1
Systemic risk and macroeconomic shocks: Evidence from the crude oil market
and G7 countries
Lu Yanga Kaiji Motegib Shigeyuki Hamoric
a School of Finance, Zhongnan University of Economics and Law,
182# Nanhu Avenue, East Lake High-tech Development Zone,
Wuhan 430-073 P. R. China
E-mail: [email protected], [email protected]
b Graduate School of Economics, Kobe University
2-1 Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8501 Japan
E-mail: [email protected]
c (Corresponding author) Graduate School of Economics, Kobe University
2-1 Rokkodai-cho, Nada-ku, Kobe, Hyogo 657-8501 Japan
E-mail: [email protected]
Abstract
In this paper, we examine the systemic risk in the crude oil market and its relationship
with macroeconomic shocks worldwide. We extract monthly systemic risk via
GARCH and DCC models augmented by a Mixed Data Sampling (MIDAS) technique.
We then investigate the predictive ability of systemic risk on monthly macroeconomic
shocks via quantile regression. We find that the predictability has been justified for
the one-month scale. However, for the short-term variations of the wavelet component,
a stable predictability does not exist while it becomes real for the inflation shocks in
the long-term and the output shocks in the mid-term and the long-term. In sum, we
find that systemic risk in the crude oil market predicts output shocks better than
inflation shocks. Our results can provide solid information for both investors and
policy makers.
Keywords: Conditional Value-at-Risk (CoVaR), macroeconomic shock, Mixed Data
Sampling (MIDAS), quantile regression, systemic risk, wavelet transform.
JEL codes: C22, C58, G15.
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1. Introduction
As part of the commodity market, crude oil plays an important role in linking
financial markets to the real economy. For example, a large decline in crude oil price
always comes with an economic meltdown. Since crude oil is the most important
input of industry production, a minor change in crude oil price will significantly
influence costs across industries, which will in turn influence the expectations of the
public as well as investors. Therefore, understanding the relationship between crude
oil price and the economy will provide investors and policy makers first-hand
information about the future of the economy.
There are numerous papers that also discuss how a crude oil price shock can
influence macroeconomic outcomes as well as the financial market based on different
approaches (Beck, 2001; Byrne et al., 2013; Cashin et al., 2002; Mallick et al., 2018;
Reboredo, 2015). The majority of the studies provided evidence that oil price shocks
damage the world’s economies and increase financial market volatility. As pointed in
the studies of Kilian (2008a, 2008b, 2009), different sources of oil price fluctuations
will cause different economic outcomes. Therefore, in his studies, demand shocks and
supply shocks have been extracted to overcome a reverse causality from
macroeconomic aggregates to oil prices. His studies show that oil supply shocks are
the main resource to cause the fluctuations in the macroeconomy. Similar studies are
followed by Kilian (2010, 2014), and Lorusso and Pieroni (2018). For example, based
on data from the UK, Lorusso and Pieroni (2018) show that the shortfalls in crude oil
supply cause an immediate fall in gross-domestic-product growth while inflation
increases following a rise in real oil prices. In contrast to the pervious literature, we
start our research from the financial market perspective based on systemic risk
measures on the crude oil price return to avoid the possible problem of reverse
3
causality (Adrian and Brunnermeier, 2016; Giglio et al., 2016).
The relationship between systemic risk in major financial markets (e.g., foreign
exchange markets and stock markets) and macroeconomic shocks has been studied in
many recent papers (Borri, 2018; Calmès and Théoret, 2014; Duca and Peltonen,
2013; Giglio et al., 2016; Jin and Zeng, 2014; Wang et al., 2017). The above
researches discussed systemic risk as only limited to the financial markets by
excluding the commodity market. For example, Giglio et al. (2016) provide the
compressive framework for evaluating the predictability of systemic risk measures in
the financial markets (mainly focusing on the stock and bond markets) on economic
shocks by employing 17 systemic risk measures. They find systemic risk can provide
a good anchor to forecast future economy. In contrast, by employing the data from the
currency market, Borri (2018) finds the large cross-country differences in
vulnerability to systemic risk measured by Conditional Value-at-Risk (CoVaR).1
The commodity market is closely related with the real economy due to the
properties as the important input to the real economy. However, with the continued
financialization of commodity markets (Silvennoinen and Thorp, 2013), the systemic
risk in the commodity markets increases as well. Although the systemic shocks in the
commodity market may not crush the economy immediately like a financial crisis, it
will damage the economy in the long-term. Crude oil as the most critical asset in the
commodity market can be considered to be the main source of systemic risk. For
example, oil crises that occurred in 1973, 1979, and 1990 caused huge recessions in
G7 countries and elsewhere worldwide. Given that crude oil is closely related to the
1 There is also a series of research that quantifies systemic risk in commodity markets (Algieri and Leccadito,
2017; Kerste et al., 2015; Prokopczuk et al., 2017). However, the systemic risk measures in these literatures are
varied. For example, in the recent study of Algieri and Leccadito (2017), they employ the delta conditional Value
at Risk approach based on quantile regression to identify a measure of contagion risk for energy, food and metals
commodity markets. In contrast, our research estimates the value of conditional Value at Risk through the
conditional covariance matrices as well as marginal distribution to capture the time-varying nature of systemic
exposure to crude oil risk, which fills the gap of this field. Moreover, how systemic risk of crude oil in the
commodity market can influence or predict macroeconomic shocks is still new to the current literatures.
4
financial market as well as the economy with the quick financialization process, the
spillover of a crisis or systemic risk to other countries or other financial markets
occurs more easily. Therefore, research on the relationship between systemic risks in
the crude oil market and macroeconomic shocks should be given more attention. Even
though the linkage between crude oil price and the economy is complex, the systemic
risk in the crude oil market still has meaningful information containing the future
economy. Therefore, our research provides the first insight on this issue in the
literature.
In this paper, based on the CoVaR framework, we investigate this issue by
estimating conditional covariance matrices of the commodity market returns and
crude oil returns by following the studies of Colacito et al. (2011), Engle et al. (2009),
and Engle and Rangel (2008). Firstly, we estimated the conditional variance of each
return via univariate Generalized Autoregressive Conditional Heteroscedasticity
models with Mixed Data Sampling specifications (GARCH-MIDAS). Secondly, we
estimate the conditional covariance between the commodity market return and crude
oil returns via bivariate Dynamic Conditional Correlation models with MIDAS
specifications (DCC-MIDAS).2 Finally, using the estimated conditional covariance
matrices, we compute CoVaR for the pair of commodity market and crude oil, which
is a well-known measure of time-varying systemic risk that captures the tail behavior
of one asset when the other asset incurs an extreme return (Adrian and Brunnermeier,
2016; Girardi and Ergün, 2013).
Nevertheless, the systemic risk in the crude oil market based on the above
approach has never been discussed in previous literature. While crude oil is the most
important commodity in the commodity market, the systemic risk in the crude oil
2 The GARCH-MIDAS and DCC-MIDAS approaches are of course not the only approaches of estimating
conditional covariance matrices of asset returns. For alternative approaches, see Chen et al. (2015) and Dhaene and
Wu (2016), among others.
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market will definitely be a reason of a macroeconomic fluctuation. Therefore, in this
study, we investigate the probability of the systemic risk in the crude oil market to
predict the macroeconomic shocks worldwide. Since different investors and policy
makers may well be interested in different prediction horizons, we perform wavelet
transform to decompose the CoVaR-based systemic risk into multiple frequencies.
This step is a novel contribution to the literature since, to the best the authors’
knowledge, wavelet transformation has never been applied to CoVaR. In fact, we
found significantly positive correlations between systemic risk and inflation shocks at
shorter horizons and significantly negative correlations at longer horizons. However,
we did not identify the significantly positive correlations between systemic risk and
output shocks at short horizon but at mid- and long-term horizons. It is easy to
understand that an increase in systemic risk in the crude oil market will increase the
inflation rate in G7 countries in the short term, but damage the whole global economy
at longer horizons. Those empirical results can be obtained only if systemic risk is
decomposed into multiple timescales, and hence our empirical finding is new to the
literature.
Finally, we run quantile regressions for the frequency-specific CoVaR versus
macroeconomic shocks based on monthly inflation and output. Giglio et al. (2016)
also perform quantile regressions on various measures of systemic risk versus
macroeconomic shocks, but they do not decompose the systemic risk into multiple
frequencies. In that regard our work serves as an extension of Giglio et al. (2016)
based on the quarterly data. In contrast, we estimate the monthly CoVaR based on the
daily frequency data through the GARCH-MIDAS and DCC-MIDAS techniques
which allows us to obtain more information through the wavelet approach in the next
step. Therefore, understanding the real parts of the predictive ability of systemic risks
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on macroeconomic shocks will serve another new contribution to the literatures.
Our main findings can be summarized as follows. Firstly, for the raw data,
systemic risk in the crude oil market can predict negative future output shocks for all
the G7 countries. However, it is not true for inflation shock when it comes to the UK
and Canada. Secondly, the ability to predict both inflation shock and output shock
with consistent results increases as the timescales increase, especially from the
8-month timescale to the 64-month timescale. Moreover, the ability to predict output
shock is stronger than that for inflation shock. In this sense, the ability of systemic
risk to predict output shock is better than that for inflation shock. Thirdly, the
predictive ability of systemic risk in the crude oil commodity market on
macroeconomic shocks may not come from the variations of short-term wavelet
components but from the synchronization of long-term wavelet components. In other
words, systemic risk in the crude oil market has a stable relationship with
macroeconomic shocks in the long term. Specifically, the stable relationship between
systemic risk in the crude oil market and macroeconomic shocks is much stronger for
output shock than inflation shock.3
The remainders of this study are organized as follows. In the next section, we
provide the methodology employed in this paper and discuss our innovations in
details: GARCH-MIDAS, DCC-MIDAS, CoVaR, wavelet transform, and quantile
regressions. In Section 3, we discuss the data we used and specify macroeconomic
shocks. In Section 4, we provide the empirical results and robustness check. In
Section 5, we conclude the paper. In Appendix, we perform a further analysis based
on ΔCoVaR.
3 Our proposed procedure is useful in a wide range of empirical applications, since it can be applied to not only
the crude oil market but also any other financial market of interest. In a separate work in progress, the authors are
analyzing the predictive ability of the systemic risk of agricultural commodity markets on macroeconomic shocks
(see Yang, Motegi, and Hamori, 2018).
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2. Methodology
2.1 Measuring systemic risk in the crude oil markets
2.1.1 GARCH-MIDAS and DCC-MIDAS models for commodity returns
We first specify the marginal distribution of each asset return, taking into account
two major characteristics of asset returns: conditional heteroscedasticity and seasonal
heterogeneity. Engle et al. (2009) and Engle and Rangel (2008) develop a novel class
of models that deal with both of the two characteristics by combining GARCH and
MIDAS models.4
Following the framework of Turhan et al. (2014), we specify a GARCH-MIDAS
model as follows. Let signify each asset. In our empirical study, we
analyze commodity market index, West Texas Intermediate (WTI) crude oil price, and
Brent crude oil price so that 𝑛 = 3. Let 𝜏 = 1, … , 𝑇 signify each month; let 𝑡 =
1, … , 𝑁𝑇 signify each trading day, where we assume that each month has 𝑁 = 21
trading days. Let 𝑟𝑖,𝑡 be the return of asset 𝑖 on day 𝑡. The GARCH–MIDAS model
is specified as follows:
𝑟𝑖,𝑡 = 𝜇𝑖 + √𝑚𝑖,𝜏 ∙ 𝑔𝑖,𝑡𝜉𝑖,𝑡, ∀𝑡 = (𝜏 − 1)𝑁 + 1, … , 𝜏𝑁, ∀𝜏 = 1, … , 𝑇.
(1)
Note that 𝑔𝑖,𝑡 captures daily evolution of the conditional volatility while
captures monthly evolution. We fit a mean-reverting unit-variance GARCH (1,1)
model for the former:
𝑔𝑖,𝑡 = (1 − 𝛼𝑖 − 𝛽𝑖) + 𝛼𝑖(𝑟𝑖,𝑡−1−𝜇𝑖)
2
𝑚𝑖,𝜏+ 𝛽𝑖𝑔𝑖,𝑡−1. (2)
We impose 𝛼𝑖 > 0 , 𝛽𝑖 ≥ 0 , and 𝛼𝑖 + 𝛽𝑖 < 1 in order to ensure 𝑔𝑖,𝑡 > 0 and
E[𝑔𝑖,𝑡2 ] < ∞.
4 See Turhan et al. (2014) for an empirical application of GARCH-MIDAS models.
8
Define a monthly realized variance as the sum of N = 21 daily squared returns:
𝑅𝑉𝑖,𝜏 = ∑ 𝑟𝑖,𝑡2𝜏𝑁
𝑡=(𝜏−1)𝑁+1 . (3)
We assume that 𝑚𝑖,𝜏 is determined by a polynomial of lagged realized variances:
𝑚𝑖,𝜏 = �̅�𝑖 + 𝜃𝑖 ∑ 𝜑𝑙(𝜔𝑣𝑖 )
𝐾𝑣𝑙=1 𝑅𝑉𝑖,𝜏−𝑙, (4)
where we use 𝐾𝑣 = 36 in accordance with Colacito et al. (2011), and we assume that
�̅�𝑖 > 0 and 0 < 𝜃𝑖 < 1. We use the beta polynomial with parameter 𝜔𝑣𝑖 > 1 in
order to capture decaying impacts of {𝑅𝑉𝑖,𝜏−1, … , 𝑅𝑉𝑖,𝜏−𝐾𝑣} on 𝑚𝑖,𝜏:
𝜑𝑙(𝜔𝑣𝑖 ) =
(1−𝑙/𝐾𝑣)𝜔𝑣𝑖 −1
∑ (1−𝑗/𝐾𝑣)𝜔𝑣𝑖 −1𝐾𝑣
𝑗=1
. (5)
The larger (smaller) value of 𝜔𝑣𝑖 implies the faster (slower) decay of 𝜑𝑙(𝜔𝑣
𝑖 ).
For each asset i, we compute maximum likelihood estimators of the parameters
{𝜇𝑖, 𝛼𝑖, 𝛽𝑖, 𝜃𝑖 , 𝜔𝑣𝑖 , �̅�𝑖} based on the univariate Gaussian likelihood function. Using
those estimators, we compute the standardized residual 𝜉𝑖,𝑡 = (𝑟𝑖,𝑡 − 𝜇𝑖)/√𝑚𝑖,𝜏 ∙ 𝑔𝑖,𝑡.
Following Colacito et al. (2011) and Engle and Rangel (2008), we now use a
mixture of DCC and MIDAS models in order to specify the time-varying correlation
between asset returns. We use the standardized residual 𝜉𝑖,𝑡 = (𝑟𝑖,𝑡 − 𝜇𝑖)/√𝑚𝑖,𝜏 ∙ 𝑔𝑖,𝑡
obtained from the GARCH-MIDAS model as an input to the DCC-MIDAS model.
We use a bivariate model of crude oil and commodity market index so that asset i is
understood as crude oil price and asset j is understood as commodity market as a
whole.
Let 𝑄𝑡 = [𝑞𝑖,𝑗,𝑡]𝑖,𝑗
be an 𝑛 × 𝑛 conditional covariance matrix at time 𝑡. The
DCC-MIDAS specification is as follows:
𝑞𝑖,𝑗,𝑡 = �̅�𝑖,𝑗,𝜏(1 − 𝑎𝑖,𝑗 − 𝑏𝑖,𝑗) + 𝑎𝑖,𝑗 × 𝜉𝑖,𝑡−1𝜉𝑗,𝑡−1 + 𝑏𝑖,𝑗 × 𝑞𝑖,𝑗,𝑡−1, (6)
�̅�𝑖,𝑗,𝜏 = ∑ 𝜑𝑙(𝜔𝑐𝑖,𝑗
)𝑐𝑖,𝑗,𝜏−𝑙𝐾𝑐𝑙=1 , (7)
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𝑐𝑖,𝑗,𝜏 =∑ 𝜉𝑖,𝑘
𝜏𝑁𝑘=(𝜏−1)𝑁+1 𝜉𝑗,𝑘
√∑ 𝜉𝑖,𝑘2𝜏𝑁
𝑘=(𝜏−1)𝑁+1 √∑ 𝜉𝑗,𝑘2𝜏𝑁
𝑘=(𝜏−1)𝑁+1
. (8)
We impose that 𝑎𝑖,𝑗 > 0, 𝑏𝑖,𝑗 > 0, and 𝑎𝑖,𝑗 + 𝑏𝑖,𝑗 < 1. The long-term correlation
�̅�𝑖,𝑗,𝜏 is calculated as a weighted sum of 𝐾𝑐 lagged realized correlations. We use
𝐾𝑐 = 144 in accordance with Colacito et al. (2011). The realized correlations are
computed from 𝑁 = 21 non-overlapping standardized residuals. Using (6)–(8), daily
conditional correlations between assets i and j are given by
𝜌𝑖,𝑗,𝑡 =𝑞𝑖,𝑗,𝑡
√𝑞𝑖,𝑖,𝑡√𝑞𝑗,𝑗,𝑡 . (9)
We compute maximum likelihood estimators for the parameters {𝑎𝑖,𝑗 , 𝑏𝑖,𝑗, 𝜔𝑐𝑖,𝑗
}
based on the bivariate Gaussian likelihood function, and obtain estimated conditional
covariance matrix {�̂�𝑡}.
2.1.2 CoVaR
In order to quantify the systemic risk of the commodity markets, we adopt the
CoVaR approach proposed by Adrian and Brunnermeier (2016) and Girardi and
Ergün (2013). First, the Value-at-Risk (VaR) of the crude oil price return 𝑟𝑡𝑖 is
implicitly defined as
Pr(𝑟𝑡𝑖 ≤ 𝑉𝑎𝑅𝛼,𝑡
𝑖 ) = 𝛼,
where α ∈ (0,1) is a given level of tail probability. 𝑉𝑎𝑅𝛼,𝑡𝑖 represents a threshold
that 𝑟𝑡𝑖 exceeds with probability α . It can be computed from the estimated
conditional variance of 𝑟𝑡𝑖 via the GARCH-MIDAS model.
The Conditional Value-at-Risk (CoVaR) of commodity market 𝑟𝑡𝑚𝑎𝑟𝑘𝑒𝑡 given
the crude oil price return, written as 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
, is implicitly defined as
Pr (𝑟𝑡𝑚𝑎𝑟𝑘𝑒𝑡 ≤ 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡
𝑚𝑎𝑟𝑘𝑒𝑡|𝑖 | 𝑟𝑡
𝑖 ≤ 𝑉𝑎𝑅𝛼,𝑡𝑖 ) = 𝛽 (10)
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where 𝛽 ∈ (0,1) is a given level of tail probability. 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
represents,
given 𝑟𝑡𝑖 ≤ 𝑉𝑎𝑅𝛼,𝑡
𝑖 , a threshold that 𝑟𝑡𝑖 exceeds probability 𝛽 . Given Eq. (10),
𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
takes negative values almost by construction. The larger (smaller)
absolute value of 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
implies that, given that the crude oil price return is
taking an extreme value at the lower tail, we expect the commodity market to take a
larger (smaller) negative value. 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
can therefore be interpreted as a risk
measure of commodity market. In particular, we set 𝛼 = 5% as well as 𝛽 = 5% in
this paper. 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
can be computed from the estimated conditional
correlation between crude oil price 𝑖 and the commodity market via the
DCC-MIDAS model (Reboredo and Ugolini, 2015; Adrian and Brunnermeier, 2016).
As a well-accepted convention, we take the absolute value |𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
| in order
to make discussions simpler. Actually, the absolute value form of systemic risk makes
us understand the changes in risk clearly. The higher the value of 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑖 is, the
higher the systemic risk in the crude oil market. In the following studies, the
coefficients of quantile regression can be also interpreted clearly.5 Therefore, by
employing GARCH-based estimator, we can perform more accurate forecast at the
tails when the extreme condition occurs. In other words, the quantile regression
applied in the following manner seems to be our best choice to investigate how
systemic risk is able to predict macroeconomic shocks accordingly. And in the next
section, we provide the methodology of time-domain approach comprising wavelet
transform to better understand the issue.
2.2 Wavelet analysis of systemic risk and macroeconomic indicators
5 The negative value of coefficients indicates the recession forecast while the positive value of coefficients
indicates the boom forecast. In addition, only the sign of coefficients changes if we employ original
𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
.
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In order to examine changes in the ability to predict within the different
timescales, we employ discrete wavelet transform (DWT) to decompose the variables
in accordance with the timescales. With a multi-resolution decomposition, the
decomposed signals can be described as follows:
, (11)
. (12)
The functions and denote the smooth and detail signals, respectively.
They decompose a signal into orthogonal components at different timescales. A signal
(raw data), , can be rewritten as
. (13)
The highest-level approximation, , is the smooth signal, while the detail signals
, , …, and are associated with oscillations of lengths 2 months, 4
months, …, and 2𝑗 months in this paper . In particular, we consider Maximal
Overlap Discrete Wavelet Transform6 (MODWT) as an alternative because the
sensitivity of wavelet and scaling coefficients to circular shifts means that the
coefficients are not shift-invariant. Moreover, in contrast to the limitations of
orthogonal DWT, MODWT does not require a dyadic length requirement (i.e., a
sample size divisible by 2𝐽). Thus, in order to solve the problem of sample sizes that
are multiples of 2, we employ MODWT to address any sample size without
introducing phase shifts, which would change the location of events over time.
Specifically, assume ℎ𝑙 = (ℎ1,0, … , ℎ1,𝐿−1, … ,0, … ,0)𝑇 represents the wavelet
filter coefficients for unit scales, zero-padded to length N. Three conditions must be
satisfied by a wavelet filter: ∑ ℎ1,𝑙 = 0𝐿−1𝑙=0 ; ∑ ℎ1,𝑙
2 = 1𝐿−1𝑙=0 ; ∑ ℎ1,𝑙ℎ1,𝑙+2𝑛 = 0𝐿−1
𝑙=0 for
all non-zero integers n. Meanwhile, suppose 𝑔𝑙 = (𝑔1,0, … , 𝑔1,𝐿−1, … ,0, … ,0)𝑇 to be
6 See Yang and Hamori (2015) for more details on MODWT.
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the zero-padded scaling filter coefficients with the integration function of 𝑔1,𝑙 =
(−1)𝑙+1ℎ1,𝐿−1−𝑙. When any sample size N is divisible by 2𝑗, wavelet coefficients,
�̃�𝑗,𝑡 and scaling coefficients �̃�𝑗,𝑡 at levels j∈ 1, … , 𝐽 can be defined as: �̃�𝑗,𝑡 =
∑ �̃�𝑙�̃�𝑗−1,𝑡−1 𝑚𝑜𝑑𝑁𝐿−1𝑙=0 and �̃�𝑗,𝑡 = ∑ ℎ̃𝑙�̃�𝑗−1,𝑡−1 𝑚𝑜𝑑𝑁
𝐿−1𝑙=0 where wavelet �̃�𝑙 is
rescaled as �̃�𝑗 = 𝑔𝑗/2𝑗/2, and scaling filters is rescaled as ℎ̃𝑗 = ℎ𝑗/2𝑗/2.
Further, without changing the pattern of wavelet transform coefficients, the
translation invariant is enabled in MODWT as a shift in the signal. Finally, we obtain
the details of components in the different timescales using MODWT.7
2.3 Quantile regressions on systemic risk and macroeconomic indicators
Following the study of Giglio et al. (2016), we employ quantile regression (QR)
as an effective tool to investigate the potentially nonlinear dynamics between
systemic risk and macroeconomic shocks. As suggested by Giglio et al. (2016),
QR-based methodology can provide robust results for forecasting economic outcomes.
As discussed by Hansen (2013), even though QR is unable to detect a specific
mechanism of transference between systemic risk and a future economic outcome, it
is still relatively accurate at predicting information about the future economy.
In this section, we briefly discuss QR methodology before presenting our
empirical results. Since its introduction by Koenker and Bassett (1978), QR has been
widely employed to estimate coefficient differences across quantiles. Compared with
traditional regressions, QR provides a more accurate landscape for analyzing the
effect of conditional variables on a dependent variable (Koenker, 2005), taking into
account the quantiles of the dependent variable's conditional distribution. QR not only
measures the degree of the average or linear dependence between variables. It also
measures the degree of both lower and lower-tail dependence (Baur, 2013; Chuang et
7 In order to save space, the details of the components are available upon request. See Yang et al. (2018) for more
details on the wavelet-based quantile regression approach.
13
al., 2009; Lee and Li, 2012). Thus, QR enables us to estimate the differences of the
dynamic coefficients between systemic risk and economic outcomes across quantiles.
Let denote the macroeconomic shocks whose conditional quantiles we wish to
forecast by using systemic risk. The th conditional quantile function of is the
inverse probability distribution function thus specified as follows:
. (14)
Specifically, the conditional quantiles of are affine functions of the observables
. Thus:
. (15)
In particular, may differ across the quantiles that provide the overall
landscape of target distribution when conditioning information disrupts the
distribution’s location. As suggested in equation (15), it is important for policymakers
and regulators to make economic forecasts because the leading indicators are more
suitable than contemporaneous regression.
3. Data and preliminary analysis
In this section, we describe our data and perform some preliminary analysis. See
Section 3.1 for daily commodity prices. See Section 3.2 for monthly macroeconomic
indicators.
3.1 Daily commodity prices
In Figure 1 we draw time series plots of daily spot prices and log returns of
commodity market index, WTI crude oil spot price and Brent crude oil spot price
from January 1, 1991 through December 29, 2017 (7,044 days). We use Standard and
Poor's Goldman Sachs Commodity Index (S&P GSCI) Commodity Total Return
14
Indexes as a proxy of commodity market. Since the crude oil price is traded
worldwide, we can analyze the systemic risk in the crude oil market in a global view
through an international commodity index. The S&P GSCI Commodity Total Return
Indexes, hereby, meet our criteria. All data are in terms of US dollars, and retrieved
from Datastream. In view of Figure 1, it is evident that the price of each commodity
was substantially affected by the subprime mortgage crisis around 2008. The crude oil
price experienced extremely large price declines in the crisis period for both WTI and
Brent. In terms of log return, each asset exhibits conditional heteroscedasticity as
expected. The WTI crude oil price returns seem to have the largest volatility; the
Brent comes next; the market index seems to have the smallest volatility.
[Insert Figure 1.]
In Table 1, we report sample statistics of the log return of each commodity.
Standard deviation is 7.216 for commodity market, 16.414 for WTI crude oil price,
and 15.993 for Brent crude oil price. Skewness is negative for all commodities,
suggesting that extreme negative returns are more likely to occur than extreme
positive returns. Kurtosis is as large as 11.693 for commodity market, 19.931 for WTI
crude oil price, and 15.413 for Brent crude oil price. The negative skewness and large
kurtosis are stylized facts of asset returns. Due to those characteristics, the
unconditional distribution of each commodity return is far from Gaussian, which is
confirmed from the very small p-values of the Jarque-Bera test.
[Insert Table 1.]
3.2 Monthly macroeconomic indicators
We are interested in the relationship between systemic risk and macroeconomic
indicators. As proxies of macroeconomic indicators, we use inflation, output, and their
shocks defined as residuals from univariate AR(p) models (cf. Bai and Ng, 2006;
15
Giglio et al., 2016; Stock and Watson, 2012). For inflation, we use the annual growth
rate of the consumer price index. For output, we use the annual growth rate of
industrial production. For each series, we use monthly data from January 1998
through December 2016, spanning 240 months. To achieve the best results, we
employ data on G7 countries to investigate the issue. The macroeconomic shocks are
selected based on the Akaike Information Criterion (AIC). Specifically, optimal lag
lengths are 𝑝 = 3 for inflation and 𝑝 = 5 for output in Germany; 𝑝 = 3 for
inflation and 𝑝 = 4 for output in Canada; 𝑝 = 4 for inflation and 𝑝 = 5 for output
in France; 𝑝 = 4 for inflation and 𝑝 = 5 for output in Italy; 𝑝 = 5 for inflation
and 𝑝 = 6 for output in Japan; 𝑝 = 3 for inflation and 𝑝 = 3 for output in UK;
and 𝑝 = 3 for inflation and 𝑝 = 6 for output in the United States. For each series
we use monthly data from January 2003 through December 2016, spanning 180
months to match the sample of systemic risk measures. All data are retrieved from
Datastream.
See Figures 2-8 for time series plots of the macroeconomic indicators. Inflation
and output declined substantially in 2008–2009, reflecting the large negative impact
of the subprime mortgage crisis on the world economy. Both inflation and output have
high persistence, a well-known characteristic of macroeconomic time series. The AR
residual series, in contrast, have sufficiently small persistence throughout the sample
period.
[Insert Figure 2.]
See Tables 2-3 for sample statistics of the macroeconomic indicators. Inflation
and output have relatively large standard deviations, but their shocks have much
smaller standard deviations as expected. For the G7 group, the United States shows
the highest standard deviation of inflation rate (shock) and Japan shows the highest
16
standard deviation of industry production growth rate (shock). In contrast, the lowest
standard deviation of inflation rate (shock) was observed in Germany and for industry
production growth rate (shock), it was in the UK. According to the Jarque-Bera test,
the distribution of each series is most likely non-Gaussian.
[Insert Tables 2-3.]
4. Empirical analysis
4.1 Estimated systemic risk in the crude oil markets
We first report results of the GARCH-MIDAS models. See Table 4 for estimates
of {𝜇𝑖, 𝛼𝑖 , 𝛽𝑖, 𝜃𝑖 , 𝜔𝑣𝑖 , �̅�𝑖} and their standard errors. For each commodity, all estimates
except for 𝜇𝑖 are highly significant. The point estimate of the beta polynomial
parameter, 𝜔𝑣𝑖 , is 8.106 for commodity market, 1.106 for WTI crude oil price, and
16.471 for Brent crude oil price. Those results suggest that relatively steep weighting
schemes are chosen for commodity market and Brent crude oil price while nearly flat
weighting schemes are chosen for WTI crude oil price.
[Insert Table 4.]
We next report results of the bivariate DCC-MIDAS models of commodity
market and crude oil price. See Table 5 for estimates of {𝑎𝑖,𝑗 , 𝑏𝑖,𝑗, 𝜔𝑐𝑖,𝑗
} and their
standard errors. All estimates are highly significant for each pair. The point estimates
of 𝜔𝑐𝑖,𝑗
are 2.531 for WTI crude oil price and 30.226 for Brent oil price. Those results
suggest that each pair exhibits relatively fast decaying patterns in conditional
correlations.
[Insert Table 5.]
Using the results of GARCH-MIDAS and DCC-MIDAS, we now compute
CoVaR as a measure of systemic risk. In Figure 9, we draw time series plots of the
17
monthly 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
with α =0.05 and β = 0.05 for both WTI crude oil price
and Brent crude oil price.8 We plot the dynamics of systemic risk in Figure 9.
[Insert Figure 9 Here]
Systemic risk in the crude oil market is quite similar between WTI crude oil and
Brent crude oil, reflecting the similar conditional correlation between commodity
market and crude oil. For both WTI and Brent crude oil, systemic risk soars
dramatically to 20% or even 22% during the subprime mortgage crisis. The level of
systemic risk is only around 4% during the European debt crisis in 2012, suggesting
that the subprime mortgage crisis brought much greater uncertainty to the commodity
markets than the European debt crisis.
4.2 Systemic risk versus inflation and production
Since the lead-lag correlations only show us the possible cause and effect
relationship between system risk in crude oil market and macroeconomic shocks, it is
of great interest to investigate the predictive ability of systemic risk on
macroeconomic shocks during bad or extreme market conditions. Therefore,
employing the quantile regression allows us to further explore the ability of systemic
risk to forecast macroeconomic shocks. In this paper, we focus attention on the 20th
percentile, , in order to capture bad or extreme market conditions. Moreover,
we employ the median regression, , as the benchmark to study the impacts of
systemic risk on the central tendency of macroeconomic shocks or tranquil market
conditions. Meanwhile, we consider the 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼 (-1) as the main
benchmark for our analysis while other systemic risk measures are treated as
robustness check.
We provide our estimation results in Table 6, which present several instances of
8 Daily CoVaR is omitted since they are basically similar to the monthly CoVaR.
18
solid evidence of the relationship between systemic risk and macroeconomic
lower-tail risk. Based on Table 6, we find that only Canada and the UK show little
evidence on this issue. Beyond that, we detect that the systemic risks in the crude oil
market have a strong ability to predict inflation shock for the 20th percentile while
there is little evidence of the ability to predict the inflation shock in the tranquil
market conditions. The only exception is Japan which also shows high predictive
ability of systemic risk on inflation shock on the tranquil market conditions.
As shown in Table 6, systemic risk shows strong ability to forecast the output
shocks in G7 countries without exceptions. Even though the significant level may
differ, we can confirm this issue at the 10% significant level. Moreover, both Canada
and France show that systemic risk can predict output shocks on tranquil market
conditions. For the raw data or one-month period, we find that systemic risk has better
predictability on output shock than inflation shock. The findings are consistent with
the studies of Kilian (2014), who states the rise in crude oil price may make output
fluctuate more easily. Table 6 also reports t-statistics to test the hypothesis that the
20th percentile and median regression coefficients are equal.9 If the difference in
coefficients (the 20th percentile minus the median) is negative, the variable predicts a
downward shift in the lower tail relative to the median. Similarly, our estimation
results of individual systemic risk support the conclusion that the predictors of
downside risk are more accurate than those of central tendency in most cases.
However, the consistency of the ability to predict is justified. In sum, we find that an
increase in systemic risk will cause negative macroeconomic shocks or worse
economic outcomes (recession). The results are similar to the results of Giglio et al.
(2016).
9 The t -statistics for differences in coefficients are calculated with a residual block bootstrap using block lengths
of four months and 5,000 replications.
19
[Insert Table 6.]
4.3 Systemic risk versus inflation and production: short-term versus long-term
To understand how the predictability changes across the timescales, we run the
quantile regression based on the wavelet components. In Tables 7-12, we summarize
the estimations based on the same approach shown in Table 6. During the short-term
scale (D1, D2), we find that most cases show a significant ability to predict the
inflation shock for the 20th percentile during the two-month period with positive
value like for France in D1 and for the UK in D2. However, we do not detect any
predictability information on output shocks. Based on the above discussion, we argue
that the short-term wavelet component hardly explains the predictability between
systemic risk and output shocks while the short-term wavelet component can predict
the inflation shock positively. In other words, the short-term systemic risk in the crude
oil market will increase the inflation rate. It also provides an explanation why
systemic risk in the crude oil market can predict inflation shock negatively (deflation).
Although the short-term components of systemic risk in the crude oil market will
increase the inflation rate, the mid- and long-term components of systemic risk in the
crude oil market will decrease inflation rate more which, in turn, makes sense of our
empirical results based on raw data. The reason behind that is the medium-run
overshoot of the economy (Bloom, 2009).
[Insert Tables 7-12]
As the time period increases (from D3 to D6), we find that the systemic risk in
the crude oil market can predict the negative output shocks consistently even though
there are differences for the countries, timescales, and market condition. In contrast,
there are still no consistent results for the ability of systemic risk to predict inflation
shocks. For example, we did not observe the ability of systemic risk to predict
20
inflation shocks in D3, in which no significant results are estimated. The only
exception is Japan which show positive predictive ability of systemic risk in the crude
oil market. However, the significant negative coefficients continue to apply from D4
to D6, regardless of the timescale and country. It makes sense that a greater systemic
risk in the crude oil market causes a greater negative output shock. In other words, the
ability of systemic risk, i, at the 20th percentile to predict a macroeconomic downturn
is justified in most cases. Moreover, we find that the predictive ability of systemic risk
in the median show greatest significance for all the countries in the long-term scales.
Overall, we find that systemic risk has better predictability on output shock than
inflation shock. It is a little contrast to the study of Kara (2017) who states that the
commodity price contains information in predicting inflation shocks. Even though the
systemic risk in the crude oil price can predict inflation shocks to a certain degree, it
predicts the output shocks better. In other words, crude oil behaves like an industrial
good rather than a consumer good. In sum, we find that existing predictive ability of
systemic risk in the crude oil market comes from the mid- and long-term wavelet
components, which indicate the stable predictability relationship between crude oil
and macroeconomic shocks. As to the final macroeconomic outcome from the
systemic risk in the crude oil market, we find our research follows the observation of
the majority of literatures that the negative relationship is justified. That is, the higher
the systemic risk, the worse the economic outcomes, especially for the mid- and long-
term.
However, with regard to the coefficient equability test, we conclude that the
predictors of downside risk are more accurate than during the central tendency in the
mid-term and long-term timescales. In other words, in the mid-term and long-term
timescales, our conclusion supports the strong relationship between the financial
21
stress in the commodity market and output shock. However, it is true for inflation
shock only in the long-term timescales. Further, rather than a simple downward
movement in distribution, there is still the probability of a large negative shock to the
real economy. However, in the long term, the median may become a good indicator
for forecasting a negative shock to the real economy. In other words, we should focus
more on the systemic risk level in the long term, which is closely related to
macroeconomic shocks.
4.4 Robustness checks
In this study, we provide three ways to robustness check our results.10 First, we
employ Brent crude oil price as the replacement for WTI crude oil price to measure
systemic risk in the crude oil market. Generally speaking, we identify the same
significant level with WTI crude oil price and there is no significant difference on the
wavelet components estimations. Therefore, Brent crude oil price as a proxy provides
the exact same results across timescales for our study.
Second, we employ principal component analysis to construct the systemic risk
index in the crude oil market: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼 and 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇 as well
as macroeconomic shocks in G7 countries as a whole. Since the systemic risk
measures are calculated in the same way, we can combine them by employing
principal component analysis. In addition, since G7 countries are the most developed
countries in the world and have most similar economic conditions, we can extract the
principle components from their inflation shocks or output shocks. By estimating the
quantile regression again, we still obtain the similar results as the individual measures
provided. The results are reported in Table 13. In this sense, our results are robust.
[Insert Table 1]
10 Analysis using ΔCoVaR is reported in Appendix.
22
5. Conclusion
We extend the framework of Giglio et al. (2016) by employing both MIDAS and
the wavelet approach. Our objective is to investigate the ability of systemic risk in the
crude oil market to predict macroeconomic shocks. By employing the
GARCH-MIDAS and DCC-MIDAS techniques, we obtain the monthly CoVaR by
using daily frequency data to match the macroeconomic data that is usually monthly
based. This approach enables us to drive the monthly CoVaR without losing too much
high-frequency data. Further, by employing the wavelet approach, we can capture the
whole landscape of the ability of systemic risk in the crude oil market to make
predictions across different timescales; namely, from the short term to the long term.
We present three new stylized facts. First, in contrast to central tendency,
systemic risk in the crude oil market has an especially strong negative relationship
with future macroeconomic shocks for the one-month period. Second, the ability to
predict both inflation shock and output shock increases as the timescales increase with
consistent results, especially from the 8-month timescale to the 64-month timescale.
However, the ability to predict output shock is stronger than that for inflation shock.
In this sense, the ability to predict output shock is better than that for inflation shock.
Third, the predictive ability of systemic risk in the crude oil market on
macroeconomic shocks may not come from the variations of short-term wavelet
components but from the synchronization of long-term wavelet components. In other
words, systemic risk in the crude oil market has a stable relationship with
macroeconomic shocks in the long-term. Specifically, the stable relationship between
systemic risk in the crude oil commodity market and macroeconomic shocks is much
stronger for inflation shock than output shock.
These empirical findings can potentially serve as guidelines for investors and
23
policy makers. From the policy maker view, the systemic risk in the crude oil
commodity market does contain the information of future inflation, which will
provide a useful tool for central banks to keep inflation under control. Even though
the systemic risk in the crude oil commodity market shows lower predictability
information on inflation shock, there is still an incentive to take a further step to
understand the relationship between crude oil and inflation. Moreover, since crude oil
is a main input for the industry, the systemic risk in the crude oil market should be
paid attention to as it concerns more in affecting the output gap as well as the industry.
From the investors’ perspective, systemic risk in the crude oil market should be
monitored as it also has significance on the economy as well as on the financial
market. How to manage the specific risk for investors will be the next question in
future researches.
Declaration of interest
The authors declare no conflicts of interest. The research of the first author was
supported by a grant-in-aid from the National Natural Science Funds for Young
Scholar of China (Grant No. 71601185).
Appendix
A1. Specifications of ∆CoVaR
We consider ∆𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
by standardizing 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
relative to a
benchmark condition where 𝑟𝑡𝑖 is equal to or less than its conditional median. The
median 𝐶𝑜𝑉𝑎𝑅0.5,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
is defined by,
Pr (𝑟𝑡𝑚𝑎𝑟𝑘𝑒𝑡 ≤ 𝐶𝑜𝑉𝑎𝑅0.5,𝛽,𝑡
𝑚𝑎𝑟𝑘𝑒𝑡|𝑖 | 𝑟𝑡
𝑖 ≤ 𝑉𝑎𝑅0.5,𝑡𝑖 ) = 𝛽 (1a)
24
and thus, ∆𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
is defined as follows:
∆𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
= 𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
− 𝐶𝑜𝑉𝑎𝑅0.5,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
(2a)
∆𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
is called the delta CoVaR (△CoVaR), and can be used as an
alternative measure for the systemic risk of commodity market conditional on the
crude oil price. In order to gauge the size of the potential tail spillover effects,
equation (2a) is estimated based the contemporaneous correlation with extreme
market conditions through the GARCH-MIDAS model as an input to the
DCC-MIDAS model. In other words, the marginal contribution of crude oil price to
overall systemic risk with time-varying nature can be captured effectively by such a
specification. Therefore, we can match systemic risk measures with the
macroeconomic data.
Following the study of Adrian and Brunnermeier (2016), we outline a Gaussian
framework under a bivariate diagonal GARCH model where ∆ CoVaR has a
closed-form expression and assume that crude oil price and market returns follow a
bivariate normal distribution:
(𝑟𝑡𝑖, 𝑟𝑡
𝑚𝑎𝑟𝑘𝑒𝑡)~𝑁 (0, ((𝜎𝑡
𝑖)2 𝜌𝑡𝜎𝑡𝑖𝜎𝑡
𝑚𝑎𝑟𝑘𝑒𝑡
𝜌𝑡𝜎𝑡𝑖𝜎𝑡
𝑚𝑎𝑟𝑘𝑒𝑡 (𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡)2
)) (3a)
According to the properties of the multivariate normal distribution, the distribution of
market return conditional on the crude oil return can be expressed as:
𝑟𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑟𝑡
𝑖~𝑁 (𝑟𝑡
𝑖𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡𝜌𝑡
𝜎𝑡𝑖 , (1 − 𝜌𝑡
2)(𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡)2) (4a)
Hereby, we can rewrite equation (10) to be:
Pr [𝑟𝑡
𝑚𝑎𝑟𝑘𝑒𝑡−𝑟𝑡
𝑖 𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡𝜌𝑡
𝜎𝑡𝑖
𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡√1−𝜌𝑡
2≤
𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
−𝑟𝑡
𝑖 𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡𝜌𝑡
𝜎𝑡𝑖
𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡√1−𝜌𝑡
2|𝑟𝑡
𝑖 ≤ 𝑉𝑎𝑅𝛼,𝑡𝑖 ] = 𝛽, (5a)
25
where 𝑟𝑡
𝑚𝑎𝑟𝑘𝑒𝑡−𝑟𝑡
𝑖 𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡𝜌𝑡
𝜎𝑡𝑖
𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡√1−𝜌𝑡
2~𝑁(0, 1). Particularly, the crude oil VaR is given by
𝑉𝑎𝑅𝛼,𝑡𝑖 = Φ−1(𝛼) 𝜎𝑡
𝑖. Combining that, then we have
𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
= Φ−1(β)𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡√1 − 𝜌𝑡
2 − Φ−1(𝛼)𝜌𝑡𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡. (6a)
Because Φ−1(50%) = 0, equation (2a) can be solved for
∆𝐶𝑜𝑉𝑎𝑅𝛼,𝛽,𝑡𝑚𝑎𝑟𝑘𝑒𝑡|𝑖
= Φ−1(𝛼)𝜌𝑡𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡. (7a)
As suggested by Adrian and Brunnermeier (2016), GARCH-based estimator
captures tail risk a bit more strongly.
A2. Quantile Regression using CoVaR
In this appendix, we employ CoVaR as an alternative measure to estimate the
systemic risk in the crude oil market as well as run quantile regression. Table 1a
indicates the results for raw data, and Tables 2a-7a indicate the results for wavelet
transformation. In most cases, there is no difference in significance between the
results based on CoVaR and CoVaR. Thus, our empirical findings are robust to
different measures.
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Table 1. Sample statistics of the daily log returns of commodity market and crude oil.
Market WTI Brent
Mean× 10−3 0.654 1.069 1.287
Std. Dev. 7.216 16.414 15.993
Skewness −0.574 −0.820 −0.529
Kurtosis 11.693 19.931 15.413
Prob(JB) 0.000 0.000 0.000
# Observations 7044 7044 7044
Notes: Prob(JB) means a p-value of the Jarque-Bera test for normality. The sample period is from
January 1, 1991 to December 29,2017.
Table 2. Sample statistics of monthly macroeconomic indicators.
Notes: Prob(JB) means a p-value of the Jarque-Bera test for normality. The sample period is from
January, 1998 to December,2017.
Canada France German Italy Japan UK US
Inflation rates
Mean 1.855 1.335 1.374 1.816 0.051 1.972 2.147
Std. Dev. 0.895 0.844 0.742 1.022 1.028 1.122 1.252
Skewness 0.163 −0.045 0.064 −0.427 1.165 0.588 −0.284
Kurtosis 3.774 2.535 2.918 2.505 5.365 3.111 3.693
Prob(JB) 0.029 0.327 0.891 0.007 0.000 0.001 0.018
# Observations 240 240 240 240 240 240 240
Industry production growth rates
Mean 0.967 0.252 1.554 −0.697 −0.260 −0.299 1.116
Std. Dev. 0.0456 0.043 0.056 0.061 0.089 0.029 0.0435
Skewness −1.299 −2.173 −1.988 −2.249 −1.605 −1.756 −2.048
Kurtosis 5.497 9.974 9.587 10.300 8.805 7.391 8.121
Prob(JB) 0.000 0.000 0.000 0.000 0.000 0.000 0.000
# Observations 240 240 240 240 240 240 240
31
Table 3. Sample statistics of monthly macroeconomic shocks.
Notes: Prob(JB) means a p-value of the Jarque-Bera test for normality. The sample period is from
January, 1998 to December, 2017.
Table 4. Results of GARCH–MIDAS Models for each commodity
Market WTI Brent
μ × 10−2 1.634(1.336) 0.037 (1.838) 3.246 (2.018)
Α 0.049 (0.004)*** 0.060 (0.003)*** 0.056 (0.005)***
β 0.917 (0.013)*** 0.929 (0.004)*** 0.878 (0.018)***
θ 0.199 (0.007)*** 0.156 (0.021)*** 0.208 (0.005)***
𝜔𝑣 8.106 (2.404)*** 1.106 (0.367)*** 16.471 (2.722)***
�̅� 0.539 (0.063)*** 1.839 (0.191)*** 0.641 (0.077)***
Notes: The number of monthly lags for the MIDAS polynomial is 𝐾𝑣 = 36, which deletes the first
36 × 21 = 756 daily observations. The effective sample size is therefore 6288, covering November
23, 1985 through December 29, 2017. Figures in the parentheses are standard errors. *** indicates
significance at the 1% level.
Canada France German Italy Japan UK US
Inflation rates
Mean −0.021 −0.004 0.004 −.009 0.012 0.004 −0.021
Std. Dev. 0.415 0.238 0.285 0.222 0.329 0.276 0.418
Skewness 0.0176 −0.054 −0.252 −0.414 0.387 0.065 −0.581
Kurtosis 3.354 3.675 3.479 3.259 8.732 3.246 5.890
Prob(JB) 0.623 0.174 0.163 0.059 0.000 0.748 0.000
# Observations 180 180 180 180 180 180 180
Industry production growth rates
Mean −0.037 −0.036 0.022 −0.032 0.035 0.0004 −0.022
Std. Dev. 1.442 2.014 1.928 2.199 3.111 1.424 0.896
Skewness 0.244 −0.247 −0.294 −0.285 −0.277 0.069 −0.383
Kurtosis 3.909 2.855 4.796 3.662 12.506 4.464 7.299
Prob(JB) 0.018 0.371 0.000 0.057 0.000 0.000 0.000
# Observations 180 180 180 180 180 180 180
32
Table 5. Results of Bivariate DCC–MIDAS Models for commodity market and crude oil.
WTI Brent
A 0.091 (0.005)*** 0.064 (0.008) ***
b 0.850 (0.010)*** 0.473 (0.089) ***
𝜔𝑐 2.531 (0.193)*** 30.226 (5.370)***
Notes: The number of monthly lags for the MIDAS polynomial is 𝐾𝑐 = 144, which deletes the first
144 × 21 = 3024 daily observations. The effective sample size is therefore 4020, covering August 5,
2002 through December 29, 2017. Figures in the parentheses are standard errors. *** indicates
significance at the 1% level. ** indicates significance at the 5% level.
33
Table 6. Individual systemic risks and inflation (output) shocks
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼 (-1)
Canada −0.020 −0.018 0.002
France −0.008 −0.016*** −0.008
German −0.007 −0.026*** −0.018**
Italy −0.001 −0.011*** −0.010
Japan −0.018*** −0.018* 0.000
UK 0.005 −0.008 −0.014
US −0.008 −0.025** −0.016
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada −0.095*** −0.044* 0.051**
France −0.150** −0.121*** 0.029
German −0.095 −0.152** −0.057
Italy −0.075 −0.180*** −0.105
Japan −0.071 −0.403*** −0.332***
UK −0.043 −0.099 −0.056
US −0.031 −0.046** −0.018
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇 (-1)
Canada −0.021 −0.018 0.003
France −0.009 −0.017* −0.008
German −0.007 −0.027*** −0.020***
Italy −0.001 −0.012* −0.011
Japan −0.019** −0.017* −0.002
UK 0.005 −0.009 −0.014
US −0.009 −0.026* −0.017
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇 (-1)
Canada −0.100*** −0.048* 0.052
France −0.161** −0.130*** 0.031
German −0.101 −0.141*** −0.040***
Italy −0.079 −0.192*** −0.113
Japan −0.074 −0.426*** −0.352***
UK −0.046 −0.106 −0.060
US −0.032 −0.052** −0.020
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression.
34
Table 7 Individual systemic risks and inflation (output) shocks for wavelet transform D1
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada −0.012 0.023 0.034
France 0.085** 0.124*** 0.039
German 0.050 −0.011 −0.062
Italy −0.009 −0.071 −0.062
Japan −0.011 −0.116 −0.105
UK 0.014 −0.033 −0.047
US 0.280*** 0.081 −0.199
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼 (-1)
Canada 0.023 0.080 0.057
France 0.300 0.201 −0.009
German 0.138 0.477 0.339
Italy −0.248 0.174 0.422
Japan −0.118 −0.404 −0.286
UK −0.536 0.270 0.806*
US −0.007 −0.067 −0.060
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇 (-1)
Canada −0.012 0.024 0.036
France 0.090** 0.133*** 0.043
German 0.053 −0.010 −0.063
Italy −0.009 −0.083 −0.074
Japan −0.011 −0.145* −0.134*
UK 0.014 −0.035 −0.048
US 0.297*** 0.188 −0.109
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇 (-1)
Canada −0.012 0.024 0.036
France 0.090 0.134 0.043
German 0.053 −0.010 −0.063
Italy −0.009 −0.083 −0.074
Japan −0.011 −0.145 −0.134*
UK 0.014 −0.035 −0.048
US 0.297 0.189 −0.109
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D1 denotes 2-month scale.
35
Table 8 Individual systemic risks and inflation (output) shocks for wavelet transform D2
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada 0.096** 0.110*** 0.013
France 0.081*** 0.018 −0.063***
German 0.070*** 0.087** 0.018
Italy 0.027 0.026 −0.001
Japan 0.002 −0.010 −0.012
UK 0.047* 0.071** 0.024
US 0.160*** 0.113*** −0.048*
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada −0.061 −0.008 0.053
France −0.236 0.179 0.415
German −0.133 0.034 0.166
Italy −0.926*** −0.919*** 0.007
Japan −0.497 −0.548 −0.050
UK 0.047 0.144 0.097
US −0.158*** −0.123*** 0.036
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(-1)
Canada 0.104** 0.117*** 0.013
France 0.087*** 0.019 −0.067***
German 0.075*** 0.093** 0.018
Italy 0.029 0.029 −0.0003
Japan 0.002 −0.017 −0.019
UK 0.045* 0.076** 0.030
US 0.175*** 0.121*** −0.053
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(-1)
Canada −0.065 −0.008 0.057
France −0.250 0.190 0.440*
German −0.142 0.036 0.178
Italy −0.794*** −0.983*** −0.189
Japan −0.524 −0.562 −0.037
UK 0.050 0.149 0.099
US −0.223*** −0.132*** 0.091
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D2 denotes 4-month scale.
36
Table 9 Individual systemic risks and inflation (output) shocks for wavelet transform D3
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada 0.002 −0.002 −0.004
France 0.003* 0.002 −0.001
German −0.002 −0.003 −0.001
Italy −8.34E−05 −0.0009 −0.0009
Japan 0.0004 0.003*** 0.002**
UK 0.002 0.002 −3.15E−05
US 0.0007 −0.0006 −0.001
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.070* −0.158*** −0.088*
France −0.272*** −0.131** 0.141**
German −0.065 −0.144 −0.079
Italy −0.116 −0.208*** −0.092
Japan 0.039 −0.088 −0.127
UK 0.043 −0.033 −0.075
US 0.011 −0.060 −0.071
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada 0.002 −0.002 −0.004
France 0.003 0.002 −0.001
German −0.002 −0.003 −0.001
Italy 0.000 −0.001 −0.001
Japan 0.000 0.003*** −0.003**
UK 0.002 0.002 1.80E−05
US 0.001 −0.001 −0.002
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
German −0.069 −0.153 −0.084
Canada −0.075* −0.154*** −0.079
France −0.289*** −0.128* 0.161**
Italy −0.119 −0.223*** −0.104
Japan 0.040 −0.093 −0.134
UK 0.041 −0.035 −0.075
US 0.011 −0.061 −0.072
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D3 denotes 8-month scale.
37
Table 10 Individual systemic risk and inflation (output) shocks for wavelet transform D4
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.048*** −0.053*** −0.005
France −0.013* −0.020*** −0.007
German −0.023*** −0.026*** −0.003
Italy −0.008 −0.015*** −0.007
Japan −0.036*** −0.036*** 0.0006
UK −0.033*** −0.040*** −0.007
US −0.038*** −0.049*** −0.011
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼 (−1)
Canada −0.134*** −0.110*** 0.024
France −0.155*** −0.145*** 0.010
German −0.136*** −0.118*** 0.018
Italy −0.100*** −0.137*** −0.037
Japan −0.128** −0.181*** −0.053
UK −0.120*** −0.151*** −0.031
US 0.020 0.017 −0.004
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.051*** −0.055*** −0.004
France −0.014* −0.021*** −0.007
German −0.023*** −0.027*** −0.004
Italy −0.008 −0.015*** −0.007
Japan −0.038*** −0.038*** −0.0007
UK −0.031*** −0.042*** −0.011
US −0.039*** −0.051*** −0.012
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.139*** −0.115*** 0.024
France −0.157*** −0.151*** 0.006
German −0.143*** −0.120*** 0.023
Italy −0.100 −0.143*** −0.043
Japan −0.126* −0.189*** −0.063
UK −0.126*** −0.146*** −0.020
US 0.022 0.021 −0.001
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D4 denotes 16-month scale.
38
Table 11 Individual systemic risks and inflation (output) shocks for wavelet transform D5
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.033*** −0.040*** −0.007**
France −0.019*** −0.018*** 0.001
German −0.026*** −0.027*** −0.001
Italy −0.016*** −0.015*** 0.001
Japan −0.021*** −0.026*** −0.005***
UK −0.012*** −0.018*** −0.006***
US −0.031*** −0.027*** 0.004**
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.060*** −0.050*** 0.010
France −0.068*** −0.113*** −0.045**
German −0.091*** −0.125*** −0.034*
Italy −0.047* −0.084*** −0.037
Japan −0.153*** −0.164*** −0.011
UK −0.057*** −0.066*** −0.009
US −0.008 −0.006 0.002
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.035*** −0.044*** −0.009***
France −0.020*** −0.019*** 0.001
German −0.028*** −0.029*** −0.001
Italy −0.017*** −0.016*** 0.001
Japan −0.023*** −0.027*** −0.004***
UK −0.013*** −0.019*** −0.006***
US −0.033*** −0.029*** 0.004**
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.064*** −0.055*** 0.009
France −0.071*** −0.120*** −0.049**
German −0.098*** −0.134*** −0.036*
Italy −0.050* −0.089*** −0.039
Japan −0.161*** −0.174*** −0.014
UK −0.061*** −0.071*** −0.010
US −0.009 −0.006 0.003
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D5 denotes 32-month scale.
39
Table 12 Individual systemic risks and inflation(output) shocks for wavelet transform D6
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.006* −0.006*** −2.18E−05
France −0.003* −0.001 0.002
German −0.015*** −0.012*** 0.003**
Italy −0.003** −0.002** 0.001
Japan −0.017*** −0.018*** −0.001
UK 0.006*** 0.008*** 0.002
US −0.019*** −0.020*** −0.001
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.021** −0.012 0.009
France 0.006 −0.016 −0.022
German −0.051*** −0.073*** −0.022*
Italy −0.021 −0.047*** −0.026*
Japan −0.095*** −0.132*** −0.037**
UK 0.003 −0.009 −0.012**
US −0.061*** −0.062*** −0.001
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.007** −0.008*** −0.001
France −0.003* −0.001 0.002
German −0.016*** −0.013*** 0.003
Italy −0.003*** −0.002** 0.001
Japan −0.018*** −0.019*** −0.001
UK 0.006*** 0.009*** 0.003
US −0.019*** −0.023*** −0.004
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.022** −0.013 0.009
France 0.007 −0.017 −0.024
German −0.056*** −0.079*** −0.023
Italy −0.022 −0.050*** −0.028*
Japan −0.100*** −0.141*** −0.041**
UK 0.003 −0.009 −0.012*
US −0.065*** −0.066*** −0.001
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D6 denotes 64-month scale.
40
Table 13. Principle component analysis of systemic risk and macroeconomic shocks
Median 20th pctl Difference
Inflation shocks
Raw −0.138 −0.275*** −0.137
D1 0.154*** −0.027 0.181
D2 0.355** 0.311*** −0.044
D3 0.047 −0.039 −0.086
D4 −0.735*** −0.741*** −0.006
D5 −0.473*** −0.603*** −0.130
D6 −0.277*** −0.257*** −0.020
Output shocks
Raw −0.130 −0.398*** −0.267***
D1 0.037 0.045 0.008
D2 −0.131 −0.009 0.122
D3 −0.186** −0.302*** −0.116
D4 −0.309*** −0.563*** −0.254
D5 −1.045*** −0.972*** 0.073
D6 −0.221*** −0.459*** −0.238*
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression.
41
WTI crude oil price (level) WTI crude oil price (log difference)
Brent crude oil price (level) Brent crude oil price (log difference)
Commodity market (level) Commodity market (log difference)
Figure 1. Time Series Plots of Daily Crude Oil Prices and Returns
Notes: Time series plots of daily prices and returns of commodity market, wheat, corn, and soybean
from January 1, 1991 through December 29, 2017 (7044 days). The left-hand panels plot the level
series, where the starting value on January 1, 1991 is normalized at 100 for each commodity in order to
enhance visual comparisons. The right-hand panels plot the log differences.
42
CPI Inflation Shock (AR(3) Residual)
Output Output Shock (AR(4) Residual)
Figure 2: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for Canada
Notes: Time series plots of monthly inflation and output from January 1998 through December 2017
(240 months). We also plot shocks that are defined as residuals from AR(p) models from January 2003
through December 2017 (180 months) Based on Akaike Information Criterion (AIC), we use p = 3 for
the inflation and p = 4 for the output.
43
CPI Inflation Shock (AR(4) Residual)
Output Output Shock (AR(5) Residual)
Figure 3: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for France
Notes: Time series plots of monthly inflation and output from January 1998 through December 2017
(240 months). We also plot shocks that are defined as residuals from AR(p) models from January 2003
through December 2017 (180 months) Based on Akaike Information Criterion (AIC), we use p = 4 for
the inflation and p = 5 for the output.
44
CPI Inflation Shock (AR(3) Residual)
Output Output Shock (AR(5) Residual)
Figure 4: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for Germany
Notes: Time series plots of monthly inflation and output from January 1998 through December 2017
(240 months). We also plot shocks that are defined as residuals from AR(p) models from January 2003
through December 2017 (180 months) Based on Akaike Information Criterion (AIC), we use p = 3 for
the inflation and p = 5 for the output.
CPI Inflation Shock (AR(4) Residual)
45
Output Output Shock (AR(5) Residual)
Figure 5: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for Italy
Notes: Time series plots of monthly inflation and output from January 1998 through December 2017
(240 months). We also plot shocks that are defined as residuals from AR(p) models from January 2003
through December 2017 (180 months) Based on Akaike Information Criterion (AIC), we use p = 4 for
the inflation and p = 5 for the output.
46
CPI Inflation Shock (AR(5) Residual)
Output Output Shock (AR(6) Residual)
Figure 6: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for Japan
Notes: Time series plots of monthly inflation and output from January 1998 through December 2017
(240 months). We also plot shocks that are defined as residuals from AR(p) models from January 2003
through December 2017 (180 months) Based on Akaike Information Criterion (AIC), we use p = 5 for
the inflation and p = 6 for the output.
47
CPI Inflation Shock (AR(3) Residual)
Output Output Shock (AR(3) Residual)
Figure 7: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for UK
Notes: Time series plots of monthly inflation and output from January 1998 through December 2017
(240 months). We also plot shocks that are defined as residuals from AR(p) models from January 2003
through December 2017 (180 months) Based on Akaike Information Criterion (AIC), we use p = 3 for
the inflation and p = 3 for the output.
48
CPI Inflation Shock (AR(3) Residual)
Output Output Shock (AR(6) Residual)
Figure 8: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for US
Notes: Time series plots of monthly inflation and output from January 1998 through December 2017
(240 months). We also plot shocks that are defined as residuals from AR(p) models from January 2003
through December 2017 (180 months) Based on Akaike Information Criterion (AIC), we use p = 3 for
the inflation and p = 6 for the output.
49
Figure 9: The plots of CoVaR
Notes: We fit the bivariate DCC-MIDAS models for commodity market and crude oil. In the panels of
this figure, we plot monthly 5% CoVaR as a measure of systemic risk of crude oil price. The upside
denotes WTI crude oil while downside denotes Brent crude oil. CoVaR is measured in absolute value.
50
Table 1a. Individual systemic risks and inflation (output) shocks
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada −0.042 −0.041 0.001
France −0.017 −0.033* −0.016
German −0.013 −0.060*** −0.047***
Italy −0.001 −0.033* −0.028
Japan −0.032*** −0.041* −0.008
UK 0.012 −0.021 −0.033
US −0.017 −0.051** −0.034
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada −0.193*** −0.085* 0.108**
France −0.322*** −0.279*** 0.043
German −0.229 −0.407** −0.178
Italy −0.173 −0.373*** −0.200
Japan −0.168 −0.801*** −0.633***
UK 0.107 −0.217* −0.033
US −0.074 −0.111** −0.037
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(-1)
Canada −0.032 −0.027 0.005
France −0.013 −0.025*** −0.012
German −0.011 −0.040*** −0.029**
Italy −0.001 −0.017*** −0.016
Japan −0.027** −0.030* −0.003
UK 0.008 −0.013 −0.021
US −0.014 −0.041** −0.027
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(-1)
Canada −0.150*** −0.070* 0.081**
France −0.234*** −0.189*** −0.045
German −0.149 −0.243*** −0.599
Italy −0.117 −0.275*** −0.158
Japan −0.112 −0.619*** −0.507***
UK −0.068 −0.156 −0.088
US −0.049 −0.077** −0.029
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression.
51
Table 2a Individual systemic risks and inflation (output) shocks for wavelet transform D1
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada −0.021 0.046 0.067
France 0.177** 0.173 −0.004
German 0.031 −0.027 −0.058
Italy −0.020 0.065 0.085*
Japan −0.019 −0.175 −0.156
UK 0.043 0.194 0.151
US 0.578*** 0.045 −0.533***
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada 0.095 0.201 0.107
France 0.649 1.472 0.823*
German 0.279 0.997 0.718
Italy 1.495 0.342 −1.153
Japan −0.221 −0.917 −0.697
UK −0.788 0.351 1.138
US −0.473 −0.126 0.347
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(-1)
Canada −0.012 0.024 0.036
France 0.090 0.134 0.043
German 0.053 −0.010 −0.063
Italy −0.009 −0.083 −0.074
Japan −0.011 −0.145 −0.134*
UK 0.014 −0.035 −0.048
US 0.297 0.189 −0.109
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(-1)
Canada −0.018 0.036 0.054
France 0.134** 0.171*** 0.037
German 0.080 −0.025 −0.105
Italy −0.014 −0.086 −0.072
Japan −0.018 −0.219* −0.201*
UK 0.016 −0.052 −0.068
US 0.439*** 0.125 −0.313
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D1 denotes 2-month scale.
52
Table 3a Individual systemic risk and inflation (output) shocks for wavelet transform D2
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada 0.196*** 0.158*** −0.039
France 0.147*** 0.076 −0.071
German 0.125*** 0.151* 0.026
Italy 0.050* 0.035 −0.016
Japan 0.049 −0.001 −0.050
UK 0.197*** 0.141*** −0.056
US 0.292*** 0.204*** −0.088
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(-1)
Canada −0.113 −0.086 0.027
France −0.402 0.125 0.527
German −0.366 −0.709 −0.343
Italy −1.267*** −1.693*** −0.425**
Japan −1.839 −1.470 0.369
UK 0.096 0.292 0.196
US −0.223*** −0.220** 0.002
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(-1)
Canada 0.152** 0.172*** 0.020
France 0.128*** 0.028 −0.010***
German 0.112*** 0.138** 0.025
Italy 0.042 0.040 −0.002
Japan 0.010 −0.016 −0.026
UK 0.067* 0.111** 0.045
US 0.252*** 0.180*** −0.073
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(-1)
Canada −0.096 −0.013 0.083
France −0.368 0.283 0.651
German −0.208 0.053 0.261
Italy −1.185*** −1.449*** −0.264
Japan −0.737 −0.834 −0.097
UK 0.074 0.243 0.168
US −0.330*** −0.194*** 0.136
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D2 denotes 4-month scale.
53
Table 4a. Individual systemic risk and inflation (output) shocks for wavelet transform D3
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada 0.005 −0.004 −0.009
France 0.007* 0.004 −0.003
German −0.004 −0.011 −0.006
Italy −5.76E−05 −0.002 −0.002
Japan 0.001 0.005*** 0.004**
UK 0.004 0.004 −5.30E−05
US 0.001 −0.001 −0.002
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
German −0.378 −0.255 0.123
Canada −0.094 −0.289*** −0.195**
France −0.584*** −0.439* 0.145
Italy −0.499** −0.453*** 0.045
Japan −0.077 −0.167 −0.091
UK 0.099 −0.063 −0.162
US −0.095 −0.198* −0.103
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada 0.003 −0.003 −0.006
France 0.005* 0.003 −0.002
German −0.003 −0.006 −0.003
Italy 0.000 −0.002 −0.002
Japan 0.001 0.004*** 0.003**
UK 0.003 0.003 −0.0001
US 0.001 −0.0009 −0.002
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.109* −0.258*** −0.149**
France −0.427*** −0.203* 0.224**
German −0.102 −0.224 −0.123
Italy −0.269 −0.328*** −0.059
Japan 0.098 −0.138 −0.236
UK 0.060 −0.051 −0.111
US 0.017 −0.091 −0.107
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D3 denotes 8-month scale.
54
Table 5a Individual systemic risks and inflation (output) shocks for wavelet transform D4
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.048*** −0.053*** −0.005
France −0.013* −0.020*** −0.007
German −0.023*** −0.026*** −0.003
Italy −0.008 −0.015*** −0.007
Japan −0.036*** −0.036*** 0.0006
UK −0.033*** −0.040*** −0.007
US −0.038*** −0.049*** −0.011
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
German −0.318*** −0.268*** 0.051
Canada −0.287*** −0.244*** 0.043
France −0.417*** −0.392*** 0.025
Italy −0.234*** −0.324*** −0.090
Japan −0.286* −0.383* −0.096
UK −0.263*** −0.280*** −0.017
US 0.035 0.035 −0.0006
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.139*** −0.115*** 0.024
France −0.157*** −0.151*** 0.006
German −0.143*** −0.120*** 0.023
Italy −0.100 −0.143*** −0.043
Japan −0.126* −0.189*** −0.063
UK −0.126*** −0.146*** −0.020
US 0.022 0.021 −0.001
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.213*** −0.174*** 0.039
France −0.235*** −0.230*** 0.005
German −0.222*** −0.184*** 0.038
Italy −0.156*** −0.214*** −0.058
Japan −0.197* −0.283*** −0.086
UK −0.186*** −0.238*** −0.052
US 0.032 0.026 −0.005
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D4 denotes 16-month scale.
55
Table 6a Individual systemic risks and inflation (output) shocks for wavelet transform D5
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.065*** −0.068*** −0.003
France −0.038*** −0.035*** 0.003
German −0.054*** −0.054*** 0.000
Italy −0.030*** −0.028*** 0.002
Japan −0.044*** −0.053*** −0.009***
UK −0.020*** −0.023*** −0.003
US −0.059*** −0.047*** 0.012**
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.105*** −0.073*** 0.032
France −0.124*** −0.240*** −0.116***
German −0.169*** −0.246*** −0.077**
Italy −0.071 −0.186*** −0.115**
Japan −0.277*** −0.323*** −0.046
UK −0.111*** −0.122*** −0.011
US −0.022* −0.023 −0.001
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.053*** −0.062*** −0.009
France −0.030*** −0.028*** 0.002
German −0.042*** −0.042*** 0.000
Italy −0.025*** −0.024*** 0.001
Japan −0.033*** −0.040*** −0.007***
UK −0.020*** −0.028*** −0.0088***
US −0.050*** −0.043*** 0.007**
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.053*** −0.062*** −0.009
France −0.030*** −0.028*** 0.002
German −0.042*** −0.042*** 0.000
Italy −0.025*** −0.024*** 0.001
Japan −0.033*** −0.040*** −0.007***
UK −0.020*** −0.028*** −0.0088***
US −0.050*** −0.043*** 0.007**
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D5 denotes 32-month scale.
56
Table 7a. Individual systemic risks and inflation (output) shocks for wavelet transform D6
Median 20th pctl Difference
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.008 −0.009* −0.001
France −0.003 0.005 0.008**
German −0.030*** −0.016*** 0.014***
Italy −0.004* −0.002 0.002
Japan −0.037*** −0.039*** −0.002
UK 0.014*** 0.023*** 0.009**
US −0.034*** −0.038*** −0.004
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝑊𝑇𝐼(−1)
Canada −0.025 −0.007 0.018
France 0.046** −0.018 −0.064**
German −0.085*** −0.115*** −0.030
Italy −0.018 −0.082** −0.064**
Japan −0.165*** −0.229*** −0.229
UK 0.009 −0.017 −0.026**
US −0.112*** −0.111*** 0.001
Inflation shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.013*** −0.011*** 0.002
France −0.005** −0.002 0.003
German −0.023*** −0.018*** 0.005*
Italy −0.005*** −0.003** 0.002
Japan −0.027*** −0.028*** −0.001
UK 0.009*** 0.015*** 0.006*
US −0.030*** −0.032*** −0.002
Output shocks: 𝐶𝑜𝑉𝑎𝑅𝑚𝑎𝑟𝑘𝑒𝑡|𝐵𝑅𝐸𝑁𝑇(−1)
Canada −0.035*** −0.023 0.012
France 0.008 −0.028 −0.036
German −0.085*** −0.109*** −0.024
Italy −0.032 −0.075*** −0.043*
Japan −0.154*** −0.206*** −0.052**
UK 0.004 −0.016 −0.020**
US −0.099*** −0.103*** −0.004
Notes: *** means significance at the 1% level; ** means the 5% level; * means the 10% level.
Difference indicates the difference between coefficients of 20% quantile regression and
coefficients of mean regression. D6 denotes 64-month scale.
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