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INTERNATIONAL EFFECTS OF EURO AREA VERSUS U.S. POLICY UNCERTAINTY: A FAVAR APPROACH.

I. INTRODUCTION

Uncertainty has gained much attention as one of the main drivers of the depth and duration of the Great Recession (Bloom et al. 2013; Caggiano, Castelnuovo, and Pellegrino 2017). For example, the Federal Open Market Committee minutes repeatedly emphasize uncertainty as a key factor driving the 2001 and 2007-2009 recessions. Uncertainty shocks are generally interpreted as one of the main factors behind the decline in output and employment during the 2007-2009 U.S. recessions (Stock and Watson 2012). Bordo, Duca, and Koch (2016), for instance, find negative effects of policy uncertainty on bank credit growth in the United States. The results of other studies which have found important macroeconomic effects of bank lending growth on the economy are consistent with the interpretation that high economic uncertainty has slowed down the U.S. recovery by limiting overall credit growth through the bank lending channel.

The European Central Bank (ECB) argues that uncertainty in the Euro area rose substantially during the Great Recession and the sovereign debt crisis and that a high degree of uncertainty has the potential to significantly dampen economic activity, above all investment (ECB 2016). (1) However, there is no consensus yet about what the sign of the impact of uncertainty is on economic and financial activities and what the international spillovers of uncertainty look like. Via business cycle correlations, the possibility arises that the impact of an uncertainty shock originating in the United States may influence global business cycles (Kamber et al. 2016). This view is supported by the rapid and accelerating process of financial globalization and new technologies (Kang, Ratti, and Vespignani 2017). Our study is directly geared toward an empirical assessment of these emanating issues.

Apart from the most recent crises, the impact of uncertainty on the real and the financial sector is a constantly recurring topic in the academic literature. Some intriguing questions that typically emerge in this context: How does uncertainty affect the economy and financial variables (Belke, Dubova, and Osowski 2017; Belke and Goecke 2005)? What are the transmission channels of uncertainty (Bloom 2013; Dixit 1989; Pindyck 1991)? What exactly is the magnitude and the sign of these impacts on a variety of macroeconomic variables such as gross domestic product (GDP), the consumer price index (CPI), and the monetary policy stance and financial variables such as the long-term interest rate, equity, and the exchange rate and their common components?

In this paper, we use data from 18 Organisation for Economic Co-operation and Development (OECD) countries and focus our analysis on the impact of economic policy uncertainty on real and financial variables by estimating a factor-augmented vector autoregressive model (FAVAR). The basic idea of a FAVAR model rests on merging a large amount of macroeconomic data into a sufficiently small number of factors which are subsequent used for the sparing estimation of a vector autoregressive model (VAR) (Geweke 1977; Sargent and Sims 1977). Therefore, we extract the information about common components of business cycle movements from a large cross section of national time series (Beckmann, Belke, and Czudaj 2014; Belke and Rees 2014; Kose, Otrok, and Whiteman 2003). (2)

We use impulse response functions (IRFs) to interpret out results. In this respect, we argue that the VAR methodology is well suited to capture the effects of uncertainty. As impulse responses only contain the effect of an unexpected change (a "shock") in a specific variable, this procedure appears especially useful for the evaluation of uncertainty effects. While monetary policy contains unanticipated changes as well as systematic changes, uncertainty measures should not contain such a systematic component (Beckmann, Belke, and Dreger 2016; Bernanke, Boivin, and Eliasz 2005). Therefore, the general critique that IRFs only estimate the effect of unexpected changes is not valid for the evaluation of uncertainty effects.

We use this framework to answer the following research questions: Is the FAVAR approach an adequate framework to model cross-country developments? What are the global effects of economic policy uncertainty shocks on variables such as national GDP? What is the sign of the estimated uncertainty impact coefficient? What are the channels of policy uncertainty transmission between the Euro area and the United States in both directions? For this purpose, we compare a U.S. and a Euro area policy uncertainty shock and put a special focus on non-EMU (European Monetary Union) countries in Europe.

The remainder of our paper proceeds as follows: Section II briefly reviews the literature on the international impact of uncertainty. In Section III, the data and the empirical approach are introduced. The empirical results are delivered and discussed in Section IV. In Section IV.A, the impact of a shock to Euro area economic policy uncertainty is investigated. For reasons of comparison, Section IV.B then derives the impacts of a shock to U.S. economic policy uncertainty. In Section IV.C, we present some robustness checks. In Section IV.D we summarize and discuss our results and confront the latter with the pertinent literature. Section V finally concludes.

II. INTERNATIONAL EFFECTS OF ECONOMIC POLICY UNCERTAINTY ON THE ECONOMY--A REVIEW

There are a few VAR-type studies related to ours which assess the impacts of economic policy uncertainty on macroeconomic variables. The study closest to ours is Colombo (2013) who investigates the effects of economic policy uncertainty shocks from the United States to the Euro area by using aggregated data for the Euro area also using indicators presented by Bloom et al. (2013). Colombo (2013) uses standard VARs and focuses on shocks to U.S. economic policy uncertainty which induce a negative and significant reaction of Euro area price and quantity indicators. Furthermore, she finds strong co-movements between U.S. and Euro uncertainty indicators. According to her estimations, the Fed but also the ECB reacts to uncertainty shocks originating in the United States by reducing their policy rate. Overall, our FAVAR approach allows to include disaggregated, country-specific data and therefore to evaluate uncertainty effects on and uncertainty transmission to individual national economies, a topic extremely relevant in the Euro area debt crisis. In this respect, our (FAVAR) approach attempts to generate more detailed evidence about the cross-border effects and is a natural extension of Colombo (2013) and Beckmann, Belke, and Czudaj (2014).

We focus on U.S. and Euro area economic policy uncertainty whereas Colombo (2013) solely estimates the effects of U.S. policy uncertainty and then continues with a variance decomposition exercise to compare the effects of U.S. and European uncertainty. However, her impulse-responses and specifications only consider U.S. uncertainty shocks. In addition, throughout the study she puts U.S. uncertainty before European uncertainty in her Cholesky orderings. Having said this, we would like to argue that the results would probably change significantly if one would in turn put European uncertainty before U.S. uncertainty. In the end, the ordering of both uncertainty measures depends on the assumed transmission of the uncertainty shock. Therefore, we will change the ordering dependent on the shocked variable in our paper because we would otherwise determine our estimation result a priori. Another motivation to proceed like this is a strong contemporaneous bilateral correlation between Euro area and U.S. policy uncertainty, thus questioning the usefulness of a variance decomposition exercise in our context. (3) This is because Colombo (2013) imposes that U.S. policy uncertainty can impact Euro area uncertainty contemporaneously but not the other way around (for more details see Section III.C).

Different from us, De Wind and Grabska (2016) do not estimate a FAVAR model interconnecting different regions of the world but separate structural VARs with a similar specification as Bloom (2009) for the various countries in their data set. In contrast to our approach, they focus on the domestic effects of an uncertainty shock. They include 11 countries from Europe and North America in their sample and put a large emphasis on differences of uncertainty effects between continental European and Anglo-Saxon countries. Their choice of uncertainty focuses more on financial markets as they primarily use equity volatility indicators.

The authors find that uncertainty shocks cause deeper recessions in Continental Europe than in Anglo-Saxon countries. According to the results of their variance decomposition, the conditional variance of economic activity relative to uncertainty shocks is much smaller for Anglo-Saxon countries. The authors explain their findings with country heterogeneity in labor and capital market flexibility. As continental European countries have a larger amount of labor and capital market restrictions, the authors conclude that these restrictions enhance the effects of uncertainty shocks, since firms are less capable of dealing with uncertain situations when investment and hiring decisions are less easy to reverse, as suggested by Bloom (2009).

Kang, Ratti, and Vespignani (2017) use FAVAR as well as factor-augmented Bayesian VAR estimation techniques to analyze the effects of global financial uncertainty shocks. Although their country sample is smaller than ours (15 countries), they also include several emerging markets. Their research focus is more on the effects of a global rise in financial uncertainty, while we focus more on cross-country spillovers. In contrast to our study ("national on national") they estimate the impact of global uncertainty on key global macroeconomic variables ("global on global") and national variables ("global on national"). They find that global uncertainty shocks cause a strong reduction in global output, prices, and interest rates. Similar effects are identified at the country level.

As we also do in our study, Kamber et al. (2016) utilize a FAVAR model to estimate the impact of U.S. economic uncertainty on several developed economies and New Zealand as a small open economy in particular. For the Euro area, the authors use aggregated Euro area variables which do not allow for individual country analyses for Euro area countries. Besides the indicator presented by Jurado, Ludvigson, and Ng (2015), they also employ the volatility index VIX (S&P 500 Volatility) and the economic policy uncertainty index developed by Bloom et al. (2013). In contrast to our study in which we compare the effects of U.S. and Euro area uncertainty shocks, the authors are solely interested in the effects of a U.S. uncertainty shock. They find that an increase in U.S. uncertainty leads to strong adverse domestic effects in the United States and other developed countries. Among developed countries, they observe a rather high degree of synchronization in the response of national variables (especially stock markets).

III. DATA AND EMPIRICAL APPROACH

A. Empirical Approach

In order to use a coherent and appropriate framework, we estimate a FAVAR as proposed by Bemanke, Boivin, and Eliasz (2005). In this regard, we use the FAVAR as a multicountry framework, assuming that developments of economic variables share strong similarities which can be approximated by common factors. Our empirical approach is also motivated and encouraged by the results of Georgiadis (2015). His results show that multicountry models such as the FAVAR (and GVAR, global vector autoregressive) are, in contrast to bilateral VARs, more appropriate to model global and regional shocks as well as cross-country spillovers, because these models are capable of modeling higher-order spillovers.

As we include at least four variables for each of the 18 countries in our sample, the FAVAR appears to be a sufficient solution to the curse of dimensionality (Chudik and Pesaran 2009). As mentioned in the Introduction, the main advantage of the FAVAR is the possibility to simultaneously model a large amount of time series and thereby including a large amount of economic information. The curse of dimensionality is handled by generating principal components and thereby reducing the number of endogenous variables (Chudik and Pesaran 2009). The principal components represent "unobservable" factors [F.sub.t] which are supposed to explain a sufficient amount of variance in the data set. Besides the factors in [F.sub.t], the model also contains a set of "observable" factors [Y.sub.t].

While variables in [Y.sub.t] are directly observable, the elements of [F.sub.t] need to be estimated. The unobservable factors are estimated based on an informational data set [X.sub.t] containing N variables while accounting for the impact of the observable factors [Y.sub.t]:

(1) [X.sub.t] = [[lambda].sup.f][F.sub.t] + [[lambda].sup.y][Y.sub.t] + [e.sub.t]

where [[lambda].sup.f] is an N x K matrix of factor loadings, [[lambda].sup.y] is N x M, and the N X 1 vector of (idiosyncratic) error terms e, are mean zero and assumed to be either weakly correlated or uncorrelated. K represents the number of unobserved factors and M equals the number of variables in [Y.sub.t].

In essence, [Y.sub.t] and [F.sub.t] are common forces that drive the dynamics of [X.sub.t]. The elements of [F.sub.t] may also be regarded as the primary common drivers of international economic developments while [e.sub.t] contains idiosyncratic or variable/country-specific components. The number of (unobservable) factors is generally assumed to be small (K [much less than] N). Factors are orthogonal to each other and factors and idiosyncratic components are orthogonal. Furthermore, it is important to note that, if Equations (1) and (2) adequately describe the data generation process, omitting [F.sub.t] from the system will result in biased estimates.

Although Equation (1) indicates that [X.sub.t] only depends on current values of the factors, it can be interpreted as a dynamic factor model because [F.sub.t] can include lags of the fundamental factors (Stock and Watson 2005). Altogether, a FAVAR is a standard VAR in which some of the variables are factors taken from a dynamic factor model:

(2) [[F.sub.t]/[Y.sub.t]] = [PHI](L) [[F.sub.t-1]/[Y.sub.t-1]] + [[epsilon].sub.t]

where [PHI](L) is a polynomial in the lag operator. The error term [[epsilon].sub.t] is mean zero with covariance matrix Q. It is important to note that if Equations (1) and (2) correctly describe the data-generating process, omitting [F.sub.t] from the system will result in biased estimates.

Equations (1) and (2) are jointly estimated by likelihood-based Gibbs sampling techniques presented by Geman and Geman (1984), Gelman and Rubin (1992), and Carter and Kohn (1994). We use the single-step Bayesian likelihood approach developed by Bemanke, Boivin, and Eliasz (2005) which is a multimove version of the Gibbs sampling technique. (4) In setting the prior distributions, we use a "Minnesota"-type prior but with a zero mean for all coefficients. We estimate the model based on monthly data for the period January 1996 to December 2015. Additionally, and consistent with other studies as, for instance, Bernanke, Boivin, and Eliasz (2005), we divide our economic data set [X.sub.t] into two subgroups. While the first group contains measures of economic activity and price developments which are supposed to react slowly to shocks in the system, the second subgroup includes financial data which immediately react to innovations. The split between slow - and fast-moving helps to identify the unobservable factors and to identify the model using a Cholesky decomposition. Since one of our aims is to analyze possible heterogeneity in the responses of economic variables of the different countries in our sample, we decided not to impose more structural restrictions for the factor extractions and on the individual series. (5) We use six lags and employ 50,000 Gibbs replications while discarding the first 10,000 as burn-in sample for the Gibbs sampler.

As common in VAR literature, we use impulse response analysis in order to examine the international impact of policy uncertainty in the Euro area. We present 15%-significance bands in order to interpret the significance of our (median) impulse responses. Because a lot of variables in [X.sub.t] enter in growth rates (or first differences in case of the interest rates) rather than levels (see Section III.C), we plot cumulated impulse responses for those variables. (6)

Regarding the statistical identification of economic shocks, we use a Cholesky decomposition. Although the Cholesky decomposition is the standard identification scheme which has been used by nearly every FAVAR study in the literature, its appropriateness can be questioned in principle (Christiano, Eichenbaum, and Evans 2005). However, we argue that in particular the division between slow - and fast-reacting variables helps with the identification of shocks and supports this choice. In this regard, we follow Bernanke, Boivin, and Eliasz (2005) and use a standard recursive ordering in which factors representing output and inflation are ordered first, followed by the factors of the "fast-moving" variables--in our case interest rates and stock prices. Afterward, the stances of monetary policy and eventually uncertainty in the Euro area and the United States are ordered last (Belke, Orth, and Setzer 2010). Thereby, we assume that uncertainty responds endogenously and immediately to changes in other variables, but that innovations in uncertainty affect the remaining variables with a lag of at least 1 month--depending on the position of the ordering.

The most crucial step of our analysis is to determine the number of factors to be included in our models. Although there are several procedures for this choice available, Bernanke, Boivin, and Eliasz (2005) argue that these criteria may not be useful for the FAVAR as these do not address the question of how many factors to include in the VAR specification. In general, the empirical literature does not (yet) generate a final solution to the determination of the number of factors. This is especially true for the Bayesian FAVAR approach used in this study. Therefore, several authors simply chose their number of factors in a more or less ad hoc fashion (see, for instance, Bemanke, Boivin, and Eliasz 2005; McCallum and Smets 2007; Shibamoto 2007).

We base our choice on two aspects: First, we determine the number by examining the cumulative amount of variance explained by a predefined number of factors. As a lower bound for the amount of variance explained, we set 80% as a common threshold in the empirical literature. (7) In our context, this procedure only gives a first indication which can be expected to be (too) high, as it does not consider that we also include observable factors ([Y.sub.t]) in the model.

Second, we evaluate the amount of variance in [X.sub.t] which is explained by our (unobserved and observed) factors. For the second method, we obtain the adjusted [R.sup.2] values by regressing the respective series on the common factors [[??].sub.t] and [Y.sub.t]. If the variation of the variables in [X.sub.t] is to a large extent explained by our factors, we can assume that the estimated factors summarize the information contained in these series well, which enables us to put more confidence in the results of our impulse responses (Blaes 2009). However, both procedures can at best generate evidence of the adequate choice of factors, because, especially, the first method does not incorporate all features of the FAVAR approach. The findings by Fomi and Gambetti (2014) in the context of fundamental information embedded in VAR models also show that there is no silver bullet when it comes to identify the optimal number of principal components.

It is important to underline that the space spanned by the factors is still estimated consistently when the number of factors is overestimated, although efficiency is reduced. On the other hand, an underestimation of factors results in an inconsistent model as potentially important dynamics will not be captured by the factor set (Stock and Watson 1998). This argument can be used to check the adequacy of the number of factors. If the number of factors was chosen to be too low and important dynamics of [X.sub.t] were left out, results based on a larger number of factors might reveal fundamentally different results. Therefore, even if we start with too many unobserved factors, the estimation is still unbiased. Bernanke and Boivin (2003) argue "it is important to note that if the additional information was irrelevant then adding one factor to the VAR would render the estimation less precise, but the estimate should remain unbiased. We would thus not expect the estimated response to change considerably." Our robustness checks in Section

IV. A also contain reestimations of the benchmark models with a higher number of factors.

B. Data

Our sample includes data between January 1996 and December 2015 for the following 18 countries: Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom, and the United States. We have chosen 1996 as the starting point of our estimation due to data constraints. As other contributions in the field which include Euro area member countries (Kang, Ratti, and Vespignani 2017; Kamber et al. 2016; and others), we do not set a dummy for the start of EMU in 1999. (8)

For each country, we include the following variables into the data set of [X.sub.t]: a proxy of economic activity, an indicator of the price development, nominal equity prices, and 10-year interest yields. (9) Additionally, we include the nominal effective exchange rate for the Euro area with an increase of this index implying an appreciation of the home currency. Regarding the indicator of economic activity, we choose two indicators in separate specifications: (Monthly) real GDP (10) and industrial production. As price variables, we use the CPI and core price index. (11) Overall, every specification of [X.sub.t] contains 72 time series. Table 1 summarizes the data used in our study.

As observed factors ([Y.sub.t]), we include two sets of variables for the Euro area and the United States: first, an indicator of economic policy uncertainty and second, a variable which tries to measure the monetary stance of the central bank. The inclusion of U.S. and Euro area variables as observed factors does not only enable us to simulate uncertainty shocks originating from both currency areas. Both regions are economically powerful and can be considered as "large" in comparison to the other countries which can be considered to be "small" in our empirical model. Therefore, U.S. and Euro area variables--especially those measuring monetary policy--can be seen as important global factors themselves and probably explain a large amount of variation in national variables (Beckmann, Belke, and Dreger 2016). Therefore, their inclusion in [Y.sub.t] further increases the probability that our FAVAR model captures all relevant dynamics in [X.sub.t].

Furthermore, even if one is merely interested in analyzing the effects of a shock to Euro area (U.S.) policy, uncertainty including U.S. (Euro area) variables in [Y.sub.t] appears to be important (especially in a framework similar to ours). As uncertainty in both currency areas is highly correlated (see Section III.C), our framework (and, more specifically, the IRFs) might attribute too large impacts to a Euro area uncertainty shock if we do not explicitly control for developments in the United States. This is because in that case effects of U.S. uncertainty would be attributed to the Euro area shock.12 This aspect is especially relevant for our international perspective as we analyze the effects on countries outside both economic powers.

As indicators of monetary policy, we employ shadow rates ([SR.sup.i.sub.t]) (Belke and Dubova 2018 and Belke, Dubova, and Volz 2017). As policy rates cannot significantly drop below zero, common short-term interest rates like the Federal Funds Rate and the Euro OverNight Index Average do not correctly reflect the general stance of monetary policy in times of unconventional monetary policies anymore. In this regard, the use of shadow rates appears to be a necessary and sufficient solution. When the policy rates hover near zero, many economic models stop working. Researchers developed a "shadow rate" that can stand in for the policy rate, drop into negative territory, and render those models functional again. It eliminates statistical problems, as the shadow rate cannot, like the policy rate, be regarded as a truncated variable at the zero-lower bound and it is supposed to include information about unconventional monetary policies used during the recent crisis. So far, however, there is no commonly agreed way to construct a shadow rate available in the empirical literature. Hence, we decided to use the widely used shadow rates proposed by Krippner (2016). The shadow rate is based on a continuous-time Gaussian term structure model using yield curve data. (13)

As an indicator of uncertainty, we employ economic policy uncertainty ([EPU.sup.i.sub.t]), an indicator developed and provided online by Baker, Bloom, and Davis (2015). The authors create a newspaper-based economic policy uncertainty variable. While an indicator for the United States is already available, the authors have not (yet) published a measure of policy uncertainty for the Euro area. Instead, only a measure of European policy uncertainty is available which is based on the respective single-country indicators for France, Germany, Italy, Spain, and the United Kingdom. The country-specific indices are constructed by drawing articles from two newspapers per European country. These are Le Monde and Le Figaro for France, Corriere Della Sera and La Repubblica for Italy, El Mundo and El Pais for Spain, and Handelsblatt and Frankfurter Allgemeine Zeitung for Germany. The papers are searched monthly for keywords such as "economic," "uncertainty," "deficit," "European Central Bank," and "regulation." As with their American newspaper index, the number of newspaper articles dealing with uncertainty, economy, or policy is considered. (14) The number of articles including the keywords was then divided by the total number of articles to address changes over time. Standardizing the values results in a multipaper index. (15) In analogy with the measure of European economic policy uncertainty, we construct an economic policy uncertainty index for the Euro area based on the individual indicators of the four members (France, Germany, Italy, and Spain) which are then weighted by their share of GDP. (16) We feel legitimized to follow this approach, as the inventors of the indicators use an (almost) identical approach to construct their European and their "global" indicator of policy uncertainty.

In our study, we decided to use the indicators of Baker, Bloom, and Davis (2015) also for several other reasons. Although there is a variety of different indicators available which put emphasis on different forms of economic uncertainty, we argue that especially in the recent years of the sovereign debt crisis the largest amount of uncertainty was related to economic policy in the Euro area. However, the main advantage of using the indicators of Baker et al. is that the authors publish indicators for a large variety of countries, a relatively large time period, and--especially relevant in our context--based on a single estimation procedure. It would be clearly problematic to compare the effects of uncertainty originating from different regions, if the indicators would alternatively be based on different procedures and if one would put emphasis on different types of uncertainty. Obviously, this is relevant in our case as we attempt to compare the sign and magnitude of the impact of uncertainty originating from the United States and the Euro area. Therefore, we primarily focus our analysis on newspaper-based uncertainty measures.

Finally, as shown by Caldara et al. (2016), shocks to uncertainty have an especially large macroeconomic effect if they signal a worsening of financial conditions. Their robust finding that uncertainty increases immediately as a reaction to an adverse financial shock (which is corroborated by Belke, Dubova, and Osowski 2017 in the context of Brexit) makes it possible that changes in uncertainty are driven by fluctuations in financial conditions. This suggests that an increase in economic policy uncertainty (the variable implemented by us in this paper) may be a "general symptom of financial market volatility" (Caldara et al. 2016). Hence, we alternatively substitute policy uncertainty by financial volatility and test for robustness of our results by using monthly averaged values of stock exchange volatility ([EQVol.sup.i.sub.t]). In this regard, we use the volatility index VIX for the United States and the "European VIX" VSTOXX, the most watched European volatility index, for the Euro area. (17) We choose this measure instead of the others also presented in Section III.C, because both measures are comparable regarding construction and the specific uncertainty component analyzed. By using these indicators, we put more emphasis on financial (equity) uncertainty in comparison to the news-based measures. Data about the VSTOXX is only available from January 1999 onward.

C. Preliminary Findings, Diagnostics, and VAR Specification

Based on Augmented Dickey-Fuller and Kwiatkowski-Phillips-Schmidt-Shin tests, we obtain large evidence of nonstationarity. Therefore, every variable in [X.sub.t] enters in month-on-month growth rates (18) except for interest rate variables which enter in first differences. (19) While our uncertainty indicator is clearly I(0), both shadow rates turn out to be I(1) as in Belke and Dubova (2018) and Belke, Dubova, and Volz (2017). As these variables are included into the [Y.sub.t] vector and are therefore not part of the factor estimation, we include both shadow rates in levels. In case of seasonality, we used the X-12 ARIMA procedure to eliminate seasonal patterns.

As a starting point of our analysis, we focus on the relationship between economic policy uncertainty in the United States and the Euro area. We use simple Granger-causality tests to obtain first evidence.

We find significant support that the EPU variables Granger-cause each other which is, however, sensible regarding the lag length assumed. Evidence of Granger-causality is throughout larger for the equity volatility variables. Overall, we find moderate evidence that U.S. uncertainty and Euro area uncertainty Granger-cause each other.

Although a Granger-causality exercise can be used as a preliminary step for a deeper VAR analysis, it does not include the possibility of contemporaneous effects or relationships. Therefore, we want to take a further look at the relationships between the indicators used in this study. Furthermore, we present several other indicators suggested by the literature. (20) ECB (2013) proposes two additional indicators to measure uncertainty, which are available on a monthly basis: first, a composite indicator of systematic stress in the financial system ([FUI.sup.EA.sub.t]) (21) published by the ECB for a period starting January 1999 and, second, a dispersion indicator based on a forward-looking questionnaire of the Business and Consumer Survey ([BCS.sup.EA.sub.t]) of the European Commission. (22) The latter relies on expectations of businesses and consumers about the economic development within the next year. For the United States, we include a financial indicator provided by the Federal Reserve Bank of Kansas ([FUI.sup.US.sub.t]). (23) Table 3 presents a first correlation analysis.

Looking at the correlations between indicators from a specific region, we observe overall strong communalities. Regarding cross-country correlations, we obtain very strong correlations for indicators whose conceptions are similar. We observe a very strong correlation of .716 between the U.S. and the Euro area EPU indicator. For the equity volatility indicators VIX and VSTOXX the correlation turns out to be even higher (0.830).

Additionally, Figure 1 sheds further light on the evolution of the indicators over time. Comparing indicators for each region separately, we observe that the indicators tend to follow a similar pattern, but we also detect a certain amount of heterogeneity across the indicators. Figure 2 compares the developments of EPU and EQVol in both regions. We observe even stronger co-movements without clear evidence of a leader-follower relationship. Overall, we argue that the commonalities across indicators are relatively high even though the indicators put different emphasizes on specific uncertainty aspects and are based on different methods.

The preliminary results are relevant for the specifications used in Section IV. As we use a Cholesky decomposition, the ordering of our factors in general and especially of the observable factors in [Y.sub.t] is of importance. Regarding the ordering of [Y.sub.t], Colombo (2013) and Giavazzi and Favero (2008) assume that shocks hitting the Euro area do not exert contemporaneous effects on the U.S. variables. This ordering appears appropriate for the research question addressed by Colombo (20 T13), because she focuses on the effects of a shock to U.S. policy uncertainty.

In our study, however, we are interested in the effects of economic policy uncertainty shocks originating from both economic regions. As shown above, we observe a strong contemporary correlation and comovements between each pair of variables. By choosing an ordering which prohibits Euro area uncertainty to have a contemporary effect on U.S. uncertainty we would ex ante exclude a potentially important transmission channel. As we also aim to compare the effects of both shocks, this might drive our results and the subsequent interpretation. Therefore, we choose two different orderings for both shocks to make sure that the policy uncertainty variable shocked can have a contemporary effect on uncertainty of the other region. We feel legitimized to do so with an eye on the results in this section and our results in Section IV which clearly show that uncertainty shocks spread very quickly through the entire system.

IV. EMPIRICAL RESULTS

A. Shocking Euro Area Economic Policy Uncertainty

Our benchmark specification [Z.sup.1.sub.t] = ([X.sup.1.sub.t], [Y.sup.1.sub.t]) contains the following set of variables: [X.sup.1.sub.t]: ([GDP.sup.i], [CPI.sup.i.sub.t], [Equity.sup.i.sub.t], [LTIR.sup.i.sub.t], [EXR.sup.EA.sub.t]) and [Y.sup.1.sub.t]: ([SR.sup.US.sub.t], [SR.sup.EA.sub.t], [EP.sup.US.sub.t], [EPU.sup.EA.sub.t]), with: [GDP.sup.i.sub.t]: real GDP of country i in period t, [CPI.sup.i.sub.t]: consumer price inflation, [Equity.sup.i.sub.t]: Equity price measure, [LTIR.sup.i.sub.t]: 10-year sovereign yield, [EXR.sup.EA.sub.t]: Euro-Dollar exchange rate (quantity quotation), [SR.sup.EA.sub.t]: Euro area Shadow rate, [SR.sup.US.sub.t]: Shadow rate of the United States, [EPU.sup.EA.sub.t]: Economic Policy Uncertainty Index for the Euro area, EPUltJS: Economic Policy Uncertainty index for the United States.

The results of our principal component analysis suggest that six factors are explaining roughly 80% of the total variation of [X.sub.t]. We take this as a first indication of the adequate number of factors and proceed by evaluating the amount of variation explained by our factors.

Table 5 presents the [R.sup.2] based on regressions of [X.sub.t] and the observed and unobserved factors. We observe that in general a large and sufficient amount of variation is explained by our factors. For national GDP and CPI, we explain 79% and 77%, respectively. The Norwegian and the Greek CPI are important outliers which are explained to a lesser extent. (24) Our results are even better for financial variables, as the average [R.sup.2] of equity variables is almost 90% and for the long-term interest rate it is around 81%. This pattern came quite expected, because it is well known that interlinkages or common movements of financial data are generally higher than for GDP or CPI. Overall, the combination of six unobserved factors and four observed factors in [Y.sub.t] explain 81.6% of the total variance. When we increase the number of factors to 7, the average [R.sup.2] only increases very slightly to 83.7% (GDP: 80.2%; CPI: 80.2%; equity: 91.2%, long-term interest rate: 83.5%). Due to the apparently small amount of additional explanation power of the seventh factor, we decided to proceed by including only six factors. Overall, the reasonably high [R.sup.2] values endow us with a fair amount of confidence that our FAVAR framework is capturing the most important dynamics in [X.sub.t].

In the following, we interpret the impulse responses of a positive shock to [EPU.sup.EA.sub.t] (one standard deviation) presented in Figure 3. One standard deviation roughly equals an increase of 50% of the policy uncertainty index. (25) However, the interpretation of an uncertainty shock itself is inherently difficult because the variable has no dimension. Nevertheless, we focus our analysis and interpretation on qualitative aspects as well as quantitative effects as we attempt to compare the overall effects of an uncertainty shock in the Euro area and a shock to U.S. uncertainty. We include six lags in the VAR model. The dotted lines indicate the 15% confidence intervals.

We start by analyzing the effect on the other observable factors in [Y.sub.t] and [Exr.sup.EA.sub.t]. The response of [EPU.sup.EA.sub.t] over time shows that the effects quickly vanish over time and are only significant for the first periods. Regarding the spillover effect of Euro area uncertainty on U.S. uncertainty, we observe a moderate increase of roughly 18% which is highly significant, but quickly vanishes over time. Both central banks react to an uncertainty shock in the Euro area by taking a more expansionary stance. As expected, the shadow rate of the ECB shows a stronger reduction (up to 20 bp) (26) than the Fed's (up to 10 bp). Equally as expected, the Euro significantly depreciates by approximately 0.25%.

Regarding the effects on GDP, our results indicate a universally negative effect on economic activity which is highly significant for the majority of countries. However, the size of the uncertainty impact highly depends on the individual countries. In general, the effect stabilizes and therefore reaches its maximum after around 10-15 periods. (27) For the North American economies, we observe low but significant effects of a GDP reduction of 0.5% for the United States and 0.6% for Canada.

We find the largest effects (approximately 0.7 to 1.2%) for EMU countries such as Austria, Belgium, Greece, the Netherlands, Portugal, and Spain which is not surprising given the origin of the shock. Therefore, large effects are observable for many countries which have been at the epicenter of the sovereign debt crisis (Greece, Portugal, and Spain). For Germany and Ireland the effects on GDP do not turn out to be significant. And for non-EMU member countries in Europe, we observe overall smaller effects (0.25%-0.5%). However, there is one exception as Swiss GDP is highly affected by a Euro area uncertainty shock (up to 1%).

In contrast with the results of the other--especially financial--variables, the CPI responses display a larger share of insignificant results and overall heterogeneity. The median impulses, however, show a negative response for almost every country. For EMU countries, we observe the strongest effects for Spain, Greece, Germany, and Italy (up to 1%). For several countries of the EMU, we do not observe significant responses (Austria, Belgium, Finland, the Netherlands, and Portugal). Except for Denmark and Switzerland, there is only small and partly even no significant response for the non-EMU countries in Europe. Again, we come up with a very large effect for Switzerland (1.5%). A shock to Euro area uncertainty appears to be highly significant for the U.S. CPI.

The effects on equity are, as expected, negative and significant. We observe similar reductions in terms of size and duration of nominal equity prices in all countries. In contrast to the real economy variables, we observe an even larger amount of commonalities across countries indicating a very large degree of financial integration and interdependencies. The average reduction in equity prices as a response to an uncertainty shock amounts to roughly 0.8%. The responses are significant over the entire 60 periods for a large majority of countries, indicating that uncertainty has especially large and persistent effects on financial markets.

Regarding the uncertainty impacts on the long-term interest rates, we observe a clear division between Portugal, Spain, Italy, Ireland, and the remaining countries. (28) For the latter, we observe decreases of up to 1 percentage point. The strongest decrease is observed for Switzerland (up to 150 bp) followed by Germany, the Netherlands, and the United States (up to 125 bp). The decrease is strong but expected because several factors might cause a reduction in nominal yields. While the reduction in the monetary policy rate in the EMU is only moderate (around 20 bp), we observe a negative impact on economic growth as well as an overall negative effect on the CPI which might have negative effects on inflation expectations. Furthermore, during times of crisis and uncertainty, an increase of risk-aversion might lead investors to shift out of high-risk toward low-risk investments. Furthermore, central banks of smaller European countries might mimic the policy of the ECB to a certain extent (29) and might become targets for capital inflows. Thereby, the ECB policy might influence interest rates outside the EMU. All effects mentioned would contribute to a very strong effect on sovereign bond yields as indicated by our results. (30)

The estimated effects on Italian, Irish, Portuguese, and Spanish yields are not significant and close to zero. As the GUPS countries (Greece, Ireland, Italy, Portugal, Spain) are at the heart of the sovereign debt crisis and experienced strong increases in yields in recent years, our results do not come unexpected. We would like to argue that an increase in the risk premia is the most probable explanation for our result as observed since 2010. We conclude that the effects of uncertainty on these countries cancel out the impacts of several mechanisms mentioned above which should reduce yields in theory. According to the "flight to quality" argument, investors might have also reduced their amount of exposure to the GUPS, as these bonds have been regarded as increasingly risky during the sovereign debt crisis.

Regarding the uncertainty effects on Switzerland, we find very strong effects. We argue that this finding is mainly driven by country-specific effects. While the Euro area is the main trading partner of Switzerland, the Swiss Franc has strongly appreciated against the Euro especially due to large capital inflows. As Euro area products get relatively cheaper, the CPI in Switzerland decreases in reaction to the uncertainty shocks. This aspect is also highly relevant for the strong reduction of the Swiss long-term interest rates. Trade relationships alone are not capable of explaining the large effects on Swiss variables, especially if compared to a country like the United Kingdom with equally strong economic ties (see, e.g., De Carvalho Filho 2013).

B. Shocking U.S. Economic Policy Uncertainty

As a next step, we compare the effects of a shock to Euro area policy uncertainty to the impact of a similar size shock originating in the United States. For this purpose, we slightly change our specification (or rather the ordering) to [Z.sup.2.sub.t] = ([X.sup.1.sub.t], [Y.sup.2.sub.t]). In contrast to the specification in Section IV.A, U.S. economic policy uncertainty can now affect uncertainty in the Euro area contemporaneously.

[mathematical expression not reproducible].

Figure 4 presents the estimated impulse responses of a positive shock to [EPU.sup.US.sub.t]. The shock size is set to equal the size of the shock to [EPU.sup.EA.sub.t] in order to ensure comparability.

We again start by analyzing the effect on the other observable factors in [Y.sub.t] and [Exr.sup.EA.sub.t]. Similar to the shock in the Euro area, U.S. policy uncertainty decreases quickly after the shock. Monetary policy in the United States and Euro area responds immediately by taking a more expansive stance as indicated by reductions of the shadow rates (United States: up to 20 bp). As before, we observe that an increase in uncertainty quickly leads to a large increase of uncertainty in the other region.

For national GDP, we find uniformly negative and significant effects. For the United States, we observe a decrease of roughly 0.7%. The size of the effects is overall comparable. The most obvious differences versus their reactions to a shock to Euro area uncertainty emerge for the responses of German and Irish GDP. Both are significant and larger (Germany: approximately 0.7%, Ireland: 0.5%). Both countries react stronger to a U.S. uncertainty shock (a result also gained by Colombo 2013). In contrast to before, we do not observe a clear pattern between EMU and non-EMU countries.

As before, the responses of the CPIs are more difficult to interpret. Overall, we observe decreases in national CPIs for most countries, although they are only partly significant. The United States are heavily affected as the CPI decreases by approximately 1%. We find limited evidence of a positive response of the CPI. In this regard, we only find evidence for the Netherlands and Norway as the CPIs of both countries show an unexpected positive response. However, the response of the latter has to be interpreted with caution as only a small amount of the Norwegian CPI is explained by our factors. Comparing the effects to those of an uncertainty shock originating from the Euro area, the effects are of similar size but we partly observe strong differences between individual countries.

As before, we find very strong commonalities between responses of national equity variables. All responses indicate a large and significant reduction. The reduction of U.S. equity amounts to about 0.9% after 1 year. For other countries, we observe similar reductions in size and significance alike indicating that equity markets are highly connected. In comparison to the Euro area economic policy uncertainty shock, the effects are rather similar in size, significance, and duration. For long-term interest rates, the effects are negative and significant for the majority of countries. Again, we observe no reduction for Italy, Portugal, and Spain and no significant effect on Irish yields.

C. Robustness Tests

As common in empirical literature, we performed several robustness tests in order to confirm that our results do not depend on a specific specification. (31) As a first step, we experimented with the number of lags in the VAR model and the number of factors. Regarding the number of lags, the results are quantitatively and also quantitatively identical. We employed lag orders of four to eight. We only observe a few changes when the number of lags is increased to eight as few impulse-responses lose their significance.

Next, we proceeded by increasing the number of factors up to eight. We argue that qualitative and strong quantitative changes may indicate that our dynamic factor model (using six factors) is not capable of capturing all relevant dynamics in [X.sub.t]. Changing the number of factors to seven or eight does not appear to change our results or interpretation qualitatively. While the median impulses are very similar, the inclusion of further factors (especially in the case of eight factors) strongly increases the number of insignificant responses at the 15%-significance level. In our opinion, these results indicate that we have used a sufficient number of factors (and lags), and that a further inclusion strongly reduces the efficiency of our estimations.

In our study, we use a Cholesky decomposition. Also, we argue that the subdivision of the variables in [X.sub.t] into fast - and slow-moving variables of the Gibbs sampling is theoretically reasonable; the ordering of the variables in [Y.sub.t] is less obvious. Therefore, we changed the ordering in two respects. First, we changed the ordering by putting the shadow rates before the policy uncertainty variables in each specification. We obtain very similar results compared to our results presented in Sections IV.A and IV.B. Second, we switch the positions of the uncertainty variables set earlier in Section IV.A. As explained before, this prohibits a contemporary effect of the Euro area uncertainty variable on U.S. uncertainty. Qualitatively, we arrive at an identical interpretation although the effects are lower, but still largely significant. In this setting, the U.S. uncertainty variable does not respond significantly anymore and thus the overall reduction of effects does not come unexpected.

In addition, we check the robustness of our results for the variable measuring economic activity. Although the temporal disaggregation of Litterman (1983) is used in several papers to obtain monthly estimates of GDP, the time series are not (directly) observed and are based on an empirical relationship between GDP and monthly economic indicators. Therefore, we slightly change our [X.sub.t]-data set and include industrial production ([IP.sup.i.sub.t]) instead of our monthly GDP estimates. (32) For the shock to Euro area policy uncertainty, we use the specification[ [Z.sup.3.sub.t] = ([X.sup.2.sub.t], [Y.sup.1.sub.t]) which contains the following set of variables and the corresponding ordering:

[mathematical expression not reproducible].

For the shock to U.S. uncertainty, we use the specification [Z.sup.4.sub.t] = ([X.sup.2.sub.t], [Y.sup.2.sub.t]). (33)

While the responses of [IP.sup.i.sub.t] to policy uncertainty shocks are qualitatively similar to the responses of [GDP.sup.i.sub.t] there are some country-specific differences especially regarding the size of the effects. (34) However, the effects are difficult to compare as [IP.sup.i.sub.t] only focuses on one specific part of the economy. With an eye on the overall similarity, we argue that our results are generally robust with regard to the variable used as indicator of economic activity. The responses for the other variables ([Equity.sup.i.sub.t], [LTIR.sup.i.sub.t], and [EXR.sup.EA.sub.t]) are omitted as they are almost identical to the ones presented before.

As an additional robustness check, we substitute our price index [CPI.sup.i.sub.t] with a core price index ([CORE.sup.i.sub.t]). We can only explain a small and not sufficient amount of variation of the core price variables (on average: <60%, large discrepancy between country variables) even if we use up to eight factors. Apparently, core price indices only share a limited (smaller) number of commonalities or common developments which can be used to construct unobserved factors. (35) This shows that the FAVAR approach has specific limitations--especially if used in an international context--when the variables in the information set do not share a large amount of similarities.

As a final check of robustness, we changed the operationalization of our uncertainty variable. Instead of [EPU.sup.i.sub.t] we included [EQVol.sup.i.sub.t] in the specifications used in Sections IV.A and IV.B. As this indicator of uncertainty does not only put emphasis on another aspect of uncertainty but is also constructed differently, it is overall difficult to directly compare the results with those presented before (especially in the quantitative dimension). We observe that the responses of [GDP.sup.i.sub.t] are qualitatively identical, as every response is negative and significant. Furthermore and in contrast to our benchmark results for [EPU.sup.US.sub.t] and [EPU.sup.EA.sub.t], a shock to [EQVol.sup.US.sub.t] and [EQVol.sup.EA.sub.t] has larger effects on the equity markets relative to the effects on GDP. As [EQVol.sup.i.sub.t] measures uncertainty on equity markets, this result does not come unexpected. For long-term interest rates, we again find a large reduction in most yields as a reaction to an uncertainty shock. Again, the yields of Italy, Spain, Ireland, Portugal, and Spain do not respond significantly with a negative sign. Instead, we find an increase in yields for the countries mentioned. The effects on the CPI are again difficult to interpret. Most of the responses are not significant and we again find limited evidence of a positive CPI responses.

D. Discussion: International Spillovers of Policy Uncertainty?

In the following, we put all our empirical results together and compare them with our priors briefly formulated in Section I and similar studies presented in Section II. We expected a priori that policy uncertainty hampers growth, credit, thus reducing investment and output, employment, consumption, trade, and inflation. What is more, uncertainty is often viewed to lead to a depreciation of the domestic currency. Finally, uncertainty should have a dampening impact on asset prices as well. (36) In other words, the sign of uncertainty should be negative in all these cases (Caggiano, Castelnuovo, and Pellegrino 2017). Hence, it turns out to be rather easy to compare our results with these priors. Seen overall, our priors are in general corroborated by our FAVAR estimation results. Our results also indicate that uncertainty shocks emerging in the United States have larger impacts in terms of size and duration.

For national GDP, we find uniformly negative and significant effects of Euro area policy uncertainty for most countries of the Euro area, with the notable exception of Germany. As expected, the effects on the peripheral countries' GDP (Greece, Portugal, and Spain) but also on one EMU - and EU-out country, namely Switzerland, are the largest. Less significant and permanent effects emerge in the case of the other countries in the sample. If we employ U.S. instead of Euro area uncertainty, the results become even more significant and enduring. This mirrors the fact the United States is more relevant for the world economy and world financial markets than Europe (also outside the countries under investigation here). Expressed equivalently, the U.S. shock has stronger effects because it is more correlated with the "global" uncertainty component. The number of countries, for which persistent uncertainty effects with the theoretically expected sign emerge, increases. Most notably, persistently negative GDP effects are now indicated for Germany as well. U.S. economic policy uncertainty thus appears so dominant on a global scale that it makes the lack of an "option value of waiting under uncertainty" irrelevant also for Germany.

With respect to the national CPIs, effects of Euro area policy uncertainty turn out to be significantly negative but only temporary for France, Germany, Greece, Ireland, Italy, Spain (even persistently), Switzerland, and the United States. The impacts of U.S. policy uncertainty on the CPIs are temporarily significant and negative for France and Spain and permanently negative for Germany, Greece, Switzerland, and the United States.

For country-specific equity as a financial variable, the negative effects of both policy uncertainty variables are very strong as expected from theory (see Section II). In all cases with Euro area policy uncertainty as the uncertainty variable, however, it is temporary but not persistent in accordance with the Fama hypothesis. If U.S. policy uncertainty is used, the estimates even suggest a persistent negative impact of uncertainty on equity prices in nearly every country.

Regarding long-term interest rates, the effect of Euro area policy uncertainty on country-specific rates is impressive as well. Significant permanent effects with the expected negative sign emerge for the vast majority of the countries under investigation. Only the impulse responses for Ireland, Italy, and Portugal turn out to be insignificant. If one considers the results prevailing if U.S. policy uncertainty is implemented, the results change in a way that temporary effects emerge for a higher share of countries. In this case, only the impulse responses for Ireland, Italy, Portugal, and Spain turn out to be insignificant.

Euro area monetary policy rates measured by shadow rates go down significantly but temporarily in the wake of a Euro area policy shock (which is consistent with an inflation-targeting approach), whereas U.S. rates show the same pattern but to a lesser extent. The reverse pattern emerges if a shock to U.S. policy uncertainty is considered.

The external value of effective nominal Euro exchange rate decreases temporarily in the case of a Euro area policy uncertainty shock and increases in the case of a U.S. policy uncertainty shock. Finally, U.S. policy uncertainty increases temporarily if Euro area policy uncertainty increases and vice versa. Hence, there seems to exist a bilateral policy uncertainty spillover across the Atlantic.

Interestingly enough, in most of our cases (Figures 3 and 4) the effects of policy uncertainty on real GDP are lower and less persistent in the Anglo-Saxon World (United States, United Kingdom, and Canada) than in Europe. In other words, uncertainty appears to cause deeper recessions in Continental Europe than in the Anglo-Saxon world. (37) This result seems to underline the traditional story that adjustment costs are generally larger in Continental Europe, except Germany where the flexibility-enhancing Hartz reforms took effect around 2005. This represents the "hysteresis under uncertainty" type of explanation that firms are less capable of dealing with uncertainty in Continental Europe due to too rigid institutions (see Section II.A). (38) Maybe it also reflects that the Euro area is considerably more open than the United States and is thus more exposed to (foreign) uncertainty (Belke and Gros 2002).

That said, we now roughly compare our results qualitatively with those in the literature, although the methods, the data, and the magnitude of shocks cannot be compared directly (as became clear in Section II.B). The results of Colombo (2013) are very similar to ours. Her results indicate that a U.S. uncertainty shock has negative and significant effects on prices, real economic variables, and policy rates. Furthermore, Colombo (2013) also finds evidence of a very fast and strong transatlantic transmission of uncertainty. Overall and in line with our results, a U.S. uncertainty shock has similar effects in terms of magnitude on U.S. and Euro area variables.

Our results also parallel the results gained by Kang, Ratti, and Vespignani (2017) and Kamber et al. (2016). Both studies find strong evidence that uncertainty has negative effects on output and prices as real economy variables and on interest rates as a financial variable. What is more, both studies find large evidence that national variables respond similarly to (foreign/global) uncertainty shocks. Both studies support our result of a strong synchronicity of the responses of national variables to an (foreign/global) uncertainty shock. Therefore, our results might also be interpreted as evidence of an international business cycle affecting financial variables and real economic variables alike.

As a reaction to a positive U.S. uncertainty shock, domestic currencies depreciate in all countries except the United States, Japan, and Switzerland in the Kamber etal. (2016) study. The authors argue that this pattern of exchange rate reactions corresponds with the reserve currency status of the U.S. dollar, the Yen, and the Swiss Franc and the flight to safety usually observed during uncertain times. However, in our case, the Euro depreciates as a reaction to a Euro area uncertainty shock but appreciates in the case of a U.S. uncertainty shock suggesting that from the perspective of Europe the dollar is no safe haven if the uncertainty emerges in the United States. As far as the spread of corporate yields over bond yields is concerned, Kamber etal. (2016) find a strong positive impact. This result is consistent with our finding that equity prices are significantly negatively affected by an increase in uncertainty.

Finally, with respect to the sign of the uncertainty impact, we corroborate the findings of De Wind and Grabska (2016). Contrary to us, they only assess the impact of domestic uncertainty shocks on industrial production. Like us, they come up with a significantly negative sign of the uncertainty-industrial production relationship.

V. CONCLUSIONS

The research questions tackled within this paper have been the following ones. Is the FAVAR approach an adequate framework to model cross-country developments? What are the global effects of policy uncertainty shocks? What is the sign of the estimated uncertainty impact coefficient? What are the channels of uncertainty transmission between the Euro area and the United States in both directions? For this purpose, we compare a U.S. and a Euro area policy shock and put a special focus on non-EMU countries in Europe.

Our results indicate that economic policy uncertainty has large cross-border effects and not only impacts the country where the shock originates. This argument appears to be especially valid for financial variables. Our results show that uncertainty shocks emerging in one region quickly raise uncertainty outside the region of origin which appears to be an important transmission channel. In our case, shocks to either U.S. or Euro area policy uncertainty contemporaneously affect uncertainty in the other region. However, this result raises the question whether uncertainty (in general and also in our model) is purely regional, as we cannot differentiate between a spillover or a "pure" global shock in our framework.

What kind of spillovers do we have in mind for the EPU variable? Let us take the foreign trade nexus as an illustrating example. Policy uncertainty measured for an EU country may thus, beyond uncertainty in its own country, also be related to policy uncertainty prevailing in an export destination country such as the United States. This kind of uncertainty is prominently reported in the sending countries' media as well. What is more, policy uncertainty in the receiving countries tends to quickly transform into uncertainty in the sending country and may even change governance structures there (which are, like tax legislature, also part of the policy uncertainty index). Hence, one may well feel legitimized to employ the uncertainty index for the sending country to proxy uncertainty for the exporters in the exporting countries. In other words, economic policy uncertainty is based on local political and economic factors but relevant also for other countries which are trade partners. Based on the experiences of the financial crisis which originated in the United States and the sovereign debt crisis which originated in the Euro area, we support the former hypothesis. Therefore, due to the strong comovements of uncertainty, it is difficult to strictly compare a U.S. and Euro area policy shock in terms of the size of the effects. However, we find evidence that U.S. uncertainty shocks have slightly larger cross-border effects compared to a Euro area shock. Our results overall reveal strong and significant adverse effects on economic activity and especially equity which are similar across countries, while the impact on prices is more ambiguous.

But seen on the whole, thus, uncertainty has a strong negative impact on economic activity, consumer prices, equity prices, and interest rates. Uncertainty shocks cause deeper recessions in Continental Europe than in Anglo-Saxon countries. Economic policy uncertainty does not only impact that country where the shock originates but also has large cross-border effects. In that respect, Switzerland is the most affected non-Euro area member country. In this regard, we find a strong synchronization of the responses of national variables to a (foreign) uncertainty shock, indicating evidence of international business cycles. Regarding the response of long-term yields, we find a clear "North-South" divide in the Euro area with rates decreasing less in the South. Another important result is that uncertainty shocks emerging in one region quickly raise uncertainty outside the region of origin which appears to be an important transmission channel of uncertainty.

As a particularly interesting aspect of our research we detect differences between how shocks affect economic versus financial variables: uncertainty has larger and more persistent effects on financial than on economic variables.

We would like to stress again that we used only the aggregate Euro area indicator of EPU instead of its national components. We show that the aggregate Euro area indicator has a quite different impact on individual Euro area countries. We feel legitimized to argue that it makes sense to limit ourselves to an aggregate Euro area indicator of EPU with an eye on a common monetary policy, implicit debt mutualization, and contagion within the Eurozone. Formally, different effects on individual Euro area member countries could be of course due to, among others, the different national contributions to the aggregate from the four countries. However, different country-specific degrees of rigidities in the countries are certainly also relevant (see Sections II.A and the discussion of the results in Section IV.D, for instance for Germany after the Hartz reforms).

With respect to our modeling approach, we conclude that the FAVAR is capable of jointly modeling economic developments in a lot of countries. Each specification explains a very large amount of the overall variation in our data set. Therefore, we feel legitimized to argue that our model (or the factors extracted) most probably includes all relevant dynamics in our data set. Therefore, we conclude that the FAVAR is not only capable of jointly analyzing a lot of economic information (i.e., a very large amount of variables) for a specific country, but it can also be used to analyze cross-country developments.

In order to generate further evidence on the effects of different specifications of uncertainty, we see further potential for research. The most obvious approach is to check the robustness of our results by using alternative indicators of uncertainty. As mentioned, there is no commonly accepted measure of uncertainty. Furthermore, the use of other multiequational models like GVAR models, Panel-VAR models, and Bayesian VARs, developed by Banbura, Gianonne, and Reichlin (2008) appears promising for generating additional evidence.

Additionally, our approach might be expanded in several other ways. In our opinion, the most promising way is to drop the underlying assumption of linearity (because it contradicts some of the transmission mechanisms of uncertainty mentioned in Section II and nonlinearity may become relevant especially in crisis times which are covered by parts of our sample period) in our model (Pellegrino 2017). First, the effect of uncertainty might be regime-dependent, indicating that uncertainty shocks have different effects when uncertainty is already high or when uncertainty is low or moderate (Belke and Goecke 2005). Regime-dependency may also emerge with respect to the monetary policy stance, if the economy is close to the zero-lower bound or is, for instance, bound to an inflation targeting regime (Mumtaz, Zabczyk, and Ellis 2011). And, second, uncertainty impacts might be time-varying in general.

ABBREVIATIONS

CPI: Consumer Price Index

ECB: European Central Bank

EMU: European Monetary Union

FAVAR: Factor-Augmented Vector Autoregressive Model

GDP: Gross Domestic Product

GUPS: Greece, Ireland, Italy, Portugal, Spain

GVAR: Global Vector Autoregressive Model

IMF: International Monetary Fund

IRF: Impulse Response Function

OECD: Organisation for Economic Co-operation and Development

VAR: Vector Autoregressive Model

doi: 10.1111/ecin.12701

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ANSGAR BELKE and THOMAS OSOWSKI *

* We are grateful for valuable comments from two anonymous referees, Keith Pilbeam, and participants in the 2017 Annual Conference of the EEFS in Ljubljana/Slovenia, and the 2018 International Atlantic Economic Conference, Montreal, Canada.

Belke: Ad personam Jean Monnet Professor Dr., Department of Economics and Business, University of Duisburg-Essen, Essen 45117, Germany; Centre for European Policy Studies, Brussels 1000, Belgium; IZA Bonn, Bonn 53113, Germany; King's Business School, London, WC2R 2LS, UK. Phone 0049-201-183-2776, Fax 0049-201-183-4181, E-mail ansgar.belke@uni-due.de

Osowski: Dr., Department of Economics and Business, University of Duisburg-Essen, Essen 45117, Germany. E-mail thomas.osowski@uni-due.de

1. Similar views have been shared and propagated by the IMF (2016), the OECD, and other international institutions.

2. For a comparable procedure in the context of panel vector error correction models see Belke, Dobnik, and Dreger (2011).

3. By means of a variance decomposition, the effects of several exogenous shocks (i.e., their contributions) are compared. In this context, the ordering of the variables is decisive if they are correlating as strongly as in our case. Accordingly, Colombo (2013) endows U.S. uncertainty with a higher impact ex ante due to her specific ordering. If U.S. uncertainty is shocked and the Euro area uncertainty is able to react on it contemporaneously (corresponding with Colombo's chosen ordering), the impact of U.S. uncertainty is larger, because U.S. uncertainty is now impacting all variables also through its impact on the Euro area uncertainty. If, however, the ordering was the other way around and U.S. uncertainty is shocked, one would find only a smaller effect of U.S. uncertainty on the Euro area uncertainty variable and. hence, smaller impacts on all other variables as well.

4. See Bernanke, Boivin, and Eliasz (2005) for further details and mathematical derivations of the estimator. They also present an additional two-step estimation procedure where the factors in [X.sub.t] are extracted and estimated according to Stock and Watson (2002) and afterward included in a VAR. From an econometric perspective, it is difficult to discriminate between both. Furthermore, Bernanke, Boivin, and Eliasz (2005) show that both procedures generate similar results. Therefore, our choice to use the Bayesian approach is primarily based on convenience.

5. See, for instance, Vasisthta and Maier (2013) and Fernald, Spiegel, and Swanson (2014) who generate one factor for a given subset of variables instead of jointly generating the factors from the entire sample. Their approach enables them to better interpret the estimated factors which is important for their research question and estimation procedure as both studies use two-step estimation procedure instead of the Bayesian approach. In our approach, we do not put emphasis on the interpretation of the factors as we are not explicitly interested in the estimation of common factors but in the effects on individual country variables and therefore the elements of [X.sub.t]. Thus, we decided not to impose further restrictions on the factor estimation.

6. For a derivation of impulse responses for the elements of [X.sub.t], see Gupta and Kabundi (2010), Blaes (2009), and Bernanke, Boivin, and Eliasz (2005).

7. Alternatively, one may also use the criteria presented by Bai and Ng (2002) or the Kaiser criterion (all factors with eigenvalues greater than one). However, according to our results, the Kaiser criterion tends to propose rather large factor numbers (see Table 4).

8. Moreover, the probability and technical possibility to identify a break at around 1999 would not be very high because the break would be located at the very beginning of the sample. And we would be forced to start our Granger-causality tests not earlier than in 1999 for technical reasons. What is more, some variants of our FAVAR are in the end estimated from 1999 on anyway. For instance, data about the VSTOXX is only available from January 1999 onward. The same is valid for the composite indicator of systematic stress in the financial system ([FUI.sup.EA.sub.t]) published by the ECB.

9. Due to data limitations, Greek interest yields are not included in the baseline model.

10. We use the procedure of Litterman (1983) to construct monthly realizations of GDP. Industrial production, retail sales, and nominal export data are used as high(er)-frequency data.

11. In contrast to CPI, core price indices exclude developments of energy and food prices.

12. This is exactly what we find if we exclude the U.S. uncertainty variables from [Y.sub.t].

13. For a deeper explanation and the exact measurement of shadow rates see https://www.rbnz.govt.nz/-/ media/ReserveBank/Files/Publications/Research/Additional %20research/Leo%20Krippner/5892888.pdf.

14. A second component reflects the number of federal tax code provisions set to expire in future years. The third component uses disagreement among economic forecasters as a proxy for uncertainty.

15. See www.policyuncertainty.com.

16. At the start of the sample period (January 1996) only values for Germany and France are available. The Italian indicator is available from January 1997 and the Spanish one from January 2001. Unfortunately, indicators for other Euro area countries are currently not available.

17. Euro Stoxx 50 is the most widely followed European equity index.

18. The growth rates have been tested again for nonstationarity.

19. We are aware of the empirical discussion whether interest rates can contain a unit roots. In our specification, we do not explicitly reject this assumption and therefore include interest rate variables in first differences.

20. We only present evidence for a selective number of indicators. Additional indicators relevant in this context are presented by Ludvigson. Ma, and Ng (2015) and Jurado, Ludvigson, and Ng (2015).

21. See Hollo, Kremer, and Lo Duca (2012) for further details.

22. See European Commission (2013) for details.

23. Both indicators are conceptually close to the composite indicator of the ECB. See Hakkio and Keeton (2009).

24. In general, we find that the Norwegian economic variables are least explained by our model--independent of the specification. This may be explained by structural differences between the Norwegian and the other European economies due to Norway's international role as an exporter of primary products (e.g., oil).

25. This roughly equals the increase of uncertainty at the beginning of 2010 in the Euro area.

26. From the perspective of the ECB, these results might be explained by an expected decrease in the CPI as indicated by our results.

27. The stabilization of the median impulse responses over time also indicates that our VAR model is stable.

28. We do not include the Greek interest rate. However, due to the evidence generated, we would expect the Greek interest rate to behave similarly to or even stronger than the Portuguese yield.

29. This might be most relevant for Denmark which is part of the ERM II.

30. For strong evidence of bond yield spillovers from major advanced economies to Emerging Asia see Belke, Dubova, and Volz (2017).

31. The results presented in this section are available on request.

32. We again use six factors and six lags.

33. The results are available on request.

34. As an example, we find stronger and significant effects for economic activity in Germany when industrial production is used instead of GDP.

35. This observation does not come unexpected, as core price indices are excluding developments of energy and food prices which are known to be settled at the global stage and are therefore very similar on the national level.

36. See Belke and Dubova (2018) for international spillovers in global asset markets, Belke, Orth, and Setzer (2010) for the transmission of global liquidity, and Belke and Verheyen (2014) for the currently low interest rate environment and global liquidity spillovers. The above-mentioned uncertainty effects may thus spillover internationally.

37. Accordingly, Belke and Gros (2002) find that the variability of the Euro (i.e., exchange rate uncertainty) has a statistically significant negative impact on labor markets in the Euro area. In the United States a similar effect seems to be operating, but it is statistically less strong. According to the authors who have the option value of waiting with investment-type decisions in mind, these results fit the general observation that U.S. labor markets are more flexible and that the Euro area is considerably more open than the United States. See also Bentolila and Bertola (1990) and Leduc and Zheng (2016).

38. Note, however, that this strong pattern for Germany only emerges in the case of European uncertainty but not for U.S. uncertainty.

Caption: FIGURE 1 Development of Uncertainty by Economic Region

Caption: FIGURE 2 Development of Uncertainty by Indicator

Caption: FIGURE 3 Impulse-Responses ([Z.sup.1.sub.t])--Shock to Euro Area Uncertainty ([EPU.sup.EA.sub.t])

Caption: FIGURE 4 Impulse-Responses ([Z.sup.2.sub.t])--Shock to U.S. Uncertainty ([EPU.sup.US.sub.t])
TABLE 1
Overview of Variables

Variable                           Name

Real GDP                           [GDP.sup.i.sub.t]
Industrial production              [IP.sup.i.sub.t]
CPI                                [CPI.sup.i.sub.t]
Core price index                   [CORE.sup.i.sub.t]
Equity prices                      [EQ.sup.i.sub.t]
Long-term interest rate (10-year   LTIR.sup.i.sub.t]
  government bonds)
Nominal effective exchange rate    [EXR.sup.EA.sub.t]
  of the Euro area
Shadow rates as proposed by        [SR.sup.i.sub.t]
  Krippner (2016)
Economic policy uncertainty        [EPU.sup.i.sub.t]

Equity volatility (VSTOXX/VIX)     [EQVol.sup.i.sub.t]

Variable                           Source

Real GDP                           Own calculations
Industrial production              OECD/IMF
CPI                                OECD
Core price index                   OECD
Equity prices                      MSCI
Long-term interest rate (10-year   Thomson Reuters Datastream
  government bonds)
Nominal effective exchange rate    Bank for International
  of the Euro area                   Settlements
Shadow rates as proposed by        Reserve Bank of New Zealand
  Krippner (2016)
Economic policy uncertainty        http://www.policyuncertainty.
                                     com/own calculations
Equity volatility (VSTOXX/VIX)     Thomson Reuters Datastream

Variable                           Subgroup   Treatment

Real GDP                           Slow           5
Industrial production              Slow           5
CPI                                Slow           5
Core price index                   Slow           5
Equity prices                      Fast           5
Long-term interest rate (10-year   Fast           2
  government bonds)
Nominal effective exchange rate    Fast           5
  of the Euro area
Shadow rates as proposed by                       1
  Krippner (2016)
Economic policy uncertainty                       4

Equity volatility (VSTOXX/VIX)                    4

Note: The transformation codes are: 1--no transformation; 2--first
difference; 4--logarithm; 5--first difference of logarithm.

TABLE 2
Granger-Causality Tests, P Values

                         Sample: 1996-2015

             [EPU.sup.US.sub.t]    [EPU.sup.EA.sub.t]
                 Does Not GC           Does Not GC
Lag Length   [EPU.sup.EA.sub.t]    [EPU.sup.US.sub.t]

1                   0.037#                0.031#
2                   0.266                 0.132
3                   0.359                 0.336
6                   0.113                 0.268

                         Sample: 1999-2015

             [EQVol.sup.US.sub.i]    [EQVol.sup.EA.sub.i]
                  Does Not GC             Does Not GC
Lag Length   [EQVol.sup.EA.sub.i]    [EQVol.sup.US.sub.i]

1                   0.003#                  0.122
2                   0.003#                  0.022#
3                   0.008#                  0.045#
6                   0.052                   0.119

Notes: Schwarz-Bayes and Hannan-Quinn information criteria indicate a
lag length of one for both specifications. GC, Granger-cause. Bold
indicates significant entries (5%).

Note: Bold indicates significant entries (5%) are indicated with #.

TABLE 3
Correlation Matrix of Uncertainty Indicators

                        [EPU.sup.EA.sub.t]    [EQVol.sup.EA.sub.t]

[EPU.sup.EA.sub.t]               1                    0.293
[EQVol.sup.EA.sub.t]                                    1
[FUI.sup.EA.sub.t]
[BCS.sup.EA.sub.t]
[EPU.sup.US.sub.t]
[EQVoL.sup.US.sub.t]
[FUI.sup.US.sub.t]

                        [FUI.sup.EA.sub.t]    [BCS.sup.EA.sub.t]

[EPU.sup.EA.sub.t]             0.348                 0.488
[EQVol.sup.EA.sub.t]           0.660               -0.023
[FUI.sup.EA.sub.t]               1                   0.345
[BCS.sup.EA.sub.t]                                     1
[EPU.sup.US.sub.t]
[EQVoL.sup.US.sub.t]
[FUI.sup.US.sub.t]

                        [EPU.sup.US.sub.t]    [EQVoL.sup.US.sub.t]

[EPU.sup.EA.sub.t]             0.716                  0.216
[EQVol.sup.EA.sub.t]           0.572                  0.830
[FUI.sup.EA.sub.t]             0.486                  0.683
[BCS.sup.EA.sub.t]             0.205                -0.145
[EPU.sup.US.sub.t]               1                    0.532
[EQVoL.sup.US.sub.t]                                    1
[FUI.sup.US.sub.t]

                        [FUI.sup.US.sub.t]

[EPU.sup.EA.sub.t]             0.087
[EQVol.sup.EA.sub.t]           0.679
[FUI.sup.EA.sub.t]             0.773
[BCS.sup.EA.sub.t]           -0.173
[EPU.sup.US.sub.t]             0.411
[EQVoL.sup.US.sub.t]           0.798
[FUI.sup.US.sub.t]               1

Notes: If [FUI.sup.EA.sub.t] or [EQVol.sup.EA] is considered, the time
period is reduced to January 1999 to December 2015. Sample: January
1996 to December 2015.

TABLE 4
Principal Components Analysis ([X.sup.1.sub.t])

Factors    Eigen Value    Proportion    Cumulative

1             24.071         0.339         0.339
2             15.139         0.213         0.552
3              9.345         0.131         0.683
4              4.335         0.061         0.744
5              2.897         0.040         0.785
6              2.187         0.030         0.816 (b)
7              1.718         0.024         0.840
8              1.356 (a)     0.019         0.859
9              0.927         0.015         0.875
10             0.675         0.015         0.891

(a) Factor number proposed by the Kaiser criterion.

(b) Factor number which explains at least 80% of the
variance in [X.sub.t].

TABLE 5
Fraction of [X.sup.1.sub.t] Explained by Common Factors ([R.sup.2]
([Z.sup.1.sub.t], [Z.sup.2.sub.t]))

Variable    [R.sup.2]

GDP AUST       80.5
GDP BEL        76.8
GDP CAN        83.6
GDP DEN        68.6
GDP FIN        82.1
GDP FRA        91.2
GDP GER        82.1
GDP GRE        79.1
GDP ITA        88.4
GDP IRE        66.5
GDP NET        89.1
GDP NOR        33.1
GDP POR        72.3
GDP SWE        83.3
GDP SWI        82.1
GDP SPA        95.0
GDP UK         85.1
GDP US         86.5
CPI AUST       82.6
CPI BEL        89.0
CPI CAN        66.6
CPI DEN        83.5
CPI FIN        77.4
CPI FRA        87.4
CPI GER        85.0
CPI GRE        57.7
CPI ITA        71.5
CPI IRE        84.0
CPI NET        59.2
CPI NOR        41.1
CPI POR        83.1
CPI SWE        81.3
CPI SWI        81.9
CPI SPA        87.4
CPI UK         72.3
CPI US         87.3
EQ AUST         90
EQ BEL         91.5
EQ CAN         86.1
EQ DEN         93.3
EQ FIN         91.1
EQ FRA         96.2
EQ GER         95.3
EQ GRE         87.2
EQ ITA         90.9
EQ IRE         84.4
EQ NET         94.1
EQ NOR         91.4
EQ POR         84.0
EQ SWE         89.8
EQ SWI         89.2
EQ SPA         91.0
EQ UK          91.9
EQ US          90.1
LTIR AUST      92.8
LTIR BEL       87.3
LTIR CAN       74.7
LTIR DEN       92.0
LTIR FIN       84.2
LTIR FRA       91.0
LTIR GER       94.2
LTIR ITA       78.2
LTIR IRE       55.6
LTIR NET       93.5
LTIR NOR       73.1
LTIR POR       70.8
LTIR SWE       79.8
LTIR SWI       83.8
LTIR SPA       74.5
LTIR UK        85.5
LTIR US        78.1
EXR EURO       57.5

Note: [R.sup.2] refers to the fraction of the variance of the variable
explained by the common factors, ([[??].sub.t], [Y.sub.t]).
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