Download Threshold Models for Monetary Policy Rules for the Euro Area

Threshold Models for Monetary Policy Rules
for the Euro Area
Thanassis Kazanas 1
Elias Tzavalis2
Bank of Greece
November 2009
1
Athens University of Economics and Business, Department of Economics, 76 Patission Str., 104 34,
Athens, Greece. Email: [email protected]
2
Athens University of Economics and Business, Department of Economics, 76 Patission Str., 104 34,
Athens, Greece. Email: [email protected]
1
Threshold Models for Monetary Policy Rules
for the Euro Area
Abstract
The purpose of this paper is to analyse the monetary policy in Euro Area after the Maastricht
treaty. The simple instrument policy rule developed by Taylor (1993) has become a useful tool for
evaluating monetary policy of central banks. Using this rule we test empirically whether Euro Area has
monetary policy reaction function that changes depending on the level of the inflation. For this reason
we employ threshold type nonlinear monetary policy models that allow the existence of two policy
regimes according to whether the inflation is above or below a threshold value. The first model allows
for endogenous variables and an exogenous threshold variable while the second allows for an
endogenous threshold variable. We estimate the threshold parameter with two stage least squares and
the slope parameters with the generalized method of moments. The results give evidence of
nonlinearity in the way that the Euro Area conducted its monetary policy.
JEL Classification: E52, C13, C30
Keywords: Nonlinear Taylor rules, monetary policy, inflation targets, two stage least
squares, generalized method of moments, threshold value, switching regime
2
1. Introduction
The modeling of central banks’ monetary policy functions has become very
popular during the last decades. There is a growing number of economists who try to
unveil the variables that affect the behavior of the monetary authorities and analyse
the way that these variables affect such behavior. The rule that is assumed by the
researchers to capture the central bank’s strategy is an interest rate reaction function.
The estimation of such rules is very popular for many reasons. These rules can be
used for forecasting the path of the central bank’s policy instrument, namely the short
term nominal interest rate. They also can provide a useful tool for policy evaluation in
the context of a macro model or for estimating the entire model under the assumption
of rational expectations.
The increasing interest for estimating such rules was encouraged by John
Taylor’s (1993) remarkable work on interest rate policy rules. These simple empirical
reaction functions illustrate the way that the short term nominal interest rates were set
in the past indicating possible paths for future policy. They also capture the main
characteristics underlying a central bank’s interest rate behavior. Especially the so
called Taylor rule has received considerable attention mainly due to the fact that it’s
simple and describes the actual behavior of the Federal Funds rate in the United States
in a meaningful way. It also fits euro area data surprisingly well. This rule relates the
short term nominal interest rate to inflation and output deviation from its target.
However, as shown by Svensson (2003) even if the primary objective of the monetary
authorities is to stabilize inflation and output, a simple Taylor rule will not be optimal
in a reasonable macroeconomic model. For this reason the setting of the short term
nominal interest rate has to be based on expected inflation and output. This means that
the monetary policy has to be forward looking. Consequently, monetary policy rules
seem to be more complicated than the simple Taylor rule.
The establishment of the European Monetary Union on 1st January 1999 has led
the member countries to be subject to a centralized monetary policy conducted by the
European Central Bank (ECB) and a common currency. This centralized monetary
policy has to be directed towards maintenance of price stability over the medium term
in the euro area supporting sustainable and non inflationary growth. The focus of the
ECB is on price stability in the euro area as a whole. This fact has led in the
increasing research on the ECB’s monetary policy strategy in recent years. Most of
this research has focused on the specification of the appropriate monetary policy rule
3
and the welfare improvement that is achieved by using this rule. Many researchers
estimate contemporaneous, backward and forward Taylor type rules for the ECB or
for the hypothesized euro area (before the establishment of the ECB). They also allow
for smoothing interest rate preferences in the spirit of Clarida, Gali and Gertler
(1999).
Even though most of the studies assume symmetry in the way that the monetary
policy is conducted by the authorities, the ignorance of the possible asymmetry
reaction of the short term nominal interest rate to the main economic variables can
lead to misleading results. Therefore, it is interesting to examine the existence of a
non linear policy reaction function in which the weights on inflation and output
deviations will be regime dependent. In order to investigate this claim, we extend the
relating literature in Taylor type policy rules in euro area and estimate non linear
forward looking reaction functions using monthly data over the period 1994:1 –
2008:8. The paper contributes to the literature on the Taylor rules for the euro area by
estimating the interest rate behavior of the monetary authorities in a switching regime
framework using two approaches. First, we follow Caner and Hansen (2004)
Instrumental Variable Threshold (IVTR) approach. Under this procedure we allow for
endogenous variables and an exogenous threshold variable. The endogenous variables
are the expected inflation and output deviations while the exogenous threshold
variable is the inflation gap of the previous period. Second, we estimate the
asymmetric policy reaction function following the Kourtellos, Stengos, and Tan
(2008) Threshold Regression with Endogenous Threshold variables and Slope
parameters (THRETS) approach. In this specification we allow the threshold variable
to be the expected inflation gap over the current period. The results of our study
reveal that the monetary authorities react in an asymmetric way to the main economic
variables. When the threshold variable is below its estimated value the monetary
authorities seem to abandon the Taylor rule. In the other regime, where the threshold
variable is above its estimated value, the Taylor principle is followed by the policy
makers.
The plan of the paper is as follows. Section 2 presents an overview of the
relating literature on Taylor rules and section 3 discusses the baseline features of the
nonlinear monetary policy rules. Section 4 presents the estimation procedures of our
threshold type models and the corresponding results. Section 5 concludes the paper.
4
2. Relating literature
Although there are numerous studies on the behavior of the Federal Reserve the
approach has been extended to other economies and central banks. Based on this
framework, Clarida, Gali and Gertler (1998, 2000) examine a forward looking (12months ahead) monetary policy reaction function that the central bank adjusts the
interest rate according to the expected future deviation of inflation and output from
their target values. The authors first study the behavior of three major central banks
(US, Japan and Germany) in the setting of short term nominal interest rate. After that
they examine the monetary policy behavior of three main European countries (Italy,
France and UK). Their results for the first set of countries support the argument for
price stability through the adoption of a form of inflation targeting as the inflation
coefficient is greater than unity. This means that these major central banks raise the
nominal interest rate so that to increase the real interest rate when the expected
inflation is above its target. They also show that this baseline forward looking
specification works quite well against various alternatives including the backward
looking model. Although these simple forward looking rules seem to characterize the
monetary policy of the three major central banks do not describe well the behavior of
the European authorities. The monetary policy in these countries seem to be restricted
by the Bundesbank as the nominal interest rate setting is significant and destabilizing
towards to inflation gap and also significant towards to the German interest rate. Even
though the study examines more complex policy rules specifications allowing the
central bank to respond to variables other than output and inflation however, doesn’t
take into consideration the possibility that the policymakers’ preferences may be
asymmetric with respect to inflation deviations and the output.
Many empirical studies have been conducted since the establishment of the
ECB in 1999. Most of the papers have estimated a Bundesbank or a hypothetical ECB
policy rule prior to 1999. Also, many researchers, despite the short history of the
ECB, estimate actually ECB reaction functions. Fourçans and Vranceanu (2007)
analyse the ECB monetary policy over the period 1999-2006. They estimate
contemporaneous
and
forward
looking
rules
using
monthly
data.
The
contemporaneous rules do not seem to be supported by the data while in the forward
looking rules the inflation and the output gap seem to play a significant role. More
specifically the inflation coefficient is greater than unity indicating a stabilizing
reaction of the ECB toward to the inflation. The coefficient of the output gap is
5
greater than zero pointing out the focus of the ECB on the real economic activity a
fact that contradicts the announcements of the ECB about price stability being the
ultimate target. As the authors point out, the achievement of the desired ECB’s
credibility will be difficult if the inflation objective is sacrificed to the boosting real
economic activity in bad times. Fourçans and Vranceanu (2006) also analyse the
monetary policy that was followed by the ECB and the Fed over the period 19992005. They estimate forward looking interest rate rules and VAR models for the two
economies. Their results reveal a strong reaction of the ECB and the Fed to inflation
expectations. The authors suggest that the goals of the ECB are not significantly
different from the Fed’s. Despite the ECB’s attempt to build in credibility the existing
differences in the behavior between the two banks are attributed to differences in the
economic structures of the two areas.
Ullrich (2003) estimates Taylor type policy rules of the Euro Area and the Fed
before and after the start of the European Monetary Union. She estimates a significant
break in the ECB’s reaction to inflation with the beginning of the monetary union in
1999. The interest rate reaction to inflation seems to be strong in the period before
1999 with the corresponding coefficient to be greater than unity. After the beginning
of the monetary union the ECB seems to behave with a destabilizing manner towards
to the inflation as the estimated coefficient is below unity. The study also concludes
that the Fed’s interest rate policy has an impact on the ECB policy after 1999 as the
short term interest rate of the Fed is significant in the ECB’s reaction function.
Gerlach-Kristen (2003) studies the behavior of short term interest rates in the
euro area comparing the traditional formulation of the Taylor rule, which is estimated
on level data, to an interest rate reaction function which takes into consideration the
nonstationarity of the data. Her estimations show that the traditional Taylor rule
exhibits signs of instability and mis-specification. She estimates the Taylor rule using
a cointegration approach regarding an unrestricted and a restricted version of the I(1)
model of the Taylor rule. The unrestricted model uses a cointegrating vector that is
composed of the short term and long term nominal interest rates, inflation and the
output gap. The long rate can be used as a proxy for the long run public’s inflation
expectations as the study reveals. This conclusion is in favor of a forward looking
behavior in the interest rate policy rule in the euro area. The results of the unrestricted
I(1) model, in which a unit coefficient on inflation is imposed, give evidence that the
monetary policy is set in a way that the Taylor principle is met. This model also
6
exhibits better out of sample forecasts than the traditional Taylor rule and the
unrestricted model.
Gerdesmeier and Roffia (2003) estimate a series of alternative monetary policy
reaction functions for the euro area over the period 1985-2002 using monthly and
quarterly data. They specifically assess the performance of Taylor type interest rate
rules describing the euro area interest rate setting. For this reason they consider
additional variables, which are not included in the classical Taylor specification, to
which the monetary authorities might have responded to. The general finding is that a
Taylor rule that includes an interest rate smoothing seems to describe the monetary
policy in the euro area very well. The coefficients are according to the Taylor
principle meaning that there is a stabilizing interest rate reaction to inflation
deviations and a positive response to the output gap. These results do not seem to
change considerably when quarterly data are used.
Apart from the increasing number of studies which focus on the estimation of
Taylor type rules for the euro area there are many papers that investigate the
performance of these rules. Gerlach and Schnabel (2000) find that the fall in the
average interest rate of euro area in the last decade is explained well by the original
Taylor rule with parameter of 1.5 on inflation and 0.5 on the output gap. Adding other
explanatory variables in the Taylor rule doesn’t seem to significantly affect the
weights on inflation and the output gap.
Most studies on the central bank behavior use current or ex-post data neglecting
the fact that the policy makers set their short term nominal interest rate according to
the latest available information. So, as the central bankers react in real time they can
only use real time data, data that are available at the time they take their decision.
Orphanides (2001) shows that the use of ex-post revised data in estimated interest rate
reaction functions can lead to misleading descriptions of historical policy in the case
of the US. Sauer and Sturm (2003) estimate several interest rate reaction functions for
the ECB using monthly data over the period 1999:1 - 2003:3 and for the Bundesbank
over the period 1991:1-1998:12. The estimation of contemporaneous Taylor rules
suggests that the ECB is accommodating changes in inflation following a
destabilizing policy. Regarding a forward looking perspective of the ECB the
estimates reveal a stabilizing path to be followed. This means that the changes in the
nominal interest rate were large enough to stimulate the short term real interest rate.
Using real time data the estimated contemporaneous and forward looking
specifications don’t seem to lead to significantly different results. They also use
7
survey data that their real time character combined with their forward looking nature
seems to produce the best fit confirming the stabilizing role of the ECB. Similar
results are found by Gorter, Jacobs and Haan (2007) using euro area consensus data
for the period 1997:1-2006:12.
All the previous mentioned studies examine the central bank behavior in a
symmetric way. They estimate linear Taylor type rules without taking into
consideration any specification to capture possible nonlinearities. It’s possible for the
policymakers to dislike positive inflation deviations more than negative ones or to
react more aggressively to the output gap when the inflation lies below its target. The
political power may influence the monetary authorities in favor of the population,
especially in election periods. And this happens because of the possible fact that
people dislike unemployment more than inflation, especially when the inflation rates
are low. Blinder (1998) suggests that political demands may lead to an asymmetric
policy reaction.
Recent literature explores the existence and the effects of asymmetries or
nonlinearities in monetary policy rules. Wesche (2003) estimates monetary policy
reaction functions for France, Germany, Italy, the United Kingdom and the United
States. She uses a Markov-switching model that incorporates switching in the
coefficients of the monetary policy regime as well as an independent switching
process for the residual variance. The results encourage the aspect that the central
banks have assigned changing weights in the inflation and the output gap. The one
regime entails reaction function with high weight on output and low weight on
inflation while in the other regime the opposite happens. The switching in the residual
variance seems to capture the effects of other factors that are not modeled explicitly in
the monetary policy rule.
Gredig (2007) tests whether the monetary policy reaction of the Bank of Chile
depends on the actual state of the economy and in particular the output gap, the
inflation deviation and the GDP growth rate. He estimates a threshold model for the
Central Bank of Chile’s policy rule that allows the existence of two policy regimes
according to whether the output gap, the inflation deviation or the GDP growth rate is
above or below an estimated threshold value. His estimations show that the monetary
authorities respond strongly to inflation deviations but weakly to the output gap when
the gap is larger than a specific threshold value. Under simulations his estimated
monetary policy rule behaves asymmetrically in the inflation rate inducing a small
negative bias.
8
The estimations of Surico (2003) show that the ECB and the Fed respond
asymmetrically to the output gap during the period 1997:07-2002:10. The central
banks’ reaction is stronger to positive than negative output gap deviations while their
behavior is symmetric towards inflation deviations. Taylor and Davradakis (2006)
find nonlinearity in the Bank of England’s monetary policy setting during the period
1992:10-2003:1. Their estimations give evidence that the standard Taylor rule begins
to bite once expected inflation is significantly above a threshold value of 3.1%.
Karagedikli and Lees (2004) find that the Reserve Bank of Australia views negative
output gaps more costly than positive output gaps, while the central bank of New
Zealand reacts symmetrically during the inflation targeting period. Martin and Milas
(2004) investigate the monetary policy in the U.K. for the period 1963-2000. They
find that the adoption of inflation targets led to significant changes in monetary policy
in the post-1992 period. The Bank of England seems to react stronger to positive than
negative inflation deviations as well as to attempt to keep inflation within a range of
1.4%-2.6% rather than achieve the desired target of 2.5%.
Kim, Osborne, and Sensier (2005) investigate the nature of nonlinearities in the
central bank’s reaction function without assuming a specific parametric model. They
use a flexible approach to nonlinear inference developed by Hamilton (2001). The
methodology of Hamilton provides a test of the null hypothesis of linearity against a
broad range of alternative nonlinear models as well as consistent estimation of what
the nonlinear relation looks like allowing for comparison of alternative nonlinear
models. The authors, following Clarida et al (2000) and others, consider the monetary
policy reaction function for the postwar US economy from 1960 until recently. They
split the sample in two periods before and after Volcker’s appointment as Fed
Chairman in 1979. Although they don’t find evidence of nonlinearity in the monetary
policy reaction function in the whole period, they find strong evidence for
nonlinearity in the pre-Volcker era but unimportant evidence in the VolckerGreenspan era. They come to the conclusion that possible asymmetries in the Fed’s
reactions to inflation deviations from target and the output gap in the 1960s and 1970s
may tell something, but do not capture the entire nature of nonlinearity.
3. Monetary Policy Rules
3.1 Linear Taylor Rules
The ECB has become very independent since the Maastricht Treaty a fact that is
according to restraining inflation in a low level. It is highly believed that an
9
independent central bank can give full priority to the price stability. According to the
Governing Council of the ECB the price stability can be attained by keeping the year
on year increase of the harmonized index of consumer prices (HICP) for the euro area
below, but close to 2% over the medium term. Price stability is one of the two pillars
that the monetary policy strategy of the ECB is based on. The other pillar gives a
prominent role to money according to which the annual growth rate of a broad
monetary aggregate (M3) has to be according to a reference value. This is done
because the inflation in the long run is considered to be a monetary phenomenon.
For this reason maybe it is possible to describe the monetary policy in the euro
area by a similar to the US simple policy rule in which the policy instrument is
depended on inflation and output deviations. The simplest monetary rule has proposed
by Taylor (1993). This is a feedback policy rule where the nominal interest rate
responds to observed deviations of inflation and output from their target values rather
than their expected, i.e.:
it* = a + β (π t − π * ) + γ yt
( 3.1)
where it* is the target rate, π t is the rate of inflation, π * is the inflation target and yt
is the output gap. yt is defined as the percent change between actual GDP and the
corresponding target (e.g. potential GDP). The parameter a is the desired nominal
interest rate when inflation and output are at their target values ( a = r * + π * ) with r *
being the long run equilibrium real interest rate and β > 1 and γ > 0 . Taylor showed
that this rule provides a reasonable good description of the U.S. economy for the
period 1987-1992. The values of the parameters of model ( 3.1) are r * = 2 , π * = 2 ,
β = 1.5 and γ = 0.5 .
Svensson (1999) shows that such a rule is the optimal reaction function for a
central bank adopting an inflation target in a simple backward looking model which
includes an IS and a Philips curve. The output gap is a useful tool in forecasting future
inflation so that it enters the reaction function even if the central bank has an inflation
target.
Using this simple form for monetary policy, several authors have tried to
estimate the weights on inflation and output deviations from their targets than
choosing the values proposed by Taylor. Such models take the following form:
it* = a + β (π t − π * ) + γ yt + ε t
( 3.2)
10
where the ε t is the usual i.i.d. error term. An empirical question that arrives through
this estimation is if the estimated coefficients follow the so-called Taylor principle.
Since it is the real interest rate that actually drives the private decisions, the inflation
coefficient has to be greater than unity so that the nominal interest rate to be
responded enough to inflation deviations and to actually increase the real interest rate.
If this doesn’t hold then self-fulfilling bursts of inflation may be possible (Bernanke
and Woodford 1997; Clarida et al, 1998). The coefficient of the output gap has also to
be positive in order for the monetary policy to have a stabilizing influence on output.
The Taylor policy rules are in general contemporaneous or backward looking as
they relate the interest rate to current or lagged values of inflation and the output gap.
As an enhancement of these standard rules many authors following Clarida et al.
(1998) relate the monetary policy to expected economic conditions. They specifically
use forward looking rules where the target interest rate it* is set in response to
expected inflation and output deviations from their target levels:
(
it* = i + β ( E [π t + n | Ωt ] − π * ) + γ E ⎡⎣ yt + k − yt*+ k | Ωt ⎤⎦
)
( 3.3)
The constant i is the long run equilibrium nominal interest rate (the desired nominal
interest rate when inflation and output are at their target values), π t + n is the rate of
inflation n periods ahead, yt + k is real output k periods ahead and π * , yt* are the
desired targets for inflation and real output accordingly. E is the expectation operator
and Ωt is the information set that is available to the central bank at the time it sets its
nominal interest rate. This specification allows for the possibility that when the
central bank chooses the target interest rate may not have direct information about the
current values of either output or the price level.
The monetary policy rules given by ( 3.2 ) and ( 3.3) seem to be too restrictive if
someone wants to describe the actual changes in the nominal interest rate. One main
reason for this is the fact that these forms do not take into account the central bank’s
tendency to smooth changes in interest rates but assumes an immediate adjustment of
the interest rate to its target value. This central banks’ tendency for smoothing stems
from various reasons such as the fear of disrupting capital markets, the loss of
credibility from sudden large policy reversals or the need for consensus building to
support a policy change. Moreover, the central bank may regard the interest rate
smoothing as a learning device due to imperfect information. All these factors that
mentioned are indeed very difficult to be captured. For this reason we assume
11
following Clarida et al. (1998) that the actual rate adjusts partially to its target
according to:
it = (1 − ρ ) it* + ρ it −1 + ε t
( 3.4)
with the parameter ρ ∈ [ 0,1] capturing the degree of smoothness. The randomness of
policy or the imperfect forecast of demand for reserves derived by the central bank
could be reflected by the random shock ε t . Under this partial adjustment behavior the
central bank wishes to adjust its instrument in order to eliminate only a fraction
(1 − ρ ) of the gap between its current target level and some linear combination of its
past values. Substituting ( 3.2 ) or ( 3.3) into ( 3.4 ) , the following specifications for the
contemporaneous or the forward looking model are derived:
(
)
it = (1 − ρ ) a + β (π t − π * ) + γ yt + ρ it −1 + ε t ,
(
( 3.5)
)
it = (1 − ρ ) i + β ( E [π t + n | Ωt ] − π * ) + γ ( E [ yt + k | Ωt ]) + ρ it −1 + ε t ,
( 3.6)
where ε t is an i.i.d. exogenous shock with zero mean. This forward looking Taylor
rule is an approximation to forecast based rules of the kind proposed by Rudebusch
and Svensson (1999) and Batini and Haldane (1998). These rules are the outcome of
dynamic structural optimizing models that take into account lags in the monetary
transmission mechanism attributable to price stickiness (Rotemberg and Woodford,
1999) or to rigidities in the money market (Christiano, Eichenbaum and Evans, 1997).
Table 1 presents a review of different Taylor rule estimations for the euro area
using monthly or quarterly data. From these estimations it is shown clearly that the
monetary policy prior to 1999 followed the Taylor principle as the β coefficient
exceeds unity. It is also shown that the forward looking behavior do not seem to differ
significantly from the contemporaneous under this period. One main reason for this
may be the relative stable environment in which the actual measures of the business
cycle and of the inflation may indicate pretty well the future developments. In less
stable environments, as is the period after the establishment of the ECB, the
contemporaneous measures may be inadequate future indicators.
Regarding the actual ECB monetary policy, the Taylor rule estimations lead to
contradicting results. The estimations of Fourçans and Vranceanu (2002, 2006)- who
take the annual growth rate of industrial production as a business cycle measurereveal a strong reaction of the ECB to variations in the inflation rate and a much less
reaction to the output gap. Gerdesmeier and Roffia (2003) and Ullrich (2003), using
12
standard output gap measures based on the Hodrick-Prescott filtered industrial
production, estimate ECB reaction functions that reveal a destabilizing role of the
monetary authorities to the inflation deviation and a strong reply to the output gap.
Ullrich (2003) also estimates a structural break dated at the start of the monetary
union. Summarizing, in contrast to the hypothetical euro area, the actual ECB policy
since 1999 does not seem to be consistent with the Taylor principle.
3.2 Non-Linear Taylor Rules
The monetary policy rules that are mentioned in the previous section assume
that the monetary authorities respond symmetrically to their policy objectives. But in
empirical applications different forms of monetary policy reaction functions allowing
for time varying coefficients have been developed. Some authors (see Clarida et al.
2000 or Judd and Rudebusch 1998) split the sample at a presumed date break and
estimate the equations for the two regimes separately. Doing this method the previous
two studies investigate the possible effects of different central bank presidents over
the conduct of the Fed’s monetary policy. Neumann and von Hagen (2002) also
examine for changes in the Taylor rule due to the introduction of inflation targeting in
six countries.
The common feature of the inflation targeting regimes is the built in flexibility.
Taking as given the difficulty of forecasting future patterns of inflation and the fact
that many economic shocks may have temporary effects on inflation, all inflation
targeting regimes allow the central bank to miss the target in a specified range. So, it
is natural to believe that when the output gap is negative and the unemployment high
most inflation targeting regimes allow inflation to exceed temporarily its target.
However, sometimes may be difficult to explain (at least politically) the existence of
negative inflation deviation taking into consideration that the political power and the
population are concerned more about unemployment than inflation. Under these
circumstances, especially when the economy is at recession, it is obvious that
monetary policy rules allowing asymmetrical responses to output gap and/or inflation
deviations should be considered. For this reason, some approaches use dummy
variables to estimate different coefficients depending on inflation or output being
above or below target (see Dolado, María-Dolores and Naveira 2000). The main
disadvantage of these two methods, the sample splitting and the dummy variable
approach, as it’s pointed out by Wesche (2003) is the fact that the researcher has to
13
find exogenous information indicating that a switch regime has occurred. The
estimation generally assumes that the long run inflation and the long run real interest
rate equal their equilibrium value something that holds only if the sample period is
sufficiently long. So, as the sample splitting shortens the available data set the
assumptions may be violated. While this problem is avoided under the dummy
variable approach again the researcher has to find the factors that are responsible for a
shift in regime.
Including non linear relations for the coefficients in a Taylor rule is an
alternative specification. Gerlach (2000) estimates simple reaction functions for the
Fed allowing for a non linear impact of the output gap. His results suggest that
asymmetric policy reactions are relevant for explaining average inflation rates. This
non linear specification implies a gradual change in the monetary authorities’ reaction
to the main variables in contrast to a sudden switch in regime.
Markov switching is an alternative way to model the possible asymmetries that
may arise in central banks’ policy reaction functions. These models have been used in
business cycles and exchange rate analysis (Hamilton 1989, Engel and Hamilton
1990). The regime switching does not occur deterministically but with a certain
probability. Not only does the researcher estimate the central bank’s weights on
inflation and output but also examines the way that these weights change over time.
Finally, threshold models seem to play a significant role to the non linear
specifications of the interest rate reaction functions. According to these models the
monetary authorities’ reactions depend on whether a threshold variable is lesser or
greater than a specific value that is estimated from the data. These models are
estimated consistently through a sophisticated method developed by Hansen (1997,
2000) and Caner and Hansen (2004) who allow for exogenous and endogenous
variables and an exogenous threshold variable. Kourtellos, Stengos, and Tan (2008)
extend the previous approach allowing for an endogenous threshold variable.
Based on these last approaches for threshold modeling we estimate the
following monetary policy rule:
(
(
)
⎧(1 − ρ ) i + β ( E [π t + n | Ωt ] − π * ) + γ E [ yt + k | Ωt ] + ρ it −1 + ε t , if qt -d ≤ q
⎪
it = ⎨
*
⎪⎩(1 − ρ ) i + β ′ ( E [π t + n | Ωt ] − π ) + γ ′E [ yt + k | Ω t ] + ρ it −1 + ε t , if qt -d > q
)
(3.7)
14
where q is the estimated threshold value for the threshold variable and the
disturbance term, ε t , is assumed to be white noise. As a threshold variable we will
consider the inflation deviation from target.
4. Empirical Results
In this section we carry out estimates of the euro area policy reaction functions
using monthly data over the period 1994:01-2008:8. The data set that comes from the
ECB 3 website ends before the time that the financial crisis hit the European economy.
We report our data set and after that we describe the estimation procedure to obtain
our results.
4.1. Data
The dependent variable is a relevant measure of the target short term interest
rate. We use as a proxy the Euro Overnight Index Average (EONIA) lending rate on
the money market. 4 The inflation rate is measured by a year on year increase of the
⎛
⎞
P −P
harmonized index of consumer prices (HICP) for the euro area ⎜ π t = t t −12 ⋅100 ⎟
Pt −12
⎝
⎠
and the inflation target is set equal to 2%. As a measure of the output gap we employ
the deviation of the industrial production index growth rate from the over the period
average (see Fourçans and Vranceanu 2007). The growth rate is calculated as the
percentage change of the industrial production index from one month to the same
month of the previous year. Our data set also includes the M3 money growth rate, the
Eurostoxx 50 stock price index and the economic sentiment indicator (ESIN).
4.2. Estimation of the baseline model
Before we estimate the baseline model, we give some descriptive statistics for
our main economic variables. These statistics are given in Table 2. The average
growth rate of the industrial production index is 2.37% and the unemployment rate is
around 9%. The inflation rate seems to be close to the target of 2% and the nominal
interest to a higher rate of 3.75%.
Our baseline model is:
3
4
Appendix 1 includes all the times series that are used in this study and their sources.
The EONIA is the European equivalent of the Federal Funds rate for the US.
15
(
)
it = (1 − ρ ) α + β ( E [π t + n | Ωt ] − π * ) + γ E [ yt + k | Ωt ] + ρ it −1 + ε t
( 4.1)
We can substitute the unobserved forecast variables with their realized values as
follows:
(
)
it = (1 − ρ ) α + β (π t + n − π * ) + γ yt + k + ρ it −1 + ut
( 4.2 )
{
}
where the error term ut = − (1 − ρ ) β (π t + n − E [π t + n | Ωt ]) + γ ( yt + k − E [ yt + k | Ωt ]) + ε t
is a linear combination of the forecast errors of inflation, output and the exogenous
disturbance ε t . Suppose that z t is a vector of variables within the central bank’s
information set at the time it chooses the interest rate that are orthogonal to ut . Any
lagged variables that help central bank to forecast inflation and output as well as
contemporaneous variables that are uncorrelated with the current interest rate shock
ε t are possible to be included in the instruments set z t . Since E [ut | z t ] = 0 we have
the following set of orthogonality conditions:
(
)
E ⎡it − (1 − ρ ) α + β (π t + n − π * ) + γ yt + k − ρ it −1 | z t ⎤ = 0
⎣
⎦
( 4.3)
We estimate the parameter vector (α , β , γ , ρ ) through the Generalized Method of
Moments. The disturbance term of our model has a MA ( l − 1) representation where
l = max {n, k } (Hansen and Hodrick, 1980). The instrument set z t includes beside a
constant, one to three lagged values of interest rates, inflation, output gap, money
growth, stock price index and the economic sentiment indicator. We set n = 3 and k = 0
and the estimates are obtained using a Newey-West optimal weighting matrix with 11
lags.
Most of the relating studies to the Taylor type reaction functions do not pay
much attention to the properties of time series. Many authors assume that the
variables of interest that included in the Taylor rule are stationary. Clarida et al.
(2000) find this assumption as reasonable for the postwar U.S. even though the null of
a unit root in either variable is often hard to reject at conventional significance levels,
given the persistence of both series and the low power of unit root tests. So, given that
our sample is relatively small, we follow this approach assuming that the variables of
interest do not present a unit root.
16
Table 3 reports estimates 5 for the baseline model’s parameters. The results of
this table show that our estimates are statistically significant at the significance level
of 1% with a high R 2 and a J-statistic that leads to the acceptance of the null
hypothesis of overidentifying restrictions. We see that the coefficient of inflation, β ,
is below than unity and the coefficient of output gap, γ , is greater than zero. These
results indicate a destabilized monetary policy rule concerning the reaction of the
EONIA rate according to inflation deviation from its target. On the other hand, the
positive response of the central banker to the real economic activity contradicts the
official position as the economic activity seems to be a direct objective of the policy
maker. Moreover, the smoothing parameter ρ is close to unity indicating a strong
evidence of smoothing policy in the monetary authorities.
4.3. Estimation of the nonlinear model with known threshold value
Our estimate of the threshold model ( 3.7 ) starts first with the case that the
threshold value q is known. Allowing the threshold variable to be the inflation
deviation of the previous period and taking the zero as a natural value for the inflation
deviation threshold ( qπ = 0 ) we split the sample according to this threshold and
estimate the two possible regimes with GMM. The results of this estimation which are
in Table 4 do not show a strong asymmetric behavior of the central bank as the Wald
test rejects the null hypothesis of linearity at a significance level of 10%. Specifically,
when the inflation of the previous month is below or equal to its target the monetary
authorities seem to follow the Taylor principle with a strong reaction to inflation
deviation ( β = 3.17 ) and the output gap ( γ = 1.21) . In the other regime where the
inflation exceeds its target the coefficient of the inflation is statistically insignificant
while the coefficient of the output gap is significant and positive. This is a really
implausible result as one would expect the stronger reaction of the central bank to the
inflation deviation. The interest rate smoothing parameter is relative high
( ρ = 0.86 ) and the long run nominal interest rate is almost equal to its sample mean.
The implementation of inflation deviation over the current period as a threshold
variable leads to similar results to that found in the previous case. So, it’s possible for
5
All estimates are carried out with RATS.
17
the central bank to behave asymmetrically to the main economic variables considering
a different value for the threshold parameter.
4.4 Estimation of the nonlinear model with unknown threshold value
The results of the previous section state that the assumption of a pre-specified
value for the threshold parameter may be restrictive in estimating the model. If the
true threshold variable is different than the known, then our estimates will not be
correct. For this reason we estimate the nonlinear monetary policy model allowing the
threshold parameter to be unknown. We use two different approaches in order to
estimate the threshold parameter and the slope parameters of the model. First, we use
the Caner and Hansen (2004) approach in which the threshold variable is allowed to
be the inflation deviation of the previous period. Second, following the Kourtellos,
Stengos and Tan (2008) approach we regard as an endogenous threshold variable the
inflation deviation over the current period.
4.4.1 Instrumental Variable Threshold Model (IVTR)
Considering as a threshold variable the inflation deviation of the previous
month, we estimate the threshold parameter and the coefficients of the model
following the method developed by Caner and Hansen (2004). The threshold value q
is estimated by finding the value q * that minimizes the sum of squared residuals of
the following model:
(
(
)
⎧(1 − ρ ) α + β (π t +3 − π * ) + γ yt + ρ it −1 + ut , if π t -1 ≤ q
⎪
it = ⎨
*
⎪⎩(1 − ρ ) α + β ′ (π t +3 − π ) + γ ′ yt + ρ it −1 + ut , if π t -1 > q
)
which also may be written in the form
it = (1 − ρ ) (α + ( βπ t +3 + γ yt ) 1 (π t -1 ≤ q ) + ( β ′π t + 3 + γ ′ yt ) 1 (π t -1 > q ) ) + ρ it −1 + ut (4.4)
The method is based on a two-stage least squares procedure that allows for
endogenous explanatory variables and an exogenous threshold variable. The estimator
is based on estimation of the reduced form regressions for the endogenous variables
( π t , yt ) as a function of exogenous instruments ( z t ):
π t = Π1′z t + et and yt = Π ′2 z t + vt
where z t is a m×1 vector of instruments and Π1 , Π 2 are m×1 parameter vectors.
Estimating the reduced form parameters Π1 and Π 2 we obtain the predicted values
18
(
for the endogenous variables. After that we substitute these predicted values πˆt , yˆ t
)
into the structural equation of interest:
( (
)
(
)
)
it = (1 − ρ ) α + βπˆt +3 + γ yˆt 1 (π t -1 ≤ q ) + β ′πˆt +3 + γ ′ yˆt 1 (π t -1 > q ) + ρ it −1 + ut
(4.5)
The threshold parameter is estimated through sequential conditional least-squares
estimation. For each possible value of the threshold parameter we estimate the
equation (4.5) and keep the residual sum of squared errors. This procedure is repeated
from the 15th up to the 85th percentile of the threshold variable so that each regime
includes an adequate number of observations. The 2SLS estimator for q is the
minimizer of the sum of squared errors:
qˆ = arg min S n ( q )
q ∈Q
where
n
(
( (
)
(
)
)
S n ( q ) = ∑ it − (1 − ρ ) α + βπˆt +3 + γ yˆt 1 (π t ≤ q ) + β ′πˆt + 3 + γ ′ yˆt 1 (π t > q ) − ρ it −1
t =1
)
2
and Q is the set that includes the values of the threshold variable. In order to estimate
the structural equation’s slope parameters we split the sample according to the
estimated threshold and perform GMM estimation.
To
test
model
linearity ( H 0 : β = β ′ ∧ γ =γ ′ vs H1 : β ≠ β ′ ∨ γ ≠ γ ′ )
we
construct a quasi likelihood ratio (Q-LR) test statistic as follows:
Q − LR = J restricted − J unrestricted
where J restricted and J unrestricted are the objective functions that GMM minimizes for the
restricted and unrestricted models respectively. In order to derive the empirical
significance levels of this test statistic we carry out a non-parametric bootstrap
simulation procedure according to Hansen (1996). First, we estimate the baseline
(restricted) model with GMM and we store the residuals and the fitted values of the
interest rate. Second, we draw with equal probability and with replacement from the
vector of residuals to construct a new vector of residuals. Third, adding the new
vector of residuals to the fitted values of the interest rate we obtain a new artificial
vector for the interest rate. Fourth, using the artificial vector of the interest rate we
estimate the linear and the threshold model constructing a value for the Q-LR statistic.
Finally, repeating the last three steps two thousand times we have two thousand
simulated values for the Q-LR statistic and the threshold parameter. The empirical
significance level of the actual Q-LR statistic corresponds to the percentage of the
19
occasions that the simulated values of the Q-LR statistic exceed the actual value of the
statistic. We can also obtain the confidence interval for the threshold parameter from
the simulated estimated values of the threshold variable.
The estimations presented in Table 5 show an asymmetric response of the
central bank depending on the inflation deviation. The Q-LR statistic rejects the linear
model at the 5% significance level. The estimated threshold value is -0.5% with a
95% confidence interval [ −0.5, 0.6] . This means that the monetary authorities switch
regime when the observed inflation of the previous period is less than or equal to
1.5%. Under this regime the coefficients of the inflation deviation and the output gap
are not statistically significant a fact that indicates that the Taylor principle is
abandoned. In the other regime which corresponds to inflation values of the previous
period greater than 1.5% the policymaker seems to follow the Taylor rule as all the
coefficients are statistical significant with the coefficient of the inflation deviation to
be greater than unity and the output gap coefficient to be positive. The monetary
authorities present a strong reaction of the nominal interest rate to the inflation
deviation from its target value. Considering that the official target is 2%, the
estimated threshold value of 1.5% indicates how strict inflation targeter may be the
euro area’s monetary authorities. The long run nominal interest rate is 2.73% and the
smoothing parameter is relative high indicating the strong smoothing process of the
central banker.
Figure 1 entails the graphs of the inflation rate with its threshold value and the
interest rate with its fitted values that are derived from the IVTR model. It’s obvious
that the inflation rate was systematically below the estimated threshold value of 1.5%
during the last two years before the official starting of the monetary union and a year
later. After that it remained above this threshold for all the rest period with sudden
bursts that exceeded the official target. This means that the idea of a common
currency had led the monetary authorities to keep strictly the inflation rate below of
the desired levels in order to achieve the future price stability. After the successful
transmission to the monetary union, the ECB seems to loosen its monetary policy
allowing higher inflation rates than the official announcements.
The IVTR model seems to describe very well the euro area’s interest rate setting
as the fitted values of the interest rate are very close to the actual values. A relatively
large deviation between the two series arises during the last year of our examined
period as the model overestimates the interest rate setting. It’s also notable to say that
20
during the 00’s where the inflation rate was above its target the interest rate was
below the value that prevailed at the start of the monetary union under low inflation
levels.
4.4.2 Threshold Regression with Endogenous Threshold and Slope
(THRETS) variables
In this section the inflation deviation over the current period is allowed to be the
threshold variable. As the central bank doesn’t know the inflation rate over the current
period when it sets its nominal interest rate the expectations about the price level have
to be formed. This means that the threshold variable is endogenous in this case so a
different approach has to be developed that allows for endogenous variables and
endogenous threshold variable. Following Kourtellos, Stengos and Tan (2008)
approach we estimate the threshold parameter and the coefficients of interest of the
following THRETS model:
⎧⎪(1 − ρ )(α + βπ t +3 + γ yt ) + ρ it −1 + ut , if π t ≤ q
it = ⎨
⎪⎩(1 − ρ )(α + β ′π t +3 + γ ′ yt ) + ρ it −1 + ut , if π t > q
π t = Π1′z t + υt
The last equation is the selection equation that determines the regime that applies.
Using a proper indicator function we can rewrite the structural model in the following
form:
it = (1 − ρ ) (α + ( βπ t +3 + γ yt ) 1 (π t ≤ q ) + ( β ′π t +3 + γ ′ yt ) 1 (π t > q ) ) + ρ it −1 + ut (4.6)
The reduced form regressions for the endogenous variables ( π t , yt ) as a function of
exogenous instruments ( z t ) are given by:
π t = Π1′z t + υt and yt = Π′2 z t + vt
where z t is a m×1 vector of instruments and Π1 , Π 2 are m×1 parameter vectors.
Taking the conditional expectations of the model (4.6) we have:
⎛ α + ( β E (π t +3 / z t ) + γ E ( yt / z t ) + E ( ut / z t ) ) 1 (π t ≤ q ) ⎞
⎟ + ρ it −1 (4.7)
E ( it / z t ) = (1 − ρ ) ⎜
⎜ + ( β ′E (π t +3 / z t ) + γ ′E ( yt / z t ) + E ( ut / z t ) ) 1 (π t > q ) ⎟
⎝
⎠
Assuming that the covariance between υt and ut is the same across both regimes we
can define as κ = σ uυ = ϑσ u . Then by the properties of the joint Normal distribution
we obtain:
21
E ( ut / z t , π t ≤ q ) = κ E (υt / z t , π t ≤ q ) = κλ1 ( q − Π1′z t )
(4.8)
E ( ut / z t , π t > q ) = κ E (υt / z t , π t > q ) = κλ2 ( q − Π1′z t )
(4.9)
where λ1 ( q − Π1′z t ) = −
φ ( q − Π1′z t )
Φ ( q − Π1′z t )
and λ2 ( q − Π1′z t ) =
φ ( q − Π1′z t )
1 − Φ ( q − Π1′z t )
are the
inverse Mills ratio bias correction terms and φ ( i ) , Φ ( i ) are the normal pdf and cdf
respectively. Therefore, using (4.7), (4.8) and (4.9) the THRETS model can be
defined as follows:
⎛ α + ( β E (π t +3 / z t ) + γ E ( yt / z t ) + κλ1 ( q − Π1′z t ) ) 1 (π t ≤ q ) ⎞
⎟ + ρ it −1 +ε t (4.10)
it = (1 − ρ ) ⎜
⎜ + ( β ′E (π t +3 / z t ) + γ ′E ( yt / z t ) + κλ2 ( q − Π1′z t ) ) 1 (π t > q ) ⎟
⎝
⎠
The estimation procedure takes place in three steps. First, we estimate the
parameter vectors Π1 and Π 2 obtaining the predicted values for the endogenous
variables. Second, we estimate the threshold parameter by minimizing a concentrated
two stage least squares (THRETS-C2SLS) criterion using the estimates of Π̂1 and Π̂ 2
from the first stage:
qˆ = arg min Sn ( q )
q
where
(
(
(
))
))
⎛
⎞
⎛ α + βπˆ + γ yˆ + κλ q − Π
ˆ ′z 1 (π ≤ q ) ⎞
t +3
t
t
1
1 t
⎜
⎟
⎜
⎟
Sn ( q ) = ∑ ⎜ it − (1 − ρ ) ⎜
− ρ it −1 ⎟
⎟
ˆ ′ z 1 (π > q ) ⎟
t =1 ⎜
⎜ + β ′πˆt +3 + γ ′ yˆt + κλ2 q − Π
⎟
t
1 t
⎝
⎠
⎝
⎠
n
(
2
Third, splitting the sample according to the estimated threshold value q̂ we estimate
the slope parameters using GMM. As it is proved by Kourtellos et al. (2008) this
estimation procedure that allows the Mills ratio bias correction terms leads to a
consistent threshold estimator.
In order to test for model linearity we construct the Q-LR test finding its
empirical significance level through the bootstrap procedure described in the case
with exogenous threshold. Table 6 presents the results that are in favor of an
asymmetric response of the central bank depending on the inflation deviation. The QLR statistic rejects the linear model at the 1% significance level. The estimated
threshold value is -0.4% with a 95% confidence interval [ −0.5, 0.6] that is derived
through a bootstrap procedure. When the inflation over the current period is less than
or equal to 1.6% the monetary authorities switch regime and abandon the Taylor rule
22
as the coefficients of the inflation deviation and the output gap are not statistically
significant. On the contrary, when the inflation is expected to exceed 1.6% the Taylor
principle is hold as the policymaker reacts with a stabilizing manner to the inflation
deviations and weaker but significantly to the output gap. These results are similar to
that found in the case with an exogenous inflation rate confirming the central bank’s
behavior of being a strict inflation targeter. The long run nominal interest rate is
2.44% and the smoothing parameter is relative high indicating the strong smoothing
tendency of the central banker.
Regarding the Figure 2, graphically presenting the threshold variable and the
interest rate with its fitted values, we observe similar patterns to that of Figure 1. The
THRETS model describes perfectly well the monetary policy in the euro area
indicating the loosening in the conduct of the monetary policy throughout the 00’s.
5. Conclusions
This paper presents a study of the euro area monetary policy allowing for
threshold effects. The key finding of our research was that the estimating threshold
models for the euro area’s policy reaction function gives us empirical evidence to an
asymmetric response of the monetary authorities depending on the price level.
Using a forward looking Taylor rule as suggested by Clarida et al. (1998) the
presented evidence clearly suggests that the monetary authorities are accommodating
changes in inflation for the period under scrutiny and hence follow a destabilizing
policy. Their reaction to the output gap is also weak and significant.
Therefore, this impression seems to be largely due to the lack of incorporating
threshold effects in the forward looking policy reaction function. The results show
that the weights assigned to inflation deviation and the output gap by the policymaker
switch between different states of the inflation rate. The one regime is associated with
a high weight on inflation and a weak weight on the output gap while the other
implies that the monetary authorities do not obey the Taylor principle and they
abandon the interest rate rule. The aspect of modeling threshold effects seems to be
responsible for finding an inflation parameter that supports an inflation stabilizing
policy in the euro area. The real activity also seems to play a significant role in the
policy process a fact that contradicts the official announcements of the monetary
authorities.
23
Regarding the smoothing tendency of the policymakers the results show a large
degree of partial adjustment in the interest rate under the linear and the threshold
model a fact that is according to other euro area studies (see Sauer and Sturm 2003).
Since our estimations show that we cannot reject a nonlinear monetary rule for
the euro area this might have an effect on the achievement of the inflation target in the
long run. So, the possible effects on inflation behavior and the approach to the
monetary transmission mechanism can be evaluated in a standard New Keynesian
model. But this model has a discrete nonlinearity, due to the nonlinear policy rule,
which demands the implementation of numerical methods using a monotone map
algorithm. As it is stated by Sims (1994) that the fiscal policy plays an equally
important role to that of the monetary policy in the existence and uniqueness of the
equilibrium price level a threshold type system that is composed of a monetary and a
fiscal policy rule may be estimated. The problem that arises for the euro area is that
there isn’t a common fiscal policy rule so a weighted average of the countries’ fiscal
characteristics that compose the monetary union is needed. Whether these fiscal
heterogeneities have a serious impact in the contact of the common monetary policy
in euro area is a question that is left to future research.
24
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29
Appendix
A) Data
Series
Source
Description
Short term nominal
European Central
Euro Overnight Index Average
interest rate
Bank
(EONIA), Euro area (changing
composition)
Industrial Production
Eurostat
Index
Euro area 16 (fixed composition),
total industry excluding
construction
Consumer price index
Eurostat
Harmonized Index of Consumer
Prices, (HCPI), Euro area
(changing composition), neither
seasonally nor working day
adjusted
Money growth rate
Eurostat
M3 level, Euro area (changing
composition), working day and
seasonally adjusted
Stock price index
Eurostat
Dow Jones Euro STOXX - Price
index, Euro area (changing
composition)
Economic sentiment
indicator
Eurostat
ESIN, Euro area 16 (fixed
composition)
30
B) Tables
Table 1: Taylor Rule estimations for the euro area
Sample Period
α
β
γ
1980:I-1997:IV
3.87
1.2
0.76 0.76
1990:I-1998:IV
1990:I-1998:IV
1990:I-1998:IV
1979:I-1996:IV
2.4
3.9
2.38
4.07
1.58
2.22
1.84
2.15
0.45
0.72 0.32
0.34 0.18
2.12 0.86
1988:I-2002:II
-1.23
(ns)
1.97
2.73 1.44 0.88
Contemporaneous 1999:4-2002:2
1.22
1.16 0.18 0.73
Forward looking
1999:1-2006:3
1.9
4.25 1.28 0.96
Contemporaneous 1999:1-2002:1
2.6
0.45 0.3
Contemporaneous
Forward looking
(ex-post data)
Forward looking
(real time data)
Contemporaneous
1999:1-2003:3
1999:1-2003:3
2.58
1.72
0.51 0.37
0.86 0.86 0.88
1999:1-2003:3
0.25
(ns)
2.96
2.31 2.35 0.92
Study
Type of rule
Hypothetical euro area
Peersman and
Forward looking
Smets (1998)
Gerlach and
Contemporaneous
Schnabel (2000)
Contemporaneous
Forward looking
Clausen and Hayo Contemporaneous
(2002)
Gerlach-Kristen
Contemporaneous
(2003)
Ullrich (2003)
Contemporaneous
Actual euro area
Fourçans and
Vranceanu (2002)
Fourçans and
Vranceanu (2006)
Gerdesmeier and
Roffia (2003)
Sauer and Sturm
(2003)
Ullrich (2003)
1995:1-1998:12
1999:1-2002:8
ρ
1.25 0.29 0.23
0.72
0.25 0.63 0.19
Table 2: Descriptive Statistics
EURO Area (1994:1-2008:8)
Standard
Variables
Mean
Nominal Interest Rate
3.75
1.28
Inflation
2.11
0.6
IPI growth
2.37
2.5
Unemployment Rate
9.06
1.15
Deviation
31
Table 3: Estimates of the baseline forward looking model
1994:01-2008:8
it = (1 − ρ ) ⎡⎣⎢ a + β E t ( π t + 3 − π * ) + γ E t y t ⎤⎦⎥ + ρ it −1 + ε t
α
β
γ
ρ
R2
MSE
J-stat
3.05***
0.89***
0.64***
0.95***
0.98
0.03
7.94
(0.19)
(0.26)
(0.13)
(0.01)
[16.34]
[3.41]
[5.1]
[133]
(0.54)
Estimates are obtained by GMM. Newey-West optimal weighting matrix is used with 11 lags.
***, **, * denote 1%, 5%, 10% significance.
Instruments : c, int(-1 to -2), infgap(-1 to -3), gap(-1 to -2), m3g(-1 to -2), stock(-1 to -2), esin(-2).
32
Table 4: Forward looking threshold monetary policy models with
known threshold
1994:01-2008:8
⎧ (1 − ρ ) ⎡ a + β 1 E t (π t + 3 − π * ) + γ 1 E t y t ⎤ + ρ it −1 + ε t ,
⎪
⎣
⎦
it = ⎨
*
⎪⎩ (1 − ρ ) ⎡⎣ a + β 2 E t (π t + 3 − π ) + γ 2 E t y t ⎤⎦ + ρ it −1 + ε t ,
Parameters
Threshold:
if q t -1 ≤ q
if q t -1 > q
π t −1
α
3.86***
(0.32)
β1
3.17***
(1.16)
γ1
1.21***
(0.40)
β2
-1.43
(1.18)
γ2
0.86***
(0.27)
ρ
0.96***
(0.01)
q
0
Wald-test
(p-value)
5.13
( 0.07)
Percentile
0.44
J-stat
8.19
(p-value)
(0.32)
MSE.
0.031
Estimates are obtained by GMM. Newey-West optimal weighting matrix is used with 11 lags.
***, **, * denote 1%, 5%, 10% significance.
Instruments : c, int(-1 to -2), infgap(-1 to -3), gap(-1 to -2), m3g(-1 to -2), stock(-1 to -2), esin(-2).
33
Table 5: Forward looking threshold monetary policy models
(IVTR)
1994:01-2008:8
⎧ (1 − ρ ) ⎡ a + β 1 E t (π t + 3 − π * ) + γ 1 E t y t ⎤ + ρ it −1 + ε t ,
⎪
⎣
⎦
it = ⎨
*
⎪⎩ (1 − ρ ) ⎡⎣ a + β 2 E t (π t + 3 − π ) + γ 2 E t y t ⎤⎦ + ρ it −1 + ε t ,
Parameters
Threshold:
2.73***
(0.55)
β1
-0.42
(1.95)
γ1
-0.98
(0.87)
β2
3.83***
(1.44)
γ2
0.64***
(0.12)
ρ
0.92***
(0.02)
q
-0.5
q
if q t -1 > q
π t −1
α
CI of
if q t -1 ≤ q
[ −0.5,0.6]
Q-LR
5.59
(p-value)
(0.017 )
Percentile
0.16
J-stat
2.34
(p-value)
(0.94)
MSE.
0.06
Estimates are obtained by GMM. Newey-West optimal weighting matrix is used with 11 lags.
***, **, * denote 1%, 5%, 10% significance.
Instruments : c, int(-1 to -2), infgap(-1 to -3), gap(-1 to -2), m3g(-1 to -2), stock(-1 to -2), esin(-2).
34
Table 6: Forward looking threshold monetary policy models
(THRETS)
1994:01-2008:8
⎧ (1 − ρ ) ⎡ a + β 1 E t (π t + 3 − π * ) + γ 1 E t y t ⎤ + ρ it −1 + ε t ,
⎪
⎣
⎦
it = ⎨
*
⎪⎩ (1 − ρ ) ⎡⎣ a + β 2 E t (π t + 3 − π ) + γ 2 E t y t ⎤⎦ + ρ it −1 + ε t ,
Parameters
Threshold:
α
2.44***
(0.43)
β1
-1.23
(1.78)
γ1
-0.65
(0.78)
β2
4.84***
(1.03)
γ2
0.54***
(0.11)
ρ
0.90***
(0.02)
q
-0.4
CI of
q
if E t q t ≤ q
if E t q t > q
πt
[-0.5 , 0.6]
Q-LR
6.18
(p-value)
(0.01)
Percentile
0.19
J-stat
1.76
(p-value)
(0.97)
MSE.
0.08
Estimates are obtained by GMM. Newey-West optimal weighting matrix is used with 11 lags.
***, **, * denote 1%, 5%, 10% significance.
Instruments : c, int(-1 to -2), infgap(-1 to -3), gap(-1 to -2), m3g(-1 to -2), stock(-1 to -2), esin(-2).
35
C) Figures
Figure 1: IVTR Model
Threshold Variable:Inflation
Graph of Threshold Variable
4.0
3.5
INF_THRESH
INF
3.0
2.5
2.0
1.5
1.0
0.5
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Interest rate
7.2
INT
6.4
INT_THRESH_HAT
5.6
4.8
4.0
3.2
2.4
1.6
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2004
2005
2006
2007
2008
Figure 2: THRETS Model
Threshold Variable:Inflation
Graph of Threshold Variable
4.0
3.5
INF_THRESH
INF
3.0
2.5
2.0
1.5
1.0
0.5
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
Interest rate
7
INT
6
INT_THRESH_HAT
5
4
3
2
1
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
36