## 1. Case Study: 2018 Peru FSAP

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---

### I. Introduction: purpose and rationale
- Changes in the state of the financial system and the evolution of macrofinancial vulnerabilities provide signals about evolving risks to future economic activity.
- Macrofinancial vulnerabilities often increase in times of buoyant economic conditions when funding is widely available and risk measures are subdued.
- Tightening of financial conditions, particularly when macrofinancial vulnerabilities are elevated, pose significant downside risks to economic activity.
- Tracking financial conditions and macrofinancial vulnerabilities can inform policymakers about risks to future growth and form a basis for targeted preemptive action.
- The growth-at-risk (GaR) framework:
  - Draws attention to the entire growth distribution (downside and upside risks) rather than just point forecasts.
  - Provides a framework for analyzing key drivers of future GDP growth and their relative importance across the growth distribution and forecasting horizon.
  - Helps quantify the impact of systemic risk on future GDP growth, with potential guidance for macroprudential policy.
- Policymakers can use an entire distribution to minimize risks rather than optimize outcomes under central scenarios, verify whether central scenarios are too optimistic or pessimistic, and better communicate risks.

### II. Growth-at-Risk: conceptual underpinnings
- Theory and evidence:
  - Macrofinancial vulnerabilities grow when investment opportunities seem abundant and financing is easily and cheaply available.
  - Recessions accompanied by financial crises are typically much more severe and protracted than ordinary recessions.
- Mechanisms of buildup:
  - Ease of borrowing and high asset prices reduce incentives to manage liquidity and solvency risks.
  - Perceptions of high investment returns and improved collateral quality incentivize increased leverage.
  - Booming asset prices and low volatility boost solvency, lending capacity, and risk appetite of financial intermediaries.
  - Accumulation of macrofinancial vulnerabilities: increased leverage, maturity and financial mismatches, growing indebtedness, reduced debt servicing capacity, and balance sheet weaknesses.
- Amplification of shocks:
  - Deleveraging and balance sheet corrections can clog financial intermediation and undermine growth for an extended period.
  - Even small negative shocks can cause significant adjustments when vulnerabilities are elevated.
  - Defaults transmit pressure to lenders’ profits and balance sheets, rising volatility, falling asset prices, and widening risk spreads constrain lenders, prompting deleveraging and asset liquidation.
  - Concerns about access to funds can further reduce risk-bearing capacity.
  - Highly leveraged firms and households may face financial constraints.
- Empirical literature:
  - Financial conditions and asset prices can improve point forecasts of future output.
  - Corporate bond spreads and volatility measures provide predictive information about investment returns, profitability, credit worthiness, and output contractions.
- GaR emphasis:
  - Asset prices tend to be more informative about downside risks to growth in the short term; credit aggregates (e.g., corporate and household leverage) more robustly signal downside risks in the medium term.
  - GaR corresponds to the probability of future real GDP growth falling below a prespecified threshold.

### III. Empirical approach: quantile regressions and distribution fitting
- Methodology:
  - Use quantile regression approach to establish relationships between future GDP growth and macrofinancial conditions.
  - Fit a parametric distribution using estimated growth quantiles (skewed t-distribution).
- Advantages:
  - Captures nonlinear interaction between shocks, financial conditions, and outcomes.
  - Produces density forecasts that quantify both upside and downside risks and enable definition of risk tolerance in GDP growth terms.
  - Parsimonious, reduced-form framework to analyze macrofinancial linkages and estimate relative importance of key drivers across growth quantiles and horizons.
- Limitations:
  - Reduced-form, not structural—cannot ascertain causal links; most appropriate for comparative statics analysis.

### IV. Variable classification: three partitions for GaR analysis
- Three partitions:
  - Financial conditions:
    - Capture price of risk embedded in asset prices, ease of financing, cost of funding, and degree of financial stress; constructed using price-based financial market indicators.
  - Macrofinancial vulnerabilities:
    - Reflect macrofinancial imbalances and sectoral balance sheet weaknesses beyond simple leverage metrics; candidates include measures of indebtedness, debt-servicing, maturity and foreign-exchange mismatches.
  - Other factors:
    - Include determinants likely to influence future growth such as external demand and commodity prices; can reflect country-specific Risk Assessment Matrix (RAM) risks.
- Note:
  - Partitions could be interrelated and mutually reinforcing; exposition focuses on three partitions without modeling interactions.

### V. Application in IMF bilateral macrofinancial surveillance
- Timeline and adoption:
  - Fund began using GaR in macrofinancial surveillance in 2017.
  - April 2017 GFSR introduced GaR concept; October 2017 GFSR provided analytical underpinnings.
  - The 2018 Peru FSAP pioneered GaR use in bilateral surveillance.
  - Several Article IV consultations (including Canada, Panama, Portugal, and Singapore) have included GaR.
- Role in surveillance:
  - GaR informs assessments of tail risks to growth based on prevailing macrofinancial conditions and supports scenario analysis.

### GaR applications and objectives (Box 3 summary)
- Objectives:
  - Identify main risk factors to future growth using partitions: (1) financial conditions (domestic price of risk); (2) macrofinancial vulnerabilities (leverage metrics); (3) other factors (external conditions).
  - Assess relative importance of variables across entire future growth distribution and across forecasting horizons.
  - Assess likelihood of economic contraction or plausibility of adverse scenarios as early warning indicators to inform policy and stress-test design.
- External factors:
  - External factors (e.g., China’s growth and commodity prices) can disproportionately influence downside risks in some cases.

### Case study — 2018 Peru FSAP: GaR implementation and findings
- Purpose and inputs:
  - GaR first introduced in bilateral surveillance to determine and prioritize groups of macrofinancial variables based on impact on future GDP growth.
  - Peru’s GaR estimation incorporated almost 30 macroeconomic and financial variables.
  - Variables partitioned into: (1) domestic “price of risk” (spreads and volatility variables); (2) “leverage” (credit growth, credit-to-GDP ratio, bond market capitalization); (3) “external conditions” (China’s growth and commodity prices, among others).
- Key findings:
  - External conditions, leverage, and the price of risk were major factors influencing tail risks to future GDP growth.
  - External conditions were nearly twice as likely to lead to tail outcomes for GDP growth compared with other partitions.
- Stress-testing application:
  - Baseline and adverse scenarios spanned three-year horizons.
  - Adverse scenario envisioned annual real GDP growth shocks (relative to the baseline) of -3.6 percent, -5.1 percent, and -0.9 percent, respectively over the three-year scenario.
  - The likelihood of the adverse GDP growth of -1.2 percent (corresponding to a 5.1 percent deviation from the baseline) in the second year is estimated to be 4.2 percent.

### Case study — 2018 Article IV Consultation with Portugal: GaR insights
- Context and partitions:
  - Portugal’s variables partitioned into: (1) price of risk (interest rates, spreads, asset price returns); (2) credit aggregates (ratios and growth rates of credit); (3) external conditions (VIX, oil prices, euro area growth excluding Portugal).
- Key findings:
  - Quantile regressions reveal nonlinear relationships with asymmetries in output response.
  - Price of risk provides strong near-term signals for downside risks and is more informative at tails than at the median.
  - Price of risk becomes uninformative over longer horizons; credit aggregates forecast downside risks well over the medium term.
  - Conclusion: downside risks to Portugal’s growth outlook appeared contained in the near term, but medium-term vulnerabilities persisted due to elevated leverage and potential repricing of risk.

### Case study — 2018 Article IV Consultation with Singapore: GaR application and results
- Model and inputs:
  - Country-specific FCI summarized 17 financial variables and was used to derive the one-year-ahead growth distribution; model augmented by housing market indicators and China’s growth.
- Historical behavior and GaR results:
  - External financial conditions, leverage-based indicators, and domestic price-based indicators explain most FCI fluctuations; major crises are reflected by sharp FCI tightenings.
  - GaR suggested reduced tail risks in 2018 compared to 2017:
    - The 5 percent GaR improved from -2 percent at end-2017 to -0.7 at end-2018.
    - The probability of recession declined from about 15 percent in 2017 to 8 percent in 2018, below its historical average.
    - The historical average is about 12 percent (average across three models including FCI, residential house prices, and China’s real GDP growth).

### Practical guidance on conducting GaR analysis (three main steps)
- Step 1: Select relevant macrofinancial variables and group them into partitions (typical three partitions: financial conditions; macrofinancial vulnerabilities; other factors). Partition construction methods include PCA; PCA factor loadings indicate relative importance of variables.
- Step 2: Run quantile regressions to establish the relationship between prevailing macrofinancial conditions and future GDP growth.
- Step 3: Derive the conditional distribution of future GDP growth and use it for scenario analysis and early warning indicators.

### Guidance on partition content and country tailoring
- Financial conditions partition aims to capture:
  - price-of-risk metrics: term premiums; interbank spreads; corporate bond spreads; sovereign bond yield spreads; bond returns and return volatility; equity returns and volatility.
  - ease of obtaining financing: bank lending standards; house price growth; real long-term interest rates.
  - cost of funding: cost of U.S. dollar funding.
  - degree of financial stress: VIX; foreign exchange market pressures; probability of default of financial institutions (CDS spreads).
- Country-specific considerations:
  - Advanced economies: price of risk in asset prices is informative.
  - Emerging markets: cost of U.S. dollar funding and FX pressures may be important.
  - Bank-dominated systems: bank lending rates and lending standards matter.
  - Large mortgage-debt economies: house prices matter.
  - Small open economies: inclusion of a global FCI may be warranted.
- Caveats:
  - GaR analysis can be sensitive to variable choice and methodology; partitions may not be uncorrelated; data quality and availability materially affect results.

### Constructing a Financial Conditions Partition (Box 4 summary)
- Objective: capture four concepts—(1) the price of risk; (2) the ease of obtaining financing; (3) the cost of funding; (4) global financial conditions.
- Variable composition highlights:
  - Price of risk: interbank spreads; term premiums; bond returns and return volatility; equity returns and volatility.
  - Ease of obtaining financing: bank lending standards; house price growth.
  - Cost of funding proxied by real long-term interest rates.
  - Global financial conditions captured by Global FCI (first principal component of country-level FCIs).
- Influence of Global FCI:
  - Inclusion changes profile of the partition; Global FCI, equity and bond return volatility, and lending standards appear to be main drivers.
- Methodological note:
  - PCA used to determine relative importance via factor loadings.

### Macrofinancial vulnerabilities: scope, indicators, and aggregation
- Scope:
  - Capture macrofinancial imbalances and sectoral balance sheet weaknesses; conceptually broader than credit aggregates alone.
- Illustrative indicators (non-exhaustive):
  - Credit boom-bust: Credit-to-GDP gap; Credit growth.
  - Housing: House prices relative to fundamentals; House price growth; Growth of construction activity; Housing inventory; Sales to new listings; Growth of residential mortgage.
  - External imbalances: External debt or net foreign liabilities; Current account deficit; External financing need; External financing gap.
  - Borrowers’ balance sheets (Corporate, Household, Government): Leverage metrics; debt servicing capacity; indebtedness measures; currency mismatch; fiscal financing need.
  - Financial sector balance sheet weaknesses — Bank indicators: capital adequacy ratios; equity to assets; liquidity and funding metrics; profitability measures.
- Aggregation approaches:
  - PCA and simple aggregation/standardization can yield different time series patterns; PCA factor loadings can identify main drivers (household, corporate, credit gap).

### “Other factors” partition and alignment
- Composition example for small, open advanced economy:
  - U.S. growth; China’s growth; Commodity prices (energy and non-energy).
- PCA factor loadings in example suggest commodity prices more important than trading-partner activity.
- Caveat:
  - Ensure forecasting horizons aligned between future GDP growth and other factors to avoid spurious correlations.

### Quantile regression context and technical parameters
- Quantiles explicitly referenced: 10th, 25th, 50th, 75th, and 90th percentiles.
- Forecasting horizons:
  - GaR capable up to 12 quarters ahead in many countries.
  - Examples focus on h=4 and h=8 (4 and 8 quarters ahead).
- Quantile regression specification (for horizons ℎ ∈{1,...,12}):
  - y_{t+h|t}^q = α^q + β1^q X1,t + β2^q X2,t + β3^q X3,t + ε_{t+h|t}^q
  - q ∈ {0.1,0.25, 0.5, 0.75 ,0.9}; X1,t, X2,t, X3,t are partitions; β_j^q capture linkages at different growth distribution points.
- Parametric fit:
  - Use t-skew distribution (Azzalini and Capitanio 2003) characterized by location, degree of freedom, scale, and skewness.
  - Estimate t-skew parameters by minimizing squared distance between empirical quantiles and t-skew quantiles.
  - Optionally constrain location (mode) to align distribution with a country economist’s point forecast.

### Scenario analysis and tool features
- Scenario exercises:
  - Static comparative-static exercises recompute conditional quantiles using shocked partitions X~_j,t = X_j,t * (1 + shock) with baseline beta coefficients.
  - Generate new t-skew distribution from counterfactual quantiles; shocks to individual variables within partitions are possible.
  - Multiple correlated shocks can be considered given user-provided covariance structures.
- Example impacts:
  - Tighter global financial conditions reduce average future growth and change distribution skewness and tails.
  - Under a tightened-conditions scenario, probability of an economic contraction increases to 18 percent from 8 percent.
- Excel-based GaR tool capabilities:
  1. compute country-specific FCIs and estimate tailored partitions;
  2. rank variables by informational content;
  3. estimate quantile regression coefficients;
  4. generate fitted future growth distributions (can be centered on point forecasts);
  5. facilitate scenario analysis.

### Selected empirical outputs and illustrative statistics (Box 8)
- Baseline distribution mode: 2.1 percent.
  - GaR at 5 percent is −0.7 (5 percent chance that real GDP over the next 4 quarters will fall by at least 0.7 percent).
- Alternative optimistic distribution mode: 4.1 percent (2 percentage points above baseline):
  - Likelihood of real GDP growth being below 4.1 percent is 75 percent.
  - Distribution negatively skewed under optimistic mode, signaling higher downside risks.
- Time evolution of GaR:
  - Before the global financial crisis, GaR at 5 percent was about 0.4 percent.
  - Postcrisis, GaR at 5 percent declined to about −1 percent.
  - Postcrisis risks to growth have remained elevated.
- Frequency statement:
  - Such an adverse scenario is expected to occur "once every twenty years on average."

### GaR framework: role, strengths, limitations, and extensions
- Role and strengths:
  - GaR-based fan charts are conditional on current macrofinancial conditions, potentially asymmetric, and allow for fat-tailed growth distributions.
  - GaR quantifies likelihood of future GDP growth outcomes and provides alternative benchmarks for adverse scenarios.
  - GaR can account for elevated macrofinancial vulnerabilities increasing likelihood of severe scenarios.
- Limitations:
  - Not a structural model; cannot make causal inferences.
  - Data preconditions (length, breadth, cyclical variation) required for robust GaR analysis.
  - Sensitivity to variable choice, partitioning, and methodology; partitions may be correlated.
- Extensions and future work:
  - Investigate GaR’s term structure and intertemporal tradeoffs for macroprudential policy.
  - Extend GaR to other variables or multivariate "at-risk" frameworks (growth, financial conditions, bank capital).
  - Use GaR to quantify severity of systemic risk and to support macroprudential policy implementation.

*Source: Excerpt from “1. Case Study: 2018 Peru FSAP” (IMF working paper PDF content provided).*

### 1. Case Study: 2018 Peru FSAP _________________________________________________________ 11

### 1. Case Study: 2018 Peru FSAP

### I. Introduction: purpose and rationale
- Changes in the state of the financial system and the evolution of macrofinancial vulnerabilities provide signals about evolving risks to future economic activity.
- Macrofinancial vulnerabilities often increase in times of buoyant economic conditions when funding is widely available and risk measures are subdued.
- Tightening of financial conditions, particularly when macrofinancial vulnerabilities are elevated, pose significant downside risks to economic activity.
- Tracking financial conditions and macrofinancial vulnerabilities can inform policymakers about risks to future growth and form a basis for targeted preemptive action.
- The growth-at-risk (GaR) framework links macrofinancial conditions to the probability distribution of future real GDP growth and offers features that enhance macrofinancial surveillance:
  - Draws attention to the entire growth distribution (downside and upside risks) rather than just point forecasts.
  - Provides a framework for analyzing key drivers of future GDP growth and their relative importance across the growth distribution and forecasting horizon.
  - Helps quantify the impact of systemic risk on future GDP growth, with potential guidance for macroprudential policy.
- Policymakers can use an entire distribution to minimize risks rather than optimize outcomes under central scenarios, verify whether central scenarios are too optimistic or pessimistic, and better communicate risks.

### II. Growth-at-Risk: conceptual underpinnings
- Theory and evidence:
  - Macrofinancial vulnerabilities grow when investment opportunities seem abundant and financing is easily and cheaply available.
  - Once vulnerabilities are high, they can amplify and prolong the impact of shocks on economic activity.
  - Recessions accompanied by financial crises are typically much more severe and protracted than ordinary recessions (IMF, 2008; Cardarelli, Elekdag, and Lall, 2011; Claessens, Kose, and Terrones, 2012).
- Mechanisms of buildup:
  - Ease of borrowing and high asset prices reduce incentives to manage liquidity and solvency risks.
  - Perceptions of high investment returns and improved collateral quality incentivize increased leverage (Bianchi 2011; Korinek and Simsek 2016).
  - Booming asset prices and low volatility boost solvency, lending capacity, and risk appetite of financial intermediaries (Brunnermeier and Pedersen 2009; Adrian, Moench, and Shin 2010; Adrian and Shin 2014).
  - Accumulation of macrofinancial vulnerabilities: increased leverage, maturity and financial mismatches, growing indebtedness, reduced debt servicing capacity, and balance sheet weaknesses.
- Amplification of shocks:
  - Deleveraging and balance sheet corrections can clog financial intermediation and undermine growth for an extended period (He and Krishnamurthy 2013; Brunnermeier and Sannikov 2014).
  - Even small negative shocks can cause significant adjustments when vulnerabilities are elevated.
  - Defaults transmit pressure to lenders’ profits and balance sheets, rising volatility, falling asset prices, and widening risk spreads constrain lenders, prompting deleveraging and asset liquidation.
  - Concerns about access to funds can further reduce risk-bearing capacity (Gertler, Kiyotaki, and Prestipino 2017).
  - Highly leveraged firms and households may face financial constraints (Kiyotaki and Moore 1997).
- Empirical literature:
  - Financial conditions and asset prices can improve point forecasts of future output (Laurent 1988; Estrella and Hardouvelis 1991; Bernanke and Blinder 1992; Estrella and Mishkin 1998; Ang, Piazzesi, and Wei 2006).
  - Corporate bond spreads and volatility measures provide predictive information about investment returns, profitability, credit worthiness, and output contractions (Philippon 2009; Gilchrist and Zakrajšek 2012; Campbell and others 2001).
- GaR goes beyond point forecasts by using financial conditions and macrofinancial vulnerabilities to forecast the entire distribution of GDP growth.
  - Asset prices tend to be more informative about downside risks to growth in the short term; credit aggregates (e.g., corporate and household leverage) more robustly signal downside risks in the medium term (IMF 2017b).
  - GaR corresponds to the probability of future real GDP growth falling below a prespecified threshold; formally defined in Adrian and others (2018) notation.

### III. Empirical approach: quantile regressions and distribution fitting
- GaR centers on empirically forecasting the probability distribution of future GDP growth allowing for nonlinearity and state dependence.
- Methodology:
  - Use quantile regression approach to establish relationships between future GDP growth and macrofinancial conditions.
  - Fit a parametric distribution using estimated growth quantiles (technique advocated by Adrian, Boyarchenko, and Giannone).
- Advantages:
  - Captures nonlinear interaction between shocks, financial conditions, and outcomes.
  - Produces density forecasts that quantify both upside and downside risks and enable definition of risk tolerance in GDP growth terms (e.g., probability of negative GDP growth one-year ahead given current environment).
  - Parsimonious, reduced-form framework to analyze macrofinancial linkages and estimate relative importance of key drivers across growth quantiles and horizons.
- Limitations:
  - Reduced-form, not structural—cannot ascertain causal links; most appropriate for comparative statics analysis.

### IV. Variable classification: three partitions for GaR analysis
- The paper generalizes variable classification into three “partitions” of related macrofinancial variables:
  - Financial conditions:
    - Aim: capture price of risk embedded in asset prices, ease of financing, cost of funding, and degree of financial stress.
    - Constructed using price-based financial market indicators; akin to many FCIs used in literature.
  - Macrofinancial vulnerabilities:
    - Reflect macrofinancial imbalances and sectoral balance sheet weaknesses beyond simple leverage metrics.
    - Candidates: measures of indebtedness, debt-servicing, maturity and foreign-exchange mismatches; capture deterioration in corporate and household balance sheets, construction booms, house price bubbles, dependence on foreign-currency funding.
  - Other factors:
    - Include other determinants likely to influence future growth, such as external demand and commodity prices.
    - Can reflect risks summarized in country-specific Risk Assessment Matrices (RAMs) not captured by the other partitions.
- Interaction:
  - Partitions could be interrelated and mutually reinforcing; for exposition the paper focuses on three partitions without modeling interactions.

### V. Application in IMF bilateral macrofinancial surveillance
- Timeline and adoption:
  - The Fund began using the GaR framework in macrofinancial surveillance in 2017.
  - April 2017 GFSR introduced GaR concept (IMF 2017a); October 2017 GFSR provided analytical underpinnings (IMF 2017b).
  - The 2018 Peru Financial Sector Assessment Program (FSAP) pioneered GaR use in bilateral surveillance.
  - A number of Article IV consultations, including Canada, Panama, Portugal, and Singapore, have included GaR to assess risks to the economic outlook.
- Common themes across bilateral reports:
  - GaR has been used to inform bilateral surveillance reports such as the 2018 Peru FSAP and 2018 Article IV consultations with Portugal and Singapore.
  - GaR analysis informs assessments of tail risks to growth based on prevailing macrofinancial conditions and supports scenario analysis in surveillance work.

*Source: Excerpt from “1. Case Study: 2018 Peru FSAP” (IMF working paper PDF content provided).*

### Box 3, respectively, and can be summarized as follows:

### wpiea2019036 - Box 3, respectively, and can be summarized as follows:

### GaR applications and objectives
- GaR was used to identify the main risk factors to future growth based on a comprehensive set of macrofinancial variables grouped into three broad partitions:
  - (1) financial conditions—usually the domestic price of risk;
  - (2) macrofinancial vulnerabilities—typically emphasizing leverage metrics;
  - (3) other factors—giving prominence to external conditions.
- External factors (for example, China’s growth and commodity price fluctuations) were identified as disproportionately influencing downside risks to future growth in some cases (Peru, Singapore).
- GaR was used to:
  - identify the relative importance of selected macrofinancial variables across the entire future growth distribution and across multiple forecasting horizons;
  - assess the likelihood of an economic contraction or the plausibility of an adverse scenario as an early warning indicator to inform policy and stress-test scenario design.

### Case study — 2018 Peru FSAP: GaR implementation and findings
- Purpose and inputs:
  - GaR was first introduced in bilateral surveillance during the 2018 Peru FSAP to determine and prioritize groups of macrofinancial variables based on their impact on future GDP growth.
  - Peru’s GaR estimation incorporated almost 30 macroeconomic and financial variables.
  - Variables were partitioned into three categories: (1) domestic “price of risk” (spreads and volatility variables); (2) “leverage” (credit growth, credit-to-GDP ratio, bond market capitalization); (3) “external conditions” (China’s growth and commodity prices, among others).
- Key findings:
  - External conditions, leverage, and the price of risk were identified as major factors influencing tail risks to future GDP growth.
  - External conditions were nearly twice as likely to lead to tail outcomes for GDP growth compared with other partitions.
- Stress-testing application:
  - Baseline and adverse scenarios spanned three-year horizons.
  - The adverse scenario envisioned annual real GDP growth shocks (relative to the baseline) of -3.6 percent, -5.1 percent, and -0.9 percent, respectively over the three-year scenario.
  - The likelihood of the adverse GDP growth of -1.2 percent (corresponding to a 5.1 percent deviation from the baseline) in the second year is estimated to be 4.2 percent, indicating the scenario is harsh, yet plausible.

### Case study — 2018 Article IV Consultation with Portugal: GaR insights
- Context:
  - Following a period of lackluster recovery, Portugal’s real GDP growth gained strength in 2017; the baseline assumed favorable medium-term prospects, but low interest rates and compressed risk premia posed amplification risks via leverage.
- Partitions and variables:
  - Macrofinancial variables partitioned into: (1) price of risk (interest rates, spreads, asset price returns); (2) credit aggregates (ratios and growth rates of credit); (3) external conditions (VIX, oil prices, euro area growth excluding Portugal).
- Key findings:
  - Quantile regressions reveal a nonlinear relationship between macrofinancial conditions and future GDP growth with asymmetries in the output response.
  - The price of risk provides strong near-term signals for downside risks to growth; its impact is stronger at the tails of the growth distribution than around the median.
  - The price of risk becomes uninformative over longer horizons; credit aggregates forecast downside risks well over the medium term.
  - Conclusion: downside risks to Portugal’s growth outlook appeared contained in the near term, but medium-term vulnerabilities persisted due to elevated leverage and potential repricing of risk.

### Case study — 2018 Article IV Consultation with Singapore: GaR application and results
- Model and inputs:
  - A country-specific financial conditions index (FCI) summarized 17 financial variables (price-based, leverage-based, external, and other indicators) and was used to derive the one-year-ahead growth distribution.
  - The model was augmented by housing market indicators and China’s growth rate.
- Historical behavior:
  - External financial conditions, leverage-based indicators, and domestic price-based indicators explain most FCI fluctuations; major crises (Asian financial crisis 1997-98, global financial crisis 2007-09) are reflected by sharp FCI tightenings.
- Key GaR results:
  - GaR analysis suggested reduced tail risks in 2018 compared to 2017:
    - The 5 percent GaR improved from -2 percent at end-2017 to -0.7 at end-2018.
    - The probability of recession declined from about 15 percent in 2017 to 8 percent in 2018, below its historical average.
    - The historical average (dotted red line in the referenced panel) is about 12 percent (average across three models including FCI, residential house prices, and China’s real GDP growth).

### Practical guidance on conducting GaR analysis (three main steps)
- Step 1: Select relevant macrofinancial variables and group them into partitions.
  - Partitions help extract common trends and remove idiosyncratic noise, improving quantile regression quality.
  - Typical three partitions: (1) financial conditions; (2) macrofinancial vulnerabilities; (3) other factors (country-specific).
  - Partition construction methods include principal component analysis (PCA); PCA factor loadings indicate relative importance of variables within partitions.
  - Use of partitions reduces number of parameters and mitigates limited data challenges.
- Step 2: Run quantile regressions to establish the relationship between prevailing macrofinancial conditions and future GDP growth.
- Step 3: Derive the conditional distribution of future GDP growth and use it for scenario analysis and early warning indicators.

### Guidance on partition content and country tailoring
- Financial conditions partition aims to capture:
  - price of risks embedded in asset prices;
  - ease of obtaining financing;
  - cost of funding;
  - degree of financial stress.
- Illustrative variables for financial conditions include (non-exhaustive):
  - price-of-risk metrics: term premiums; interbank spreads; corporate bond spreads; sovereign bond yield spreads; bond returns and return volatility; equity returns and volatility.
  - ease of obtaining financing: bank lending standards; house price growth; real long-term interest rates (government bond yields, mortgage rates, prime business lending rates).
  - cost of funding: cost of U.S. dollar funding.
  - degree of financial stress: VIX; foreign exchange market pressures (exchange rates, foreign reserves, short-term interest rates); probability of default of financial institutions (CDS spreads or contingent claims analysis).
- Country-specific considerations:
  - Advanced economies: price of risk embedded in asset prices is informative.
  - Emerging market and developing economies: cost of U.S. dollar funding and foreign exchange market pressures may be important.
  - Bank-dominated systems: bank lending rates and lending standards matter.
  - Large mortgage-debt economies: house prices matter.
  - Small open economies: inclusion of a global FCI may be warranted.
- Caveats:
  - GaR analysis can be sensitive to variable choice and methodology.
  - Partitions may not be uncorrelated; additional partitions should be considered if variables exhibit distinctive dynamics.
  - Data quality and availability materially affect results.

*Source: IMF staff calculations and case material from the GaR framework applications described in the provided content.*

### Box 4. Constructing a Financial Conditions Partition

### Box 4. Constructing a Financial Conditions Partition

### Objective and conceptual coverage
- Purpose: example of selecting macrofinancial variables to construct a financial conditions partition for a small, open advanced economy.
- Partition designed to capture four underlying concepts:
  - (1) the price of risk
  - (2) the ease of obtaining financing
  - (3) the cost of funding
  - (4) global financial conditions

### Variable composition
- Price of risk comprises:
  - interbank spreads
  - term premiums
  - interbank spreads
  - bond returns
  - bond returns volatility
  - equity returns
  - equity returns volatility
- Ease of obtaining financing comprises:
  - bank lending standards
  - house price growth
- Cost of funding proxied by:
  - real long-term interest rates
- Global financial conditions captured using:
  - the global financial conditions index (Global FCI) used in IMF (2017b), defined as the first principal component of the country-level FCIs (capturing both the price of risk and leverage dynamics, among others)

### Influence of including Global FCI
- Inclusion of the global FCI changes the profile of the financial conditions partition:
  - Without the global FCI, the partition based on purely domestic indicators suggests slightly tighter financial conditions during the early 1990s, but a less abrupt tightening during the global financial crisis.
  - Differences are not stark, but estimated partitions should be carefully examined to ensure they reflect historical developments accurately.
- Global FCI, equity and bond return volatility, and lending standards appear to be the main drivers of domestic financial conditions.
- Relative importance of underlying variables is determined by PCA factor loadings.

### Methodological note
- PCA refers to principal component analysis.
- The Global FCI is the first principal component of country-level FCIs, per IMF (2017b).

---

### Macrofinancial vulnerabilities: scope and indicators
- Aim: capture macrofinancial imbalances and sectoral balance sheet weaknesses; indicators vary across countries.
- Conceptually broader than credit aggregates alone (such as credit growth and the credit-to-GDP gap).
- Potential sources of imbalances include:
  - credit boom-bust cycles
  - housing market imbalances
  - external sector imbalances
  - sectoral balance sheet weaknesses of corporates, households, and governments
  - balance sheet weaknesses of financial institutions, particularly banks

### Illustrative list of potential variables (conceptual categories)
- Macrofinancial imbalances indicators:
  - Credit boom-bust cycles:
    - Credit-to-GDP gap
    - Credit growth
  - Housing market imbalances:
    - House prices relative to fundamentals (income or rent)
    - House price growth
    - Growth of construction activity (such as construction investment, residential permit value, dwelling starts, dwelling under construction, and housing completion)
    - Housing inventory
    - Sales to new listings
    - Growth of residential mortgage
  - External imbalances:
    - External debt or net foreign liabilities
    - Current account deficit
    - External financing need; external financing gap
- Borrowers’ sectoral balance sheet weaknesses indicators:
  - Corporate:
    - Leverage: liabilities to assets
    - Debt servicing capacity: interest coverage ratios
    - Indebtedness: debt to GDP
    - Currency mismatch
  - Household:
    - Leverage: liabilities to assets
    - Debt servicing capacity: interest coverage ratios
    - Indebtedness: debt to GDP; debt to income
    - Currency mismatch
  - Government:
    - Fiscal financing need; fiscal financing gap
    - Indebtedness: debt to GDP
- Financial sector balance sheet weaknesses — Bank indicators:
  - Solvency and leverage: capital adequacy ratios; equity to assets
  - Liquidity and funding: short-term liabilities to liquid assets; stable funding to total funding
  - Profitability and viability: return on assets; return on equity

### Purpose and applications
- Indicators are typical for systemic risk monitoring and calibrating macroprudential policy (see IMF, 2014).
- GaR analysis can evaluate the severity of systemic risk attributable to increasing macrofinancial vulnerabilities and implications for growth.
- GaR framework is promising for quantifying intertemporal tradeoffs associated with tighter macroprudential policies (area for future research): a tighter stance could subdue short-term activity but lower medium-term risks via reduced macrofinancial vulnerabilities.

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### Illustration and aggregation approaches (Box 5 summary)
- Example macrofinancial vulnerabilities partition constructed from:
  - household sector vulnerabilities
  - corporate sector vulnerabilities
  - housing market imbalances
  - credit-to-GDP gap
- Two aggregation approaches:
  - principal component analysis (PCA)
  - simple aggregation and standardization of indicators
- Observation:
  - The two methodologies yield different time series patterns; corporate sector vulnerabilities can show starkly different dynamics (notably during the early 1990s).
  - Household sector appears to influence overall macrofinancial vulnerabilities partition the most.
  - PCA factor loadings indicate household and corporate sector aggregates and the credit gap are the most important drivers.

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### “Other factors” partition (Box 6 summary)
- Purpose: capture factors other than financial conditions and macrofinancial vulnerabilities that affect future growth.
- Example composition for a small, open advanced economy:
  - U.S. growth
  - China’s growth
  - Commodity prices (energy and non-energy)
- PCA factor loadings suggest:
  - Commodity prices appear more important than trading-partner economic activity for explaining future growth fluctuations.
- Important caveat:
  - Ensure forecasting horizons are properly aligned between future GDP growth and other factors; misalignment (e.g., using current values of trading-partner growth) could produce negative correlation and distort regression analysis.
- Commodity prices are synchronized with future real GDP growth in the example.

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### Quantile regression context and parameters (link to later steps)
- Quantile regressions estimate nonlinear relationships between explanatory partitions (financial conditions, macrofinancial vulnerabilities) and quantiles of future GDP growth.
- Quantiles referenced explicitly: 10th, 25th, 50th, 75th, and 90th percentiles.
- Forecasting horizons discussed:
  - GaR capable up to 12 quarters ahead in many countries.
  - Examples and figures focus on forecasting horizons h=4 and h=8 (4 and 8 quarters ahead).
- Interpretation examples:
  - Tight financial conditions can be negatively correlated with near-term growth (lower quantiles) but positively correlated at longer horizons (reversion to mean).
  - Elevated macrofinancial vulnerabilities are associated with downside risks across forecasting horizons.

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*Source: Authors’ estimates.*

### Appendix and Lafarguette (2019) for further details.

### wpiea2019036 - Appendix and Lafarguette (2019) for further details.

### GaR framework: role and strengths
- GaR-based fan charts are conditional on current macrofinancial conditions, potentially asymmetric, and allow for fat-tailed growth distributions.
- GaR quantifies the likelihood of future GDP growth and provides an alternative benchmark for evaluating the severity of adverse scenarios.
- GaR can account for existing macrofinancial vulnerabilities: "a more severe scenario will likely materialize when macrofinancial vulnerabilities are more elevated."
- GaR is not a structural model and should not be used to make causal inferences.
- Data preconditions (length, breadth, cyclical variation) are required for robust GaR analysis.

### Selected empirical outputs and illustrative statistics (Box 8)
- Baseline distribution with a mode of 2.1 percent:
  - GaR at 5 percent is −0.7, implying that there is a 5 percent chance that real GDP over the next 4 quarters will fall by at least 0.7 percent.
- Alternative optimistic distribution with mode of 4.1 percent (2 percentage points above the baseline):
  - The likelihood of real GDP growth being below 4.1 percent is 75 percent.
  - The distribution is negatively skewed under the optimistic mode, signaling higher downside risks.
- Time evolution of GaR:
  - Before the global financial crisis, the estimate of GaR at 5 percent was about 0.4 percent.
  - In the postcrisis period, GaR at 5 percent declined to about −1 percent.
  - Postcrisis risks to growth have remained elevated, reflecting growing macrofinancial vulnerabilities.
- Frequency statement for adverse scenarios:
  - Such an adverse scenario is expected to occur "once every twenty years on average."

### Scenario analysis and risk materialization (Section E and Box 9)
- The GaR framework enables scenario analysis by shocking underlying macrofinancial conditions and assessing changes in the entire future growth distribution.
- Comparative-statics caveat:
  - The current GaR framework is a parsimonious reduced-form forecasting system; scenario analysis is based on comparative statics considering uncorrelated shocks without feedback.
  - Multiple correlated shocks can be considered given user-provided covariance structures.
- Example (impact of tighter global financial conditions):
  - Tighter global financial conditions reduce average future growth (leftward shift in the peak) and change distribution shape (skewness and tails).
  - Under the tightened-conditions scenario, the probability of an economic contraction increases to 18 percent from 8 percent (the difference indicated by the shaded area between distributions).

### Practical tool features and applications
- An Excel-based GaR tool developed to support bilateral surveillance can:
  1. compute country-specific FCIs and estimate tailored partitions of macrofinancial variables,
  2. rank variables according to their informational content,
  3. estimate quantile regression coefficients (over selected forecasting horizons and quantiles),
  4. generate fitted future growth distributions (which can be centered on point forecasts in line with a country economist’s projections),
  5. facilitate scenario analysis.
- GaR analysis helps quantify probability, impact, and nature of risks to future growth and supports preemptive policy design and risk communication.

### Growth-at-Risk: Technical Appendix — empirical strategy overview
- Strategy: estimate future conditional growth distribution via a parsimonious approach involving (1) data reduction (partitioning), (2) quantile regressions, and (3) parametric fit to generate the future growth distribution.

Step 1: Partitioning macrofinancial variables
- Aggregate macrofinancial variables into economically meaningful groups ("partitions") such as the price of risk, macrofinancial vulnerabilities (for example, leverage), and other (external) factors.
- Partitions can be computed using principal component analysis (PCA) or linear discriminant analysis (LDA).
  - LDA links financial variables with GDP growth during dimensionality reduction.
  - PCA aggregates common trends among financial variables.
- Advantages of partitioning include improved forecasting via extraction of common trends and filtering idiosyncratic noise.

Step 2: Quantile regressions
- Dependent variable real GDP growth can be calculated as:
  - an annualized quarterly compound growth rate between period t and period t+h, where h is the horizon defined by the user; or
  - the year-on-year growth rate, h periods ahead.
- For horizons ℎ ∈{1,...,12} (quarters ahead), the following specification is estimated:
  - y_{t+h|t}^q = α^q + β1^q X1,t + β2^q X2,t + β3^q X3,t + ε_{t+h|t}^q
  - where y_{t+h|t}^q represents future growth h quarters ahead for quantile q, and q ∈ {0.1,0.25, 0.5, 0.75 ,0.9};
  - X1,t, X2,t, X3,t represent three partitions (price of risk, macrofinancial vulnerabilities, and other factors) with coefficients β1^q, β2^q, β3^q;
  - α^q is a constant term and ε_{t+h|t}^q the residual.
- Quantile regressions estimate conditional quantiles Q[y_{t+h|t}^q] and each coefficient β_j^q captures the linkage between partition X_j,t and future growth at different points of the growth distribution.
- Advantages of quantile regressions:
  - Best unbiased linear estimator for conditional quantiles under standard assumptions;
  - Robust to outliers;
  - Well-known asymptotic properties.

Step 3: Parametric fit of the conditional distribution of future growth
- Conditional quantiles are sufficient statistics for describing the conditional cumulative distribution function (CDF).
- A parametric t-skew fit (skewed version of the t-distribution as in Azzalini and Capitanio 2003) is used to derive the probability density function from the CDF.
- The t-skew distribution is characterized by four parameters: location, degree of freedom, scale, and skewness; it summarizes variance (volatility), skewness, and kurtosis.
- Estimation approach:
  - Obtain conditional quantiles Q[y_{t+h|t}^q] from quantile regressions.
  - Estimate t-skew parameters (loc, df, scale, skew) by minimizing the distance between empirical quantiles and t-skew quantiles:
    - loc,scale,skew = argmin Σ_q { tsk.quantile(q,loc,df,scale,skew) − Q[y_{t+h|t}^q] }^2
  - Once estimated, derive the fitted t-skew CDF and PDF to facilitate GaR analysis.
- Constraining the location (mode):
  - The t-skew distribution can be fit by constraining the location (the mode) to align with a more accurate forecast or a country economist’s point forecast.
  - Imposing a mode different from the unconstrained mode forces adjustments in variance and skewness; e.g., an optimistic ad hoc mode greater than the unconstrained mode will result in inflated downside risks.

Scenario analysis (technical)
- Static comparative-static scenario exercises:
  - Recompute conditional quantiles using shocked partitions X~_j,t = X_j,t * (1 + shock).
  - Beta coefficients remain those from baseline regressions so scenarios are comparable.
  - Generate new t-skew distribution from counterfactual quantiles (with option for constrained or unconstrained modes).
  - Shocks to individual variables within partitions are also possible.

### Conclusion and policy relevance (Section V)
- GaR provides a basis for preemptive policies by quantifying macrofinancial risks to growth and by assessing the relative importance of macrofinancial factors impacting the full probability distribution of future GDP growth.
- GaR enables better communication of risks to growth to the public and can enrich Fund bilateral surveillance.
- Extensions and future work:
  - Investigate GaR’s term structure and intertemporal tradeoffs for macroprudential policy.
  - Extend GaR to other variables (asset prices, returns, valuation metrics) or multivariate "at-risk" frameworks (growth, financial conditions, bank capital).
  - Support for macroprudential policy implementation by quantifying the severity of systemic risk based on current macrofinancial vulnerabilities.

*Source: IMF authors’ calculations and technical appendix (Lafarguette 2019) as provided in the source document.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019036.pdf_