Bertrand Candelon
email: candelonb@gmail.com

Laurent Ferrara
email: laurent.ferrara@banque-france.fr

Marc Joëts
email: marc.joets@banque-france.fr

Monica Billio

Celso Brunetti

Laura Kodres

Alessandro Galesi

Christophe Hurlin

Georges Kapetanios

Chiara Scotti

Global …nancial interconnectedness: A non-linear assessment of the uncertainty channel

Keywords: JEL Classi…cation: G15, C31, D84 Financial markets, Network interconnectedness, Uncertainty, Non-linear model

) by allowing for non-linear e¤ects through the estimation of a non-linear Threshold VAR model whose regimes depend on the level on uncertainty. Results clearly show that high uncertainty tends to generate more connectedness among equity indexes of a set of advanced and emerging countries. From an economic policy point of view, this result suggests that in the presence of high uncertainty, an adverse …nancial shock in a speci…c country is likely to propagate more widely and more strongly to the whole …nancial system. This result advocates for a close real-time monitoring of uncertainty measures.

Introduction

The di¤usion of a …nancial crisis is one of the greatest fear among international …nancial authorities. The last Global Financial Crisis has made clear that looking at …nancial institutions in isolation gives an incomplete and misleading assessment of the impact of shocks to the …nancial system. Indeed, even a country with strong macroeconomic fundamentals can be hit by a negative …nancial shock stemming from other countries and experience severe …nancial turmoil.

In this respect, a recent economic literature has investigated …nancial contagion in the form of networks by looking either at contractual agreements between banks or equity stock market comovements (see Braverman and Minca 2014, Acemoglu et al. 2015, and Brunetti et al. 2015 among others). [START_REF] Acemoglu | Systemic Risk and Stability in Financial Networks[END_REF] In this literature, …nancial networks are mainly established between banks or mutual funds and are often considered as self-organized without accounting for the in ‡uence of external forces. Another strand of the literature, without using any explicit network structure, tries to analyze the channel through which …nancial disruption is likely to spread across the world. For example, Glick and Rose (1999) and Weber and van Rijckenghem (2001) highlight the role of trade channel and …nancial ‡ows. Other studies have also stressed that uncertainty also constitutes a channel for markets connectedness (see Kaminsky and Reinhart 2000, Rigobon and Wei 2003, Kannan and Köhler-Geib 2009). They show that …nancial contagion is quicker and stronger when it has not been anticipated by …nancial markets. In the same vein, Kodres and Pritsker (2002) theoretically demonstrate that investors reallocate their portfolio positions given the uncertainties around the expected future macroeconomic state.

Our paper aims at bridging the gap between the literature on uncertainty and the one on connectedness. On the one hand, we evaluate connectedness among international …nancial markets using a network approach. On the other hand, we investigate uncertainty as a potential channel shaping interconnections between markets. Unlike the traditional network literature, this paper is more macro-oriented since we look at contagion between countries (i.e. equity indexes) rather than between speci…c classes of assets. This framework seems to be more suitable when looking at global systemic risk and the e¤ects of exogenous macroeconomic shocks on the pattern of connections. Regarding exogenous factors our assumption goes to the role that incomplete information about future outcomes (i.e. forecasting errors) plays on …nancial actors.

Correctly anticipating future …nancial or macroeconomic outcomes is related to the concept of uncertainty. Although de…nitions of uncertainty are generally unspeci…c, a widely accepted de…nition is given by Knight (1921), who distinguishes between risk, described as a situation in which the probability distribution over a set of events is known, and uncertainty, a situation in which people are unable to forecast the likelihood of events happening (see also Bloom 2014, for a review on this topic). In this article, we refer to this de…nition of uncertainty and assume that the ability to correctly anticipate future state of the economy is directly given by the degree of uncertainty. However, as uncertainty is an unobservable variable, various empirical measures have been proposed in the recent literature, ranging from …nancial uncertainty, measured by market volatility, through macroeconomic uncertainty, as proposed for example by Jurado et al. (2015) and Scotti (2016), to economic policy uncertainty, as de…ned by Baker et al. (2016). [START_REF] Adamic | Trading Networks[END_REF] In the empirical part of this paper, we will use various measures of uncertainty to check the robustness of our results.

In order to focus on the role of uncertainty on …nancial networks we exclude other propagation mechanisms. In particular, we exclude the e¤ect of international currency markets or other types of ‡ows in the propagation mechanisms. The aim of this paper is threefold: (i) investigate empirically interconnectedness between international …nancial markets, (ii) evaluate …nancial network stability over time and (iii) test for …nancial system resilience to uncertainty shocks. economies, the US being the main driver, while emerging countries appear much less …nancially interconnected. In addition, although China is often considered as a regional leader, our results do not support the view that it is a global driver of …nancial interconnectedness, at least over the considered period of time.

Then, by allowing for non-linearity, we get that the degree of connectedness within the global …nancial system is stronger when uncertainty is high, and conversely. This …nding is supported regardless of the proxy for uncertainty used. This is in line with our intuition. Second, within the linear system of 13 countries, we identify the US and the UK as net givers to the system; China and Germany are rather neutral, while all other countries are net receivers. However, when allowing for regime-switching in uncertainty, only the roles of Germany and China become ambiguous, depending on the nature of uncertainty. For example, in the case of high (US) macroeconomic uncertainty, both countries become net givers to the system (as well as France), indicating that both countries gain importance as drivers of the …nancial system during troughs in the US business cycle. This re ‡ects the pivotal role of those countries in the global …nancial system when the US economy falls into recession. Furthermore, when Economic Policy Uncertainty (EPU) in Europe is in its high regime, Germany shifts from a position of net giver to net receiver, pointing out its nodal role in Europe.

These results have potential practical implications. First, it may be useful for …nancial regulators to better evaluate the potentially contagious (and thus systemic) features of a particular crisis by integrating a monitoring of uncertainty measures. Moreover, the results represent a strong call for …nancial regulators and authorities to implement adequate policies to limit uncertainty. For example, …nancial regulations intended to guarantee the stability of the banking system reduce uncertainty and hence are likely to limit the transmission of a crisis. Reducing uncertainty can also be achieved by maintaining predetermined or pre-announced rules rather than applying discretionary policies. On the contrary, we can infer from our results that the persistently high level of economic policy uncertainty in Europe linked to the Brexit negotiations is likely to constitute a favorable environment for a …nancial shock to spread more widely, especially because the UK has been characterized as a net giver to the global …nancial system.

The paper proceeds as follows. The second section reviews some papers on network interconnectedness literature, with particular emphasis of the role of uncertainty on network stability. Our empirical strategy relying on Diebold and Yilmaz (2009, 2014) is presented in section 3. Data and uncertainty measures are presented in section 4, whereas section 5 reports the empirical results. Section 6 presents robustness checks and additional results. It performs sensitivity analysis to model speci…cation and time horizon, then achieves a geographical analysis using the novel database of Scotti (2016) and investigates the speci…c consequences of the Brexit. We draw some conclusions and tentative policy recommendations in section 7.

Network interconnectedness 2.1 Literature review

Since the seminal paper of Allen and Gale (2000), network structures have become a suitable framework to evaluate contagion in interconnected …nancial systems. In the network literature, …nancial interconnectedness is usually de…ned as a broad set of relationships among …nancial markets participants. [START_REF] Adrian | Liquidity and Leverage[END_REF] The nature of the relationships can widely vary from direct contractual agreements such as those stemming from interbank lending and borrowing (i.e. physical trading networks) to economic connections through common assets holding [START_REF] Aizenman | Monetary Policy Spillovers and The Trilemma in The New Normal: Periphery Country Sensitivity to Core Country Conditions[END_REF] inferred from market price data (i.e. correlation networks of stock prices).

From a technical point of view, the former approach is usually based on balance sheets of banks or mutual funds while the latter is inferred from equity stock returns (see Kara et al. 2015). From an economic point of view, it is by now generally accepted in the literature that correlation networks are the main source of systemic risk among …nancial institutions since interconnectedness is driven by common factors (see Elsinger et al. 2006, Braverman and Minca 2014, and Brunetti et al. 2015 among others). [START_REF] Aizenman | The Transmission of Federal Reserve Tapering News to Emerging Financial Markets[END_REF] Focusing on equity market returns, our paper is related to the correlation network literature on which contagion mechanism between participants may work as follows. Consider two institutions A and B that each holds the same asset in their portfolios. Suppose now that an exogenous shock (whatever its origin [START_REF] Alfaro | The …nance-uncertainty multiplier[END_REF] ) forces institution A to liquidate the asset, the price of the asset will decline and modify the value of the portfolio of the other institution B generating networks between institutions. Of course, the origin of the exogenous shock may be common to all participants and su¢ ciently larger to a¤ect all institutions simultaneously forcing A and B to liquidate the asset and rebalancing their portfolios. Our focus on market returns rather than accounting framework is further motivated by the desire to incorporate the most current market information to investigate …nancial interconnectedness (see Billio et al. 2012 for that point).

On this burgeoning literature on correlation network, most papers are focused on microeconomic interconnectedness …nancial systems such as those occurring between …rms in a speci…c country. Braverman and Minca (2014) for instance investigate how interrelations between US equity mutual fund are generated by common asset holdings and liquidity shocks. They further develop a vulnerability index that equals to the sum of funds's exposures through common as- [START_REF] Adrian | Liquidity and Leverage[END_REF] While a number of research papers usually looked at bank interconnectedness, participants can be of di¤erent natures such as institutions, countries, …rms, etc. [START_REF] Aizenman | Monetary Policy Spillovers and The Trilemma in The New Normal: Periphery Country Sensitivity to Core Country Conditions[END_REF] This form of contagion occurs via transmission of shocks such as a sudden drop in the ‡ow of revenues to one bank which a¤ects other institutions connected to it through …nancial linkages (see Cabrales et al. 2015 for a discussion). [START_REF] Aizenman | The Transmission of Federal Reserve Tapering News to Emerging Financial Markets[END_REF] Brunetti et al. (2015) investigate both physical and correlation networks between European interbank markets and shows that during the recent crisis period, physical network connectedness dropped signi…cantly while correlation networks increased. [START_REF] Alfaro | The …nance-uncertainty multiplier[END_REF] By de…nition, the shock should be su¢ ciently larger to force the institution to liquidate the asset and generate contagion (see Puliga et al. 2014).

set holdings to other funds. They …nd that the index is useful in predicting returns in periods of mass liquidations. In the same vein, Cont and Wagalath (2011) develop a simple tractable model to investigate the impact of "…re sales" on variance and correlation of mutual fund assets. [START_REF] Allen | Financial Contagion[END_REF] By decomposing realized covariance into a fundamental and a liquidity-dependent component, they show that excess covariance leads to endogenous risk for large portfolios during …nancial and economic turmoil limiting the bene…ts of diversi…cation when needed. In the spirit of Allen and Gale (2000) on the bene…t of interconnectedness on …nancial stability8 , Cabrales et al. ( 2014) investigate the trade-o¤ between higher risk-sharing and greater exposure to contagion when the connectivity increases. The idea of the paper is to study how the capacity of the system to absorb shocks depends on the pattern of interconnections among …rms. They show that contagion among …rms, as a pathologic disease, originates from an exchange of asset among them (i.e. portfolio reallocation). Overall the literature claims that, by holding similar portfolios, institutions are necessarily dependent and exposed to the same exogenous …nancial and economic shocks. [START_REF] Bech | The Topology of the Federal Funds Market[END_REF] The origin of the exogenous shock at a microeconomic level may be of several forms such as leverage targeting (see Unlike previous papers that focus on banks, …rms or insurances, we take a more global perspective by assuming that correlation networks between risky assets corresponds to an individual country's entire asset market (i.e. equity index). In this framework, the contagion mechanism from one equity market to others re ‡ects contagion between countries. Network interconnectedness here indicates global …nancial connection between countries whatever the composition of the considered equity indices. Our assumption is that this framework is more suitable to evaluate macroeconomic systemic risk rather than interconnectedness at microeconomic level especially in case of macroeconomic exogenous shocks.

Uncertainty shocks and network stability

While previous research assumes static network overtime, it turns out that the topology of …nancial markets interconnections may evolve dynamically. It means that interconnections among assets at a given date are not necessarily the same at another one. Against this background, Billio et al. (2016) have recently proposed a statistical approach based on Granger causality and MS-GARCH to deal with such dynamic networks. Treating network as information di¤usion, they show that some structures inherent to the system, such as the number of connections among stock exchanges and their associated strengths, are regime-dependent. The dynamic of …nancial markets networks is however assumed to be endogenous in the sense that instability of the system emerges without any external shocks. This assumption leaves aside the question of the di¤usion of exogenous shocks on the network stability, while external forces may shape the resilience of the network structure.

As regards exogenous factors, evidence recently blossomed as regards the role of uncertainty about the future state of the economy as a driver of macroeconomic and …nancial ‡uctuations. At a macroeconomic level, the e¤ect of uncertainty has been widely documented in the economics literature, especially with respect to the mechanism whereby it a¤ects growth and investment, which has been extensively discussed both theoretically and empirically (see Bloom 2014, and Ferrara et al. 2017, for a review). Overall, studies generally agree that high uncertainty gives …rms an incentive to delay investment and hiring under the irreversibility condition or …xed costs through an option value to wait (see Bernanke 1983, Bloom et al. 2007, and Bloom 2009, 2014).

In the …nancial markets literature, while theoretical studies have highlighted that uncertainty constitutes a propagation channel for …nancial connections (see Kodres and Pritsker 2002, Kaminsky et al. 2003, Rigobon and Wei 2003, and Mondria and Quintana-Domeque 2012, inter alii) little empirical evidence exists. [START_REF] Bernanke | Irreversibility, Uncertainty, and Cyclical Investment[END_REF] It is supposed that uncertainty in ‡uences investors'behaviors leading them to re-allocate their portfolio positions, amplifying thus …nancial markets contagion (see Kodres and Pritsker 2002, and Connolly et al. 2005). Uncertainty not only changes economic agents behaviors, but it is also a huge shock to the system on itself since it is often counter-cyclical. Yet, as stressed by Allen and Gale (2000), it turns out that highly interconnected networks are more resilient to small exogenous shocks but not to large ones. This means that a large shock is likely to shift a well interconnected system to another equilibrium. In this paper, we empirically investigate the role that uncertainty can have on network stability. Speci…cally, we assess to what extent the level of uncertainty is likely to shape the connectedness of international …nancial markets.

Measures of connectedness: The Diebold-Yilmaz network index

In the network literature, to evaluate the …nancial interconnectedness between equity markets one needs to analyze the structure of the connected systems such as nodes, edges, degree, and diameter. [START_REF] Billio | Econometric Measures of Connectedness and Systemic Risk in the Finance and Insurance Sectors[END_REF] In this paper, we rely on econometric time series modelling to compute the structure of equity markets network. [START_REF] Billio | Clustering in Dynamic Causal Networks as a Measure of Systemic Risk on the Euro Zone[END_REF] In the literature, two recent econo-1 0 Two notable exceptions can be nevertheless found. Connolly et al. (2005), who examine whether time variation in the comovements of daily stock and Treasury bond returns can be linked to stock market uncertainty, as well as Alfaro, Bloom and Lin (2016). Hasse (2016) further shows using stability tests that uncertainty, complexity and networks structure are cobreaking, supporting hence the idea of strong relationship between them. 1 1 In network theory, nodes are collection of points connected together by edges that can be de…ned as the lines from one node to another (i.e. directed graphs) or as the strength of a given connection (i.e. weighted graphs). The degree of a node is the number of links to other nodes, and the diameter of a network is the maximum distance between any two nodes. 2012) propose a two-step procedure which consists in quantifying the degree of connectedness between …nancial assets through principal components analysis and then investigate the directionality within the system by Granger causality tests. Second, Diebold and Yilmaz (2014) develop a network approach based on variance decomposition of vector auto-regressive (VAR) model. While both measures are in some sense quite close, for several reasons variance decomposition is more appealing in our context than using pairwise Granger causality. Indeed unlike VAR setting, Granger causal approach is directional but exclusively pairwise and unweighted, tests zero versus non-zero coe¢ cients with somewhat arbitrary signi…cance levels, and does not track the magnitude of non-zero coe¢ cients. [START_REF] Bloom | Uncertainty and Investment Dynamics[END_REF] On the other hand, it is well known that variance decomposition and impulse response analysis su¤er from identifying assumptions inherent to VAR setting. However, this restriction can be partially mitigated by careful robustness checks as we do in the empirical part of the paper.

Assessing connectedness using the Diebold-Yilmaz approach

Our approach is based on the Diebold and Yilmaz (2014)'s de…nition of interconnectedness as the share of forecast error variation in one market due to shocks arising elsewhere. In order to provide an analysis of interconnectedness in a multivariate setting across N various countries over time, let's start with the following VAR representation of dimension p as follows:

x t = p X i=0 B i x t i + t ; (1)
Equation ( 1) describes a covariance-stationary N -variable VAR(p) model, where x is a vector of equity market returns and t N (0; ) is a vector of independently and identically distributed disturbances. Assuming weak stationarity, x t follows the following in…nite-order moving-average representation:

x t = 1 X l=0 A l t l ; (2)
where A(L) = (I B(L))1 , and A l = 0 for l 0.

After obtaining the moving-average representation, Diebold and Yilmaz (2014) rely on variance decompositions to compute …nancial interconnectedness. Variance decompositions allow an assessment of the fraction of the H-step-ahead forecast error variance in forecasting one variable with respect to shocks from other variables in the system. However, this approach calls for the identi…cation of structural shocks by imposing a su¢ cient number of identi…cation restrictions to cope with contemporaneous correlated VAR innovations. Cholesky factorization is often used to achieve this goal but requires some limitations that depend on the VAR-ordering spe-ci…cation. The generalized forecast error variance decomposition is often used as an alternative invariant counterpart when there is a lack of credible identi…cation restrictions (see Koop et al. 1996 and Pesaran and Shin 1998). The main di¤erence between the two approaches is that while in the former shocks are uncorrelated and carry an economic meaning, in the latter they may be correlated and the interpretation is somewhat ambiguous, as share sums are not necessarily unity. As in Diebold and Yilmaz (2009), our preference is the Cholesky decomposition. Moreover, as will see in the empirical application, our results are robust to Cholesky ordering, that is, the range of total connectedness estimates across the ordering is quite small. [START_REF] Bloom | The impact of Uncertainty Shocks[END_REF] Let's rewrite Equation ( 2) as

x t = 1 X l=0 l ! t l ; (3)
where ! t = P1 t is the orthogonalized error for which P 1 is the unique lower-triangular Cholesky factor of the covariance matrix of t . E (! t ! 0 t ) = I, meaning that shocks of ! t are uncorrelated. Let us now assume that a variable x i t , for i = 1; : : : ; N , is a stock index in a speci…c country and that N is large enough to adequately represent a large proportion of the world. Following Diebold and Yilmaz (2014), the approach to obtain the interconnectedness between countries is to rely on variance decomposition from the orthogonalized moving-average representation (3) and to compute the H-step-ahead forecast error variances of each variable within the system. Thus, for any variable x j t in the system, its contribution to variable x i t 's H-step-ahead forecast error variance is given by

' ij (H) = H 1 X h=0 e 0 i h e j 2 ; (4)
where e j is the selection vector with the j-th element being unity and zeros elsewhere, and h is the coe¢ cient matrix multiplying the h-lagged shock vector in the in…nite moving-average representation of the orthogonalized model.

Hence, ' ij (H) can be interpreted as a measure of pairwise directional connectedness from j to i at a given forecast horizon H. In the results, we express those …gures in percentage terms, such that for any country i

N X j=1 ' ij (H) = 100:
To facilitate the analysis from the N N tables of pairwise connections, we also examine two measures to assess (i) the contribution that a country i receives from the rest of the world (RoW) [START_REF] Bloom | Fluctuations in Uncertainty[END_REF] , denoted C i RoW (H), and (ii) the contribution of a country j to the rest of the world, termed C j!RoW (H). Those measures are de…ned such that, for all countries i; j,

C i RoW (H) = N X j=1;j6 =i ' ij (H) (5)
and

C j!RoW (H) = N X i=1;i6 =j ' ij (H): (6)
Obviously we have that for any country i, C i RoW (H) = 100 ' ii (H).

A useful measure, often used in this type of analysis, is the net contribution of a country i to the system, obtained by analyzing how much this country contributes to the system minus how much it receives from the system. For any country i, this measure is intuitively given by

C i (H) = C i!RoW (H) C i RoW (H) (7)
Based on this measure, we can classify countries between net givers, i.e., countries that contribute more to the system than they receive, for which C i (H) > 0, and net receivers, i.e., countries that receive more from the system than they contribute, for which C i (H) < 0. Obviously we have that

P N i=1 C i (H) = 0.
Finally, a measure C(H) of the system-wide connectedness can be obtained to assess the degree of connectedness of the whole system. This measure will be useful to compare systems depending on the level of uncertainty. It is obtained by either averaging all the contributions that countries receive from the rest of the world or by averaging all the contributions countries give to the rest of the world:

C(H) = 1 N N X i=1 C i RoW (H) = 1 N N X j=1 C j!RoW (H) (8)

Non-linear extension of the Diebold-Yilmaz approach

The idea of this paper is that uncertainty might be a potential driver of the dynamics within equity markets'networks. Allowing for shifts in interconnectedness with respect to uncertainty, we propose to extend to a nonlinear framework the standard approach of Diebold and Yilmaz (2014). Starting from the standard linear setting, we assume that uncertainty may be a nonlinear propagator of shocks across equity markets that a¤ects the pattern of connectedness between price returns. We thus assume that the parameters of the VAR model given in Equation ( 1) can switch over time from one regime to the other, depending on a threshold controlled by a speci…c transition variable. In this respect, we replace Equation ( 1) with the following Threshold VAR (TVAR) model ( 9) whose parameters switch from a low-uncertainty regime to a high-uncertainty regime:

x t = 1 + B 1 (L) x t 1 + ( 2 + B 2 (L) x t 1 ) I t (u t d ) + t ; (9)
where x t is a vector of endogenous variables containing the stock price indexes of N countries. [START_REF] Braverman | Networks of Common Asset Holdings: Aggregation and Measures of Vulnerability[END_REF] The lag polynomial matrices B 1 (L) and B 2 (L) re ‡ect structural relationships within each of the two states, 1 and 2 are vectors of constants, and t denotes the vector of orthogonalized error terms. u t d is the d-lagged threshold variable, which serves as a measure of uncertainty in our setting. We consider the lagged transition variable to avoid potential endogeneity issues that would bias our estimation. 17 I t (u t d

) is an indicator function that equals 1 when u t d and 0 otherwise, where denotes the threshold uncertainty critical value that has to be endogenously estimated. In other words, two states are identi…ed: the low-uncertainty state corresponding to a weak degree of uncertainty (I t (:) = 0) and the high-uncertainty state related to a high degree of uncertainty (I t (:) = 1). The coe¢ cients of the TVAR model are allowed to change across states depending on the level of uncertainty. Note that in our framework we only allow for two regimes of uncertainty, but in theory this framework can be easily extended to three or more regimes. The only empirical issue is that each regime has to be frequently visited; otherwise, a given regime cannot have su¢ cient observations to correctly estimate the number of parameters in the TVAR model. Once tests for the regime have been conducted and the coe¢ cients and covariance matrix have been saved from the estimation step, the pairwise and system-wide connectedness between countries can be computed.

Data

In this section, we describe the database that we use in the empirical part of the paper.

To have an overview of …nancial interconnectedness across international …nancial markets, we consider a dataset of 13 equity indices classi…ed into two categories: (i) advanced countries (the U.S., the U.K., Germany, France, Italy, the Netherlands, Spain, Portugal, and Greece) and (ii) emerging countries (China, Brazil, Russia and India). All series are sampled at a monthly frequency starting in January 1998 and ending in December 2015, thereby covering several periods of economic and …nancial turmoil with common or idiosyncratic consequences, such as the Argentine economic crisis (1999-02), the dot-com bubble (2001), the global …nancial crisis (2007-08), and the European sovereign debt crisis (2011-13). To achieve stationarity, all the series have been transformed into …rst-logarithmic di¤erences (i.e., log-returns). [START_REF] Bussière | Explaining The Recent Slump in Investment: The Role of Expected Demand and Uncertainty[END_REF] Choosing the adequate measure of uncertainty is a more complex issue since it can take several forms. Thus, to be as unrestrictive as possible, we consider three di¤erent measures of uncertainty: (i) a measure of …nancial uncertainty based on implied volatility, (ii) a measure of macroeconomic uncertainty based on aggregate macroeconomic information, and (iii) a mesure of economic policy uncertainty estimated from news-based metrics. Since each proxy is related to di¤erent components of uncertainty, they may have di¤erent impacts on international …nancial networks.

As regards …nancial uncertainty, we employ the Chicago Board of Option Exchange VXO index of percentage implied volatility based on a hypothetical at-the-money S&P100 option. This proxy, as the VIX index based on the S&P500, is widely used in the literature since it refers to the market's expectation of volatility implicit in the prices of options (see Connolly et al. 2005 and Bloom 2009, among others). However, as stressed by Jurado et al. (2015), most of the commonly used approaches based on the implied or realized volatility of stock market returns vary over time due to several factors (risk aversion, leverage e¤ect, etc) even if there is no signi…cant change in uncertainty. In other words, Jurado et al. (2015) note that ‡uctuations that are actually predictable can be erroneously attributed to uncertainty. To overcome this constraint, those latter authors de…ne a measure of macroeconomic uncertainty based on the common variation contained in hundreds of primarily macroeconomic and …nancial monthly indicators (mainly US oriented) [START_REF] Cabrales | Risk-Sharing and Contagion in Network[END_REF] , and propose to remove the forecastable component of the considered series before computing the conditional volatility. This measure has the advantage of agreeing with uncertainty-based business cycle theories that assume common variation in uncertainty across a large number of series. [START_REF] Cabrales | Financial Contagion in Networks[END_REF] Turning to economic policy, concerns about uncertainty have intensi…ed in the wake of the global …nancial crisis. For instance, the Federal Open Market Committee (2009) and the IMF (2012, 2013) argue that uncertainty over U.S. monetary policies contributed to a steep economic decline in 2008-09 (see also Stock and Watson 2012). Other studies also show that economic policy uncertainty played a non-negligible role in explaining the slump in investment during the recovery (see, for example, Bussiere et al. 2015). The same concern holds for policy uncertainty regarding European and Asian countries that may impact global economic 1 8 See Table 4 in the Appendix for further details on the dataset. 1 9 Speci…cally, 132 macroeconomic time series are considered, including real output and income, employment and hours, real retail, manufacturing and trade sales, consumer spending, housing starts, inventories and inventory sales ratios, orders and un…lled orders, compensation and labor costs, capacity utilization measures, price indexes, bond and stock market indexes, and foreign exchange measures. Turning to the …nancial indicators, 147 time series are retained, including dividend-price and earning-price ratios, growth rates of aggregate dividends and prices, default and term spreads, yields on corporate bonds of di¤erent ratings grades, yields on Treasuries and yield spreads, and a broad cross-section of industry equity returns. Both sets of data are used to estimate the forecasting factors, but macroeconomic uncertainty is proxied using the 132 macroeconomic time series only. 2016) that re ‡ects the frequency of articles in leading newspapers that contain the following triple: "economic" or "economy"; "uncertain" or "uncertainty"; and one or more policy-relevant terms. [START_REF] Caldara | The Macroeconomic Impact of Financial and Uncertainty Shocks[END_REF] Together with the U.S. EPU, we also investigate how both European and Chinese EPUs could contribute to systemic risks. [START_REF] Carriero | Measuring Uncertainty and Its Impact on the Economy[END_REF] Figure 1 depicts the various measures of interest for uncertainty over the period from January 1998 to December 2015 (…nancial, macroeconomic and economic policy uncertainties). Comparing the various measures of uncertainty suggests that uncertainty may take di¤erent forms and thus are likely to have a di¤erentiate impact on …nancial networks.

2 1 For the US, the terms used are: "congress", "de…cit", "Federal Reserve", "legislation", "regulation", or

Empirical results

This section investigates interconnectedness across international …nancial markets for a set of 13 countries over the sample period going from January 1998 to December 2015. It further examines how non-linearity and uncertainty may shape the pattern of relationships and in ‡uence the transmission of shocks.

International …nancial markets connectedness through the standard Diebold-Yilmaz approach

In the …rst part of our empirical analysis, we use the standard linear approach of Diebold and Yilmaz (2014) for a set of 13 international equity markets, in order to obtain benchmark results on global …nancial market connectedness. Table 5 in the Appendix reports results for international pairwise directional connectedness ' ij (H) between countries for H = 5 months and shows some stylized facts. [START_REF] Connolly | Stock Market Uncertainty and the Stock-Bond Return Relation[END_REF] It also tests the signi…cance of each country's contribution using bootstrap con…dence bands. [START_REF] Coval | Asset Fire Sales (and Purchases) in Equity Markets[END_REF] First, we get that the degree of system-wide connectedness is relatively high, C(H) being equal to 68.3%. Some blocks of high pairwise directional connectedness ' ij (H) appear in the table, especially between the US and European countries (Germany, France and the U.K., at more than 50%). The US case is notable in the sense that the country is extremely closed as it does not receive much from other countries: its contribution to its own variance is ' ii (H) = 75:3%. However, the US substantially contribute to the variance of other countries, especially advanced economies. The relationships with the four BRIC countries (Brazil, Russia, India, and China) is much lower, especially with China (only 8:6% of the Chinese variance is explained by the US). This can be explained by the fact that China cannot be considered as an open-market economy over the sample period. The Chinese capital account is very closed, as can be seen in its high contribution to its own variance (' ii (H) = 70:3%). Thus, the role of China in global …nancial markets networks appears to be very limited. Although China is often considered as a regional leader, our results show that it does not appear as an international leader over the whole period 1998-2015. So, if China is now a driver of the global economy, as often read in the media, then it has been since only very recently. Within this …nancial system, the net contributions C i (H) give a broad view of the role of each country. In this respect, as expected, the US (C i (H)=428) is by far the main driver of global …nancial markets, as it contributes much more than it receives. To a lesser extent, the UK (C i (H)=34) is also a net contributor to the system. China (C i (H)=2) appears to be relatively neutral and not signi…cant; its independence vis-à-vis the global …nancial system has to be related to its closed …nancial account. All other countries in the system are net receivers. The main receivers appear to be small open economies that are usually identi…ed in the literature as followers either because their markets are not mature enough or because of their relatively small size, such as the Netherlands, Spain, Portugal or Greece.

We now turn to the row and column sums "FROM" and "TO", which denote the share of returns shocks received from (resp. contributed to) …nancial markets in the total variance of the forecast error for each market, respectively. The dispersion of the "FROM" column ranges between 25% for the US and 91% for France (re ‡ecting the substantial openness of France to other countries in the system, mainly the US, UK and Germany) and is lower than the dispersion in the "TO" row, which ranges between 16% for Portugal to 453% for the US. [START_REF] Diebold | Measuring Financial Asset Return and Volatility Spillovers with Application to Global Equity Markets[END_REF] As an additional result, we divide the countries into two sub-groups: advanced countries and the BRICs. Presenting parallel results for the sub-groups in Tables 6 and7, we con…rm that total spillovers within emerging equity markets are much lower than within advanced markets (24% against 72%). It further reveals how the role of each market may change depending on the system and economic environment considered since the positions of net contributors of each country ‡uctuate. Among advanced economies, the hierarchy in the system is similar to that of the global system, but among the reduced BRIC system, China and Brazil are now clearly net contributors.

5.2

The role of uncertainty in international …nancial markets interconnectedness 5.2.1 Financial markets and uncertainty: A non-linear relationship?

Our hypothesis, as written in equation ( 9), is that uncertainty may a¤ect …nancial markets networks and that the propagation mechanism is non-linear and characterized by two regimes of high and low uncertainty. To check this assumption, we …rst test for non-linearity in three various groups of countries, namely global, advanced and emerging markets. We will further test for di¤erent measures of uncertainty as transition variable to determine whether the source of uncertainty matters (economic policy uncertainty, …nancial uncertainty and macroeconomic uncertainty).

To discriminate between models, one needs to test for model speci…cation with respect to a threshold variable. In practice, the testing procedure is however not straightforward because under the null hypothesis of no threshold e¤ect, the threshold value is not known a priori and has to be estimated. Here, we therefore determine the threshold value endogenously using a grid search over all possible values of the threshold variable. [START_REF] Diebold | On the Network Topology of Variance Decompositions: Measuring the Connectedness of Financial Firms[END_REF] We then test for a threshold e¤ect by relying on a nonstandard inference procedure over all possible threshold values in a least squares regression framework. Using Hansen (1996)'s procedure, we generate three Wald-type statistics to test for the null hypothesis of no di¤erence between states. [START_REF] Eichengreen | Tapering Talk: The Impact of Expectations of Reduced Federal Reserve Security Purchases on Emerging Markets[END_REF] Using the bootstrap procedure of Hansen (1996) to simulate distribution and conduct inference, the estimated threshold values are those that maximize the log-determinant of the variance-covariance matrix of residuals.

Tables 8, 9, and 10 contain threshold test results for global, developed and emerging markets, respectively. Together with linearity tests, we also report proportion and average duration of the high-uncertainty regime. We reject linearity for all models (regardless of the measure of uncertainty and the groups of countries considered), meaning that a non-linear relationship between equity markets and uncertainty is likely to be at play. Comparing …rst the results for advanced and emerging markets from Tables 9 and10, we …nd that the threshold values of the uncertainty proxies are quite di¤erent. [START_REF] Elsinger | Risk Assessment for Banking System[END_REF] Indeed, the proportions of the high-uncertainty regime (i.e., when the uncertainty measures exceed the corresponding threshold values) are quite di¤erent between groups of markets. For instance, we get that periods of high uncertainty are more frequent, for both …nancial and macroeconomic uncertainty, in advanced equity markets than in emerging markets (advanced markets are in the high regime 26% and 40% of the time, when considering …nancial and macroeconomic uncertainty, respectively, against only 20% and 17% for emerging markets). However, accounting for economic policy uncertainty in Europe and in the US as a threshold leads to more frequent high-uncertainty periods in emerging markets (55% and 45%, respectively) than in advanced ones (24% for both). This result is in line with the literature on the global e¤ects of US economic policy, especially monetary policy, is likely to a¤ect emerging market asset prices (see for example Eichengreen and Gupta 2014, Aizenman et al. 2015, and Aizenman et al. 2016). We also show here that economic policy in Europe is likely to a¤ect …nancial markets in emerging countries. In terms of average duration [START_REF] Ferrara | Uncertainty ‡uctuations: Measures, e¤ects and macroeconomic policy challenges[END_REF] , periods of macroeconomic uncertainty last longer (approximately 13 months for both groups of countries), underlining the higher persistence of macroeconomic uncertainty by comparison with …nancial and economic policy uncertainty.

Financial markets connectedness in low and high regimes of uncertainty

Now that evidence of non-linearity in the relationship between uncertainty and …nancial markets dynamic has been put forward, we compute the non-linear version of the Diebold-Yilmaz index described in Section 3.2 by estimating the TVAR model. To save space, we only focus on the results for global equity markets, namely the full set of countries. [START_REF] Gai | Complexity, Concentration and Contagion[END_REF] In Tables 11 to 15, we report the results for the nonlinear Diebold-Yilmaz index in high-and lowuncertainty regimes for international equity markets. The method reported in the tables is identical to the traditional Diebold-Yilmaz approach; they report directional connectedness between countries ' ij (H) and system-wide connectedness (C (H)). The main di¤erence here is that we are able to evaluate pairwise and system-wide connections between …nancial markets with respect to the level of uncertainty (i.e., in low-and high-uncertainty states). [START_REF] Glick | Contagion and Trade: Why are Currency crises Regional[END_REF] First, our results reveal that accounting for nonlinearity when evaluating …nancial markets networks is of crucial importance since both system-wide and pairwise connectedness are signi…cantly di¤erent across economic environments. From a global perspective, global connectedness (C (H)) increases on average by 11.3 percentage points (p.p.) when moving from the low-to the high-uncertainty state. This behavior is a bit less pronounced when the …nancial volatility is considered as transition variable (an increase of only 4.3 p.p.). At a more granular level, as in the linear model, the behavior of the U.S. and China vis-a-vis their own variances is quite speci…c in the sense that they are both very closed markets that do not receive much from other countries. In the low-uncertainty regime, their own variance contributions are of the same order as those in the benchmark model (approximately 75%). However, when moving into high-uncertainty states, countries become more open. As uncertainty increases, global …nancial markets become more connected and hence the degree of closedness of these two countries becomes lower (i.e., the contribution of each country to its own variance decreases). For instance, in periods of high US macroeconomic uncertainty, the US auto-contribution goes down from 74.6% in the low regime of uncertainty to 27.8% in the high regime. This movement is also similar for China (from 72.4% to 28.1%). This re ‡ects the fact that an increase in US macroeconomic uncertainty is a strong mover as it is generally associated to US economic recessions. It seems that in that case, we observe a rebalancing of the …nancial system away from the US. An increase in the Chinese EPU tends to lead to similar results, acting also as a rebalancing driver.

Let us turn to net contributions, which are the di¤erences, for a given country, between contributions given to and received by the system (i.e., the last rows in the tables). In contrast to the traditional approach, our framework enables to evaluate how uncertainty shapes the nature of each market in giving or receiving shocks. Figures 1,2, and 3 in Appendix depict the net positions of each market given the nature and level of uncertainty. Several results emerge from these …gures. First, the US appear to be the main leader of other …nancial markets. This is especially true when looking at …nancial and macroeconomic uncertainty and EPU US. The US market's leading in ‡uence on others is however not linear and varies according to the level of uncertainty. For instance, it decreases during periods of …nancial and macroeconomic uncertainty and the Chinese EPU (by approximately 102pp, 356pp, and 244pp, respectively) and increases during episodes characterized by high US and European EPU (by approximately 303pp and 59pp, respectively). In other words, the role of the U.S. is reinforced during periods of European and American policy turmoil. Second, the U.K. also emerges as a second leader, especially during episodes of high European, US, and Chinese EPU, while most of the other countries (advanced and emerging) are clearly followers. Third, the role of China as a non-signi…cant net contributor is also quite interesting since it runs counter to the common understanding that the domestic economic situation in China is likely to spill over to other markets. Its role during periods of increasing Chinese EPU appears to switch from a contributor in the low regime to a receiver in the high regime. Another interesting result is the changing role of Germany shifting from one position to the other depending on the regime. For instance, it switches from being a net contributor in the low regime to a net receiver in the high regime during periods of US and European EPU, while it shifts from being a net receiver to neutral contributor in periods of macroeconomic uncertainty. Germany thus appears to be an international leader when uncertainty is low but loses this position when uncertainty is high.

At a global perspective, our results also show that uncertainty by increasing …nancial markets connections makes risk-sharing more ine¢ cient to absorb shocks.

How does uncertainty a¤ect the distribution of contributors to the system?

In the previous section we found that uncertainty shapes …nancial market networks (i.e., system-wide and pairwise connectedness) by increasing the transmission of equity market shocks. By a¤ecting global market comovements, the level of uncertainty may necessarily change the way shocks are given (C j!RoW (H)) and received (C i RoW (H)) within the system.

To gauge the e¤ect of uncertainty on equity market shock transmission, we estimate probability density functions of "FROM" directional connectedness (C i RoW ) and compare it in three di¤erent scenarios: (i) no uncertainty; (ii) low uncertainty; and (iii) high uncertainty. [START_REF] Gorton | Securitized Banking and the Run on Repo[END_REF] Figure 2 below depicts a smooth probability density function for C i RoW for …nancial and macroeconomic uncertainty, as well as economic policy uncertainty (in the U.S., Europe, and China) (i.e., the column sum in Tables 11, 12, 13, 14, and 15). Two salient facts emerge. First, while networks play a key role in the linear framework and in the low regime (the two present similar pictures, with most of the mass being above 50%), they tend to change after accounting for uncertainty. Whatever the nature of uncertainty, networks are indeed stronger when uncertainty is high. Second, the source of uncertainty matters in the transmission of equity shocks since the kernel density functions do not always follow the same pattern. Regarding …nancial uncertainty, C i RoW ranges between 38% and 92%, and most of the mass is located around 80%. Almost the same picture holds in periods of EPU in the US, where directional connectedness ranges between 31% and 93% and is polarized around the same level of 80%. The two most interesting cases are those for which global interconnectedness increased more, that is for high economic policy uncertainty in China and high macroeconomic uncertainty. Indeed, during both periods, C i RoW concentrates mainly on the highest values (above 90%), in the range 64%-95% for the former and 70%-89% for the latter.

Additional results

This section presents some robustness checks and additional results on the global bonds market and on Brexit-related issues.

6.1 Sensitivity analysis 6.1.1 Uncertainty and …nancial markets' interconnectedness Does forecasting horizon matter?

In the previous sections, we found that uncertainty is of crucial importance when evaluating …nancial markets networks since during periods of high uncertainty (i) global network connectedness increases; (ii) the role of each market in the global system as a leader or follower changes; and (iii) the ways in which shocks are received and transmitted are not the same. Those results are obtained when decomposing the variance of forecasting errors at a speci…c horizon of H = 5 months. The current subsection examines how the e¤ect of uncertainty on …nancial interconnectedness evolves across various forecasting horizons H. We therefore compute the Diebold-Yilmaz spillover index for international equity markets in the high-uncertainty regime for various predictive horizons ranging from H = 1 to H = 12. Figure 3 reports the global network connectedness for international equity markets in the high-uncertainty regime, for the 5 sources of uncertainty, for each considered horizon from 1 month to 12 months. It shows that results are quite robust to the predictive horizon. On average, the e¤ect of uncertainty on network increases, peaks at 5 months, and then stabilizes at the same level. Note: We plot global spillover index (in %) for international equity markets in high uncertainty regime for financial, macroeconomic, and economic policy uncertainty respectively over horizon going from 1 month to 12 months. Blue and purple lines are financial and macroeconomic uncertainty respectively; green, red and orange lines are respectively EPU for the U.S., Europe, and China.

Figure 3. Global international equity markets interconnectedness in the high-uncertainty regime across maturities

Di¤erent VAR Cholesky ordering speci…cation

In order to estimate …nancial interconnectedness between equity markets returns, Diebold-Yilmaz's approach requires some identifying assumptions. As stressed in the empirical part of the paper, our preference goes to Cholesky factorization. However, this approach depends on the VAR-ordering speci…cation. Table 1 below performs robustness checks by computing max-min interval based on 100 randomly-selected VAR ordering of global interconnectedness index in periods of low and high …nancial, macroeconomic and economic policy uncertainties. It shows that our results are robust since the range of global connectedness estimate across ordering is quite small.

Macroeconomic uncertainty and …nancial markets networks: a geographic perspective

The macroeconomic uncertainty measure considered so far in the paper is the one proposed by Jurado et al. (2015). This measure is well established and is available over a long sample but has the drawback of being only available for the US. More recently, Scotti (2016) put forward macroeconomic uncertainty measures for a bunch of advanced economies (U.S., Europe, the U.K., Japan, and Canada), though the sample size is shorter (May 2003-December 2015). This section proposes to investigate the e¤ect those real-time macro-uncertainty measures on equity market networks. A brief examination of Figure 4 shows that real-time macro-uncertainty measures are counter-cyclically increasing during the Great Recession in 2008-2009. Table 2 reports global equity market spillovers in low-and high-uncertainty states with respect to the geographic area. [START_REF] Hansen | Inference When a Nuisance Parameter is Not Identi…ed under the Null Hypothesis[END_REF] As before, …nancial markets connectedness signi…cantly increases in periods of high macro-uncertainty, especially in the presence of high uncertainty in Europe, the U.S. and Japan. Figure 4 to 6 in Appendix completes our results by plotting the net contributions of each country with respect to the level of uncertainty and the geographic area. As in previous sections, the contributions of each country in the system change depending on the uncertainty regime. Whatever geographic area is considered as generating macro uncertainty, the U.S. are always the main net contributor to the global system while other equity markets are net receivers or do not make signi…cant contributions to the system. The role of the U.S. tends to be less important when moving into the high-uncertainty regime. While the contribution is more or less stable (approximately 350%) in periods of high macro-uncertainty in the U.K., it signi…cantly decreases by approximately 200pp in times of uncertainty in the US and Europe (from 445% to 244% for the former and from 428% to 250% for the latter), and by more than 350pp in times of uncertainty in Japan (from 469% to 94%). This behavior is less pronounced during periods of macro-uncertainty in Canada, where the U.S. contribution to net uncertainty decreases by approximately 90pp when moving from the low to the high regime.

Results on the global bonds market

As a robustness check of the e¤ect of uncertainty on network, we also apply our model to government bond markets for the overall sample (except Brazil) over the period from April 2004 to December 2015. Results are presented in the Table 3. We note that those results are qualitatively similar to those for equity markets, meaning that global interconnectedness on the bond market increases with respect to uncertainty. It is noteworthy that the increase in connectedness is stronger than for equity markets and that the economic policy uncertainty in China appears to be the most important driver of this upward shift in connectedness. Notes: The table summarizes global government bonds interconnectedness in the low-and high-uncertainty regimes with respect to uncertainty. Models are computed over 10,000 parametric bootstrap replications. 0 denotes that interconnectedness are signi…cant at the 5% level.

Discussion of Brexit-related uncertainty and consequences for European countries'interconnectedness

While it is always di¢ cult to capture the e¤ect of uncertainty on economic and …nancial interconnectedness, a recent event in the United Kingdom provides an interesting case study for a discussion of Brexit-related uncertainty and potential consequences for European countries.

Recall the facts of the case: on Thursday, 23 June, the United Kingdom voted in favor of Brexit, with the consequence that the country would leave the European Union, leading to possible important economic disruptions. Together with market ‡uctuations, uncertainty in UK also increased signi…cantly over the period, as the Economic Policy Uncertainty index of Baker et al. (2016) shows. It is clear when examining Figure 6 that recent movements in UK EPU are related to Brexit-related uncertainty. [START_REF] Hasse | Complexity in …nancial markets : networks, uncertainty and globalization[END_REF] Despite the lack of a wide perspective on the phenomenon, this section attempts to evaluate the contribution of Brexit-related uncertainty to European equity market interconnectedness.

Our investigation focuses on core and periphery European markets such as those of the United Kingdom, France, Germany, Italy, the Netherlands, Spain, Portugal, and Greece. Uncertainty over the period is measured using the UK EPU of Baker et al. (2016). As a neutral point of comparison, we consider two di¤erent sample periods: from January 2000 to June 2016, which includes the Brexit period, and from January 2000 to August 2015, which does not capture recent events related to Brexit. [START_REF] Jurado | Measuring Uncertainty[END_REF] We consider our non-linear two-regime approach discussed in this paper. Figure 7 depicts the contribution of UK EPU to European market spillovers for the 1 month to 12 months predictive horizon for the variance decomposition. It compares the contribution of uncertainty in the samples with and without the Brexit-related period, both in the high-uncertainty regime. [START_REF] Kaminsky | On Crises, Contagion, and Confusion[END_REF] This shows that when including the recent Brexit period, the contribution of UK EPU to equity market networks is on average more than twice as high, meaning that the recent period of uncertainty is of primary importance in terms of network reactions among European countries. 3 4 The Brexit-related uncertainty index is constructed by scaling the UK EPU index by the share of EPU articles that also contain "Brexit", "EU" or "European Union". It can be freely download at http://www.policyuncertainty.com/brexit.html. 3 5 While the selection of sub-sample periods could be considered subjective, this choice was been made by comparing the evolution of UK EPU and Brexit-related uncertainty, which were both at a low in August 2015. 3 6 We perform a nonlinear test for the period not including Brexit-related uncertainty (i.e., from Jan. 2000 to August 2015), and the results con…rm that the nonlinear speci…cation is preferable to the linear one with a threshold level of 186.16. The level is substantially below that when including Brexit-related uncertainty, meaning that the recent period signi…cantly increased the level of uncertainty.

Conclusion

This paper proposes to test and to empirically evaluate the role of the uncertainty channel in …nancial markets networks. We empirically show that higher uncertainty leads to more connectedness within the international system of asset prices.

In this paper, we assess …nancial spillovers among 13 stock markets (including developed and emerging countries) by allowing for non-linear e¤ects in the spillover index of Diebold and Yilmaz (2009) through the estimation of a non-linear Threshold VAR model whose regimes depend on the level on uncertainty. Our main result is that the global equity market is much more connected during periods of high uncertainty than during periods of low uncertainty. Empirical results are robust to the choice of uncertainty measures (economic, political or macroeconomic). We also …nd that United-States are the main source of spillovers within the global equity system, as well as the United Kingdom but to a lesser extent. All other countries tend to act as net receivers of spillovers. These …ndings are among the …rst to support empirically an uncertainty channel of contagion. At the light of the actual economic and political environment this result has strong implications. Indeed, according to the current high degree of economic policy uncertainty, and given interdependence within the global equity network, a small negative shock may now turn out to spread over and amplify in the rest of the world creating hence a global turmoil. This potential threat should be at the core of the preoccupation of public authorities, whose objectives should included a decrease in uncertainty. Such a goal requires of course a real-time monitoring of the uncertainty indicators in order to propose adequate measures. Still, the policy required to reach such an objective are far from being obvious and concern policy actions (monetary, …scal, foreign a¤airs) but also regulation; no doubt that this topic will fuel up future research works. Notes: The table depicts Diebold-Yilmaz interconnectedness measure for international equity markets over a predictive horizon of 5 months. The "FROM" column gives row sums (from all others to j); the "TO" row gives the column sums (to all others from j); and the "NET" row gives the di¤erence between "TO" and "FROM". The botton-right value is the percent of forecast error variance coming from interconnectedness. denotes rejection of the null hypothesis at the 5% signi…cance level computed using a parametric bootstrap procedure (10,000 replications). Notes: The table depicts Diebold-Yilmaz interconnectedness measure for developed equity markets over a predictive horizon of 5 months. The "FROM" column gives row sums (from all others to j); the "TO" row gives the column sums (to all others from j); and the "NET" row gives the di¤erence between "TO" and "FROM". The botton-right value is the percent of forecast error variance coming from interconnectedness. denotes rejection of the null hypothesis at the 5% signi…cance level computed using a parametric bootstrap procedure (10,000 replications). Notes: The table depicts Diebold-Yilmaz interconnectedness measure for emerging equity markets over a predictive horizon of 5 months. The "FROM" column gives row sums (from all others to j); the "TO" row gives the column sums (to all others from j); and the "NET" row gives the di¤erence between "TO" and "FROM". The botton-right value is the percent of forecast error variance coming from networks. denotes rejection of the null hypothesis at the 5% signi…cance level computed using a parametric bootstrap procedure (10,000 replications). Notes: The table depicts nonlinear interconnectedness measure in the low-and high-…nancial-uncertainty regimes for international equity markets over a predictive horizon of 5 months. denotes rejection of the null hypothesis at the 5% signi…cance level computed using a parametric bootstrap procedure (10,000 replications). Notes: The table depicts nonlinear interconnectedness measure in the low-and high-macroeconomic-uncertainty regimes for international equity markets over a predictive horizon of 5 months. denotes rejection of the null hypothesis at the 5% signi…cance level computed using a parametric bootstrap procedure (10,000 replications). Notes: The table depicts nonlinear interconnectedness measure in the low-and high-U.S.-economic-policy-uncertainty regimes for international equity markets over a predictive horizon of 5 months. denotes rejection of the null hypothesis at the 5% signi…cance level computed using a parametric bootstrap procedure (10,000 replications). Notes: The table depicts nonlinear interconnectedness measure in the low-and high-European-economic-policy-uncertainty regimes for international equity markets over a predictive horizon of 5 months. denotes rejection of the null hypothesis at the 5% signi…cance level computed using a parametric bootstrap procedure (10,000 replications). Notes: The table depicts nonlinear interconnectedness in the low-and high-Chinese-economic-policy-uncertainty regimes for international equity markets over a predictive horizon of 5 months. denotes rejection of the null hypothesis at the 5% signi…cance level computed using a parametric bootstrap procedure (10,000 replications).

Figure 1 .

 1 Figure 1. Di¤erent sources of uncertainty: …nancial, macroeconomic and EPU

Figure 2 .

 2 Figure 2. Uncertainty and …nancial networks

Figure 4 .

 4 Figure 4. Real-time macro-uncertainty indexes

Figure 6 .no

 6 Figure 6. United Kingdom Economic Policy Uncertainty: All and Brexit/EU (source Baker al. 2016)

Figure 7 .

 7 Figure 7. Does Brexit-related uncertainty a¤ect European equity market interconnectedness?

Figure 1 :

 1 Figure 1: Equity markets' net contributions during periods of …nancial and macroeconomic uncertainty

Figure 2 :

 2 Figure 2: Equity markets'net contributions during periods of EPU US and EPU Europe

Figure 3 :

 3 Figure 3: Equity markets'net contributions during periods of EPU China

Figure 4 :

 4 Figure 4: Macroeconomic uncertainty (US, Europe) and interconnectedness: a geographic perspective

Figure 5 :

 5 Figure 5: Macroeconomic uncertainty (UK and Japan) and interconnectedness: a geographic perspective

Figure 6 :

 6 Figure 6: Macroeconomic uncertainty (Canada) and interconnectedness: a geographic perspective

  To investigate the role of economic policy uncertainty on …nancial markets networks, we use the Economic Policy Uncertainty (hereafter, EPU) index developed by Baker et al. (

2 0 The proxy is freely available on Ludvigson's homepage http://www.econ.nyu.edu/user/ludvigsons/ prospects.

Table 1 :

 1 Global equity market interconnectedness and uncertainty: the e¤ect of model spe-ci…cationNotes: The table summarizes global interconnectedness in the low-and high-uncertainty regimes with respect to the source of uncertainty. Models are computed over 10,000 parametric bootstrap replications. Between parenthesis are minimum and maximum spillover interval based on 100 randomly selected VAR orderings.

	Uncertainty source	Low uncertainty High uncertainty
	Financial uncertainty	69:8%	74:1%
		(67:7 74:0)	(70:1 77:1)
	Macro uncertainty	69:6%	84:0%
		(66:9 71:5)	(80:2 89:1)
	EPU US	64:0%	75:0%
		(60:1 70:9)	(72:1 79:9)
	EPU Europe	64:0%	77:7%
		(60:1 70:4)	(74:3 79:2)
	EPU China	69:9%	83:0%
		(67:2 72:1)	(78:1 85:4)

Table 2 :

 2 Global equity market interconnectedness in times of macroeconomic uncertainty: a geographic perspective Notes: The table summarizes global interconnectedness measure in the low-and high-uncertainty regimes with respect to geographic area. Models are computed over 10,000 parametric bootstrap replications and 100 randomly selected VAR orderings. + denotes that interconnectedness are signi…cant at the 5% level and robust to randomly selected VAR orderings.

	Geographic area	Low uncertainty High uncertainty
	U.S.	75.3% +	82.6% +
	Europe	75.7% +	80.4% +
	UK	78.4% +	79.9% +
	Japan	76.1% +	86.5% +
	Canada	77.6% +	79.5% +

Table 3 :

 3 Global government bond yields interconnectedness in times of uncertainty

	Uncertainty source	Low uncertainty High uncertainty
	Financial uncertainty	65.1% 0	78.6% 0
	Macro uncertainty	66.9% 0	75.1% 0
	EPU US	64.8% 0	72.8% 0
	EPU Europe	63.6% 0	87.6% 0
	EPU China	63.2%	0	89.4% 0

Table 5 :

 5 Diebold-Yilmaz network index for international equity markets

		USA UK GER FRA ITA NLD SPA PRT GRC CHN BRA RUS IND FROM
	USA	75.3	1.9	5.4	0.8	0.4	2.2	0.3	1.2	3.9	1.4	1.7	3.5	2.0
	UK	56.3 24.8	3.3	0.5	1.2	0.7	0.3	1.2	5.0	3.1	0.8	1.9	1.0
	GER 54.1	6.3	24.4	1.6	0.2	1.5	0.1	0.4	2.6	2.3	0.1	4.1	2.3
	FRA 54.6 12.0	11.5	9.3	0.9	0.3	0.6	0.7	2.4	3.2	0.4	2.8	1.5
	ITA	40.7 13.9	13.3	8.4	11.7	0.3	1.0	1.2	4.2	1.1	0.6	1.2	2.4
	NLD 53.0 13.2	8.5	3.6	0.3	10.5	0.2	0.5	2.6	3.6	0.6	1.4	2.0
	SPA	43.8 13.8	6.5	8.5	3.6	0.4	13.7	1.1	4.2	2.0	0.4	1.1	1.0
	PRT	30.2 17.9	7.5	11.5	3.8	0.1	3.5	18.1	2.2	1.8	1.6	1.7	0.4
	GRC 25.2 14.1	6.5	6.4	2.4	1.4	4.3	2.9	29.7	2.4	0.8	1.3	2.0
	CHN	8.6	3.4	2.2	1.3	0.7	0.2	0.6	3.5	2.9	70.3	1.0	1.8	3.4
	BRA 35.8	7.0	1.9	1.0	1.3	4.2	0.9	0.3	5.0	2.5	36.7	0.4	3.0
	RUS 26.1	6.1	1.3	2.7	0.8	2.9	1.5	0.6	5.1	1.6	7.3	39.5	4.4
	IND	24.1	5.0	2.2	2.5	5.0	1.1	1.7	2.2	3.3	1.5	1.5	1.9	47.4
	TO	453	115	70	49	21	15	15	16	43	26	17	23	25	68:3%
	NET 428	34	-6	-42	-68	-74	-71	-66	-27	-3	-46	-38	-27

Table 6 :

 6 Diebold-Yilmaz network index for developed equity markets

		USA UK GER FRA ITA NLD SPA PRT GRC	FROM
	USA	86.0	0.7	3.7	1.3	2.9	2.2	0.6	1.7	1.0	14
	UK	62.1 27.3	6.6	0.5	0.5	1.4	0.3	0.8	0.4	73
	GER	62.1	6.6	23.9	1.1	2.0	2.9	0.4	0.4	0.7	76
	FRA	60.8 11.4 12.6	9.8	1.7	1.4	0.4	0.8	1.1	90
	ITA	44.5 12.8 12.6	9.6	16.5	1.3	0.7	0.6	1.2	83
	NLD	59.1 14.0	8.3	3.1	2.5	10.9	0.1	1.2	0.8	89
	SPA	48.3 12.0	6.3	8.0	6.5	1.2	15.1	0.4	2.3	85
	PRT	33.2 14.8	8.5	12.2	4.0	1.9	3.7	19.7	2.0	80
	GRC	30.0 11.9	5.0	8.3	4.5	0.9	3.6	1.5	34.3	66
	TO	400	84	64	44	25	13	10	7	9	72:9%
											(71:4 74:1)
	NET	386	12	-13	-46	-59	-76	-75	-73	-56

Table 7 :

 7 Diebold-Yilmaz network index for emerging equity markets

		CHN BRA RUS IND	FROM
	CHN	96.7	0.4	1.6	1.3	3
	BRA	9.2	88.3	0.7	1.8	12
	RUS	8.0	37.3	53.9	0.8	46
	IND	13.6	19.1	5.5	61.7	38
	TO	31	57	8	4	24:9%
						(21:4 29:9)
	NET	29	42	-38	-34

Table 8 :

 8 Tests for the threshold e¤ect in international equity markets Notes: VXO is the CBOE index of percentage implied volatility used to proxy for …nancial uncertainty. M1 denotes macroeconomic uncertainty at 1 month according toJurado et al. (2015). EPU indexes are policy uncertainty measures developed byBaker et al. (2016). Sup-Wald: maximum Wald statistic over all possible threshold values, avg-Wald: average Wald statistic over all possible values, exp-Wald: function of the sum of exponential Wald statistics. denotes the rejection of the null hypothesis at the 5% signi…cance level.

	Threshold	Threshold		Wald Statistics		% high uncertainty Average duration
	variables	value	Sup-Wald Avg-Wald Exp-Wald		(in months)
	VXO	22.375	773.77	605.34	382.27	41.01%	6.4
	M1	0.714	847.45	678.49	419.11	19.36%	7.3
	EPU US	104.89	576.77	500.09	283.77	49.77%	7.4
	EPU Europe	138.42	779.95	592.92	385.36	39.17%	5.5
	EPU China	150.27	609.85	514.33	300.35	23.50%	3.5

Table 9 :

 9 Tests for the threshold e¤ect in developed equity markets Notes: VXO is the CBOE index of percentage implied volatility used to proxy for …nancial uncertainty. M1 denotes macroeconomic uncertainty at 1 month according to Jurado et al. (2015). EPU indexes are policy uncertainty measures developed by Baker et al. (2016). Sup-Wald: maximum Wald statistic over all possible threshold values, avg-Wald: average Wald statistic over all possible values, exp-Wald: function of the sum of exponential Wald statistics. Corresponding p-values are given in parentheses. denotes the rejection of the null hypothesis at the 5% signi…cance level.

	Threshold	Threshold		Wald Statistics		% high uncertainty Average duration
	variables	value	Sup-Wald Avg-Wald Exp-Wald		(in month)
	VXO	25.555	467.15	311.28	228.77	26.72%	3.8
	M1	0.685	435.06	362.90	213.32	40.55%	13
	EPU US	137.95	370.93	306.27	181.25	24.88%	6.6
	EPU Europe	164.23	380.37	324.13	186.07	24.58%	3.6
	EPU China	150.27	390.14	337.24	190.89	29.49%	3.7

Table 10 :

 10 Tests for the threshold e¤ect in emerging equity markets

	Threshold	Threshold		Wald Statistics	% high uncertainty Average duration
	variables	value	Sup-Wald Avg-Wald Exp-Wald		(in month)
	VXO	27.495	123.46	82.05	57.99	20.27%	3.9
	M1	0.723	150.47	79.59	70.52	17.05%	12.3
	EPU US	113.42	132.17	102.17	62.23	55.76%	7.8
	EPU Europe	126.62	122.43	84.40	56.79	45.62%	10.5
	EPU China	167.17	121.41	90.46	56.13	17.05%	3.1
	Notes: VXO is the CBOE index of percentage implied volatility used to proxy for …nancial
	uncertainty. M1 denotes macroeconomic uncertainty at 1 month according to Jurado et al.
	(2015). EPU indexes are policy uncertainty measures developed by Baker et al. (2016).
	Sup-Wald: maximum Wald statistic over all possible threshold values, avg-Wald: average
	Wald statistic over all possible values, exp-Wald: function of the sum of exponential Wald
	statistics. Corresponding p-values are given in parentheses. denotes the rejection of the null
			hypothesis at the 5% signi…cance level.

Table 11 :

 11 Nonlinear Diebold-Yilmaz network index in international equity markets under …nancial uncertainty

	low uncertainty

Table 12 :

 12 Nonlinear Diebold-Yilmaz network index in international equity markets under macroeconomic uncertainty

	low uncertainty

Table 13 :

 13 Nonlinear Diebold-Yilmaz network index in international equity markets under U.S.

	economic policy uncertainty
								low uncertainty
		USA UK GER FRA ITA NLD SPA PRT GRC CHN BRA RUS IND FROM
	USA	81.9	2.3	0.7	1.5	2.5	1.0	0.6	2.1	1.1	0.5	0.3	4.5	1.0
	UK	45.0 38.3	1.1	2.2	1.0	1.4	0.5	2.4	2.3	0.2	0.6	3.1	1.8
	GER 46.7	6.4	29.1	1.6	2.5	0.6	0.9	0.9	1.2	0.2	1.4	7.0	1.5
	FRA 48.5 12.3	12.8	13.1	1.5	1.1	0.7	0.8	0.8	0.2	0.4	6.8	1.1
	ITA	25.7 12.7	14.7	9.9	23.7	0.2	1.0	1.7	3.4	1.4	1.4	3.7	0.5
	NLD 41.4 15.8	13.2	4.7	3.0	13.9	0.3	0.4	0.8	0.1	0.8	4.7	1.1
	SPA 35.5 10.8	8.0	5.4	5.7	0.7	22.9	1.4	2.1	0.3	1.0	3.5	2.8
	PRT 21.3 11.5	9.3	17.2	4.2	0.5	4.8	22.1	2.3	0.2	0.5	4.1	2.0
	GRC 11.3	9.4	3.8	12.8	0.4	1.1	5.6	1.7	43.4	3.2	2.0	0.8	4.4
	CHN	6.6	0.5	1.3	1.9	1.1	1.5	0.5	1.0	3.3	78.5	1.8	0.3	1.8
	BRA 27.8	7.6	3.1	0.6	2.4	1.1	4.3	2.3	5.2	2.1	40.4	0.5	2.7
	RUS 21.1	2.5	3.7	0.7	2.1	4.3	1.9	1.8	6.4	2.0	9.0	40.0	4.3
	IND	21.7	3.0	0.6	1.3	4.7	0.8	0.3	1.8	0.9	2.5	2.9	1.6	57.9
	TO	240	114	113	96	26	18	47	27	42	23	35	29	22	64.0%
	NET 212	51	48	13	-54	-71	-30	-48	-13	-11	-23	-34	-40
								high uncertainty
		USA UK GER FRA ITA NLD SPA PRT GRC CHN BRA RUS IND FROM
	USA	48.4	8.9	6.5	1.8	0.6	3.3	6.2	4.4	2.0	4.6	2.7	6.7	3.6
	UK	38.0 17.2	7.2	1.5	1.7	1.5	3.6	3.1	3.1	3.7	3.1	9.8	6.5
	GER 48.7	5.5	16.8	0.7	0.5	43.8	3.2	4.4	3.3	1.5	1.9	5.9	3.7
	FRA 46.6 TO 546	97	73	40	24	30	25	13	18	52	30	13	13	75.0%
	NET 515	16	-8	-53	-67	-60	-65	-76	-63	17	-45	-57	-57

Table 14 :

 14 Nonlinear Diebold-Yilmaz network index in international equity markets under European economic policy uncertainty

	low uncertainty

Table 15 :

 15 Nonlinear Diebold-Yilmaz network index in international equity markets under Chinese economic policy uncertainty

	low uncertainty

See section

for a review of literature.

Other more sophisticated approaches such as that developed by[START_REF] Carriero | Measuring Uncertainty and Its Impact on the Economy[END_REF] simultaneously estimate uncertainty measures and their impact on the economy by accounting for both …nancial and macroeconomic uncertainty.

Fire sales denote the liquidation of large position by market participants.

[START_REF] Allen | Financial Contagion[END_REF] show that more complete networks are less susceptible to contagion since they provide better risk diversi…cation than incomplete networks.

Another branch of the literature on …nancial networks looks at contractual agreement among …rms (see Gai et al. 2011, Acemoglu et al. 2015, among others). Some others consider both correlation and physical networks (see Brunetti et al. 2015).

3 See Diebold and Yilmaz (2014) for a discussion on those points

[START_REF] Aizenman | Monetary Policy Spillovers and The Trilemma in The New Normal: Periphery Country Sensitivity to Core Country Conditions[END_REF] We estimate the network index over 100 random Cholesky permutations. The decision to reduce the number of possible permutations is driven by the calculation time. For a deterministic approach, see[START_REF] Klössner | Exploring All VAR Orderings for Calculating Spillovers? Yes, We Can! A Note on Diebold and Yilmaz[END_REF].

[START_REF] Aizenman | The Transmission of Federal Reserve Tapering News to Emerging Financial Markets[END_REF] Assuming that the world is proxied by all the countries within the system.

[START_REF] Alfaro | The …nance-uncertainty multiplier[END_REF] In the empirical section, we consider three groups of countries: (i) the international markets group, which includes all of our equity markets (developed and emerging countries), (ii) the developed markets group and (iii) the emerging markets group. For each group, we estimate …ve equations with di¤erent uncertainty proxies to disentangle the e¤ects of …nancial uncertainty, macroeconomic uncertainty, and economic policy uncertainty.1 7 In so doing, we also assume that uncertainty is exogenous with respect to …nancial markets interconnectedness (seeLudvigson et al

., 2015, or Caldara et al., 2016, for further details on the endogenous or exogenous nature of uncertainty).

[START_REF] Adrian | Liquidity and Leverage[END_REF] The choice of H is discussed in section 62 4 We choose to report results for 10,000 bootstrap replications. Our results are however robust to the number of replications.

[START_REF] Aizenman | The Transmission of Federal Reserve Tapering News to Emerging Financial Markets[END_REF] As noted above, by de…nition of the column "FROM" is equal to 100% minus the diagonal elements, whereas the row "TO" is not constrained to sum to 100%.2 6 To ensure a su¢ cient number of data points for the estimation procedure in each regime, the grid is trimmed at 15% as is common in the literature. 2 7 The three statistics are (i) the maximum Wald statistic over all possible threshold values (sup-Wald), the average Wald statistic over all possible values (avg-Wald), and a function of the sum of exponential Wald statistics (exp-Wald).

[START_REF] Baker | Measuring Economic Policy Uncertainty[END_REF] While we cannot directly compare each threshold value from one group (say, developed markets) since the uncertainty measures are not in standardized units, it is possible to compare the values for di¤erent groups.2 9 The average duration of high-uncertainty periods is calculated by dividing the total number of months in the high-uncertainty regime (when the proxy is above the threshold) by the length of the whole sample.

0 Sub-group results for developed and emerging markets go in the same direction and are robust; results being available from the authors upon request.

[START_REF] Acemoglu | Systemic Risk and Stability in Financial Networks[END_REF] As for the benchmark model, we choose to report results for 10,000 bootstrap replications. Our results are however robust to the number of replications.

[START_REF] Adamic | Trading Networks[END_REF] We choose to focus on Ci RoW rather than Cj!RoW since the former is constrained to sum to 100%, which is more intuitive to depict than the latter.

[START_REF] Adrian | Liquidity and Leverage[END_REF] To save space, we do not report detailed pairwise connections. Additional results are however available from the authors upon request.

Powered by TCPDF (www.tcpdf.org)

thank Chiara Scotti for sharing her data. The usual disclaimers apply. Bertrand Candelon conducted this project as part of the research program "Risk Management and Investment Strategies (RMS)" under the aegis of the Europlace Institut

Appendix