Annex to Chapter 1

Online annexes to Chapter 1 of the Euro Area Stability Watch present the data sources, analytical frameworks, and methodologies supporting the chapter’s risk assessment. They are organised in line with the chapter structure, covering the technical underpinnings of the boxes, the design of the adverse macroeconomic and fiscal scenarios, and key indicators, alongside additional analyses and robustness checks. 

A1 Data and methodological supplement to Box 1.1

This annex provides details on the methodology underlying the analysis presented in Box 1.1. A large language model extracts structured, market-relevant news indicators from daily expert commentary, which then feed into a factor-augmented event study regression to quantify how different types of news move financial variables.  

A1.1 Large language model-based extraction of news dummies

Text data source and news extraction pipeline

The text corpus for our analysis is a daily commentary available since September 2018 and produced by experts from the International Monetary Fund's Monetary and Capital Markets Department (the Global Markets Monitor). The large language model analyses each report in the sample and extracts a small set of news items, which were reported as relevant for equity and government bond price movements, respectively. Specifically, each day’s Global Markets Monitor report is parsed by the model with a prompt that instructs it to identify the distinct market-moving news and events discussed in the commentary and assign each item to one of 15 pre-defined, economically interpretable categories following Baker et al. (2025). In a second step, for our regression analysis, we further aggregate the original classifications of Baker et al. (2025) into five headline categories as follows (original categories in brackets):  

1. Global markets (commodities, foreign markets)  
2. Macroeconomy (macroeconomic news and outlook, corporate earnings and outlook, other non-policy)
3. Monetary policy
4. Fiscal and structural policy (government spending, taxes, exchange rate policy, capital controls, international trade policy, regulation, elections and political transitions, other policy)
5. Conflicts and security (sovereign military and security actions, terrorist attacks and large-scale violence by non-state actors) 

From news items to daily news dummies

For each category, the large language model analysis generates two daily `news dummies’ (one for risk-free yields and one for equities) that take the value of 1 if the commentary for day 𝑡 contains at least one event of the category that is associated with movements in bond or equity prices. The two resulting sparse matrices of category-by-day dummies then feed into the factor-augmented event study regression (denoted \[ d_1^{news} \] and \[ d_2^{news} \] in the equation below). 

A1.2 Factor-augmented event-study model with latent news factors

Data

We combine daily financial-market data with macroeconomic release surprises, monetary policy surprises, and the news measures outlined in Section A1.1. Euro area risk-free yields are proxied by the German yield curve: the first and fourth Euribor futures and 2-, 5-, 10-, and 30-year Bund futures (Gürkaynak et al., 2022). Other variables include the EUROSTOXX 50, the VSTOXX index, aggregate corporate spreads (AAA, BBB, high-yield), and the euro area TED spread (3-month EURIBOR minus 3-month Bund yield). Since euro area macroeconomic data surprises are conceptually largely unavailable due to earlier country-specific releases and known country weights, we use 13 important indicators for the German economy, where surprises are defined as the released value minus the median expectation of survey participants. The data were obtained from Bloomberg. Monetary policy surprises comprise the monetary policy and central bank information components for the European Central Bank and the Federal Reserve (Jarocinski and Karadi, 2020), with the latter being shifted by one day (t+1) to account for time zone differences.

Econometric model

The decompositions shown in Box 1.1 are based on the following specification. The model is motivated by Gürkaynak et al. (2020), extending their analysis in terms of both dependent and explanatory variables. Our specification decomposes (de-meaned) daily changes in the yields of (risk-free) government bonds at different maturities (\[ r_t \] with dimension \[ N_1 \] × 1) and the other market-based (risk) measures (𝜎_𝑡 with dimension \[ N_2 \] × 1) as follows:

\[ \begin{bmatrix} r_t \\ \sigma_t \end{bmatrix} = \begin{bmatrix} \beta^r \\ \beta^\sigma \end{bmatrix} s_t + \begin{bmatrix} \gamma^r \\ \gamma^\sigma \end{bmatrix} d_t^s f_{1,t} + \begin{bmatrix} \delta_1^r \\ \delta_1^\sigma \end{bmatrix} \left( d_{1,t}^{news} \odot f_{2,t} \right) + \begin{bmatrix} \mathbf{0} \\ \delta_2^\sigma \end{bmatrix} \left( d_{2,t}^{news} \odot f_{3,t} \right) + \varepsilon_t \\[1em] f_{1,t} \sim N(0,1), \quad f_{2,t} \sim N\left(\mathbf{0}, I_{K_2}\right), \quad f_{3,t} \sim N\left(\mathbf{0}, I_{K_2}\right), \quad \varepsilon_t \sim N(\mathbf{0}, \Sigma) \]

with t = 1, …, \[ T \], i = 1, …, \[ N \], \[ N = N_1 + N_2 \], and where \[ s_t \] is a (\[ K_1 \] × 1) vector of observed data release surprises, \[ d^s_t \] is a dummy vector for release days (one if any of the indicators in s was published on day t), and \[ d_{1,t}^{news} \],t and \[ d_{2,t}^{news} \] are (K2 × 1) dummy matrices for bond and equity market-relevant news, respectively. The unobserved data release factor \[ f_{1,t} \] and the (\[ K_2 \] × 1) unobserved news factors \[ f_{2,t} \] and \[ f_{3,t} \] are assumed normally distributed with unit variance to identify their scales. The flexible two-factor structure for the news components is motivated by recent analyses suggesting that aggregate financial conditions can be characterised by two distinct factors, one capturing dynamics in risk-free yields and the other capturing financial risk (Lombardi et al., 2025). \[ \beta^r \], \[ \beta^\sigma \], \[ \gamma^r \], \[ \gamma^\sigma \], \[ δ^r_1 \],\[ δ^σ_1 \], and \[ δ^σ_2 \] are coefficient matrices of corresponding dimensions. Lastly, \[ \varepsilon_t \] is the error term, with diagonal covariance matrix Σ. The model is estimated with a Bayesian approach (Gibbs sampling), using relatively uninformative prior distributions. The contribution of data surprises shown in the charts includes both observed and unobserved data release surprises, with the latter being captured through \[ f_{1} \]. Finally, the contributions of the news categories for the non-yield variables reflect the combined impact of \[ f_{2} \] and \[ f_{3} \]. 

A1.3 References

Baker, S. R., N. Bloom, S. J. Davis, and M. Sammon. What triggers stock market jumps?, mimeo, 2025.

Gürkaynak, R. S., B. Kisacikoglu, and J. H. Wright. Missing events in event studies: Identifying the effects of partially measured news surprises, American Economic Review, 110(12):3871–3912, 2020.

Gürkaynak, R. S., M. Kerssenfischer, B. Kisacikoglu, and J. H. Wright. News and noise shaping international yield curves, mimeo, 2022.

Jarocinski, M. and P. Karadi. Deconstructing monetary policy surprises: the role of information shocks, American Economic Journal: Macroeconomics, 12(2):1–43, 2020.

Lombardi, M. J., C. Manea, and A. Schrimpf. Financial conditions and the macroeconomy: a two-factor view, BIS Working Papers, 1272, Bank for International Settlements, 2025.

A2 Data and methodological supplement to Box 1.2

This annex provides details on the methodology underlying the analysis presented in Box 1.2. It outlines the data and empirical framework used to estimate the effects of geopolitical risk and financial uncertainty shocks on foreign investor inflows into euro area and United States (US) government debt securities from January 1999 to December 2024. 

A2.1 Shocks

We use the global geopolitical risk (GPR) index of Caldara and Iacoviello (2022) as our main measure of adverse geopolitical episodes. The index is constructed as the share of newspaper articles containing GPR-related keywords in major Anglo‑American newspapers, relative to the total number of published articles. It provides a high-frequency, text-based measure of global geopolitical tensions. 

In addition, we include the VIX index (a measure of US stock market volatility) to proxy for global financial market uncertainty. While related, GPR and financial uncertainty are conceptually different. The former reflects geopolitical events and tensions, whereas the latter captures broader market volatility and risk sentiment. Caldara and Iacoviello (2022) show that the GPR index displays substantial independent variation relative to both the VIX and the news-based Economic Policy Uncertainty index of Baker, Bloom, and Davis (2016). This allows us to study these two distinct sources of shocks separately. 

All shock variables are standardised to have zero mean and unit variance. Therefore, the estimated coefficients can be interpreted as the response to a one standard deviation shock. To allow for nonlinear effects, we further define high-risk periods as observations in which the shock exceeds its 90th percentile. 

A2.2 Monthly portfolio debt liability flows into government securities

Data on non‑euro area investors’ net purchases of euro area government securities are sourced from the European Central Bank (ECB) balance of payments statistics dataset and are available at monthly frequency from 2008. Data coverage includes both short‑ and long‑term instruments. To ensure comparability with the US analysis, euro area flows are extended back to 1999. For the 1999–2007 period, flows are constructed by aggregating non‑resident net purchases for euro area countries with available data, using ECB balance of payment statistics and national central bank sources. These imputed flows before 2008 include transactions by investors resident in other euro area countries. Results based solely on reported ECB balance of payment statistics from 2008 onward are qualitatively similar, and including intra‑euro area flows does not materially affect the findings over the common sample period 2008–2024. 

Monthly data on foreign investors’ net purchases of US government securities are sourced from the Treasury International Capital (TIC) system. As recommended by Bertaut and Judson (2025), reported TIC data are used from 2023 onward, while earlier flows are based on valuation-adjusted estimates from Bertaut and Tryon (2007) and Bertaut and Judson (2014, 2022), using information from the TIC Survey of Long-Term Securities. US government securities include both Treasury and agency securities. Long‑term instruments (above one year) are drawn from the valuation‑adjusted datasets, while short‑term instruments are directly sourced from TIC data. Compared with the euro area data, the US data provide greater granularity along both the counterpart-sector and counterpart-country dimensions. This enables distinguishing between foreign official investors (primarily foreign central banks) and foreign private investors, and, within the latter group, between investors resident inside and outside the euro area.  

Flow data are scaled by one-year-lagged annual gross domestic product (GDP). The analysis relies on monthly flow data without any further transformation. A local projection specification, discussed in detail below, is then used to estimate cumulative flow responses to shocks. Results are robust to using three-month moving averages, which yields smoother impulse responses. 

A2.3 Local projections framework

Our empirical strategy examines how foreign investors’ flows into government securities respond to GPR and financial-market uncertainty shocks using monthly local projections in the style of Jordá (2005). The analysis is conducted separately for the US and the euro area. For each forecast horizon h=0, 1, 2,…, 12, we estimate:

\[ \sum_{j=0}^{h} y_{t+j} = \alpha^{(h)} + \beta_1^{(h)} shock_t + \beta_2^{(h)}\left(shock_t \times \mathbb{1}(shock_t > q_{0.9})\right) + \beta_3^{(h)}\left(\mathbb{1}(shock_t > q_{0.9})\right) + \\ \sum_{s=1}^{p} \delta_s^{(h)}(y_{t-s}) + \sum_{s=1}^{k} \gamma_s^{(h)} Z_{t-s} + \varepsilon_{t+h} \]

The dependent variable y is monthly portfolio liability flows into government debt securities, expressed as a share of annual GDP in period t−12 (same scaling for each h). The variable shock corresponds to either GPR or financial-market volatility (measured by the VIX), both standardised. To capture nonlinear effects, we interact the shock with an indicator for high-risk periods, defined as observations above the 90th percentile of the shock distribution.

The vector Z includes a set of lagged control variables (including lags of the shock) capturing global financial conditions and macro-financial characteristics, considered as push and pull factors of capital flows, respectively. The specification differs slightly between the euro area and the US to reflect relevant market structures. For euro area (US) specifications, the baseline controls include VIX, the STOXX 600 index (S&P 500 index), Brent oil prices (WTI oil prices), the US NFCI, and 3-month EURIBOR (3-month US government yields). All controls, except the VIX, are expressed in first differences to address non-stationarity. While all control variables are included with two lags, the dependent variable is included with up to 12 lags to account for persistence in capital flows; results are robust to alternative lag lengths of two and six.

The impulse response functions are constructed from the sequence of estimated coefficients \[ \left\{\beta_1^{(h)}\right\}_{h=0}^{H} \]​, which tracks the dynamic cumulative response of capital flows to shocks during normal periods. Specifically, the additional effect during high-risk episodes is captured by the sequence \[ \left\{\beta_2^{(h)}\right\}_{h=0}^{H} \], which measures how the cumulative response of capital flows differs when shocks occur in periods of heightened geopolitical or financial stress.

A2.4 Supplementary results 

We also employ a euro area-specific geopolitical risk measure (hereafter GPREA8) designed to capture episodes in which geopolitical tensions are directly centred on the euro area. Caldara and Iacoviello (2022) provide country-specific GPR indices based on articles combining geopolitical-risk keywords with country identifiers; we construct GPREA8 as the simple average of eight euro area country indices. It complements the global GPR index by isolating regionally relevant geopolitical shocks that may have different implications for capital flows given differences in geographical proximity and exposure to geopolitical events. As illustrated in Figure A2.1, GPR and GPREA8 do not always peak in the same periods; and even when their peaks coincide, they often differ in intensity, reflecting differences in the underlying events they capture. 

Interestingly, when extreme geopolitical tensions are closely linked to the euro area, foreign demand for US sovereigns reasserts itself. Using GPREA8, results show that periods of elevated geopolitical tensions centred on the euro area (such as the Russian invasion of Ukraine), prompt short-lived inflows into US Treasuries from foreign investors, including those of the euro area, peaking after a quarter (Figure A2.2). At the same time, foreign demand for euro area sovereign debt remains resilient, with no evidence of reversal and, if anything, a mildly positive response in the aftermath of such shocks. This reinforces our main finding that euro area sovereign debt remains resilient even during episodes of high geopolitical stress concentrated within the region.  

A2.5 References 

Caldara, D. and M. Iacoviello (2022). Measuring geopolitical risk. American Economic Review, 112(4), 1194–1225. 

Baker, S. R., N. Bloom, and S.J. Davis (2016). Measuring economic policy uncertainty. Quarterly Journal of Economics, 131(4), 1593–1636.

Bertaut, C. C. and R. W. Tryon (2007). Monthly estimates of U.S. cross-border securities positions. Federal Reserve Board International Finance Discussion Papers, No. 2007-910. 

Bertaut, C. C. and R. Judson (2014). Estimating U.S. cross-border securities positions: new data and new methods. Federal Reserve Board International Finance Discussion Papers, No. 2014-1113. 

Bertaut, C. C., and R. Judson (2022). Estimating U.S. cross-border securities flows: ten years of the TIC SLT. Federal Reserve Board FEDS Notes.

Bertaut, C. C., and R. Judson (2025). Measuring U.S. cross-border securities flows: out with the old, in with the new. Federal Reserve Board FEDS Notes.

Jordà, Ò. (2005). Estimation and inference of impulse responses by local projections. American Economic Review, 95(1), 161–182. 

A3 Data and methodological supplement to Box 1.3

This annex provides details on the data and empirical approach used to estimate the effects of the ‘new geopolitical regime’ (since the outbreak of the Russia-Ukraine war) on banks’ lending dynamics, conditional on the level of banks’ sovereign exposures.  

A3.1 Data 

The dataset is an unbalanced panel of 82 banks from 18 euro area countries that spans between Q4 2019 and Q4 2025 at quarterly frequency. Data come from the Transparency Exercise of the European Banking Authority and are merged with macro-financial variables.  

A3.2 Methodology

To estimate the effect of the ‘new regime’ on bank lending – conditional on banks’ sovereign exposures – we employ the local projections method (Jordá, 2005) and estimate the following regression: 

\[ \ln(\text{Loans}_{b,t+h}) - \ln(\text{Loans}_{b,t-1}) = \alpha + \beta_{1,h}\,\text{new regime} + \beta_{2,h}\,\text{sovereign exposures}/TA_{b,t-1} \\ + \beta_{3,h}\,\text{new regime} \times \text{sovereign exposures}/TA_{b,t-1} + \beta_{4,h}\,\text{Controls}_{b,t-1} + \delta_{b,h} + \varepsilon_{b,t+h} \]

Here, $\mathrm{Ln}\left({\mathrm{Loans}}_{b,t+h}\right)-\mathrm{Ln}\left({\mathrm{Loans}}_{b,t-1}\right)$ is the log difference of loans of bank $b$ between quarter $t-1$ and $t+h$, with $h=0,1,\dots 8$. Specifically, we consider loans to energy-intensive sectors (mining, manufacturing, transport, and water supply) and loans to non-energy-intensive sectors as identified by the European Systemic Risk Board (2026).

represents a dummy that assumes the value of 1 from Q2 2022 onwards, corresponding to the quarter after the start of the Russia-Ukraine war, and 0 otherwise. $\text{Sovereign exposures}/{\mathrm{TA}}_{b,t-1}$ captures the share of each bank's sovereign exposures (loans and bonds) over total assets. The key term of interest is ${\beta }_{3,h}$ (i.e. the interaction $\text{new regime}\times \text{sovereign exposures}/{\mathrm{TA}}_{b,t-1}$), which measures the differential effect of sovereign exposures on bank lending between the ‘old regime’ and the ‘new regime’.

${\mathrm{Controls}}_{b,t-1}$is a vector of lagged financial sector and macroeconomic controls. It includes a Covid-19 dummy (dummy=1 for 2020), CET1 ratio (capital position of bank), stage 2 ratio (loans classified as stage 2 over total loans), return on assets, cash ratio (cash over assets), non-bank financial institution asset growth (quarter-on-quarter growth in assets of the non-bank financial institution sector), quarter-on-quarter gross domestic product growth, quarter-on-quarter changes in Euribor, government debt growth (quarter-on-quarter growth rate of government debt) and European Central Bank asset growth (quarter-on-quarter growth of bank's balance sheet). ${\delta }_{b,h}$ is bank fixed effects and ${\epsilon }_{b,t+h}$ the error term. Standard errors are clustered at the bank level.

A3.3 References

European Systemic Risk Board (2026), Financial stability risks from geoeconomic fragmentation, January 2026.  

Jordà, Ò. (2005), Estimation and Inference of Impulse Responses by Local Projections, American Economic Review, 95(1), 161–182. 

A4 Data and methodological supplement to Box 1.4

This annex provides details on the data and implementation of the granular instrumental variables (GIV) estimation used to determine the impact of aggregate investor demand shocks on sovereign yield spreads presented in Box 1.4.

A4.1 Granular instrumental variables

While derivations and discussions are provided in Gabaix and Koijen (2021, 2022, 2024), the GIV approach requires modelling choices specific to the application at hand. Refinements to the GIV method create a range of possibilities for construction of the instruments. Specific choices for the results presented in Box 1.4 are outlined below.

Isolating the causal relationship between bond flows and yield movements is challenging due to the endogeneity of bond supply and demand. Within a demand system-based asset pricing framework, the GIV approach addresses this issue by constructing an exogenous instrument Z_t from a weighted sum of idiosyncratic shocks u_it to different investor groups. Because these shocks u_i,t are exogenous investor-specific flows, they are orthogonal to common macroeconomic factors and aggregate market movements, while remaining correlated with the yields. Thus, considering N different investor groups with time-varying market shares S_i,t, the GIV instrument is defined as: 

\[ z_t = \sum_{i=1}^{N} S_{i,t-1}\, u_{i,t} \]

Given the instrument z_t, the price impact captured via the change in the spreads Δs_t (vis-à-vis German Bunds) can then consistently be estimated using the regression:

\[ \Delta s_t = c + M z_t + \lambda'\eta_t + \varepsilon_t \]

where M denotes the impact on the spreads, z_t is the GIV instrument, and η_t denotes a vector of observed and latent common factors \[ \eta_t = (\eta_t^o,\ \eta_t^l) \], such as macroeconomic conditions or global uncertainty. However, as investor-specific shocks u_i,t and latent controls \[ \eta_t^l \] are unobserved, they need to be estimated from data to construct the instrument.

To take heterogeneity across different investor groups into account, we use precision weights: 

\[ E_i = \frac{\bar{\sigma}_{u_i}^{-2}}{\sum_{i=1,\ldots,N} \bar{\sigma}_{u_i}^{-2}} \]

where σ̄_ui = max(σ_ui, median(σ_ui)) and σ_ui is the standard deviation of u_it computed along the time dimension1. The algorithm cycles through three steps2: 

1. Estimate weighted panel regression including observed controls and fixed effects using E_i as regression weights to obtain first stage residuals Δq̌_i,t:
   \[ \Delta q_{i,t} = \alpha_i + \gamma'\eta_t^o + \Delta\check{q}_{i,t} \]

2. Perform principal component analysis on precision-weighted residuals \[ E_i^{\frac{1}{2}} \Delta \check{q}_{i,t} \] to recover latent factors \[ \eta_t^l \] given by the principal components.

3. Run ordinary least squares regression of common factors \[ \eta_t^l \] on first stage residuals Δq̌_i,t: to estimate investor-specific shocks ǔ_i,t  and update precision weights σ̄_ui, and iterate again, where:

\[ \Delta\check{q}_{i,t} = \beta'\eta_t^l + \check{u}_{i,t} \]

Once we have obtained estimates \[ ǔ_{ji,t} \] for each country, we construct the GIV instrument as:

\[ z_{j,t} = \sum_{i=1}^{N} S_{ji,t-1}\, \hat{u}_{ji,t} \]

and collect the recovered latent factors \[ η_t^l \] as controls in the main regression. Once the instruments are obtained for each country in a group, the impact effect is estimated running the group-specific panel regression

\[ \Delta s_t = c + M z_{j,t} + \lambda'\eta_t + \varepsilon_t \]

using the observed and recovered unobserved factors for each country group as controls.
Similarly, we estimate the panel local projections for each country group as follows:

\[ s_{t+h} - s_{t-1} = c_h + M_h z_{j,t} + \lambda_h'\eta_t + \varepsilon_{t+h} \]

We specify three iterations as no significant changes of the precision weights are apparent, suggesting convergence of the algorithm. The regression includes the same set of observed factors to \[ \eta_t^0 \] as Chaudhary et al. (2025) and one additional latent factor \[ \eta_t^l \]obtained from the principal component analysis in step 2.

A4.2  Data

Price sensitivities are measured using 10‑year sovereign yields, obtained from Bloomberg, consistent with an average residual maturity of around 7.5 years over the sample period. 

The estimation is based on quarterly data on investor shares and flows. The sample spans Q4 2014–Q4 2025 and compiles estimates of investor holdings at market value, together with quarterly transactions in debt securities issued by the general government. The data are compiled from several sources, including the European Central Bank (ECB)’s quarterly sector accounts (QSA), securities holdings statistics (SHS), and securities holdings statistics by sector (SHSS), data on the Eurosystem’s asset purchase programmes, the International Monetary Fund’s International Financial Statistics and Eurostat’s balance of payments statistics. 

Data compilation inevitably relies on assumptions. Notably, non-euro area holdings are computed as a residual, while investor flows (net purchases) prior to 2021 – when ECB SHSS data become available – are inferred from valuation-adjusted changes in holdings. Hence, any measurement limitations affecting euro area investor coverage and valuation adjustments are reflected in the residual non-euro area category.

Specifically, the primary data source is the ECB’s QSA which reports, for each country, government debt securities holdings and net transactions for all investors, including a breakdown of domestic investors by sector and a single aggregate category for non-resident investors. For several countries, data on domestic central bank holdings are missing for some periods; coverage is therefore extended using the International Monetary Fund’s International Financial Statistics series on gross claims of monetary authorities on general government at market value. 

A second key source is the ECB’s SHSS, which provides, for each country, a sectoral breakdown of holdings and transactions for euro area investors. SHSS data are available from Q1 2021. Coverage is extended back to 2014 using the discontinued SHS dataset, which reports holdings at market value but not flows. Flows are therefore approximated using changes in holdings, adjusted for valuation effects. Investor-specific valuation changes are computed using QSA data for domestic investors, assuming that valuation effects are comparable across domestic and other euro area investors. As the SHS dataset does not provide a series for Eurosystem holdings, the SHSS coverage is extended using constructed series on stocks and flows implied by asset purchase programmes (securities markets programme, public sector purchase programme, and pandemic emergency purchase programme).

Overall, total holdings are taken from QSA data, with domestic and sectoral breakdowns based on QSA, euro area investor breakdowns based on SHSS, and non‑euro area holdings calculated as a residual. 

For the analysis, euro area countries are classified into two groups based on their latest share of non‑euro area investors, distinguishing five countries with relatively high non‑euro area investor shares and four countries with a more euro area‑dominated investor base (Figure A4.1, panel a). Over the sample period, non‑euro area investor shares average around 31% in the first group and 14% in the second. As regards euro area investors, insurance corporations and pension funds are also more prominent in the first group, whereas the Eurosystem, banks and households account for larger shares in the second group (Figure A4.1, panel b).

• 1

  The floor on the median precision weight prevents investor groups with very stable flows from playing too extreme a role in the weighted regression.

• 2

  For notational simplicity we drop the country-specific index j of relevant variables in the exposition of the GIV iterations.

A4.3  References

Gabaix, X. and R. Koijen (2024). Granular Instrumental Variables. Journal of Political Economy. 123(7), 2274-2303.

Gabaix, X. and R. Koijen (2021). In Search of the Origins of Financial Fluctuations:
The Inelastic Markets Hypothesis. NBER Working Paper, No. w28967.

Chaudhary, M., J. Z. Fu, and H. Zhou (2024). Anatomy of the Treasury Market: Who Moves Yields?. Olin Business School Center for Finance & Accounting Research Paper, No. 2024/14.

A5  Data and methodological supplement to Box 1.5

Results of the ESM Sovereign Sentiment Survey are based on a survey of 31 financial market participants active in euro area sovereign bond markets, conducted between 27 March and 17 April 2026. The sample includes issuers (debt management offices and treasuries), intermediaries, and investors. Sample euro area growth (1.0% median, 1.1% average) and euro area inflation (2.9% average, 3.0% median) expectations over the next 12 months are in line with market consensus; recession probability for the euro area (30% average, 33% median) is above consensus. In addition to the survey, structured interviews were conducted with 18 market participants in April 2026. The survey will be repeated twice a year from now on (Q2 and Q4). 

A6  Methodological notes on the macroeconomic adverse scenario

A6.1  Overview of the modelling framework

This annex describes the framework used to design and quantify the adverse macroeconomic scenario underpinning the risk assessment in Chapter 1. It documents the modelling toolkit, identification strategies, and calibration assumptions used to translate the underlying risk narrative into a consistent set of macroeconomic projections. 

The scenario is constructed relative to a baseline consistent with the European Commission’s spring 2026 economic forecast, which sets the starting point for all variables. A no-policy-change assumption is imposed, whereby neither monetary nor discretionary fiscal policy respond to the materialisation of adverse shocks beyond what is already embedded in the baseline or implied by automatic stabilisers. As a result, the scenario isolates the macroeconomic effects of the identified risk factors. 

The modelling strategy follows a top-down, multi-layered approach. The adverse scenario is developed first at the euro area level and subsequently translated into country-specific projections, ensuring consistency between aggregate and national outcomes. The scenario reflects the joint materialisation of the three risk layers discussed in Chapter 1: persistently high geopolitical tensions and energy prices, a repricing of financial assets of the United States (US), and second-round effects on inflation. Given the multi-dimensional nature of the risks considered, the framework relies on a set of complementary models. Each model captures a specific risk layer or transmission channel, rather than a one-size-fits-all model. Their outputs are combined to derive a single internally consistent macroeconomic path. 

The framework proceeds in three main steps (Figure A6.1):  

1. First, the short-term euro area impact (2026–2027) is quantified. This step translates the identified risk layers of the adverse scenario (rise in geopolitical risks and energy prices, repricing of US assets, and second-round effects on inflation) into macroeconomic outcomes. To calibrate the different shocks and capture the relevant transmission channels, the analysis draws on a combination of empirical and structural models, including factor-augmented vector autoregressions (FAVAR), Bayesian vector autoregressions (BVAR), and dynamic stochastic general equilibrium (DSGE) models. The resulting effects on growth and inflation reflect the joint contribution of the impacts of each of three risk layers. 
2. Second, the scenario is extended to the medium to long term (2028–2035). Persistent geopolitical tensions and higher energy prices are assumed to weigh on productivity and external competitiveness, generating scarring effects on output. These channels are quantified using empirical (BVAR) and semi-structural models to derive a medium- to long-term trajectory for gross domestic product (GDP) consistent with the adverse environment described above. Other shocks, particularly those related to US asset repricing, are assumed to have temporary effects and therefore do not materially affect long-term dynamics. 
3. Third, the euro area adverse scenario is translated into country-specific projections. This is done using a set of two-region open-economy semi-structural New Keynesian (NK) models, which link each member state to the rest of the euro area. This approach allows for heterogeneity in exposure and transmission while maintaining consistency with the aggregate scenario and the underlying risk narrative. 

Throughout the framework, real GDP and inflation are the primary variables of interest. They summarise the macroeconomic impact of the adverse scenario and provide the basis for the assessment of fiscal and financial implications in Chapter 1. 

The remainder of the annex follows this structure. Section A6.2 presents the short-term euro area scenario. Section A6.3 describes its extension to the medium and long term. Section A6.4 explains the derivation of country-level projections. A summary table of the key conditioning assumptions used in the calibration is provided at the end of the annex (Table A6.1).  

A6.2 Euro area short-term impact (2026–2027) 

This section describes the modelling approach to the short-term adverse scenario for the euro area. The scenario is constructed by aggregating the estimated impacts of the three risk layers, each modelled using a tailored approach (Figure A6.2). 

Geopolitical tensions and energy prices: non-linear Bayesian FAVAR model

To assess the macroeconomic and financial impact of geopolitical risks and energy shocks on the euro area economy, we employ a non-linear Bayesian FAVAR. The model is described in Capolongo et al. (2026), in the spirit of Brignone et al. (2025). It summarises a large cross-section of macroeconomic and financial variables through 11 latent factors extracted via principal components from a panel covering 10 euro area economies and six other major advanced economies.3 The panel comprises country-level national accounts, prices, trade, financial indicators, and sovereign spreads as well as global indices, including wholesale commodity prices.4 The model is estimated at monthly frequency from January 2000 to June 2026. Results are eventually converted into quarterly frequency.

In a first step, we identify structural shocks using a Cholesky decomposition of the FAVAR. The identified structural shocks are used to calibrate the paths for four variables: wholesale oil and gas prices, an ESM proprietary energy geopolitical risk index, and a euro area geopolitical risk index (following the approach of Caldara and Iacoviello, 2022). The identification strategy imposes the restriction that contemporaneous innovations to observed variables (geopolitical risk indices and energy prices) are not driven by shocks to the remaining macro-financial panel within the same period.  

In a second step, the identified structural shocks enter as exogenous regressors in a non-linear FAVAR with exogenous variables (FAVARX). Each variable is included both in linear and in squared terms. This specification follows the non-linear FAVAR with exogenous variables (FAVARX) framework, extending the methodology of Forni and Gambetti (2024) and Brignone et al. (2025). The linear component captures the standard propagation of each shock, while the squared term captures magnitude-dependent amplification: larger geopolitical or commodity price shocks have a disproportionately stronger impact on the economy than that implied by a linear extrapolation from small shocks. Both stages are estimated with 20,000 posterior draws under a Minnesota prior. 

Based on this framework, we run a conditional forecast under a specific geopolitical scenario: a large initial spike during a single month of the forecast horizon (three standard deviations for the oil shock and four standard deviations for each of the two geopolitical risk shocks), followed by moderate persistence at 0.1 standard deviations for five months, after which no further shocks are imposed. This shock profile captures a sudden, severe geopolitical event with a short-lived tail of elevated risk. The framework compares the resulting conditional forecast with the baseline. It attributes forecast movements to individual shocks by passing each shock through the median vector moving-average impulse-response kernels, thereby combining standard linear propagation with non-linear amplification. 

US asset repricing: BVAR and DSGE models

Spillovers from a sharp repricing of US assets to the euro area are quantified using a combination of models. In the scenario, the repricing is triggered by a sharp rise in US policy uncertainty. Satellite BVARs are used to calibrate the shock, assess its financial and macroeconomic effects in the US, and trace its implications for euro area financial conditions. In a second step, these results are mapped into euro area macroeconomic outcomes using a DSGE framework. 

We assess the macro-financial impact of a rise in policy uncertainty and repricing of US assets with a BVAR model tailored towards US macroeconomic and financial variables. The model comprises the ESM proprietary economic policy uncertainty (EPU) index for the US, the VIX (an option-implied measure of US stock market volatility), the S&P500, the 10-year overnight index swap (OIS) yield, the federal funds rate, the excess bond premium,5 employment, inflation, GDP, consumption, investment, the EUR/USD exchange rate, the Euro Stoxx 600, and the10-year German government bond yield. It is estimated at quarterly frequency starting in Q1 1996 and ending in Q4 2025. The macroeconomic variables are considered in real terms. Based on this model, we run a conditional forecast, conditioning on a path for the EPU, the VIX, the OIS spread, and the excess bond premium to extract the relevant shocks aligned with our narrative. 

We use a separate BVAR to explore implications for euro area borrowing conditions. The variables in the model comprise the US EPU index, the VIX, the excess bond premium for the US, the S&P500, the Euro Stoxx 600, the BBB spread for the euro area, the 10-year German government bond yield, the Euribor, the spread between the lending rate  (non-financial corporations) and the Euribor, and the increase in bank loans to non-financial corporations (deflated). The model is estimated over a slightly shorter period due to data availability constraints for euro area loan data (from Q1 2001 to Q2 2025). A conditional forecast is conducted by conditioning on the paths of US variables derived from the US-focused BVAR.  

The final impact on the euro area economy of both financial and trade channels is obtained by combining the results of two separate simulation exercises: 

• To assess the macroeconomic implications of financial amplification in the euro area, the resulting paths are fed into a macro-financial euro area DSGE model. Specifically, the paths for credit spreads, the loan spread, credit growth, and interest rates from the euro area markets' BVAR are included in a DSGE model like the one described in Kühl (2018). The model is estimated for the euro area (closed economy) and has an emphasis on financial amplification via an elaborate financial sector.  
• In addition, to capture the trade channel of transmission to the euro area, we use a three-region DSGE model for an open economy following Cardani et al. (2023). The model features the euro area, the US, and the rest of the world. The model emphasises trade linkages. We run a conditional forecast, conditioning on the US macroeconomic variables that result from the first step BVAR approach. We simulate the impact on the euro area economy while keeping euro area interest rates unchanged. 

Second-round effects on inflation: DSGE approach

The second-round effects on inflation from the rise in energy prices are assessed by using the macro-financial DSGE model for the euro area. A conditional forecast is conducted targeting real wage growth reflecting recent experience. Specifically, it is assumed that workers can negotiate higher wages (around one percentage point higher wage growth than otherwise), which is implemented in the model with a wage mark-up shock. Real wages in the adverse scenario are therefore higher than when abstracting from second-round effects.  

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  Germany, France, Spain, Italy, Belgium, Finland, Greece, Ireland, the Netherlands, Portugal, the United Kingdom, the US, Canada, Australia, Japan, and Switzerland.

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  National accounts' variables (GDP and its components, savings, and income) enter as three-period percentage changes (quarter-on-quarter growth rates) with interpolation. Price indices (consumer price index and producer price index), trade, equity indices, and exchange rates enter as month-on-month log differences. Interest rates and sovereign spreads enter in first differences. Oil and gas prices and purchasing managers' indices enter in log levels. Harmonised index of consumer prices measures enters as year-on-year percentage changes. All panel variables are standardised to zero mean and unit variance prior to factor extraction.

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  The excess bond premium is defined as the component of corporate bond spreads not directly attributable to the expected default risks, as argued in Gilchrist and Zakrajsek (2012). It is a measure of investor sentiment or risk appetite in the corporate bond market.

A6.3 Euro area medium- to long-term impact (2028–2035)

This section explains how the short-term adverse scenario is translated into medium- to long-run macroeconomic paths for the euro area. The approach combines evidence on the persistent effects of geopolitical and energy price shocks on productivity and external competitiveness (Section A6.2) with a semi-structural framework. This framework allows us to map these long-run forces into a coherent path for a broader set of macroeconomic variables. 

GDP scarring via impaired innovation and export-sector productivity: BVAR

The long-term impact of persistently high geopolitical tensions is identified using a BVAR model and a combination of sign and zero restrictions (Furlanetto et al., 2025; Bratsiotis and Theodoridis, 2022). The model comprises oil and gas prices, geopolitical risk, and the following variables for the euro area: real GDP, inflation, real investment, the relative price of investment, unemployment, the 10-year government bond yield, real wages, investment in research and development as a share of GDP, and total factor productivity. All series are expressed in log levels, except for research and development. The model is estimated using quarterly data from Q1 1999 to Q4 2025, two lags are specified, and a Minnesota-type prior is used to facilitate estimation. To identify the shock of persistently elevated geopolitical tensions, we assume it has zero contemporaneous impact on oil and gas prices, suppresses investment in physical capital and research and development in the short run, and has a permanent impact on total factor productivity and relative price of investment.  

The identified shock captures the narrative that persistent uncertainty discourages corporates from investing in innovation. This harms productivity not only in high-productivity sectors but across the economy. Neither the sign nor the magnitude of the shock's effect on GDP are restricted, letting the data determine the shock's statistical and economic significance for economic activity. Once the shock is identified, its effect on GDP is calculated by conditioning on short- and long-term oil and gas prices and the geopolitical risk profiles presented in Table A6.1 at the end of the document, and the GDP path of the short-term adverse scenario between Q3 2026 and Q4 2027 discussed in the previous section (Section A6.2) 

The second shock, a deterioration of export-sector productivity, is proxied by a persistent increase in the ratio of export prices to the GDP deflator. In the spirit of Schmitt-Grohe and Uribe (2025) and Gortz et al. (2022), we employ state-space estimation techniques to identify the long-run effect of a permanent increase in the ratio of export prices to the GDP deflator (RPX) on GDP. Given that the RPX for the euro area displays a pronounced downwards sloping trend, we assume that euro area potential supply is driven by two stochastic trends: the (standard) economy-wide trend and an export-specific technological trend. The second technological trend operates within the export sector, expanding at a faster pace than the rest of the economy, consistent with the downward trend in RPX. 

We use a two-sector open-economy DSGE model to identify the shares of the two trends in the economy. The approach followed is like Gortz et al. (2022). The model comprises real GDP growth, real export growth, and RPX growth. It is estimated using quarterly data from Q1 1970 to Q4 2025. Two lags are included to capture cyclical dynamics, and prior information is incorporated in the form of a Minnesota-type prior.6 Finally, the shock is calibrated by gradually unwinding the reduction in the RPX the European Commission foresees over the forecast horizon (European Commission spring 2026 economic forecast).

Taken together, these two channels – innovation and export-sector productivity – drive the medium- to long-term impact on GDP. 

Broader macroeconomic long-term effects: semi-structural model

The medium- to long-run profiles of all variables other than GDP are derived using an open-economy semi-structural NK economic model. Similar to Angelini et al. (2019), a semi-structural macroeconomic NK open-economy model is developed to reconcile the short- and long-term baseline forecasts produced by the European Commission. This also helps assess how alternative assumptions impact the evolution of key series of interest. The model features nominal, real, and financial frictions. The model is estimated with Bayesian maximum likelihood techniques on data from Q1 1995 to Q4 2025.  

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  To improve the estimation precision of the long-term dynamics we use the Area Wide Model database from the Euro Area Business Cycle Network.

The semi-structural model generates internally consistent paths for the remaining economic variables conditional on the short-term scenario and long-run restrictions. Given the conditioning assumptions reported in Table A6.1, the short-term (T+1 and T+2) profiles of the economic variables explained in Section A.6.2 and the estimated T+3 to T+10 GDP paths, the model derives conditional forecasts for all other economic variables over theT+3 to T+10 horizon. This ensures that the resulting T+10 scenario extends captures the broader macroeconomic environment in a way that is coherent with the overall adverse narrative. 

A6.4 Euro area countries (2026–2035)

With the euro area medium- to long-run impact of the adverse scenario quantified, the next step is to translate it into country-specific paths. This requires a framework that preserves consistency with the aggregate euro area outlook while allowing for heterogeneity in trade and country-specific exposures, fiscal space, and domestic propagation mechanisms. 

The medium- to long-run profiles of country-specific economic variables are produced using a two-region open-economy semi-structural NK economic model. The model mentioned in the Section A6.3 is further extended into a two-region model comprising the country of interest and the rest of the euro area for each of the euro area member states. From the country's perspective, trade and financial transactions occur with both the rest of the euro area and the rest of the world. 

The two-region structure allows each country’s outlook to be conditioned on the euro area adverse scenario while preserving country-specific transmission mechanisms. In this way, the country scenarios remain consistent with the aggregate euro area narrative but are not constrained to react identically across jurisdictions. 

Country-specific adverse scenarios for T+1 to T+10 profiles are produced in two steps. In the first step, country-specific forecasts are derived conditional on the T+1 to T+10 euro area profiles discussed in Section A6.3. In a second step, the resulting country profiles are reviewed to determine whether country-specific forecasts align with the narrative adopted. For example, persistently higher oil and gas prices should have more severe effects in countries that rely more heavily on fossil fuels and have more limited fiscal space. If this is not the case, then further iterations are undertaken to align the resulting profiles with the judgement of country experts and the euro area risk narrative. This iterative procedure is intended to ensure that the final country paths are aligned with both country-specific expertise and the broader scenario narrative. The result is therefore a set of country projections that is both model-consistent and tailored to the structural characteristics and vulnerabilities of each jurisdiction. 

Strengths and limitations of the framework  

The main strength of the framework is that it combines empirical grounding with structural discipline. Empirical models use data-rich information sets to identify shocks and measure spillovers, while structural models map these shocks into internally consistent macroeconomic outcomes. This design is well suited to adverse scenarios in which non-linear amplification, trade spillovers, and financial frictions all matter. The multi-layered approach also allows the contribution of individual risk layers to be traced and communicated clearly. 

At the same time, the framework also carries limitations. Combining outputs across models with different samples and identifying assumptions introduces aggregation uncertainty. To address this, cross-model consistency and coherence with the scenario narrative are used as organising principles throughout the exercise. Long-run projections are additionally sensitive to assumptions about the persistence of scarring effects. All these considerations suggest the results are best interpreted as one plausible adverse path, to be read alongside the qualitative risk narrative in Chapter 1.