## ch2annex

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### Global economic policy uncertainty: coverage and context
- Time coverage:
  - Global series: 2010:M1-2024:M6
  - Europe, United Kingdom, and the US series: 2010:M1-2024:M7
- Contextual findings:
  - Global debt has increased over the past two decades, particularly during the COVID-19 pandemic; government debt-to-GDP ratios have increased steadily.
- Related referenced figures (titles preserved):
  - Total Debt Breakdown, 2005-23 (Percent of GDP)
  - Public Debt, 2005–23 (Percent of GDP; trillions of US DOLLAR)

### Market volatility spillovers and bond/stock correlations
- Observed patterns:
  - Correlation between bond and stock market volatility has generally increased over time.
  - Correlation panels reported for periods: 2000-19, 2020-21, 2022-24 (by region: Eurozone, Australia, Japan, EM).
- Documented cross-border stress episodes (cumulative changes in 10-year government bond yields, percentage points):
  - March 2020 dash for cash: March 9–27, 2020 (Australia, Eurozone, Japan, United Kingdom, United States)
  - US Fed Tapering and tightening announcement: December 20, 2021–January 19, 2022 (Australia, Eurozone, Japan, United Kingdom, United States)
  - U.K. Gilt Crisis 2022: September 15–30, 2022 (Australia, Eurozone, United States, United Kingdom, Japan)
- Data sources cited: Barclays; ICAP; Bloomberg Finance L.P.; Fannie Mae; IMF staff calculations.

### Social media, AI, and financial-system signals
- March 2023 US banking turmoil:
  - Social media text indices tracked mentions of Silicon Valley Bank (SVB) on Twitter and negative sentiment mentions relative to bank price indices.
  - Price indices: composite of banks in the S&P 500 (“Bank S&P"), subgroup of regional banks (“Bank regional”), and SVB stock price in US DOLLAR; price indices re-based with first observation available in March 2006.
- AI indicators:
  - Share of companies mentioning AI in Russell 3000 earnings calls (Percent).
  - Business value derived from AI in the banking industry (billions of US Dollar).
- Data sources: Bloomberg Finance L.P.; HIS Markit; Statista; IMF staff calculations.

### Correlation dynamics across uncertainty measures
- Comparisons:
  - Correlation Between Selected Measures of Macroeconomic and Financial Uncertainty for 1990–2009 and 2010–23.
- Summary:
  - Correlation between selected uncertainty measures has increased over time.
- Sources: Online Annex 2.1; IMF staff calculations.

### Taxonomy of uncertainty measures and new bank-level text measure
- Uncertainty measure types (Online Annex Table 2.2.1) — selected entries preserved:
  - Macroeconomic — Econometric based: aggregate of the conditional volatility of the unforecastable component of a set of economic variables (Jurado and others (2015)).
  - Macroeconomic — Text based: share of news articles discussing uncertainty about various aspects of economic policy (Baker and others (2016)).
  - Macroeconomic — Survey based: deviations of macroeconomic data projections (Consensus projections).
  - Geopolitical (text-based): share of news articles discussing risks from geopolitical events (Caldara and Iacoviello (2022)).
  - Financial — Econometric based: aggregate of the conditional volatility of the unforecastable component of a set of financial variables (Ludvigson and others (2021)).
- New bank-level measure:
  - Text analysis of banks’ earnings calls to capture uncertainty perceived by banks that could affect lending behavior.

### A. Construction of econometric-based measures (REU and FINU)
- h-period ahead uncertainty definition:
  - U_{i,t}(h) ≡ sqrt{E[(y_{i,t+h} − E[y_{i,t+h}|I_{i,t}])^2 | I_{i,t}]}
- Aggregation for REU:
  - REU_{i,t}(h) ≡ plim_{N_i→∞} (1/N_i) ∑_{j=1}^{N_i} U_{i,t}(h) ≡ E[U_{i,t}(h)]
- Factor structure assumed:
  - y_{i,t} = Λ_i F'_i F_{it} + e_{it}
- Estimation details:
  - Conditional expectations derived from forecasts using factors; log volatility assumed time-varying following an autoregressive (stochastic volatility) model.
  - Factors F_{it} are static principal components from large sets of real economic indicators for REU and selected financial indicators for FINU (following Ludvigson and others (2021)).
  - Estimations performed separately for each country for a one-quarter forecasting horizon.
  - Indicators included if observations available since 1998 (or earlier); missing data imputed using multiple imputation by chained equations.
  - Forecast window for good/bad uncertainty analysis set to three years.

### Data series for REU (Table 2.2.2) — main groups and examples
- Group A: Output, Trades, Sales, and Orders (selected examples)
  - Capacity utilization rate; Order books; Orders inflow; Production tendency; Export order books or demand; Orders, manufacturing; Production, excluding construction; Production, manufacturing consumer goods; Production, manufacturing intermediate goods; Production, manufacturing total; Sales, manufacturing value; Sales, retail trade volume; Sales, retail trade value; Sales, whole trade value; Stocks, Manufacturing; Exports; Imports; Net trade; Industrial production, index; Gross domestic product, constant prices (percent change y/y); Real imports; Retail sales, percent change (y/y); Total domestic demand, constant prices, percent change (y/y); Real exports; Manufacturing PMI; Merchandise trade balance, percent of GDP; National Gross Domestic Product, Constant Price; National Gross Domestic Product, Current Price; Industrial Production, Manufacturing, Index; Industrial Production, Mining, Index; Industrial Production, Index; Oil Production, Crude, Index.
- Group B: Prices (examples)
  - CPI, all items, growth; CPI, all items, index; CPI, all Items non-food non-energy; Core CPI, index; Harmonized CPI, index; Producer Price Index; Core producer price index.
- Group C: Labor Market Activity (examples)
  - Hours worked, industry excluding construction; Earnings, manufacturing; Employment series by sector and age groups; Harmonized unemployment by age groups; Job vacancies; Activity rates; Employment rates; Total labor force.
- Group D: Monetary Instruments
  - Nominal effective exchange rate; Short-term interest rate; Long-term interest rate; Policy-related interest rate; Broad money; Narrow money.
- Group E: Consumer and Business Confidence
  - Business tendency surveys (manufacturing), business situation, employment; Consumer opinion surveys, confidence; Consumer opinion surveys, economic situation; Consumer confidence Units.
- Group F: Stock Market
  - MSCI stock price index; Benchmark stock market index; Share Prices, broad.
- Group G: Residential and non-residential investment
  - Construction permit issued; Production, construction.
- Data sources: OECD Main Economic Indicators database; IMF Global Data Source database; IMF IFS database.
- Note: Use of large datasets within each country is crucial to minimize biases.

### Data series for FINU (Table 2.2.3) — selected indicators
- Financial series and risk factors listed (selected):
  - Log price-to-dividend ratio (LSEG Datastream and IMF staff calculations).
  - Change in stock price (raw and seasonally adjusted).
  - Risk-free rate (3-month government bond yield).
  - Market return - risk free rate (MKT_RF); Small-minus-big (SMB); High-minus-low (HML).
  - Portfolio return constructions: 25 portfolios (5x5), 6 portfolios (2x3), 23 Industry portfolios, 16 country portfolios using ratios B/M, E/P, CE/P, D/P (local currency and US DOLLAR returns).
  - Regional risk factors: SMB, HML, MKT_RF computed in the region of the domestic country.
- Data library references: Kenneth French Dartmouth website.
- Note: Portfolio formation depends on data availability for each country.

### B. Financial spanning of macroeconomic uncertainty measures — empirical summary
- Approach:
  - Regress macroeconomic uncertainty measures on PCA components of “risk” variables in the Chicago Financial Condition Index (CFCI) or directly on “risk” variables where available.
  - PCA components selected to cover around 90 percent of variation.
- Key empirical findings:
  - Financial indicators explain around 80 percent of the variation in commonly used macroeconomic uncertainty measures for the United States.
  - Financial indicators explain about 40-50 percent of the variation for major emerging market economies such as Brazil.
  - Conclusion: Financial indicators may not fully capture macroeconomic uncertainty; macroeconomic uncertainty measures are important for systemic risk assessments and forecasting frameworks, particularly for countries with less developed financial markets.
- Supporting citations: Valkanov and Zhang 2018; Dew-Becker and Giglio 2023.

### C. “Good” and “bad” uncertainty — decomposition and empirical proxies
- Concept:
  - Macroeconomic uncertainty decomposed into “good” (positive) and “bad” (negative) components depending on realized semivariances.
- Decomposition method (Segal, Shaliastovich, and Yaron 2015):
  - RV_{i,t+1}^n = ∑_{j=1}^{N} 1_{(Δy_{i,t+j/N} < 0)} (Δy_{i,t+j/N})^2
  - RV_{i,t+1}^p = ∑_{j=1}^{N} 1_{(Δy_{i,t+j/N} ≥ 0)} (Δy_{i,t+j/N})^2
  - Predictable components (s = p,n):
    - log( (1/h) ∑_{j=1}^{h} RV_{i,t+j}^s ) = β_{i}^s + ν_{i}^s X_{i,t} + ε_{i}
    - V_{i,t}^g = exp(β_{i}^p + ν_{i}^p X_{i,t}); V_{i,t}^b = exp(β_{i}^n + ν_{i}^n X_{i,t})
- Implementation:
  - Monthly observations; forecast window h set to three years.
  - Predictors X_{i,t}: positive and negative realized semivariances, consumption growth, real market return, market price–dividend ratio, real risk-free rate, default spread.
  - Estimations performed separately for each country.
- Empirical patterns:
  - ‘Bad’ uncertainty increases before the global financial crisis and during the COVID-19 pandemic (and before the Asian Financial Crisis in Korea).
  - ‘Good’ uncertainty is higher during tech revolutions such as the US dot-com bubble and during post-crisis reform periods.

### United States: Good and Bad Uncertainty across Time — notes
- Axes and data: left axis z-scores; right axis percent.
- Orthogonalized positive and negative uncertainty measures standardized with mean zero.
- Source: Haver Analytics; LSEG Datastream; IMF staff calculations.

### Growth-at-Risk (GaR) approaches — standard econometric and machine learning
- Standard panel quantile regression (baseline, equation (7)):
  - y_{i,t+h}(τ) = β_{h,i}(τ) + β_{h,y}(τ) y_{i,t} + β_{h,FCI}(τ) FCI_{i,t} + ε_{i,t+h}(τ)
  - y_{i,t+h}(τ): h-quarter ahead annualized GDP growth; τ quantiles τ = 0.05, 0.10, ..., 0.95; h = 1, .., 12.
- Extended model including uncertainty (equation (8)):
  - y_{i,t+h}(τ) = β_{h,i}(τ) + β_{h,y}(τ) y_{i,t} + β_{h,FCI}(τ) FCI_{i,t} + β_{h,u}(τ) U_{i,t} + ε_{i,t+h}(τ)
  - U_{i,t} is a vector of uncertainty measures.
- Endogeneity/addressing concerns:
  - Orthogonalized uncertainty measures (two-stage residual approach).
  - Instrumental variable (IV) approach using exogenous shocks; IV example: a one standard deviation increase in the real economic uncertainty index is associated with an increase in downside real GDP risk (decline in the 10th percentile of one-period ahead GDP growth distribution) of 1.8 percentage points compared to 2 percentage points in the baseline analysis.

### Machine learning GaR (ML-GaR) — algorithms and procedures
- Algorithms:
  - Quantile Random Forest (QRF) following Meinshausen (2006).
  - Quantile Neural Network (QNN) / panel quantile neural network.
- QRF hyperparameters:
  - number of trees = 1,000; minimum samples per node = 5; number of predictors for split = square root of total predictors.
- QNN details:
  - Minimizes quantile loss ρ_τ; x_{i,t} = (y_{i,t-1}, FCI_{i,t}, U_{i,t}, α_i).
  - Hyperparameter selection via three-fold block cross-validation and grid search.
  - Learning rate = 0.001; dropout rate = 0.
  - Baseline network structures use one hidden layer (selected by cross-validation).
- Out-of-sample testing:
  - Block K-fold with K = 3; training excludes the last 4 quarters preceding test start and the next quarter after test end; COVID training exclusions described.
  - Expanding window checks: QRF accuracy broadly unchanged; QNN marginally decreased under expanding window.
- Variable importance:
  - SHAP (Shapley values) used to evaluate feature contributions.

### Forecast accuracy metric
- Accuracy change metric (equation (11)):
  - (1 − [ΣΣ ρ_τ(y_{i,t+h} − ŷ_{i,t+h,ML}) / ΣΣ ρ_τ(y_{i,t+h} − ŷ_{i,t+h,QR})]) * 100%
  - y_{i,t+h} is 1- or 4-quarter GDP growth; ŷ_{i,t+h,ML} prediction from ML model; ŷ_{i,t+h,QR} prediction from benchmark GaR quantile regression.

### Key out-of-sample accuracy changes: Quantile Random Forest (QRF) — Accuracy change from benchmark (in percent)
- Advanced Economies, One Quarter Ahead:
  - Excluding uncertainty: 7.4
  - Including real economic uncertainty: 11.7
  - Including orthogonal component: 8.2
  - Including w/o forward looking bias: 8.0
  - Financial uncertainty: 8.2
  - Economic policy uncertainty: 5.9
  - Geopolitical uncertainty: 13.8
  - GDP Forecast dispersion: 15.1
  - World uncertainty index: 10.8
  - Text-based uncertainty: 4.3
- Advanced Economies, Four Quarters Ahead:
  - Excluding uncertainty: 2.2
  - Including real economic uncertainty: 9.4
  - Orthogonal component: 5.8
  - w/o forward looking bias: 4.4
  - Financial uncertainty: 5.9
  - Economic policy uncertainty: 9.1
  - Geopolitical uncertainty: 5.1
  - GDP Forecast dispersion: 5.2
  - World uncertainty index: 3.7
  - Text-based uncertainty: 1.7
- Emerging Market Economies, One Quarter Ahead:
  - Excluding uncertainty: -0.1
  - Including real economic uncertainty: 4.7
  - Orthogonal component: 4.5
  - w/o forward looking bias: 3.0
  - Financial uncertainty: 5.0
  - Economic policy uncertainty: 7.6
  - Geopolitical uncertainty: 8.5
  - GDP Forecast dispersion: 8.6
  - World uncertainty index: 8.7
  - Text-based uncertainty: 4.3
- Emerging Market Economies, Four Quarters Ahead:
  - Excluding uncertainty: 5.7
  - Including real economic uncertainty: 12.2
  - Orthogonal component: 11.9
  - w/o forward looking bias: 3.7
  - Financial uncertainty: 1.1
  - Economic policy uncertainty: 11.4
  - Geopolitical uncertainty: 0.2
  - GDP Forecast dispersion: 4.1
  - World uncertainty index: 2.6
  - Text-based uncertainty: 5.5

### Key out-of-sample accuracy changes: Quantile Neural Network (QNN) — Accuracy change from benchmark (in percent)
- Advanced Economies, One Quarter Ahead:
  - Excluding uncertainty: 3.6
  - Including real economic uncertainty: 12.5
  - Orthogonal component: 6.3
  - w/o forward-looking bias: 6.2
  - Financial uncertainty: -1.2
  - Economic policy uncertainty: -4.2
  - Geopolitical uncertainty: 2.3
  - GDP Forecast dispersion: 3.1
  - World uncertainty index: 1.0
  - Text-based uncertainty: -3.8
- Advanced Economies, Four Quarters Ahead:
  - Excluding uncertainty: 4.8
  - Including real economic uncertainty: 9.1
  - Orthogonal component: 5.7
  - w/o forward-looking bias: 5.9
  - Financial uncertainty: 4.8
  - Economic policy uncertainty: 7.0
  - Geopolitical uncertainty: 3.1
  - GDP Forecast dispersion: 4.8
  - World uncertainty index: 3.0
  - Text-based uncertainty: 1.2
- Emerging Market Economies, One Quarter Ahead:
  - Excluding uncertainty: 1.0
  - Including real economic uncertainty: 6.4
  - Orthogonal component: 2.1
  - w/o forward-looking bias: 3.4
  - Financial uncertainty: -0.2
  - Economic policy uncertainty: 5.7
  - Geopolitical uncertainty: -0.5
  - GDP Forecast dispersion: 2.1
  - World uncertainty index: 1.6
  - Text-based uncertainty: -2.2
- Emerging Market Economies, Four Quarters Ahead:
  - Excluding uncertainty: 3.9
  - Including real economic uncertainty: 11.6
  - Orthogonal component: 5.2
  - w/o forward-looking bias: 4.9
  - Financial uncertainty: 0.3
  - Economic policy uncertainty: 1.9
  - Geopolitical uncertainty: 0.5
  - GDP Forecast dispersion: 4.3
  - World uncertainty index: 2.5
  - Text-based uncertainty: 0.9
- Note: Percentage improvements of out-of-sample quantile loss when moving from benchmark GaR without an uncertainty index to ML-GaR with/without one of the uncertainty indices; out-of-sample analysis used block K-folds with K = 3.

### Predictive accuracy: panel versus country-level ML-GaR (Quantile Random Forest and Quantile Neural Network)
- QRF: Accuracy change from the country-level model, in percent (Advanced Economies / Emerging Market Economies)
  - One Quarter Ahead, Excluding uncertainty / Including uncertainty; Four Quarters Ahead, Excluding uncertainty / Including uncertainty
  - Advanced Economies:
    - First quartile: -0.3 0.3 -1.1 -3.6
    - Median: 1.8 3.4 3.3 2.2
    - Third quartile: 6.8 5.2 6.8 10.9
  - Emerging Market Economies:
    - First quartile: -2.9 -1.5 -1.1 0.2
    - Median: 0.1 2.7 0.4 4.5
    - Third quartile: 6.8 4.8 6.3 6.6
- QNN: Accuracy change from the country-level model, in percent
  - Advanced Economies:
    - First quartile: -4.3 -1.5 -2.7 -1.1
    - Median: -1.7 6.4 4.0 5.7
    - Third quartile: 8.5 9.2 10.5 9.2
  - Emerging Market Economies:
    - First quartile: -0.2 8.7 -0.5 1.3
    - Median: 2.4 16.2 1.7 8.3
    - Third quartile: 9.8 16.9 11.8 11.7
- QNN hyperparameters noted: one layer with eight neurons, number of epochs = 300, batch size = 32 (models referenced).

### Prediction accuracy for past crisis episodes
- Evaluation windows:
  - Global Financial Crisis: realizations between 2007Q4 and 2009Q2.
  - COVID-19 pandemic: realizations in 2020Q2 and 2020Q3 (only one-quarter ahead forecasts evaluated).
- Finding:
  - ML approaches that include the real economic uncertainty measure are generally useful to predict past crisis episodes.
- Out-of-sample procedure: block K-folds with K=3; models estimated on panels of advanced or emerging market economies.

### Interaction of macroeconomic uncertainty with macrofinancial vulnerabilities
- Extended linear quantile specification (equation (12)):
  - y_{i,t+h}(τ) = β_h(τ) + β_{h,y}(τ) y_{i,t} + β_{h,FCI}(τ) FCI_{i,t} + β_{h,u}(τ) HighUncertainty_{i,t} + β_{h,v}(τ) V_{i,t} + β_{h,uv}(τ) HighUncertainty_{i,t} x V_{i,t} + ε_{i,t+h}(τ)
  - HighUncertainty_{i,t} = 1 when real economic uncertainty is above the median.
- Main empirical findings:
  - Higher uncertainty predicts lower values for the 10th percentile of future GDP growth.
  - The adverse impact of increased uncertainty on downside tail risk is amplified when credit-to-GDP and public debt-to-GDP gaps are high.
- Interaction with financial conditions (equation (13)):
  - y_{i,t+h}(τ) = β_h(τ) + β_{h,y}(τ) y_{i,t} + β_{h,FCI}(τ) FCI_{i,t} + β_{h,u}(τ) HighUncertainty_{i,t} + β_{h,uf}(τ) HighUncertainty_{i,t} x FCI_{i,t} + ε_{i,t+h}(τ)
  - β_{h,FCI}(τ): effect of one-standard deviation change in FCI in low uncertainty regime; β_{h,uf}(τ): additional impact under high uncertainty.
- Macro-market disconnect (equation (14)):
  - HighDis_{i,t} = 1 when ratio between real economic uncertainty and realized market volatility is above its mean.
  - Disconnect can increase downside risks by up to 0.3 percentage points (annualized) over the next five quarters (baseline model including only HighDis_{i,t}).

### Macroprudential policy effectiveness on intertemporal risk-return tradeoff
- Regime specification (equation (15)): separate parameter regimes depending on macroprudential tightening in past 4 quarters.
  - θ_{i,t} = 1 if sum of net macroprudential policy tightening in past 4 quarters is positive, 0 otherwise.
- Macroprudential tightening indicator:
  - SUM17 variable in the iMapp database (net number of macroprudential tightening actions in a quarter).
  - Aggregates measures across six categories: borrower-based measures; bank capital measures; banks' foreign currency exposure measures; bank liquidity measures; credit measures; other measures (stress testing, restrictions on profit distribution, limits on exposures).
- Purpose:
  - Examine whether macroprudential tightening curbs sectoral leverage buildup and mitigates downside risks to growth.
- Data: IMF's Integrated Macroprudential Policy Database, period 1990-2021.

### Online Annex 2.5 — channels: market tail risk and bank lending
- Empirical approach:
  - Dynamic panel quantile regressions (Canay (2011) estimator with bootstrapped standard errors).
  - Main uncertainty measures: REU, financial economic uncertainty, EPU, WUI.
  - Monthly panel for 19 AEs and 9 EMs; robustness checks include implied volatility measures and pre-COVID-19 sample restrictions.
- Market tail risk specification (equation (16)):
  - Dependent variable: τ quantile of h-period-ahead average stock returns or change in sovereign bond spreads; includes interaction UitVit.
- Bank lending tail risk specification (equation (17)):
  - Dependent variable: τth percentile of real credit growth between t and t+h; controls: real GDP growth, domestic FCI; vulnerabilities: credit-to-GDP gap, regulatory capital deviations, return on assets, NPL ratio, banks’ government debt exposure.

### Tail risk in sovereign spreads — core quantitative findings
- Sovereign spread dependent variable: 90th percentile of change in spreads over horizons 1, 3, 6, 12 months (basis points).
- Controls Zit include: VIX; Excess bond premium (EBP); foreign real 2y Treasury Yield; foreign term spread; one-month S&P500 return; 3-month domestic stock returns residual; 3-month domestic stock return volatility; 3-month change in local currency exchange rate vs US DOLLAR in excess of US DOLLAR index; 3-month exchange rate volatility.
- Core findings:
  - Increase in REU significantly raises upside tail risks to sovereign spreads in both AEs and EMs for up to six months.
  - Effect amplified in EMs with high fiscal and financial vulnerabilities: debt service to GDP and banks' exposure to sovereign debt.
  - In AEs interaction results are opposite in sign but much lower magnitude and only borderline significant; pre-COVID restriction makes AE results insignificant.
- Representative coefficient magnitudes (selected entries from Online Annex Table 2.5.1):
  - REU coefficients (1-, 3-, 6-, 12-month regressions): 102.016**, 281.735***, 278.996**, -54.443 with standard errors 45.958, 75.608, 114.810, 192.208.
  - Comparable EM column REU coefficients: 196.296**, 501.164**, 926.044***, 292.725 with standard errors 97.584, 199.039, 237.837, 277.033.
  - Reported sample totals (N) include 5714 and 2551 for some specifications; reported Pseudo R2 values include 0.038, 0.06, 0.074, 0.121.
- Interaction results (3-month horizon, Online Annex Table 2.5.2):
  - (Debt Service)*REU interaction coefficients: -142.126** (Advanced Economies) and 478.789*** (Emerging Markets).
  - (Banks' Sovereign Exposure)*REU interaction coefficients: -23.443* (Advanced Economies) and 101.177*** (Emerging Markets).

### Tail risk in stock returns — findings
- Dependent variable: 10th percentile of average future stock returns over horizons 1, 3, 6, 12 months (downside tail risk).
- Baseline controls (standardized at country level): 3-month domestic CPI inflation; 3-month % change in real industrial production; average dividend yield; detrended short (3-month) rate; domestic term spread; 3-month daily stock volatility; price-to-earnings ratio.
- Core result:
  - An increase in REU significantly reduces stock returns in both AEs and EMs by up to 12 months.
  - Effect strongest in first month in AEs; similar magnitude at 3- and 6-month horizons.
  - Fiscal and financial vulnerabilities do not significantly magnify uncertainty's effect on stock returns.
- Representative reported coefficients: some large magnitudes (e.g., 625.324*** in an AE column) reported in Online Annex Table 2.5.3.

### Tail risk in bank lending — setup, variables, and findings
- Dependent variable: τth percentile of real credit growth (annualized) between t and t+h.
- Vulnerabilities Vit: credit-to-GDP gap; deviation of regulatory capital-to-asset ratio from trend; return on assets; NPL ratio; banks’ government debt exposure.
- Controls Zit: real GDP growth; domestic FCI; other macro-financial variables captured via FCI and time effects.
- Core findings (from panel quantile regressions):
  - Higher macroeconomic uncertainty negatively associated with downside risks to future (four-quarter ahead) credit growth across measures.
  - When including four uncertainty measures together, forecast dispersion, REU, and the text-based bank-level indicator are negative and statistically significant — they capture different aspects useful for forecasting tail risks to lending.
  - Covariate behavior as expected: tighter financial conditions, larger credit-to-GDP gap, higher banking system NPL ratios → lower future credit growth; stronger profitability and capital → higher future credit growth.
- Robustness:
  - Results robust to alternative estimators (Powell (2022), Machado and Silva (2019)), use of total credit (BIS total credit), and sample choices.

### Text-based bank-level uncertainty measure: construction and empirical relationships
- Construction:
  - Count sentences containing uncertainty-related words in each bank’s earnings calls; scale by number of sentences.
  - Word list: Loughran-McDonald Master Dictionary (2024) (~300 uncertainty words).
  - Country-level measure: simple average of bank-specific scores.
  - Alternative narrow list: three words: “uncertain”, “uncertainty”, “uncertainties”.
  - Binscatter: standardized text-based uncertainty ordered into 25 bins (Cattaneo, Crump, Farrell and Feng (2024)).
- Pairwise correlation matrix (selected exact entries and significance markers):
  - Forecast dispersion vs REU: 0.61***
  - Forecast dispersion vs EPU: 0.24***
  - Forecast dispersion vs Text-based: 0.02
  - REU vs EPU: 0.37***
  - REU vs Text-based: 0.03
  - EPU vs Text-based: -0.05
  - Alternative text-based vs Text-based: 0.77***
  - Significance legend: * p < 0.05, ** p < 0.01, *** p < 0.001
- Relationship with credit growth:
  - Binscatter slope of standardized text-based uncertainty (25 bins) vs average quarterly annualized real credit growth over next four quarters: slope = -0.38 (significant at 1 percent).
  - Text-based bank-level measure has little correlation with other indicators but is negatively correlated with credit growth — suggesting it captures lender-specific uncertainty affecting loan supply.
- Panel quantile regression evidence (equation (17)):
  - Quarterly panel: 18 AEs and 13 EMs, 2001–2023.
  - Dependent variable: 10th percentile of country-level real credit growth (average quarterly annualized growth over next 4 quarters).
  - Main findings: higher macroeconomic uncertainty negatively associated with downside risks to future credit growth; multiple uncertainty measures jointly significant; robustness to alternative estimators and use of total credit.

### Cross-border spillovers, buffers, and policy interactions
- Extended GaR model (equation (18)) includes foreign uncertainty U_-i,t: weighted averages of partner uncertainties (weights: trade or portfolio exposures normalized by country i GDP).
- Buffers and mitigation (equation (19) and Figures 2.6.1–2.6.2):
  - International reserves-to-GDP used as High Buffer dummy (above median).
  - Interaction of foreign uncertainty with High Buffer: international reserves mitigate spillover effects.
  - Flexible exchange rate regimes and large external debt: flexible regimes mitigate spillovers; larger external debt amplifies spillovers.
- Robustness: results hold across alternative uncertainty measures, estimators, total credit growth dependent variable, additional controls, and pre-COVID or excluded-2020Q1–Q3 samples.

### Robustness checks and extensions (selected)
- Robustness exercises performed include:
  i. Prediction at longer horizons and across different uncertainty measures (orthogonal components, forward-looking bias corrections).
  ii. Comparison panel vs country-level ML-GaR: panel models generally outperform country-level; neural networks benefit from larger panels.
  iii. Alternative estimators: Machado and Silva (2019), Powell (2021).
  iv. Controls: global financial crisis dummy; inflation; policy rate; unemployment.
  v. Estimation windows: pre-COVID only or excluding 2020Q1–Q3.
  vi. Alternative bootstrap and CI construction: percentile bootstrap with pairwise resampling.
- MIDAS extension:
  - Combining daily/high-frequency uncertainty with quarterly indicators can improve out-of-sample performance.
  - Example: incorporating seven most recent daily observations of the economic policy uncertainty index into QRF improves four-quarter-ahead forecast accuracy by up to 2.5 percent for the US and by 9.0 percent for the UK compared to a model using quarterly EPU.

*Sources: Haver Analytics; LSEG Datastream; and IMF staff calculations.*

### 1. Global Economic Policy Uncertainty, 2010:M1-2024:M6

### ch2annex - 1. Global Economic Policy Uncertainty, 2010:M1-2024:M6

### Global and regional economic policy uncertainty (Index)
- Time coverage reported:
  - Global series: 2010:M1-2024:M6
  - Europe, United Kingdom, and the US series: 2010:M1-2024:M7
- Contextual note: Global debt has increased over the past two decades, particularly during the COVID-19 pandemic. Government debt-to-GDP ratios have increased steadily.
- Related debt and composition figures referenced:
  - Total Debt Breakdown, 2005-23 (Percent of GDP)
  - Public Debt, 2005–23 (Percent of GDP; trillions of US DOLLAR)

### Market volatility spillovers and bond/stock correlations
- Observed patterns:
  - Correlation between bond and stock market volatility has generally increased over time.
  - Correlation panels reported for periods: 2000-19, 2020-21, 2022-24 (by region: Eurozone, Australia, Japan, EM).
- Episodes of rapid cross-border stress documented (cumulative changes in 10-year government bond yields, percentage points):
  - March 2020 dash for cash episode: March 9–27, 2020 (daily cumulative changes shown for Australia, Eurozone, Japan, United Kingdom, United States)
  - US Federal Reserve Tapering and Monetary Policy Tightening Announcement: December 20, 2021–January 19, 2022 (daily cumulative changes shown for Australia, Eurozone, Japan, United Kingdom, United States)
  - U.K. Gilt Crisis 2022: September 15–30, 2022 (daily cumulative changes shown for Australia, Eurozone, United States, United Kingdom, Japan)
- Data sources cited for volatility and yield series: Barclays; ICAP; Bloomberg Finance L.P.; Fannie Mae; and IMF staff calculations.

### Social media, AI, and financial-system signals
- March 2023 US banking turmoil:
  - Social media text indices tracked mentions of Silicon Valley Bank (SVB) on Twitter and negative sentiment mentions (“SVB twitter”, “SVB negative sentiment”) relative to bank price indices.
  - Price indices include composite of banks in the S&P 500 (“Bank S&P"), subgroup of regional banks (“Bank regional”), and SVB stock price in US DOLLAR. Price indices re-based with first observation available in March 2006.
- AI in corporate disclosures and banking:
  - Share of companies mentioning AI in Russell 3000 earnings calls (Percent).
  - Use of AI in the banking industry (Business value derived from AI, billions of US Dollar).
- Data sources: Bloomberg Finance L.P.; HIS Markit; Statista; and IMF staff calculations.

### Correlation between uncertainty measures over time
- Comparisons presented:
  - Correlation Between Selected Measures of Macroeconomic and Financial Uncertainty, 1990–2009 (Index)
  - Correlation Between Selected Measures of Macroeconomic and Financial Uncertainty, 2010–23 (Index)
- Summary statement: Correlation between selected uncertainty measures has increased over time.
- Sources: See Online Annex 2.1; and IMF staff calculations.

### Measures of uncertainty — taxonomy and construction
- Uncertainty measure types summarized (Online Annex Table 2.2.1):
  - Macroeconomic — Econometric based: Aggregate of the conditional volatility of the unforecastable component of a set of economic variables (Jurado and others (2015)).
  - Macroeconomic — Text based: Share of news articles discussing uncertainty about various aspects of economic policy (Baker and others (2016)).
  - Macroeconomic — Survey based: Deviations of macroeconomic data projections (Consensus projections).
  - Macroeconomic — Text based: Frequency of the word “uncertainty” in the quarterly Economist Intelligence Unit country reports (Ahir and others (2022)).
  - Macroeconomic — Text based: Frequency of words referring jointly to “economic” or “economy”; and “uncertain” or “uncertainty” (Banks’ earnings calls transcripts).
  - Geopolitical (text-based): Share of news articles discussing risks from geopolitical events (Caldara and Iacoviello (2022)).
  - Financial — Econometric based: Aggregate of the conditional volatility of the unforecastable component of a set of financial variables (Ludvigson and others (2021)).
- New bank-level measure: Text analysis of banks’ earnings calls to capture uncertainty perceived by banks that could affect lending behavior.

### A. Construction of econometric-based measures (REU and FINU)
- Definitions and formulas:
  - h-period ahead uncertainty for series y_{i,t}:
    - U_{i,t}(h) ≡ sqrt{E[(y_{i,t+h} − E[y_{i,t+h}|I_{i,t}])^2 | I_{i,t}]}
  - REU_{i,t}(h) computed by aggregating individual series uncertainty:
    - REU_{i,t}(h) ≡ plim_{N_i→∞} (1/N_i) ∑_{j=1}^{N_i} U_{i,t}(h) ≡ E[U_{i,t}(h)]
  - Each series y_{i,t} assumed stationary and follows factor structure:
    - y_{i,t} = Λ_i F'_i F_{it} + e_{it}
- Estimation details:
  - Conditional expectations derived from forecasts using factors; log volatility assumed time-varying and follow an autoregressive model (stochastic volatility assumption).
  - Factors F_{it} are static principal components from large sets of real economic indicators for REU and selected financial indicators for FINU following Ludvigson and others (2021).
  - Estimations performed separately for each country for one-quarter forecasting horizon to align with main analysis.
  - Input data indicated in Table 2.2.2 (real economic series) and Table 2.2.3 (financial series).
  - Indicators included if observations available since 1998 (or earlier); missing data imputed using multiple imputation by chained equations.
  - Forecast window for good/bad uncertainty analysis set to three years in empirical applications.

### Data series for REU (Table 2.2.2) — main groups
- Group A: Output, Trades, Sales, and Orders (selected examples)
  - Capacity utilization rate; Order books; Orders inflow; Production tendency; Export order books or demand; Orders, manufacturing; Production, excluding construction; Production, manufacturing consumer goods; Production, manufacturing intermediate goods; Production, manufacturing total; Sales, manufacturing value; Sales, retail trade volume; Sales, retail trade value; Sales, whole trade value; Stocks, Manufacturing; Exports; Imports; Net trade; Industrial production, index; Gross domestic product, constant prices (percent change y/y); Real imports; Retail sales, percent change (y/y); Total domestic demand, constant prices, percent change (y/y); Real exports; Manufacturing PMI; Merchandise trade balance, percent of GDP; National Gross Domestic Product, Constant Price; National Gross Domestic Product, Current Price; Industrial Production, Manufacturing, Index; Industrial Production, Mining, Index; Industrial Production, Index; Oil Production, Crude, Index.
- Group B: Prices (examples)
  - CPI, all items, growth; CPI, all items, index; CPI, all Items non-food non-energy; Core CPI, index; Harmonized CPI, index; Producer Price Index; Core producer price index.
- Group C: Labor Market Activity (examples)
  - Hours worked, industry excluding construction; Earnings, manufacturing; Employment series by sector and age groups; Harmonized unemployment by age groups; Job vacancies (public, private, total); Activity rates; Employment rates; Total labor force.
- Group D: Monetary Instruments
  - Nominal effective exchange rate; Short-term interest rate; Long-term interest rate; Policy-related interest rate; Broad money; Narrow money.
- Group E: Consumer and Business Confidence
  - Business tendency surveys (manufacturing), business situation, employment; Consumer opinion surveys, confidence; Consumer opinion surveys, economic situation; Consumer confidence Units.
- Group F: Stock Market
  - MSCI stock price index; Benchmark stock market index; Share Prices, broad.
- Group G: Residential and non-residential investment
  - Construction permit issued; Production, construction.
- Data sources: OECD Main Economic Indicators database; IMF Global Data Source database; IMF IFS database.
- Notes: Use of large datasets within each country is crucial to minimize biases. Indicators included if observations available since 1998 (or earlier).

### Data series for FINU (Table 2.2.3) — selected indicators
- Financial series and risk factors:
  - Log price-to-dividend ratio (LSEG Datastream and IMF staff calculations).
  - Change in stock price (raw and seasonally adjusted for dividend payments).
  - Risk-free rate (3-month government bond yield).
  - Market return - risk free rate (MKT_RF).
  - Small-minus-big (SMB) factor.
  - High-minus-low (HML) factor.
  - Small stock value spread.
  - 25 portfolios formed on size and book market (5x5) — Value-weighted return by portfolio.
  - 6 portfolios formed on size and book market (2x3) — Value-weighted return by portfolio.
  - 23 Industry portfolios — Value-weighted return by industries.
  - 16 country portfolios formed across different reference ratios — Value and growth portfolios' returns using four ratios: Book-to-market (B/M); earnings-price (E/P); cash earnings to price (CE/P); and dividend yield (D/P). Measures calculated using local currency and US DOLLAR returns.
  - Data library of Kenneth French Dartmouth website.
  - Regional risk factors: SMB, HML, MKT_RF computed in the region of the domestic country.
- Note: Portfolio formation (5x5 or 2x3) depends on data availability for each country.

### B. Financial spanning of macroeconomic uncertainty measures
- Assessment approach:
  - Macroeconomic uncertainty measures regressed on financial factors derived from PCA components of “risk” variables in Chicago Financial Condition Index (CFCI) or directly on the “risk” variables where available.
  - Number of PCA components selected to cover around 90 percent of variation across underlying risk indicators.
- Key empirical findings:
  - Financial indicators explain around 80 percent of the variation in commonly used macroeconomic uncertainty measures for the United States.
  - Financial indicators explain about 40-50 percent of the variation for major emerging market economies such as Brazil.
  - Conclusion: Financial indicators, such as asset prices and measures of implied volatility, may not fully capture macroeconomic uncertainty — underscoring the importance of incorporating macroeconomic uncertainty measures into systemic risk assessments and forecasting frameworks, particularly for countries with less developed financial markets.
- Supporting citations: Valkanov and Zhang 2018; Dew-Becker and Giglio 2023.
- Note: Online Annex Table 2.2.4 reports R-squared from regressions (United States, Brazil) and details on PCA components and variable specifications (e.g., “PCA 1-10 CFCI”, “Variable in CFCI”).

### C. “Good” and “bad” uncertainty — decomposition and empirical proxies
- Concept:
  - Macroeconomic uncertainty can be “good” or “bad” depending on whether uncertainty stems from favorable or unfavorable sources; episodes can have positive or negative effects on output and asset prices.
- Decomposition method (Segal, Shaliastovich, and Yaron 2015):
  - Realized positive and negative semivariances in annual terms for country i:
    - RV_{i,t+1}^n = ∑_{j=1}^{N} 1_{(Δy_{i,t+j/N} < 0)} (Δy_{i,t+j/N})^2
    - RV_{i,t+1}^p = ∑_{j=1}^{N} 1_{(Δy_{i,t+j/N} ≥ 0)} (Δy_{i,t+j/N})^2
    - Here 1_{(∙)} is an indicator function, Δy_i is demeaned monthly growth rate in industrial production, and N = number of observations in one period (i.e., twelve months).
  - Predictable components used as ex-ante proxies for good and bad uncertainty:
    - log( (1/h) ∑_{j=1}^{h} RV_{i,t+j}^s ) = β_{i}^s + ν_{i}^s X_{i,t} + ε_{i}, where s={p,n}
    - V_{i,t}^g = exp(β_{i}^p + ν_{i}^p X_{i,t}), V_{i,t}^b = exp(β_{i}^n + ν_{i}^n X_{i,t})
- Implementation details:
  - Monthly observations used; forecast window h set to three years to minimize measurement noise.
  - Benchmark predictors X_{i,t} include: positive and negative realized semivariances, consumption growth, real market return, market price–dividend ratio, real risk-free rate, and default spread.
  - Residual positive (negative) variance obtained by isolating orthogonal component of positive (negative) variance from the negative (positive) variance of industrial production growth.
  - Estimations conducted separately for each country.
- Empirical patterns cited:
  - Online Annex Figure 2.2.1 shows good and bad uncertainty results and four-quarter ahead realized GDP growth for selected countries (e.g., US and Korea).
  - Descriptive observations:
    - ‘Bad’ uncertainty increases (is above the mean) before the global financial crisis and during the COVID-19 pandemic (and before the Asian Financial Crisis in Korea).
    - ‘Good’ uncertainty is higher during tech revolutions such as the US dot-com bubble in the 1990s, and during the post-crisis reform period in Korea (1998).

*Sources: International Institute of Finance; IMF, World Economic Outlook; Baker, Bloom and Davis (2016); Ludvigson and others (2021); Jurado and others (2015); Ahir and others (2022); Caldara and Iacoviello (2022); Brave and Butters (2018); Fannie Mae; Bloomberg Finance L.P.; LSEG Datastream; HIS Markit; Statista; IMF staff calculations.*

### 1. United States: Good and Bad Uncertainty across Time

### ch2annex - 1. United States: Good and Bad Uncertainty across Time

### Data and Notes
- Left axis: z-scores; right axis: percent.
- Source: Haver Analytics; LSEG Datastream; and IMF staff calculations.
- Note: The panels show the orthogonalized measures of positive and negative uncertainty, calculated using the method from Segal and others (2015). The uncertainty measures are standardized with mean zero.

### Standard econometric Growth-at-Risk (GaR) approach
- Baseline panel quantile regression specification (equation (7)):
  - y_{i,t+h}(τ) = β_{h,i}(τ) + β_{h,y}(τ) y_{i,t} + β_{h,FCI}(τ) FCI_{i,t} + ε_{i,t+h}(τ)
  - y_{i,t+h}(τ) is h-quarter ahead GDP growth for country i realized at t+h (annualized).
  - τ denotes the quantile level (τ = 0.05, 0.10, ..., 0.95).
  - h is the forecasting horizon in quarters (e.g. h = 1, .., 12).
- Extended model including uncertainty (equation (8)):
  - y_{i,t+h}(τ) = β_{h,i}(τ) + β_{h,y}(τ) y_{i,t} + β_{h,FCI}(τ) FCI_{i,t} + β_{h,u}(τ) U_{i,t} + ε_{i,t+h}(τ)
  - U_{i,t} is a vector of uncertainty measures.
- Estimation details:
  - Models estimated for the full panel of countries with available data from 1990 (or earliest) to 2023.
  - Standard errors are bootstrapped.
  - Primary objective: prediction of future downside tail risks to output growth, conditioning on variables such as financial conditions and macroeconomic uncertainty (not causal identification).
- Endogeneity/addressing concerns:
  - Use of orthogonalized uncertainty measures with respect to financial indicators (two-stage residual approach).
  - Instrumental variable (IV) approach exploiting exogenous shocks (natural disasters, terrorist attacks, political coups, revolutions) following Baker and others (2016).
  - IV result example: a one standard deviation increase in the real economic uncertainty index is associated with an increase in downside real GDP risk (decline in the 10th percentile of one-period ahead GDP growth distribution) of 1.8 percentage points compared to 2 percentage points in the baseline analysis.

### Decomposing good vs bad uncertainty
- Approach:
  - Construct proxies for good and bad uncertainty for each country at quarterly frequency (methodology in Online Annex 2.2.C).
  - Regress the real economic uncertainty index on these measures to isolate predicted values arising from positive (good) and negative (bad) macroeconomic uncertainty.
  - Use predicted values to estimate the 90th (good) and 10th (bad) percentiles of future GDP growth.
- Finding:
  - Positive (negative) uncertainty have a stronger association with the upper (lower) quantiles compared to the combined real economic uncertainty measure used in the baseline.

### Machine learning GaR (ML-GaR) approach
- Algorithms used:
  - Quantile Random Forest (QRF) following Meinshausen (2006).
  - Quantile Neural Network (QNN) / panel quantile neural network.
- QRF details:
  - Predictors x_{i,t} include lagged one-quarter GDP growth, financial conditions index, country dummies, and an uncertainty measure.
  - QRF hyperparameters used across specifications: number of trees = 1,000; minimum samples per node = 5; number of predictors for split = square root of total predictors.
- QNN details:
  - Optimization problem minimizes quantile loss ρ_τ over panel observations (equation (10)).
  - x_{i,t} = (y_{i,t-1}, FCI_{i,t}, U_{i,t}, α_i).
  - Hyperparameter selection via three-fold block cross-validation and grid search.
  - Learning rate = 0.001; dropout rate = 0.
  - Baseline uses network structures with one hidden layer based on cross-validation results.
- Out-of-sample procedure:
  - Block K-fold with K = 3: timeline divided into three equal blocks; train on two blocks and test on the hold-out block, repeated to cover all periods.
  - To avoid spillovers, the last 4 quarters preceding test sample start and the next quarter after test end are dropped from training; training sample excludes observations overlapping COVID period (2020Q2 and 2020Q3), though COVID period is included in test subsample.
  - Expanding window checks performed; QRF accuracy broadly unchanged; QNN marginally decreased under expanding window.
- Variable importance:
  - SHAP (Shapley values) used to evaluate feature contributions.

### Forecast accuracy metric
- Accuracy change metric (equation (11)):
  - (1 − [ΣΣ ρ_τ(y_{i,t+h} − ŷ_{i,t+h,ML}) / ΣΣ ρ_τ(y_{i,t+h} − ŷ_{i,t+h,QR})]) * 100%
  - y_{i,t+h} is 1- or 4-quarter GDP growth realized in quarter t+h.
  - ŷ_{i,t+h,ML} prediction from machine learning model; ŷ_{i,t+h,QR} prediction from benchmark GaR quantile regression.

### Robustness checks and extensions
- Robustness tests included:
  i. Prediction at longer horizons and across different macroeconomic uncertainty measures, including:
     - Orthogonal component of real economic uncertainty relative to financial factors.
     - Forward-looking bias corrected REU (projecting onto current values and lags of cross-sectional mean of squared errors using a stochastic volatility model).
  ii. Comparison of panel vs country-level ML-GaR: panel models generally outperform country-level models; neural networks particularly benefit from larger panel data.
  iii. Alternative estimators: Machado and Silva (2019), Powell (2021).
  iv. Controls: global financial crisis dummy; additional factors (inflation, policy rate, unemployment).
  v. Estimation windows: pre-COVID 19 period only or excluding first three quarters of 2020.
  vi. Alternative bootstrap and confidence interval construction: percentile bootstrap with pairwise resampling.
- MIDAS extension:
  - Combining daily/high-frequency uncertainty measures with quarterly indicators can improve out-of-sample performance. Example: incorporating seven most recent daily observations of the economic policy uncertainty index into QRF improves four-quarter-ahead forecast accuracy by up to 2.5 percent for the US and by 9.0 percent for the UK compared to a model using quarterly EPU.

### Key quantitative out-of-sample accuracy changes (ML-GaR versus benchmark GaR)
- Table: Quantile Random Forest — Accuracy change from the benchmark model (in percent)

  - Advanced Economies, One Quarter Ahead:
    - Excluding uncertainty: 7.4
    - Including real economic uncertainty: 11.7
    - Including orthogonal component: 8.2
    - Including w/o forward looking bias: 8.0
    - Financial uncertainty: 8.2
    - Economic policy uncertainty: 5.9
    - Geopolitical uncertainty: 13.8
    - GDP Forecast dispersion: 15.1
    - World uncertainty index: 10.8
    - Text-based uncertainty: 4.3

  - Advanced Economies, Four Quarters Ahead:
    - Excluding uncertainty: 2.2
    - Including real economic uncertainty: 9.4
    - Orthogonal component: 5.8
    - w/o forward looking bias: 4.4
    - Financial uncertainty: 5.9
    - Economic policy uncertainty: 9.1
    - Geopolitical uncertainty: 5.1
    - GDP Forecast dispersion: 5.2
    - World uncertainty index: 3.7
    - Text-based uncertainty: 1.7

  - Emerging Market Economies, One Quarter Ahead:
    - Excluding uncertainty: -0.1
    - Including real economic uncertainty: 4.7
    - Orthogonal component: 4.5
    - w/o forward looking bias: 3.0
    - Financial uncertainty: 5.0
    - Economic policy uncertainty: 7.6
    - Geopolitical uncertainty: 8.5
    - GDP Forecast dispersion: 8.6
    - World uncertainty index: 8.7
    - Text-based uncertainty: 4.3

  - Emerging Market Economies, Four Quarters Ahead:
    - Excluding uncertainty: 5.7
    - Including real economic uncertainty: 12.2
    - Orthogonal component: 11.9
    - w/o forward looking bias: 3.7
    - Financial uncertainty: 1.1
    - Economic policy uncertainty: 11.4
    - Geopolitical uncertainty: 0.2
    - GDP Forecast dispersion: 4.1
    - World uncertainty index: 2.6
    - Text-based uncertainty: 5.5

- Table: Quantile Neural Network — Accuracy change from the benchmark model (in percent)

  - Advanced Economies, One Quarter Ahead:
    - Excluding uncertainty: 3.6
    - Including real economic uncertainty: 12.5
    - Orthogonal component: 6.3
    - w/o forward-looking bias: 6.2
    - Financial uncertainty: -1.2
    - Economic policy uncertainty: -4.2
    - Geopolitical uncertainty: 2.3
    - GDP Forecast dispersion: 3.1
    - World uncertainty index: 1.0
    - Text-based uncertainty: -3.8

  - Advanced Economies, Four Quarters Ahead:
    - Excluding uncertainty: 4.8
    - Including real economic uncertainty: 9.1
    - Orthogonal component: 5.7
    - w/o forward-looking bias: 5.9
    - Financial uncertainty: 4.8
    - Economic policy uncertainty: 7.0
    - Geopolitical uncertainty: 3.1
    - GDP Forecast dispersion: 4.8
    - World uncertainty index: 3.0
    - Text-based uncertainty: 1.2

  - Emerging Market Economies, One Quarter Ahead:
    - Excluding uncertainty: 1.0
    - Including real economic uncertainty: 6.4
    - Orthogonal component: 2.1
    - w/o forward-looking bias: 3.4
    - Financial uncertainty: -0.2
    - Economic policy uncertainty: 5.7
    - Geopolitical uncertainty: -0.5
    - GDP Forecast dispersion: 2.1
    - World uncertainty index: 1.6
    - Text-based uncertainty: -2.2

  - Emerging Market Economies, Four Quarters Ahead:
    - Excluding uncertainty: 3.9
    - Including real economic uncertainty: 11.6
    - Orthogonal component: 5.2
    - w/o forward-looking bias: 4.9
    - Financial uncertainty: 0.3
    - Economic policy uncertainty: 1.9
    - Geopolitical uncertainty: 0.5
    - GDP Forecast dispersion: 4.3
    - World uncertainty index: 2.5
    - Text-based uncertainty: 0.9

- Note: Tables show percentage improvements of out-of-sample quantile loss when moving from benchmark GaR without an uncertainty index to ML-GaR without or with one of the uncertainty indices. Out-of-sample analysis performed using block K-folds with K = 3.

*Source: Haver Analytics; LSEG Datastream; and IMF staff calculations.*

### 1. Quantile Random Forest

### 1. Quantile Random Forest

### Predictive accuracy: Quantile Random Forest (QRF)
- Table: Accuracy change from the country-level model, in percent (Advanced Economies / Emerging Market Economies)
  - One Quarter Ahead, Excluding uncertainty / Including uncertainty; Four Quarters Ahead, Excluding uncertainty / Including uncertainty
  - Advanced Economies
    - First quartile: -0.3 0.3 -1.1 -3.6
    - Median: 1.8 3.4 3.3 2.2
    - Third quartile: 6.8 5.2 6.8 10.9
  - Emerging Market Economies
    - First quartile: -2.9 -1.5 -1.1 0.2
    - Median: 0.1 2.7 0.4 4.5
    - Third quartile: 6.8 4.8 6.3 6.6
- Methodology notes:
  - The tables compare the predictive accuracy of panel ML-GaR relative to country-level time series ML-GaR with and without real economic uncertainty.
  - The out-of-sample analysis is performed by estimating the model on block K-folds, with K=3.
  - The accuracy improvement is defined as one minus the percentage change in realized quantile loss for the 10 percentile, where the accuracy is calculated to each sample country.
  - GaR = growth-at-risk.

### Predictive accuracy: Quantile Neural Network (QNN)
- Table: Accuracy change from the country-level model, in percent (Advanced Economies / Emerging Market Economies)
  - One Quarter Ahead, Excluding uncertainty / Including uncertainty; Four Quarters Ahead, Excluding uncertainty / Including uncertainty
  - Advanced Economies
    - First quartile: -4.3 -1.5 -2.7 -1.1
    - Median: -1.7 6.4 4.0 5.7
    - Third quartile: 8.5 9.2 10.5 9.2
  - Emerging Market Economies
    - First quartile: -0.2 8.7 -0.5 1.3
    - Median: 2.4 16.2 1.7 8.3
    - Third quartile: 9.8 16.9 11.8 11.7
- Methodology notes:
  - For the QNN, hyperparameters for the neural network models are chosen based on three block cross validation.
  - The QNN models referenced later have one layer with eight neurons where the number of epochs is 300, and batch size is 32.

### Prediction accuracy for past crisis episodes
- Evaluation periods:
  - Global Financial Crisis: forecasts made for realizations between 2007Q4 and 2009Q2.
  - COVID-19 pandemic: forecasts made for realizations in 2020Q2 and 2020Q3.
  - For the COVID-19 pandemic, only one-quarter ahead forecasts are evaluated because uncertainty measures could not plausibly predict the pandemic in 2019Q2.
- Key finding:
  - The machine learning approach, when considering the real economic uncertainty measure, is generally useful to predict past crisis episodes.
- Accuracy metric:
  - The accuracy improvement is defined as one minus the percentage change in the realized quantile loss function for 0.10 quantile when moving from the benchmark GaR without the uncertainty index to an alternative model.
- Out-of-sample analysis:
  - Performed by estimating the model on block K-folds, with K=3.
  - Models are estimated on a panel of advanced or emerging market economies.

### In-sample and out-of-sample forecasts (QRF and QNN)
- Coverage:
  - Forecasts generated across percentiles: 10th, 50th, and 90th.
- Findings:
  - For in-sample forecasts, the 10th-90th percentile band effectively captures GDP growth realizations.
  - Even in out-of-sample forecasts, the 10th-90th percentile range broadly encompasses actual GDP growth, including during the Global Financial Crisis.
  - In-sample and out-of-sample forecasts broadly track each other.
- Model inputs (examples shown):
  - Include real economic uncertainty index, lagged GDP growth, and FCI. AEs and EMs model applies to the United States and Brazil, respectively.
  - One-quarter ahead GDP growth forecasts are annualized.
  - Out-of-sample analysis uses block K-folds, with K=3.

### How macroeconomic uncertainty interacts with macrofinancial vulnerabilities
- Extended linear quantile specification (notation preserved):
  - Equation (12) introduces interaction terms between uncertainty and vulnerability measures:
    - y_{i,t+h}(τ) = β_h(τ) + β_{h,y}(τ) y_{i,t} + β_{h,FCI}(τ) FCI_{i,t} + β_{h,u}(τ) HighUncertainty_{i,t} + β_{h,v}(τ) V_{i,t} + β_{h,uv}(τ) HighUncertainty_{i,t} x V_{i,t} + ε_{i,t+h}(τ)
  - V_{i,t} represents a vector of vulnerabilities; HighUncertainty_{i,t} is a dummy equal to one when real economic uncertainty is above the median.
- ML-GaR implementation:
  - For ML models, conditional predictions of h-quarter ahead GDP growth G(x_{i,t}, w*) use an expanded predictor set x_t = (FCI_{i,t}, U_{i,t}, V_{i,t}), which includes vulnerability measures.
- Main empirical findings (from Online Annex Figure 2.4.1 and Figure 2.6, panel 1):
  - Higher uncertainty generally predicts lower values for the 10th percentile of the future GDP growth distribution.
  - The impact of increased uncertainty on downside tail risk to future GDP growth is amplified when credit-to-GDP and public debt-to-GDP gaps are high, indicating interaction between uncertainty and these vulnerabilities.
- Additional interaction with financial conditions:
  - Equation (13) introduces interaction between uncertainty and FCI:
    - y_{i,t+h}(τ) = β_h(τ) + β_{h,y}(τ) y_{i,t} + β_{h,FCI}(τ) FCI_{i,t} + β_{h,u}(τ) HighUncertainty_{i,t} + β_{h,uf}(τ) HighUncertainty_{i,t} x FCI_{i,t} + ε_{i,t+h}(τ)
  - Coefficients of interest:
    - β_{h,FCI}(τ): effect of a one-standard deviation change in FCI in low uncertainty regime (High Uncertainty = 0).
    - β_{h,uf}(τ): additional impact of a change in FCI under a high uncertainty regime (High Uncertainty = 1).
  - Figure 2.6 (panel 2) shows the impact of a one standard deviation easing shock to financial conditions on the term-structure of GaR amid low real economic uncertainty and the overall effect during high uncertainty (β_{h,FCI}(τ) + β_{h,uf}(τ)).
- Macro-market disconnect:
  - Equation (14) replaces the high uncertainty dummy with HighDis_{i,t}, a dummy equal to one when the ratio between real economic uncertainty and realized market volatility is above its mean.
  - Results from this exercise are presented in Figure 2.6 (panel 3) of the main text.
- Robustness checks (findings robust to):
  - i) estimating GaR jointly incorporating different macroeconomic uncertainty measures along with the financial uncertainty measure;
  - ii) constructing confidence intervals based on percentile bootstrap with pairwise resampling;
  - iii) controlling for the global financial crisis using a dummy variable;
  - iv) using alternative panel quantile estimators such as Machado and Silva (2019) and Powell (2021);
  - v) controlling for additional confounding factors (such as inflation, policy rate, unemployment);
  - vi) using instrumented uncertainty as described in Online Annex 2.3;
  - vii) estimating the model on the pre-COVID period or by excluding the first three quarters of 2020.
- Quantified effect of disconnect:
  - A baseline model including only HighDis_{i,t} indicates that the disconnect can increase downside risks by up to 0.3 percentage points (annualized) over the next five quarters.

### Effectiveness of macroprudential policies on intertemporal risk-return tradeoff
- Specification (preserved notation):
  - Equation (15) models separate regimes based on macroprudential tightening:
    - y_{i,t+h}(τ) = θ_{i,t}[α_{i,h}(τ, tight) + β_{h,y}(τ,tight) FCI_{i,t} + β_{h,d}(τ,tight) HighDis_{i,t} + β_{h,df}(τ,tight) HighDis_{i,t} x FCI_{i,t} + λ_{h,x}(τ,tight) y_{i,t}] + (1−θ_{i,t})[α_{i,h}(τ,no_tight) + β_{h,y}(τ,no_tight) FCI_{i,t} + β_{h,d}(τ,no_tight) HighDis_{i,t} + β_{h,df}(τ,no_tight) HighDis_{i,t} x FCI_{i,t} + λ_{h,x}(τ,no_tight) y_{i,t}] + ε_{i,t+h}(τ)
- Regime dummy:
  - θ_{i,t} is a regime dummy that equals one if the sum of net macroprudential policy tightening in the past 4 quarters is positive, and zero otherwise.
- Macroprudential measures:
  - A variety of tools considered to define the macroprudential policy regime, including borrower-based measures and measures targeting bank lenders—capital adequacy requirements, liquidity regulations, and controls on foreign currency exposure.
  - Data sourced from the IMF's Integrated Macroprudential Policy Database, covering the period 1990-2021.
- Purpose:
  - To examine the effectiveness of macroprudential measures in curbing buildup of sector-specific leverage and mitigating downside risks to economic growth.
- Empirical alignment:
  - The empirical methodology and results in this section are aligned with the approach and findings presented in the main text.

*Sources: Haver Analytics; OECD, Main Economic Indicators database; LSEG Datastream; and IMF staff calculations.*

### Chapter 2 of the April 2021 GFSR. Figure 2.6 (panel 4) in the main text illustrates the impact of a one

### ch2annex - Chapter 2 of the April 2021 GFSR. Figure 2.6 (panel 4) in the main text illustrates the impact of a one

### Robustness and identification of the macroprudential–financial-conditions interaction
- Main comparison: impact of a one standard deviation easing in financial conditions during a period of “macroprudential tightening” amidst high macro-market disconnect, versus the effect of FCI loosening without macroprudential tightening in a similar context.
- Additional robustness checks (in addition to Online Annex 2.3) include:
  - i) directly interacting the macroprudential measures with the interaction effects of disconnect and financial conditions;
  - ii) using macroprudential policy shocks as in Brandao-Marques and others (2020);
  - iii) controlling for the global financial crisis using a dummy variable;
  - iv) controlling for additional factors (such as inflation, policy rate, unemployment) that could also affect future downside risks.

### Description and construction of the macroprudential tightening indicator
- The macroprudential tightening measure used is the discrete SUM17 variable in the iMapp database (net number of macroprudential tightening actions in a quarter).
- The indicator aggregates measures across six categories:
  - (1) borrower-based measures (loan-to-value (LTV), debt-service-to-income (DSTI) limits);
  - (2) bank capital measures (capital requirements, leverage limits, loan-loss provisioning, countercyclical capital buffers, capital conservation buffers, regulations targeting systemically important banks);
  - (3) banks' foreign currency exposure measures (limits on foreign currency lending, restrictions on gross open foreign currency positions, reserve requirements on foreign currency assets);
  - (4) bank liquidity measures (reserve requirements, liquidity mandates, limits on loan-to-deposit ratio);
  - (5) credit measures (limits on credit growth and loan restrictions);
  - (6) other measures (stress testing, restrictions on profit distribution, limits on exposures between financial institutions).

### Online Annex 2.5 — Does macroeconomic uncertainty influence activity through market tail risk and bank lending channels?
- Empirical approach:
  - Uses dynamic panel quantile regressions (Canay (2011) estimator with bootstrapped standard errors).
  - Main uncertainty measures: Real Economic Uncertainty (REU), financial economic uncertainty, Economic Policy Uncertainty (EPU), World Uncertainty Index (WUI).
  - Monthly data panel for 19 advanced and 9 emerging market economies (sample windows described below).
  - Robustness: checks using implied volatility measures and restricting to pre-COVID-19 period.
- Key regression specifications:
  - Market tail risk (equation (16)): dependent variable is the τ quantile of h-period-ahead average stock returns or change in sovereign bond spreads; includes interaction term UitVit to capture uncertainty×vulnerability.
  - Bank lending tail risk (equation (17)): dependent variable is the τth percentile of real credit growth between quarter t and t+h; controls include real GDP growth and domestic FCI, and vulnerabilities include credit-to-GDP gap, regulatory capital deviations, return on assets, NPL ratio, banks’ government debt exposure.

### Tail risk in sovereign spreads — findings and model controls
- Sovereign spread definition: difference between domestic government bond yields and US or German government bond yields of same maturity, measured in basis points.
- Dependent variable in sovereign spread regressions: 90th percentile of the change in spreads over horizons of 1, 3, 6, and 12 months (captures upside tail risk).
- Controls (Zit) when estimating equation (16) for sovereign spreads follow Gilchrist and others (2009) and include:
  - VIX index;
  - Excess bond premium (EBP) of Gilchrist and Zakrajšek (2012);
  - Foreign real 2y Treasury Yield (benchmark economy based on TIPS);
  - Foreign term spread (10-year minus 2-year yields);
  - One-month S&P500 return;
  - 3-month domestic stock market returns (residual from panel regression on S&P500);
  - 3-month daily domestic stock return volatility;
  - 3-month change in local currency exchange rate vis-à-vis the US DOLLAR in excess of changes in broad nominal US DOLLAR index;
  - 3-month exchange rate volatility.
- Sample sizes and estimation notes:
  - Separate regressions use monthly data for 20 AEs and 9 EMs from 1990m1 to 2023m12 (Online Annex Table 2.5.1).
  - Table estimates are based on the Canay estimator, include country fixed effects, and report results at the 90th percentile of the distribution of spread changes.
  - Standard errors are reported below coefficients; *, **, *** denote significance at 10, 5 and 1 percent levels.

### Sovereign spreads — core quantitative findings
- REU effect on upside tail risk in sovereign spreads:
  - An increase in REU significantly raises upside tail risks to sovereign bond spreads in both advanced and emerging market economies for up to six months.
  - The effect of REU is amplified in emerging market economies with high macrofinancial and fiscal vulnerabilities, specifically:
    - Debt service to GDP (nominal general government debt service payments as a percentage of nominal GDP);
    - Domestic banks’ exposure to sovereign debt (domestic sovereign debt held by banks as a percentage of banks’ total assets).
  - In advanced economies the interaction results are opposite in sign but of much lower magnitude and only borderline significant; results for advanced economies become insignificant when restricted to the pre-COVID period (possible influence of central bank interventions during COVID).
- Representative reported coefficient magnitudes and precision (selected entries from Online Annex Table 2.5.1):
  - REU coefficients (1-, 3-, 6-, 12-month regressions): 102.016**, 281.735***, 278.996**, -54.443 with reported standard errors 45.958, 75.608, 114.810, 192.208.
  - For the comparable emerging market column: REU coefficients 196.296**, 501.164**, 926.044***, 292.725 with reported standard errors 97.584, 199.039, 237.837, 277.033.
  - Reported sample totals (N) include 5714 observations for some specifications and 2551 for others; reported Pseudo R2 values range across specifications (examples: 0.038, 0.06, 0.074, 0.121).
- Interaction results (selected figures from Online Annex Table 2.5.2 for 3-month horizon):
  - (Debt Service)*REU interaction coefficients reported as -142.126** (Advanced Economies) and 478.789*** (Emerging Markets).
  - (Banks' Sovereign Exposure)*REU interaction coefficients reported as -23.443* (Advanced Economies) and 101.177*** (Emerging Markets).

### Tail risk in stock returns — findings and estimation
- Dependent variable: 10th percentile of average future stock returns over horizons of 1, 3, 6, and 12 months (captures downside tail risk in stock markets).
- Baseline controls (standardized at country level) follow Schmeling (2009) and Goyal and Welch (2008): 3-month domestic CPI inflation; 3-month % change in real industrial production; average dividend yield; detrended short (3-month) rate (HP filter); domestic term spread (10-year minus 3-month yields); 3-month daily stock market volatility; price-to-earnings ratio.
- Core result: an increase in real economic uncertainty (REU) significantly reduces stock returns in both advanced and emerging market economies by up to 12 months.
  - The effect is strongest in the first month in advanced economies, but is of similar magnitude at 3- and 6-month horizons.
  - Unlike sovereign spreads, fiscal and financial vulnerabilities do not appear to significantly magnify the effect of uncertainty on stock market returns.
- Representative reported coefficients (selected entries from Online Annex Table 2.5.3):
  - REU coefficient examples for stock-tail regressions show large magnitudes and statistical significance in some columns (e.g., 625.324*** in an advanced-economy column), with corresponding entries for emerging markets including negative and mixed signs in some specifications.

### Tail risk in bank lending — setup and variables
- Specification (equation (17)) models the τth percentile of real credit growth (annualized) between quarter t and t+h.
- Vulnerabilities Vit include:
  - credit-to-GDP gap;
  - deviation of regulatory capital-to-asset ratio from country-specific trend;
  - return on assets;
  - non-performing loans (NPLs) ratio;
  - banks’ government debt exposure (share of domestic sovereign bond holdings in banks’ total assets).
- Control variables Zit include real GDP growth and domestic Financial Conditions Index (FCI); additional macro and financial variables (house price growth, stock market changes, broad money-to-GDP, US Fed Funds rate, policy rate, yield-curve slope, bank lending rate, nominal exchange rate changes) are captured through FCI and time effects.

### Text-based uncertainty indicator (banks’ earnings calls)
- The chapter constructs a text-based measure of uncertainty from banks’ earnings calls.
- Key empirical relationships shown:
  - The text-based uncertainty indicator is not strongly correlated with other measures of macroeconomic uncertainty.
  - The text-based uncertainty indicator is negatively correlated with real credit growth.

*Source: Chapter 2 (Online Annex 2.5) of the April 2021 GFSR (as provided in the content unit).*

### 1. Correlations between measures of uncertainty 2. Text-based bank-level uncertainty measure and real credit growth

### 1. Correlations between measures of uncertainty 2. Text-based bank-level uncertainty measure and real credit growth

### Measures and construction
- U_i,t includes four measures: the Economic Policy Uncertainty index (EPU), the Real Economic Uncertainty index (REU), dispersion of the forecast of one-year ahead real GDP growth (Forecast dispersion), and a text-based measure constructed using banks’ earnings call reports.
- Text-based measure construction:
  - Count sentences that contain uncertainty-related words in each bank’s earnings calls.
  - Scale the count by the number of sentences in earnings calls for each bank using the list of words provided by the Loughran-McDonald Master Dictionary (2024) (around 300 words that convey a sense of uncertainty).
  - At each time point, the country-level measure is a simple average of the bank-specific scores.
- Alternative text-based measure: constructed from the same earnings calls but using a narrow list of key words (three words: “uncertain”, “uncertainty”, “uncertainties”).
- Binscatter construction for country-level analysis: standardized text-based uncertainty is ordered and grouped into 25 bins following Cattaneo, Crump, Farrell and Feng (2024).

### Pairwise correlations (Panel 1)
- Correlation matrix (significance shown exactly as in source):
  - Forecast dispersion vs Forecast dispersion: 1.00
  - Forecast dispersion vs REU: 0.61***
  - Forecast dispersion vs EPU: 0.24***
  - Forecast dispersion vs Text-based: 0.02
  - REU vs REU: 1.00
  - REU vs EPU: 0.37***
  - REU vs Text-based: 0.03
  - EPU vs EPU: 1.00
  - EPU vs Text-based: -0.05
  - Text-based vs Text-based: 1.00
  - Alternative text-based correlations:
    - Alternative text-based vs Forecast dispersion: 0.12***
    - Alternative text-based vs REU: 0.17***
    - Alternative text-based vs EPU: 0.04
    - Alternative text-based vs Text-based: 0.77***
- Significance legend reproduced from source: * p < 0.05, ** p < 0.01, *** p < 0.001

### Relationship between text-based uncertainty and real credit growth (Panel 2 and related findings)
- Binscatter result: standardized text-based uncertainty (25 bins) vs real credit growth (average quarterly annualized growth of real credit over the next four quarters); the fitted line has a slope of -0.38 (statistically significant at the 1 percent level).
- The text-based bank-level measure has little correlation with other indicators (as shown in the correlation matrix) but is negatively correlated with credit growth (Online Annex Figure 2.5.1, panel 2).
- Interpretation: uncertainty conveyed in banks’ earnings calls may reflect aspects of uncertainty not measured by other indicators and therefore can be an additional determinant of bank loan supply.

### Panel quantile regression evidence (equation (17) and robustness)
- Sample and period: quarterly data for a panel of 18 advanced economies and 13 emerging market economies from 2001 to 2023.
- Dependent variable: 10th percentile of the distribution of country-level real credit growth; real credit growth defined as the average quarterly annualized growth over the next 4 quarters.
- Main empirical findings:
  - Higher macroeconomic uncertainty is negatively associated with downside risks to future (four-quarter ahead) credit growth across measures of uncertainty.
  - When the four measures of uncertainty are included together (col. 5), the coefficients on forecast dispersion, REU, and the text-based bank-level indicator are all negative and statistically significant, indicating they capture different useful aspects of uncertainty for forecasting tail risks to lending.
  - Covariates behave as expected: tighter financial conditions, larger credit-to-GDP gap, and higher banking system NPL ratios are associated with lower future credit growth; stronger banking system profitability and capital position are associated with higher future credit growth.
- Estimation methods and robustness:
  - Baseline estimated through a two-step procedure for panel quantile regressions following Canay (2011).
  - Results robust to alternative estimation method proposed by Powell (2022) (tends to generate tighter confidence intervals).
  - Results for three out of four measures of uncertainty (except the text-based uncertainty) are robust to Machado and Silva (2019) (their approach tends to generate larger confidence intervals compared with Canay (2011)).
  - Using total credit (BIS total credit data, covering banks and nonbanks) instead of bank credit produces similar results; total credit and bank credit correlation is 99.6 percent. Estimations using total credit generally point to larger and more persistent effects of uncertainty on tail risks of lending.

### Subsample and additional analyses
- Subsample results: Online Annex Figure 2.5.3 shows estimation results for advanced economies (AEs) and emerging market economies (EMs); main findings hold though significance of measures varies by group.
- Cross-border spillovers (summary of approach):
  - Extended GaR model (equation (18)) includes foreign uncertainty U_-i,t computed as weighted averages of uncertainty in major trading and financial partners (weights: trade or portfolio exposures normalized by country i GDP).
  - Results robust to alternative measures of uncertainty, alternative panel quantile estimators, total credit growth as dependent variable, additional controls (inflation, policy rate, unemployment), and estimation on pre-COVID period or excluding first three quarters of 2020.
- Role of buffers and policies (equation (19) and Figures 2.6.1–2.6.2):
  - International reserves-to-GDP used as High Buffer dummy (above median).
  - Interaction of foreign uncertainty with High Buffer shows international reserves help mitigate spillover effects from foreign uncertainty.
  - Substituting High Buffer with dummy for flexible exchange rate regimes (Ilzetzki and others (2021) coarse classification: value of 3 or higher on a scale from 1 to 6 indicates more flexible exchange rate regimes) or with a dummy for large external debt-to-GDP yields:
    - International buffers and flexible exchange rate regimes help mitigate spillovers.
    - Larger external debt amplifies spillovers.

*Italic: Sources: IMF staff calculations (Online Annex figures and tables as indicated).*

### References

### ch2annex - References

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*ch2annex - References (PDF chapter/section) — content provided as supplied.*

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