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 worldโs 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; Calmรจs and Thรฉoret, 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 Ergรผn, 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 authorsโ
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 ฮCoVaR.
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 ๐ = 3. Let ๐ = 1, โฆ , ๐ signify each month; let ๐ก =
1, โฆ , ๐๐ signify each trading day, where we assume that each month has ๐ = 21
trading days. Let ๐๐,๐ก be the return of asset ๐ on day ๐ก. The GARCHโMIDAS model
is specified as follows:
๐๐,๐ก = ๐๐ + โ๐๐,๐ โ ๐๐,๐ก๐๐,๐ก, โ๐ก = (๐ โ 1)๐ + 1, โฆ , ๐๐, โ๐ = 1, โฆ , ๐.
(1)
Note that ๐๐,๐ก 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:
๐๐,๐ก = (1 โ ๐ผ๐ โ ๐ฝ๐) + ๐ผ๐(๐๐,๐กโ1โ๐๐)
2
๐๐,๐+ ๐ฝ๐๐๐,๐กโ1. (2)
We impose ๐ผ๐ > 0 , ๐ฝ๐ โฅ 0 , and ๐ผ๐ + ๐ฝ๐ < 1 in order to ensure ๐๐,๐ก > 0 and
E[๐๐,๐ก2 ] < โ.
4 See Turhan et al. (2014) for an empirical application of GARCH-MIDAS models.
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Define a monthly realized variance as the sum of N = 21 daily squared returns:
๐ ๐๐,๐ = โ ๐๐,๐ก2๐๐
๐ก=(๐โ1)๐+1 . (3)
We assume that ๐๐,๐ is determined by a polynomial of lagged realized variances:
๐๐,๐ = ๏ฟฝฬ ๏ฟฝ๐ + ๐๐ โ ๐๐(๐๐ฃ๐ )
๐พ๐ฃ๐=1 ๐ ๐๐,๐โ๐, (4)
where we use ๐พ๐ฃ = 36 in accordance with Colacito et al. (2011), and we assume that
๏ฟฝฬ ๏ฟฝ๐ > 0 and 0 < ๐๐ < 1. We use the beta polynomial with parameter ๐๐ฃ๐ > 1 in
order to capture decaying impacts of {๐ ๐๐,๐โ1, โฆ , ๐ ๐๐,๐โ๐พ๐ฃ} on ๐๐,๐:
๐๐(๐๐ฃ๐ ) =
(1โ๐/๐พ๐ฃ)๐๐ฃ๐ โ1
โ (1โ๐/๐พ๐ฃ)๐๐ฃ๐ โ1๐พ๐ฃ
๐=1
. (5)
The larger (smaller) value of ๐๐ฃ๐ implies the faster (slower) decay of ๐๐(๐๐ฃ
๐ ).
For each asset i, we compute maximum likelihood estimators of the parameters
{๐๐, ๐ผ๐, ๐ฝ๐, ๐๐ , ๐๐ฃ๐ , ๏ฟฝฬ ๏ฟฝ๐} based on the univariate Gaussian likelihood function. Using
those estimators, we compute the standardized residual ๐๐,๐ก = (๐๐,๐ก โ ๐๐)/โ๐๐,๐ โ ๐๐,๐ก.
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 ๐๐,๐ก = (๐๐,๐ก โ ๐๐)/โ๐๐,๐ โ ๐๐,๐ก
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 ๐๐ก = [๐๐,๐,๐ก]๐,๐
be an ๐ ร ๐ conditional covariance matrix at time ๐ก. The
DCC-MIDAS specification is as follows:
๐๐,๐,๐ก = ๏ฟฝฬ ๏ฟฝ๐,๐,๐(1 โ ๐๐,๐ โ ๐๐,๐) + ๐๐,๐ ร ๐๐,๐กโ1๐๐,๐กโ1 + ๐๐,๐ ร ๐๐,๐,๐กโ1, (6)
๏ฟฝฬ ๏ฟฝ๐,๐,๐ = โ ๐๐(๐๐๐,๐
)๐๐,๐,๐โ๐๐พ๐๐=1 , (7)
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๐๐,๐,๐ =โ ๐๐,๐
๐๐๐=(๐โ1)๐+1 ๐๐,๐
โโ ๐๐,๐2๐๐
๐=(๐โ1)๐+1 โโ ๐๐,๐2๐๐
๐=(๐โ1)๐+1
. (8)
We impose that ๐๐,๐ > 0, ๐๐,๐ > 0, and ๐๐,๐ + ๐๐,๐ < 1. The long-term correlation
๏ฟฝฬ ๏ฟฝ๐,๐,๐ is calculated as a weighted sum of ๐พ๐ lagged realized correlations. We use
๐พ๐ = 144 in accordance with Colacito et al. (2011). The realized correlations are
computed from ๐ = 21 non-overlapping standardized residuals. Using (6)โ(8), daily
conditional correlations between assets i and j are given by
๐๐,๐,๐ก =๐๐,๐,๐ก
โ๐๐,๐,๐กโ๐๐,๐,๐ก . (9)
We compute maximum likelihood estimators for the parameters {๐๐,๐ , ๐๐,๐, ๐๐๐,๐
}
based on the bivariate Gaussian likelihood function, and obtain estimated conditional
covariance matrix {๏ฟฝฬ๏ฟฝ๐ก}.
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
Ergรผn (2013). First, the Value-at-Risk (VaR) of the crude oil price return ๐๐ก๐ is
implicitly defined as
Pr(๐๐ก๐ โค ๐๐๐ ๐ผ,๐ก
๐ ) = ๐ผ,
where ฮฑ โ (0,1) is a given level of tail probability. ๐๐๐ ๐ผ,๐ก๐ represents a threshold
that ๐๐ก๐ exceeds with probability ฮฑ . It can be computed from the estimated
conditional variance of ๐๐ก๐ via the GARCH-MIDAS model.
The Conditional Value-at-Risk (CoVaR) of commodity market ๐๐ก๐๐๐๐๐๐ก given
the crude oil price return, written as ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
, is implicitly defined as
Pr (๐๐ก๐๐๐๐๐๐ก โค ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก
๐๐๐๐๐๐ก|๐ | ๐๐ก
๐ โค ๐๐๐ ๐ผ,๐ก๐ ) = ๐ฝ (10)
10
where ๐ฝ โ (0,1) is a given level of tail probability. ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
represents,
given ๐๐ก๐ โค ๐๐๐ ๐ผ,๐ก
๐ , a threshold that ๐๐ก๐ exceeds probability ๐ฝ . Given Eq. (10),
๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
takes negative values almost by construction. The larger (smaller)
absolute value of ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
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. ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
can therefore be interpreted as a risk
measure of commodity market. In particular, we set ๐ผ = 5% as well as ๐ฝ = 5% in
this paper. ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
can be computed from the estimated conditional
correlation between crude oil price ๐ 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 |๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
| 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 ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐ 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
๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
.
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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
, , โฆ, and are associated with oscillations of lengths 2 months, 4
months, โฆ, and 2๐ 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 2๐ฝ). 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 โ๐ = (โ1,0, โฆ , โ1,๐ฟโ1, โฆ ,0, โฆ ,0)๐ represents the wavelet
filter coefficients for unit scales, zero-padded to length N. Three conditions must be
satisfied by a wavelet filter: โ โ1,๐ = 0๐ฟโ1๐=0 ; โ โ1,๐
2 = 1๐ฟโ1๐=0 ; โ โ1,๐โ1,๐+2๐ = 0๐ฟโ1
๐=0 for
all non-zero integers n. Meanwhile, suppose ๐๐ = (๐1,0, โฆ , ๐1,๐ฟโ1, โฆ ,0, โฆ ,0)๐ 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 ๐1,๐ =
(โ1)๐+1โ1,๐ฟโ1โ๐. When any sample size N is divisible by 2๐, wavelet coefficients,
๏ฟฝฬ๏ฟฝ๐,๐ก and scaling coefficients ๏ฟฝฬ๏ฟฝ๐,๐ก at levels jโ 1, โฆ , ๐ฝ can be defined as: ๏ฟฝฬ๏ฟฝ๐,๐ก =
โ ๏ฟฝฬ๏ฟฝ๐๏ฟฝฬ๏ฟฝ๐โ1,๐กโ1 ๐๐๐๐๐ฟโ1๐=0 and ๏ฟฝฬ๏ฟฝ๐,๐ก = โ โฬ๐๏ฟฝฬ๏ฟฝ๐โ1,๐กโ1 ๐๐๐๐
๐ฟโ1๐=0 where wavelet ๏ฟฝฬ๏ฟฝ๐ is
rescaled as ๏ฟฝฬ๏ฟฝ๐ = ๐๐/2๐/2, and scaling filters is rescaled as โฬ๐ = โ๐/2๐/2.
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
distributionโs 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 ๐ = 3 for inflation and ๐ = 5 for output in Germany; ๐ = 3 for
inflation and ๐ = 4 for output in Canada; ๐ = 4 for inflation and ๐ = 5 for output
in France; ๐ = 4 for inflation and ๐ = 5 for output in Italy; ๐ = 5 for inflation
and ๐ = 6 for output in Japan; ๐ = 3 for inflation and ๐ = 3 for output in UK;
and ๐ = 3 for inflation and ๐ = 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 2008โ2009, 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 {๐๐, ๐ผ๐ , ๐ฝ๐, ๐๐ , ๐๐ฃ๐ , ๏ฟฝฬ ๏ฟฝ๐} and their standard errors. For each commodity, all estimates
except for ๐๐ are highly significant. The point estimate of the beta polynomial
parameter, ๐๐ฃ๐ , 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 {๐๐,๐ , ๐๐,๐, ๐๐๐,๐
} and their
standard errors. All estimates are highly significant for each pair. The point estimates
of ๐๐๐,๐
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 ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
with ฮฑ =0.05 and ฮฒ = 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 ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ (-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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ and ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐ 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 ฮCoVaR 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 investorsโ 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 โCoVaR
We consider โ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
by standardizing ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
relative to a
benchmark condition where ๐๐ก๐ is equal to or less than its conditional median. The
median ๐ถ๐๐๐๐ 0.5,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
is defined by,
Pr (๐๐ก๐๐๐๐๐๐ก โค ๐ถ๐๐๐๐ 0.5,๐ฝ,๐ก
๐๐๐๐๐๐ก|๐ | ๐๐ก
๐ โค ๐๐๐ 0.5,๐ก๐ ) = ๐ฝ (1a)
24
and thus, โ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
is defined as follows:
โ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
= ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
โ ๐ถ๐๐๐๐ 0.5,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
(2a)
โ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
is called the delta CoVaR (โณCoVaR), 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 โ CoVaR has a
closed-form expression and assume that crude oil price and market returns follow a
bivariate normal distribution:
(๐๐ก๐, ๐๐ก
๐๐๐๐๐๐ก)~๐ (0, ((๐๐ก
๐)2 ๐๐ก๐๐ก๐๐๐ก
๐๐๐๐๐๐ก
๐๐ก๐๐ก๐๐๐ก
๐๐๐๐๐๐ก (๐๐ก๐๐๐๐๐๐ก)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:
๐๐ก๐๐๐๐๐๐ก|๐๐ก
๐~๐ (๐๐ก
๐๐๐ก๐๐๐๐๐๐ก๐๐ก
๐๐ก๐ , (1 โ ๐๐ก
2)(๐๐ก๐๐๐๐๐๐ก)2) (4a)
Hereby, we can rewrite equation (10) to be:
Pr [๐๐ก
๐๐๐๐๐๐กโ๐๐ก
๐ ๐๐ก๐๐๐๐๐๐ก๐๐ก
๐๐ก๐
๐๐ก๐๐๐๐๐๐กโ1โ๐๐ก
2โค
๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
โ๐๐ก
๐ ๐๐ก๐๐๐๐๐๐ก๐๐ก
๐๐ก๐
๐๐ก๐๐๐๐๐๐กโ1โ๐๐ก
2|๐๐ก
๐ โค ๐๐๐ ๐ผ,๐ก๐ ] = ๐ฝ, (5a)
25
where ๐๐ก
๐๐๐๐๐๐กโ๐๐ก
๐ ๐๐ก๐๐๐๐๐๐ก๐๐ก
๐๐ก๐
๐๐ก๐๐๐๐๐๐กโ1โ๐๐ก
2~๐(0, 1). Particularly, the crude oil VaR is given by
๐๐๐ ๐ผ,๐ก๐ = ฮฆโ1(๐ผ) ๐๐ก
๐. Combining that, then we have
๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
= ฮฆโ1(ฮฒ)๐๐ก๐๐๐๐๐๐กโ1 โ ๐๐ก
2 โ ฮฆโ1(๐ผ)๐๐ก๐๐ก๐๐๐๐๐๐ก. (6a)
Because ฮฆโ1(50%) = 0, equation (2a) can be solved for
โ๐ถ๐๐๐๐ ๐ผ,๐ฝ,๐ก๐๐๐๐๐๐ก|๐
= ฮฆโ1(๐ผ)๐๐ก๐๐ก๐๐๐๐๐๐ก. (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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30
Table 1. Sample statistics of the daily log returns of commodity market and crude oil.
Market WTI Brent
Meanร 10โ3 0.654 1.069 1.287
Std. Dev. 7.216 16.414 15.993
Skewness โ0.574 โ0.820 โ0.529
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 โ0.045 0.064 โ0.427 1.165 0.588 โ0.284
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 โ0.697 โ0.260 โ0.299 1.116
Std. Dev. 0.0456 0.043 0.056 0.061 0.089 0.029 0.0435
Skewness โ1.299 โ2.173 โ1.988 โ2.249 โ1.605 โ1.756 โ2.048
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 GARCHโMIDAS Models for each commodity
Market WTI Brent
ฮผ ร 10โ2 1.634(1.336) 0.037 (1.838) 3.246 (2.018)
ฮ 0.049 (0.004)*** 0.060 (0.003)*** 0.056 (0.005)***
ฮฒ 0.917 (0.013)*** 0.929 (0.004)*** 0.878 (0.018)***
ฮธ 0.199 (0.007)*** 0.156 (0.021)*** 0.208 (0.005)***
๐๐ฃ 8.106 (2.404)*** 1.106 (0.367)*** 16.471 (2.722)***
๏ฟฝฬ ๏ฟฝ 0.539 (0.063)*** 1.839 (0.191)*** 0.641 (0.077)***
Notes: The number of monthly lags for the MIDAS polynomial is ๐พ๐ฃ = 36, which deletes the first
36 ร 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 โ0.021 โ0.004 0.004 โ.009 0.012 0.004 โ0.021
Std. Dev. 0.415 0.238 0.285 0.222 0.329 0.276 0.418
Skewness 0.0176 โ0.054 โ0.252 โ0.414 0.387 0.065 โ0.581
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 โ0.037 โ0.036 0.022 โ0.032 0.035 0.0004 โ0.022
Std. Dev. 1.442 2.014 1.928 2.199 3.111 1.424 0.896
Skewness 0.244 โ0.247 โ0.294 โ0.285 โ0.277 0.069 โ0.383
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 DCCโMIDAS 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) ***
๐๐ 2.531 (0.193)*** 30.226 (5.370)***
Notes: The number of monthly lags for the MIDAS polynomial is ๐พ๐ = 144, which deletes the first
144 ร 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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ (-1)
Canada โ0.020 โ0.018 0.002
France โ0.008 โ0.016*** โ0.008
German โ0.007 โ0.026*** โ0.018**
Italy โ0.001 โ0.011*** โ0.010
Japan โ0.018*** โ0.018* 0.000
UK 0.005 โ0.008 โ0.014
US โ0.008 โ0.025** โ0.016
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada โ0.095*** โ0.044* 0.051**
France โ0.150** โ0.121*** 0.029
German โ0.095 โ0.152** โ0.057
Italy โ0.075 โ0.180*** โ0.105
Japan โ0.071 โ0.403*** โ0.332***
UK โ0.043 โ0.099 โ0.056
US โ0.031 โ0.046** โ0.018
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐ (-1)
Canada โ0.021 โ0.018 0.003
France โ0.009 โ0.017* โ0.008
German โ0.007 โ0.027*** โ0.020***
Italy โ0.001 โ0.012* โ0.011
Japan โ0.019** โ0.017* โ0.002
UK 0.005 โ0.009 โ0.014
US โ0.009 โ0.026* โ0.017
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐ (-1)
Canada โ0.100*** โ0.048* 0.052
France โ0.161** โ0.130*** 0.031
German โ0.101 โ0.141*** โ0.040***
Italy โ0.079 โ0.192*** โ0.113
Japan โ0.074 โ0.426*** โ0.352***
UK โ0.046 โ0.106 โ0.060
US โ0.032 โ0.052** โ0.020
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada โ0.012 0.023 0.034
France 0.085** 0.124*** 0.039
German 0.050 โ0.011 โ0.062
Italy โ0.009 โ0.071 โ0.062
Japan โ0.011 โ0.116 โ0.105
UK 0.014 โ0.033 โ0.047
US 0.280*** 0.081 โ0.199
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ (-1)
Canada 0.023 0.080 0.057
France 0.300 0.201 โ0.009
German 0.138 0.477 0.339
Italy โ0.248 0.174 0.422
Japan โ0.118 โ0.404 โ0.286
UK โ0.536 0.270 0.806*
US โ0.007 โ0.067 โ0.060
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐ (-1)
Canada โ0.012 0.024 0.036
France 0.090** 0.133*** 0.043
German 0.053 โ0.010 โ0.063
Italy โ0.009 โ0.083 โ0.074
Japan โ0.011 โ0.145* โ0.134*
UK 0.014 โ0.035 โ0.048
US 0.297*** 0.188 โ0.109
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐ (-1)
Canada โ0.012 0.024 0.036
France 0.090 0.134 0.043
German 0.053 โ0.010 โ0.063
Italy โ0.009 โ0.083 โ0.074
Japan โ0.011 โ0.145 โ0.134*
UK 0.014 โ0.035 โ0.048
US 0.297 0.189 โ0.109
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada 0.096** 0.110*** 0.013
France 0.081*** 0.018 โ0.063***
German 0.070*** 0.087** 0.018
Italy 0.027 0.026 โ0.001
Japan 0.002 โ0.010 โ0.012
UK 0.047* 0.071** 0.024
US 0.160*** 0.113*** โ0.048*
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada โ0.061 โ0.008 0.053
France โ0.236 0.179 0.415
German โ0.133 0.034 0.166
Italy โ0.926*** โ0.919*** 0.007
Japan โ0.497 โ0.548 โ0.050
UK 0.047 0.144 0.097
US โ0.158*** โ0.123*** 0.036
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(-1)
Canada 0.104** 0.117*** 0.013
France 0.087*** 0.019 โ0.067***
German 0.075*** 0.093** 0.018
Italy 0.029 0.029 โ0.0003
Japan 0.002 โ0.017 โ0.019
UK 0.045* 0.076** 0.030
US 0.175*** 0.121*** โ0.053
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(-1)
Canada โ0.065 โ0.008 0.057
France โ0.250 0.190 0.440*
German โ0.142 0.036 0.178
Italy โ0.794*** โ0.983*** โ0.189
Japan โ0.524 โ0.562 โ0.037
UK 0.050 0.149 0.099
US โ0.223*** โ0.132*** 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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada 0.002 โ0.002 โ0.004
France 0.003* 0.002 โ0.001
German โ0.002 โ0.003 โ0.001
Italy โ8.34Eโ05 โ0.0009 โ0.0009
Japan 0.0004 0.003*** 0.002**
UK 0.002 0.002 โ3.15Eโ05
US 0.0007 โ0.0006 โ0.001
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.070* โ0.158*** โ0.088*
France โ0.272*** โ0.131** 0.141**
German โ0.065 โ0.144 โ0.079
Italy โ0.116 โ0.208*** โ0.092
Japan 0.039 โ0.088 โ0.127
UK 0.043 โ0.033 โ0.075
US 0.011 โ0.060 โ0.071
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada 0.002 โ0.002 โ0.004
France 0.003 0.002 โ0.001
German โ0.002 โ0.003 โ0.001
Italy 0.000 โ0.001 โ0.001
Japan 0.000 0.003*** โ0.003**
UK 0.002 0.002 1.80Eโ05
US 0.001 โ0.001 โ0.002
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
German โ0.069 โ0.153 โ0.084
Canada โ0.075* โ0.154*** โ0.079
France โ0.289*** โ0.128* 0.161**
Italy โ0.119 โ0.223*** โ0.104
Japan 0.040 โ0.093 โ0.134
UK 0.041 โ0.035 โ0.075
US 0.011 โ0.061 โ0.072
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.048*** โ0.053*** โ0.005
France โ0.013* โ0.020*** โ0.007
German โ0.023*** โ0.026*** โ0.003
Italy โ0.008 โ0.015*** โ0.007
Japan โ0.036*** โ0.036*** 0.0006
UK โ0.033*** โ0.040*** โ0.007
US โ0.038*** โ0.049*** โ0.011
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ (โ1)
Canada โ0.134*** โ0.110*** 0.024
France โ0.155*** โ0.145*** 0.010
German โ0.136*** โ0.118*** 0.018
Italy โ0.100*** โ0.137*** โ0.037
Japan โ0.128** โ0.181*** โ0.053
UK โ0.120*** โ0.151*** โ0.031
US 0.020 0.017 โ0.004
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.051*** โ0.055*** โ0.004
France โ0.014* โ0.021*** โ0.007
German โ0.023*** โ0.027*** โ0.004
Italy โ0.008 โ0.015*** โ0.007
Japan โ0.038*** โ0.038*** โ0.0007
UK โ0.031*** โ0.042*** โ0.011
US โ0.039*** โ0.051*** โ0.012
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.139*** โ0.115*** 0.024
France โ0.157*** โ0.151*** 0.006
German โ0.143*** โ0.120*** 0.023
Italy โ0.100 โ0.143*** โ0.043
Japan โ0.126* โ0.189*** โ0.063
UK โ0.126*** โ0.146*** โ0.020
US 0.022 0.021 โ0.001
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.033*** โ0.040*** โ0.007**
France โ0.019*** โ0.018*** 0.001
German โ0.026*** โ0.027*** โ0.001
Italy โ0.016*** โ0.015*** 0.001
Japan โ0.021*** โ0.026*** โ0.005***
UK โ0.012*** โ0.018*** โ0.006***
US โ0.031*** โ0.027*** 0.004**
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.060*** โ0.050*** 0.010
France โ0.068*** โ0.113*** โ0.045**
German โ0.091*** โ0.125*** โ0.034*
Italy โ0.047* โ0.084*** โ0.037
Japan โ0.153*** โ0.164*** โ0.011
UK โ0.057*** โ0.066*** โ0.009
US โ0.008 โ0.006 0.002
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.035*** โ0.044*** โ0.009***
France โ0.020*** โ0.019*** 0.001
German โ0.028*** โ0.029*** โ0.001
Italy โ0.017*** โ0.016*** 0.001
Japan โ0.023*** โ0.027*** โ0.004***
UK โ0.013*** โ0.019*** โ0.006***
US โ0.033*** โ0.029*** 0.004**
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.064*** โ0.055*** 0.009
France โ0.071*** โ0.120*** โ0.049**
German โ0.098*** โ0.134*** โ0.036*
Italy โ0.050* โ0.089*** โ0.039
Japan โ0.161*** โ0.174*** โ0.014
UK โ0.061*** โ0.071*** โ0.010
US โ0.009 โ0.006 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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.006* โ0.006*** โ2.18Eโ05
France โ0.003* โ0.001 0.002
German โ0.015*** โ0.012*** 0.003**
Italy โ0.003** โ0.002** 0.001
Japan โ0.017*** โ0.018*** โ0.001
UK 0.006*** 0.008*** 0.002
US โ0.019*** โ0.020*** โ0.001
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.021** โ0.012 0.009
France 0.006 โ0.016 โ0.022
German โ0.051*** โ0.073*** โ0.022*
Italy โ0.021 โ0.047*** โ0.026*
Japan โ0.095*** โ0.132*** โ0.037**
UK 0.003 โ0.009 โ0.012**
US โ0.061*** โ0.062*** โ0.001
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.007** โ0.008*** โ0.001
France โ0.003* โ0.001 0.002
German โ0.016*** โ0.013*** 0.003
Italy โ0.003*** โ0.002** 0.001
Japan โ0.018*** โ0.019*** โ0.001
UK 0.006*** 0.009*** 0.003
US โ0.019*** โ0.023*** โ0.004
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.022** โ0.013 0.009
France 0.007 โ0.017 โ0.024
German โ0.056*** โ0.079*** โ0.023
Italy โ0.022 โ0.050*** โ0.028*
Japan โ0.100*** โ0.141*** โ0.041**
UK 0.003 โ0.009 โ0.012*
US โ0.065*** โ0.066*** โ0.001
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 โ0.138 โ0.275*** โ0.137
D1 0.154*** โ0.027 0.181
D2 0.355** 0.311*** โ0.044
D3 0.047 โ0.039 โ0.086
D4 โ0.735*** โ0.741*** โ0.006
D5 โ0.473*** โ0.603*** โ0.130
D6 โ0.277*** โ0.257*** โ0.020
Output shocks
Raw โ0.130 โ0.398*** โ0.267***
D1 0.037 0.045 0.008
D2 โ0.131 โ0.009 0.122
D3 โ0.186** โ0.302*** โ0.116
D4 โ0.309*** โ0.563*** โ0.254
D5 โ1.045*** โ0.972*** 0.073
D6 โ0.221*** โ0.459*** โ0.238*
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada โ0.042 โ0.041 0.001
France โ0.017 โ0.033* โ0.016
German โ0.013 โ0.060*** โ0.047***
Italy โ0.001 โ0.033* โ0.028
Japan โ0.032*** โ0.041* โ0.008
UK 0.012 โ0.021 โ0.033
US โ0.017 โ0.051** โ0.034
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada โ0.193*** โ0.085* 0.108**
France โ0.322*** โ0.279*** 0.043
German โ0.229 โ0.407** โ0.178
Italy โ0.173 โ0.373*** โ0.200
Japan โ0.168 โ0.801*** โ0.633***
UK 0.107 โ0.217* โ0.033
US โ0.074 โ0.111** โ0.037
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(-1)
Canada โ0.032 โ0.027 0.005
France โ0.013 โ0.025*** โ0.012
German โ0.011 โ0.040*** โ0.029**
Italy โ0.001 โ0.017*** โ0.016
Japan โ0.027** โ0.030* โ0.003
UK 0.008 โ0.013 โ0.021
US โ0.014 โ0.041** โ0.027
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(-1)
Canada โ0.150*** โ0.070* 0.081**
France โ0.234*** โ0.189*** โ0.045
German โ0.149 โ0.243*** โ0.599
Italy โ0.117 โ0.275*** โ0.158
Japan โ0.112 โ0.619*** โ0.507***
UK โ0.068 โ0.156 โ0.088
US โ0.049 โ0.077** โ0.029
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada โ0.021 0.046 0.067
France 0.177** 0.173 โ0.004
German 0.031 โ0.027 โ0.058
Italy โ0.020 0.065 0.085*
Japan โ0.019 โ0.175 โ0.156
UK 0.043 0.194 0.151
US 0.578*** 0.045 โ0.533***
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-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 โ1.153
Japan โ0.221 โ0.917 โ0.697
UK โ0.788 0.351 1.138
US โ0.473 โ0.126 0.347
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(-1)
Canada โ0.012 0.024 0.036
France 0.090 0.134 0.043
German 0.053 โ0.010 โ0.063
Italy โ0.009 โ0.083 โ0.074
Japan โ0.011 โ0.145 โ0.134*
UK 0.014 โ0.035 โ0.048
US 0.297 0.189 โ0.109
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(-1)
Canada โ0.018 0.036 0.054
France 0.134** 0.171*** 0.037
German 0.080 โ0.025 โ0.105
Italy โ0.014 โ0.086 โ0.072
Japan โ0.018 โ0.219* โ0.201*
UK 0.016 โ0.052 โ0.068
US 0.439*** 0.125 โ0.313
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada 0.196*** 0.158*** โ0.039
France 0.147*** 0.076 โ0.071
German 0.125*** 0.151* 0.026
Italy 0.050* 0.035 โ0.016
Japan 0.049 โ0.001 โ0.050
UK 0.197*** 0.141*** โ0.056
US 0.292*** 0.204*** โ0.088
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(-1)
Canada โ0.113 โ0.086 0.027
France โ0.402 0.125 0.527
German โ0.366 โ0.709 โ0.343
Italy โ1.267*** โ1.693*** โ0.425**
Japan โ1.839 โ1.470 0.369
UK 0.096 0.292 0.196
US โ0.223*** โ0.220** 0.002
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(-1)
Canada 0.152** 0.172*** 0.020
France 0.128*** 0.028 โ0.010***
German 0.112*** 0.138** 0.025
Italy 0.042 0.040 โ0.002
Japan 0.010 โ0.016 โ0.026
UK 0.067* 0.111** 0.045
US 0.252*** 0.180*** โ0.073
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(-1)
Canada โ0.096 โ0.013 0.083
France โ0.368 0.283 0.651
German โ0.208 0.053 0.261
Italy โ1.185*** โ1.449*** โ0.264
Japan โ0.737 โ0.834 โ0.097
UK 0.074 0.243 0.168
US โ0.330*** โ0.194*** 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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada 0.005 โ0.004 โ0.009
France 0.007* 0.004 โ0.003
German โ0.004 โ0.011 โ0.006
Italy โ5.76Eโ05 โ0.002 โ0.002
Japan 0.001 0.005*** 0.004**
UK 0.004 0.004 โ5.30Eโ05
US 0.001 โ0.001 โ0.002
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
German โ0.378 โ0.255 0.123
Canada โ0.094 โ0.289*** โ0.195**
France โ0.584*** โ0.439* 0.145
Italy โ0.499** โ0.453*** 0.045
Japan โ0.077 โ0.167 โ0.091
UK 0.099 โ0.063 โ0.162
US โ0.095 โ0.198* โ0.103
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada 0.003 โ0.003 โ0.006
France 0.005* 0.003 โ0.002
German โ0.003 โ0.006 โ0.003
Italy 0.000 โ0.002 โ0.002
Japan 0.001 0.004*** 0.003**
UK 0.003 0.003 โ0.0001
US 0.001 โ0.0009 โ0.002
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.109* โ0.258*** โ0.149**
France โ0.427*** โ0.203* 0.224**
German โ0.102 โ0.224 โ0.123
Italy โ0.269 โ0.328*** โ0.059
Japan 0.098 โ0.138 โ0.236
UK 0.060 โ0.051 โ0.111
US 0.017 โ0.091 โ0.107
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.048*** โ0.053*** โ0.005
France โ0.013* โ0.020*** โ0.007
German โ0.023*** โ0.026*** โ0.003
Italy โ0.008 โ0.015*** โ0.007
Japan โ0.036*** โ0.036*** 0.0006
UK โ0.033*** โ0.040*** โ0.007
US โ0.038*** โ0.049*** โ0.011
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
German โ0.318*** โ0.268*** 0.051
Canada โ0.287*** โ0.244*** 0.043
France โ0.417*** โ0.392*** 0.025
Italy โ0.234*** โ0.324*** โ0.090
Japan โ0.286* โ0.383* โ0.096
UK โ0.263*** โ0.280*** โ0.017
US 0.035 0.035 โ0.0006
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.139*** โ0.115*** 0.024
France โ0.157*** โ0.151*** 0.006
German โ0.143*** โ0.120*** 0.023
Italy โ0.100 โ0.143*** โ0.043
Japan โ0.126* โ0.189*** โ0.063
UK โ0.126*** โ0.146*** โ0.020
US 0.022 0.021 โ0.001
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.213*** โ0.174*** 0.039
France โ0.235*** โ0.230*** 0.005
German โ0.222*** โ0.184*** 0.038
Italy โ0.156*** โ0.214*** โ0.058
Japan โ0.197* โ0.283*** โ0.086
UK โ0.186*** โ0.238*** โ0.052
US 0.032 0.026 โ0.005
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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.065*** โ0.068*** โ0.003
France โ0.038*** โ0.035*** 0.003
German โ0.054*** โ0.054*** 0.000
Italy โ0.030*** โ0.028*** 0.002
Japan โ0.044*** โ0.053*** โ0.009***
UK โ0.020*** โ0.023*** โ0.003
US โ0.059*** โ0.047*** 0.012**
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.105*** โ0.073*** 0.032
France โ0.124*** โ0.240*** โ0.116***
German โ0.169*** โ0.246*** โ0.077**
Italy โ0.071 โ0.186*** โ0.115**
Japan โ0.277*** โ0.323*** โ0.046
UK โ0.111*** โ0.122*** โ0.011
US โ0.022* โ0.023 โ0.001
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.053*** โ0.062*** โ0.009
France โ0.030*** โ0.028*** 0.002
German โ0.042*** โ0.042*** 0.000
Italy โ0.025*** โ0.024*** 0.001
Japan โ0.033*** โ0.040*** โ0.007***
UK โ0.020*** โ0.028*** โ0.0088***
US โ0.050*** โ0.043*** 0.007**
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.053*** โ0.062*** โ0.009
France โ0.030*** โ0.028*** 0.002
German โ0.042*** โ0.042*** 0.000
Italy โ0.025*** โ0.024*** 0.001
Japan โ0.033*** โ0.040*** โ0.007***
UK โ0.020*** โ0.028*** โ0.0088***
US โ0.050*** โ0.043*** 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: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.008 โ0.009* โ0.001
France โ0.003 0.005 0.008**
German โ0.030*** โ0.016*** 0.014***
Italy โ0.004* โ0.002 0.002
Japan โ0.037*** โ0.039*** โ0.002
UK 0.014*** 0.023*** 0.009**
US โ0.034*** โ0.038*** โ0.004
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐๐๐ผ(โ1)
Canada โ0.025 โ0.007 0.018
France 0.046** โ0.018 โ0.064**
German โ0.085*** โ0.115*** โ0.030
Italy โ0.018 โ0.082** โ0.064**
Japan โ0.165*** โ0.229*** โ0.229
UK 0.009 โ0.017 โ0.026**
US โ0.112*** โ0.111*** 0.001
Inflation shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.013*** โ0.011*** 0.002
France โ0.005** โ0.002 0.003
German โ0.023*** โ0.018*** 0.005*
Italy โ0.005*** โ0.003** 0.002
Japan โ0.027*** โ0.028*** โ0.001
UK 0.009*** 0.015*** 0.006*
US โ0.030*** โ0.032*** โ0.002
Output shocks: ๐ถ๐๐๐๐ ๐๐๐๐๐๐ก|๐ต๐ ๐ธ๐๐(โ1)
Canada โ0.035*** โ0.023 0.012
France 0.008 โ0.028 โ0.036
German โ0.085*** โ0.109*** โ0.024
Italy โ0.032 โ0.075*** โ0.043*
Japan โ0.154*** โ0.206*** โ0.052**
UK 0.004 โ0.016 โ0.020**
US โ0.099*** โ0.103*** โ0.004
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.