to generate higher inflation expectations by credibly committing not to
raise interest rates immediately after a recovery and with this a rise in inflation. If the market
participants trust the central bank, the inflation expectations will rise and thus the real rate,
which is the important interest rate for investment and consumption decisions and that is not
bound to zero, would fall. We will show a way how the Fed and the ECB can overcome the
problem of the zero lower bound on nominal interest rates in this context. Our approach takes
explicitly the role of quantitative easing into account which has a signaling effect for market
participants (Bernanke et al. 2004, p. 18).
1
2
See Rudebusch (2009) in case of the Fed and Gorter et al. (2009) for the ECB.
See e.g. Krugman et al. (1998), Eggertsson and Woodford (2003) or Jung et al. (2005).
-2-
We can use this reasoning to estimate modified Taylor reaction functions to judge
upon the effectiveness of such rules within a crisis, since the Taylor rule has been criticized of
not leading to conclusive results in crisis periods. However, we will show with our approach
that even though the reaction to inflation and the output gap is decreasing during the crisis, the
classical Taylor reaction functions overstate this decrease which is an effect of the binding
zero lower bound.
We will proceed as follows: In section 2 a way of modifying the classical Taylor
reaction function is shown. Section 3 develops a model to estimate the inflation expectations
taking quantitative easing of central banks into account. Section 4 uses these estimates to
generate the results of modified Taylor reaction functions which are compared to the classical
ones and the interest rate path of the central banks. Section 5 concludes.
2. Modifying the Taylor rule in the presence of the zero lower bound
In 1993 John B. Taylor proposed a new reaction function which arguably covers the
interest rate setting behavior of the Fed during the period 1987-1992 quite well. According to
his rule the Fed reacts to deviations of the inflation rate from its target and to deviations of the
output from its potential, the so-called output gap. Hence, we can write the Taylor reaction
function as follows:
(1) ,
where is the interest rate set by the Fed, is the equilibrium nominal interest rate, /
are the inflation rate and its target, is the output gap and , are the reaction coefficients
to inflation and the output gap respectively. In his seminal paper, John B. Taylor set the
equilibrium real interest rate and the inflation target both equal to two and the reaction
-3-
coefficients equal to 0.5 each. With this, he was able to mimic the interest rate setting of the
Fed in the above mentioned period.
However, such a simple rule is not applicable if nominal interest rates approach the
zero lower bound, since the dependent variable can no longer be chosen freely. Therefore, the
classical Taylor reaction function has to be modified. This is done by looking at the
equilibrium nominal interest rate . This variable can be divided into the equilibrium real
interest rate and the inflation expectations . Surprisingly, the inflation expectations have
played a minor role in Taylor rule estimates up to date. In principle, there are two ways of
dealing with this issue. The first one (assumed in the original Taylor rule) is introducing static
expectations so that .3 This leads directly to the Taylor principle which requires a
reaction coefficient for inflation larger than unity in order to raise the nominal interest rate by
more than the inflation rate if it is increasing, a so-called “leaning against the wind policy” of
central banks. In the second specification is set equal to the inflation target (Clarida et
al. 1999). The rationale for this choice is that the central bank is always able to bring
expectations to its inflation target. However, this seems to be unlikely in a crisis period
because credible announcements of central banks have to be proved in this time more than
ever by complementary actions. Our approach does not make either of the assumptions
pointed out above but estimates the inflation expectations within a system of equations. We
will come back to this point in section 3. All in all equation (1) becomes:
(2) By simple rearranging the Taylor rule using the Fisher equation the dependent variable
is no longer the nominal but the real interest rate which is not bound to zero.
(3) 3
We abstract here from forward-looking Taylor rules (Clarida et al. 2000) which in fact use mainly rational
expectations forecasts (Gerdesmeier and Roffia 2004, Sauer and Sturm 2007).
-4-
Some comments on this modified Taylor rule have to be made. First, the so-called
Taylor principle is now no longer given for an inflation coefficient of above unity because
central banks now explicitly influence the real and not the nominal rate which is effectively
zero within the crisis. So in order to fulfill the Taylor principle the coefficient of the inflation
gap has to be positive, meaning that the real rate rises if inflation increases.
Second, the Fed has not announced an explicit inflation target as other central
banks have done. This might be a problem in our estimation if the inflation target is supposed
to be time varying as Leigh (2008) suggests. We do not account for adjustments in the
inflation target of the Fed but argue that the long-run inflation target is fixed but short run
deviations from this target, e.g. to influence inflation expectations, are accepted by the Fed.
Moreover, fixing the inflation target makes results comparable to those of the ECB since the
ECB has announced an explicit inflation target of close to but under two percent in the
medium term.4 So for both central banks we will assume an inflation target of two percent in
line with the announcement of the ECB and the suggestion of Taylor (1993).
Third, there is considerable evidence that the equilibrium real interest rate is also a
time varying variable.5 So we account for a possible change of this measure in our sample by
applying the HP-filter (Hodrick and Prescott 1997) to the real interest rate series as Belke and
Klose (2009) suggest it.6
Fourth, as in the case of the classical Taylor rule the policy rate of the central banks
might be subject to a substantial degree of interest rate smoothing. In our modified Taylor
reaction functions there is no difference in introducing a smoothing parameter compared to
the classical rules, except that we have to use the lagged real instead of the nominal rate.
4
Recently, Blanchard et al. (2010) proposed to increase the inflation target to dampen shocks. But up to date
there is no announcement of central banks that they have adjusted their target rates.
5
See Laubach and Williams (2003), Cuaresma et al. (2004) or Arestis and Chortareas (2007) for different
approaches to estimate the equilibrium real interest rate.
6
Wu (2005) argues that this is the easiest and least precise way of measuring time variations within this variable,
but it should nevertheless be more appropriate than simply assuming a constant equilibrium rate.
-5-
(4) · 1 · Using an interest smoothing term7 we are able to show whether the central banks react
only to the fundamentals of the Taylor rule ( equal to 0) or do not target those variables at all
( equal to 1). However, reasonable results should lie somewhere in between. Using a
smoothing parameter we can test the “Mishkin principle” that central banks react less inertial
during a crisis (Mishkin 2008 and 2009). This is the case if the smoothing parameter drops
significantly for the sample including the financial crisis.
With the help of this modification we are able to estimate Taylor reaction functions
with are not subject to the restriction of the zero lower bound. Moreover, we can compare
these results to those of the classical reaction functions in order to show whether there are
substantial differences in the policy judgment by these two approaches. But before we can do
so, we need to model the inflation expectations which are a crucial part of the real interest
rate. This will be done in the next section.
3. Inflation Expectations
In order to construct our model we need to find a measure of quantitative easing. The
natural candidate for this is the length of the central banks balance sheet. We also use this
measure but specify a so-called balance sheet gap being the deviation of the balance sheet
from its “natural” level. This equilibrium balance sheet is constructed by taking the end of
month length of the balance sheet8 from 1996M6 to 2008M8 for the Fed and 1999M1 to
7
We do not only add a smoothing coefficient to our modified rule but also to the classical Taylor reaction
function. In this case (4) changes to:
· 1 · Further modifications of the classical Taylor reaction function are explained later on.
8
Since the end of month length of the balance sheet might be influenced by the minimum reserve requirements
the financial institutions have to fulfill, we also checked whether there is a bias by comparing this measure to the
average length of the balance sheet for each month. However, the results are not altered by this, so we can
conclude that there is no bias in taking the end of month values.
-6-
2008M8 for the ECB. The starting date is chosen because of data availability with respect to
the Fed balance sheet. In our opinion it is advisable to rely on the longest possible sample
period in order to not bias the results by taking a shorter period which does not cover the
overall trend. However, the Fed balance sheet length evolved smoothly before the financial
crisis started, so the results are not influenced by our choice of the sample. In case of the ECB
the starting date is chosen corresponding to stage III of the EMU because here ECB took over
responsibility for monetary policy in the euro area. So this is the first time we have a ECB
balance sheet and not a constructed one relying on data of the individual member states. The
choice of the sample periods of the balance sheet and inflation expectations/ real interest rate
determines the sample of the Taylor reaction function in section 4 which range from
1996M12 onwards for the Fed and 1999M7 for the ECB. So we cover a period before the
crisis that is sufficiently long to get reliable pre-crisis estimates.
The end date for the construction of the equilibrium balance sheet is chosen because
from 2008M9 there is evidence of quantitative easing of the Fed and the ECB as can be seen
in Figure 1, so the balance sheet expands from its equilibrium value from this time onwards.
As can be seen from this figure the expansion in the balance sheet was more pronounced for
the Fed since their balance sheet more than doubled immediately after quantitative easing was
introduced. This stronger response might be due to the fact that the Fed had at this point less
room to cut rates any further since interest rates already approached values of about two
percent when quantitative easing started while the ECB interest rate was at four percent.
For 1996M6-2008M8 we construct a linear trend to find the natural level and subtract
this measure in a second step from the true values for the whole sample period (thus including
also the crisis period) using the following formula:
'
(5) 100log !"# log !"#$%
$% ,
-7-
with being the balance sheet gap, !"# being the length of the balance sheet and
'
!"#$%
$% as the trend value up to 2008M8. This procedure leads to the balance gap given
in Figure 2. As expected, before quantitative easing started the balance sheet gap is mainly
close to zero and rises sharply after 2008M8. It is also obvious that the balance sheet of the
Fed evolves more smoothly compared with the ECB before quantitative easing is applied.
This might possibly be due to the shorter history of the ECB which especially in the years
after its establishment followed not such a clear trend as the Fed balance sheet in the same
period.
- Figure 1 and 2 about here The model used to estimate is a modified version of the one brought forward by
Laubach and Williams (2003) to estimate the unobservable equilibrium real interest rate. In
contrast to their approach our focus is on modeling inflation expectations instead of the real
equilibrium interest rate. Therefore, we did not use the real rate gap in the IS-equation but the
real interest rate itself which is explicitly modeled by incorporating inflation expectations.
Those are partly driven by quantitative easing of central banks. Therefore, our model consists
of the following four equations:
(6) ( ) * +,4
.
+,-
. / 0 5 $ (7) "( ") * .
89( 89) 89- 2
89.
+6
*
+,1
.
* 7
. / 0 2 3 % 5 $ ?
": ;
< = "> " 7*
(8) (9) "+ ,
2 3 % -8-
with as the output gap, the real interest rate, the nominal interest rate, the inflation
rate, the expected future inflation, < import price inflation, ? oil price inflation and
7 , 7* the contemporaneously and serially uncorrelated error terms. So the model consists of
an IS-equation (6), a Phillips-curve (7), the Fisher-equation (8) and an equation giving the
inflation expectations which rely on the lagged inflation rate and the balance sheet gap (9). So
we also assume static expectations if the balance sheet is at its equilibrium value and thus equals zero. However, if this is not the case inflation expectations deviate from the observed
inflation rate.
Due to our shorter sample period we decided to rely on monthly instead of quarterly
data.9 This leads us to include more lags of the dependent variable in equations (6) and (7)
compared to Laubach and Williams (2003). The best specification, being identical for both
central banks, was found when including eleven lags of the output gap and the inflation rate.10
In order to save degrees of freedom, only the coefficients of the first two lags are estimated
explicitly while for the other lags a weighted coefficient of the sum of three to six lags is built.
Moreover, in line with Laubach and Williams (2003), the lagged inflation coefficients are
expected to sum to unity. The real interest rate influences output with a lag. This is because
interest rate induced investments need some time to be produced and thus become available
only in the next period(s). We include two lags in our analysis since we assume that the
majority of the investments is produced within the first two months after a change in the real
interest rate takes place. However, including more than two lags does not alter the results
significantly. The coefficients of the real interest rate are again chosen to have equal weight.
Import price inflation and oil price inflation are included in equation (7) to absorb possible
9
The sources and the construction of the data are described in the appendix.
The choice of the lag structure is a trade-off between comparability of the results for both central banks and
the optimal lag structure. Single equation determination of the optimal lag structure (as measured by the highest
adjusted @* ) reveals that for the US and the euro area the optimal lag of the IS-equation is 10 and 11 and for
the Phillips equation it is 12 and 9 respectively. Therefore using the average optimal lag structure of 11 to make
the models comparable is most suitable for our analysis.
10
-9-
price shocks in these sectors. One comment on the timing of the inflation rate and the inflation
expectations has to be made. We assume that inflation expectations are built before the
contemporaneous inflation rate becomes available, thus the inflation expectations have to be
made knowing only lagged data. However, we also checked the other option where inflation
expectations rely on contemporaneous inflation data and the results are almost the same.
With respect to the coefficient of the balance sheet gap in (9) we suspect a positive
reaction, thus indicating that a larger positive deviation of the balance sheet from its
equilibrium level leads to higher inflation expectations. The rationale for this relationship is
that the central banks try to influence the real interest rate and as the nominal rate is (close to)
zero this can only be achieved by changing the inflation expectations, i.e. increasing those to
lower the real rate. One way of influencing the inflation expectations is by credibly
committing to keep nominal interest rates low, even if the crisis is over (Krugman et al. 1998,
Eggertsson and Woodford 2003, Jung et al. 2005). However, the Fed and the ECB need to
prove that interest rates will remain low for a long time because the simple announcement of
doing so would be subject to a time inconsistency problem and if market participants realize
that inflation expectations are not altered. Expanding the balance sheet is one way to credibly
commit to low interest rates because the balance sheet cannot be brought back to its
equilibrium level immediately after the crisis, so the additional funds issued by the Fed and
the ECB within the crisis are triggering higher future inflation rates in the view of Friedman
(1963). Moreover, it is a way of signaling that interest rates will remain low even if the crisis
is over, since the additional funds need to be withdrawn from markets before interest rates can
be raised.11
The estimation technique used for this system of equations is Full Information
Maximum Likelihood. With this we obtain the estimation results given in Table 1.
11
This argument is also brought forward by Bernanke et al. (2004), p. 18.
- 10 -
- Table 1 about here –
Table 1 reveals that there is indeed a positive relationship between the inflation
expectations and the balance sheet gap. However, this relationship is stronger for the Fed than
for the ECB. With the help of these results the inflation expectations and the real interest can
be calculated which are displayed in Figure 3.
- Figure 3 about here –
As can be seen from Figure 3 before 2008M9 the inflation expectations were mainly
driven by the lagged inflation rate. However, with the beginning of quantitative easing the
inflation expectations rose sharply and remained consistently higher than before in case of the
US.12 In the euro area the inflation expectations more or less peaked at the end of 2008 by
around five percent and declined afterwards to normal levels. This peak is also observed for
the Fed but, in contrast to the ECB inflation expectations, they remain high due to the
enormous amount of quantitative easing. This effects the real interest rate which is not bound
to zero as the nominal rate and which as a consequence approaches values of up to minus
eight percent in the end of 2008 and in the beginning of 2010 in the US. For the euro area the
effect is smaller due to lower inflation expectations. However, also in the euro area the real
interest rate is about minus three percent at the end of the sample. So we have verified that
there are indeed negative real interest rates within the crisis on both sides of the Atlantic.
According to this we have the potential to use this measure in our modified Taylor reaction
functions and capture possible differences to the classical Taylor rule or more specifically the
response coefficients of the rule. This will be done in section 4.
12
Note that these exceptionally high inflation expectations are not observed by the either the survey of
professional forecasters or the Fed itself. This might be due to the fact that those are confident that the Fed can
reduce the balance sheet to normal levels immediately after a recovery is foreseeable. However, the danger of
not being able to reduce the balance sheet or acting too late is always present which may boost inflation
expectations to even higher levels than the ones observed in our study. Therefore, the issue of quantitative easing
should be taken seriously by the Fed.
- 11 -
4. Classical and modified Taylor reaction functions – Is there a crisis
effect?
In this section we will present our estimation results of the classical and the modified
Taylor reaction functions. The modification of the Taylor rule has been described in section 2.
However, we did not yet present our estimation equation of the classical Taylor reaction
function. This will be done before the results are presented.
4.1. The classical Taylor rule
In line with Taylor (1993) we will assume that the inflation expectations of (2) are
proxied by the current realization of inflation. Thus holds. This changes (2) in the
following way:
(10) 1 In order to facilitate the interpretation of the coefficients, i.e. accounting for the Taylor
principle of an inflation coefficient of above unity, we set A 1 . So (10) changes to:
(11) 1 A A As already introduced in section 2 the classical and the modified Taylor reaction
functions will be estimated using for both central banks a constant inflation target of two
percent and a time-varying equilibrium real interest rate. This measure is simply a HP-filtered
version of the real interest rate which is in case of the modified Taylor rule given by the
model in section 3 and for the classical Taylor rules assuming the Fisher equation with static
expectations to hold. In contrast to most other studies we do not include a constant term in our
estimation equation since all factors influencing the right hand side variables are explicitly
modeled. These are the equilibrium real interest rate and the inflation target.
- 12 -
The procedure used to estimate the different Taylor reaction functions is GMM. This
method appears highly adequate for our purposes because at the time of its interest rate setting
decision, the central banks cannot observe the ex-post realized right hand side variables. That
is why the central banks have to base their decisions on lagged values only (Belke and Polleit
2006). We decided to use the first six lags of inflation and the output gap as instruments. So
our sample ranges from 1996M12 to 2010M5 for the Fed and 1999M7 to 2010M5 for the
ECB due to the shorter history of this central bank. Moreover, we perform a J-test to test for
the validity of over-identifying restrictions to check for the appropriateness of our selected set
of instruments.13 As the relevant weighting matrix we choose, as usual, the heteroskedasticity
and autocorrelation consistent HAC matrix by Newey and West (1987).
In order to identify differences before and within the crisis we decided to estimate the
corresponding reaction functions for two sample periods. The first one covers only data up to
2007M7 since the start of the crisis is normally dated to 2007M8 because on August 9th 2007
overnight interbank rates in Europe shot up and the ECB injected additional liquidity as a
response.14 Note that with the choice of beginning of the crisis we deviate from the date of
quantitative easing which started in 2008M9. That is because at the beginning of the crisis
quantitative easing was not performed by both central banks. Moreover, they relied on the
traditional interest rate policy in this period.
The second estimation period includes the crisis period and thus uses all available
data. With this approach we follow Gorter et al. (2009) who estimated forward looking Taylor
reactions functions using real time data for the ECB.
13
Four of our modified Taylor reaction functions indicate the use of inappropriate instruments when only six
lags of inflation and the output gap are set as instruments. However, we still rely on these estimates to have a
constant set of instruments over all specifications. We checked whether the use of additional instruments (i.e. six
lags of the real interest rate or its equilibrium value) alters the results. This is not the case. But using these
additional instruments makes us pass the J-test in all cases. The results are available upon request.
14
See e.g. Cecchetti (2008) pp. 12-17, Taylor and Williams (2009) p. 60. For a detailed schedule what happened
around that time and the decisions made by the most important central banks as a reaction to this see Bank for
International Settlements (2008) pp. 56-74. They should not be repeated here.
- 13 -
4.2 Results for the pre-crisis period
Before the crisis started the zero lower bound on nominal interest rates was never hit
by the Fed or the ECB. Therefore we will first compare whether there are any substantial
differences concerning the classical and the modified Taylor reaction function which should
not be the case in the pre-crisis period.
- Table 2 about here Table 2 reveals that the interest rate smoothing term of the modified Taylor reaction
functions is consistently lower than for the classical Taylor reaction function. So there is some
evidence that using our modified approach improves upon the classical Taylor rule by making
reactions to inflation and output more reliable. Moreover, the high degrees of interest rate
smoothing in the classical Taylor reaction functions lead to quite imprecise estimates of
inflation rate and the output gap.
This ends up in e.g. an inflation coefficient of above unity (column 2.2) which is not
consistent with the remaining estimation results. All other inflation coefficients indicate that
the Taylor principle is violated. However, only for the modified Taylor reaction functions we
are able to find significant deviations from the Taylor principle (columns 2.6-2.8). The
remaining estimates (columns 2.1, 2.3, 2.4 and 2.5) point to an inflation coefficient of below
unity for the classical Taylor reaction function and of below zero for the modified one but the
difference is not significant. Even more important, we are unable to identify any significant
differences in the inflation coefficients between the classical and the modified Taylor reaction
function, except for the Fed specification including an interest rate smoothing term
(comparing columns 2.2 and 2.6). However, this result seems to be driven by the high degree
of interest rate smoothing in 2.2.
- 14 -
The reaction to the output gap shows always significantly positive results in line with
theory. With the exception of the Fed Taylor reaction function without interest rate smoothing
(comparing columns 2.1 and 2.5), there seems to be no difference in the reaction coefficients
between both approaches. However, for the exception the Fed reacts stronger in the modified
Taylor reaction function.
So, all in all, it can be concluded from these results that the reaction functions are not
different if the zero lower bound is not binding. This is exactly what we have suggested and
with this result we are able to investigate whether this is still true if we expand the sample to
the crisis period where central banks in fact faced the lower bound.
4.3 Results for the crisis period
Expanding the sample period to the crisis means including a switch in the central bank
monetary policy implementation from setting interest rates to influencing the inflation
expectations via quantitative easing. Since the latter effect can only be captured by our
modified Taylor reaction functions we would suspect that some differences between this
approach and the classical Taylor reaction functions occur. Whether this is true can be seen in
Table 3.
- Table 3 about here Again we find a significantly lower interest rate smoothing coefficient if the modified
Taylor reaction function is estimated. The difference between both approaches becomes even
more pronounced compared to the results for the pre-crisis period. While the classical Taylor
reaction function reveals even higher estimates which are consistently close to unity (columns
3.2 and 3.4) the smoothing coefficient of the modified Taylor reaction decreases when the
crisis is included (3.6 and 3.8). The reason for both developments is simple. In the classical
Taylor reaction functions only interest rate policy is included. But there is no interest rate
- 15 -
policy of the Fed since 2008M12 and of the ECB since 2009M5. So it is evident that for
(more than) a year the lagged interest rate is the best predictor for the future interest rate
which is signaled by higher smoothing coefficients in Taylor reaction functions. Since both
coefficients are almost unity the inflation and output gap reaction cannot be significantly
estimated. The decreased smoothing coefficient in the modified estimates is reasonable since
a substantial quantitative easing of the central banks is used in order to shape the inflation
expectations. Since the amount of quantitative easing was much larger in the US than in the
euro area, leading to a higher volatility in inflation expectations, the influence of the lagged
real interest rate is even more decreased in case of the Fed than for the ECB. In fact, the
smoothing coefficient of the Fed turns insignificant, thus the real interest rate is solely driven
by the inflation rate and the output gap.
Including the crisis leads in all specifications to a reduction in the inflation response.
Moreover, now, with the exception of columns 3.2 and 3.4 which are imprecisely estimated,
all coefficients indicate a significant violation of the Taylor principle. Thus, within the crisis
inflation is less in the focus of both central banks. Even though we identified a drop in all
inflation coefficients compared to the pre-crisis period, there is a difference in the magnitude
of the effects with respect to the Fed. The classical Taylor reaction function reveals a drop in
the inflation coefficient of 0.56 (subtracting the inflation coefficient in 3.1 from the value in
2.1) while the coefficient in the modified reaction function decreases only by 0.2. So the
classical approach overstates the true drop in the inflation coefficient. This is reasonable since
in the classical Taylor reaction function there is no response to inflation changes since the
zero lower bound is binding while for the modified reaction functions there is still the
opportunity to change the real interest rate which results in a higher reaction coefficient to
inflation. For the ECB this issue is surprisingly less of a problem.
- 16 -
Concerning the output gap response we can identify a drop in the response coefficients
in all specifications when the crisis is included.15 However, all reliable estimates remain
significantly above zero. With respect to the magnitude of the decrease in the classical and the
modified Taylor reaction function, it becomes evident that the classical approach consistently
overstates the decrease in the output gap coefficient. The reason is the same as for the
inflation rate. While in the classical Taylor reaction function there is no room for further
reductions in the policy rate, the modified reaction function can indeed influence the real
interest rate in the preferred direction which is, as the output gap decreases, lowering the rate.
So concluding from this analysis it can be said that the classical Taylor reaction
function gives the correct direction concerning the response coefficients, namely that they
decrease if the crisis period is included into the sample. However, the results of these reaction
functions tend to overstate the true effect of the coefficient drop which might lead to the
conclusion that the central banks do no longer target inflation and the output gap. But such a
conclusion is not valid since in the classical approach the central banks have no room to react
to lower inflation and output gaps if they have approached an interest rate of zero. So in this
case the modified Taylor reaction function is able to generate more reliable estimates.
However, even the modified Taylor reaction functions reveal that the response to
inflation and the output gap is decreasing when the crisis period is included. Thus, it has to be
concluded that within the crisis both central banks took also other variables like risk spreads,
asset prices or credit measures into account. Belke and Klose (2010) found indeed a
significant role of these variables within the recent crisis.
15
This finding of a decrease in the response coefficient of inflation and the output gap when the crisis is included
is consistent with the results of Gorter et.al (2009) if no adjustment concerning interest rate smoothing is applied.
Moreover, our results are consistent with the findings of Martin and Milas (2010) for the Bank of England.
- 17 -
4.4 Comparing implied and actual interest rates
Up to now we have evaluated how the ECB and the Fed reacted to the inflation rate and
output gap depending on the different sample periods and Taylor reaction functions used.
Even though the fit of the data is generally quite high in all equations as measured by the
adjusted @ * , there could be important differences in some periods for the Taylor reaction
function estimates and the actual interest rate set by the central banks. To become an intuition
of these effects we plot in Figures 4 and 5 the actual interest rates with the implied values
given by the Taylor reaction functions.
- Figures 4 and 5 about here As can be seen in both Figures, the implied nominal interest rate for the pre-crisis era is much
more volatile than the equivalent value which includes the crisis period. This becomes
especially true when making forecasts for the crisis period (2007M8-2010M5) based on the
estimates of the pre-crisis era. These forecasts imply highly negative nominal interest rates
which are de facto impossible. However, the implied nominal interest rate including the crisis
period, does not come up with negative interest rates because of the reduced response
coefficients to inflation and the output gap. But this seemingly lower reaction is simply due to
the zero lower bound.
It has to be mentioned that since mid 2009 both implied rates are higher than the actual
interest rates, meaning that both central banks should tighten their policy by raising interest
rates. This fact is also evident when looking at real interest rates because here the actual
interest rate is also below the implied rates for both central banks.
So the evidence is clear for both central banks. However, by using our modified
Taylor reaction function the central banks have two instruments at hand to influence real
interest rate. The first one is by raising interest rates as it would also be the case in the
classical Taylor reaction function. But we recommend to follow the second way by reducing
- 18 -
gradually the central bank balance sheets to “normal” levels. This will have two advantages:
First, the central banks can increase the real rate by reducing inflation expectations, so the
mechanism explained in section 3 would be reversed. Second, the central banks can indeed
leave interest rates at low levels even if signs of a recovery are observed. This will bring
about credibility for the central banks in case of a similar crisis in the future.
5. Conclusions
In this paper we have shown that using Taylor reaction functions even in times of a
crisis like the one of 2007-10 leads to reasonable results, i.e. predicts that the role of the
inflation rate and the output gap decreases, even though there is evidence that before the crisis
the Taylor principle is also violated. However, we showed in our estimations of the Fed and
the ECB reaction functions that these results are likely to be underestimated since in this crisis
both central banks faced the zero lower bound on nominal interest rates which makes it
impossible for central banks to cut rates any further even if inflation rates and output gap
changes would call for further reductions.
Therefore, we introduced modified Taylor rules which do no longer try to influence
the nominal but the real interest rate. Since real interest rates are not directly under the control
of the central banks, because future inflation rates are not known, the central banks need to
influence the expectations of the market participants. Simple announcements to keep interest
rates low for a long time will not be promising to those within a crisis because it is subject to
a time inconsistency problem. That is why we used the length of the central banks balance
sheet to account for quantitative easing within the crisis. The readjustment of central banks
balance sheet from one asset class to another, known as qualitative easing, is not taken into
account in our analysis but it should also have played a role in the policy of central banks and
- 19 -
thus is likely to have influenced monetary policy rules like the Taylor rule. We will leave this
topic for further research.
However, also the huge amounts of additional funds issued because of quantitative
easing cannot be withdrawn from the markets immediately after a recovery and would thus
lead to higher inflation in the view of Friedman (1963). Introducing a model that estimates the
inflation expectations taking explicitly the quantitative easing of central banks into account,
we were able to show that the Fed and the ECB react, in fact, stronger to inflation and the
output gap than the classical Taylor rule would predict. Moreover, and in contrast to the
classical Taylor reaction functions, the modified reactions functions are able to verify that
both central banks are less inertial within the crisis, thus having a lower interest rate
smoothing coefficient, in line with the predictions of the Mishkin principle (Mishkin 2008 and
2009).
Since mid 2009 we find that the ECB and the Fed conduct a too loose monetary
policy, since the implied rates are above the actual ones. When using the real rate as
dependent variable this would call for either a rise in interest rates or a reduction in the central
bank balance sheet. We suggest to use the latter until the balance sheets are back at normal
levels since this would pay a double dividend for central banks by achieving their target of
influencing real rates and building up credibility for similar situations in the future.
- 20 -
References
Arestis, P. and Chortareas, G. (2007): Natural Equilibrium Real Interest Rate Estimates and
Monetary Policy Design; Journal of Post Keynesian Economics, Vol. 29 No. 4, pp.621-643.
Bank for International Settlements (2008): 78th Annual Report, 1 April 2007 -31 March 2008,
Basle.
Belke, A. and Polleit, T. (2007): How the ECB and the US Fed Set Interest Rates, Applied
Economics, Vol. 39(17), pp. 2197 - 2209.
Belke, A. and Klose, J. (2009): Does the ECB Rely on a Taylor Rule? Comparing Ex-post
with Real Time Data, DIW Discussion Paper No. 917, Deutsches Institut für
Wirtschaftsforschung, Berlin.
Belke, A. and Klose, J. (2010): (How) Do the ECB and the Fed React to Financial Market
Uncertainty? The Taylor Rule in Times of Crisis, DIW Discussion Paper No. 972, Deutsches
Institut für Wirtschaftsforschung, Berlin.
Bernanke, B., Reinhart, V. and Sack, B. (2004): Monetary Policy Alternatives at the Zero
Bound: An Empirical Assessment, Brookings Papers on Economic Activity, Vol. 2004 No. 2,
pp. 1-100.
Blanchard, O., Dell’Ariccia, G. and Mauro, P. (2010): Rethinking Macroeconomic Policy,
International Monetary Fund Staff Position Note, February 12, Washington D.C.
Cecchetti, S. (2008): Monetary Policy and the Financial Crisis of 2007-2008, CEPR Policy
Insight 21, Center for Economic Policy Research, London.
Clarida, R., Gali, J. and Gertler, M. (1999): The Science of Monetary Policy: A New
Keynesian Perspective; Journal of Economic Literature, Vol. XXXVII, pp. 1661-1707.
- 21 -
Clarida, R., Gali, J. and Gertler, M. (2000): Monetary Policy Rules and Macroeconomic
Stability: Evidence and some Theory; The Quarterly Journal of Economics, Vol. 115 No. 1,
pp. 147-180.
Cuaresma, J., Gnan, E. and Ritzberger-Gruenwald, D. (2004): Searching for the Natural Rate
of Interest: A Euro Area Perspective, Empirica, Vol. 31, pp. 185-204.
Eggertsson, G. and Woodford, M. (2003): The Zero Bound on Interest Rates and Optimal
Monetary Policy, Brookings Papers on Economic Activity, Vol. 2003 No. 1, pp. 139-211.
Friedman, M. (1963): Inflation: Causes and Consequences. Asia Publishing House, New
York.
Gerdesmeier, D. and Roffia, B. (2004): Empirical Estimates of Reaction Functions for the
Euro Area, Swiss Journal of Economics and Statistics, Vol. 140 No. 1, pp. 37-66.
Gorter, J., Jacobs, J. and de Haan, J. (2009): Negative Rates for the Euro Area?, Central
Banking, Vol. 20 No. 2, pp. 61-66.
Hodrick, R. and Prescott, E. (1997): Postwar U.S. Business Cycles: An Empirical
Investigation, Journal of Money, Credit and Banking, Vol. 29(1), pp. 1-16.
Jung, T., Teranishi, Y. and Watanabe, T. (2005): Optimal Monetary Policy at the ZeroInterest-Rate Bound; Journal of Money, Credit, and Banking, Vol. 37 No. 5, pp. 813-835.
Krugman, P., Dominquez, K. and Rogoff, K. (1998): It’s Baaack: Japan’s Slump and the
Return of the Liquidity Trap, Brookings Papers on Economic Activity, Vol. 1998 No.2, pp.
137-205.
Laubach, T. and Williams, J. (2003): Measuring the Natural Rate of Interest, Review of
Economics and Statistics, Vol. 85(4), pp. 1063-1070.
- 22 -
Leigh, D. (2008): Estimating the Federal Reserve’s implicit Inflation Target: A State Space
Approach, Journal of Economic Dynamics and Control 32, pp. 2013-2020.
Martin, C. and Milas, C. (2010): Financial Stability and Monetary Policy, University of Bath
working paper series, No. 05/10, Bath (UK).
Mishkin, F. (2008): Monetary Policy Flexibility, Risk Management and Financial
Disruptions, Speech given at the Federal Reserve Bank of New York, January 11.
Mishkin, F. (2009): Is Monetary Policy Effective during Financial Crises?, NBER Working
Paper No. 14678, National Bureau of Economic Research, Cambridge/MA.
Newey, W. and West, K. (1987): A Simple, Positive Definite, Heteroscedasticity and
Autocorrelation Consistent Covariance Matrix, Econometrica, Vol. 55(3), pp. 703-708.
Rudebusch, G. (2009): The Fed’s Monetary Policy Response to the Current Crisis, Federal
Reserve Bank of San Francisco Economic Letters 2009-17, San Francisco (CA).
Sauer, S. and Sturm, J. (2007): Using Taylor Rules to Understand European Central Bank
Monetary Policy, German Economic Review, Vol 8(3), pp. 375-398.
Taylor, J. (1993): Discretion versus Policy Rules in Practice, Carnegie-Rochester Conference
on Public Policy, Vol. 39, pp. 195-214.
Taylor, J. and Williams, J. (2009): A Black Swan in the Money Market, American Economic
Journal: Macroeconomics, Vol. 1(1), pp. 58-83.
Wu, T. (2005): Estimating the “Neutral” Real Interest Rate in Real Time, Federal Reserve
Bank of San Francisco Economic Letters 2005-27, San Francisco (CA).
- 23 -
Appendix
Data Sources USA:
Variable
Interest Rate
Inflation Rate
Output Gap
Import Price Inflation
Oil Price Inflation
Data Sources Euro Area:
Variable
Interest Rate
Inflation Rate
Output Gap
Import Price Inflation
Oil Price Inflation
Measure
Federal Funds Rate
Year on year change in the
personal consumption
expenditure (PCE) price
index
Industrial production
subtracted by its potential
value, estimated with an HPFilter (smoothing
parameter=14400)
Year on year change in the
price index for import goods
Year- on year change in the
price index for imports of
petroleum and petroleum
products
Measure
EONIA
Year on year change in the
harmonized index of
consumer prices (HICP)
Industrial production
subtracted by its potential
value, estimated with an HPFilter (smoothing
parameter=14400)
Year on year change in the
price index for import goods
and services
Year- on year change in oil
prices
Source
Federal Reserve
Bureau of Economic
Analysis
Federal Reserve
Bureau of Economic
Analysis
Bureau of Economic
Analysis
Source
European Central Bank
European Central Bank
European Central Bank
European Central Bank
European Central Bank
- 24 -
Figures
Figure 1: Interest Rates and Central Bank Balance Sheets
8
2,400,000
8
2,400,000
7
2,200,000
7
2,200,000
6
2,000,000
6
2,000,000
5
1,800,000
5
1,800,000
4
1,600,000
4
1,600,000
3
1,400,000
3
1,400,000
2
1,200,000
2
1,200,000
1
1,000,000
1
1,000,000
0
2006
2007
2008
Balance Sheet Fed
2009
800,000
2010
0
2006
Fed Funds Rate
Source: Fed and ECB.
Figure 2: Balance Sheet Gap
100
80
60
40
20
0
-20
1996
1998
2000
2002
Balance Gap Fed
2004
2006
2008
Balance Gap ECB
Source: Fed and ECB, own calculations.
2010
2007
2008
2009
Balance Sheet ECB
EONIA
800,000
2010
- 25 Figure 3: Expected Inflation and Real Interest Rate
8
12
10
4
8
0
6
-4
4
-8
2
0
1996
1998
2000
2002
2004
2006
2008
2010
-12
1996
1998
2000
Expected Inflation US
Expected Inflation Euro Area
2002
2004
2006
2008
2010
Real Interest Rate US
Real Interest Rate Euro Area
Source: own calculations
Figure 4: Nominal and Real (Implied) Interest Rates US
8
8
6
4
4
0
2
-4
0
-8
-2
-4
-12
97
98
99
00
01
02
03
04
05
06
07
08
09
97
98
99
Nominal Interest Rate
Implied Nominal Interest Rate Pre-Crisis
Implied Nominal Interest Rate Crisis
00
01
02
03
04
05
06
07
08
09
Real Interest Rate
Implied Real Interest Rate Pre-Crisis
Implied Real Interest Rate Crisis
Source: own estimations
Figure 5: Nominal and Real (Implied) Interest Rates Euro Area
8
3
2
6
1
4
0
2
-1
0
-2
-2
-3
-4
-4
00
01
02
03
04
05
06
07
08
Nominal Interest Rate
Implied Nominal Interest Rate Pre-Crisis
Implied Nominal Interest Rate Crisis
Source: own estimations
09
00
01
02
03
04
05
06
07
Real Interest Rate
Real Interest Rate Pre Crisis
Real Interest Rate Crisis
08
09
- 26 -
Tables
Table 1: Estimates inflation expectations model
Coefficient
Fed
ECB
(
0.83
(0.07)
0.14
(0.10)
0.03
(0.16)
-0.20
(0.17)
-0.02
(0.11)
0.04
(0.02)
1.32
(0.09)
-0.33
(0.15)
0.09
(0.11)
0.01
(0.01)
-0.01
(0.00)
0.05
(0.03)
0.09
(0.11)
-168.71
0.83
(0.10)
0.44
(0.14)
-0.56
(0.13)
0.24
(0.14)
-0.16
(0.12)
0.12
(0.08)
1.05
(0.12)
-0.20
(0.15)
-0.11
(0.11)
0.03
(0.01)
0.00
(0.00)
0.05
(0.02)
0.04
(0.06)
-147.73
)
1
4
B
"(
")
"" :
" >
"
"+
Log-Likelihood
Standard errors in parentheses.
- 27 Table 2:Classical and modified Taylor reaction functions in the pre-crisis period
Classical Taylor Reaction Function
Fed
ECB
Modified Taylor Reaction Function
Fed
ECB
2.1
2.5
A /C
D
EF @ *
J-Stat
0.86
(0.11)
0.38***
(0.08)
0.88
0.10
(0.22)
2.2
0.94***
(0.03)
1.33
(0.50)
0.71**
(0.31)
0.99
0.10
(0.27)
2.3
0.84
(0.13)
0.33***
(0.04)
0.84
0.13
(0.25)
2.4
0.86***
(0.04)
0.91
(0.25)
0.43***
(0.08)
0.98
0.12
(0.23)
-0.17
(0.12)
0.66***
(0.11)
0.85
0.08
(0.39)
2.6
0.70***
(0.06)
-0.40**
(0.16)
0.79***
(0.13)
0.96
0.12
(0.07)
2.7
-0.30**
(0.11)
0.21***
(0.04)
0.67
0.17
(0.10)
2.8
0.58***
(0.06)
-0.69***
(0.24)
0.33***
(0.05)
0.87
0.17
(0.06)
Notes: GMM estimates, Sample period 1996M12-2007M7 (Fed) and 1999M7-2007M7 (ECB), Number of
observations = 128 (Fed) and 97 (ECB), */**/*** denote significance at the 10%/5%/1% level (GH is tested for
to verify the Taylor principle of one, thus significance in this situation means differences from a coefficient of
unity), standard errors in parentheses, for J-statistic p-value in parentheses, columns 2.1, 2.3, 2.5 and 2.7 show
the results of regressions without a smoothing term while the remaining columns include this measure.
Table 3:Classical and modified Taylor reaction functions including the crisis period
Classical Taylor Reaction Function
Fed
ECB
3.1
3.2
3.3
3.4
A /C
D
EF @ *
J-Stat
0.30***
(0.14)
0.18***
(0.07)
0.86
0.05
(0.57)
0.98***
(0.03)
0.55
(1.30)
-0.24
(0.87)
0.99
0.08
(0.18)
0.62***
(0.09)
0.06***
(0.02)
0.86
0.10
(0.21)
1.03***
(0.04)
0.84
(0.51)
-0.49
(0.68)
0.98
0.07
(0.47)
Modified Taylor Reaction Function
Fed
ECB
3.5
3.6
3.7
3.8
-0.37***
(0.11)
0.34***
(0.07)
0.92
0.07
(0.39)
0.10
(0.16)
-0.41***
(0.13)
0.36***
(0.08)
0.93
0.07
(0.25)
-0.37***
(0.08)
0.10***
(0.02)
0.82
0.11
(0.13)
0.43***
(0.10)
-0.97***
(0.17)
0.17***
(0.03)
0.88
0.12
(0.07)
Notes: GMM estimates, Sample period 1996M12-2010M5 (Fed) and 1999M7-2010M5 (ECB), Number of
observations = 162 (Fed) and 130 (ECB), */**/*** denote significance at the 10%/5%/1% level (GH is tested for
to verify the Taylor principle of one, thus significance in this situation means differences from a coefficient of
unity), standard errors in parentheses, for J-statistic p-value in parentheses, columns 2.1, 2.3, 2.5 and 2.7 show
the results of regressions without a smoothing term while the remaining columns include this measure.