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Does Economic Policy Uncertainty Lead Systemic Risk? A Comparative Analysis of Selected European Countries.

Introduction

Systemic risk has become one of the central issues in macro-financial research. It emerges from the financial sector and has a potentially severe impact on the broader economy. The buildup of systemic risk and the way it can spread to the real sector have been modeled extensively, and as a result, there are numerous empirical measures of it (Bisias et al. 2012). Yet, there is an obvious lack of studies which investigate potential precursors of systemic risk.

In this paper, we pinpoint one of them-economic policy uncertainty-and study its lead-lag linkages with systemic risk for such European countries as France, Germany, Ireland, Italy, the Netherlands, Russia, Spain, Sweden and the UK. The choice of countries is largely motivated by data availability. However, the sample we compiled allows for a promising analysis from the comparative perspective, since it includes both the major European economies and peripheral countries which were in the spotlight during the European financial crisis. We will compare and assess the economic policy uncertainty-systemic risk nexus for these countries during the crisis period and beyond. Our sample runs from January 2010 to September 2016, encompassing not only the European financial crisis, but also a number of political events which strongly affected economic and financial decision-making in these countries, e.g., the Brexit referendum and the Ukrainian crisis in 2014, one of the triggers of the economic crisis in Russia.

The theoretical literature on macroeconomic and political uncertainty provides a conceptual background for systemic risk. It builds on the Knightian distinction between uncertain and risky outcomes. According to Knight (2006[1921]), under uncertainty there is no information about the likelihood of events happening. In contrast, risk implies a known probability distribution over a set of events. In line with such logic, assessing systemic risk involves inferring the probability distributions of financial stress indicators, even though they may deviate from standard patterns and exhibit heavy tails. If it appears problematic to estimate the probabilities, thereby passing from uncertainty to risk, economic agents start to manifest uncertainty aversion, which has adverse repercussions for financial stability.

For example, Dicks and Fulghieri (2015) propose a theory of systemic risk based on Knightian uncertainty, showing how idiosyncratic risks can snowball into systemic risk due to contagion. The latter is triggered by uncertainty aversion among investors when bad news about one asset class shapes worse expectations about other asset classes. As a result, systemic rather than individual runs on financial institutions occur.

To test for lead-lag linkages between economic policy uncertainty and systemic risk, we need tractable measures for both. In recent years, diverse uncertainty measures have been proposed (Creal and Wu 2014; Baker et al. 2016; Jurado et al. 2015; Pastor and Veronesi 2013; Rossi and Sekhposyan 2015), which primarily boosted the empirical literature studying the impact of uncertainty on stock market returns and volatility. (1) Volatility belongs in the category of systemic risk measures but gauges turbulence in a single segment of the financial sector. There have been attempts to bridge uncertainty and other systemic risk measures. Manzo (2014) studies the determinants of sovereign systemic risk for 24 European countries embedded in their credit default swap (CDS) term structures and finds that uncertainty in the EU as a whole adds up a significant amount of this risk, with a lead-lag effect of 1 month. Bernal et al. (2016) investigate the effect of uncertainty on systemic risk in the Eurozone bond market. They adopt the well-known systemic risk measure, delta conditional value-at-risk ([DELTA]CoVaR) by Adrian and Brunnermeier (2016), to quantify risk spillovers from France, Germany, Italy, and Spain to the Eurozone bond market as a whole, and find strong evidence that economic policy uncertainty in core (France, Germany) and peripheral (Italy, Spain) countries is an important predictor of these spillovers. Both studies exploit Economic Policy Uncertainty (EPU) indices (Baker et al. 2016), reflecting the coverage of policy-related uncertainty in major newspapers. However, these papers assess the linkage between uncertainty and a relatively narrow aspect of systemic risk. Sun et al. (2017) investigate the dynamic interaction between the US EPU index and an aggregate indicator, the St. Louis Fed Financial Stress Index, and find strong, but drastically varying correlations in the short and medium run. In the short run, unidirectional spillovers from financial stress to uncertainty prevail, while in the longer run they become bidirectional.

In this research, we opt for the EPU index as a proxy for economic policy uncertainty and construct composite systemic risk measures for the sample countries. We base our analysis on the premise that the EPU index is a metric aimed at capturing changes in public sentiment with respect to economic developments through the media data. By definition, it can gauge qualitative shifts but can hardly provide accurate estimates of the probabilities of these changes. Therefore, we believe the EPU index to correspond to the Knightian concept of uncertainty. On the contrary, when constructing composite systemic risk measures, we rely on the financial variables which can be used to derive the likelihood of a systemic crisis either directly, e.g., probabilities of default, or indirectly, e.g., CDS spreads or bond yields. These measures mesh well with the Knightian concept of risk.

Our contribution to the literature is two-fold. First, to conduct an in-depth analysis of the relationship between systemic risk and the EPU indices in the time series framework, namely, in (1) time and (2) time-frequency domains, allowing for bivariate linkages, and in (3) a multivariate setting, we construct novel composite measures of systemic risk. Following Freixas et al. (2015) and Giglio et al. (2016) who assert that aggregate systemic risk metrics can be more informative and coherent compared to individual ones, we do not confine ourselves to a single aspect of systemic risk. Rather, we consider three complementary types of systemic risk: (1) domestic financial sector fragility, (2) sovereign creditworthiness and (3) vulnerability to external shocks associated with sudden capital outflows. To derive the composite measure, twelve variables across these types are aggregated by means of the dynamic factor model estimated with the aid of the maximum likelihood method for January 2010-September 2016.

Second, we investigate the lead-lag relationship between the composite systemic risk measures and the EPU indices in the three different settings.

As a starting point of our analysis, standard and nonparametric bivariate Granger causality (Diks and Panchenko 2006) tests apply, yielding controversial results for four out of nine sample countries. In this light, we proceed to test for the bivariate linkages, combining time and frequency domains through the continuous wavelet transform (CWT). Namely, we assess wavelet coherence between the EPU indices and composite systemic risk measures to find regions in time-frequency space where the two time series co-move. To our knowledge, this paper is the first to apply this multi-scale approach to systemic risk modeling. (2) This statistical technique reveals that there is significant variation in lead-lag patterns between economic policy uncertainty and systemic risk across frequencies and time spans, thereby legitimizing the inconclusive findings of the bivariate Granger causality tests. However, based on the wavelet coherence, it is possible to distill prevailing lead-lag patterns for some countries. We find that EPU indices tend to lead systemic risk for Ireland, the Netherlands, Russia, Spain and the UK. This directional pattern becomes more visible at lower frequencies, i.e., over longer time periods.

We next study the linkages in a data-rich environment, combining financial and macroeconomic indicators. To this end, Bayesian vector autoregressions (BVAR) with endogenous and exogenous variables are estimated. The set of endogenous variables includes the composite leading indicator for a given country, the EPU index dynamics, dynamic factor-based measure of systemic risk, unemployment rate, consumer price index and the year-on-year growth rate of industrial production index. We use the VIX index, TED spread, US yield curve spread, composite systemic stress index for the EU, and IMF commodity price index as exogenous variables. Therefore, our aim is to examine simultaneously the lead-lag relationship between EPU and systemic risk as well as the impact of uncertainty on key macroeconomic variables, conditional on the changes in global, regional risk factors and on the shocks in the world commodities market.

Based on impulse-response functions and forecast error variance decompositions, we arrive at the findings which resonate with the CWT analysis. The EPU index leads systemic risk in case of Ireland, Italy, Russia and Spain. In Russia, it explains up to 19% of the variance in the composite systemic risk measure while for Ireland, Italy and Spain this proportion oscillates around 6-7%. In a nutshell, we find evidence that economic policy uncertainty can exacerbate systemic risk and its impact is particularly pronounced in more financially fragile economies. We also document direct negative effects which the EPU indices exert over employment and/or industrial production. An increase in the EPU index leads to a statistically significant decline in industrial production in Ireland and Russia. In Italy and the Netherlands, economic policy uncertainty raises unemployment. In Spain, the EPU index fuels systemic risk which increases unemployment and suppresses industrial production.

Finally, we estimate a panel BVAR with the same sets of endogenous and exogenous variables to examine if our results hold for the sample as a whole. In this framework, the EPU index is also found to lead systemic risk, which in its turn produces a negative real effect through a surge in the unemployment rate. Hence, policymakers need to elaborate specific instruments to tame economic policy uncertainty as a part of their macroprudential toolkit aimed at mitigating systemic risk. Given its impact on real variables, deterring high uncertainty about economic policy and politics at large also contributes to the overall economic stability.

The remainder of the paper is as follows. "Data" section introduces the data, describing how composite systemic risk measures are built from numerous raw indicators. It also characterizes the features of the systemic risk measures as well as the EPU index. The econometric methodology encompassing conventional and nonparametric Granger causality tests, wavelet coherence and BVAR is explained in "Econometric Methodology for the Analysis of the Economic Policy Uncertainty-Systemic Risk Nexus" section. "Results" section characterizes bivariate lead-lag relationships between the EPU index and systemic risk for the sample countries and documents such linkages in the BVAR and panel BVAR frameworks. "Conclusions" section concludes.

Data

Deriving Composite Systemic Risk Measures

Systemic risk is unobservable and it is not straightforward to measure it. Freixas et al. (2015) and Giglio et al. (2016) emphasize that individual systemic risk measures can send incoherent and imprecise signals about financial instability while their performance tends to improve if they are compressed and their common trend is considered. We propose a proxy for systemic risk by constructing a single indicator capturing the overall state of financial stability in the sample countries. It is based on a dynamic factor model estimated by means of the maximum likelihood. This technique and its more sophisticated extensions allowing for mixed data frequencies and arbitrary patterns of missing observations has become a widespread approach to assessing financial stress (Aboura and van Roye 2017; Dovern and van Roye 2014; Schwaab et al. 2014; van Roye 2014). We adopt the baseline model set up in the following form:

[y.sub.it] = [[LAMBDA].sub.i][f.sub.it-1] + [[epsilon].sub.it], [[epsilon].sub.it] ~ (0,[C.sub.i]), (1)

In this equation, [y.sub.it] is a vector of normalized systemic risk measures for country i, [f.sub.it] is a single country-specific latent factor, and [[LAMBDA].sub.i] is a n x 1 vector of the factor loadings. Likelihood ratio tests confirm our assumption of a single dynamic factor versus two or more latent factors for all the sample countries. The extracted dynamic factor corresponds to our composite systemic risk measure (DF). The following transition equation describes the dynamics of this measure, [f.sub.it]:

[f.sub.it] = [A.sub.i][f.sub.it-1] + [[xi].sub.it], [[xi].sub.it] ~ (0,[D.sub.i]), (2)

where [A.sub.i] is an autoregressive coefficient. For each time period, we compute a country-specific DF as the estimate of the latent factor [f.sub.it] at this time point.

To construct an informative DF measure, we exploit systemic risk measures of three types. The first type of measures characterizes the fragility of the domestic financial sector. Most of these indicators come from the HEC Lausanne systemic risk dataset. Specifically, we use monthly series of long run marginal expected shortfall (LRMES), conditional capital shortfall (SRISK), leverage (LEVERAGE), inverted value of cumulative stock market capitalization (MCAP), stock market volatility (VOLAT). The LRMES is defined as the sensitivity coefficient of a domestic financial institution capitalization to a 40% semiannual world stock market decline. The SRISK assesses the capital shortage (in bln US dollars) which this institution is to experience under the above-mentioned adverse conditions in the world market. The nationwide LRMES and SRISK are weighted sums of the metrics for individual financial institutions. (3) The volatility indicator is derived from the GARCH models while leverage is the mean of domestic financial institutions' balance sheet-based indicator. We modify one of the measures, using the inverse ratio of cumulative stock market capitalization. By doing so, we ensure that increases in all the series are uniformly interpreted as a systemic risk buildup. To capture the fragility of the domestic financial sector in a more comprehensive way, we also need a specific corporate credit risk measure. We use the probability of default (PD) averaged across the main institutional sectors of the sample countries as a proxy for this risk. The PD measure is an aggregate estimate of the likelihood of a default in the private sector of the sample countries over a 1-year horizon. These data series are provided by the Risk Management Institute of the National University of Singapore. (4)

Given the credit risk transfer from the corporate to the sovereign sector in Europe prior to the outbreak of the debt crisis and mutually reinforcing linkages between the sectors ("diabolic loop"), our second type of measures is based on sovereign creditworthiness. Five-year sovereign CDS spreads (CDS) and long-term sovereign bond yields (GOVBOND) serve as its proxies.

We consider vulnerability to external shocks as the third type of systemic risk measures. It is proxied by four indicators. We adopt the correlation of a national stock market with the world one (WMCorr), assuming that its higher positive values indicate an increased proness to external shocks. The next indicator is the Diebold-Yilmaz net connectedness indices (DY) for stock market volatilities (Diebold and Yilmaz 2014). The original data are available on daily basis. If this metric takes on positive values, a country is categorized as a net generator of stock market volatility spillovers. In the opposite case, this country turns out a net recipient. Taking these features of the connectedness indices into account, we use their monthly averages multiplied by minus one so that positive values indicate a higher level of vulnerability. Finally, we add two variables capturing cross-border capital flows, namely the changes in allocations to a country's bond (BONDALLOC) and equity (EQALLOC) markets by international portfolio investment funds. Both monthly series are retrieved from Emerging Portfolio Fund Research (EPFR). We assume that a decline in the amount allocated, primarily arising from net outflows, is associated with an increase in systemic risk. Again, to ensure the uniformity of the data we use the series with the opposite sign.

Features of the Composite Systemic Risk Measures

There is much commonality in the relative importance of the three types of systemic risk measures for the sample countries. The maximum likelihood estimates of the factor loadings in Eq. 1 indicate that domestic financial sector fragility and sovereign credit risk measures are by far more important than external vulnerability indicators (Table 1). However, there is notable heterogeneity with respect to the significance of individual measures within these types. As for domestic financial sector fragility, LEVERAGE, MCAP and SRISK appear more important than LRMES, PD and VOLAT. Notably, LEVERAGE has very high factor loadings across all the sample countries.

There is slightly more variation in the factor loadings of MCAP and SRISK, both having values in the range of 0.75-0.99. LRMES has statistically significant factor loadings on all the countries' composite systemic risk measures, albeit their magnitude is less than in case of LEVERAGE, MCAP and SRISK. For Ireland, the LRMES measure has an atheoretical negative sign. The factor loadings of the PD measure tend to be lower, except for Spain. VOLAT closes the list with the marginally significant loadings for Ireland and Italy and insignificant ones for the Netherlands, Sweden and the UK. LEVERAGE and MCAP are inputs for SRISK computation (Brownlees and Engle 2017), and the latter fares well as an individual systemic risk measure versus alternative metrics (Pankoke 2014; Stolbov and Shchepeleva 2018). Against this backdrop, their tight connectedness with the composite measure is not surprising. LRMES also underpins SRISK algebraically but its value as a standalone systemic risk indicator is questionable, given its close link with systematic risk, i.e., the market beta (Benoit et al. 2017).

As for the second type, sovereign CDS spreads make more sizeable contribution to the composite systemic risk measure than long-term bond yields. This finding lends support to the view that over the past years sovereign CDS contracts have become more important than bonds in terms of price discovery in the sovereign debt market (Arce et al. 2013; Coudert and Gex 2013). Interestingly, CDS spreads have bigger factor loadings on the composite systemic risk measures even despite the EU ban on speculative trading in sovereign CDS contracts enacted November 1st, 2012.

As regards external vulnerability, WMCorr and DY appear the most salient covariates of the composite system risk measure. However, they do not adhere to a uniform pattern. Increasing correlations with the world stock market imply a surge in systemic risk for Spain and the UK while for Ireland, Italy and the Netherlands they are associated with a drop in the overall financial stress. Similarly, the growing proness to stock market spillovers from abroad heightens systemic risk for France, Ireland and the Netherlands, while mitigating it for Sweden and the UK. Changes in the BONDALLOC and EQ ALLOC measures have significant factor loadings for Russia, suggesting that its systemic risk is highly sensitive to the global investors' sentiment. Implicitly, it means that measures tracking portfolio investment flows can improve the performance of composite systemic risk metrics for some emerging markets.

The composite systemic risk measures largely tend to co-move across the sample countries, except for Ireland and Russia (Fig. 1). The Irish systemic risk appears the most acute in the sample during January 2010-June 2011 but considerably diminishes ever since. It mirrors the fact that Ireland was the first in the EU to enter the crisis and, to a great extent, managed to implement the resolution of its banking sector by 2011, followed by the first signs of economic recovery. Meanwhile, other EU countries were only nearing the peak of the crisis.

Overall, Fig. 1 shows that the dynamic factors accurately capture common hikes in systemic risk for the EU countries in the late 2011 and early 2012. As for Russia, its systemic risk is largely asynchronous with the rest of the countries, gradually increasing since early 2013 and reaching its climax in December 2014-January 2015.

Economic Policy Uncertainty Indices

The EPU index was originally developed for the USA by Baker et al. (2016). It reflects the standardized frequency of articles published in ten leading US newspapers which simultaneously contain the following terms: "economy" or "economic", "uncertainty" or "uncertain", and one from a selection of terms related to policy (such as "Federal Reserve", "Congress", "deficit", etc.).

As of April 2018, the index covers 21 countries, both advanced economies and emerging markets. In each case, it largely builds on the US approach, but is constructed in cooperation with persons with native-level fluency and economics expertise. Thus, term searches in the newspaper archives are conducted in the native language of the country in question. The choice of newspapers and terms is also country-specific. The list of newspapers and terms for the sample countries is provided in Table 2.

Figure 2 represents the dynamics of the EPU indices. They remain within relatively narrow bounds during the European financial crisis. There are few outliers, which are associated with the Russian and British economic policy uncertainty, denoting the outbreak of the Ukrainian crisis in the early 2014 and the Brexit referendum in June 2016, respectively.

Based on ordinary correlations, positive and statistically significant contemporaneous linkages prevail between the EPU indices and composite systemic risk measures in the sample (Table 3).

However, the coefficients are far from indicating a close relationship. We conjecture that the linkages can vary over time and frequencies, with one variable leading the other. Therefore, the insignificance of correlations for Ireland and Sweden does not imply the absence of such linkages since they can be gauged in non-contemporaneous and/or nonlinear bivariate settings, which we examine next.

Econometric Methodology for the Analysis of the Economic Policy Uncertainty-Systemic Risk Nexus

In this section, we investigate lead-lag patterns between the EPU indices and composite systemic risk measures, using a number of econometric methods. First, conventional and nonparametric Granger causality tests as well as wavelet coherence are described. They allow to test comprehensively for bivariate linkages between systemic risk and economic policy uncertainty. Then, we specify the Bayesian VAR models, which are feasible in a setting with multiple macroeconomic and financial variables. We aim to provide an intuitive and largely non-technical explanation for the techniques here, while "Results" section conveys the results of our empirical exercise, based on the methods mentioned above.

Standard and Nonparametric Granger Causality Tests

To run the standard Granger causality tests, we first estimate bivariate VAR models. We employ the Toda and Yamamoto (1995) approach instead of taking first differences to secure stationarity in the data. Under this approach, a VAR(p) model should be set up in levels, regardless of the orders of integration of the time series. An appropriate lag length for the variables in the VAR model is then determined based on information criteria. The Bayesian Schwarz Information Criteria (BSIC) is used as a benchmark. The model is also examined for overall stability, i.e., the eigenvalues are within the unit circle, and there is no serial correlation in the residuals. If the maximum order of integration of the variables is m, then the preferred VAR model should be extended to include these in additional lags. For example, if the maximum order of integration is I = 1 and the optimal model is VAR(2), the specification that ensures the validity of Granger causality test will be VAR(3). It is important to note that the test should be based on the initial number of lags, i.e., p=2, while the additional lagged variables are necessary to fix up the asymptotics. That is, these lagged variables enter the augmented VAR model exogenously.

Let the lag-augmented bivariate vector autoregressive (VAR) representation of the two series have the following form:

[x.sub.t] = [a.sub.1] + [[summation].sup.p.sub.i=1] [[alpha].sub.i] [x.sub.t-i] + [[summation].sup.p.sub.i=1] [[beta].sub.i][y.sub.t-i] + [[epsilon].sub.it] (3)

[y.sub.t] = [b.sub.1] + [[summation].sup.p.sub.i=1] [[gamma].sub.i] [x.sub.t-i] + [[summation].sup.p.sub.i=1] [[delta].sub.i][y.sub.t-i] + [[xi].sub.it] (4),)

where p is the lag length of [x.sub.t] and [y.sub.t] variables. Two null hypotheses can be tested: (1) y does not Granger cause x, which implies that [[beta].sub.1] = ... = [[beta].sub.p] = 0; and (2) x does not Granger cause y, expressed as [[gamma].sub.1] = ... = [[gamma].sub.p] = 0. The test statistic for the null hypotheses is Chi-square, since the VAR Granger (no) causality test is equivalent to the block exogeneity Wald test.

A descriptive analysis of the composite systemic risk measures and the EPU indices unveils signs of nonlinearity in both data series. (5) Therefore, we also adopt the Diks-Panchenko nonparametric test for bivariate causality (Diks and Panchenko 2006) which effectively captures causal linkages in the presence of nonlinearities. This test applies to the levels of the series and runs in both directions for lags from 1 to 10 and for the bandwidth equal to 1.5, taking into account the time series length. Its null hypothesis resembles that of the standard Granger causality test, namely X does not help predict Y and Y does not help predict X. The T-statistic, which obeys normal distribution, is calculated to test the null at each lag.

Wavelet Coherence

The causality tests described in the previous section are performed in the time domain while the frequency domain is left out. However, the linkages between systemic risk and economic policy uncertainty may vary at different frequencies. Since the individual systemic risk measures underpinning our composite metric are based on high frequency (daily and weekly) data while the EPU indices are compiled monthly, it is natural to assume that the former can trigger the latter in the short run, i.e., at high frequencies. Over longer time horizons, however, economic policy uncertainty may persist and cluster for various reasons, e.g., due to uncertain electoral outcomes alongside an ongoing recession (a typical scenario for some EU countries) or an economic downturn accompanied by the tensions in foreign policy (the case of Russia). Thus, one cannot rule out that at medium and lower frequencies economic policy uncertainty can start to lead systemic risk.

We use the continuous wavelet transform (CWT) and a specific tool pertaining to this approach - the wavelet coherence. One should perceive it as a localized correlation coefficient between two data series previously decomposed in the time-frequency space. There are different wavelet functions available for such decomposition. In this study, we adopt the Morlet wavelet,

[PSI](t) = [[pi].sup.[1/4]] exp(i[[omega].sub.0]t) exp (-1/2[t.sup.2]), (5)

which is a complex valued wavelet with an optimal joint time-frequency concentration. This wavelet function is the most common in economic and financial studies, e.g., Funashima (2017), Reboredo et al. (2017), since it secures the best trade-off between time and frequency localization (Aguiar-Conraria and Soares 2010, 2011). Typically, the frequency parameter co0 is set to 6, making the so-called wavelet scale (the parameter accounting for the wavelet length) inversely related to the frequency.

The wavelet coherence is a convenient tool to analyze lead-lag relationships because it also enables to test if two series move in-phase or anti-phase. Moving in-phase suggests that both series change in the same direction. Corresponding wavelet coherence plots for the sample countries are represented in "Causalities and Comovement Between Systemic Risk and Economic Policy Uncertainty in the Bivariate Setting" section.

Bayesian VARs

The linkages between systemic risk and economic policy uncertainty may alter if tested in the settings with multiple macroeconomic and financial variables. To this end, we estimate Bayesian vector autoregressions (BVAR) for each of the sample countries. We include both endogenous and exogenous variables into our specification. The list of endogenous variables comprises the OECD composite leading indicator for a given country (CLI), its EPU index dynamics, dynamic factor-based measure of systemic risk (DF), unemployment rate (U), consumer price index (CPI) and the growth rate of industrial production index (IP). We choose this variable ordering, assuming that it reflects an increasing degree of variable endogeneity. (6) Hence, we believe that CLI depends the least on the other indicators, while IP depends the most. The VIX index (VIX), TED spread (TED), US yield curve spread (YCURVE), composite systemic stress index for the EU (CISS), and IMF commodity price index (COMINDEX) enter the BVAR models as exogenous variables. Therefore, we seek to examine simultaneously the lead-lag relationship between EPU and DF and the impact of uncertainty on key macroeconomic variables, conditional on the changes in global (VIX, TED, YCURVE), regional (CISS) risk factors as well as on the shocks in the world commodities market (COMINDEX). The Minnesota/Litterman prior is adopted to estimate the BVAR models. The specification includes one lag of all variables. We base our inference on the impulse-response functions (IRF) and forecast error variance decompositions (FEVD). (7) To derive orthogonal shocks, we use a structural triangular factorization. In contrast to a Choleski ordering, this method allows for shocks with a different magnitude.

Finally, we specify a panel BVAR to examine if our findings in the country-level estimations are consonant with the conclusions derived for the whole sample.

Results

Causalities and Co-movement Between Systemic Risk and Economic Policy Uncertainty in the Bivariate Setting

We first report the findings of the conventional Granger causality tests described in "Standard and Nonparametric Granger Causality Tests" section. Table 4 summarizes the results of the ADF unit root tests, (8) which are used to determine the maximum order of integration for the Toda-Yamamoto correction. It appears that this correction only applies to the vector autoregression models, estimated for France, Italy and Germany. Table 5 reports the results of the Granger causality tests, based on these VARs.

Systemic risk Granger causes economic policy uncertainty at the 5% level in Germany, Russia and Spain, while for France and Italy it is significant at the ten percent level. In this linear bivariate setting, there is no evidence of causality running in the opposite direction. (9)

The Diks-Panchenko nonparametric test corroborates the causality running from systemic risk to economic policy uncertainty for France, Germany and Italy and the absence of any causal linkage for Ireland and the Netherlands. Yet, it indicates that uncertainty leads systemic risk in Spain and Sweden. According to this test, no causality between the variables is found for Russia. It also rejects the neutrality hypothesis for the UK where systemic risk appears to drive uncertainty. Except for France, the causalities are significant at the ten percent level (Table Al in the Online Appendix).

The two causality tests yield only partly overlapping results. Therefore, we explore bivariate linkages between economic uncertainty and systemic risk in the combined time-frequency domain, deriving wavelet coherences, as suggested in "Wavelet Coherence" section.

In Fig. 3, we report the graphical output of such analysis for France. (10)

Time is displayed on the horizontal axis, while the vertical axis shows frequency (the lower the frequency, the higher the periodic scale). Grey and white colors in the time-frequency space denote regions with stronger interrelations between the EPU index and composite systemic risk measure. Darker colors (black) are associated with no dependence between the series. The delineated areas in grey or white indicate statistically significant wavelet coherences. Darker cone lines leave out edge effects, shaping the so-called cone of influence. Arrows show if the series move inphase (if they point to the right) or anti-phase (to the left). The order of variables as inputs for the analysis matters for the interpretation of its results: for all the sample countries, we designate systemic risk (DF) as the first variable. Thus, arrows pointing to the right-down (left-up) signify that systemic risk leads economic policy uncertainty when they move in-phase (anti-phase). Conversely, if the arrows direct to the right-up or left down, it means that the EPU index drives systemic risk.

In case of France, we find a few minor spots with significant coherences. They correspond to very high and medium frequencies. In terms of timescale, they refer to the early 2011, late 2012 and late 2015. The arrows tend to point to the right or slightly right-down or left-up, suggesting that DF leads EPU. This evidence is relatively weak, albeit supportive of the time domain causality tests' findings.

Similar to France, our analysis reveals weak wavelet coherence for Ireland, Italy, the Netherlands, Sweden and the UK (Figs. 4, 5, 6, 7 and 8). However, the plots show distinct patterns of lead-lag relationships between the EPU indices and composite systemic risk measures.

In Ireland, Italy and Sweden, systemic risk and economic policy uncertainty tend to co-move, while for the Netherlands and UK their motion is anti-phase in the areas with significant wavelet coherences. The coherence is mostly present at high and medium frequencies (for the periods lasting up to 12 months), clustering around the year 2012. In contrast to the causal analysis in the time domain, there is more evidence in the wavelet coherence analysis that the EPU indices lead systemic risk. The plots indicate that this is the case for Ireland, the Netherlands and the UK. For Italy and Sweden, the leading indicator varies at different frequencies, thereby making the overall picture less clear.

We find more evidence of significant wavelet coherences for Germany, Russia and Spain (Figs. 9, 10 and 11).

In Germany, DF and the EPU index move in-phase at medium frequencies (in the tune of 12 months), while at low ones (around 24 months) there are signs of anti-phase motion. The anti-phase dynamics starts to prevail since the year 2013. It is noteworthy that systemic risk leads uncertainty when both move in-phase in 2011-2012, whereas the EPU index turns into the driver afterward in terms of the anti-phase motion. In Russia, systemic risk and economic policy uncertainty move in-phase at medium frequencies from early 2014 onwards, with the EPU index slightly leading DF. In Spain, the in-phase motion is observed at medium frequencies in 2011-2012 and in 2015-early 2016. It also persists at very low frequencies in 2014-2015. In the 2014-2016 period, economic policy uncertainty leads systemic risk.

In general, the evidence that uncertainty can lead systemic risk becomes more pervasive when we analyze their interrelation in the time-frequency space, thereby confirming our conjecture that uncertainty acts as a slow-moving variable, unleashing its impact over longer time horizons. Sun et al. (2017) obtain similar findings for the US, applying empirical mode decompositions (EMD) to conduct their multi-scale correlational analysis between the EPU index and the St. Louis Fed Financial Stress Index. However, unlike the wavelet coherence, their approach desentangles varying correlations only in the time domain.

Linkages Between Systemic Risk and Economic Policy Uncertainty in the Multivariate Setting

Finally, we present the evidence based on the BVAR methodology described in "Bayesian VARs" section. We first do it for individual countries and then for the whole sample. The impulse-response functions (IRFs) are reported in the Online Appendix (Figures A1-A9). The forecast error variance decompositions (FEVDs) for some countries are briefly described in the text below, though their detailed output is available upon request from the authors.

The EPU index leads DF for Ireland, Italy, Russia and Spain. In Russia, an increase in the EPU index by one standard deviation (SD) involves a rise in the composite systemic risk measure by 0.15 SD In Spain, it is equal to 0.12 SD, while for Italy and Ireland it totals 0.07 and 0.05, respectively. The statistically significant shocks persist most in Russia and Ireland (up to 10 months), while for Spain and Italy they are short-lived, lasting four and 2 months. The EPU index explains up to 19% of the variance of DF for Russia. In Ireland, Italy and Spain this proportion oscillates around 6-7%. We underscore no significant effect of the EPU index on DF or vice versa for France, Germany, the Netherlands, Sweden and the UK.

Thus, the empirical evidence suggests that economic policy uncertainty can exacerbate systemic risk, but its impact is pronounced in more financially fragile economies. In the countries with a more resilient financial sector, the adverse effect is leveled off due to better supervisory practices, which prevent unsustainable credit and asset price booms. Historical experience and general attitude toward financial institutions may also explain why economic policy uncertainty translates into a systemic risk more easily. For example, Russia faced three acute financial crises during past 20 years (1998, 2008, 2014). Given potential signs of financial distress, economic agents may be more susceptible to panic since past crises erode trust in domestic financial institutions. Other significant determinants of such erosion include lower individual wealth and less democratic social values (Fungacova et al. 2018). According to the World Values Survey 2010-2014, (11) the countries with more resilient financial sectors fare better than the financially fragile ones in terms of these institutional parameters.

We also document direct negative effects the EPU indices exert over employment and/or industrial production. An increase in the EPU index by 1 SD leads to the decline in industrial production by 0.24 SD in Ireland and by 0.03 SD in Russia. The EPU index contributes to the variance of the Irish industrial production by nearly 21%, while in Russia it explains only 2.9%. In Italy and the Netherlands, economic policy uncertainty raises unemployment. An innovation to the EPU index equal to 11 1 SD entails a rise in the unemployment rate by 0.02 SD in Italy and by 0.04 SD in the Netherlands. The EPU index accounts for 3.9 and 1.9% of the variance in unemployment rates for Italy and the Netherlands, respectively. This evidence of the contractionary impact which economic policy uncertainty exerts is in line with the findings in other studies, e.g., Baker et al. (2016), Balcilar et al. (2016), Karnizova and Li (2014). Thus, economic policy uncertainty appears a potent determinant of economic activity, as it retains its significance for these four countries even in the presence of the OECD composite leading indicators, which are intuitively expected to be "first-moment" predictors of the real variables in the BVAR models. These findings are robust to alternative variable orderings.

In Spain, the EPU index fuels DF which in its turn increases unemployment and suppresses industrial production. Although deciphering the channels though which this roundabout effect of uncertainty on economic activity works is beyond the scope of the paper, we assume that it may be due to frozen credit growth. This explanation echoes the findings by Bordo et al. (2016) who argue that increases in the EPU index significantly curtail loan supply in the US economy, especially by bigger banks with fragile balance sheets. The developments in the Spanish economy over 2008-2013 support this conjecture. After the Great Recession, it failed to rebound while uncertainty was rising as big banks, which were heavily engaged in mortgage loans and financing the construction sector, started to face solvency problems. Eventually, the Spanish economy plunged into a twin financial crisis (banking and a public debt one) in 2011, causing a protracted recession with a further decline in employment.

In the panel BVAR framework, the EPU index is also found to lead DF. Systemic risk in its turn causes an adverse real effect through an increase in the unemployment rate (Fig. 12). This transmission channel-from uncertainty to unemployment via systemic risk-remains unchanged if we re-estimate our panel BVAR, excluding Spain where it exists in the country-level BVAR (Fig. 13). It is also noteworthy that in both specifications the EPU index is cushioned from any significant effects by other variables, including the OECD composite leading indicator. Thus, the results of the panel BVAR estimation mirror the linkage between systemic risk and economic policy uncertainty found for the financially fragile economies. (12)

From the policymaking perspective, our results in the data-rich environment support the view that economic policy uncertainty can be a precursor of systemic risk. In order to mitigate the latter, it is crucial to deal with economic agents' sentiment and expectations, shaped not necessarily within the financial sector or even broader economy. Obviously, it involves rethinking the macroprudential policy mandate. The policy needs to be largely preemptive and equipped with an efficient communication strategy to be able to tame uncertainty feeding systemic risk.

Conclusions

This paper studies lead-lag linkages between economic policy uncertainty and systemic risk for nine European countries. The following conclusions can be drawn from the research.

First, we propose a novel composite systemic risk measure by applying dynamic factor analysis to twelve individual indicators of three risk types, capturing domestic financial sector fragility, sovereign credit worthiness and vulnerability to external shocks. The variables belonging in the first two types make the most sizeable contribution to our composite measure, judging by respective factor loadings. In particular, leverage, the inverse ratio of market capitalization, SRISK and sovereign CDS spreads stand out. For some sample countries, e.g., Russia, the indicators related to external vulnerability also matter.

Second, the lead-lag patterns between economic policy uncertainty and systemic risk are found to vary significantly, conditional on analysis settings. We assess bivariate linkages in time and time-frequency domains. The paper is the first to apply continuous wavelet transform and a related technique, wavelet coherence, to investigate the linkages in the time-frequency space. In the bivariate framework, our composite systemic risk measures tend to lead uncertainty in the short run (or at high frequencies). France exemplifies such lead-lag pattern best of all. Nonetheless, once we focus on a longer run relationship (i.e., medium and low frequencies), the number of countries where economic policy uncertainty indices drive systemic risk increases. Furthermore, for Russia and Spain, we observe a reversal of lead-lag patterns, arising from this shift.

Third, the leading role of economic policy uncertainty becomes more pronounced in a multivariate analysis. We specify country-level Bayesian VAR models and a panel BVAR to examine simultaneously the lead-lag relationship between uncertainty and systemic risk as well as the impact of uncertainty on key macroeconomic variables in the presence of several global and regional risk factors. We find that uncertainty leads systemic risk for Ireland, Italy, Russia and Spain. It can affect economic activity in an indirect way, fueling systemic risk, and directly, as in some countries it exerts a contractionary impact on industrial production or leads to yawning unemployment rates.

Overall, our findings call for macroprudential policy to address uncertainty issues to curb systemic risk. Since the negative effect of uncertainty appears more pronounced at longer time horizon and in data-rich environments, macroprudential authorities need to design their policy, attaching more importance to lower frequency data and multiple interactions between macroeconomic and financial variables.

https://doi.org/10.1057/s41294-018-0065-5

Acknowledgements The paper was presented at the Second World Congress of Comparative Economics, "Revolution and Evolution in Economic Development," in St. Petersburg, Russia, June 15-17, 2017. Comments by two anonymous referees have been welcome. We are also grateful to Paul Wachtel for his support and patience.

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(1) An apparently inexhaustive list includes Araengual and Xiu (2013), Brogaard and Detzel (2015), Christou et al. (2017), Chulia et al. (2017), Dakhlaoui and Aloui (2016), Ko and Lee (2015), Liu and Zhang (2015), Wu et al. (2016).

(2) Over the past years, the CWT has penetrated financial research but it mainly applies to investigate linkages between different asset classes, commodities and economic development in a bivariate setting, e.g. the effect of oil prices on industrial production in the long run (Aguiar-Conraria and Soares 2010, 2011).

(3) See the methodological note for details http://www.crml.ch/index.php?id=44.

(4) Technical details of this metric are given in the corresponding White Paper http://d.rmicri.org/static/ pdf/Probability%20of%20Default%20White%20Paper.pdf.

(5) Based on the BDS test. Detailed results are available upon request.

(6) This choice is also motivated by Baker et al. (2016) who first place the EPU index, then financial variables (S&P 500 index and federal funds rate) and, finally, macroeconomic fundamentals (employment and industrial production) in their VAR models, examining the dynamic effect of uncertainty on economic activity in the US and other countries.

(7) We implement the BEAR (Bayesian Estimation, Analysis and Regression) toolbox elaborated by a group of ECB economists to estimate the BVAR models (Dieppe et al. 2016).

(8) In addition to conventional ADF unit root tests, we apply breakpoint ADF unit root tests with an innovation outlier, accounting for possible structural breaks in the data. Their results do not affect the maximum order of integration for the Toda-Yamamoto correction.

(9) We also conduct an impulse-response analysis based on generalized impulses. It complements the causality tests and gives consistent results under any ordering of variables in the VAR model. We find that a one standard deviation innovation in the EPU indices leads to statistically significant changes in the composite systemic risk in Russia and Spain, thereby emphasizing the need for further analysis of the linkages going beyond standard Granger causality tests.

(10) In our study, we implement the cross wavelet and wavelet coherence toolbox for Matlab provided by Grinsted et al. (2004). As for the theoretical background of the CWT analysis and its applications in economics, we refer an interested reader to a primer on the topic by Aguiar-Conraria and Soares (2010, 2011).

(11) See http://www.worldvaluessurvey.org/WVSOnline.jsp.

(12) However, this result should not be taken for granted for a wider sample of European economies.

Mikhail Stolbov (1) * Alexander Karminsky (2) * Maria Shchepeleva (2)

Published online: 24 May 2018

Electronic supplementary material The online version of this article (https://doi.org/10.1057/ s41294-018-0065-5) contains supplementary material, which is available to authorized users.

[mail] Mikhail Stolbov

stolbov_mi@mail.ru

(1) Moscow State Institute of International Relations, Moscow, Russia

(2) National Research University Higher School of Economics, Moscow, Russia

Caption: Fig. 1 Dynamics of composite systemic risk measure for sample countries, January 2010-September 2016

Caption: Fig. 2 Dynamics of the EPU indices for sample countries, January 2010-September 2016

Caption: Fig. 3 Results of the wavelet coherence analysis for France

Caption: Fig. 4 Results of the wavelet coherence analysis for Ireland

Caption: Fig. 5 Results of the wavelet coherence analysis for Italy

Caption: Fig. 6 Results of the wavelet coherence analysis for the Netherlands

Caption: Fig. 7 Results of the wavelet coherence analysis for Sweden

Caption: Fig. 8 Results of the wavelet coherence analysis for the UK

Caption: Fig. 9 Results of the wavelet coherence analysis for Germany

Caption: Fig. 10 Results of the wavelet coherence analysis for Russia

Caption: Fig. 11 Results of the wavelet coherence analysis for Spain

Caption: Fig. 12 IRFs for the panel BVAR model (all countries)

Caption: Fig. 13 IRFs for the panel BVAR model (Spain is omitted)
Table 1 Results of the dynamic factor model estimation

                   France      Germany    Ireland

Domestic financial sector fragility

SRISK              0 79 ***    0 94 ***   0.92 ***
                   (0.09)      (0.13)     (0.08)

LRMES              0.56 ***    0.28 **    -0.58 ***
                   (0.10)      (0.12)     (0.10)

LEVERAGE           0.99 ***    0.98 ***   0.99 ***
                   (0.08)      (0.12)     (0.08)

VOLAT              0.33 ***    0.24 **    0.21 *
                   (0.11)      (0.11)     (0.11)

MCAP               0.96 ***    0.95 ***   0.99 ***
                   (0.08)      (0.12)     (0.08)

PD                 0.77 ***    0.56 ***   0.03
                   (0.09)      (0.11)     (0.11)

Sovereign creditworthiness

CDS                0.88 ***    0.83 ***   0.45 ***
                   (0.09)      (0.12)     (0.11)

Govbond            0.45 ***    0.49 ***   0.61 ***
                   (0.10)      (0.11)     (0.10)

External vulnerability

WMCorr             -0.15       0.05       -0.46 ***
                   (0.11)      (0.12)     (0.10)

DY                 0.37 ***    0.09       0.34 ***
                   (0.11)      (0.11)     (0.11)

EQALLOC            0.17        0.06       0.03
                   (0.11)      (0.11)     (0.11)

BONDALLOC          0.15        0.07       0.06
                   (0.11)      (0.11)     (0.11)

Log likelihood     - 1094.69   -1127.63   - 1090.49

Obs.               82          82         82

                   Italy        Nether Lands   Russia     Spain

Domestic financial sector fragility

SRISK              0.78 ***     0.97 ***       0.78 ***   0.95 ***
                   (0.09)       (0.08)         (0.09)     (0.08)

LRMES              0.39 ***     0.66 ***       0.63 ***   0.59 **
                   (0.11)       (0.10)         (0.10)     (0.10)

LEVERAGE           0 98 ***     0.99 ***       0 99 ***   0 99 ***
                   (0.08)       (0.08)         (0.08)     (0.08)

VOLAT              0.21 *       0.13           0.42 ***   0.43 **
                   (0.11)       (0.11)         (0.10)     (0.10)

MCAP               0.97 ***     0.98 ***       0.92 ***   0.89 ***
                   (0.08)       (0.08)         (0.08)     (0.08)

PD                 0.61 ***     0.34 ***       0.71 ***   0.86 ***
                   (0.10)       (0.11)         (0.09)     (0.09)

Sovereign creditworthiness

CDS                0.93 ***     0.85 ***       0.65 ***   0.75 ***
                   (0.09)       (0.09)         (0.10)     (0.09)

Govbond            0.83 ***     0.57 ***       0.31 ***   0.48 ***
                   (0.09)       (0.10)         (0.11)     (0.10)

External vulnerability

WMCorr             - 0.27 ***   -0.32 ***      -0.01      0.21 *
                   (0.11)       (0.11)         (0.11)     (0.11)

DY                 0.10         0.51 ***       -0.04      0.08
                   (0.11)       (0.10)         (0.11)     (0.11)

EQALLOC            0.02         0.14           0.25 **    0.19 *
                   (0.11)       (0.11)         (0.11)     (0.11)

BONDALLOC          0.09         0.16           0.26 **    0.10
                   (O.H)        (0.11)         (0.11)     (0.11)

Log likelihood     -1072.43     -990.76        -1178.40   -1093.10

Obs.               82           82             82         82

                   Sweden     UK

Domestic financial sector fragility

SRISK              0.53 ***   0.82 ***
                   (0.10)     (0.09)

LRMES              0.66 ***   0.45 ***
                   (0.10)     (0.10)

LEVERAGE           0 99 ***   0.99 ***
                   (0.08)     (0.08)

VOLAT              0.09       -0.09
                   (0.11)     (0.11)

MCAP               0.97 ***   0.94 ***
                   (0.08)     (0.08)

PD                 0.59 ***   0.61 ***
                   (0.10)     (0.10)

Sovereign creditworthiness

CDS                0.60 ***   0.82 ***
                   (0.10)     (0.09)

Govbond            0.58 ***   0.03
                   (0.10)     (0.11)

External vulnerability

WMCorr             0.04       0.30 ***
                   (0.11)     (0.11)

DY                 -0.27 **   -0.50 ***
                   (0.11)     (0.10)

EQALLOC            -0.01      0.11
                   (0.11)     (0.11)

BONDALLOC          -0.16      0.04
                   (0.11)     (0.11)

Log likelihood     -1175.53   -1161.65

Obs.               82         82

*, **, *** significant at the 10, 5 and 1%, respectively

Table 2 List of newspapers and terms related to economic policy
uncertainty for the sample countries Source: Baker et al. (2016)

Country        Newspaper                  Terms (English equivalents)

France         Le Monde, Le Figaro        Uncertain/uncertainty,
                                          economic/economy, tax, policy,
Germany        Frankfurter Allgemeine     regulation, spending, deficit,
               Zeitung, Handelsblatt      budget, central bank

Ireland        The Irish Times            Uncertain/uncertainty,
                                          economic/economy, regulation,
                                          legislation, Dail, deficit,
                                          government, central bank or
                                          Taoiseach

Italy          La Stampa, Corriere        Uncertain/uncertainty,
               Della Sera                 economic/economy, tax,
                                          policy, regulation, spending,
                                          deficit, budget, central bank

Netherlands    Algemeen Dagblad, NRC      Uncertainty, economics,
               Handelsblad, De            policy, minister, budget, tax
               Telegraaf, Trouw, and
               De Volkskrant

Russia         Kommersant                 Uncertain/uncertainty,
                                          economic/economy, policy,
                                          tax, spending regulation,
                                          central bank, law, budget,
                                          Duma

Spain          El Pais, El Mundo          Uncertain/uncertainty,
                                          economic/economy, tax,
                                          policy, regulation, spending,
                                          deficit, budget, central bank

Sweden         Aftonbladet, Expressen,    Uncertain/uncertainty,
               Dagens Industri, and       economic/economy, central
               Svenska Dagbladet          bank (Riksbank), government,
                                          regulation, ministry

UK             The Times, the             Uncertain/uncertainty,
               Financial Times            economic/economy, tax,
                                          policy, regulation, spending,
                                          deficit, budget, central bank

Table 3 Correlations between
the EPU indices and composite
systemic risk measures for the
sample countries

Country         Ordinary correlations   p value

France          0.39                    0.00
Germany         0.23                    0.04
Ireland         0.04                    0.70
Italy           0.54                    0.00
Netherlands     0.33                    0.00
Russia          0.53                    0.00
Spain           0.48                    0.00
Sweden          -0.11                   0.33
UK              0.23                    0.04

Table 4 Results of ADF unit
root tests for the EPU indices
and composite systemic risk
measures

Country        EPU index   DF

France         I(0)        I(0)
Germany        I(0)        I(0)
Ireland        I(0)        I(0)
Italy          I(0)        I(1)
Netherlands    I(0)        I(1)
Russia         I(0)        I(0)
Spain          I(0)        I(0)
Sweden         I(0)        I(0)
UK             I(0)        I(0)

Table 5 Results of standard Granger causality tests between the EPU
indices and composite systemic risk measures

Country        Optimal lag length   Toda-Yamamoto
               of the VAR model     correction for
                                    exogenous lags

France         VAR(1)               VAR(2)
Germany        VAR(1)               --
Ireland        VAR(1)               --
Italy          VAR(1)               VAR(2)
Netherlands    VAR(1)               VAR(2)
Russia         VAR(1)               --
Spain          VAR(1)               --
Sweden         VAR(1)               --
UK             VAR(1)               --

               VAR Granger (no) causality/block exogeneity
               Wald test

Country        DF does not      p value   EPU does not     p value
               cause EPU                  cause DF
               ([chi square])             ([chi square])

France         3.73             0.05      0.70             0.40
Germany        4.27             0.04      0.34             0.56
Ireland        0.01             0.92      0.46             0.50
Italy          3.51             0.06      0.03             0.87
Netherlands    1.62             0.20      0.32             0.57
Russia         7.61             0.00      0.01             0.92
Spain          7.96             0.00      0.95             0.33
Sweden         0.69             0.41      1.13             0.29
UK             1.70             0.19      0.39             0.53
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