## 1. Estimated Coefficients on FCI, Credit Growth, and Credit Boom

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### Objective, scope, and data
- Objective: characterize the distribution of forecast real GDP growth conditional on financial conditions using a panel of advanced economies (AEs).
- Sample: panel of 11 AEs (Australia, Canada, Switzerland, Germany, Spain, France, Great Britain, Italy, Japan, Sweden, and the US) with data for most from 1973 to 2017; sample estimation periods start in 1975, 1980, or 1981 for most countries.
- Forecast horizon: one to twelve quarters; distributional focus on the median and the lower 5th percentile (growth-at-risk, GaR).
- Key data and summary statistics (N = 1600):
  - GDP growth: Mean 2.221, Std Dev 3.446, Median 2.454, 10th Percentile -1.607, 90th Percentile 5.932.
  - Inflation: Mean 3.565, Std Dev 3.425, Median 2.620, 10th Percentile 0.364, 90th Percentile 8.582.
  - FCI: Mean -0.011, Std Dev 1.038, Median 0.013, 10th Percentile -1.378, 90th Percentile 1.175.
  - Credit-to-GDP growth (8-quarter moving average): Mean 0.543, Std Dev 1.068, Median 0.450, 10th Percentile -0.663, 90th Percentile 1.831.
  - Credit boom indicator: Mean 0.079, Std Dev 0.269, Median 0.000.

### Methodology
- Estimation:
  - Panel quantile regression methods combined with local projections (Jorda, 2005) to track conditional distribution dynamics up to twelve quarters.
  - Report quantile estimates at the 5th, 50th, and 95th percentiles; map quantiles into a skewed t-distribution (Azzalini and Capitanio, 2003) to recover time-varying mean, volatility, skewness, and kurtosis.
  - Block-bootstrap inference with block widths considered 4, 6, and 10 quarters; reported results use block width 4 quarters; standard errors based on 10,000 bootstrap samples; bands represent 90 percent confidence intervals.
- Key conditioning variables (x_{i,t}):
  1. Current GDP growth, inflation, FCI, and a constant.
  2. Specification (1) plus private nonfinancial credit-to-GDP growth (measured over previous eight quarters).
  3. Specification (2) plus credit boom dummy (Credit boom_{i,t} = 1 if FCI_{i,t} in loosest 3 deciles of FCI_i and credit-to-GDP growth in highest decile of (credit-to-GDP)_i).
- FCI construction:
  - Country-specific FCIs estimated as an unobserved common factor using a TVP-FAVAR (Koop and Korobilis, 2014 combining Primiceri (2005) TVP-FAVAR and Doz, Giannone, and Reichlin (2011) dynamic factor model) from up to 17 price-based variables.
  - TVP-FAVAR advantages: dynamic interactions evolve over time; accommodates differing start dates for indicators.

### Main empirical findings — coefficients and GaR term structure
- FCI effects on the 5th percentile versus median:
  - Coefficients on FCI differ significantly between the 5th percentile and the median.
  - Near-term (h up to about 6): negative coefficients on FCI for the 5th percentile and median — looser financial conditions (lower FCI) raise expected growth and GaR.
  - Over the projection horizon: FCI coefficients increase and for the 5th percentile switch sign from negative to positive (reversal), indicating an intertemporal tradeoff.
- Selected exact coefficients (Model 3, 5th percentile; significance noted as in source):
  - FCI: h=2: -0.864***; h=4: -0.739***; h=6: -0.349**; h=8: -0.000; h=10: 0.233*; h=12: 0.236**.
  - Credit-to-GDP growth: h=2: -0.252; h=4: -0.419**; h=6: -0.705***; h=8: -0.705***; h=10: -0.535***; h=12: -0.457***.
  - Credit boom indicator: h=2: 0.158; h=4: -0.111; h=6: -2.252***; h=8: -2.030***; h=10: -1.039**; h=12: -0.264.
- Interpretation:
  - Looser initial financial conditions compress the lower tail (higher GaR) in the near-term but are associated with lower GaR (worse downside risk) in the medium term (after about quarter 8).
  - Rapid credit growth amplifies the medium-term deterioration in GaR when combined with loose FCI.

### Key quantitative magnitudes and examples
- GaR under Loose FCI with rapid credit growth:
  - Near-term GaR: about -0.5 percent.
  - Medium-term GaR: less than -2 percent (around h≈8), a swing of about 2.5 percentage points from near- to medium-term in examples.
- Expected growth differences:
  - Near-term expected growth from loose FCI with high credit growth is about 0.5 percentage points higher than expected growth associated with average initial FCI; this difference dissipates and becomes modestly negative after the first year while GaR declines much more sharply.
- Probabilities:
  - Probability GaR < 0: Loose FCI + credit boom rises to almost 20 percent in medium-term; Loose FCI without credit boom rises to about 9 percent.

### PDFs, asymmetry, and distributional dynamics
- PDFs fitted from quantile estimates using skewed-t:
  - Model 1 (loose FCI): tight distribution at h=4; left tail widens and becomes more left-skewed by h=8 and h=12.
  - Model 3 (with credit boom): tightens distribution at h=4 and widens it at h=8 — credit boom is an amplification channel.
- Time-series statistics (Model 3, h=4, averaged across countries):
  - Mean GaR: -1.22 percent.
  - Std Dev of GaR: 1.23.
  - Mean 95th percentile: 5.25 percent.
  - Std Dev of 95th percentile: 0.36.
- Finding: GaR is highly variable over time; upside (95th percentile) shows little variation — downside risks drive most distributional changes.

### Causality checks — Granular Instrumental Variable (GIV)
- GIV approach:
  - Instrument aggregate bank EDF index using GIV constructed from bank-level EDFs and market-cap shares following Gabaix and Koijen (2019); EDF replaces FCI in panel quantile regressions (model 1) for GIV analysis.
  - GIV sample: nine countries (France and Spain excluded) from 1999:Q4 to 2015:Q4; first-stage EDF on GIV: coefficient 0.439***, first-stage F-test reported as 29, Observations 567, R-squared 0.136.
- GIV results:
  - Instrumented EDF coefficients on the 5th percentile follow the same sign-reversal pattern over the horizon as FCI-based estimates.
  - Instrumented coefficients are larger in outer horizons than non-instrumented coefficients — consistent with a causal effect of financial conditions on GaR (evidence against attenuation bias).
  - Term-structure from GIV: low EDF group shows GaR declining to about -2 percent in medium-term in the GIV sample.

### Robustness checks and alternative specifications
- Alternative FCI (FP-FAVAR / PCA) in Appendix B:
  - PCA FCI produces qualitatively similar results; selected PCA coefficients for 5th percentile (horizons h=2..12) reported exactly:
    - PCA: -2.383*** (0.535), -2.321*** (0.589), -1.482*** (0.445), -0.290 (0.371), 0.169 (0.240), 0.363** (0.171).
    - Credit boom: 0.060 (0.436), -0.414 (0.478), -2.313*** (0.697), -2.136*** (0.544), -1.121*** (0.410), -0.407 (0.317).
- Alternative indicators:
  - Corporate bond spreads substituted for FCI yield similar patterns for the 5th percentile; FCI effects remain significant when corporate spreads included.
  - Equity return volatility and exchange-rate changes tested with less robust significance.
- Additional checks:
  - Adding lags (three-lag model) does not materially change GaR term structure (Appendix E).
  - Disaggregating credit (household vs business) does not show a single type driving results; business credit more likely driver of credit boom effect in this sample.
  - Controlling for monetary policy (US): intertemporal risk tradeoff for 5th percentile robust to adding Taylor rule residuals.
  - Excluding Global Financial Crisis (2005–2009): FCI coefficients remain negative and significant in near-term for 5th percentile; credit growth and credit boom coefficients remain negative and significant but smaller; left-tail skewness reduced (full sample skew = -0.761; excluding GFC skew = -0.272) but term-structure shape persists.

### Interpretation and mechanisms
- Mechanism: changes in financial conditions affect the price of risk and volatility via financial frictions and intermediary capital constraints, linking price of risk and volatility to credit supply.
- Economic intuition:
  - Loose initial financial conditions imply lower price of risk, higher predicted GDP growth, and a tighter growth distribution in the near-term.
  - Lower price of risk and low volatility encourage risk-taking and excess credit accumulation, increasing medium-term vulnerabilities and downside risk — consistent with the volatility paradox.
- Modeling implication: mean and variance of GDP growth are endogenous and covary out to twelve quarters; macro models should incorporate time-varying higher-order moments and endogenous volatility.

### Policy implications and recommendations
- Metric and coordination:
  - GaR provides a common metric for expressing financial stability risks across macroeconomic policymakers to promote coordination and accountability.
- Policy approach:
  - Macroprudential policies could aim to tighten financial conditions when conditional expected growth and GaR are relatively high to reduce endogenous risk-taking and future systemic risks.
  - Monetary policy faces tradeoffs between lower near-term risks to growth and greater medium-term risks from macrofinancial linkages; policymakers should weigh modest near-term benefits of looser conditions against larger medium-term increases in downside risk, especially with rapid credit growth.
- Need for structural analysis:
  - Structural models are needed to evaluate how alternative macroprudential policies could affect GaR and to quantify treatment effects.
- Welfare considerations:
  - Time-discounting may underweight high-cost large downside risks; severe recessions and banking crises produce persistent and large welfare losses; policy-tool constraints (zero-lower bound, QE limits, fiscal debt) increase the cost of future downside risks.

*Source: IMF staff estimates, "Estimated Coefficients on FCI, Credit Growth, and Credit Boom" (excerpt from wp18180).*

### 1. Estimated Coefficients on FCI, Credit Growth, and Credit Boom ........................................6

### 1. Estimated Coefficients on FCI, Credit Growth, and Credit Boom

### Objective and scope
- Objective: characterize the distribution of forecast real GDP growth conditional on financial conditions using a panel of advanced economies (AEs).
- Sample: panel of 11 AEs (Australia, Canada, Switzerland, Germany, Spain, France, Great Britain, Italy, Japan, Sweden, and the US) with data for most from 1973 to 2017.
- Forecast horizon: up to twelve quarters.
- Distributional focus: median and the lower 5th percentile of predicted real GDP growth (termed growth-at-risk, GaR).

### Methodology and variables
- Estimation methods:
  - Panel quantile regression methods.
  - Local projections to forecast out to twelve quarters.
  - Bootstrapping techniques for standard errors; bands represent 90 percent confidence intervals.
- Key explanatory variables:
  - Financial Conditions Index (FCI) constructed for each country using a vector autoregression model with time-varying parameters based on up to 17 price-based variables (including short-term interbank risk spreads, corporate bond spreads, volatility of stock returns). Higher FCI represents tighter financial conditions.
  - Credit-to-GDP growth.
  - Credit boom indicator: interaction of loosest three deciles of FCI and highest three deciles of credit-to-GDP growth.
  - Controls: initial output growth and inflation.
- Instrumental strategy for causality checks:
  - Granular instrumental variables (GIV) approach using an expected default frequency (EDF) index for financial firms in place of the FCI; panel limited to nine countries starting in 1999 due to bank-level data availability.

### Main empirical findings on coefficients and term structure of GaR
- FCI effects:
  - Estimated coefficients on FCI differ significantly for the 5th percentile versus the median of GDP growth.
  - Near-term: negative coefficients on FCI for both the 5th percentile and median indicate looser financial conditions (lower FCI) significantly boost expected growth and the GaR value.
  - Over projection horizon: coefficients increase, more pronounced for the 5th percentile than the median; the 5th percentile coefficients switch sign from negative to positive, indicating an intertemporal tradeoff associated with financial conditions.
- Credit-to-GDP growth effects:
  - Effects on the 5th percentile and median are similar in pattern over the forecast horizon and do not vary over time across quantiles.
- Credit boom interaction:
  - Credit boom indicator has a significant negative effect for the 5th percentile in quarter five and after; effect on the median does not vary.
  - Loose FCI combined with rapid credit growth yields GaR falling from about -0.5 percent in the near-term to less than -2 percent in the medium term.
  - When financial conditions are at “average” levels (middle four deciles of FCI), the near-term benefits of loose financial conditions fade more quickly than when comparing loose FCI to average FCI.
  - Loose FCI without rapid credit growth: GaR values fall over the projection horizon, but by less than when credit growth is rapid.
- Amplification channel:
  - High credit acts as an amplification channel of loose financial conditions, leading to greater downside risks.

### Quantitative comparisons and key magnitudes
- GaR for loose FCI when credit growth is rapid:
  - Near-term GaR: about -0.5 percent.
  - Medium-term GaR: less than -2 percent.
- Expected growth differences:
  - Near-term expected growth from loose FCI with high credit growth is about 0.5 percentage points higher than expected growth associated with average initial FCI; this difference dissipates and becomes modestly negative after the first year, while the decline in GaR is much sharper.
- Confidence and estimation details:
  - Estimates reported with 90 percent confidence intervals.
  - FCI and other variables measured in percent where applicable.

### Causality and robustness evidence
- GIV results:
  - Instrumented financial firm EDF index exhibits the same properties as the coefficients on FCI: coefficients switch signs over the projection horizon and produce a similar term structure for GaR, consistent with a causal effect of financial conditions on GaR.
  - GIV panel constrained to nine countries starting in 1999 due to data limits.
- Robustness checks and alternative specifications:
  - Using corporate bond spreads in place of FCI yields similar patterns for the 5th percentile; FCI effects remain significant when corporate bond spreads are included, indicating other FCI components matter.
  - FCI constructed with fixed parameters (instead of time-varying) does not materially change results (see Appendix B).
  - Adding lags of independent variables does not materially change results (Appendix E).
  - For the US, intertemporal risk tradeoff is robust to controlling for monetary policy.
  - Disaggregation of nonfinancial credit into business and household credit does not show one type driving results.
  - Sensitivity to global financial crisis: GaR estimates continue to show intertemporal tradeoff when credit growth is high, though the tradeoff is weaker when observations of significant negative growth are excluded; coefficients on FCI for median and 5th percentile remain significantly different, with 5th percentile more responsive to FCI.

### Interpretation and mechanisms
- Mechanism: changes in financial conditions affect the price of risk and volatility via financial frictions and intermediary capital constraints, tying the price of risk and volatility to the credit supply of financial intermediaries.
- Economic intuition:
  - Loose initial financial conditions imply lower price of risk, higher predicted GDP growth, and a tighter growth distribution in the near-term.
  - Low price of risk and low volatility can lead to greater risk-taking and higher vulnerabilities, increasing medium-term downside risks—consistent with the volatility paradox.
- Link to literature and models:
  - Results build on and extend Adrian, Boyarchenko, and Giannone (2019) to a cross-country panel and a twelve-quarter horizon.
  - Findings imply a violation of certainty equivalence: mean and variance of GDP growth are endogenous and covary out to twelve quarters.
  - Suggests macroeconomic models (including DSGE) should incorporate time-varying higher-order moments and endogenous volatility.
  - The intertemporal tradeoff has implications for macroprudential and monetary policy design and coordination.

### Policy implications and recommendations
- Metric and coordination:
  - GaR provides a common metric for expressing financial stability risks that can be used across macroeconomic policymakers to promote coordination and accountability.
- Policy approach:
  - Macroprudential policies could aim to tighten financial conditions when conditional expected growth and GaR are relatively high to reduce endogenous risk-taking and future systemic risks.
  - Monetary policy faces tradeoffs between lower near-term risks to growth and greater medium-term risks arising from macrofinancial linkages.
- Need for structural analysis:
  - Structural models are needed to evaluate how alternative macroprudential policies could be used to affect GaR and quantify treatment effects.

*Source: IMF staff estimates, "Estimated Coefficients on FCI, Credit Growth, and Credit Boom" (excerpt).*

### Section 3 presents the data and estimation of FCI. Section 4 presents estimates of the

### wp18180 - Section 3 presents the data and estimation of FCI. Section 4 presents estimates of the

### Modeling Growth-at-Risk (GaR): scope and horizons
- Projection horizon: one to twelve quarters.
- Panel of 11 AEs (countries with systemically important financial sectors and sufficient data).
- Conditional distributions estimated for:
  - Near-term horizons: one-to-four quarters ahead.
  - Medium-term horizons: five-to-twelve quarters ahead.
- GaR defined as the value-at-risk of future GDP growth: the lower 5th percentile of the GDP growth distribution.
- Methodology emphasizes forecasting effects of FCIs on GDP growth distribution, not necessarily causal effects (although empirical support for causal effects is provided elsewhere).

### Model estimation: panel quantile regressions and local projections
- Dependent variable: ∆y_{i,t+h} = annualized average growth rate of GDP for country i between quarters t and t+h.
- Conditioning vector: x_{i,t} includes current GDP growth, inflation rate, and financial variables (an index of financial conditions, private nonfinancial credit-to-GDP growth, and a credit boom indicator).
- Quantile regression estimator:
  - δ̂_α(h) = argmin ∑∑ (α·1_{∆y_{i,t+h}>x_{i,t}δ}|∆y_{i,t+h}−x_{i,t}δ| + (1−α)·1_{∆y_{i,t+h}<x_{i,t}δ}|∆y_{i,t+h}−x_{i,t}δ|) over t=1..T−h, i=1..N.
  - Predicted quantile: Q̂_{∆y_{i,t+h}|x_{i,t}}(α) = x_{i,t} δ̂_α(h).
- GaR implicit definition:
  - Pr(∆y_{i,t+h} ≤ GaR_{i,h}(α | Ω_t)) = α.
- Estimation approach:
  - Use Jorda’s (2005) local projection method to track conditional distribution dynamics and allow exploration of nonlinear interactions between FCIs and economic state.
  - Panel quantile regressions with country fixed effects; feasible because T ≫ N in the application.
- Inference and bootstrap:
  - Resample rows from the temporal dimension of each country, preserving cross-sectional panel structure.
  - Use block-bootstrap to account for temporal dependence (block widths considered: 4, 6 and 10 quarters).
  - Reported results use block width of 4 quarters (alternative specifications similar).
  - All standard error estimates based on 10,000 bootstrap samples.
- Reporting conventions:
  - Direct estimates from quantile regressions reported for the 5th, 50th, and 95th percentiles.
  - Also recover probability density functions by mapping quantile estimates into a skewed t-distribution to capture time-varying conditional mean, volatility, skewness, and kurtosis.

### Distribution smoothing: skewed t-distribution specification
- Use Azzalini and Capitanio (2003) skewed t-distribution to smooth quantile function:
  - f(y; μ, σ, θ, ν) = (2/σ) d_T((y−μ)/σ; ν) · T(θ (y−μ)/σ √((ν+1)/(ν + ((y−μ)/σ)^2)); ν+1),
    where d_T(·) and T(·) denote the PDF and CDF of the skewed t-distribution.
- Four parameters pin down location μ, scale σ, fatness ν, and shape θ.
- Rationale: flexible parametric form capturing first four moments.

### Financial conditions, credit measures, and model specifications
- Three model specifications for x_{i,t}:
  1. Current GDP growth, inflation, FCI, and a constant.
  2. Specification (1) plus private nonfinancial credit-to-GDP growth.
  3. Specification (2) plus a credit boom dummy (interaction of loose FCI and high credit-to-GDP growth).
- Credit boom dummy definition:
  - Credit boom_{i,t} = 1 if FCI_{i,t} is in the loosest 3 deciles of FCI_i and (credit-to-GDP growth)_{i,t} is in the highest decile of (credit-to-GDP)_i; = 0 otherwise.
- Credit-to-GDP growth measured over the previous eight quarters.
- Choice of loosest 3 deciles for FCI to simplify presentation; results robust to alternative thresholds (e.g., bottom two deciles or one-third).
- Economic interpretation and channels:
  - Negative coefficients on the credit boom indicator are consistent with financial conditions affecting output via macrofinancial linkages (vulnerabilities from indebted households and businesses when price of risk is low).
  - Loose FCIs can reduce price of risk, encourage risk-taking, and lead to excess credit accumulation, increasing future downside risk to GDP.
  - Potential medium-term reversal: lower near-term downside risk (higher GaR) but higher medium-term downside risk (lower GaR) after a large decline in net worth or aggregate demand.

### Data and construction of FCIs
- Quarterly data sources:
  - Real GDP growth and CPI (year-to-year percent change) for the 11 countries: International Financial Statistics (IFS).
  - Nonfinancial credit-to-GDP ratios: BIS (nonfinancial credit = household + business credit).
- FCI construction:
  - Up to 17 price-based variables used to construct country-specific FCIs.
  - Financial factors include: short-term funding spreads, corporate bond risk spreads, equity prices and volatility, banking sector expected default frequencies (EDFs), term spreads, sovereign spreads, equity implied volatilities, changes in real long-term rates, interest rate implied volatilities, house price returns, percent changes in equity market capitalization of financial sector to total market capitalization, equity trading volumes, expected default frequencies for banks, market capitalizations for equities, market capitalizations for bonds, domestic commodity price inflation rates, and foreign exchange movements.
  - FCIs estimated as an unobserved common factor using Koop and Korobilis (2014) methodology combining Primiceri’s (2005) TVP-FAVAR and Doz, Giannone, and Reichlin (2011) dynamic factor model.
  - Benefits of TVP-FAVAR approach:
    - Allows dynamic interactions between FCIs and macroeconomic conditions to evolve over time.
    - Accommodates differences in starting dates for financial indicators with flexible estimation.
- Data coverage and sample:
  - Data availability varies across countries; starting dates and start date for model estimation by country shown in Appendix A (not reproduced here).
  - Summary statistics presented in Table 1 as averages across countries and time.
  - Sample estimation periods start in 1975, 1980, or 1981 for most countries.
- Treatment of unbalanced data and alternatives:
  - Two alternative solutions mentioned (not implemented here):
    1. Replace missing observations with zeros and estimate FCI via fixed-parameter factor model (FP-FAVAR) — risks underweighting late-available series.
    2. Restrict FP-FAVAR estimation to period with all series available — would severely restrict sample.
  - Chosen TVP-FAVAR avoids imposing constant weights and accommodates changing relationships over time.

*Source: wp18180 - Section 3 presents the data and estimation of FCI. Section 4 presents estimates of the (IMF working paper content provided)*

### Appendix B compares our FCI using TVP-FAVAR and compares its results relative to a FP-FAVAR where

### wp18180 - Appendix B compares our FCI using TVP-FAVAR and compares its results relative to a FP-FAVAR where

### Summary statistics and sample
- Sample: 11 advanced economies (Australia, Canada, Switzerland, Germany, Spain, France, Great Britain, Italy, Japan, Sweden, and the US); start of estimation period is either 1975 or 1980 for most countries (specific starting dates in Appendix A).
- Sample length: roughly 40 years for most countries; sample for many variables covers 1973 to 2017.
- Table 1 key statistics (N = 1600):
  - GDP growth: Mean 2.221, Std Dev 3.446, Median 2.454, 10th Percentile -1.607, 90th Percentile 5.932.
  - Inflation: Mean 3.565, Std Dev 3.425, Median 2.620, 10th Percentile 0.364, 90th Percentile 8.582.
  - FCI: Mean -0.011, Std Dev 1.038, Median 0.013, 10th Percentile -1.378, 90th Percentile 1.175.
  - Credit-to-GDP growth (8-quarter moving average): Mean 0.543, Std Dev 1.068, Median 0.450, 10th Percentile -0.663, 90th Percentile 1.831.
  - Credit boom indicator: Mean 0.079, Std Dev 0.269, Median 0.000, 10th Percentile 0.000, 90th Percentile 0.000.
- Additional descriptive points:
  - Average annual real growth is 2.2 percent and inflation is 3.6 percent.
  - Average credit-to-GDP ratio is 1.34 and the eight-quarter moving average growth in the ratio is 0.54 percent.
  - Periods when credit boom = 1 are 8.0 percent of sample.
- Correlations (Table 2) of country FCI with selected components across 11 countries:
  - Interbank spread: Mean 0.57, Std dev 0.24, Median 0.58, Min -0.08, Max 0.84.
  - Corporate spread: Mean 0.66, Std dev 0.23, Median 0.69, Min 0.08, Max 0.89.
  - Term spread: Mean 0.19, Std dev 0.2, Median 0.24, Min -0.29, Max 0.39.
  - Equity return volatility: Mean 0.68, Std dev 0.09, Median 0.7, Min 0.48, Max 0.82.
- Regression evidence (not shown) indicates FCIs have significant coefficients for credit-to-GDP growth multiple quarters ahead.

### Empirical approach and objectives
- Focus: how financial conditions (FCI), credit growth, and credit booms affect the distribution of forecasted real GDP growth, emphasizing the lower 5th percentile (GaR) over horizons h = 1 to 12 quarters.
- Methods: panel quantile regressions with local projections; models control for current GDP growth and inflation; include country indicator variables; standard errors via block bootstrapping.
- Models:
  - Model 1: FCI, GDP growth, Inflation.
  - Model 2: Model 1 + Credit-to-GDP growth.
  - Model 3: Model 2 + Credit boom indicator (interaction of loosest three deciles of FCI and highest three deciles of credit-to-GDP growth).
- Interpretation: lower FCI values represent looser financial conditions; higher FCI represents tighter financial conditions. Credit-to-GDP growth measured over the past eight quarters. Sample: 11 AEs with data for most from 1973 to 2017. Significance levels: ***p<0.01, **p<0.05, *p<0.1.

### Quantile regression results — coefficients for the 5th percentile (Table 3)
- General pattern across models:
  - Coefficients on FCI are negative and significant in the near-term and become positive and significant in later quarters (reversal over forecast horizon).
  - Coefficients on GDP growth are positive and significant in the near-term and diminish toward zero after h=8.
  - Coefficients on Inflation are negative and significant in the near-term and diminish over time.
- Selected exact coefficients (with reported standard errors in parentheses in source):
  - Model 1, FCI on 5th percentile:
    - h=2: -0.908***; h=4: -0.757***; h=6: -0.329*; h=8: 0.247; h=10: 0.324***; h=12: 0.231***.
  - Model 2, Credit-to-GDP growth coefficients:
    - h=2: -0.252; h=4: -0.419**; h=6: -0.705***; h=8: -0.705***; h=10: -0.535***; h=12: -0.457***.
  - Model 3, Credit boom coefficients:
    - h=2: 0.158; h=4: -0.111; h=6: -2.252***; h=8: -2.030***; h=10: -1.039**; h=12: -0.264.
  - Model 3, FCI on 5th percentile:
    - h=2: -0.864***; h=4: -0.739***; h=6: -0.349**; h=8: -0.000; h=10: 0.233*; h=12: 0.236**.
- Key inference:
  - Looser FCI (lower FCI) associated with a higher 5th percentile (tighter predicted growth distribution) through quarter 6, then associated with a lower 5th percentile after quarter 8 — indicating greater medium-term downside risk.
  - Credit-to-GDP growth coefficients are negative and significant from h=4 onward.
  - Credit boom indicator is large and significant around h=6 to 10, indicating initial credit booms substantially increase downside risk in the second year.

### Time series of average GaR and distributional asymmetry
- Model 3, h=4 (averaged across countries):
  - Mean GaR for AEs over sample: -1.22 percent.
  - Standard deviation of GaR: 1.23.
  - Mean 95th percentile: 5.25 percent.
  - Standard deviation of 95th percentile: 0.36.
- Finding: GaR is highly variable over time while the 95th percentile shows little variation — greater variability arises from downside risk than upside risk.

### Probability density functions and GaR term structures
- PDFs fitted to skewed-t distribution from quantile estimates show:
  - Model 1 (loose FCI): tight distribution at h=4; left tail widens and becomes more left-skewed by h=8 and h=12; 5th percentile lower at h=8 and h=12 than at h=4.
  - Model 2 (includes credit-to-GDP growth): PDFs similar to Model 1; credit coefficients significant but magnitudes on predicted distribution modest in many periods.
  - Model 3 (with credit boom): credit boom significantly tightens distribution at h=4 and widens it at h=8 — amplification channel for rapid credit growth when FCIs are loose.
- GaR term-structure dynamics (from Figures and text):
  - Models 1 and 2: GaR values high in near term then fall sharply.
  - Model 3 with credit boom: negative effects on downside risk most evident starting in second year (h≈5–10).
  - Differences in GaR between credit boom and not boom are significantly different from zero for h from 5 to 11.
- Numerical example from term-structure discussion:
  - For Loose FCI with credit boom: GaR ≈ -0.5 percent in near-term, falls to less than -2.0 percent at around h=8 (a swing of about 2.5 percentage points).
- Distribution group comparisons (Model 3):
  - Near-term (h=4): mid and tight FCI groups have wider predicted GDP distributions than loose FCI.
  - Medium-term (h=12): mid and tight groups tighten while loose FCI widens, especially with credit boom.
- Probability of GaR < 0 (from footnote):
  - Loose FCI + credit boom: probability rises to almost 20 percent in medium-term.
  - Loose FCI without credit boom: probability rises to about 9 percent.

### Term structures by initial FCI groups and interpretation
- Term structures (Model 3) grouped by initial FCI (loosest decile, tightest decile, mid — middle four deciles) and by credit boom indicator:
  - Loose FCI + credit boom: GaR initially high then falls over horizon; sharper downward slope than without boom.
  - Mid FCI: GaR rises initially then levels out at about -0.5 percent in medium-term.
  - Tightest FCI decile: GaR very low in short-run (less than -6 percent) and converges in medium-term to about same GaR as moderate financial conditions.
- Statistical tests on differences:
  - Difference (Loose minus Mid) with credit boom: positive and statistically significant in near-term, negative and statistically significant in medium-term (90 percent confidence interval).
  - Difference (Loose minus Mid) without credit boom: positive and significant in short-term; falls over horizon with smaller magnitude of decline.
- Quantified amplification:
  - Under credit boom, difference in GaR about 2 percentage points lower at around h=8 to 10 than when no credit boom — credit growth amplifies medium-term downside risk.

### Predicted median growth vs GaR — intertemporal risk-return tradeoff
- Projected median (expected) growth:
  - Loose FCI yields slightly higher median growth in near-term versus mid FCI, but the additional expected growth declines modestly over projection horizon.
  - Mid FCI median is flat over horizon at slightly under 2 percent.
- Tradeoff summary:
  - Loose initial financial conditions deliver lower downside risk and modestly higher median growth in near-term, but GaR deteriorates substantially in medium-term while median growth differential declines only modestly — implying higher downside risks without compensating higher expected growth later.
- Differences plotted (Figure 9): decline in GaR steeper than decline in median for Loose vs Mid FCI, especially under credit boom.

### Granular Instrumental Variable (GIV) evidence on causality
- Motivation: address endogeneity (FCI reacting faster than real variables) by instrumenting a bank EDF index using GIV (Gabaix and Koijen, 2019).
- Data and sample for GIV:
  - Bank-level EDFs from Moody’s; market capitalization shares used to construct bank shares.
  - Earliest data: 1999:Q4; firms with insufficient data dropped; France and Spain excluded due to only two banks each.
  - Final GIV sample: nine countries with a minimum of six firm-level EDFs covering the period; estimation period 1999:Q4 to 2015:Q4 for GIV analysis.
- GIV construction steps (summary):
  - Construct aggregate bank EDF index via market-cap-weighted aggregation.
  - Apply PCA to individual series; retain factors with eigenvalues above unity.
  - Use idiosyncratic errors and market shares to construct GIV per Gabaix and Koijen equation (24).
  - Use GIV to instrument aggregate EDF in panel quantile regressions (EDF replaces FCI); focus on model 1 due to shorter EDF sample.
- First-stage result (Table 4):
  - EDF on GIV: coefficient 0.439*** (standard error -0.088 reported in source table); Observations 567; R-squared 0.136; Countries 9. First-stage F-test reported as 29.
- GIV results and interpretation:
  - Instrumented EDF coefficients on the 5th percentile follow same pattern as FCI-based estimates: looser financial conditions (lower EDF) compress downside risk in near-term and increase downside risk in medium-term.
  - Instrumented coefficients are larger in magnitude in outer horizons than non-instrumented coefficients — evidence against attenuation bias and consistent with a causal effect of financial conditions on GaR.
  - Term-structure of GaR from GIV (Figure 10b): low EDF group shows decrease in GaR over projection horizon, with GaR values declining to about -2 percent (compared to about -1 percent for loose FCI in longer sample) — differences may reflect sample/measure coverage.

### Robustness checks
- Alternative FCI construction:
  - Appendix B: alternative FCI using fixed parameters yields qualitatively similar effects.
- Alternative financial indicators:
  - Corporate bond spreads used in place of FCI produce the same qualitative pattern for the 5th percentile and median; adding corporate spreads does not materially change FCI coefficients.
  - Equity return volatility and exchange-rate changes tested; results less significant for median and 5th percentile than corporate bond spreads; FCI remains highly significant.
- Monetary policy controls (US-specific):
  - Re-estimated FCI for US controlling for current monetary policy (equations (B.1) and (B.2)); added Taylor rule residuals to quantile regressions.
  - Coefficients on adjusted FCI for the 5th percentile remain similar to those without policy residuals (reversal pattern persists); statistical significance affected modestly in single-country estimation.
- Credit disaggregation:
  - No significant difference in GaR term structure between household and business credit for panel; business credit more likely driver of credit boom effect in this sample.
- Adding lags:
  - Including multiple lags of independent variables slightly affects contemporaneous coefficients but does not materially change GaR term structure (Appendix E shows three-lag model similar to model 3 without lags).
- Excluding Global Financial Crisis (2005–2009):
  - Re-estimating model 3 excluding 2005–09: FCI coefficients remain negative and significant in near-term for 5th percentile and decline over medium-term; credit growth and credit boom coefficients remain negative and significant but smaller in magnitude.
  - Distributional effects: sample excluding GFC has less left-skew (=-.272) than full sample (=-.761); GaR declines over forecast horizon but less steeply when excluding GFC.
  - GaR probabilities: sample exclusion reduces magnitude of left-tail experiences but term-structure shape persists.
- Overall: robustness checks affirm main empirical findings that initial financial conditions and credit growth matter for future downside risks to GDP growth.

### Policy implications and interpretation
- Main empirical conclusion: financial conditions affect the lower tail (GaR) of forecasted GDP growth distribution, with signs reversing from short- to medium-term horizons — consistent with an intertemporal risk tradeoff.
- Implications for policymaking:
  - GaR can serve as a metric linking financial stability risks to macroeconomic outcomes and help calibrate macroprudential tools (stress tests, countercyclical capital buffers, loan-to-value or loan-to-income ratios).
  - Expressing financial stability risks in terms of output risk distribution could improve integration into monetary policy decisions and regular policy discussions.
  - The intertemporal tradeoff suggests policymakers should weigh modest near-term benefits of looser financial conditions against larger medium-term increases in downside risk, especially when credit growth is rapid.
- Considerations for welfare evaluation:
  - Simple time-discounting may underweight high-cost large downside risks; welfare losses from severe recessions and banking crises can be persistent and large.
  - Constraints on policy tools (zero-lower bound, QE limitations, unsustainable fiscal debt) can make future downside risks more costly and harder to counter.

*Source: IMF staff estimates and analyses as presented in the supplied content of wp18180 (Appendix B and associated sections).*

### References

### wp18180 - References

### Appendix A — Start Dates for Model Estimation and for Individual Components of FCI
- Table provides start dates (quarter precision) for model estimation and for individual components of the Financial Conditions Index (FCI) by country.
- Selected exact start dates:
  - USA: Start date for estimation 1975q1; Interbank Spread 1973q1; Corporate Spread 1973q1; Sovereign Spread 1973q1; Term Spread 1973q1; Equity Returns Volatility 1973q1.
  - AUS: Start date for estimation 1975q1; Interbank Spread 1979q1; Corporate Spread 1983q2; Sovereign Spread 1973q1; Term Spread 1979q1; Equity Returns Volatility 1973q1.
  - CAN: Start date for estimation 1981q2; Interbank Spread 1973q1; Corporate Spread 1979q1; Sovereign Spread 1973q1; Term Spread 1973q1; Equity Returns Volatility 1973q1.
  - JPN: Start date for estimation 1975q3; Interbank Spread 1979q1; Corporate Spread 1973q1; Sovereign Spread 1973q1; Term Spread 1979q1; Equity Returns Volatility 1973q1.
- Additional variable start dates (selected):
  - Equity Returns (second column set): all listed countries mostly 1973q1 except ESP 1990q1.
  - Change in real long-term rate: earliest 1970q1 for many countries.
  - VIX: 1986q1 for all countries listed.
  - MOVE: 1988q2 for all countries listed.
  - House price return: most 1973q1; ESP 1990q2.
- Later-start series:
  - Change in equity market capitalization of financial sector to total market: predominantly 2000q1; ITA 2016q1; ESP 2000q2.
  - Equity trading volume: varies (examples: AUS 1994q2, CAN 1990q4, USA 1990q4).
  - Market capitalization for equities: varies (examples: AUS 2001q1, CAN 2000q3, DEU 1973q4).
  - Market capitalization for bonds: most series begin 1995q4.
  - Expected default frequencies for banks: most series begin 1999q4.

### Appendix B — Constructing FCI and Sensitivity Analysis
- Model specification (TVP-FAVAR):
  - (B.1) Z_t = θ_t^y Y_t + θ_t^f f_t + v_t
  - (B.2) [Y_t f_t] = c_t + B_{t,1} [Y_{t-1} f_{t-1}] + ⋯ + B_{t,p} [Y_{t-p} f_{t-p}] + ε_t
  - Definitions preserved: Z_t observed vector of financial variables; Y_t vector of macroeconomic variables (real GDP growth and CPI inflation); θ_t^y regression coefficients; θ_t^f factor loadings; f_t latent factor interpreted as the FCI.
  - Time-varying coefficients θ_t and B_t evolve as multivariate random walks with time-varying covariances. Identification achieved by restricting the time-varying covariance matrix to be diagonal.
- Interpretation and advantages:
  - Equation (B.1) extracts latent FCI from financial variables Z_t while purging effects of current macroeconomic conditions so the estimated FCI reflects information solely associated with the financial sector.
  - TVP-FAVAR allows dynamic interactions between FCIs and macroeconomic conditions to evolve over time and accommodates differences in starting dates for some financial indicators.
  - If coefficients are restricted to be constant, the model collapses to FP-FAVAR (fixed-parameter FAVAR).
- Estimation algorithm and steps (Koop and Korobilis (2014) approach using variance discounting and Kalman filter):
  1. a. Initialize all parameters
     b. Obtain the principal components estimates of the factors f_t.
  2. Estimate the time varying parameters given f_t
     a. Estimate covariance matrices using Variance Discounting
     b. Estimate (θ_t, B_t) given the covariance matrices using the Kalman filter (using data up to t) and smoother (using data up to t+1)
  3. Estimate the factor f_t using (θ_t, B_t) using the Kalman filter (using data up to t) and smoother (using estimated data up to t+1).
- Practical notes:
  - The dual linear Kalman filter conditions parameter updates on the factor and factor updates on the parameters, allowing two distinct linear Kalman filters/smoothers (one for parameters, one for the unobserved factor).
  - To balance unbalanced data availability when comparing TVP-FAVAR and FP-FAVAR, missing values are replaced by zeros as common practice when estimating factor models.
  - The two FCI series (TVP-FAVAR and FP-FAVAR/PCA) are reported as very similar; the lowest correlation reported is 0.9 (for Germany).
- Sensitivity and alternative specification results (Model 3 re-estimated using PCA FCI — FP-FAVAR):
  - Table B1: Estimated Coefficients for the 5th Percentile with FCI Alternative Based on FP-FAVAR (PCA)
    - Columns correspond to horizons h=2, h=4, h=6, h=8, h=10, h=12.
    - PCA coefficients and standard errors (exactly as presented):
      - PCA: -2.383*** (0.535), -2.321*** (0.589), -1.482*** (0.445), -0.290 (0.371), 0.169 (0.240), 0.363** (0.171)
    - GDP growth coefficients and standard errors:
      - 0.270*** (0.073), 0.190*** (0.049), 0.136*** (0.050), 0.060 (0.038), 0.023 (0.029), 0.018 (0.025)
    - Inflation rate coefficients and standard errors:
      - -0.332*** (0.091), -0.258*** (0.082), -0.231*** (0.083), -0.154** (0.065), -0.089* (0.047), -0.056 (0.038)
    - Credit-to-GDP growth coefficients and standard errors:
      - -0.291* (0.171), -0.401** (0.161), -0.438** (0.175), -0.384** (0.179), -0.427*** (0.125), -0.418*** (0.103)
    - Credit boom coefficients and standard errors:
      - 0.060 (0.436), -0.414 (0.478), -2.313*** (0.697), -2.136*** (0.544), -1.121*** (0.410), -0.407 (0.317)
  - Model description line: "Model 3: PCA FCI, GDP growth, Inflation, Credit growth and Credit boom"

### Appendix C — FCI and Credit-to-GDP Growth
- Appendix label included; contents indicate figures and analysis linking FCI and Credit-to-GDP growth (figure pages referenced).

### Appendix D — Probability Density Functions from Models 1 and 2, by FCI Groups and Projection Horizons
- Probability density functions estimated from:
  - Model 1 at h = 4 and h = 12
  - Model 2 at h = 4 and h = 12
- PDFs are estimated using panel quantile regression methods and local projections and fitted to a skewed t distribution.
- PDFs are shown for:
  - The loosest decile
  - The tightest decile
  - Mid (middle four deciles) of FCI
- Real GDP growth horizontal axis measured in percent.
- Advanced economies sample: 11 countries with data mostly from 1973 to 2017.

### Appendix E — Term Structure of GaR, Model 3, No Lags and Three Lags
- Plots present GaR (projected growth at the 5th percentile) at an annual rate for:
  - a. Model 3, no lags, Credit Boom
  - b. Model 3, three lags, Credit Boom
  - c. Model 3, no lags, Not Boom
  - d. Model 3, three lags, Not Boom
- GaR projections grouped by initial FCI deciles: loosest decile, tightest decile, and mid (middle four deciles).
- Estimates are based on quantile regressions with local projection estimation methods.
- Real GDP growth (vertical axis) measured in percent.
- Advanced economies include 11 countries with data for most from 1973 to 2017.

*Source: wp18180 - References (PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18180.pdf_