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Understanding the time-frequency dynamics of money demand, oil prices, and
macroeconomic variables: The case of India
Rabeh KhalfaouiCollege of Science and Humanities, Shaqra University, SA
Email: [email protected]
Hemachandra Padhan Department of Humanities and Social Sciences (HSS),
Indian Institute of Technology (IIT), Madras, IndiaEmail: [email protected]
Aviral Kumar Tiwari*Department of Finance Law and Control, Montpellier
Montpellier Business School, Montpellier, FranceEmail: [email protected]
Shawkat HammoudehLebow College of Business, Drexel University, USA
Email: [email protected]
*Corresponding author.
1
Understanding the time-frequency dynamics of money demand, oil prices, and
macroeconomic variables: The case of India
Abstract
This study investigates the multi-scale lead-lag nexuses between money demand and real GDP,
interest rate, exchange rate, oil prices, inflation-defining CPI for the third global oil consumer,
India, using the monthly data ranging from 1994 M1 to 2017 M11. A special focus is placed on
the effect of changes in oil prices and inflation-defining CPI on money demand. The paper uses
the wavelet coherency and the partial wavelet coherency techniques to achieve the goals. The
univariate empirical analysis reveals that during the whole sample period, the underlining
variables show the same pattern in terms of wavelet power spectra, suggesting weak volatility
levels across the time-frequency plane. The bivariate analysis indicates that the partial wavelet
coherent empirical results underscore the presence of either a unidirectional or a bidirectional
causal relationship between money demand and the underlining oil and macroeconomic
variables. In particular, in terms of the wavelet coherency results, money demand exhibits the
greatest interdependency with real GDP across the time-frequency domain, while it has a much
lower interdependency with interest rate, exchange rate and oil prices.
Keywords: Demand for money; Oil prices; Wavelet coherency; Partial wavelet coherency.
JEL Codes: E41, Q41, F31, Q4, C18
2
1. Introduction
The present work aims to study how variations in real gross domestic product (GDP), oil prices,
exchange rate, interest rate, inflation-defining CPI and money demand in the world’s third
largest oil-consuming country, India, following the United States and China. Its oil demand is
expected to rise considerably in the future, as the projected size of its population is expected to
surpass that of China, and the growth rate of its GDP is anticipated to remain above 7% in the
long run. These relevant factors will enhance demand for money. As GDP growth and industrial
development are highly correlated with oil consumption, the Indian economy is thus extremely
vulnerable to oil price variations which will cause fluctuations in money demand that connects
the real and monetary sides of the economy1. Furthermore, India is the third largest economy by
the purchasing power parity (PPP) GDP after China in 2018 (IMF, 2018)2. Therefore, we are
motivated to examine whether India is able stabilize its demand for money in the presence of
changes in oil prices, exchange rate, interest rate, inflation-defining CPI and real gross domestic
product (GDP).
Moreover, the stability of demand for money has received a special attention by
macroeconomists. This importance stems mainly from the fact that this demand is associated
with the real and monetary sides of the economy through the quantitative theory of money3. The
issue of stability of the demand for money has been recognized by S. M Goldfeld of Brookings
Institution since 19734. Although, Goldfeld initiated the stability of demand for money in the
case of United States, most of the subsequent studies have emphasized the stability of demand 1 Exchange rate, interest rate, price level etc. 2 China (1st) is (25.1 billion$), United States (2nd) is (20.2 billion$) and India (3rd) is (10.3 billion$). "Report for Selected Country Groups and Subjects (PPP valuation of country GDP)" 3 See Friedmand (1956) and Poole (1970) for more details. 4 According to Goldfeld, S. M., Duesenberry, J., & Poole, W, (1973, p.579) “Has the demand function for money remained stable over the post war period? Put another way; is there any evidence of either systematic long-run shifts or marked short-run instabilities that make historically estimated relationships unsuitable for forecasting purposes?
3
for money that links the real and monetary flanks of the U.S. economy by focusing on the pivotal
quantitative theory of money (Friedman, 1956; Poole, 1970). Later, the literature has placed a
special attention on the monetary side of the economy.
In the same vein, given the Keynesian framework of money demand, the literature has focused
on the relationship between demand for real money balances and the motives for holding money
(e.g., transaction, precautionary and speculative motives). Furthermore, Friedman (1953), Miles
(1978), and Mundell (2000) argue that the exchange rate insures a degree of monetary autonomy
for the monetary systems in the rest of the world. McKinnon et al. (1984) also find that exchange
rate is a better indicator of shifts or stability of money demand in the United States. In the same
line of thinking, Girton and Roper (1981) show that exchange rate variance5 increases with the
degree of currency substitution in the face of exogenous expected rate of depreciations.
Therefore, it is important to include the exchange rate in the money demand function in India.
On the other hand, the price of oil which is the most volatile commodity has demonstrated its
importance as a phenomenon that should be reckoned with in the global economy. This is due to
the fact that virtually all economic activities including consumption and production require the
use of the volatile oil whether as an input or a final output, which affects the stability of money
demand. Oil prices affect consumers’ budget and companies’ investment plans. Spikes in oil
prices that result from idiosyncratic oil shocks, and not from aggregate demand, may not
morphed into more inflation but may affect money demand through risk, exchange rate and other
channels.
5 Girton and Roper, (1981) explain that the exchange rate would be a determinant of money demand at the value of unity if the transaction cost is developed more fully in the aggregate money demand. For more details, see Mundell (1971), and Kareken and Wallace (1978).
4
Accordingly, oil prices, inflation-defining CPI, exchange rate, interest rate and real GDP can
each have different effects on the demand for money balances. In this case, the early studies like
Hamilton (1983), Burbidge and Harrison (1984), and Gisser and Goodwin (1986) argue that oil
price shocks had lowered the world output through reductions in the supply of inputs of
production. On the other hand, Darby (1982) and Ahmed et al. (1988) blame the poor economic
performance in the 1970s and 1980s on the macroeconomic policies that were implemented in
many industrial countries in the aftermath of the oil price shocks. Those policies have been
undertake in order to combat the prevailing high inflation rates, and thereby may have worsened
the recessions that were already associated with the increases in energy prices.
To this end, none of the studies has examined the causal relationship between the volatile oil
prices, exchange rate, inflation rate, interest rate and real GDP and the stability of money
demand function. Therefore, we contribute a new view to the literature on money demand by
using the wavelet analysis (wavelet coherency and partial wavelet coherency) in order to analyse
the impact of those oil and macroeconomic variables on the money demand function for the
world’s third largest oil consumer and the world’s largest democracy. Existing studies in the
literature have used traditional time series methods such as simple regression models, ARDL and
the Johensen cointegration models, or other time varying estimation methods. However, the use
of wavelet helps us to analyse the relationship between money demand and its determinants (e.g.,
income and interest rate) in a time-varying framework, without losing the information of the time
frequency counterpart of the data. It also shows both cyclical and anti-cyclical effects of the
relation of money demand with their variables, particularly income and interest rates. As we
know economic agents are heterogeneous and behave differently. For example, for some agents’
money demand due to income can be a short run phenomenon, while it can be a long run for
5
some others. Similarly, for some economic agents’ money demand due interest rates can be a
short run phenomenon while it can be cast in the long-run perspective for others.
The objective of this study based on the new methodology is to examine the multi-scale lead-lag
nexus between changes in oil price, exchange rate, inflation-defining CPI, interest rate and real
GDP and changes in money demand. This methodology uses the wavelet coherency and the
partial wavelet coherency and the phase-differences to decompose the time frequency effects of
changes in oil prices, exchange rate, inflation–defining CPI, interest rate and real GDP on
changes in money demand over the period January 1994 to November 2017 for India.
The results show there exists a bi-directional direction between changes in oil prices, exchange
rate, inflation rate, interest rate and real GDP, and changes in money demand. In addition, the
wavelet coherency and partial wavelet coherency approaches reveal time-varying pockets of low
and high coherences among the different series under study, showing both cyclical and anti-
cyclical effects. Furthermore, the degree of co-movement and the causal effects for the pairs of
the variables occur in the time scale band from one year to two years in the short-term horizon.
The remainder of the study is organized as follows. Section 2 presents a brief overview of money
demand in India. Section 3 provides the literature review. Section 4 discusses the methodology
and data. Section 5 explains the results and provides policy implications. Finally, Section 6
concludes the study.
2. Role of Money demand in India
According to Poole (1970), money demand is the appropriate monetary policy tool that central
banks use to achieve macroeconomic goals if the money demand function (MDF) is stable.
However, if MDF is not stable, then central banks should target the interest rate. Therefore, the
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Indian government has witnessed significant changes in the financial system as a result of
enlarging the financial innovations and financial efficiency. These noticeable changes are due to
variations in interest rate, inflation, oil prices and exchange rate. Moreover, they are due to the
shift to the market-based exchange rate system and current account convertibility. The Financial
Stability Report (RBI; 2018) reflects an assessment of the stability of India’s financial system
and its resilience to risks emanating from global and domestic factors. It also discusses issues
related to developments and regulation of the financial sector, connected to stabilizing the
demand for money in India6. Moreover, it shows that the Reserve Bank of India (RBI) is
introducing multiple indicators to assist with stabilizing the money demand, which would initiate
a more effective policy prospective.
Jadhav (1994) finds a stability of demand for money in India as a result of the financial
deregulations and financial innovations that occurred. At the same line, Rao and Bajpai (1995)
and Ramachandran (2004) find a stability in money demand in the short-run by using output and
prices. On the other hand, a study by Arif (1996) demonstrates the stability of money demand in
the long-run. Based on Arif (1996), we can conclude that money demand in India has been
considered as less volatile. Furthermore, the studies by Reddy (1998), Mohanty and Mitra
(1999), Bhanumurthy (2000), Das and Mandal (2000), Rao and Ramachandran (2003) and
Padhan (2016) support the stability of money in India. Therefore, we can conclude that empirical
studies support a stable demand for money function in India.
3. Review of the related studies
6 See, The Financial Stability Report (RBI; 2018) https://rbi.org.in/Scripts/FsReports.aspx.
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Theoretically, the modelling of the stability of money demand function was done within the
framework of macroeconomics, particularly the monetary model (Friedman, 1956)7, the New
Classical model (Lucas and Thomas, 1981), the monetary approach with the exchange rate
(Dornbusch, 1976), the monetary approach with the balance of payments framework (Hahn,
1977; Frenkel & Johnson, 2013), and the New Keynesian model (Lee, 2009; Giordani, 2004).
The demand for money theory has typically focused on the elasticities of money demand with
respect to income and the interest rate (Goldfeld 1973; Arango and Nadiri 1981; Boughton 1981;
Butter and Fase 1981; McKinnon et al. 1984; Rose 1985; Payne 1992; Hueng 2000).
From the empirical statistical prospective, the earlier studies focused on the cointegration
technique, assessing the stability of money demand function. These include Hafer and Jansen,
1991; Hoffman and Rasche, 1991; McNown and Wallace, 1992,) for the United States. Karfakis
and Parikh (1993) for Australia; Adams (1991) and Johansen (1992) for the United Kingdom;
Muscatelli and Papi (1990) for Italy; Bahmani-Oskooee and Shabsigh (1996) for Japan; Melnick
(1990) for Argentina; Frenkel and Taylor (1993) for Yugoslavia; Bahmani-Oskooee and Rhee
(1994) for Korea; Hafer and Kutan (1994) for China; and Bahmani-Oskooee (1996) for Iran.
Moreover, in contrast to the earlier studies on stability of money demand, the more recent
research uses the traditional8 cointegration techniques without analysing the stability of money
demand function. The recent research places attention only on the long-run relationship by using
cointegration techniques. These include Prasad (1994), Bhattacharya (1995), Rao and Shalabh
(1995) and Pradhan and Subramanian (1997) for India; Khan (1980, 1994), Khan and Reza 7 Friedman’s quantity theory of money is based on the portfolio approach to the demand for money by considering the price level, interest rate on bonds and interest rate on equities, non-human wealth, human wealth and income level. 8 Traditional techniques include the ordinary least squares and second stage least squares in estimating the elasticity of the variables. They also suffer from the spurious regression problem. Therefore, they use the cointegration approach to solve the spurious regression problem. In the same line, those approaches interpret their finding of the presence of cointegration as a sign of stability but without performing a stability test.
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(1989), Ahmad and Khan (1990), Khan (1992) and Hossain (1994) for Pakistan; Tan (1997),
Ibrahim (1998, 2001) for Malaysia; Arize et al. (1991), Chowdhury (1997) and Bahmani-
Oskooee and Techaratanachai (2001) for Thailand; Bahmani-Oskooee and Rhee (1994) and Lee
and Chung (1995) for Korea. However, some newer studies use the ARDL method including
Bahmani-Oskooee and Barry (2000) for Russia, Bahmani-Oskooee and Bohl (2000) for
Germany and Cheong Tang (2007) for the ASEAN 5 countries. Others use panel data models
with structural breaks and the PMG model.
But recently the new developments in money demand apply distinct modelling procedures to
investigate the variance of exchange rate, structural change and the specification of the
contextual setting (Lungu et al. 2012; Sahin 2013). Concerning the short-run versus long-run
money demand, Chow (1966) investigated the determinants of the long-run and short-run
demand for money and concluded that there is indeed a difference between the long-run and
short-run demand and that permanent income is more important than current income as the long-
run asset constraint.
For better understanding of the literature on money demand, we have tabulated the
characteristics of the more recent studies in more details in Table 1:
Table 1. A review summary of the findings of previous studies
Authors Country/Region Period Approach Findings
Bahmani-Oskooee and Barry (2000)
Russia Post-1970 ARDL Not stable
Bahmani-Oskooee and Bohl (2000)
Germany 1965q1-1991q4 ARDL Not stable
Sriram (2002) Malaysia 1973:1-1995:12 ECM Stable
9
Nell (2010)South Africa 1965–1997 Engle and
Granger
Cointegration
Both stable and unstable
Akinlo (2005) Nigeria 1970:01-2004:04 ARDL Stable
Bahmani-Oskooee & Rehman (2005)
Asian developing countries
1973-2000 Johansen Maximum Likelihood
Unstable
Bahmani-Oskooee & Tanku (2006)
LCDs 1974q1-1998q4 ARDL Cointegration
Cheong Tang (2007)
ASEAN-5 1975-1994 ARDL Stable
Narayan (2007) Indonesia 1970-2005 Johansen Maximum Likelihood
Cointegration
Nwafor et al (2007)
Nigeria 1986Q3–2005Q4 VAR Stable
Bahmani-Oskooee and Wang (2007)
China 1983.1–2002.4 ARDL Stable
Owoye and Onafowora (2007)
Nigeria 1986.1–2001.4 Johansen Maximum Likelihood
Stable
Hamori and Hamori (2008)
11 EU countries 1999m1-2006m3 Johansen Maximum Likelihood
Stable
Hamori (2008) Sub-Saharan African
1980-2005 Non-stationary panel data analysis
Cointegration
Inoue and Hamori (2008)
India 1980-2007
1976-2007
Cointegration test Cointegration
Bahmani-Oskooee and Gelan (2009)
21 African Countries
1971q1-2004q3 Johansen Maximum Likelihood
Cointegration
Baharumshah et al. (2009)
China 1990:02-2007:04 ARDL Stable
Darrat and Al- Bahrain, UAE and 1973-2005 Johansen and Cointegration
10
Sowaid (2009) Qatar Juselius
Yu and Gan (2009)
ASEAN-5 1987m1-2007m4 Engle and Granger
Cointegration
Stable
Singh and Pandey (2009)
India 1953-2007 Cointegration With structural breaks
Stable with structural breaks
Rao and Kumar ( 2009,b)
14Asian developing countries
1970-2005 Cointegration With structural breaks
Stable with structural breaks
Rao and Kumar ( 2009,a)
Bangladesh 1973-2003 Cointegration With structural breaks
Unstable
Siddiki (2010) Bangladesh 1975-1995 Johansen Maximum Likelihood
Stable
Chukwu et al. (2010)
Nigeria 1986q1-2006q4 Cointegration and structural breaks
Stable
Hossain (2010) Bangladesh 1973-2008 Johansen Maximum Likelihood
Stable with structural breaks
Kumar et al. (2013,b)
11 OECD Countries
1975q1-2008q4 Panel Data With structural breaks
Stable with structural breaks
Kumar (2011) 20 developing countries
1975-2005 ARDL With structural breaks
Stable
Kumar and Rao (2012)
14 Asian countries
1970-2009 ECM & ARDL Stable
Kumar et al. (2013,a)
Nigeria 1960-2008 Cointegration with structural breaks
Stable with structural breaks
Dreger and Wolters (2014)
Euro area 2003q4-2010q4 Cointegration Stable
Sani et al. (2014) Nigeria 1991:Q1-2013:Q4 Gregory and Hansen cointegration (1996)
Stable with structural breaks
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Ben-Salha and Jaidi (2014)
Tunisia 1979-2011 ARDL Stable
Hamdi et al (2015)
GCC countries 1980.1 2011.4 FMOLS, PDOLS and PMG
Stable
4. Methodology and Data
4.1. The wavelet coherency.
In this paper we employ a continuous wavelet transform (CWT) for our analysis. We used the
complex Morlet wavelet (Percival and Walden, 2000), which is defined as
ψ0 (η)=π−1/4 e iω0η e−1
2 η2
, (1)
where ω0 and denote the frequency and the time, respectively. To reach an optimal balance,
Torrence and Compo (1998) argue thatω0=6 .
The ratio of the cross-spectrum between two times series X and Y to the product of the spectrum
of each time series defines the wavelet coherency. This ratio indicates the local correlation in the
time-frequency space. The formula of the wavelet coherency between X and Y is as follows
(2)
S denotes the smoothing operator; defines the cross-spectrum and is the
complex conjugate of . Following Torrence and Compo (1998), the time convolution is
12
carried out with a Gaussian process, while the scale convolution is accomplished using a
rectangular window (for further details, see Torrence and Compo, 1998).
According to Aguirar-Conraria and Soares (2011) and for the partial continuous wavelet
transform approach, the wavelet coherency is given by the following:
Rm2 ( s )X ,Y|ZU=
|QXYM |2
QXXM QYY
M ,
(3)
where QXYM
, QXXM
and QYYM
denote the minors linked with the smoothed cross wavelet
transforms |S (s−1W m
XY (s ))|2
, S (s−1|Wm
X( s )|2) and S (s−1|W m
Y (s )|2) , respectively, in the 4×4
matrix Q .
The lead-lag relationship (phase-difference) between X and Y can be defined as the following
(4)
where ℑdenotes the imaginary part of the smoothing power spectrum and ℜ indicates the real
part of the smoothing power spectrum. A phase-difference coefficient equal to zero demonstrates
that the signals move together at a specified frequency. If , then the series are in-
phase, with leading . On the other hand, if then is leading Y. One may
experience an anti-phase relation (analogous to negative covariance) if the phase difference is of
π (or −π ) meaning . If then is leading, while
Y is leading if .
13
4.2. Data
This study covers the monthly data over the period January1994 to November 2017 for India.
The data are collected from the Reserve Bank of India (RBI) and the US Energy Information
Administration (EIA). Moreover, we use the broad money (M3) as a proxy of money demand, the
consumer price index as a proxy of inflation CPI (base year, 2010=100), real GDP per capita as
economic growth, interest rate, exchange rate and crude oil prices as a proxy of oil prices. This
analysis follows the Goldfeld (1989), Hossain (2010) and Alsamara et al. (2017). It is based on
the following empirical model
where MD is money demand, SV is the scale variable proxied by the oil price (OP), real GDP (Y)
and OC is the opportunity cost proxied by the inflation rate CPI (INF), interest rate (R) and
exchange rate (ER). Therefore Eq. (8) can be rewritten as
For a first assessment of the patterns of oil prices, inflation CPI, money demand, real GDP,
interest rate and exchange rate in the case of India through the time-frequency space, we
represent the individual wavelet power of each variable which indicates the intensity of the
volatility of the time series at a certain time (point of time) and scale (period). Regarding the
wavelet power spectra (right panel of Figure 1), the horizontal axis shows the time component
while the vertical axis denotes the period in terms of years (the frequency is converted into time
units; years), i.e. the frequency component. The thick black contour represents the region of the
5% significance level, while the curved black line indicates a cone of influence which denotes
areas affected by the edge effects.
14
In Figure 1, we portray on the left the time series under study. On the right side of the figure, we
show the wavelet power spectra of the six variables.
Looking at Figure 1, it is clearly noticeable that the individual wavelet power plots exhibit a
quite similar behaviour featured by slight concentration of power at coarser scales (at 8-16 years
frequency band). Further, referring to the dispersion of the areas color and the degree of intensity
concentration, it is interesting to note that oil price changes and inflation were more volatile than
the four other variables. Obviously, we observe less significant islands of the deep blue for the
oil price and consumer price index wavelet powers than for the other variables.
Referring to the diagram of the inflation wavelet power spectra, at the frequency band of 1-2
years, the periods 1998-2000 and 2008-2011 are marked by high volatility levels as indicated by
the significant red-yellow areas. Those years are concomitant with the 2007 Asian fanatical
crisis, the 2008 global financial crisis and the 2010 European sovereign debt crisis.
Summing up, given the individual wavelet power spectra diagrams, several remarks merit
emphasis. First, one general finding can come out is this is that the variables used in the study
show weak volatility across all wavelet scales and during the entire sample period. Second, oil
prices and the consumer price index (inflation) appear to be more volatile than the other
variables across the time-frequency domain. Third, it is interesting to emphasize that the six
variables seem to exhibit the same pattern in terms of individual wavelet power spectra, which
points to weak volatility powers in the whole.
The individual wavelet power spectra are used in the volatility investigation and do not uncover
any common characteristics between the different pairs, as they do not examine the causal
interplays and the co-phases between the selected time series. Therefore, the wavelet coherency,
15
the partial wavelet coherency, the phase and partial phase relations are employed in order to
connect the different variables.
1999 2002 2005 2008 2011 2014 20172
3.5
5
6.5
8MD
Perio
d (y
ears
)
Wavelet Power
1999 2002 2005 2008 2011 2014 2017
1
2
4
810
1999 2002 2005 2008 2011 2014 20177
8.25
9.5
10.75
12GDP
Perio
d (y
ears
)
Wavelet Power
1999 2002 2005 2008 2011 2014 2017
1
2
4
810
1999 2002 2005 2008 2011 2014 20175
7
9
11
13IR
Perio
d (y
ears
)
Wavelet Power
1999 2002 2005 2008 2011 2014 2017
1
2
4
810
1999 2002 2005 2008 2011 2014 20173
3.75
4.5
5.25
6ER
Perio
d (y
ears
)
Wavelet Power
1999 2002 2005 2008 2011 2014 2017
1
2
4
810
1999 2002 2005 2008 2011 2014 2017-4
-1.5
1
3.5
6Inflation
Perio
d (y
ears
)
Wavelet Power
1999 2002 2005 2008 2011 2014 2017
1
2
4
810
1999 2002 2005 2008 2011 2014 20175
5.75
6.5
7.25
8Oil Price
Perio
d (y
ears
)
Wavelet Power
1999 2002 2005 2008 2011 2014 2017
1
2
4
810
Figure 1. Log-level time series plots and individual wavelet power spectra plots.
Note: The 5% significance level against the red noise is denoted by the thick black contour. The color code for power spans from blue (low power) to red (high power). The region affected by the edge effects (the cone of influence) is designated by a black line.
5. Results’ Discussions and Implications
16
In this section, we aim to quantify the intensity of the time-frequency lead-lag nexus of the real
GDP, interest rate, exchange rate, inflation-defining CPI, oil price versus money demand in the
case of India. To this end, we employ the wavelet coherency, partial wavelet coherency, phase
relation and partial phase relation methods to examine the relations between the variables in the
nexus. The results of those methods allow policymakers, different types of investors,
researchers, etc. to evaluate the frequency and the power of interconnection at any point of time
and discover the causal effects and synchronization of two phenomena we analyse the wavelet
(partial) coherency diagrams and the phase-difference plots.
We have five figures in our analysis which indicate the wavelet (partial) coherent and (partial)
phase structures for: (i) the money demand-real GDP pair; (ii) the money demand-interest rate
pair; and (iii) the money demand-exchange rate pair; (iv) the money demand-inflation defining
CPI pair; (v) the money demand-oil price pair in the time-frequency plane. Each figure contains
two panels where in the top panel the coherency diagram (the left-hand side) and the partial
coherency (the right-hand side) are displayed. In the bottom panel the phase relation (the left-
hand-side) and the partial phase relation (the right-hand side) are plotted.
As shown in the coherency and partial coherency diagrams, the strength of the nexus between
two variables is indicated through the colours of the regions which vary from blue to red.
However, the blue islands indicate lower interconnection between the considered time series,
whereas the red areas demonstrate the presence of higher intensity of interdependencies between
the two variables. The (partial) coherent structure of the investigated variables is given in a time-
frequency plane.
On each diagram, the x- and y-axes denote the time and frequency, respectively. The statistically
significant coherence intervals are denoted by the black outlined contours, while the opaque
17
areas are the regions of the diagram which refer to the so-called the cone of influence (i.e., the
area which is affected by edge effects). The lead-lag relationship via the time-frequency plane is
analysed across two business cycles: a 1-4 year frequency band (will be analysed as the short-
term horizon) and a 4-8 year frequency band (which corresponds to the long-term horizon). As it
can be seen in a first glance from the (partial) coherency diagrams for all possible pairs, one may
reveal that the nexus between real GDP, interest rate, exchange rate, inflation-defining CPI, oil
price and money demand in India is not stable across the time and over wavelet scales. As a
point of fact, with reference to the wavelet coherency and partial wavelet coherency diagrams
one might claim out a varying nature in the dynamics between the investigated time series
showed by the time-varying pockets of weak and high nexuses for the money demand-real GDP
pair, money demand-interest rate pair, money demand-exchange rate pair, money demand-
inflation defining CPI pair and money demand-oil price pair i.e. regarding both the diagrams of
coherency and partial coherency, we observe a plenty of red islands (a high power of
interdependency) and a great deal of blue islands (low power of interdependency).
Some exceptions are registered for the wavelet coherency structure of the money demand-
interest rate, money demand-exchange rate and money demand-oil price pairs with weak strength
of connectivity at almost all frequency bands and during the entire sample period. Interestingly,
regarding the wavelet coherency maps, another striking finding is the very low interdependency
of money demand with exchange rate and oil price across all frequencies and time periods. In
fact, inside the significance area we observe only blue and light blue islands, which indicates
lack of co-movement between exchange rate, oil price and money demand.
In terms of the phase relation, it is evident that we can highlight a similar lead-lag behaviour in
the short-term (1-4 year frequency band) and long-term (4-8 year frequency band) horizons for
18
all the possible pairs emphasized by the phase-difference values, ranging between and
suggesting a cyclical effect (in-phase relation) between the studied variables. This finding
reveals that money demand is positively correlated with all other variables across time and
frequencies, suggesting that real GDP, interest rate, exchange rate, inflation-dinging CPI, oil
price and money demand move in the same directions during a long time period. The exception
is for the period before 2003 at the two frequency bands for the money demand-interest rate pair
and for the period after 2014 at the 4-8 business cycle for the couple money demand-inflation
CPI as the phase-difference values range from to , implying that money demand moves with
an anti-phase phenomenon versus interest rate which leads in the short- and long-term and versus
inflation CPI with CPI leading in the long-term.
Comparing the findings driven by the partial phase relation diagrams with those displayed by the
phase relation diagrams in the short- and long-term horizons and doing robustness checking in
order to control for the effect of several factors on the direction of interdependencies and
causalities when comparing two variables, it is evident that the findings have been changed at the
same frequency bands. This suggests either in-phase (cyclical effects) or anti-phase (anti-cyclical
effects) relations (i.e., the partial phase-differences values lie between and ) during various
periods of times. For instance, looking at the money demand-real GDP pair, for the period 2010-
2016 and at the 4-8 year frequency band, as the values of the partial phase-difference ranging
between and , money demand causes real GDP with a negative sign.
Contrariwise, real GDP causes money demand for the same time period and the same business
cycle regarding the phase relation structure. Further, comparing the findings of the partial phase
19
relation with those of the phase relation shown for the money demand-exchange rate pair in the
long-run (a 4-8 years frequency band) during the period 1999-2008, it is clearly noticeable that
money demand and real GDP co-move with an anti-phase relation in terms of the partial phase-
differences, while the two variables are in-phase in terms of the phase-differences. In addition, if
we look at the money demand-oil price couple for the period 2000-2005 and across the
frequency cycle of 4-8 years, the oil price leads money demand as the partial phase-differences
ranging between and . On the other hand, money demand leads in terms of the phase
relation for both the same period of time and frequencies. Accordingly, one might infer that not
taking into account the partial coherency approach in our case study may drive us to spurious
conclusions. However, performing the partial coherency technique provides valuable information
to policymakers, market participants, and short- and long-term horizon investors.
With reference to the partial coherency diagrams depicted in Figures 2, 3, 4, 5 and 6, we observe
more significant red-yellow islands at all frequency bands during the whole sample under study.
This interesting finding that is inferred from the partial coherency diagrams indicates that the
level of causalities between the different pairs, after eliminating the influence of all other
variables, increase across time and frequencies. Additionally, the most important causality
interplays for the underlined pairs, after controlling for the other variables appeared at the lower
frequencies, which may suggest that short- and long-term investors and market participants pay
greater attention to the dynamics between real GDP, interest rate, exchange rate, inflation
defining CPI and oil prices from one side, and money demand from another side in India.
Furthermore, Figure 2 in connection with the phase and partial phase diagrams displays quite
similar patterns as featured by time-varying pockets of cyclical (in-phase) effects with a positive
20
long-term leading role of real GDP over the whole sample period, as the phase and partial phase-
difference values switching between and zero.
Summing up, in regard to the aforementioned findings of both the coherent structure (the
coherency and phase relation analysis) and the partial coherent structure (the partial coherency
and partial phase relation analysis), one can highlight the following major findings. (i) The
highest (partial) coherence of money demand with the underling variables is shown for the
money demand-real GDP pair. The finding underlines the importance of the transactions motive
for demanding money, which arises from the absence of perfect synchronization of receipts and
payments. It also highlights the significance of demand for assets in liquid forms. This high
dependency appears at lower frequencies, indicating perfect integration and interdependency
between money demand and real GDP.
(ii) Compared to the results of the partial wavelet coherency, the wavelet coherency exhibits
weak common power of interdependency for all the different pairs, except for the money
demand-real GDP pair. However, controlling the effects for all other variables when comparing
two factors leads to prominent results and provide crucial information on the dynamics of the
behaviour of money demand in India towards real GDP, interest rate, exchange rate, inflation
defining CPI and oil prices.
(iii) With respect to the phase structure, it is apparent that in the short- and long-term horizons
there is an in-phase behaviour between the related time series, as the values of the phase-
difference switching between and . Whereas controlling for the effects of all other
21
variables when investigating the two others provides more suitable information in the short- and
medium-terms with the in-phase or the anti-phase patterns.
(iv) At last, overall one may claim that during the entire sample period the nexuses between the
related variables depict a time-varying behaviour across the different time scales and that the
powerful partial coherences are more pronounced in the long-term horizon. Additionally, the
most prominent causal effects between the related variables are concentrated in the C-term, thus
providing us with a high significant long-term impact of changes in oil prices, interest rate,
exchange rate and inflation CPI on money demand.
Figure 2. Wavelet (partial) coherency and phase differences between money demand and real
GDP.
22
Note: In plots (a.1) and (a.2), we have the wavelet coherency (at the top left) and its respective phase relation (at the bottom left). In plots (b.1) and (b.2), we have the partial wavelet coherency (at the top right) and its respective phase relation (at the bottom right). The partial coherency and phase relations between money demand and real GDP are computed after controlling for the effects of interest rate, exchange rate, inflation defining CPI and oil prices. The black contour denotes the 5% statistical significance level. The color code for the coherency spans from blue (low coherency where coherence values are close to zero) to red (high coherency where coherence values are close to one). The phase relation is computed for the four frequency bands. The cone of influence represents the region affected by the edge effects and the values outside this line indicate no statistical significance.
Figure 3. Wavelet (partial) coherency and phase differences between money demand and
interest rate.
Note: Please refer to the notes in Figure 2. The partial coherency and phase relations between money demand and interest rate are computed after controlling for the effects of real GDP, exchange rate, inflation and oil prices.
23
(a.1) Wavelet Coherence(m,er)Pe
riod
1
2
4
8
1999 2002 2005 2008 2011 2014 2017-pi
-pi/2
0
pi/2
pi(a.2) Phase-difference
1~4 f requency band 4~8 f requency band
(b.1) Partial Wavelet Coherence(m,er|r,y,inf,op)
1999 2002 2005 2008 2011 2014 2017
(b.2) Phase-difference
Figure 4. Wavelet (partial) coherency and phase differences between money demand and
exchange rate.
Note: Please refer to the notes in Figure 2. The partial coherency and phase relations between money demand and exchange rate are computed after controlling for the effects of real GDP, interest rate, inflation and oil price.
24
(a.1) Wavelet Coherence(m,inf)Pe
riod
1
2
4
8
1999 2002 2005 2008 2011 2014 2017-pi
-pi/2
0
pi/2
pi(a.2) Phase-difference
1~4 f requency band 4~8 f requency band
(b.1) Partial Wavelet Coherence(m,inf|r,er,y,op)
1999 2002 2005 2008 2011 2014 2017
(b.2) Phase-difference
Figure 5. Wavelet (partial) coherency and phase differences between money demand and
inflation.
Note: Please refer to the notes in Figure 2. The partial coherency and phase relations between money demand and inflation are computed after controlling for the effects of real GDP, interest rate, exchange rate and the oil price.
25
(a.1) Wavelet Coherence(m,op)Pe
riod
1
2
4
8
1999 2002 2005 2008 2011 2014 2017-pi
-pi/2
0
pi/2
pi(a.2) Phase-difference
1~4 f requency band 4~8 f requency band
(b.1) Partial Wavelet Coherence(m,op|r,er,inf,y)
1999 2002 2005 2008 2011 2014 2017
(b.2) Phase-difference
Figure 6. Wavelet (partial) coherency and phase differences between money demand and oil
price.
Note: Please refer to the notes in Figure 2. The partial coherency and phase relations between money demand and oil prices are computed after controlling for the effects of real GDP, interest rate, exchange rate and inflation CPI.
6. Conclusion and policy recommendations
This empirical research aims to investigate the multi-scale lead-lag nexuses between changes in
real GDP, interest rate, exchange rate, inflation defining CPI, oil price changes and changes in
money demand in for the third global oil consumer, India. To this end, we applied two important
econometric methods employed recently in the economic and financial literature: the wavelet
coherency and the partial wavelet coherency. Our major findings can be summed up as follows.
26
First, there is a bi-directional lead-lag causality interplay between changes in real GDP, interest
rate, exchange rate, inflation CPI, oil prices and changes in money demand.
Second, the most pronounced degree of causal interplays for the studied couples occurred in the
long-term horizon (at a 4-8 years frequency band). This may indicate that the effects of oil price
shocks and those of the macroeconomic variables on money demand are not immediate, and they
would also have some periods of time for those shocks to run via the Indian real economy.
Therefore, the effects of changes in oil prices and macroeconomic factors become more visible
when taking into consideration larger time horizons. Additionally, one may claim that the
fluctuations in oil prices and the macroeconomic changes have a minor effect on the Indian
economic activity at shorter time horizons. This important finding may have crucial practical
implications for several economic agents. From the point of view of policy makers, in order to
apply some powerful long-term macro-prudential policies, the timely recognition and
expectations of unfavourable circumstances in the monetary policy and the time of intervention
should be a foremost priority for Indian policymakers and Indian policy authorities. From the
standpoint of investors and portfolio managers, it is recommended that investors and portfolio
managers pay great attention to the fluctuations in oil prices and macroeconomic variables under
consideration, in order to make optimal investment strategies, perform portfolio diversification
decisions and improve the efficiency of their risk management in the long-term horizon.
Third, the results that the high power of the causal interdependency of changes in money
demand versus changes in real GDP, interest rate, exchange rate, inflation CPI and oil prices
occurred at the lower frequencies may suggest that short-/long-term investors, portfolio
managers and market participants pay more attention to the dynamics of the shocks in real GDP,
27
interest rate, exchange rate, inflation, and oil prices and changes in money demand in India in
four to eight years business cycles.
Fourth, it is recommended that investors and decision makers design optimal investment
strategies, make portfolio diversification decisions and enhance their risk-management power, as
well formulate their asset allocation strategies, notably in long-term stock holding periods.
Fifth, at the lower frequencies policy interventions of the Indian authorities should be important
as the real GDP, interest rate, exchange rate, inflation CPI and oil prices are highly connected to
money demand.
Six, finally applying the partial coherency technique to the selected variables has led to
important results, more specifically, at the shorter and medium-term horizons. Accordingly, in
terms of the partial phase relation, the removal of the influence of all other variables when
investigating the interaction of two others led us to accurate findings, indicated by either an in-
phase or anti-phase behaviour, whereas the phase structure is revealed only as an in-phase
pattern of causal effects between the related.
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