Connectedness Among Economic Policy Uncertainties: Evidence from the Time and Frequency Domain Perspectives

Jinxin CUI; Huiwen ZOU

doi:10.21078/JSSI-2020-401-33

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Journal of Systems Science and Information ›› 2020, Vol. 8 ›› Issue (5) : 401-433. DOI: 10.21078/JSSI-2020-401-33

Connectedness Among Economic Policy Uncertainties: Evidence from the Time and Frequency Domain Perspectives

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Abstract

This paper investigates the frequency connectedness among economic policy uncertainties of G20 countries using the novel frequency connectedness proposed by Barunik and Krehlik (2018) which can depict the dynamic connectedness not only over time but also across different frequencies. The empirical results obtained in this paper demonstrate that, firstly, the connectedness among economic policy uncertainties is significant, and the spillover effects during the financial crisis and the postfinancial crisis period are stronger than the pre-financial crisis period. Secondly, the United States, France, and Australia are the main net-transmitters of the economic policy uncertainty spillovers while Brazil, Italy, Mexico, and Russia act as the main net-recipients of the spillovers. Thirdly, the major international events may significantly enhance the spillover transmissions of economic policy uncertainty among different countries, thus increasing the magnitude of the total connectedness. Finally, the economic policy uncertainty spillovers are mainly transmitted in the short term, i.e., 1~4 months instead of longer time horizons in terms of the magnitude of the frequency connectedness measures. The findings of this paper not only have profound theoretical and practical significance but also provide several significant implications for the policymakers, supervision agents, international traders, and various investors.

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economic policy uncertainty / frequency connectedness / spillover effects

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Jinxin CUI , Huiwen ZOU. Connectedness Among Economic Policy Uncertainties: Evidence from the Time and Frequency Domain Perspectives. Journal of Systems Science and Information, 2020, 8(5): 401-433 https://doi.org/10.21078/JSSI-2020-401-33

1 Introduction

During the past decades, major crisis events such as the "911" terrorist attack, the 1997 Asian financial crisis, the U.S. subprime crisis, European debt crisis, 2015 China's stock market crash, China-U.S. trade disputes, crude oil price collapse, and COVID-19 have further enhanced international political and economic uncertainties. As one of the specific manifestations of uncertainties, economic policy uncertainty (EPU) has presented significant impacts on the real economy such as investments, consumptions, employments, and domestic productions^[1-3]. It has been also widely considered as a key factor contributing to the weakness in global economic growth^[4]. Moreover, the EPU has made great influences on stock markets, bond markets, exchange rates, commodity prices, output, and inflation^[5]. Economic policy uncertainties in these major economies (such as G20 countries) have led to more significant risk spillovers to other developing economies and to poor performance in the real economic and financial markets^[6-9]. Thus, economic policy uncertainty has aroused the general concern of many governments and scholars.

The extant studies mainly concentrate on the impacts of the EPU on real economic or the prediction capability of the EPU. Several studies have also investigated the connectedness among economic policy uncertainties in different countries (or regions)^{[4, 5, 10-12]}. However, to the best of our knowledge, few studies to date have deeply analyzed the connectedness among economic policy uncertainties from time-domain as well as frequency-domain perspectives. Indeed, the interconnectedness among economic policy uncertainties may vary across different frequencies^[13]. This may be due to the heterogeneity of the multiple economic agents interacting in various markets^[14]. To be specific, market participants make their decisions on various time horizons (i.e., frequencies) ranging from seconds to several days, several months, even several years because their beliefs, risk tolerance ability, investment goals, preferences, institutional constraints are heterogeneous^[14]. For instance, the market participants with short investment horizons are more interested in the short-term operational states of the markets and make their decisions based on temporary conditions. Hence, their responses to the multi-scale economic shocks occur mainly in the short run^[14]. However, market agents with long-term investment horizons are more concerned about the long-term market performances and their reactions to market shocks mainly occur in the long-run. In addition, the economic shocks that transmit among different countries or regions may produce diverse frequency responses^[14]. Thus, it is reasonable and significant to reveal the frequency-domain features of the connectedness among economic policy uncertainties by using the novel frequency connectedness measurement and the findings may provide promising implications for global investors and regulators with diverse time-horizons in decision making.

To this end, this paper utilizes the frequency connectedness methodology proposed by Barunik and Krehlik^[15]. This method is the improved version of the spillover index methodology and connectedness framework proposed by Diebold and Yilmaz^[16-18] and it can quantify the magnitude and direction of the spillovers over time and across frequencies simultaneously. This novel method can not only depict the time-varying information spillovers but also provide different frequency domains from aggregate connectedness^[14]. Moreover, one can handle the connectedness among different variables on different short-, medium-, and long-term horizons (or frequency bands) by applying the frequency connectedness method^[19]. The frequency dynamic features of the connectedness are insightful since they enable one to better grasp the varying degree of persistence stemming from economic shocks with heterogeneous frequencies^[20] and can also identify the contribution of each frequency component in the total connectedness of the whole system^[21]. Thus, the frequency connectedness has been utilized by scholars to explore return and volatility connectedness among different financial markets, such as the studies [14, 19-26]. These fresh studies all demonstrate the effectiveness and superiority of this novel frequency connectedness methodology.

In general, this paper contributes to the literature in twofold: On the one hand, this paper is the first to depict the connectedness among economic policy uncertainties based on the novel frequency connectedness measurement from both the time-domain and frequency-domain perspectives. On the other hand, the directional connectedness networks are also documented in this paper. Moreover, we divide the whole sample period into three sub-samples (i.e., pre-financial crisis, financial crisis, and post-financial crisis period) to investigate the evolutions overtime of the directional net-pairwise connectedness networks. The empirical results obtained in this paper can not only provide valid evidence about how these economic policy uncertainties of different countries are connected within a VAR system, and how the connectedness changes with time evolution, but also can help people recognize which country is the main transmitter or recipient of the economic policy uncertainty spillovers at different time frequencies.

The key empirical conclusions obtained in this paper can be summarized as follows. Firstly, there exist significant information spillovers among economic policy uncertainties and the total spillover index is 47.55%. The frequency connectedness results demonstrate that the economic policy uncertainty spillovers are mainly transmitted in the short-term (i.e., 1~4 months) which occupied about 86% of the total connectedness. Secondly, the dynamic connectedness results present the significant time-varying features and the dates of the turning points are always consistent with the dates of major international events, implying that major international events may greatly enhance the connectedness.

Moreover, the United States, Australia, and France are the main net-transmitters of the economic policy uncertainty spillovers cause that the dynamic net spillover indices of them are always positive. Accordingly, Brazil, Italy, Mexico, and Russia are the main economic policy uncertainty spillover net-receivers cause that the dynamic net spillover indices of them are always negative. Finally, the connectedness during the financial crisis and post-financial crisis period are stronger than the pre-financial crisis period demonstrating that economic policy uncertainty shocks are more likely transmitted among different countries during the financial crisis and post-financial crisis period.

The remainder of this paper is structured as follows. A brief literature review is provided in Section 2. The methodologies applied in this paper are briefly introduced in Section 3. Section 4 displays the empirical results. The conclusions can be found in Section 5.

2 Literature Review

To quantify the spillover effects among financial markets, Diebold and Yilmaz^{[16, 17]} proposed the spillover index methodology based on the VAR model and variance decomposition technique. However, the VAR model is hard to interpret since there are too many parameters that need to be estimated. In addition, the order of the variables is hard to determine in advance. To solve this problem, Diebold and Yilmaz^[18] proposed the connectedness framework to quantify the spillover effects both numerically and graphically. Many studies have explored the connectedness among various financial markets based on this methodology, for example, crude oil, stock, and metal market^[27], carbon and energy markets^[28], global futures markets^[29], green investments^[30], oil and global assets indicators^[31], carbon and electricity power markets^[32], China's stock market sector indices^[33], China and London stock market^[34]. However, this connectedness method is not able to quantify the connectedness on the different frequency-domains. Barunik and Krehlik^[15] proposed a new measurement to depict the frequency dynamics (short-, medium- and long-term) of the connectedness. This novel methodology has been utilized to investigate the return and volatility connectedness in many studies, for instance, crude oil and Chinese sectoral equity markets^[14], oil and agriculture commodities^[19], energy, food, industry, agriculture and metals^[20], oil prices and clean energy stock returns^[21], energy futures markets^[22], renewable energy stocks and crude oil markets^[23], oil and gas markets^[24], U.S. Bitcoin and financial markets^[25], global crude oil markets^[26]. Given the verified effectiveness and superiority illustrated in this novel frequency connectedness method, we also utilize this method to investigate the frequency dynamics of the total, net, and net-pairwise spillover effects among economic policy uncertainties of G20 countries.

Generally, the existing literature on economic policy uncertainty can be divided into fourfold. Firstly, many studies have investigated the impacts that economic policy uncertainty has presented on real economics. For instance, Istiak and Serletis^[2] demonstrated that economic policy uncertainty is countercyclical and the effects of uncertainty shock on the real economic increase with size. Baker, et al.^[35] concluded that the economic policy uncertainty index can influence the intensity of economic recessions and subsequent recoveries. Huang, et al.^[36] analyzed the effect of economic policy uncertainty on China's housing market and concluded that the responses of real output to positive and negative economic policy uncertainty shocks are country-specific. In addition, Caldara, et al.^[37] studied the economic and financial shocks on macroeconomic and found that uncertainty shocks, especially those implied by uncertainty proxies are an important source of macroeconomic disturbances. Moore^[38] found that economic policy uncertainty has reduced investment and employment growth in Australia. Similarly, Caggiano, et al.^[39] studied the effects of economic policy uncertainty on unemployment in recessions and expansions and found that the economic policy uncertainty presents great shocks to the volatility of unemployment. Mumtaz and Surico^[40] concluded that the uncertainty about tax changes presents great impacts on real economic activities but the effects of spending and monetary policy uncertainty appear to be insignificant.

Another strand of literature studied the prediction capability of economic policy uncertainty. For example, Andre, et al.^[41] investigated whether economic policy uncertainty helps predict movements in real housing returns and concluded that economic policy uncertainty is useful not only for predicting future returns on housing-related investments but also for assessing related risks. Another similar research is presented in Christou, et al.^[42]. Tarassow^[43] examined the prediction performance of six different economic uncertainty variables for the growth of the real M2 and real M4. Liu, et al.^[44] proved that the economic policy uncertainty index can help to predict future volatility. Pastor and Veronesi^[45] investigated the forecasting ability of the effects of changes in government policy on stock prices. Kang and Ratti^[46] found that an increase in policy uncertainty has a negative effect on real stock returns. Moreover, Liu and Zhang^[47] examined the predictability of economic policy uncertainty to stock market volatility and concluded that the EPU index can significantly improve the prediction performance of the existing volatility prediction models. Balcilar, et al.^[48] investigated the predictability of economic policy uncertainty to stock return and its volatility of Hong Kong, Malaysia, and South Korea. Yu, et al.^[49] demonstrated that the global economic policy uncertainty index has significant predictive power for the volatility of the Chinese stock market.

Moreover, the relationships between economic policy uncertainty and the financial market have been also studied. For instance, Chiang^[50] studied the uncertainties and risks on excess stock returns G7 markets using monthly data. Jiang, et al.^[51] detected the nonlinear effect of economic policy uncertainty on the credit scale in China. Michael, et al.^[52] investigated the impact of economic policy uncertainty on aggregate bank credit growth in the United States. In addition, Guo, et al.^[53] examined the dependence of policy uncertainty and stock market returns in G7 and BRIC and concluded that economic policy uncertainty can reduce stock returns. Hu, et al.^[54] demonstrated that shocks in U.S. EPU significantly and negatively explain returns of Chinese A-shares with a lag of one week. Fang, et al.^[55] investigated the time-varying long-term correlation of U.S. stock and bond markets and found that the EPU index has a negative influence on the long-term stock-bond correlation.

Finally, the time-domain connectedness among economic policy uncertainties has been also studied recently. For example, Luk, et al.^[4] studied international spillovers of economic policy uncertainty and found large spillovers of uncertainty from major economies to Hong Kong. Kang and Yoon^[5] explored the dynamic connectedness networks among nine economic policy uncertainties and found that the EU is the largest net-transmitter of uncertainty connectedness and the Chinese EPU is an important contributor to the connectedness networks. Zhang and Chen^[1] utilized the spillover index proposed by Diebold and Yilmaz^[18] to study the dynamic spillovers among economic policy uncertainties. Liow, et al.^[56] investigated the economic policy uncertainty spillovers across seven major countries based on the connectedness approach. Wang and Yao^[57] applied the DCC-GARCH framework to study the economic policy uncertainty dynamic spillovers among China, UK, USA, and Japan. Moreover, several studies have been conducted based on a TVP-VAR connectedness method as 1) there is no need to arbitrarily set the rolling-window length; 2) there is no loss of empirical results of the rolling-window sample; 3) the empirical results are not sensitive to outliers^{[58, 59]}. For instance, Jiang, et al.^[10] applied a TVP-VAR method and found that both domestic and cross-country spillovers of China and the U.S. are mostly affected by bilateral trade, exchange rate, and investor sentiment. Antonakakis, et al.^[11] investigated the potential information spillover effects between the U.S., the E.U., the U.K., Japan, and Canada economic policy uncertainties by using a TVP-VAR framework. Similarly, Gabauer and Gupta^[12] examined the internal and external categorical economic policy uncertainty spillovers between the U.S. and Japan using a novel extension of the TVP-VAR connectedness approach.

Based on the existing literature, we find that economic policy uncertainty has been treated as a significant economic variable and studied in many studies in recent years. However, the aforementioned studies revealed the spillovers among economic policy uncertainties from a time-domain perspective. This paper differs from them in two respects. Firstly, we investigate the connectedness among economic policy uncertainties not only from the time-domain perspective but also from the frequency-domain perspective which can demonstrate how the economic policy uncertainty transmit among these countries on different frequencies. In addition, we divide the whole sample period into three sub-periods (i.e., pre-financial crisis, financial crisis, and post-financial crisis) to investigate the evolutions overtime of the net-pairwise connectedness networks. Thus, the findings obtained in this study can provide more beneficial evidence compared with the existing aforementioned research.

3 Methodology

3.1 Time-Domain Connectedness

In this paper, we utilized the method proposed by Diebold and Yilmaz^[16-18] to quantify the connectedness among economic policy uncertainties on the time domain. This method is established on a vector auto-regression model (VAR) model and variance decomposition technique which can reveal how much of the future uncertainty of variable

i

is caused by the shocks from the variable

j

. The methodology is briefly described as follows^{[1, 16, 17]}:

First of all, a VAR

(p)

model containing

n

variables and

p

lags is constructed as

\begin{aligned} X_{t} = Φ (L) X_{t} + ε_{t}, \end{aligned}

(1)

where

X_{t}

denotes an

n \times 1

vector of endogenous variables,

Φ (L) = \sum h Φ h L^{h}

is an

n \times n

p-th order lag polynomial matrix of coefficients,

L

represents the lag operator, and

ε_{t}

is a white noise error vector with zero mean and covariance matrix

Σ

. The moving average representation of Equation (1) can be given by

\begin{aligned} X_{t} = Ψ (L) ε_{t} = \sum_{i = 1}^{\infty} Ψ_{i} ε_{t - i} + ε_{t}, \end{aligned}

(2)

where

Ψ (L)

is an

n \times n

matrix of infinite lag polynomials.

Then, we can compute the generalized forecast error variance decomposition (FEVD) as

\begin{aligned} θ_{i j} (H) = \frac{σ_{j j}^{- 1} \sum_{h = 0}^{H} ((Ψ_{h} Σ)_{i j})^{2}}{\sum_{h = 0}^{H} (Ψ_{h} Σ Ψ_{h}^{'})_{i i}}, \end{aligned}

(3)

where

Ψ_{h}

represents an

n \times n

matrix of moving average coefficients,

σ_{j j}

is the

j

th diagonal elements of the

Σ

matrix, and

H

denotes the forecast horizon. As can be seen from the Equation (3), the

θ_{i j} (H)

is the contribution of the

j

th variable in the VAR system to the variance of forecast error of the

i

th variable at the

H

horizon. Since that

\sum_{j = 1}^{n} θ_{i j} (H) \neq 1

in the generalized VAR framework, the normalized effects of this contribution can be represented as

\begin{aligned} {\tilde{θ}}_{i j} (H) = \frac{θ_{i j} (H)}{\sum_{j = 1}^{n} θ_{i j} (H)} . \end{aligned}

(4)

Finally, based on the contribution ratio in the variance decomposition, the total spillover index, the directional spillover index, the net spillover index, and net-pairwise spillover index can be defined as:

\begin{aligned} S (H) = \frac{\sum_{\begin{matrix} i, j = 1 \\ i \neq j \end{matrix}}^{N} {\tilde{θ}}_{i j} (H)}{\sum_{i, j = 1}^{N} {\tilde{θ}}_{i j} (H)} \times 100 = \frac{\sum_{\begin{matrix} i, j = 1 \\ i \neq j \end{matrix}}^{N} {\tilde{θ}}_{i j} (H)}{N} \times 100, \end{aligned}

(5)

\begin{aligned} S_{\to i} (H) = \frac{\sum_{\begin{matrix} j = 1 \\ j \neq i \end{matrix}}^{N} {\tilde{θ}}_{i j} (H)}{\sum_{i, j = 1}^{N} {\tilde{θ}}_{i j} (H)} \times 100 = \frac{\sum_{\begin{matrix} j = 1 \\ j \neq i \end{matrix}}^{N} {\tilde{θ}}_{i j} (H)}{N} \times 100, \end{aligned}

(6)

\begin{aligned} S_{i \to} (H) = \frac{\sum_{\begin{matrix} j = 1 \\ j \neq i \end{matrix}}^{N} {\tilde{θ}}_{j i} (H)}{\sum_{i, j = 1}^{N} {\tilde{θ}}_{j i} (H)} \times 100 = \frac{\sum_{\begin{matrix} j = 1 \\ j \neq i \end{matrix}}^{N} {\tilde{θ}}_{j i} (H)}{N} \times 100, \end{aligned}

(7)

\begin{aligned} S_{i} (H) = S_{i \to} (H) - S_{\to i} (H), \end{aligned}

(8)

\begin{aligned} S_{i j} (H) = (\frac{{\tilde{θ}}_{i j} (H)}{\sum_{i, k = 1}^{N} {\tilde{θ}}_{i k} (H)} - \frac{{\tilde{θ}}_{j i} (H)}{\sum_{j, k = 1}^{N} {\tilde{θ}}_{j k} (H)}) \times 100 = (\frac{{\tilde{θ}}_{i j} (H) - {\tilde{θ}}_{j i} (H)}{N}) \times 100, \end{aligned}

(9)

where

S (H)

represents the total spillover index,

S_{\to i} (H)

and

S_{i \to} (H)

are both directional spillovers indices, the former denotes the total economic policy uncertainty spillovers form all the

j

th countries to

i

th country, and the latter denotes the total economic policy uncertainty spillovers form

i

th country to the

j

th country.

S_{i} (H)

is the net spillovers of

i

th country.

S_{i j} (H)

represents the net economic policy uncertainty spillovers from

j

th country to

i

th country.

3.2 Frequency-Domain Connectedness

Recently, Barunik and Krehlik^[15] proposed a novel frequency connectedness framework based on the spectral representation of variance decompositions. This new methodology can depict the frequency dynamics (the short-term, medium-term, and long-term) of the economic policy uncertainty connectedness. The frequency connectedness framework can be described as follows^[23]:

Firstly, following the methods applied in [60, 61], we apply the spectral decomposition methods to conduct the frequency connectedness framework, the frequency response function can be given as

\begin{aligned} Ψ (e^{- i h ω}) = \sum_{h = 0}^{\infty} e^{- i h ω} Ψ_{h}, \end{aligned}

(10)

where

ω

represents the frequency. Now, the power spectrum

S_{X} (ω)

can be defined as

\begin{aligned} S_{X} (ω) = \sum_{h = 0}^{\infty} E (X_{t} X_{t - h}) e^{- i h ω} = Ψ (e^{- i h ω}) Σ Ψ (e^{i h ω}) . \end{aligned}

(11)

Consequently, the generalized forecast error variance decomposition at a particular frequency

ω

can be calculated as

\begin{aligned} θ_{i j} (ω) = \frac{σ_{j j}^{- 1} \sum_{h = 0}^{\infty} (Ψ (e^{- i h ω}) Σ)_{i j}^{2}}{\sum_{h = 0}^{\infty} (Ψ (e^{- i h ω}) Σ Ψ (e^{i h ω}))_{i i}}, \end{aligned}

(12)

where

θ_{i j} (ω)

denotes the part of the spectrum of the

i

th variable at a particular frequency

ω

that can be attributed to shocks of the

j

th variable. In addition, the forecast horizon

H

doesn't play a critical role anymore cause that we utilize the unconditional GFEVD. The

θ_{i j} (ω)

in Equation (12) can be further standardized as

\begin{aligned} {\tilde{θ}}_{i j} (ω) = \frac{θ_{i j} (ω)}{\sum_{h = 1}^{n} θ_{i j} (ω)} . \end{aligned}

(13)

Then, the accumulative connectedness at an arbitrary frequency band

d = (a, b)

can be expressed as follows:

\begin{aligned} {\tilde{θ}}_{i j} (d) = \int_{a}^{b} {\tilde{θ}}_{i j} (ω) d ω . \end{aligned}

(14)

Finally, the overall connectedness within the frequency band

d

can be obtained as:

\begin{aligned} C^{d} = 100 \times \frac{\sum_{i = 1, i \neq j}^{n} {\tilde{θ}}_{i j} (d)}{\sum_{i j} {\tilde{θ}}_{i j} (d)} = 100 \times (1 - \frac{\sum_{i = 1}^{n} {\tilde{θ}}_{i i} (d)}{\sum_{i j} {\tilde{θ}}_{i j} (d)}) . \end{aligned}

(15)

The within from connectedness at frequency band

d

can be expressed as

\begin{aligned} C_{\to i}^{d} = 100 \times \sum_{j = 1, i \neq j}^{n} {\tilde{θ}}_{i j} (d) . \end{aligned}

(16)

The within to connectedness at frequency band

d

can be described as

\begin{aligned} C_{i \to}^{d} = 100 \times \sum_{j = 1, i \neq j}^{n} {\tilde{θ}}_{j i} (d) . \end{aligned}

(17)

The within net connectedness at frequency band

d

can be defined as

\begin{aligned} C_{i, n e t}^{d} = C_{i \to}^{d} - C_{\to i}^{d} . \end{aligned}

(18)

The net-pairwise connectedness at frequency band

d

can be represented as

\begin{aligned} C_{i j}^{d} = 100 \times ({\tilde{θ}}_{j i} (d) - {\tilde{θ}}_{i j} (d)) . \end{aligned}

(19)

It is necessary to be mentioned that the sum of all frequency connectedness is equal to the original total connectedness proposed by Diebold and Yilmaz^[17], i.e.,

S (H) = \sum_{d} {\tilde{C}}^{d}

4 Empirical Analysis

4.1 Data and Preliminary Analysis

The purpose of this paper is to investigate the frequency connectedness among economic policy uncertainties of different countries thus we take the index proposed by Baker, et al.^[35] as the proxy of the economic policy uncertainty. The G20 members include developed countries, developing countries, and emerging economies, which account for 90% of the world's gross domestic product and 80% of the world's total trade^[1]. Moreover, many studies^[62-64] have selected G20 members as a research sample, thus the economic policy uncertainties of G20 members in this paper are quite representative. Due to the availability of data, we finally obtain the EPU index dataset of 14 countries (Brazil, Australia, Mexico, Japan, the United Kingdom, Russia, India, Germany, Italy, France, Canada, South Korea, the United States, China). The dataset is collected on a monthly frequency basis from January 2003 to January 2019, with a total of 193 observations. All the data can be downloaded from the Economic Policy Uncertainty website: http://www.policyuncertainty.com. In addition, we calculate the logarithm difference sequence of each EPU index for the sake of further empirical analysis, i.e.,

r_{t} = \ln (P_{i . t} / P_{i, t - 1})

The raw data of economic policy uncertainties are plotted in Figure 1, and the descriptive statistics of the EPU logarithm difference sequence are presented in Table 1. It can be seen from Figure 1 that each EPU index shows the typical time-varying fluctuation feature. Moreover, the peak-point of the United Kingdom EPU index on July 2016 reached 1141, cause that on 24 June 2016, the United Kingdom held a referendum on whether to stay in the EU and the results showed that 52% of people agree, 48% object which was seen as a big "black swan" event that shocked the world. Similarly, by analyzing other economic policy uncertainty sequences, it can be found that international major events have a significant impact on the economic policy uncertainty indices. Moreover, the results in Table 1 show that all series satisfy the stationary condition according to the ADF and P-P unit root test results. From the values of the standard deviation, it can be seen that the fluctuations of the economic policy uncertainty indices of China, Brazil, Mexico, and Russia are relatively more severe.

Figure 1 Time evolutions for the time series of economic policy uncertainty index

Full size|PPT slide

Table 1 Descriptive statistics of EPU logarithm difference sequence

	Mean	Std.dev	Skewness	Kurtosis	JB	Q(20)	ADF	P-P
Brazil	0.002	0.510	0.002	0.016	0.002	36.481***	-12.512***	-40.015***
Australia	-0.001	0.395	-0.145	1.328***	14.794***	33.611***	-13.179***	-25.546***
Mexico	-0.008	0.496	0.483***	1.659***	29.487***	42.360***	-16.069***	-31.341***
Japan	0.001	0.197	-0.285	0.613*	5.602*	27.306***	-11.901***	-27.817***
United Kingdom	0.004	0.303	-0.101	-0.069	0.365	35.626***	-11.124***	-20.349***
Russia	0.008	0.587	-0.028	-0.064	0.057	48.874***	-12.355***	-55.029***
India	0.001	0.399	-0.186	1.104**	10.853***	42.569***	-16.836***	-32.895***
Germany	0.004	0.391	0.296*	0.081	2.848	28.325***	-19.573***	-34.944***
Italy	0.002	0.326	0.036	0.874**	6.150**	53.437***	-12.948***	-25.393***
France	0.003	0.375	0.068	0.613*	3.152	29.773***	-11.625***	-34.419***
Canada	0.003	0.268	0.255	0.175	2.322	18.097**	-17.278***	-21.951***
South Korea	0.001	0.324	0.327*	0.997**	11.370***	21.311***	-18.196***	-25.262***
United States	0.002	0.276	0.523***	1.410***	24.649***	27.411***	-11.749***	-24.615***
China	0.008	0.503	-0.044	0.663*	3.579	52.254***	-17.932***	-26.921***

Notes: The Jarque-Bera statistic tests for the null hypothesis of normality in sample distribution. Q(20) is the Ljung-Box statistics of the logarithm difference sequences for up to 20 order serial correlation. ADF and P-P are statistics of Augmented Dickey-Fuller and Pillips-Perron unit root tests based on the AIC criterion respectively. *, **, *** represent rejection at the 10%, 5% and 1% significance level respectively.

4.2 Static Connectedness Measures

To investigate the connectedness among economic policy uncertainties from the time-domain perspective, we primarily utilize the method proposed by Diebold and Yilmaz^[17]. Table 2 reports the static connectedness measures on the time-domain. The values illustrated in the second last row and last column in Table 2 denote the economic policy uncertainty spillovers that an individual market contributes (TO) or receives (FROM) totally in the whole economic system. The values in the last row represent the net connectedness of 14 countries. Other values in Table 2 are pairwise connectedness between one country and another country. The bold value in the bottom right corner is the total connectedness computed in the system. It is noticeable that the total connectedness is 47.55%, demonstrating a relatively strong information spillover among the selected economic policy uncertainties. Moreover, we find that the United States economic policy uncertainty makes the largest contribution to the overall connectedness in the system with a value of 5.42% which indicates that the United States economic policy uncertainty has a significant impact on the whole system. Interestingly, the United States is also the largest economic policy uncertainty receiver in the connectedness system with a value of 4.41%. This result is expected since that as one of the most developed and open countries in the world, the United States plays a vital leading role in the global economic system, and its economic fluctuations will have a negative impact on other countries and even the global economy. Therefore, it is necessary to guard against the uncertainty of the U.S. economic policy, track the economic operation of the U.S. in a timely manner, make early judgments, and establish relevant preventive measures. The bold values on the diagonals in Table 2 represent the proportion of economic policy uncertainty shocks that a country receives from its own. It is a remarkable fact that these values of developing countries are significantly higher than that of developed countries which is consistent with the conclusion obtained by Zhang and Chen^[1]. There may be two reasons for this phenomenon. On the one hand, compared with developed countries, the degree of openness of developing countries is relatively low, so the economic policy uncertainty shocks that developing countries received from outside markets are less than developed countries. On the other hand, in order to achieve rapid economic development, developing countries tend to implement more interventions in the economy^[1].

Table 2 Static Time-domain Connectedness

	Brazil	Australia	Mexico	Japan	UK	Russia	India	Germany	Italy	France	Canada	South Korea	USA	China	FROM
Brazil	64.27	3.08	0.62	2.13	1.07	3.91	1.16	3.00	4.55	4.67	3.72	2.23	3.58	2.01	2.55
Australia	1.92	42.11	2.30	5.60	5.73	2.42	7.06	4.06	2.02	4.56	7.01	4.49	7.11	3.60	4.14
Mexico	0.72	2.93	60.98	2.30	1.78	1.06	1.00	0.77	1.23	4.81	2.06	6.22	9.44	4.70	2.79
Japan	1.96	7.53	1.96	49.91	0.85	0.54	4.10	3.78	4.75	5.31	5.23	4.61	4.82	4.65	3.58
UK	1.13	7.68	1.24	4.09	49.11	2.17	1.33	6.16	3.49	6.20	6.50	3.61	5.53	1.75	3.63
Russia	2.11	0.56	1.53	1.35	0.50	82.37	3.81	0.72	0.49	0.67	0.99	1.55	0.83	2.53	1.26
India	1.46	5.44	1.88	4.46	1.96	3.13	57.33	4.07	2.17	4.17	2.11	4.57	3.33	3.91	3.05
Germany	1.75	6.38	1.14	4.49	5.94	0.72	3.24	43.67	2.24	9.55	6.13	5.60	6.58	2.56	4.02
Italy	0.37	1.23	4.25	5.32	3.51	0.63	1.36	4.11	62.46	6.14	4.27	2.35	2.14	1.86	2.68
France	3.16	4.38	2.32	5.64	4.98	0.42	0.98	8.05	4.82	42.56	6.07	6.94	7.46	2.22	4.10
Canada	1.72	6.79	1.74	5.11	5.17	0.79	3.51	6.41	4.16	7.84	39.77	4.33	10.10	2.55	4.30
South Korea	2.58	5.53	3.61	3.73	2.71	1.91	4.00	5.12	2.32	7.52	4.24	40.51	12.21	4.00	4.25
USA	2.86	7.57	5.01	4.34	4.01	1.04	2.46	5.89	1.72	6.18	8.20	10.60	38.23	1.89	4.41
China	3.56	3.56	3.76	5.58	1.49	0.83	2.18	1.33	1.45	3.97	2.12	6.47	2.71	60.99	2.79
TO	1.81	4.48	2.24	3.87	2.84	1.40	2.59	3.82	2.53	5.11	4.19	4.54	5.42	2.73	47.55
Net	-0.74	0.34	-0.55	0.29	-0.79	0.14	-0.46	-0.20	-0.15	1.01	-0.11	0.29	1.01	-0.06	TCI

Note: The column "FROM" indicates the total spillovers received by market

i

from all other markets. The row "TO" indicates the total spillovers transmitted by market

i

to all other markets. The row "Net" shows the net spillovers from market

i

to all other markets. "TCI" shows the value of the total connectedness.

To examine which country is the economic policy uncertainty spillover net-transmitter (or net-recipient), we also compute the net spillover of each country and display the numbers in the last row in Table 2. We can clearly distinguish that the United States, France, Australia, Japan, South Korea, and Russia act as the spillover net-transmitters while the United Kingdom, Brazil, Mexico, India, Germany, Italy, Canada, and China are spillover net-receivers. However, this conclusion is just obtained based on the computation results of the entire sample and it may change over time. Furthermore, the United States and the United Kingdom act as the biggest spillover net-transmitter and net-recipient respectively. Correspondingly, South Korea, Canada, and Mexico receive much more economic policy uncertainty spillovers from the United States. For one thing, Canada and Mexico geographically share a border with the United States and they all belong to the North American Free Trade Area (NAFTA). As a regional economic integration organization, the member countries of the NAFTA exhibit close economic exchanges and high economic correlations. For another thing, the United States is an important trade partner for Canada and Mexico and the trade among them is frequent. Thus the economic policy uncertainty is more easily transmitted from the United States to Canada and Mexico. As for South Korea, the United States is an ally of South Korea since the Korean War and South Korea's economic policy is largely influenced by the economic policy uncertainty of the United States. The connectedness between Chinese and Japanese economic policy uncertainty is also relatively high cause that China and Japan are geographically close to each other and share the frequent economic trade. China is also one of Japan's most important trading partners. In a word, the measurement of the time-domain connectedness over the whole sample can provide preliminary and static results of the total, net-pairwise, and net spillovers among economic policy uncertainties which can help people to better handle the spillover effects statically and roughly.

The time-domain connectedness method proposed by Diebold and Yilmaz^[17] lacks the ability to depict the connectedness on different frequencies (i.e., time scales). Therefore, we further investigate the connectedness from a frequency-domain perspective based on the methodology proposed by Barunik and Krehlik^[15]. Tables 3~5 clearly present the connectedness measurements at three different time horizons (i.e., short-term: 1~4 months, medium-term: 4~10 months, long-term: 10~inf months). The values in Tables 3~5 represent the same meanings as the values in Table 2. We can find that, firstly, the total spillovers among economic policy uncertainties at three time horizons are 40.88% (short-term), 4.64% (medium-term) and 2.03% (long-term) respectively and the results satisfy the condition that the sum of connectedness on three different frequencies is equal to the original time-domain total connectedness. Secondly, the short-term connectedness measurement is much larger than medium- and long-term connectedness, implying that the economic policy uncertainty spillovers among G20 countries are mainly transmitted in the short-run and just a few spillovers are transmitted in the medium- and long-term. Finally, the United States acts as a net-transmitter of economic policy uncertainty in the short run, but its net spillovers in the medium- and long-run have been drastically weakened. Moreover, the values decrease gradually from high frequency to low frequency, demonstrating that the total connectedness among economic policy uncertainties recedes from the short-term to the long-term. In addition, in the short-term, Brazil, the United Kingdom, and Mexico are the main spillover net-recipients, the United States, Australia and France are the main spillover net-transmitters while in the medium- and long-term, India changes to be the largest spillover net-receiver and Australia becomes the largest spillover net-transmitter, that is to say, the roles are not immutable which implying that the economic policy uncertainties of different countries play various roles on diverse time horizons. Besides, it is proven again that each country receives the most of the economic policy uncertainty spillovers from its own and this percentage of developing countries is significantly higher than developed countries on different time horizons. This can be explained by the fact that the economic exchanges between developed countries are closer than in developing countries. Moreover, the economic systems of developed countries are more open and effective than the economic systems in developing countries, and the ability to receive and process information is also stronger. In addition, the economic system of developing countries is relatively incomplete, and risk events occur frequently.

Table 3 Static frequency-domain connectedness (1 ~ 4 months)

	Brazil	Australia	Mexico	Japan	UK	Russia	India	Germany	Italy	France	Canada	South Korea	USA	China	From. ABS	From. WTH
Brazil	59.93	2.75	0.49	1.73	0.96	3.81	1.03	2.72	4.53	4.44	3.25	1.68	3.15	1.64	2.30	2.59
Australia	1.82	37.65	1.93	4.59	4.61	2.41	6.72	3.36	1.69	3.76	6.21	3.65	6.39	3.29	3.60	4.05
Mexico	0.67	2.33	56.72	2.11	1.64	1.05	0.97	0.73	1.07	4.22	1.72	5.12	8.54	4.43	2.47	2.78
Japan	1.78	5.94	1.59	43.52	0.58	0.53	3.72	3.12	3.99	4.39	4.31	3.92	4.13	3.97	3.00	3.38
UK	0.89	5.81	1.09	3.62	43.61	2.17	1.25	4.81	2.68	4.92	5.28	2.99	4.84	1.50	2.99	3.37
Russia	1.99	0.43	1.48	1.10	0.43	77.92	3.74	0.65	0.48	0.67	0.90	1.16	0.76	2.36	1.15	1.30
India	1.45	4.37	1.82	4.00	1.73	3.11	54.32	3.52	1.95	3.91	1.96	3.84	3.09	3.65	2.74	3.09
Germany	1.57	4.58	1.02	3.72	5.01	0.71	2.94	38.93	1.82	8.34	5.01	4.22	5.64	2.29	3.35	3.77
Italy	0.25	0.96	3.76	4.57	3.13	0.63	1.35	3.77	58.70	5.39	3.40	2.10	1.73	1.49	2.32	2.62
France	2.74	3.68	2.07	5.09	4.27	0.42	0.97	6.80	4.25	38.92	4.92	6.19	6.77	1.93	3.58	4.03
Canada	1.30	5.33	1.27	4.11	4.01	0.76	3.40	5.32	3.27	6.24	33.74	3.54	8.03	1.97	3.47	3.90
South Korea	2.53	4.28	3.25	3.50	2.14	1.91	3.94	4.43	1.76	6.65	3.29	35.80	10.93	3.38	3.71	4.18
USA	2.55	5.93	4.23	3.76	3.25	1.02	2.29	5.22	1.31	5.24	6.96	9.24	34.33	1.61	3.76	4.23
China	3.35	2.74	3.17	5.07	1.18	0.81	2.09	1.09	1.24	3.57	1.71	5.68	2.31	57.52	2.43	2.73
TO_ABS	1.64	3.51	1.94	3.36	2.35	1.38	2.46	3.25	2.15	4.41	3.50	3.81	4.74	2.39	40.88
TO_WTH	1.84	3.95	2.18	3.78	2.65	1.56	2.77	3.66	2.42	4.96	3.93	4.29	5.33	2.69		46.01

Table 4 Static frequency-domain connectedness (4 ~ 10 months)

	Brazil	Australia	Mexico	Japan	UK	Russia	India	Germany	Italy	France	Canada	South Korea	USA	China	From. ABS	From. WTH
Brazil	3.01	0.23	0.09	0.28	0.08	0.07	0.10	0.19	0.01	0.15	0.32	0.38	0.29	0.25	0.17	2.25
Australia	0.07	3.07	0.27	0.70	0.78	0.01	0.25	0.48	0.24	0.56	0.57	0.59	0.52	0.22	0.38	4.85
Mexico	0.04	0.42	2.98	0.13	0.10	0.00	0.02	0.03	0.11	0.42	0.23	0.77	0.63	0.19	0.22	2.85
Japan	0.12	1.08	0.26	4.41	0.18	0.01	0.27	0.45	0.52	0.65	0.66	0.48	0.50	0.48	0.40	5.22
UK	0.16	1.28	0.10	0.32	3.80	0.00	0.06	0.92	0.57	0.88	0.86	0.44	0.49	0.17	0.45	5.78
Russia	0.09	0.09	0.03	0.18	0.05	3.11	0.05	0.05	0.01	0.01	0.06	0.26	0.05	0.11	0.07	0.96
India	0.01	0.75	0.05	0.34	0.16	0.02	2.13	0.39	0.16	0.19	0.11	0.51	0.18	0.19	0.22	2.83
Germany	0.13	1.24	0.09	0.54	0.64	0.01	0.22	3.27	0.29	0.84	0.78	0.95	0.66	0.19	0.47	6.06
Italy	0.08	0.19	0.34	0.52	0.26	0.00	0.00	0.23	2.59	0.51	0.59	0.17	0.28	0.26	0.24	3.15
France	0.29	0.48	0.17	0.38	0.49	0.00	0.01	0.86	0.40	2.51	0.78	0.52	0.48	0.20	0.36	4.67
Canada	0.28	1.00	0.32	0.69	0.79	0.02	0.07	0.74	0.61	1.09	4.11	0.54	1.42	0.40	0.57	7.37
South Korea	0.04	0.87	0.26	0.17	0.39	0.00	0.05	0.49	0.38	0.61	0.66	3.27	0.89	0.43	0.37	4.84
USA	0.21	1.14	0.54	0.40	0.53	0.02	0.12	0.47	0.29	0.65	0.87	0.95	2.73	0.20	0.46	5.91
China	0.15	0.56	0.42	0.36	0.22	0.02	0.07	0.17	0.14	0.28	0.28	0.54	0.28	2.41	0.25	3.21
TO_ABS	0.12	0.67	0.21	0.36	0.33	0.01	0.09	0.39	0.27	0.49	0.48	0.51	0.48	0.23	4.64
TO_WTH	1.54	8.61	2.70	4.63	4.30	0.16	1.20	5.04	3.43	6.32	6.25	6.55	6.16	3.03		59.94

Table 5 Static frequency-domain connectedness (10 ~ Inf months)

	Brazil	Australia	Mexico	Japan	UK	Russia	India	Germany	Italy	France	Canada	South Korea	USA	China	From. ABS	From. WTH
Brazil	1.33	0.10	0.04	0.12	0.04	0.03	0.04	0.09	0.01	0.07	0.16	0.17	0.14	0.12	0.08	2.35
Australia	0.03	1.39	0.11	0.31	0.34	0.00	0.10	0.21	0.10	0.24	0.22	0.25	0.20	0.09	0.16	4.60
Mexico	0.02	0.18	1.28	0.05	0.04	0.00	0.01	0.01	0.05	0.17	0.11	0.34	0.27	0.08	0.10	2.79
Japan	0.05	0.50	0.11	1.98	0.08	0.00	0.11	0.21	0.23	0.28	0.27	0.21	0.20	0.20	0.17	5.12
UK	0.07	0.58	0.04	0.14	1.71	0.00	0.02	0.43	0.25	0.39	0.36	0.19	0.20	0.07	0.20	5.78
Russia	0.03	0.04	0.01	0.08	0.02	1.35	0.02	0.02	0.00	0.00	0.03	0.12	0.02	0.05	0.03	0.93
India	0.00	0.32	0.01	0.13	0.07	0.00	0.87	0.16	0.06	0.07	0.04	0.21	0.06	0.07	0.09	2.52
Germany	0.05	0.57	0.03	0.23	0.30	0.00	0.08	1.48	0.13	0.37	0.33	0.43	0.28	0.08	0.21	6.07
Italy	0.04	0.09	0.15	0.23	0.12	0.00	0.00	0.11	1.17	0.24	0.28	0.08	0.13	0.12	0.11	3.31
France	0.13	0.22	0.08	0.16	0.22	0.00	0.00	0.39	0.18	1.13	0.36	0.23	0.21	0.09	0.16	4.77
Canada	0.14	0.46	0.15	0.31	0.37	0.01	0.03	0.35	0.28	0.50	1.92	0.24	0.65	0.18	0.26	7.74
South Korea	0.01	0.38	0.11	0.07	0.18	0.00	0.01	0.20	0.17	0.25	0.29	1.44	0.39	0.19	0.16	4.72
USA	0.09	0.50	0.23	0.17	0.24	0.01	0.05	0.21	0.13	0.28	0.37	0.41	1.17	0.08	0.20	5.78
China	0.06	0.25	0.17	0.15	0.10	0.00	0.02	0.08	0.06	0.12	0.13	0.24	0.12	1.06	0.11	3.16
TO_ABS	0.05	0.30	0.09	0.15	0.15	0.00	0.03	0.18	0.12	0.21	0.21	0.22	0.20	0.10	2.03
TO_WTH	1.52	8.79	2.65	0.51	4.44	0.12	1.02	5.19	3.43	6.27	6.16	6.53	6.00	3.00		59.63

All in all, the numerical results obtained from the frequency connectedness table can help the policymakers, various economic supervision agents, international traders, and global investors to better handle the economic policy uncertainty spillover situations on the diverse time horizons and to make more rational and effective decisions accordingly. To sum up, the novel frequency connectedness methodology can provide much richer and deeper empirical analysis results compared with the time-domain connectedness measurement. However, the fact must be admitted is that the static connectedness measurement on the time- and frequency-domain are all estimated over the whole sample from a static view instead of a time-varying perspective. Thus, to obtain the dynamic connectedness measures on the time- and frequency-domain, we need to further apply the rolling window method to obtain the dynamic connectedness measurement results.

4.3 Dynamic Connectedness Measures

The above static connectedness measurements can provide valuable evidence and depict the total, net, and net-pairwise spillover effects from the time- and frequency-domain perspectives. However, the hypothesis that the VAR parameters remain unchanged over the entire sample period may be unreasonable because the linkages between economies are not static but change over time. Thus, it is highly necessary to investigate the dynamic evolutions of the connectedness over time, i.e. dynamic connectedness measures. Specifically, we utilize a rolling window method with a fixed length of 36 months (i.e., 3 years) to estimate the VAR system consisting of the selected economic policy uncertainty indexes. As shown in Figure 2, the dynamic total connectedness among economic policy uncertainties shows significant time-varying characteristics, ranging from almost 35% to 70%. Particularly, different from the total spillover effect of 47.55% obtained in the static connectedness results, the dynamic connectedness measures provide more valuable information, highlighting the significance and necessity of dynamic connectedness measurement. This phenomenon is probably due to the fact that the VAR model estimated over the whole sample may smooth the results when there is a time variation in the relationships between these variables^[24]. Specifically, if we split a sample into two parts and the length of each part is the same. The shocks to one variable may have a positive impact on another variable in the first sample. However, the impact caused by shocks may become negative with the same magnitude. Under this circumstance, if we estimate the VAR model in each sub-sample, the magnitude and direction of these impacts will be captured and the connectedness results will reveal the real spillovers situation. However, the VAR model estimated over the whole sample can't fully capture the relationship in each sub-sample but handle both sub-samples simultaneously. Thus, the positive and negative impacts originated from one variable to another variable will be averaged. Consequently, the magnitude of the connectedness detected in the whole sample is often significantly lower than that estimated in the sub-samples.

Figure 2 Total connectedness among economic policy uncertainties on the time domain

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Moreover, the peaks and troughs of the dynamic total connectedness are also worthy of our in-depth study. For example, before the financial crisis, total economic policy uncertainty connectedness witnessed a downward trend, ranging from 60.66% to 39.10%. However, when the financial crisis erupted in August 2007, the total connectedness increased rapidly from 39.10% to 52.39%. The euro debt crisis erupted in late 2009 also significantly increased the total EPU connectedness. Another similar example is that after the "2015 Chinese stock market crisis", the total connectedness increased rapidly from 37.61% to 68.18%. Other events like "presidential election", "geopolitical events", "terrorist attack", "trade friction and conflict" also present a significant impact on the total economic policy uncertainty connectedness. To sum up, the above findings imply that the major international events may enhance the economic policy uncertainty spillovers transmissions among different countries, and thus increase the magnitude of the total connectedness among economic policy uncertainties. With the further deepening of the trend of economic globalization and the continuous innovation of information technology, the economic connections between countries in the world are getting stronger and stronger. Once an extreme risk event occurs in one country, the negative impacts caused by economic policy uncertainty will quickly transmit to other countries through many channels, such as trade, investment, and financial markets, thus further enhancing the connectedness among economic policy uncertainties.

For the purpose of investigating the dynamic total connectedness from the frequency-domain perspective, we further decompose the total connectedness on three different frequencies and the graphical results are presented in Figure 3. Specifically, the blue shade represents the frequency total connectedness in the short-term (i.e., 1~4 months) while the red shade and yellow shades represent the medium-term (i.e., 4~10 months) and long-term (i.e., 10~inf months) total connectedness measurement. It is obvious that the magnitude of the short-term connectedness is much larger than the medium- and long-term connectedness implying that the markets process information rapidly thus the economic policy uncertainty shocks originated from one country to another country are transmitted mainly in the short-run. This result provides significant implications that a country's government should always pay persistent attention to the transmissions of economic policy uncertainties especially those spillovers transmitted at the high-frequency band (i.e., short-term component). To prevent the spillover effects of economic policy uncertainty from negatively affecting the domestic economy operation, the governments should quickly formulate relevant policies and introduce a series of countermeasures to hedge against those negative impacts on the short time-horizon. Certainly, the medium- and long-term economic policy uncertainty connectedness measurement also cannot be ignored.

Figure 3 Total connectedness among economic policy uncertainties on the frequency domain

Full size|PPT slide

After quantifying the total connectedness from the time- and frequency-domain perspectives, we focus on the directional EPU net connectedness of each country to identify the main economic policy uncertainty spillover net-transmitters and net-receivers. The time-varying directional net connectedness based on the time-domain method proposed by Diebold and Yilmaz^[17] is depicted in Figure 4. To expound more specifically, a positive value of the net directional spillover index indicates that the country in the system is a net-transmitter of economic policy uncertainty spillovers to all the other countries, i.e., spillover net-transmitter. On the contrary, the negative value of the net directional spillover index reveals that the country always receives the economic policy uncertainty spillovers from other countries, i.e., spillover net-recipient. As shown in Figure 4, the United States, Australia, and France are the main spillover net-transmitters because the dynamic net spillover indexes of them are always positive implying that the relevant changes in the economic policies of the United States, Australia, and France will present a certain impact on other countries. Accordingly, Brazil, Italy, Mexico, and Russia are the main economic policy uncertainty spillover net-recipients cause that the dynamic net spillover indexes of them are always negative. Besides, other countries such as Canada, India, the United Kingdom, and South Korea switch to be a spillover net-transmitter or net-receiver from time to time. In general, most of the developed countries always act as the economic policy uncertainty spillover net-transmitters while most of the developing countries mainly act as spillover net-recipients. This phenomenon can be explained by the following reasons. On one hand, in developed countries, the economic operation mechanisms are mature, the market mechanisms and the market systems are sound, the degree of economic internationalization is high, and the macro-economic control systems are relatively more perfect. Thus, the economic systems of developed countries are better able to withstand the risk shocks of external economic policy uncertainties. However, the market economies of developing countries are not developed enough and the operating mechanisms are not perfect, so they are weak to resist the negative impacts of external economic policy uncertainties. On the other hand, the economic policy uncertainty early warning mechanisms in developed countries are more developed than developing countries, so they can make a pre-judgment on the spillovers of external economic policy uncertainties and take forward-looking risk management measures. However, there is a little bit difference between this point and the static connectedness analysis results due to that the static connectedness is computed by the VAR estimated over the whole sample while the dynamic connectedness is obtained by the rolling window methodology. The former method may average the negative and positive spillovers while the latter is equivalent to estimate the VAR model in each sub-sample.

Figure 4 Net connectedness among economic policy uncertainties on the time domain

Full size|PPT slide

To explore the directional net connectedness on different time horizons (i.e., frequency domain), we further apply the methodology proposed by Barunik and Krehlik^[15] to conduct the frequency connectedness measures and the results are plotted in Figure 5. Similar to the conclusions obtained in previous total frequency connectedness, most of the net economic policy uncertainty spillovers are mainly transmitted at the high-frequency range (i.e., short-term). Moreover, the net connectedness measures are vulnerable to the impacts of major international events as well. For instance, before the financial crisis, the United States played the role of spillover net-receiver while once the financial crisis erupted, the United States switch to be the economic policy uncertainty spillover net-transmitter immediately. In particular, the magnitude of the spillovers that China receives from other countries become smaller and smaller while the magnitude of the spillovers that China transmits to the system becomes larger and larger implying that China's international influence is growing stronger thus the economic policy uncertainty of China may present a significant impact on other countries in the economic system. As the world's second-largest economy, China's voice in the international community is becoming stronger, China's trade with other countries is getting closer, and market mechanisms are constantly improving. Similarly, the net connectedness of South Korea was mostly negative before June 2011 but it became positive and the spillover magnitude gradually increased since then indicating that the connectedness among economic policy uncertainties of South Korea and other countries is getting stronger.

Figure 5 Net connectedness among economic policy uncertainties on the frequency domain

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For the sake of investigating the net-pairwise connectedness among economic policy uncertainties, we compute the net-pairwise spillovers between arbitrary two economic policy uncertainties. The net-pairwise connectedness measurement is shown in Figure 6. Considering the limited space in this paper, we just list the net-pairwise spillovers from the United States to other countries. We can clearly see that the net-pairwise connectedness between the economic policy uncertainties in the United States and another country presents the significant time-varying features and the values are positive in most of the sample which is consistent with the results obtained in net connectedness measures, indicating that the United States always act as the economic policy uncertainty spillover net-transmitter. With its unshakable international status, the United States constantly exerts pressure and impacts on the economies of other countries, so the uncertainty of its economic policies has an important impact on the economies of the world. Secondly, the values of the net-pairwise connectedness between the United States and another country during the financial crisis period are always positive implying that the financial crisis caused significant shocks from the United States to other countries. Interestingly, during the financial crisis, the net-pairwise spillover effect from the United States to China is inconspicuous demonstrating that the negative shocks of the financial crisis haven't presented a significant negative impact on China's economy. The reason may be that the Chinese government has introduced a host of important steps to tackle the international financial crisis including the "4 trillion RMB yuan fiscal stimulus plan". In addition, China's balance of payments capital projects have not yet fully opened up, the scale of asset securitization is still in its infancy, China has a large amount of foreign exchange reserves in 2008. Thus, the damage of the global financial crisis has been minimized in China. Moreover, the magnitude of the net-pairwise economic policy uncertainty spillovers from the United States to South Korea and Japan is relatively lager indicating that Japan and South Korea have received relatively more economic policy uncertainty shocks from the United States. This phenomenon can be explained by the fact that the United States is a longstanding ally of South Korea and Japan thus the domestic economy of South Korea and Japan are both largely influenced by the economic policy uncertainty of the United States. Another notable fact is that the magnitude of the net-pairwise spillovers from the United States to Mexico is the largest demonstrating that Mexico has been deeply affected by the economic policy uncertainty shocks from the United States which is consistent with the results obtained in the static connectedness measurement. This is due to the fact that Mexico is heavily dependent on the U.S. not only in international trade but also in the capital flow. Any small or great fluctuations in the U.S. economy will inevitably present a significant impact on Mexico's economy. Moreover, Mexico's economic system is not perfect enough, and its ability to resist external risks is still lacking.

Figure 6 Net-pairwise connectedness among economic policy uncertainties on the time domain

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Similarly, in order to study the net-pairwise connectedness from the frequency-domain perspective, we conduct the frequency connectedness measurement and plot the part of the computational results in Figure 7. The frequency connectedness results obtained in this section demonstrate that the net-pairwise connectedness between two countries is mostly transmitted on the high-frequency band (i.e., short-term: 1~4 months) indicating that the system processes the economic policy uncertainties quickly and the shocks are more easily transmitted between two countries in the short-run. This result is consistent with the conclusions obtained in the total and net connectedness measures. In addition, it is worth mentioning that the medium and low-frequency net-pairwise spillovers from the United States to South Korea and Germany are relatively more significant than other countries implying that there is a small part of the economic policy uncertainty net spillovers transmitting from the United States to South Korea and Germany in the medium- and long-term.

Figure 7 Net-pairwise connectedness among economic policy uncertainties on the frequency domain

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To sum up, firstly, dynamic connectedness measurement can provide richer information from the time-varying perspective than the static connectedness. Secondly, the dynamic total information connectedness among economic policy uncertainties presents significant time-varying features and it is easy to be affected by the shocks caused by the major international events. Moreover, the events which can bring about profound and tremendous negative impacts will significantly increase the total connectedness among economic policy uncertainties. Thirdly, the United States, Australia, and France act as the main economic policy uncertainty spillover net-transmitters while Brazil, Italy, Mexico, and Russia act as the main spillover net-recipients. Fourthly, the dynamic net-pairwise connectedness results demonstrate that the United States always acts as the economic policy uncertainty spillover net-transmitter and the spillover effects from the United States to other countries are relatively stronger during the financial crisis period. This finding highlights again the negative impact of the U.S. subprime mortgage crisis on the economies of other countries. Finally, the total, net, and net-pairwise frequency connectedness results all demonstrate that the economic policy uncertainty spillovers are mainly transmitted in the short-run indicating that the international market processes the information quickly thus economic uncertainty shocks are easily transmitted to other countries in the short-term.

4.4 Net-Pairwise Connectedness Network

We further depict the net-pairwise connectedness networks to shed light on the key net-transmitters and net-receivers of economic policy uncertainty shocks in a bivariate setting. Figure 8 plots the connectedness network graphs of the net-pairwise spillovers estimated based on the Diebold-Yilmaz methodology^[18] providing the intuitive and direct visualization of the magnitude of the net-pairwise connectedness. To be specific, the red nodes represent the spillover net-transmitters while the green nodes denote the spillover net-receivers and the size of the nodes represents the magnitude of the net spillover of each country's economic policy uncertainty. The directional arrows between arbitrary two nodes represent the net-pairwise economic policy uncertainty connectedness between arbitrary two countries. It should be noted that the color, color shade, and thickness of the edge arrows also measure the magnitude of the net-pairwise connectedness, i.e., the red color represents the highest level of connectedness while the blue and green represent the medium and lowest level of connectedness respectively. Moreover, we divide the whole sample period into three sub-samples (i.e., pre-financial crisis: From January 2003 to July 2007, financial crisis: From August 2007 to July 2012, post-financial crisis: From August 2012 to January 2019) to investigate the evolutions overtime of the net-pairwise connectedness networks.

Figure 8 Net-pairwise connectedness networks on the time domain

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Specifically, the first picture at the top left of Figure 8 represents the net-pairwise connectedness network over the whole sample. We can clearly see that the main spillover net-transmitters (i.e., the United States, France, Australia, Japan, and South Korea) are located in the center of the connectedness networks and the economic policy uncertainty connectedness among them is relatively stronger than other countries. Accordingly, the United Kingdom, Brazil, Mexico, and India are the main economic policy uncertainty spillover net-recipients. The remaining three pictures depict the net-pairwise connectedness networks during the pre-financial crisis, financial crisis, and post-financial crisis periods. Several important conclusions can be obtained from the remaining pictures. Firstly, it is obvious that the economic policy uncertainty spillovers during the financial crisis and post-financial crisis period are stronger than the pre-financial crisis period demonstrating that economic policy uncertainty shocks are more likely transmitted during the financial crisis and post-financial crisis period. Secondly, the United Kingdom and Mexico are always the economic policy uncertainty net-recipients while the United States, France, and South Korea always act as the same role of economic policy uncertainty net-transmitters during three sub-samples. Thirdly, Brazil and Canada act as the economic policy uncertainty net-recipients during the pre-financial crisis and post-financial crisis period but change their roles to be the spillover net-transmitters during the financial crisis period. Similarly, China and Germany play the roles of spillover net-transmitters during the pre-financial crisis and post-financial crisis period but they transform to be the spillover net-recipients during the financial crisis period. This phenomenon indicates that the economic policy uncertainties of different countries may change back and forth from one role to another during the different sample periods, implying that regulators and investors are supposed to consider the dynamics of the roles that each country plays according to the different market conditions in their decision making procedure. Finally, during the financial crisis period, the United States, Brazil, India, Canada, Australia, South Korea, and France act as the spillover net-transmitters while the United Kingdom, Mexico, Russia, Japan, China, Italy, and Germany act as the spillover net-recipients indicating that the latter seven countries are more easily affected by the economic policy uncertainties of the system. Moreover, before the financial crisis, India is the spillover net-receiver. However, it transforms to be the economic policy uncertainty spillover net-transmitter during the financial crisis and post-financial crisis period implying that the economic policy uncertainty of India presents a growing influence on other countries due to India's ongoing progress and economic development in recent years. India is one of the fastest-growing emerging economies and one of the top ten economies in the world. With its huge population advantage, India will see its economy take off in the next two decades, and the impacts of the economic policy uncertainty of India are growing quickly.

Figure 9 displays the net-pairwise connectedness networks on the frequency domain. As shown in these plots, according to the size of the nodes, the color and the thickness of the edge arrows on three different frequencies, we can conclude that the net-pairwise connectedness measures are much stronger at the high-frequency band (i.e., 1~4 months) than the medium (i.e., 4~10 months) and low-frequency band (i.e., 10~inf months) implying that the net-pairwise connectedness among different countries is also mainly transmitted in the short-run. What's more, the United States, France, and Japan act as the main economic policy uncertainty spillover net-transmitters while the United Kingdom, Mexico, and Brazil act as the main net-recipients of economic policy uncertainty spillovers at the high-frequency range. Moreover, we can clearly see that in the short run, the United States transmits the largest economic policy uncertainty spillover to Mexico. South Korea transmits the largest economic policy uncertainty spillover to Japan. As two major developed countries in Southeast Asia, Japan and South Korea have many economic links and their trade structures are also converging. Italy and Brazil are both net-recipients of economic policy uncertainties, but Italy transmits the largest net-spillovers to Brazil. Italy is a developed capitalist country and one of the four largest economies in Europe while Brazil is a developing country. To sum up, the net-pairwise connectedness networks can provide a more intuitionistic and direct visualization of the economic policy uncertainty net-pairwise spillovers.

Figure 9 Net-pairwise connectedness networks on the frequency domain

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4.5 Robustness Checks

In this section, we further conduct the robustness checks of our empirical results by examing the sensitivity of the estimated economic policy uncertainty connectedness measures to the selection of the rolling window sizes and the frequency bands. Specifically, we re-calculate the connectedness measures proposed by Diebold and Yilmaz^[17] based on three alternative rolling window lengths (i.e., 24, 36, and 48 months) and the results are plotted in Figure 10. In addition, the frequency connectedness measures of Barunik and Krehlik^[15] are also re-computed by choosing the different frequency bands (i.e., 1 ~ 2 months, 2 ~ 6 months, 6 ~ inf months; 1 ~ 6 months, 6 ~ 12 months, 12 ~ inf months) and the new frequency connectedness is plotted in Figures 11 and 12. As shown in Figure 10, the visual inspections of three economic policy uncertainty total connectedness measures based on different rolling window sizes clearly demonstrate that the estimated total spillover indices remain quantitatively and qualitatively uninfluenced by the selection of rolling window sizes, thus confirming the robustness of the initial empirical analysis results. Figure 11 reveals that the total connectedness on the high- and medium- frequency band (1~2 months and 2~6 months) occupies the most part of the original total connectedness. Figure 12 also illustrates that the total economic policy uncertainty connectedness is mostly transmitted on the high-frequency band (1 ~ 6 months). Thus, we can conclude based on Figures 11 and 12 that the total connectedness among economic policy uncertainties is mainly transmitted on the high-frequency range (i.e., short-term component) which is consistent with the results obtained in the former sections. All in all, by setting different rolling window sizes and frequency domains, we further confirm the robustness of the conclusions obtained in former sections based on the robustness check analysis.

Figure 10 Dynamic total connectedness with different rolling windows

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Figure 11 Dynamic total connectedness on the frequency domain-robustness check 1

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Figure 12 Dynamic total connectedness on the frequency domain-robustness check 2

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5 Conclusions

In this paper, we investigate the connectedness among 14 economic policy uncertainties from the time-domain as well as frequency-domain perspective synchronously. For this purpose, the novel frequency connectedness method proposed by Barunik and Krehlik^[15] which can be seen as the improved version of the time-domain spillover index methodology of Diebold and Yilmaz^[17] is applied in the empirical analysis. We finally obtain several significant conclusions based on empirical results. Firstly, the static connectedness measurements reveal that the connectedness among 14 economic policy uncertainties is significant with a value of 47.55%. Secondly, the momentous international events may greatly enhance the economic policy uncertainty spillover transmissions among different countries, thus increasing the magnitude of total economic policy uncertainty connectedness. Thirdly, the United States, France, and Australia act as the main spillover net-transmitters while Brazil, Italy, Mexico, and Russia are the main economic policy uncertainty spillover net-recipients. Further, the net-pairwise connectedness networks can provide a more intuitionistic and direct visualization, and the information spillovers during the financial crisis and the post-financial crisis period are stronger than the pre-financial crisis period. Finally, both the static and dynamic connectedness measurements demonstrate that the economic policy uncertainty spillovers are mainly transmitted in the short-term, i.e., less than 4 months, instead of medium or long time horizons in terms of the magnitude of the total connectedness, directional net connectedness, and directional net-pairwise connectedness measures. Last but not least, the robustness check results further validate the empirical findings obtained in this paper.

The conclusions obtained in this paper may provide significant implications for various economic supervision agents, international traders, and global investors. For one thing, since the connectedness among economic policy uncertainties is quite significant, economic supervision agents, international traders, and investors need to keep an eye on the economic policy uncertainty spillovers transmitted from other countries when making important decisions. For another thing, given the fact that Brazil, Italy, Mexico, and Russia are the main economic policy uncertainty spillover net-recipients, those countries need to develop their domestic real economic, improve the economic system and mechanisms, further enhance the ability to withstand the impact of external risks and maintain rapid and steady economic growth. In addition, global traders and investors ought to pay more attention to the economic policy uncertainties of the United States since it is the largest spillover net-transmitter. When the United States government changes the economic policy, they have to adjust their expectations in time to avoid the negative impact of shocks. What's more, supervision agents, international traders, and investors are supposed to concentrate more attention on the economic policy uncertainty spillovers transmitted in the short term (i.e., 1~4 months). Finally, the time-varying features illustrated in net connectedness also suggest that the policymakers, supervision agents, international traders, and global investors need to adjust their investment and management strategies from time to time according to the time-varying connectedness among different economic policy uncertainties.

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Funding

the National Natural Science Foundation of China(71573042)

the Natural Science Foundation of Fujian Province(2017J01794)

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Abstract
Key words
Cite this article
1 Introduction
2 Literature Review
3 Methodology
3.1 Time-Domain Connectedness
3.2 Frequency-Domain Connectedness
4 Empirical Analysis
4.1 Data and Preliminary Analysis
Figure 1 Time evolutions for the time series of economic policy uncertainty index
Table 1 Descriptive statistics of EPU logarithm difference sequence
4.2 Static Connectedness Measures
Table 2 Static Time-domain Connectedness
Table 3 Static frequency-domain connectedness (1 ~ 4 months)
Table 4 Static frequency-domain connectedness (4 ~ 10 months)
Table 5 Static frequency-domain connectedness (10 ~ Inf months)
4.3 Dynamic Connectedness Measures
Figure 2 Total connectedness among economic policy uncertainties on the time domain
Figure 3 Total connectedness among economic policy uncertainties on the frequency domain
Figure 4 Net connectedness among economic policy uncertainties on the time domain
Figure 5 Net connectedness among economic policy uncertainties on the frequency domain
Figure 6 Net-pairwise connectedness among economic policy uncertainties on the time domain
Figure 7 Net-pairwise connectedness among economic policy uncertainties on the frequency domain
4.4 Net-Pairwise Connectedness Network
Figure 8 Net-pairwise connectedness networks on the time domain
Figure 9 Net-pairwise connectedness networks on the frequency domain
4.5 Robustness Checks
Figure 10 Dynamic total connectedness with different rolling windows
Figure 11 Dynamic total connectedness on the frequency domain-robustness check 1
Figure 12 Dynamic total connectedness on the frequency domain-robustness check 2
5 Conclusions
References
Funding

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2019-07-31	2020-05-09	2020-10-25
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Abstract

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1 Introduction

2 Literature Review

3 Methodology

3.1 Time-Domain Connectedness

3.2 Frequency-Domain Connectedness

4 Empirical Analysis

4.1 Data and Preliminary Analysis

Figure 1 Time evolutions for the time series of economic policy uncertainty index

Table 1 Descriptive statistics of EPU logarithm difference sequence

4.2 Static Connectedness Measures

Table 2 Static Time-domain Connectedness

Table 3 Static frequency-domain connectedness (1 ~ 4 months)

Table 4 Static frequency-domain connectedness (4 ~ 10 months)

Table 5 Static frequency-domain connectedness (10 ~ Inf months)

4.3 Dynamic Connectedness Measures

Figure 2 Total connectedness among economic policy uncertainties on the time domain

Figure 3 Total connectedness among economic policy uncertainties on the frequency domain

Figure 4 Net connectedness among economic policy uncertainties on the time domain

Figure 5 Net connectedness among economic policy uncertainties on the frequency domain

Figure 6 Net-pairwise connectedness among economic policy uncertainties on the time domain

Figure 7 Net-pairwise connectedness among economic policy uncertainties on the frequency domain

4.4 Net-Pairwise Connectedness Network

Figure 8 Net-pairwise connectedness networks on the time domain

Figure 9 Net-pairwise connectedness networks on the frequency domain

4.5 Robustness Checks

Figure 10 Dynamic total connectedness with different rolling windows

Figure 11 Dynamic total connectedness on the frequency domain-robustness check 1

Figure 12 Dynamic total connectedness on the frequency domain-robustness check 2

5 Conclusions

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References

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Footnotes

Funding