1.motegi/Yang_Motegi_Hamori_crude_oil...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

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


.

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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.

12

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)


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≤


−𝑟𝑡


𝜎𝑡𝑖


2|𝑟𝑡

𝑖 ≤ 𝑉𝑎𝑅𝛼,𝑡𝑖 ] = 𝛽, (5a)

25

where 𝑟𝑡

𝑚𝑎𝑟𝑘𝑒𝑡−𝑟𝑡


𝜎𝑡𝑖


2~𝑁(0, 1). Particularly, the crude oil VaR is given by

𝑉𝑎𝑅𝛼,𝑡𝑖 = Φ−1(𝛼) 𝜎𝑡

𝑖. Combining that, then we have


= Φ−1(β)𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡√1 − 𝜌𝑡

2 − Φ−1(𝛼)𝜌𝑡𝜎𝑡𝑚𝑎𝑟𝑘𝑒𝑡. (6a)

Because Φ−1(50%) = 0, equation (2a) can be solved for


= 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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30

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.


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.


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


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



coefficients of mean regression. D1 denotes 2-month scale.

35




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*


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




36



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




37

Table 10 Individual systemic risk and inflation (output) shocks for wavelet transform D4



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


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


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




38




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**


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


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**


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




39

Table 12 Individual systemic risks and inflation(output) shocks for wavelet transform D6



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


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


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


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




40

Table 13. Principle component analysis of systemic risk and macroeconomic shocks


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*




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



Figure 3: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for France





44



Figure 4: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for Germany






45


Figure 5: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for Italy





46



Figure 6: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for Japan





47



Figure 7: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for UK





48



Figure 8: Time Series Plots of Monthly Macroeconomic Indicators and Shocks for US





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



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


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


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


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




51

Table 2a Individual systemic risks and inflation (output) shocks for wavelet transform D1



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***


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


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


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




52

Table 3a Individual systemic risk and inflation (output) shocks for wavelet transform D2



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


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


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


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




53

Table 4a. Individual systemic risk and inflation (output) shocks for wavelet transform D3



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


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


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


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




54




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


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


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


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




55




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**


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


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**


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**




56

Table 7a. Individual systemic risks and inflation (output) shocks for wavelet transform D6



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


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


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


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




Documents

1.motegi/Yang_Motegi_Hamori_crude_oil...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