Do central banks respond to asset volatility in making monetary policy empirical evidences from australia, the united states and the united kingdom

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Title: Monetary Policy and Stock Market: DO CENTRAL BANKS RESPOND TO ASSET
VOLATILITY IN MAKING MONETARY POLICY? EMPIRICAL EVIDENCES FROM
AUSTRALIA, THE UNITED STATES AND THE UNITED KINGDOM
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Abstract
The two key factors that determine the performance of monetary policy in any country are price
level and output stability. This paper investigates the Taylor rule in three developed countries,
comprising of Australia, the United States (US), and United Kingdom (UK), to identify whether
or not the monetary policy can be estimated by implementing the three following methods: a
standard linear Taylor rule, an augmented Taylor rule witht the inclusion of asset price volatility
and a regression model estimation using Generalized Method of Moments (GMM). After
regressing the model on sample size for the period from 1980 to 2019, is it found that the
advance economies have the tendency to follow rule-based monetary policy instead of launching
policies under some discretionary framework. In particular, the asset price volatility becomes
relevant only to the extent that they may signal potential inflationary or deflationary forces.
Otherwise, it does not explicitely influence the monetary policy regulation. In short, the results
from an augmented nonlinear Taylor rule in these studied countries turn out to offer a better
insight into the decision-making process of central banks in implementing monetary policy rules.

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Table of Contents
1. List of Tables 5
2. List of Figures 6
3. Introduction 7
4. Literature Review 10
4.1. The Augmented Taylor Rule 12
4.2. Non-linear Taylor Rule 14
5. Data 17
5.1. Data Description 17
5.2. Graphical Inspection of the Data 17
5.3. Detecting Structural Breaks and Stationary 20
6. Methodology 23
6.1. The Standard Taylor Rule 23
6.2. The Augmented Taylor Rule 24
7. Empirical Results 26
7.1. Linear Taylor Rule Results 26
7.2. The Visual Representation of Actual, Fitted, and Residual Values 28
7.3. Augmented Taylor Rule Results based on OLS 29
7.3.1. Augmented Taylor Rule Regression Results 29
7.3.2. Serial Correlation and Heterokedasticity Tests 31
7.3.3. Augmented Taylor Rule based on OLS (Newey-West) 31
7.4. Generalized Method of Moments(GMM) Estimator 32
8. Conclusion 35

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9. References 36
10. Appendix (If Applicable) 40

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1. List of Tables
Table 1. Linear unit root tests 22
Table 2. Chow’s Breakpoint tests 22
Table 3. Linear Taylor rule based on OLS 27
Table 4. Wald Test 28
Table 5. Augmented Taylor rule based on OLS 30
Table 6. Breusch-Godfrey Serial Correlation LM Test 31
Table 7. White Test for Heteroskedasticity 31
Table 8. Augmented Taylor Rule based on OLS (Newey-West) 32
Table 9. Linear Taylor Rule based on GMM 34

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2. List of Figures
Figure 1. The Visual Inspection of Policy Rates 18
Figure 2. The Visual Inspection of Inflation Gaps 19
Figure 3. The Visual Inspection of Output Gaps 20
Figure 4. The Visual Inspection of Stock Markets 20
Figure 5. The Plot of Actual, Fitted, and Residuals for Policy Rates 29

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3. Introduction
Monetary policy, at its core, involves the regulation of money supply and interest rates that is
adopted by the central banks in order to ensure that the asset price volatility, unemployment rate
and economic productivity are under control. In the world of developed economies over the past
decades, the central banks have exerted substantial influences on managing and regulating the
policy rules in order to maintain the low level of inflation. In particular, the monetary policies
have been using Taylor (1993) Rule as a simple and straightforward monetary framework.
Although the mechanism of linear Taylor rule is clearly defined, Taylor (1993) emphasized that
there comes certain periods where quantitative methods are not the final answer. Instead, the
monetary policy needs to seek adjustments for special factors and replace the rules-based
framework with a discretionary policy. Regardless, Taylor (1993) disputed that rules-based
rules-based monetary policy leads to stronger economic results in the long run than the
discretionary policy does in the long run.
Over the past decades, Bernanke and Mihov (1998) stated that while the central banks have
succeeded in managing the inflation fluctuations most of the times, these authorities come across
a greater challenge of financial instability regarding asset price volatility. Taking the boom-bust
cycles of asset prices into consideration, the “bust” period of the economy (i.e. 1990 recession)
was attributed in part to the dropping prices in commercial real estate, resulting in the banks'
deteriorating financial position and the borrowers' balance sheets shrinking. For this reason, an
increase in the financial instability and the failure of major financial institutions in regulating the
financial markets become the underlying causes of financial crises, thereby emphasizing an
importance of keeping the asset prices under control in the monetary policy framework.

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In short, the topic of whether central banks can respond to changes in stock prices has been
fiercely debated with two main schools of thought. The first one, i.e. Bernanke & Gertler (2001),
Greenspan (2007), etc., argues that the interest rate cannot be used by central banks to
manipulate stock prices. Secondaly, it is futile to break a bubble using the interest rate even in
the case of ex-ante detection in the bubble. If the bubble bursts, all the central banks can do is to
control the damage. This school of thought also emphasizes that by holding the inflation rate
down, the central bank contributes to the idea of building a sustainable growth environment
where the bubbles are less likely to occur. In addition, many would argue that a ‘leaning against
the wind’ approach can be useful in refraining stock price from experiencing large price
movements.
The second school of thought takes the opposite viewpoint (see Ceccetti et al., 2002, Bordo &
Jeanne, 2002 and Roubini, 2006). In certain cases, stock markets are subject to bubbles and
crashes and it is to the responsibility of central banks to target financial stability by tracking asset
prices and reducing the likelihood of forming bubbles (which inevitably leads to crashes). In this
view, the use of the interest rate is seen as a positive and powerful tool in preventing bubbles
from emerging. Few economists from this school would argue that a specific value of the stock
price should be targeted by the central banks in the same manner that they target an inflation rate.
The purpose of this investigation is to take part in the ongoing discussion of the relationship
between monetary policy and asset price volatility in the existing literature. In this present study,
we will specifically carry out our analysis with three estimation methods: Ordinary Least
Squares (OLS), OLS with Newey-West option and Generalized Method of Moments (GMM) in
order to tackle the issue of hetersoskedasticity, serial correlation, and endogeneity problems.
Particularly, the focus of this study will be the policy rules of the central banks of Australia, the

9
United States and the United Kingdom as well as the reflections of certain stock market
decisions between the period 1980 and 2019.
The layout of the paper is as following: Section 4 discusses some literature about the Taylor rule.
Section 5 and 6 introduces and explores about the data used in this method as well as the
econometric model. The empirical results are shown and discussed in Section 7. Finally, Section
8 concludes the results of this research with final remarks.

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4. Literature Review (Actual: 2057)
Starting from the 1990s, a number of industrialized countries, including Canada, the United
Kingdom, New Zealand, Australia, and many others, have brought about the different forms of
inflation targeting. In particular, inflation targeting has been used as a policy framework rather
than the sole methodology of monetary policy with the key advantages of increased transparency
and policy coherence; thus it is flexible to the point of accommodating "discretionary" monetary
policy tools. Bernanke and Mishkin (1997) stated that the inflation-targeting approach also
increases accountability and takes the daily policy decisions into consideration.
Obviously, when the rate of inflation is too high, it causes serious economic risks that devalue
the money distributed on the market. A strong depreciation of a domestic currency would result
in a decline in the country's economic position. For this reason, most inflation targeting policies
aim to adjust the interest rates to a lower level. However, a constantly low rate of interest might
reduce labor allocation efficiency and lead to a higher unemployment rate in the long run,
especially when inflation return reaches the rate of zero (Bernanke and Mishkin, 1997). Apart
from this, deflation or a degree of decline in price levels would pose a burden on the financial
system and economic functions (Mishkin, 1991).
With regards to Standard Linear Taylor Rule, Taylor (1993) has established a formula that
describes the relationship between nominal interest rate, output gap and inflation gap. In
particular, the deviation of current inflation on target inflation would have an effect on the
nominal interest rate with real interest rate. If the inflation gap becomes too significant and the
current level of inflation is higher than the target, it signals the government to increase nominal
rate and mitigate inflationary pressures, and vice versa. The same mechanism applies to the
output gap, which is calculated as the difference between the current real GDP and potential

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GDP. Specifically, the monetary policies would depend on the direction of the output gap as they
tighten when the output gap is positive; whereas in the case of a negative output gap, the central
banks need to ease their policies and promote the overall economy.
Since the assumptions of Standard Linear Taylor Rule have been critically built on the
performance of output and inflation gap variables with a fixed set of data measurement criteria
and without any other influences, these assumptions come across many shortcomings in practice,
particularly leaving out the central banks’ consideration of other economic factors or events that
influence beyond the scope of the rule (Castro, 2008). Clarida et al. (2000) proposes a solution to
this issue with the use of expected values for inflation gap and output gap instead of past or
current values since the expected figures could contain important information on the market
forecast based on a variety of relevant variables. Under the investigation of ECB monetary
policy, Sauer & Sturm (2007) have also emphasized the importance of using forward-looking
data in Taylor rule.
Despite the drawbacks of linear Taylor rule, its effectiveness as a monetary policy framework
has been recognized by a number of studies on the developed economies with less volatile asset
prices, specifically the Taylor (1999) research on interest rate adjustment policy of the Fed as
well as Taylor (2013) and Bernanke (2004) researches on the applicability of this rule in the
United States. Established markets, especially before the 2008 economic crisis, reportedly
showed characteristics consistent with the standard linear Taylor rule, i.e. the United Kingdom’s
policies (Stuart 1996), Canadian economy (Côté et al. 2004), or results found in G3 countries
(Clarida et al. 1998).
In response to the acceleration of financial markets and the limitation of baseline Taylor rule, the
Augmented Taylor rule with the inclusion of other variables such as the exchange rate or asset

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price volatility comes out as an advanced model that offers a closer insight into sound monetary
policy.
4.1. The Augmented Taylor Rule
Besides the studies that support the standard linear Taylor rule and prove its effectiveness, there
are many studies that have contradictory and opposing views on the practicality of this equation.
Research by Svensson (2003) shows that for open economies, which are affected by various
externalities such as foreign-market fluctuations and the impact of exports and imports, a simple
Taylor rule could not incorporate all of these key factors into the interest rate. A potential
solution suggested in many studies is the addition of a variable representing the exchange rate, a
factor calculating the correlation and volatility of domestic and foreign currencies (Ball, 2000;
Obstfeld & Rogoff, 2000; Ghosk et al., 2016, etc.). Mishkin (2007) confirmed that the exchange
rate variable might not be necessary in the developed markets but it is an indispensable factor in
the study of emerging markets.
In addition to the exchange rate factor, recent studies investigate the role of asset price volatility
in the Augmented Taylor model. In an industrial economy and financial market liberalization,
the inflation rates are likely to remain stable while the asset price fluctuates greatly, including
securities, bonds, and real estate prices. As such, many researchers have questioned whether
asset price is related to inflation rate in particular or the economy in general. Blanchard (1981)
pointed out that stock market value directly affects both monetary and fiscal policy in a country;
such a remark is confirmed and concluded in several later studies (Grüne & Semmler,
2008; Kontonikas & Montagnoli, 2004). While there are certain methodological limitations in
both of these research, such as not paying much attention to asset bubbles in potential crises or
making predictions that differ from the real market volatility, low asset prices are nonetheless

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believed to be one of the main causes of low inflation rates, or even negative inflation rates in the
long run.
There have been two main schools of thoughts regarding asset price volatility, in which one is
supportive of the idea with the work of Goodhart & Hofmann (2002) on G7 countries and
Rotondi & Vaciago (2005) on the Federal Reserve. In addition, Bernanke & Kuttner (2005) and
Chulia et al. (2010) show that stock return affects the asymmetry of monetary policy through
various economic cycles, such as bull or bear market, recession or growth economic stages.
Moreover, Cecchetti, Genberg, Lipsky, and Wadhwani (2000) find that including asset prices in
the policy making process is beneficial for the macroeconomic performance because
simultaneously targeting and smoothing the inflation rate will help lessen the output volatility
and inflation fluctuations, thus lowering the probability of asset price bubbles. The reason why
such a mechanism works for the economy is because the forming of asset price bubbles might
lead to wide fluctuations in both the real output and inflation as well as interrupt the normal
cycles of investment and consumption. Therefore, if the monetary policy acts in the manner of
“leaning against the wind”, it might influence the investors’ behaviour and caution them against
the excessive trading in risky assets, thus declining the likelihood of asset price bubbles.
Castro (2011) responded to the inclusion of asset prices in the linear Taylor rule by investigating
a financial conditions portfolio comprised of the weighted average of asset prices and concluded
that the European Central Bank (ECB) adjusted its monetary policies based on the information
included in this index to prevent the imbalances of financial markets while the Federal Reserve
and BOE do not. For this reason, the difference in the central banks’ reaction function might
explain why the recent credit crunch was worsen in the housing markets of the US and UK, but
not the Eurozone, thereby indicating that the financial conditions could provide valuable

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resources to resolve the asset markets’ imbalances and alleviate the severity of economic
downturns.
On the contrary, Bernanke & Gertler (2001) and Bullard & Schaling (2002) had a different
outlook on this discussion and recommended that central banks should not respond to
fluctuations in asset prices because of their unpredictability and large price movements. In an
open-economy environment, these studies show that central banks should only focus on the asset
price if it has a direct impact on the expectations of inflation rate, or after the economic crisis
resulting from asset bubbles. Rather than relying on monetary policy to manage the boom-and-
bust cycle, it is believed to lie in the regulatory hands to control and mitigate the investors’
exposure to the volatility of complex asset classes.
In conclusion, the Augmented Taylor Rule model for asset price volatility is more effective than
the Standard Linear Taylor Rule in certain developed markets, in which the stock market and
asset price positively improve the robustness of the model. Depending on the availability of data
sources and the target markets, the added variables will be selected accordingly.
4.2. Non-linear Taylor Rule
The studies of Linear Taylor Rule model assume that the optimal monetary policy of the central
bank depends on the loss function and linear relationship between the interest rate and the output
gap as well as inflation gap. Nevertheless, these assumptions, in practice, encountered several
objections because there existed asymmetric preference of the central bank in weighting the
influences of output gap and the inflation gap, and whether these gaps yield positive or negative
values. For this reason, studies have started to pay attention to the non-linearity in Taylor model
and its practical effectiveness in monetary policy research.

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Nonlinearities in policy function (Robert-Nobay and Peel, 2003; Dolado et al., 2005) and
asymmetric preferences (Castro, 2011; Martin and Milas, 2004) of central banks have been
proposed through numerous studies over the past few decades. In a sense, the differences in
economic cycles have a direct impact on the policy responses, thus adjusting their targets
depending on the high and low regimes of inflation. During a recession, for example, the issue of
output stabilization will be centralized. On the other hand, the inflation rate should be kept in
mind and maintained above average during an economic expansion in order to accelerate
business growth potential (Ahmad, 2016). Presence of nonlinearities are pointed out through a
linear GMM model in Surico (2007) research with ECB monetary policy, in which the output
variable was more susceptible to the inflation rate and required more intervention in the event of
a recession. At the same time, the Markov switching model studied by Assenmacher-Wesche
(2006) and Altavilla & Landolfo (2005) acknowledges the presence of asymmetries in the
monetary policy rules. However, a downside of the Markov switching model is due to its failure
to neither investigate whether the central banks are attempting to target an inflation point or a
range of inflation nor enable interest rate smoothing to occur. Studies have also shown that the
existence of asymmetries depends mainly on the economic cycle and phases. As a result, Taylor
& Davradakis (2006) found that the Bank of England initiated interest rate policy based on
nonlinearities, but not asymmetries in inflation. Martin and Milas (2013) has confirmed this
observation in the United Kingdom with their research during the Great Recession.
Nevertheless, in emerging economies, the effect of nonlinearities is considered to be minimal.
Research by Moura & De Carvalho (2010) in Latin America countries indicates the existence of
asymmetric responses but not nonlinearities. In terms of the Central Bank of Turkey, Akyürek et
al. (2011) argued that Augmented Linear Taylor Rule model was more effective than Nonlinear

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model in determining monetary policy based on the volatility of exchange rate when comparing
two methods with historical data. The smooth transition regression model (STR) is applied in the
study of Jawadi et al. (2014) in China and Brazil. Research shows that the non-existence of
nonlinearities and exchange rate is the key factor determining interest rate policy. To be
recapitulated, empirical research in emerging markets focuses more on the Augmented Linear
Taylor Rule model and argues that the Non Linear Model is too complex and hardly reflects the
true market conditions. For developed markets, where economy cycles are clearly defined,
nonlinearities relationships are more informative under different circumstances, thus supporting
central banks to initiate an appropriate policy for each case.
In this research, the model of nonlinearities temporarily has not been studied because of the
model complexity and its questionable applicability in various countries' groups. However, the
development of the model in a nonlinear relationship in the future will make a great contribution
to clearly identify the causes and factors that affect monetary policy.

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5. Data (Actual: 865 excluding table)
5.1. Data Description
The data used in this paper are obtained on three developed markets with similar development
levels, namely Australia, United States, and United Kingdom. In particular, the sample size of
this study covers quarterly data points for the period from 1 January 1980 to 31 December 2019
by obtaining these materials from Organisation for Economic Co-operation and Development
(OECD) data sources. In terms of the variables, the real Gross Domestic Product (GDP) is used
to estimate the output variable by deviating the logarithm of 3-month real GDP from its Hodrick
and Prescott (HP) trend. The inflation gap is calculated based on the log of Consumer price index
(CPI) and its deviation from the target inflation rate. Moreover, the quarterly average closing
price of stock market indices for three countries, namely Australian Securities Exchange (ASX),
New York Stock Exchange (NYSE), and Financial Times Stock Exchange (FTSE) are used to
characterize the asset price volatility, in which these data sets are seasonally and quarterly
adjusted.
5.2. Graphical Inspection of the Data
The evolution of four main variables estimated in the Augmented Taylor rule: short-term policy
rates, inflation gaps, output gaps, and stock market indices are depicted in Figure 1 to 4. To be
specific, the interest rates of three influential central banks evidently show a similar pattern of
wide fluctuations during the period leading to the dot-com bubble in 2001 and a gradual decline
from 2001 onwards. Figure 2 and 3 suggest that the inflation and output variables have deviated
greatly from their target values. In the case of stock market indices, the three stock exchanges of
Australia, United States and United Kingdom have steadily increased and maintained their
performance for the period of thirty nine years, with the exception of the United Kingdom

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experiencing a huge volume of volatility during the period from 1997 to 2008. More importantly,
the graphical representation of these variables (see Figs. 1–4) highlighted the existence of
structural breaks, in which the Great Recession occurred between 2007 and 2009 seem to
influence the policy rates in Figure 1 as well as the asset price volatility in Figure 4. For this
reason, section 5.3 below will touch on the topic of detecting stationary to examine whether the
structural breaks might weaken the power of unit root tests.
Australia United States
United Kingdom
Figure 1. The Visual Inspection of Policy Rates

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United Kingdom
Figure 2. The Visual Inspection of Inflation Gaps
United Kingdom

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Figure 3. The Visual Inspection of Output Gaps
United Kingdom
Figure 4. The Visual Inspection of Stock Markets

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5.3. Detecting Structural Breaks and Stationary
Understanding the time series properties of the variables included in the Taylor rule is critical. If
the variables in the Taylor rule are unit-root processes, then a co-integrating relationship must
exist for the coefficient estimates to be consistent. For this reason, this study has performed three
key unit root test, including the Augmented Dickey–Fuller (1981) test, Phillips and Perron
(1988) test, and Kwiatkowski–Phillips–Schmidt–Shin (1992) test in order to understand the
stochasticity of these time series. The results of these tests are shown in Table 1, implying that
the policy rates in all three countries (Australia, United States, and United Kingdom) are not
stationary in levels. However, the order of integration for this variable is a controversial topic
because there have been various studies that offer different views on the stationary of interest
rates. For instance, Nelson and Plosser (1982) found them to be non-stationary while Clarida et
al. (2000) failed to reject the existence of unit root in the tests of nominal interest rate. For the
purpose of this paper, these variables will be treated as stationary so as to simplify the process of
data estimation.
As previously mentioned, the structural breaks exist not only in the visual inspection of our
variables, but also in the results of Chow’s Breakpoint tests under the null hypothesis of no
structural breaks. Since the structural breaks might have the ability to reduce the unit root tests’
robustness, this current paper carries out the Chow’s Breakpoint tests (see Table 2) by fitting the
equation in various subsamples in order to identify whether the relationship between the
variables experience a structural change before and after a critical event. In our case, there are
two main events: the dot-com bubble in 2001 and recent 2007–8 financial crises that are
confirmed to play a role in influencing the policy-making process of the central banks. For this

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reason, this paper will consider all variables to be I(0) and estimate them for the linear Taylor
rule model in levels.
Table 1. Linear unit root tests
ADF Test PP Test KPSS Test
Intercept Intercept
& Trend
Intercept Intercept
& Trend
Intercept Intercept
& Trend
Australia 𝑖 𝑡 -1.246 -3.418 -0.709 -3.216* 1.337*** 0.101*
𝜋 𝑡 − 𝜋 𝑡
∗
-2.459 -2.346 -1.935 -1.920 0.836*** 0.186**
𝑦𝑡 − 𝑦𝑡
∗
-3.347** -3.355* -4.660*** -4.650*** 0.041 0.041
𝑠 𝑡−𝑘 -3.419** -3.376* -3.458** -3.462** 0.064 0.064
United
Kingdom
𝑖 𝑡 -1.390 -2.697 -1.160 -2.328 1.318*** 0.223***
∗
-2.263 -2.713 -3.802*** -3.840** 1.022*** 0.206**
∗
-5.154*** -5.137*** -4.830*** -4.823*** 0.028 0.028
𝑠 𝑡−𝑘 -3.180** -4.183*** -3.414** -3.400* 0.550** 0.069
United
States
𝑖 𝑡 -1.594 -1.861 -1.808 -1.998 1.131*** 0.065
∗
-3.978*** -4.926*** -4.772*** -4.871*** 1.021*** 0.103
∗
-4.734*** -4.717*** -4.630*** -4.622*** 0.025 0.025
𝑠 𝑡−𝑘 -4.784*** -5.067*** -3.374** -3.307* 0.210 0.040
* indicates a stasticical significance at the 90% level of confidence;
** indicates a stasticical significance at the 95% level of confidence;
*** indicates a stasticical significance at the 99% level of confidence.
Table 2. Chow’s Breakpoint tests
Australia
United
States
United
Kingdom
Dot-com Bubble (2001Q1)
F-statistic 50.219*** 53.218*** 46.102***

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Prob. F-stat (0.000) (0.000) (0.000)
The Great Recession (2008Q1)
F-statistic 84.566*** 57.898*** 280.205***
Prob. F-stat (0.000) (0.000) (0.000)
In addition, the probability of F-statistic is inserted in the parentheses.

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6. Methodology (Actual: 789)
6.1. The Standard Taylor Rule
The standard linear Taylor (1993) rule comes about to define and describe the behaviour of the
United States monetary policy over the period of five years from 1987 to 1992:
𝑖 𝑡 = 𝛼 + 𝛽( 𝜋𝑡 − 𝜋𝑡
∗) + 𝛾( 𝑦𝑡 − 𝑦𝑡
∗) + 𝜖𝑡 (1)
Where 𝑖 𝑡 is the target inflation rate, 𝜋𝑡 is the real rate of inflation, 𝜋𝑡
∗
is the desired inflation rate,
and ( 𝑦𝑡 − 𝑦𝑡
∗) represents the deviation of actual output from its target. In particular, the key
instrument of the monetary policy is the nominal short-term interest rate (𝑖 𝑡) and the equation
works in a way that the central banks would increase the interest rate if inflation (𝜋𝑡) is above its
target (𝜋𝑡
∗
). In addition, an increase in the interest rate also occurs when the output (𝑦𝑡) rises
above its trend value (𝑦𝑡
∗
). As such, β indicates how sensitive the interest rate policy is to a
deviation of inflation from its target while γ refers to the sensitivity of interest rate to a change in
the output gap. According to Mishkin (2011), the “Taylor principle” concluded that the desirable
properties of the rules-based policy allow the central banks to have a straightforward technique
of stabilizing inflation by monitoring and raising the policy rates at a rate higher than an increase
in the inflation.
In equilibrium, the deviation of both inflation and output from their target values is set to be
zero. Consequently, the rate of interest considered to be desirable (𝑖 𝑡) is the sum of the
equilibrium real interest rate (𝛼) plus the target rate of inflation. The rule was seen as an
accountable record of the US monetary policy back in the 1990s while it rose to popularity for
other countries as a fundamental guideline for optimal monetary policy.

25
Another important aspect to take note of in regards to the sensitivity of inflation gap and output
gap is the assumption that β and γ should be of equal weights at 50% for the monetary policy to
be conducive. Otherwise, prioritizing the inflation gap over the output gap might alter the
objectives of monetary policy into aggressively targeting inflation instead of striking a balance
between price stability and maximum unemployment. For this reason, after running the
regression, the Wald test will be conducted to see if the weight of inflation is equal to that of
output gap or not under the null hypothesis that β = γ = 0.5.
6.2. The Augmented Taylor Rule
Later studies, e.g. Rigobon et al. (2003), Castro (2011), and Patelis (1997) etc. have questioned
the practicality of this simple methodology in particular economic environments and proposed an
augmented Taylor rule with the inclusion of asset price volatility so as to further understand the
core characteristics of monetary transmission mechanisms and responses. In particular, the
previous issue might be addressed by examining the visual representation of the data fit between
the actual values and the fitted ones in the present study. After investigating the visual
description of the model, we will then estimate the augmented Taylor rule using the Ordinary
Least Squares with a Newey-West option and Generalized Method of Moments (GMM), in
which the augmented rule can be written as:
∗) + 𝛾( 𝑦𝑡 − 𝑦𝑡
∗) + ∑ 𝛿 𝑘 𝑠𝑡−𝑘
𝑛
𝑘=1 + 𝜖𝑡 (2)
Where 𝛿 𝑘 is a measure of how sensitive the asset price variable is to a change in the nominal
interest rate, and 𝑠𝑡−𝑘 is the year-over-year individual stock market index change (i.e. ASX,
NYSE, and FTSE) for the volatility of the stock market.
The purpose of estimating the augmented Taylor rule with a Newey-West option in the Ordinary
Least Squares is to produce consistent estimates for the standard errors and overcome the issue

26
of heteroskedasticity and serial correlation if this study detects any of the symptoms in the
current sample size for all three countries. In regards to the application of Generalized Method of
Moments (GMM) estimation, the instrumental variables (IV) procedure will take place in the
presence of endogeneity, in which the error distribution fails to be independent of the distribution
for the regressors. In other words, introduced by Hansen (1982), the GMM methodology is able
to estimate efficiently the augmented Taylor rule model by taking advantage of the orthogonality
conditions even if the coefficients contain any unknown form of heteroskedasticity.

27
7. Empirical Results (Actual: 1974 excluding Table)
7.1. Linear Taylor Rule Results
The estimation results for Ordinary Least Squares methodology are documented in Table 2.
Based on the results of the coefficients regarding the inflation (β) and output (γ), it can be seen
that only the inflation and output factors in the United Kingdom are statistically significant and
positive in influencing the behaviour of short-term policy rates. Whereas in the case of Australia
and the United States, the inflation gap plays an important role in determining the nominal
interest rate with the coefficients associated to the inflation of 0.184 for Australia and 0.395 for
United Kingdom, while the coefficients associated with the output gap remain positive but not
statistically significant as the OLS estimators of both countries fail to reject the null hypothesis.
Aside from examining the statistics of the model fit, the variability of dependent variables comes
across the different degree of R-squared ranging from 32.6% to 59.9%. R-squared, or known as
the coefficient of determination, is an equally important goodness-of-fit measure that allows this
study to understand what portion of the variation in the response variable can be ‘explained’ by
the model when estimating the model with more explanatory variables. Based on the results of
the table, it indicates that the classical linear Taylor rule best describes the monetary policy in
Australia and least applicable to the United Kingdom when taking the values of these three
countries into consideration.
According to Wald Test reported in Table 4, the results of the test are extremely significant with
the probability of F-statistic in all three countries recorded to be 0.000, thereby rejecting the null
hypothesis. As a result, the central banks of these three countries have historically weighted the
two key variables of inflation gap and output gap in a different manner.

28
Table 3. Linear Taylor rule based on OLS
Models Australia United States United Kingdom
𝜶 1.095*** -0.045 0.408***
(0.058) (0.140) (0.135)
𝜷 0.184*** 0.395*** 0.285***
(0.012) (0.041) (0.034)
𝜸 0.008 0.048 0.153**
(0.028) (0.060) (0.065)
R-squared 0.599 0.396 0.326
Adjusted R-squared 0.594 0.388 0.317
The estimated model is specified as
∗) + 𝛾( 𝑦𝑡 − 𝑦𝑡
∗) + 𝜖𝑡
where 𝑖 𝑡, ( 𝜋 𝑡 − 𝜋 𝑡
∗), and ( 𝑦𝑡 − 𝑦𝑡
∗) is a measure of the short-term policy rate, inflation gap, and
output gap, respectively. Standard errors are shown in the parentheses (.).
Table 4. Wald Test Results
The test is carried out under the null hypothesis of β = γ = 0.5.
F-statistic 533.11*** 38.06*** 31.77***
Probability of F-statistic 0.00 0.00 0.00

29
7.2. The Visual Representation of Actual, Fitted, and Residual Values
As previously mentioned, in order to understand how well the model explains the sample size,
one may look at the graph of Actual, Fitted, and Residuals in Figure 5 for visual representation
purpose. Since the residuals refer to the portion of equation that cannot be explained by the
model, the error terms of monetary policy in Australia and United Kingdom illustrate that the
model of this study underestimates the actual performance of short-term policy rates at the
beginning of our time series, yet overestimates the data starting from the 2007-2008 financial
crisis. The observation agrees with the results stated in the Chow’s Breakpoint test in Table 2.
The trend is reversed in the case of the United States. The graphical analysis of the graph leads to
the conclusion that there might be misspecification or an issue of omitting instrumental variables
in the model that requires further investigation, which draws us to the point of considering the
asset price volatility variable, as mentioned in the literature review section, due to its potential
influences on monetary policy.
United Kingdom

30
Figure 5. The Plot of Actual, Fitted, and Residuals for Policy Rates
7.3. Augmented Taylor Rule Results based on OLS
7.3.1. Augmented Taylor Rule Regression Results
The Actual, Fitted and Residuals plot indicates that there has been a substantial gap between the
actual values and the fitted values of the model, which gives room for this study's consideration
of the asset price volatility. After estimating the augmented Taylor rule with the addition of stock
market indices, all three cases have shown positive signals of accepting the first lag of stock
market variable in the regression models. As shown in Table 5, the adjusted R-squared - a
modified measure of R-squared that only increases in the event that the additional variable to the
model actually improves the robustness of the regression - increase by 100 - 200 basis points,
thereby indicating that the augmented Taylor rule might bring valuable information to all of
these developed countries.
In line with the results obtained from the OLS estimation in Table 3, the results re-confirm that
the inflation gap is statistically significant in all three countries, which are consistent with the
mechanism of standard linear Taylor rule. Meanwhile, the output gap is statistically significant in
the estimation of the UK model, but is not the case in that of the US and Australia, thus

31
indicating that output stabilization might not be the key consideration of these two countries in
the studied periods. In addition, the stock market variable is positive and statistically significant
at a 95% level of confidence in the monetary policy of Australia while it yields a different result
in the US and UK despite showing a positive sign.
Table 5. Augmented Taylor rule based on OLS
𝜶 1.069*** -0.127 0.358***
(0.059) (0.145) (0.137)
𝜷 0.185*** 0.417*** 0.284***
(0.012) (0.044) (0.036)
𝜸 -0.003 0.043 0.137**
(0.029) (0.063) (0.065)
𝜹 𝒌 0.004** 0.004 0.009
(0.002) (0.005) (0.006)
R-squared 0.607 0.402 0.338
The estimated model is written as
∗) + 𝛾( 𝑦𝑡 − 𝑦𝑡
∗) + ∑ 𝛿 𝑘 𝑠𝑡−𝑘
𝑛
𝑘=1
+ 𝜖𝑡
where 𝑖 𝑡, ( 𝜋𝑡 − 𝜋𝑡
∗), and ( 𝑦𝑡 − 𝑦𝑡
∗) is a measure of the short-term policy rate, inflation gap, and
output gap, respectively. Standard errors are shown in the parentheses (.).

32
7.3.2. Serial Correlation and Heterokedasticity Tests
In light of detecting heteroskedasticity and serial correlation, both the Breush-Godfrey Serial
Correlation LM Test and White Test are brought about to examine whether the model might
violate the assumptions of Classical Linear Regression Model (CLRM). An important
assumption of OLS regression is that the each observation of error terms should be uncorrelated
with each other. However, this assumption is not always satisfied, especially in time series data,
which results in serial correlation. Even though the OLS estimators are still unbiased and
consistency, they will become less efficient in the event of serial correlation, as their estimated
standard errors would be smaller than their instrinsic standard errors. From this reason, it is
necessary to conduct serial correlation test to check whether this issue appears in the regression
model and some necessary measures will be conducted to deal with potential consequences.
In addition to serial correlation, heterokedasticity is also a common violation of CLRM, where
the variance of the residuals is not constant. With the presence of heterokedasticity, the
estimators are also unbiased but less efficient, as the estimated standard errors of the independent
would be biased. In this paper, White test will be utilized to test the heterokedasticity of the
model, which is more appropriate than Breusch-Pagan test, as the later might not be suitable for
non-linear form of heterokedasticity and depend on the assumption of normal distribution of the
residuals.
Combined with the results of non-normal distribution presented in the Jarque Bera test under the
Appendix, the outcomes reported in Table 6 clearly indicate that our regression model comes
across both serial correlation and heteroskedasticity due to the statistical significance at 99%
confidence level of F-statistic. Thus, to alleviate these violations of OLS, re-estimating the
models using robust standard errors will be conducted.

33
Table 6. Breusch-Godfrey Serial Correlation LM test
F-statistic 1001.32*** 855.62*** 2816.79***
Table 7. White Test for Heteroskedasticity
F-statistic 2.739*** 1.704*** 3.464***
7.3.3. Augmented Taylor Rule based on OLS (Newey-West)
Due to the existence of serial correlation and heteroskedasticity in the error terms, this current
study needs to re-estimate the model using the Newey-West option and overcome these
problems. After running the re-estimation with robust standard errors, only the inflation variable
is statistically significant at a 1% level of significance for all the three coutries, as expected in the
literature as well.
However, other variables such as the output gaps or stock market volatility differ for these
economies, in which the output gap is essential to the monetary policy in United Kingdom while

34
the asset price volatility is reported to have an impact on Australia. When it comes to the
influence of stock market indices, both the results of United States and United Kingdom show
the expected positive sign despite not being statistically influenced. However, it might require
further investigation with the GMM estimator in order to resolve the potential issue of
endogeneity and come up with the final remark in regards to the relationship between the policy
rate and stock market.
Table 8. Augmented Taylor Rule based on OLS (Newey-West)
𝜶 1.069*** -0.127 0.358
(0.129) (0.297) (0.296)
𝜷 0.185*** 0.417*** 0.284***
(0.021) (0.081) (0.054)
𝜸 -0.003 0.043 0.137*
(0.046) (0.099) (0.082)
𝜹 𝒌 0.004** 0.004 0.009
(0.002) (0.009) (0.008)
R-squared 0.607 0.402 0.337
The estimated model is specified in Equation (2). Standard errors are shown in the parentheses
(.).
7.4. Generalized Method of Moments (GMM) Estimator

35
As already stated, GMM is used to estimate because this approach takes into consideration the
possible correlation between the independent variables; it is ideally suitable for modelling the
probably asymmetric behaviour of central banks as it solves the endogeneity problem and allows
estimating the optimal inflation threshold value for country, as monetary policy usually places
greater weight on inflation, this is chosen as the threshold indicator (Castro, 2011; Martin and
Milas, 2013; Jawadi et al. 2014).
The results of GMM estimator are provided in Table 9. The model for Australia shows the
probability associated with J-statistic is 6.5% that fails to reject the null hypothesis at 5%
significance level and may support the choice of our instrument. In addition, the coefficient
associated with asset price volatility is positive, although not statistically significant, suggesting
that asset price volatility affects the interest rate only indirectly. The same conclusion is reached
in regards to the asset price volatility in the United Kingdom. Regarding to the outcomes of US,
the probability associated with J-statistic is less than 5%, thus failing to support the choice of our
instruments. In particular, the coefficient associated with asset price volatility in the US is
negative and not statistically significant, suggesting that the stock market factor might not affect
the interest rate in this country.
Table 9. Linear Taylor Rule based on GMM
Australia United States United Kingdom
𝜶 1.065*** -0.005 0.447
(0.144) (0.318) (0.300)
𝜷 0.181*** 0.429*** 0.295***
(0.023) (0.092) (0.057)
𝜸 0.026 0.130 0.133

36
(0.050) (0.143) (0.096)
𝜹 𝒌 0.004** -0.015 0.002
(0.006) (0.018) (0.015)
R-squared 0.598 0.341 0.327
J-statistic 3.406* 4.487** 2.539
Prob(J-statistic) (0.065) (0.034) (0.111)
The estimated model is specified in Equation (2). Standard errors are shown in the parentheses
(.).

37
8. Conclusion (Actual: 271)
Nowadays, the movement of asset price has became increasingly important for an economy,
especially when financial crises happen, for example the slump of real estate prices can
significantly push the economy into recession, or the asset bubble could be an early warning sign
of risks. In addition, asset volatility can affect other important macroeconomics variables, such
as household wealth, consumption, output or even inflation, which are crucial consideration
under a monetary policy. However, the asymmetric response of central banks in regards to stock
market volatility remains limited and has not been deployed in many markets. Thus, motivated
by this situation, this study incorporates the movement of asset prices in Taylor rule and tests the
impact of the inflation gap, output gap and asset price volatility variables on the interest rate
policy.
Overall, our results support the presence of a Taylor rule in Australia, the United States and
United Kingdom. However, the output coefficients are not statistically significant in Australia
and United States in the exception of United Kingdom, and only the inflation coefficients are
statistically significant in all three countries, and the sign of these coefficients are all positive,
which are consistent with other literatures. These findings also indicate that policy makers in the
countries react more to target deviations in the case of inflation than production. Regarding the
augmented Taylor rule with the estimation of asset volatility variable, although the regression
results conclude that the asset price volatility only have an direct impact on the economies of
Australia and United Kingdom, the presence of this additional element to the Taylor rule still
provides valuable information to the monetary policy framework as it increase the adjusted R-
squared of the model and offers a higher degree of data fitting for the sample size.

38
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10. Appendix
Standard Taylor Rule with Ordinary Least-Squares Method
United Kingdom

43
Augmented Taylor Rule with Ordinary Least-Squares Analysis (ATR)
United Kingdom

44
Augmented Taylor Rule with Ordinary Least Squares Method (Newey-West Option)
United Kingdom

45
Augmented Taylor Rule with Generalized Method of Moments (GMM) Estimator
United Kingdom

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