Systemic risk and macroeconomic shocks: Evidence from the crude oil market and G7 countries Lu Yang a Kaiji Motegi b Shigeyuki Hamori c

Transcription

1 Systemic risk and macroeconomic shocks: Evidence from the crude oil market and G7 countries Lu Yang a Kaiji Motegi b Shigeyuki Hamori c a School of Finance, Zhongnan University of Economics and Law, 182# Nanhu Avenue, East Lake High-tech Development Zone, Wuhan P. R. China kudeyang@gmail.com, kudeyang@znufe.edu.cn b Graduate School of Economics, Kobe University 2-1 Rokkodai-cho, Nada-ku, Kobe, Hyogo Japan motegi@econ.kobe-u.ac.jp c (Corresponding author) Graduate School of Economics, Kobe University 2-1 Rokkodai-cho, Nada-ku, Kobe, Hyogo Japan hamori@econ.kobe-u.ac.jp 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. 1

2 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 2

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. 3

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. 4

5 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 5

6 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). 6

7 2. Methodology 2.1 Measuring systemic risk in the crude oil markets 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 r i,t be the return of asset i on day t. The GARCH MIDAS model is specified as follows: r i,t = μ i + m i,τ g i,t ξ i,t, t = (τ 1)N + 1,, τn, τ = 1,, T. (1) Note that g i,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: g i,t = (1 α i β i ) + α i (r i,t 1 μ i ) 2 m i,τ + β i g i,t 1. (2) We impose α i > 0, β i 0, and α i + β i < 1 in order to ensure g i,t > 0 and E[g 2 i,t ] <. 4 See Turhan et al. (2014) for an empirical application of GARCH-MIDAS models. 7

8 Define a monthly realized variance as the sum of N = 21 daily squared returns: τn 2 RV i,τ = t=(τ 1)N+1 r i,t. (3) We assume that m i,τ is determined by a polynomial of lagged realized variances: K m i,τ = m i + θ i v l=1 φ l (ω i v ) RV i,τ l, (4) where we use K v = 36 in accordance with Colacito et al. (2011), and we assume that m i > 0 and 0 < θ i < 1. We use the beta polynomial with parameter ω v i > 1 in order to capture decaying impacts of {RV i,τ 1,, RV i,τ Kv } on m i,τ : φ l (ω v i ) = (1 l/k v )ω v i 1 Kv (1 j/k v ) ω v i 1 j=1. (5) i The larger (smaller) value of ω v implies the faster (slower) decay of φ l (ω i v ). For each asset i, we compute maximum likelihood estimators of the parameters {μ i, α i, β i, θ i, ω i v, m i} based on the univariate Gaussian likelihood function. Using those estimators, we compute the standardized residual ξ i,t = (r i,t μ i )/ m i,τ g i,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 ξ i,t = (r i,t μ i )/ m i,τ g i,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 Q t = [q i,j,t ] i,j be an n n conditional covariance matrix at time t. The DCC-MIDAS specification is as follows: q i,j,t = ρ i,j,τ(1 a i,j b i,j ) + a i,j ξ i,t 1 ξ j,t 1 + b i,j q i,j,t 1, (6) K c ρ i,j,τ = φ l (ω i,j l=1 c )c i,j,τ l, (7) 8

9 c i,j,τ = τn k=(τ 1)N+1 ξ i,k ξ j,k τn ξ2 τn k=(τ 1)N+1 i,k ξ2 k=(τ 1)N+1 j,k. (8) We impose that a i,j > 0, b i,j > 0, and a i,j + b i,j < 1. The long-term correlation ρ i,j,τ is calculated as a weighted sum of K c lagged realized correlations. We use K c = 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 ρ i,j,t = q i,j,t q i,i,t q j,j,t. (9) We compute maximum likelihood estimators for the parameters {a i,j, b i,j, ω c i,j } based on the bivariate Gaussian likelihood function, and obtain estimated conditional covariance matrix {Q t} 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 r t i is implicitly defined as Pr(r i i t VaR α,t ) = α, where α (0,1) i is a given level of tail probability. VaR α,t represents a threshold that r t i exceeds with probability α. It can be computed from the estimated conditional variance of r t i via the GARCH-MIDAS model. The Conditional Value-at-Risk (CoVaR) of commodity market r t market given the crude oil price return, written as CoVaR market i α,β,t, is implicitly defined as Pr (r market market i t CoVaR α,β,t r i i t VaR α,t ) = β (10) 9

10 market i where β (0,1) is a given level of tail probability. CoVaR α,β,t represents, given r i i i t VaR α,t, a threshold that r t exceeds probability β. Given Eq. (10), market i CoVaR α,β,t takes negative values almost by construction. The larger (smaller) market i absolute value of CoVaR α,β,t 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 market i larger (smaller) negative value. CoVaR α,β,t can therefore be interpreted as a risk measure of commodity market. In particular, we set α = 5% as well as β = 5% in market i this paper. CoVaR α,β,t 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 CoVaR market i α,β,t in order to make discussions simpler. Actually, the absolute value form of systemic risk makes i us understand the changes in risk clearly. The higher the value of CoVaR α,β,t 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 market i. CoVaR α,β,t 10

11 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 2 j months in this paper. In particular, we consider Maximal Overlap Discrete Wavelet Transform 6 (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 2 J ). 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 h l = (h 1,0,, h 1,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: L 1 l=0 h 1,l = 0; L 1 l=0 h 2 1,l = 1; L 1 h 1,l h 1,l+2n = 0 l=0 for all non-zero integers n. Meanwhile, suppose g l = (g 1,0,, g 1,L 1,,0,,0) T to be 6 See Yang and Hamori (2015) for more details on MODWT. 11

12 the zero-padded scaling filter coefficients with the integration function of g 1,l = ( 1) l+1 h 1,L 1 l. When any sample size N is divisible by 2 j, wavelet coefficients, w j,t and scaling coefficients v j,t at levels j 1,, J can be defined as: w j,t = L 1 L 1 l=0 g lv j 1,t 1 modn and v j,t = l=0 h lv j 1,t 1 modn where wavelet g l is rescaled as g j = g j /2 j/2, and scaling filters is rescaled as h j = h j /2 j/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 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. 12

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 13

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 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 for commodity market, for WTI crude oil price, and 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 for commodity market, for WTI crude oil price, and 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; 14

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 , 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 15

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 {μ i, α i, β i, θ i, ω i v, m i} and their standard errors. For each commodity, all estimates except for μ i are highly significant. The point estimate of the beta polynomial parameter, ω i v, is for commodity market, for WTI crude oil price, and 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 {a i,j, b i,j, ω i,j c } and their standard errors. All estimates are highly significant for each pair. The point estimates of ω c i,j are for WTI crude oil price and 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 16

17 market i monthly CoVaR α,β,t 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 CoVaR market 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. 17

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. 18

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 19

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 longterm. 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 20

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: CoVaR market WTI and CoVaR market 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. 21

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 22

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 ). Appendix A1. Specifications of CoVaR market i We consider CoVaR α,β,t market i by standardizing CoVaR α,β,t relative to a benchmark condition where r t i is equal to or less than its conditional median. The market i median CoVaR 0.5,β,t is defined by, Pr (r market market i t CoVaR 0.5,β,t r i i t VaR 0.5,t ) = β (1a) 23

24 market i and thus, CoVaR α,β,t is defined as follows: CoVaR market i α,β,t = CoVaR market i market i α,β,t CoVaR 0.5,β,t (2a) market i CoVaR α,β,t 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: (r i t, r market (σ i t )~N (0, ( t ) 2 ρ t σ i market t σ t ρ t σ i market t σ t (σ market )) (3a) 2 t ) According to the properties of the multivariate normal distribution, the distribution of market return conditional on the crude oil return can be expressed as: r t market r t i ~N ( r t i σ t market ρ t σ t i, (1 ρ t 2 )(σ t market ) 2 ) (4a) Hereby, we can rewrite equation (10) to be: r market t r t i σ market t ρt σ i CoVaR α,β,t Pr [ t σ market t 1 ρ2 t market i r i tσt market ρt σ i t σ t market 1 ρ t 2 r i i t VaR α,t ] = β, (5a) 24

25 where r t market r t i σ t market ρt σ t i σ t market 1 ρ t 2 ~N(0, 1). Particularly, the crude oil VaR is given by i VaR α,t = Φ 1 (α) σ t i. Combining that, then we have CoVaR market i α,β,t = Φ 1 (β)σ market t 1 ρ 2 t Φ 1 (α)ρ t σ market t. (6a) Because Φ 1 (50%) = 0, equation (2a) can be solved for CoVaR market i α,β,t = Φ 1 (α)ρ t σ market t. (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. References Adrian, T., Brunnermeier, M.K., CoVaR. Am. Econ. Rev. 106, DOI: /aer Algieri, B., Leccadito, A., Assessing contagion risk from energy and non-energy commodity markets. Energ. Econ. 62, Bai, J., Ng, S., Evaluating latent and observed factors in macroeconomics and finance. J. Econometrics, 131(1-2),

26 Baur, D.G., The structure and degree of dependence: A quantile regression approach. J. Bank. Finan. 37, Beck, S., Autoregressive conditional heteroscedasticity in commodity spot prices. J. Appl. Econ. 16, Bloom, N., The impact of uncertainty shocks. Econometrica 77(3): Borri, N Local currency systemic risk. Emerging Markets Review, 34, Byrne, J.P., Fazio, G., Fiess, N., Primary commodity prices: Co-movements, common factors and fundamentals. J. Dev. Econ. 101, Calmès, C., Théoret, R., Bank systemic risk and macroeconomic shocks: Canadian and U.S. evidence. J. Bank. Finan. 40, Cashin, P., McDermott, C.J., Scott, A., Booms and slumps in world commodity prices. J. Dev. Econ. 69, Chen, X., Ghysels, E., Wang, F HYBRID-GARCH: A generic class of models for volatility predictions using high frequency data. Statistica Sinica, 25, Chuang, C.-C., Kuan, C.-M., Lin, H.-Y., Causality in quantiles and dynamic stock return volume relations. J. Bank. Finan. 33, Colacito, R., Engle, R.F., Ghysels, E., A component model for dynamic correlations. J. Econometrics. 164, Dhaene, G., Wu, J Mixed-frequency multivariate GARCH. Discussion Paper Series DPS16.12, Department of Economics, KU Leuven. Duca, M.L., Peltonen, T.A., Assessing systemic risks and predicting systemic events. J. Bank. Finan. 37, Engle, R.F., Ghysels, E., Sohn, B., On the economic sources of stock market volatility. New York University Working Paper. Engle, R., Rangel, J.G., The spline GARCH model for unconditional volatility and its global macroeconomic sources. Rev. Financ. Studies, 21,

27 Giglio, S, Kelly, B., Pruitt S., Systemic risk and the macroeconomy: An empirical evaluation. J. Finan. Econ. 119, Girardi, G., Ergün, A.T., Systemic risk measurement: Multivariate GARCH estimation of CoVaR. J. Bank. Finan. 37, Hansen, L.P., Challenges in identifying and measuring systemic risk, in: Brunnermeier, M., Krishnamurthy, A. (Eds.), Risk topography: Systemic risk and macro modeling. University of Chicago Press/NBER, Chicago, IL, Jin, Y., Zeng, Z., Banking risk and macroeconomic fluctuations. J. Bank. Finan. 48, Kara, E., Does US monetary policy respond to oil and food prices? J. Int. Money. Finan. 72, Kerste, M., Gerritsen, M., Weda, J., Tieben, B., Systemic risk in the energy sector Is there need for financial regulation? Energy Policy. 78, Kilian, L., 2008a. The economic effects of energy price shocks. J. Econ. Lit. 46(4), Kilian, L., 2008b. Exogenous oil supply shocks: How big are they and how much do they matter for the U.S. economy? Rev. Econ. Stat. 90, Kilian, L., Not all oil price shocks are alike: Disentangling demand and supply shocks in the crude oil market. Am. Econ. Rev. 99, Kilian, L., Explaining fluctuations in gasoline prices: A joint model of the global crude oil market and the U.S. retail gasoline market. Energy J. 31(2), Kilian, L., Oil price shocks: causes and consequences. Annual Review of Resource Economics 6, Koenker, R., Quantile regression. Econometric Society Monograph Series. Cambridge University Press, New York. Koenker, R., Bassett, Jr., G., Regression quantiles. Econometrica. 46,

28 DOI: / Lee, B.S., Li, M.-Y.L., Diversification and risk-adjusted performance: A quantile regression approach. J. Bank. Finan. 36, Lorusso, M., Pieroni, L., Causes and consequences of oil price shocks on the UK economy. Econ. Model. 72, DOI: /j.econmod Mallick, H., Mahalik, M.K., Sahoo, M., Is crude oil price detrimental to domestic private investment for an emerging economy? The role of public sector investment and financial sector development in an era of globalization. Energ. Econ. 69, Prokopczuk, M., Symeonidis, L., Simen, C.W., Variance risk in commodity markets. J. Bank. Finan. 81, Reboredo, J.C., Is there dependence and systemic risk between oil and renewable energy stock prices? Energ. Econ. 48, Reboredo, J. C., & Ugolini, A Systemic risk in European sovereign debt markets: A CoVaR-copula approach. J. Int. Money. Financ. 51, Silvennoinen, A., Thorp, S., Financialization, crisis and commodity correlation dynamics. J. Int. Fin. Mark. Instit. Money. 24, Stock, J.H., Watson, M.W Disentangling the channels of the recession, Brookings Papers on Economic Activity, the Brookings Institution. Turhan, M.I., Sensoy, A., Ozturk, K., Hacihasanoglu, E A view to the long-run dynamic relationship between crude oil and the major asset classes. Int. Rev. Econ. Finan. 33, Wang, G.-J., Jiang, Z.-Q., Lin, M., Xie, C., Stanley, H.E., Interconnectedness and systemic risk of China's financial institutions. Emerg. Mark. Rev. forthcoming. 28

29 Yang, L., Hamori, S., Interdependence between the bond markets of CEEC-3 and Germany: A wavelet coherence analysis. N. Am. J. Econ. Finan. 32, Yang, L., Motegi, K., Hamori, S Systemic risk and macroeconomic shocks:evidence from US agricultural commodity markets. Working paper. Yang, L., Tian, S., Yang, W., Xu, M., Hamori, S., Dependence structures between Chinese stock markets and the international financial market: Evidence from a wavelet-based quantile regression approach. N. Am. J. Econ. Finan. Forthcoming. 29

30 Table 1. Sample statistics of the daily log returns of commodity market and crude oil. Market WTI Brent Mean Std. Dev Skewness Kurtosis Prob(JB) # Observations 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. Canada France German Italy Japan UK US Inflation rates Mean Std. Dev Skewness Kurtosis Prob(JB) # Observations Industry production growth rates Mean Std. Dev Skewness Kurtosis Prob(JB) # Observations Notes: Prob(JB) means a p-value of the Jarque-Bera test for normality. The sample period is from January, 1998 to December,

31 Table 3. Sample statistics of monthly macroeconomic shocks. Canada France German Italy Japan UK US Inflation rates Mean Std. Dev Skewness Kurtosis Prob(JB) # Observations Industry production growth rates Mean Std. Dev Skewness Kurtosis Prob(JB) # Observations Notes: Prob(JB) means a p-value of the Jarque-Bera test for normality. The sample period is from January, 1998 to December, Table 4. Results of GARCH MIDAS Models for each commodity Market WTI Brent μ (1.336) (1.838) (2.018) Α (0.004) *** (0.003) *** (0.005) *** β (0.013) *** (0.004) *** (0.018) *** θ (0.007) *** (0.021) *** (0.005) *** ω v (2.404) *** (0.367) *** (2.722) *** m (0.063) *** (0.191) *** (0.077) *** Notes: The number of monthly lags for the MIDAS polynomial is K v = 36, which deletes the first = 756 daily observations. The effective sample size is therefore 6288, covering November 23, 1985 through December 29, Figures in the parentheses are standard errors. *** indicates significance at the 1% level. 31

32 Table 5. Results of Bivariate DCC MIDAS Models for commodity market and crude oil. WTI Brent A (0.005) *** (0.008) *** b (0.010) *** (0.089) *** ω c (0.193) *** (5.370) *** Notes: The number of monthly lags for the MIDAS polynomial is K c = 144, which deletes the first = 3024 daily observations. The effective sample size is therefore 4020, covering August 5, 2002 through December 29, Figures in the parentheses are standard errors. *** indicates significance at the 1% level. ** indicates significance at the 5% level. 32

33 Table 6. Individual systemic risks and inflation (output) shocks Median 20th pctl Difference Inflation shocks: CoVaR market WTI (-1) Canada France *** German *** ** Italy *** Japan *** * UK US ** Output shocks: CoVaR market WTI (-1) Canada *** * ** France ** *** German ** Italy *** Japan *** *** UK US ** Inflation shocks: CoVaR market BRENT (-1) Canada France * German *** *** Italy * Japan ** * UK US * Output shocks: CoVaR market BRENT (-1) Canada *** * France ** *** German *** *** Italy *** Japan *** *** UK US ** 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. 33

34 Table 7 Individual systemic risks and inflation (output) shocks for wavelet transform D1 Median 20th pctl Difference Inflation shocks: CoVaR market WTI (-1) Canada France ** *** German Italy Japan UK US *** Output shocks: CoVaR market WTI (-1) Canada France German Italy Japan UK * US Inflation shocks: CoVaR market BRENT (-1) Canada France ** *** German Italy Japan * * UK US *** Output shocks: CoVaR market BRENT (-1) Canada France German Italy Japan * UK US 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. 34

35 Table 8 Individual systemic risks and inflation (output) shocks for wavelet transform D2 Median 20th pctl Difference Inflation shocks: CoVaR market WTI (-1) Canada ** *** France *** *** German *** ** Italy Japan UK * ** US *** *** * Output shocks: CoVaR market WTI (-1) Canada France German Italy *** *** Japan UK US *** *** Inflation shocks: CoVaR market BRENT (-1) Canada ** *** France *** *** German *** ** Italy Japan UK * ** US *** *** Output shocks: CoVaR market BRENT (-1) Canada France * German Italy *** *** Japan UK US *** *** 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. 35

36 Table 9 Individual systemic risks and inflation (output) shocks for wavelet transform D3 Median 20th pctl Difference Inflation shocks: CoVaR market WTI ( 1) Canada France * German Italy 8.34E Japan *** ** UK E 05 US Output shocks: CoVaR market WTI ( 1) Canada * *** * France *** ** ** German Italy *** Japan UK US Inflation shocks: CoVaR market BRENT ( 1) Canada France German Italy Japan *** ** UK E 05 US Output shocks: CoVaR market BRENT ( 1) German Canada * *** France *** * ** Italy *** Japan UK US 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. 36

37 Table 10 Individual systemic risk and inflation (output) shocks for wavelet transform D4 Median 20th pctl Difference Inflation shocks: CoVaR market WTI ( 1) Canada *** *** France * *** German *** *** Italy *** Japan *** *** UK *** *** US *** *** Output shocks: CoVaR market WTI ( 1) Canada *** *** France *** *** German *** *** Italy *** *** Japan ** *** UK *** *** US Inflation shocks: CoVaR market BRENT ( 1) Canada *** *** France * *** German *** *** Italy *** Japan *** *** UK *** *** US *** *** Output shocks: CoVaR market BRENT ( 1) Canada *** *** France *** *** German *** *** Italy *** Japan * *** UK *** *** US 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. 37

38 Table 11 Individual systemic risks and inflation (output) shocks for wavelet transform D5 Median 20th pctl Difference Inflation shocks: CoVaR market WTI ( 1) Canada *** *** ** France *** *** German *** *** Italy *** *** Japan *** *** *** UK *** *** *** US *** *** ** Output shocks: CoVaR market WTI ( 1) Canada *** *** France *** *** ** German *** *** * Italy * *** Japan *** *** UK *** *** US Inflation shocks: CoVaR market BRENT ( 1) Canada *** *** *** France *** *** German *** *** Italy *** *** Japan *** *** *** UK *** *** *** US *** *** ** Output shocks: CoVaR market BRENT ( 1) Canada *** *** France *** *** ** German *** *** * Italy * *** Japan *** *** UK *** *** US 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. 38

39 Table 12 Individual systemic risks and inflation(output) shocks for wavelet transform D6 Median 20th pctl Difference Inflation shocks: CoVaR market WTI ( 1) Canada * *** 2.18E 05 France * German *** *** ** Italy ** ** Japan *** *** UK *** *** US *** *** Output shocks: CoVaR market WTI ( 1) Canada ** France German *** *** * Italy *** * Japan *** *** ** UK ** US *** *** Inflation shocks: CoVaR market BRENT ( 1) Canada ** *** France * German *** *** Italy *** ** Japan *** *** UK *** *** US *** *** Output shocks: CoVaR market BRENT ( 1) Canada ** France German *** *** Italy *** * Japan *** *** ** UK * US *** *** 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. 39

40 Table 13. Principle component analysis of systemic risk and macroeconomic shocks Median 20th pctl Difference Inflation shocks Raw *** D *** D ** *** D D *** *** D *** *** D *** *** Output shocks Raw *** *** D D D ** *** D *** *** D *** *** D *** *** * 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. 40

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. 41

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. 42

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. 43

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) 44

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. 45