2. Geopolitical risk data

To estimate the effects of rising geopolitical risk tensions, we employ the geopolitical risk (GPR) indices of Caldara and Iacoviello (Reference Caldara and Iacoviello2022) as proxy. The authors consider geopolitical risk as risk associated with wars, terrorist acts, and tensions between states that affect the normal and peaceful course of international relations. They aim to identify situations in which the power struggle between governments over territories is not resolved peacefully and democratically.

The GPR index is part of the rapidly growing literature on text search methods using newspaper archives. To create the GPR index, Caldara and Iacoviello (Reference Caldara and Iacoviello2022) gathered articles from electronic archives of the Chicago Tribune, the Daily Telegraph, Financial Times, The Globe and Mail, The Guardian, the Los Angeles Times, The New York Times, USA Today, The Wall Street Journal, and The Washington Post with broad worldwide coverage featuring events and threats associated with geopolitical conflicts such as wars, terrorist acts, ethnic and political violence, and geopolitical tensions. The automated text-mining search separately identifies war threats, peace threats, military buildups, nuclear threats, terror threats, beginning of war, escalation of war, and terror acts. Complementing the global geopolitical situation, GPR indices for 44 different countries are available. Country-specific indices are calculated analogously based on the overall GPR index, but with the supplementary requirement that articles must explicitly mention the name of the country or its major cities to be considered for inclusion. For each of the 10 newspapers, the authors collect monthly counts of GPR-related articles as a proportion of the total number of articles. Subsequently, the authors divide each monthly count by the mean from the year 2000 to the year 2009 of the series and multiply it by 100.Footnote ³ In essence, the GPR index acts as a barometer that captures the ebbs and flows of geopolitical risk in real-time.Footnote ⁴

Figure 1 plots the movements in the Russian GPR index from 2000Q1 through 2024Q1. The calculated Russian GPR scores line up well with past geopolitical events that would typically be associated with high levels of uncertainty and, likewise, the recent GPR spike in the wake of the Russian invasion of Ukraine. The time series is characterized by various armed conflicts and terrorist acts since the turn of the millennium. First, at the beginning of the 2000s, the guerrilla phase of the 2nd Chechen War led to several GPR spikes of different sizes. Among others, these include the killing of civilians by armed Chechen extremists in the Moscow theater hostage crisis in October 2002. Second, Russia’s war in Georgia over the breakaway territories of Abkhazia and South Ossetia in August 2008 is discernible in another GPR rise. Third, the Euromaidan, the Russian annexation of Crimea in February–March 2014, and the war in the Donbas are evident in an especially pronounced GPR increase. Fourth, the recurring GPR spikes from 2015 onwards were the result of repeatedly flaring tensions between Ukraine and Russia over Donbas. The long-run average of these spikes is about 0.8, and the standard deviation is 0.6. Fifth, in the first quarter of 2022, the score reached 5.2, highlighting the significance of the Russian invasion of Ukraine in fueling political and economic insecurity around the world.Footnote ⁵ Finally, the Russian GPR index has declined, even as the war in Ukraine continues in full. This reflects that an initial uncertainty overshooting has abated, and energy markets have shown a great deal of adaptiveness. European countries which were tied to Russian pipeline gas managed to switch to natural gas suppliers, which required building new liquefied natural gas (LNG) infrastructures.

Figure 1. Quarterly Russian GPR index from 2000Q1 through 2024Q1.

Notes: The quarterly text-mining GPR indices are calculated by the temporal aggregation of the monthly GPR indices. The GPR data were sourced from https://www.matteoiacoviello.com/gpr_country.htm.

Figure 2 depicts a comparison between the average pre- and post-war geopolitical risk levels by country. In this visualization, changes in GPR indices are represented using varying colors, with darker shades indicating higher GPR scores. First, it is evident from the Figure that there has been a notable global increase in average geopolitical risk across most countries since the outbreak of the full-blown war in February 2022. The dark orange shading of Russia confirms the assessment that the Russian war of aggression has turned the security and defense architecture of Europe upside down. Second, Ukraine, being the target of unprovoked Russian military aggression, is depicted with red GPR values, symbolizing the greatly elevated risk it faces. Finally, the map emphasizes the pivotal role of geographical proximity since countries located closer to the Russian-Ukrainian battleground have witnessed the most significant surge in domestic geopolitical risk.

Figure 2. The worldwide geopolitical risk landscape (2022Q1–2024Q1).

Notes: The map shows the average GPR indices from 2022Q1 to 2024Q1 (Index: 1985Q1–2021Q4 = 1). No GPR scores are available for countries marked in gray. The country-specific GPR indices were sourced from https://www.matteoiacoviello.com/gpr_country.htm.

In the following chapter, we will analyze how the empirical evidence stacks up, including an in-depth analysis of the impact of Russia’s invasion of Ukraine.

3. Model

In order to capture the transmission of heightened GPR, we employ the BGVAR framework (Boeck et al., Reference Boeck, Feldkircher and Huber2022) offering a balanced trade-off between parsimony and complexity. Consider that we have a panel structure with $N+1$ units. Each of the first $N$ units, $i=1,\cdots ,N$ , is modeled as a reduced VAR model with exogenous variables (VARX) of the form

(1) \begin{equation} {\boldsymbol{y}}_{i,t}={{b}}_{i}+ {\boldsymbol{B}}_{p}^{i}{\boldsymbol{y}}_{i,t-p}+{\boldsymbol{G}}_{i,0}{\boldsymbol{x}}_{i,t}+\ldots {\boldsymbol{G}}_{i,q}{\boldsymbol{x}}_{i,t-q}+{\boldsymbol{H}}_{i,0}{\boldsymbol{z}}_{t}+\ldots +{\boldsymbol{H}}_{i,r}{\boldsymbol{z}}_{r}+ \boldsymbol{\varepsilon }_{i,t}, \end{equation}

where ${\boldsymbol{y}}_{t}$ is a vector with $n_{i}$ variables for country i in time t and is a function of its past p lags as well as a function of (weakly) exogenous variables ${\boldsymbol{x}}$ and ${\boldsymbol{z}}$ , which have q and r lags, respectively. In order to capture better volatile events, such as the pandemic lockdowns or the breakout of the war, we assume that the residuals follow a stochastic volatility process and thus have a time-varying variance-covariance matrix $\boldsymbol{\varepsilon }_{i,t}\sim N(\mathbf{0},\boldsymbol{\unicode{x1D6F4}}_{\mathrm{t}}^{\mathrm{i}})$ .Footnote ⁶ The vector ${\boldsymbol{x}}_{i,t}$ has $n_{i}^{*}$ elements and is a weighted average of the variable of other units relevant for unit i, i.e.

(2) \begin{equation}{\boldsymbol{x}}_{i,t}=w_{i,1}{\boldsymbol{y}}_{1,t}+ w_{i,2}{\boldsymbol{y}}_{2,t}+\cdots + w_{i,i}{\boldsymbol{y}}_{t}^{i}+\ldots + w_{i,N}{\boldsymbol{y}}_{N,t},\end{equation}

with weights $w_{i,j}$ denoting the weight associated with unit j with respect to unit i, as measured by an international trade metric. Additionally, it holds $w_{i}^{i}=0$ and $\sum _{j}w_{j}^{i}=1$ . The vector ${\boldsymbol{z}}_{t}$ collects $n_{z}$ variables which are not unit specific (note the omission of superscript i) and affect all countries. The dynamics of the $n_{z}\times 1$ vector ${\boldsymbol{z}}$ are given by the $N^{th}+1$ unit and also follow a VAR form with a stochastic volatility process with s lags.

(3) \begin{equation}{\boldsymbol{z}}_{t}={\boldsymbol{d}}+ {\boldsymbol{D}}_{1}{\boldsymbol{z}}_{t-1}+\ldots +{\boldsymbol{D}}_{s}{\boldsymbol{z}}_{s}+ \boldsymbol{\varepsilon }_{z,t}, \boldsymbol{\varepsilon }_{z,t}\sim N(\mathbf{0},\boldsymbol{\unicode{x1D6F4}}_{z,t})\end{equation}

For example, Dées et al. (Reference Dées, di Mauro, Pesaran and Smith2007) name the $N^{th}+1$ unit the “dominant unit,” which collects commodities prices such as oil, raw materials, and metal prices. The distinction in equation (1) between the exogenous variables ${\boldsymbol{x}}$ and ${\boldsymbol{z}}$ is for expositional purposes and thus the model may be written more compactly as

(4) \begin{equation}{\boldsymbol{y}}_{i,t}={\boldsymbol{b}}_{i} +\sum _{j=1}^{p}{\boldsymbol{B}}_{i,j}{\boldsymbol{y}}_{i,t-j}+\sum _{j=0}^{q}\boldsymbol{\Lambda }_{i,j}{\boldsymbol{y}}_{i,t-j}^{\boldsymbol{*}}+ \boldsymbol{\varepsilon }_{i,t}, \boldsymbol{\varepsilon }_{i,t}\sim N\left(\mathbf{0},\boldsymbol{\unicode{x1D6F4}}_{i,t}\right)\end{equation}

where ${\boldsymbol{y}}^{\boldsymbol{*}}=[{\boldsymbol{x}}\boldsymbol{'}, {\boldsymbol{z}}\boldsymbol{'}]\boldsymbol{'}$ collects the non-domestic variables and $\boldsymbol{\Lambda }_{i,j}$ are block-diagonal matrices with ${\boldsymbol{G}}_{i,j}$ and $ {\boldsymbol{H}}_{i,j}$ along the diagonals with dimensions $n_{i}\times (n_{i}^{*}+n_{z})$ .

Given the constructed weighted averages the full GVAR specification is given by equations (3) and (4). The final assumption is that the unit residuals are uncorrelated, i.e. $\boldsymbol{\varepsilon }_{i,t}$ and $\boldsymbol{\varepsilon }_{j,t}$ are independent for all i and j and hence the joint variance-covariance matrix is block-diagonal $\boldsymbol{\unicode{x1D6F4}}_{t}=\text{diag}(\boldsymbol{\unicode{x1D6F4}}_{1,t}, \ldots , \boldsymbol{\unicode{x1D6F4}}_{N,t},\boldsymbol{\unicode{x1D6F4}}_{z,t})$ . This allows for unit-by-unit estimation which greatly facilitates computation.

The multi-country modeling framework can be motivated in two ways. Dées et al. (Reference Dées, di Mauro, Pesaran and Smith2007) have derived the GVAR approach as an approximation to a global factor model, while Chudik and Pesaran (Reference Chudik and Pesaran2011) have obtained the GVAR model as an approximation to a large system in which all variables are endogenous.

A special GVAR feature is the sparse parameterization, which allows practitioners to bypass the curse of dimensionality problem in large unrestricted VARs. By contrast, in the GVAR modeling framework, the number of parameters to be estimated for each of the units for $i=1, \cdots ,N$ is independent of $N$ and amounts to $[n_{i}p+1+n_{i}^{*}(q+1)+n_{z}(r+1)]$ coefficients. This independence from $N$ also applies to the $0.5n_{i}(n_{i}-1)$ parameters of the variance-covariance matrices $\boldsymbol{\unicode{x1D6F4}}_{i,t}$ . Nonetheless, the model offers extremely rich dynamics, as all countries mutually affect each other even in the absence of explicit cross-correlation. Thus, even at low numbers of lags, complex relationships arise (Crespo Cuaresma et al., Reference Crespo Cuaresma, Feldkircher and Huber2016).

An important consideration for the estimation stage is that the weighted variables of the other countries are at least weakly exogenous - a property that can be evaluated. Including a large variety of countries is a natural remedy, as within the limit, each VARX becomes a small open-economy specification (Chudik and Pesaran, Reference Chudik and Pesaran2011; Georgiadis, Reference Georgiadis2017). This is also important if the weights are constructed to sum to one, as a lower number of countries could overestimate the relative importance of a country.

3.1 Parameter inference

We follow Boeck et al. (Reference Boeck, Feldkircher and Huber2022) using a Bayesian approach. Since each unit can be estimated independently, parameter inference follows the classical Bayesian VAR paradigm. Estimating each unit, given by either (3) or (4) boils down to introducing a prior on the parameters and drawing from the posterior using Markov-Chain Monte Carlo (MCMC) methods.

Beginning with the coefficient matrices, we stack the parameters for country i in a large vector $\boldsymbol{\theta }_{i}=vec({\boldsymbol{b}}_{{\boldsymbol{i}}}, {\boldsymbol{B}}_{i,1},\ldots , {\boldsymbol{B}}_{i,p},\boldsymbol{\Lambda }_{1,j},\ldots ,\boldsymbol{\Lambda }_{q,j})$ and impose the popular Minnesota prior that implies the following distributions before introducing the model to the data

(5) \begin{equation}\boldsymbol{\theta }_{i}\sim N\left(\theta _{Mn},V_{Mn}\right),\end{equation}

where $\theta _{Mn}$ are entries of ones corresponding to the first lag of each variable and zero otherwise and the elements of the prior variance $V_{Mn}$ have the following structure:

(6) \begin{equation}\underline{V}_{i,jj}=\begin{cases} \dfrac{\lambda _{1}}{l^{2}}, & \text{for coefficients on own lag}\, l\text{ for }l=1,\ldots ,p \\[7pt] \dfrac{\sigma _{j}\lambda _{1}^{2}\lambda _{2}^{2}}{l^{2}\sigma _{s}}, & \text{for coefficients on lag}\, l\, \text{of variable}\, j\neq i\text{ for }l=1,\ldots ,p \\[7pt] \dfrac{\sigma _{j}\lambda _{1}^{2}\lambda _{3}^{2}}{\left(l+1\right)^{2}\sigma _{s}} & \text{ for }\text{coefficients on exogenous variables on lag}\, l \\[7pt] \lambda _{4}, & \text{for deterministic parts of the model} \end{cases}\end{equation}

Here, $\lambda _{1},\lambda _{2},\lambda _{3},\lambda _{4}$ are the standard hyperparameter of the Minnesota prior and specify the shrinkage of the model which are also estimated from the data using hierarchical Gamma prior.

The classical Minnesota setup assumes that the variance-covariance matrix is known and samples only the $\boldsymbol{\theta }_{i}$ coefficients. Since we model the errors as a stochastic volatility process, we therefore use MCMC to iterate between the conditional distributions of drawing $\boldsymbol{\theta }_{i}$ and $\boldsymbol{\Sigma}_{i}$ . To complete the specification, we express $\boldsymbol{\unicode{x1D6F4}}_{i,t}={\boldsymbol{V}}_{i}{\boldsymbol{D}}_{i,t}{\boldsymbol{V}}_{i}^{'}$ with ${\boldsymbol{V}}_{i}$ being lower triangular matrix ${\boldsymbol{D}}_{i,t}$ is a diagonal matrix with a diagonal $\exp \{d_{i,1t},\ldots ,d_{i,nt}\}$ following a log AR(1) process.Footnote ⁷ The $d_{i,1t}$ are sampled using a Metropolis-Hastings algorithm. The elements of ${\boldsymbol{V}}_{i}$ are sampled as in Carriero et al. (Reference Carriero, Clark and Marcellino2019) using a normal prior equation by equation, a feature given by the triangular decomposition.Footnote ⁸

Once posterior inference on each individual unit is complete the large global system can be solved for via an algebraic transformation of the individual units. Consider for example eq. (4) with p = 1 and q = 1, collecting all variables with time period t on the left hand-side yields

(7) \begin{equation}{\boldsymbol{y}}_{i,t}-\boldsymbol{\Lambda }_{i,1}{\boldsymbol{y}}_{i,t}^{\boldsymbol{*}}={\boldsymbol{b}}_{i} +{\boldsymbol{B}}_{i,1}{\boldsymbol{y}}_{i,t-1}+\boldsymbol{\Lambda }_{i,1}{\boldsymbol{y}}_{i,t-1}^{\boldsymbol{*}}+ \boldsymbol{\varepsilon }_{i,t}.\end{equation}

Defining a global vector ${\boldsymbol{y}}_{{\boldsymbol{t}}}=({\boldsymbol{y}}_{\mathbf{1},{\boldsymbol{t}}}\boldsymbol{'},\ldots ,{\boldsymbol{y}}_{{\boldsymbol{N}},{\boldsymbol{t}}}\boldsymbol{'},{\boldsymbol{y}}_{{\boldsymbol{z}},{\boldsymbol{t}}}\boldsymbol{'})\boldsymbol{'}$ we can express the above equation from the perspective of unit i in the large system. Introducing a selection matrix that chooses the variables ${\boldsymbol{y}}_{i,t}$ and ${\boldsymbol{y}}_{i,t}^{*}$ associated with unit i from the global vector, ${\boldsymbol{S}}_{i}$ , and a an appropriately defined weighting matrix, ${\boldsymbol{W}}_{i}$ , for the foreign variables from eq. (2)

(8) \begin{equation}\underset{{\boldsymbol{A}}_{i}}{\underbrace{({\boldsymbol{S}}_{i}-\boldsymbol{\Lambda }_{i,0}{\boldsymbol{W}}_{i})}}{\boldsymbol{y}}_{t}={\boldsymbol{b}}_{i} +\underset{{\boldsymbol{F}}_{i}}{\underbrace{({\boldsymbol{S}}_{i}{\boldsymbol{B}}_{i,1}+\boldsymbol{\Lambda }_{i,1}{\boldsymbol{W}}_{i})}}{\boldsymbol{y}}_{t-1}+ \boldsymbol{\varepsilon }_{i,t}\end{equation}

Stacking equation (8) over all units then yields the full global system, which may be formulated either with the contemporaneous matrices determined by the weights and parameters $\boldsymbol{\Lambda }_{i,0}{\boldsymbol{W}}_{i}$ for each unit or as a reduced form global VAR, i.e.

(9) \begin{equation}{\boldsymbol{A}} {\boldsymbol{y}}_{t}={\boldsymbol{b}}+{\boldsymbol{F}} {\boldsymbol{y}}_{t-1}+\boldsymbol{\epsilon }_{t}, \boldsymbol{\epsilon }_{t}\sim N\left(\mathbf{0}, \boldsymbol{\unicode{x1D6F4}}_{\mathrm{t}}\right),\end{equation}

(10)

where ${\boldsymbol{A}}$ , ${\boldsymbol{F}}$ , and ${\boldsymbol{b}}$ are constructed from stacking their respective unit specific representations.

3.2 Structural inference

Established identification procedures prevalent in the VAR literature are, in principle, applicable to the global solution of the GVAR model. However, given that the GVAR framework incorporates an exogenous measure of cross-sectional unit connectivity and the exceedingly high dimensionality of the model, the identification of shocks in a GVAR is complicated. Traditional structural identification approaches of the global system according to some a-priori economic theory would therefore be an overstretch of the data. Therefore, the literature has mostly employed local identification schemes, i.e. a shock is identified only in one unit in a structural manner (through ordering assumptions or sign restrictions) while the responses of the other units are generalized. We are following this state-of-the-art approach.

The generalized impulse response functions (GIRF) are defined as the difference between the forecast for a variable k, ${\boldsymbol{y}}_{t}^{k}$ , with a shock δ _j to variable j and the forecast in the absence of the shock, given an information set $\Omega _{\mathrm{t}-1}$ , namely

(11)

The GIRF is calculated for every draw of the parameters and integrating across the posterior distribution yields the probability intervals for assessing the statistical validity of the results. The GFEVDs are calculated as in Lanne and Nyberg (Reference Lanne and Nyberg2016), where the h-step ahead forecast error of the j-th shock from the k-th variable is decomposed as

(12) \begin{equation} \gamma _{kj}\left(h\right)=\frac{\sum _{l=0}^{h}\,\mathrm{G}IRF_{kj}^{2}\left(l\right)}{\sum _{j=1}^{K}\sum _{l=0}^{h}\,\mathrm{G}IRF_{kj}^{2}\left(l\right)}, i,j=1,\ldots ,K. \end{equation}

It is worth noting that both the GIRFs and the GFEVDs are invariant to different orderings of the variables (Pesaran and Shin, Reference Pesaran and Shin1998) and Lanne and Nyberg, Reference Lanne and Nyberg2016).

4. Model specification and data

This section gives details on the countries and country clusters in the BGVAR model. We also describe the data in detail.

4.1. Country selection

We focus our analysis on the members of the European Economic Area (EEA) and the Group of Seven (G7) countries. In the BGVAR, the twenty-six countries are grouped, as shown in Table 1. The G7 countries comprise the United States, Canada, Japan, Germany, France, Italy, and the UK. These seven major industrialized countries are modeled individually in the BGVAR. Norway, given its status as a major oil exporter, is also modeled individually to reflect its unique economic position with respect to a Russian GPR shock. The remaining countries are grouped into different country clusters. The Baltic region (BAL) subgroup consists of Estonia, Latvia, and Lithuania. The Nordics subgroup (NRD) is made up of Finland, Denmark, and Sweden, while the Central and Eastern Europe (CEE) grouping comprises Bulgaria, the Czech Republic, Hungary, Poland, Romania, and Slovakia. Finally, the remaining EEA countries in our dataset, namely Austria, Belgium, Greece, Netherlands, Portugal, and Spain, form the EEA subgroup.Footnote ⁹ Overall, the formation of country groups allows for a parsimonious modeling while still estimating heterogeneous shock responses across countries.

Table 1. Individual countries and groups of countries in the BGVAR model

5. Model validation and estimation

Before turning to the estimation, we present the calculated trade shares in Figure 3. We see an elevated level of international integration among the countries and country clusters considered, which is important for the BGVAR framework that relies on the interconnected country assumption at the estimation stage. Although Canada, Japan, and the USA have high two-way trade flows, they are also major trading partners for the remaining countries. Unsurprisingly, Germany is an important trading partner for all countries, and Canada trades predominantly with the USA.

To set the number of lags for the endogenous and exogenous variables (p, q, r, s), we use the Bayesian information criteria, which support one lag for each variable. One of the advantages of the BGVAR modeling framework is that it offers rich dynamics even without the presence of many lags due to the interconnectedness of all countries (Crespo Cuaresma et al., Reference Crespo Cuaresma, Feldkircher and Huber2016).

Table 2. F-tests for weak exogeneity of the exogenous variables in the BGVAR

Note: A star (^*) denotes a rejection of the weak exogeneity assumption at the 5% significance level.

Figure 3. Calculated trade shares.

Furthermore, the BGVAR relies on the assumption that the linear combination of the foreign variables is weakly exogenous. We follow the testing approach used by Dées et al. (Reference Dées, di Mauro, Pesaran and Smith2007), which is an F-test of the joint significance of the error-correction terms in a regression for each foreign variable. Table 2 presents the results of the test, indicating compelling evidence for no rejection of the weak exogeneity assumption.

In the existing GVAR literature, estimation has typically employed a frequentist approach, as seen in foundational works such as Pesaran et al. (Reference Pesaran, Schuermann and Weiner2004) and other contributions like Dées et al. (Reference Dées, di Mauro, Pesaran and Smith2007) and Georgiadis (Reference Georgiadis2015). However, Bayesian methods have also been utilized, for example by Crespo Cuaresma et al. (Reference Crespo Cuaresma, Feldkircher and Huber2016) and Boeck et al. (Reference Boeck, Feldkircher and Huber2022). Both approaches generally aim to achieve the same objectives, but there are some important differences in their implementation.

Table 3. Test for serial autocorrelation of cross-unit residuals

Note: P-values and shares at various significance levels, shares above 0.1 are desired.

Table 4. Test for pairwise cross-unit correlation of unit-model residuals

Note: P-values and shares at various significance levels, shares below 0.1 are desired.

The frequentist approach uses variables in (log) levels as it is specified in a Vector Error Correction (VECM) form to capture both short and long-term relationships. In contrast, the Bayesian approach relies entirely on the likelihood function, which remains Gaussian even in the presence of non-stationarity (Sims et al., Reference Sims, Stock and Watson1990). As a result, Bayesian VARs are typically specified in log levels, with the error-correction component frequently omitted, as is common in GVAR applications (e.g., Crespo Cuaresma et al., Reference Crespo Cuaresma, Feldkircher and Huber2016).

More importantly for our application, the VECM approach relies on the properly identified cointegration rank of the system to specify the individual rank models, requiring careful consideration about the presence of cointegration. This can be particularly challenging during periods of large economic shocks, such as the global pandemic and the invasion of Ukraine. Both events have caused significant fluctuations and co-movement across many macroeconomic variables. For instance, the energy price shocks following the Russian invasion of Ukraine have exacerbated supply shortages and fueled inflationary pressures. The resulting high inflation has had immediate negative impacts on consumption and investment, while higher wage demands, driven by real wage losses, have raised the risk of self-reinforcing feedback loops (Battistini et al., Reference Battistini, Di Nino, Dossche and Kolndrekaj2022). This, together with the skyrocketing GPR scores, results in significant challenges even for modern cointegration tests that explicitly consider structural breaks and cross-sectional dependence (e.g. Westerlund and Edgerton, 2008; Banerjee and Carrion-i Silvestre, Reference Banerjee and Carrion-i Silvestre2015; Arsova and Örsal, Reference Arsova and Örsal2020). This is especially true when extending the estimation period until 2024Q1. Moreover, heteroskedastic errors are typically not considered in the frequentist setting.

In this paper we opt for a VAR system instead of a VECM and rely on stochastic volatility to capture the heteroskedasticity in the data, which we assess through the in-sample model fit.Footnote ¹² We estimate the Bayesian model using the Minnesota prior and stochastic volatility, conducting 50,000 draws and discarding the first 35,000. We test the convergence of the Gibbs chain using the Geweke statistic, which is a test whether the means of the first 120% of the accepted draws and the means of the lasts 50% are statistically different from one another. If they are not, this indicates that the model has converged. We find that from a total of 5624 variables only 687 z−values exceed the 1.96 threshold (12.22%) suggesting good convergence. We further test for serial autocorrelation and cross-unit correlation. The serial autocorrelation test in Table 3 suggests moderate correlation across residuals, which is standard when stochastic volatility is explicitly modeled as a random walk. Table 4 shows the pairwise cross-unit correlations, which are more important to be in check as correlation across the units weakens the structural analysis (Boeck et al., Reference Boeck, Feldkircher and Huber2022, Dées et al., Reference Dées, di Mauro, Pesaran and Smith2007). We find that the tests reject the notion of pairwise correlation (values below 0.1 are desired).

7. Robustness

Finally, several robustness tests are presented to complement the analysis. The supplementary tests aim to identify the specific contribution of the geopolitical shock triggered by the Russian invasion of Ukraine. To achieve a meaningful cross-comparison, the Russian GPR increase following the invasion of Ukraine is assumed to be a shock in all scenarios. In other words, possible differences in the GIRFs for different sample periods and/or BGVAR model specifications are not due to different shock sizes but rather to differing economic relationships.

As part of the multi-stage approach, the BGVAR model is first estimated up to 2019Q4, thus excluding both the COVID-19 pandemic shock and the knock-on impact of the Russian invasion of Ukraine in 2022Q1. By contrast, the illegal annexation of the Crimean Peninsula in 2014 is included in the sub-sample. Appendix A1 contrasts the generalized impulse responses and associated 95% confidence intervals up to 2019Q4 with those for the entire sample period up to 2024Q1. The head-to-head comparison reveals two findings for the pre-pandemic sample period of 2000Q1–2019Q4. First, no discernible GDP setback as a result of the hypothetical Russian GPR shock is recognizable. Second, no rise in inflation has been observed. In some countries, e.g., Germany and the US prices are even decreasing initially. These findings are reflective of the rather vaguely formulated sanctions imposed by the US, the EU, and other like-minded countries against Russia in the aftermath of the annexation of the Crimean Peninsula in 2014, including the exclusion of Russia from the G8, as well as restrictions on specific firms and individuals with close ties to the Russian government. The sanctions also included restrictions on the export and re-export of technology for the Russian defense sectors, while many other technology exports—especially those aimed at the Russian energy sector—were exempt from the trade restrictions. Russian crude oil and natural gas exports were also unaffected, partly because of the fear of Russia retaliating by cutting off natural gas supplies. Overall, the sanctions at the time were rather half-hearted and had hardly any impact.Footnote ¹⁶

In the second step of the robustness analysis, the generalized impulse responses for the baseline BGVAR model estimated over the pre-pandemic sample period 2000Q1– 2019Q4 and the pre-war sample period 2000Q1–2021Q4 were compared. The pre-war sample period 2000Q1–2021Q4 includes the COVID-19 pandemic but does not account for the impacts of the full-scale invasion of Ukraine in 2022Q1. The comparison of the GIRF to the hypothetical Russian GPR shock for both sample periods is graphically illustrated in Appendix A2. One main observation emerges. While the generalized impulse responses for the sample period from 2000Q1–2021Q4 show comparatively larger pandemic-induced downturns in GDP, these downturns are not statistically significant. Exceptions are France and the country group Rest of the Eurozone members. The responses of CPI do not indicate significant effects, either. All in all, the GPR spillovers underline that the estimation results for the entire sample period from 2000Q1–2023Q2 are not due to the effects of the COVID-19 pandemic.

The baseline BGVAR variables include economic expectation but no financial variables. In a final robustness analysis, we therefore augment the global variable set with the CBOE Volatility Index (VIX) and thus control for the VIX’s contribution to the international propagation of the Russian GPR shocks. The VIX is a forward-looking measure of expected future volatility in the stock market. It captures these expectations using prices of out-of-the-money put and call options on the S&P 500 index. Implied volatility is often seen as a way to gauge market sentiment and, particularly, the degree of uncertainty among market participants. The estimates of the baseline BGVAR model augmented with the VIX fear index over the sample period 2000Q1–2024Q4 are illustrated in Appendix A3. As in the previous robustness graphs, the GPR shock GIRFs of the baseline specification are also shown for a straightforward visual comparison. The central median GIRFs display minor changes throughout. Accordingly, the classification of the GPR shock as a supply shock is confirmed. Furthermore, the aforementioned cross-country GIRF size differences are again evident. One difference is that the volatility of the VIX variable leads to widened GIRF confidence bands. The overall conclusion, nonetheless, is that the baseline BGVAR model generalizes well to the added VIX propagation mechanism.