Figure 1: Stylized model structure with funding streams (black) and
related costs (red). Banks allocate
balance-sheet capacity between direct lending and funding to NBFIs,
which in turn intermediate credit while relying on bank funding. The
non-financial sector appears on both sides, as it provides funding to
intermediaries (left) and receives credit (right).
Type: Conceptual flow diagram
Description: This figure presents a stylized representation of the model's structure, illustrating the flow of funds between three main sectors: the non-financial sector, banks, and nonbank financial institutions (NBFIs).
Key Components:
Non-financial sector appears on both the left side (as a funding source) and right side (as a credit recipient)
Banks occupy the middle-left position
NBFIs occupy the middle-right position
Funding Flows (shown in black arrows):
Deposits to banks: βrf - y
Equity to banks: rf + πb
Funding to NBFIs: rf + θn
Bank-to-NBFI funding: fbn at price pbn
Bank loans to non-financial firms: sbℓ with return rℓ
NBFI loans to non-financial firms: tnℓ with return rℓ
Costs (shown in red text):
Bank balance-sheet cost: Φb(Xb)
Cost of fragile NBFI funding: Ψn(ρn)
NBFI funding concentration risk: (ξn/2) Σℓ=1^L tnℓ²
Purpose: The diagram illustrates how banks allocate balance-sheet capacity between direct lending and funding to NBFIs, while NBFIs intermediate credit while relying on bank funding.
Figure 2: Bank convexity \(\gamma_b\)
over time. The figure plots the estimated bank balance-sheet convexity
parameter \(\gamma_b = (r - c)/X_b\) at
the quarterly frequency, separately for GSIBs and non-GSIBs. In the
computation of \(\gamma_b\), \(r\) and \(c\) are expressed as percentages and \(X_b\) in billions of dollars. Higher values
of \(\gamma_b\) correspond to a higher
marginal cost of balance-sheet usage and thus tighter effective
balance-sheet constraints. Source: Authors’ calculation based
on Y-14 dataset, Z.1 Financial Accounts (see Appendix B2), FRED 10Y rate (DGS10), FRED cpi
(CPIAUCSL), and Bloomberg Finance LP, Bloomberg Per Security Data
License.
Type: Time series line chart Time Period: 2015 Q1 to 2026 Q1 Y-axis: Gamma (γb) ranging from 0.0025 to 0.0100
Data Series:
Red line: GSIBs (Globally Systemically Important Banks)
Blue line: Non-GSIBs
Formula displayed: γb = (r - c) / Xb
Key Patterns:
Level Differences:
GSIBs consistently exhibit lower convexity than non-GSIBs throughout the sample period
This suggests GSIBs operate with relatively lower marginal costs of balance-sheet expansion
Temporal Dynamics:
2015-2019: Steady increase in convexity for both groups, consistent with heightened regulatory scrutiny post-Global Financial Crisis
2020: Sharp decline at the onset of COVID-19 pandemic, reflecting policy interventions and regulatory flexibility
Post-2021: Marked increase, reaching peak levels around 2023-2024, consistent with tighter funding conditions and regulatory normalization
Co-movement:
Despite level differences, GSIBs and non-GSIBs track each other closely, suggesting common macro-financial factors drive variation
Interpretation: Higher values of γb indicate higher marginal cost of balance-sheet usage and thus tighter effective balance-sheet constraints. The time variation demonstrates that bank convexity is an economically meaningful determinant of intermediation.
Figure 3: NBFI fragility \(\eta_n\)
by sector over time. The figure plots the estimated NBFI fragility
parameter \(\eta_n\) at the quarterly
frequency across six NBFI sectors classified by NAICS codes. Higher
values of \(\eta_n\) indicate greater
sensitivity of NBFIs to funding reliance and thus higher effective
fragility. Source: Authors’ calculation based on Y-14 dataset,
Z.1 Financial Accounts (see Appendix B2), FRED
10Y rate (DGS10), FRED cpi (CPIAUCSL), and Bloomberg Finance LP,
Bloomberg Per Security Data License.
Type: Time series line chart with multiple series Time Period: 2015 Q1 to 2026 Q1 Y-axis: NBFI Fragility (ηn) ranging from 0 to 150
Data Series (Six NAICS-classified NBFI sectors):
Credit Intermediation
Securities/Commodity
Other Financial Investment
Insurance (Life + P&C) - shown in pink
Other Investment Pools
Real Estate/Rental/Leasing
Key Observations:
Sectoral Heterogeneity:
Insurance sector (pink line) exhibits highest and most volatile fragility levels
Securities/Commodity intermediaries show smoother but steadily increasing trend
Credit Intermediation and Real Estate show relatively low, stable fragility
Temporal Patterns:
Pronounced spike across all sectors during 2020 pandemic period
Post-pandemic divergence in recovery patterns across sectors
Insurance sector reaches values above 100 at peak
Economic Significance:
Higher ηn values indicate greater sensitivity of NBFIs to funding reliance
Reflects differences in funding stability and fragility across sectors
Interpretation: NBFI fragility is both time-varying and highly heterogeneous across sectors, with important implications for the composition effects captured by the reliance channel.
Figure 4: Bank exposures to NBFI sectors over time. The figure plots
aggregate funding volumes \(f_{bn}\)
from banks to NBFI sectors at the quarterly frequency. Source:
Y-14 dataset.
Type: Stacked area chart Time Period: 2015 Q1 to 2025 Q1 Y-axis: Billions of dollars (ranging from $0B to $750B)
Color-Coded Areas (Six NBFI Sectors):
Credit Intermediation
Securities/Commodity
Other Financial Investment
Insurance (Life + P&C)
Other Investment Pools
Real Estate/Rental/Leasing
Key Patterns:
Aggregate Growth:
Steady expansion from approximately $300B in 2015 to over $600B by 2025
Represents more than doubling of bank exposures to NBFIs over the decade
Pandemic Period:
Marked acceleration during 2020-2021
Reflects policy interventions and increased funding opportunities
Sectoral Composition:
Real Estate/Rental/Leasing (green) consistently accounts for largest share
Other Financial Investment (gray) and Other Investment Pools (pink) also substantial
Insurance sector maintains relatively smaller but stable exposure
Post-Pandemic:
Continued growth trajectory through 2025
No significant retrenchment after initial pandemic expansion
Interpretation: Demonstrates the substantial and growing scale of bank-NBFI interconnectedness through funding relationships.
Figure 5: Heatmap of bank lending to NBFI sectors over time,
separately for GSIBs and non-GSIBs. Source: Y-14
dataset.
Type: Dual-panel heatmap Time Period: 2015 Q1 to 2025 Q1 Structure: Two horizontal panels (Non-GSIB top, GSIB bottom)
Rows in Each Panel:
Six NBFI sectors (by NAICS code)
Non-NBFI Loans (comparison row)
Color Scales:
NBFI Flow: 25,000 to 100,000 (darker = higher exposure)
Non-NBFI Flow: 350,000 to 400,000
Key Insights:
Exposure Concentration:
Darker intensity bands indicate persistently high exposure levels
Real Estate, Other Financial Investment, and Other Investment Pools show consistently dark coloring
Insurance and Securities/Commodity show lighter coloring (lower exposures)
Bank Type Differences:
GSIBs: More persistent exposures, particularly concentrated in Other Investment Pools
Non-GSIBs: More broadly distributed across sectors
Different shading patterns suggest different lending strategies
Temporal Evolution:
Gradual darkening over time indicates growing exposures
Particularly visible intensification during 2020-2021 pandemic period
Some sectors show more cyclical variation than others
Non-NBFI Lending:
Bottom row shows relatively stable coloring
Provides context for NBFI-specific dynamics
Interpretation: Visualizes both the concentration of exposures in specific sectors and the systematic differences between bank types in their NBFI funding strategies.
Figure 6: Decomposition of changes in NBFI funding from banks. Panel A
shows the decomposition of funding changes into capacity and reliance
channels, as derived in Section 3.6. Panel B
further decomposes these changes into underlying drivers.
Source: Authors’ calculation based on Y-14 dataset, Z.1
Financial Accounts (see Appendix B2), FRED
10Y rate (DGS10), FRED cpi (CPIAUCSL), and Bloomberg Finance LP,
Bloomberg Per Security Data License.
Type: Two-panel stacked bar chart with overlay line Time Period: 2015 Q2 to 2025 Q1 (quarterly changes)
Panel A: Capacity and Reliance Channels
Y-axis: Log Change (ranging from -0.2 to 0.2)
Components:
Black line: Total Change in bank-NBFI funding
Colored bars (stacked):
Capacity Channel (represents changes in bank balance-sheet capacity)
Reliance Channel (represents changes in funding composition)
Key Findings:
Reliance Channel Dominance:
Orange bars (reliance channel) account for most variation
Capacity channel plays more limited role
Pandemic Period:
Sharp movements in reliance channel during 2020
Capacity channel shows modest contribution
Overall Pattern:
Fluctuations in bank-NBFI interconnectedness driven primarily by how credit is intermediated between sectors
Bank balance-sheet capacity shapes feasible scale but not observed variation
Panel B: Underlying Drivers
Y-axis: Log Change (ranging from -0.4 to 0.2)
Components:
Black line: Total Change
Multiple colored bars representing different drivers:
a: Loan demand
η: NBFI fragility (dominant component)
γ: Bank convexity
π: Bank equity risk premium
r: Loan return
rf: Risk-free rate
θ: NBFI equity risk premium
Key Findings:
NBFI Fragility (η) Dominance:
Largest bars throughout most of sample
Primary driver of intermediation fluctuations
Secondary Drivers:
Loan demand (a) contributes but less volatile
Bank convexity (γ) plays limited role
Risk premia and rates show modest contributions
Pandemic Dynamics:
Particularly large η components during 2020-2021
Multiple drivers show elevated variation during stress period
Overall Interpretation: Confirms that NBFI-side factors, particularly funding fragility, dominate the dynamics of bank-NBFI intermediation, while bank balance-sheet constraints play a secondary role in explaining observed fluctuations.
Figure 7: NBFI reliance levels \(\rho_n\) for the different NBFI sectors.
Nondepository credit intermediation and other financial investment have
elevated \(\rho_n\). Source:
Authors’ calculation based on Y-14 dataset and Z.1 Financial Accounts
(see Appendix B2.)
Type: Time series line chart with multiple series Time Period: 2015 Q1 to 2026 Q1 Y-axis: NBFI Reliance (ρn) ranging from 0.0 to 0.4
Data Series (Six NAICS Sectors):
Credit Intermediation (highest line)
Securities/Commodity
Other Financial Investment (second highest)
Insurance (Life + P&C)
Other Investment Pools
Real Estate/Rental/Leasing
Formula: ρn = (Σb fbn) / tn (bank funding divided by total NBFI lending)
Key Patterns:
Sectoral Ranking:
Credit Intermediation: Consistently highest reliance (0.3-0.4 range)
Other Financial Investment: Second highest, elevated levels
Insurance and Real Estate: Lowest reliance (below 0.15)
Securities/Commodity and Other Investment Pools: Middle range
Temporal Variation:
Relatively stable patterns for most sectors
Some cyclical fluctuation, particularly around 2020
Credit Intermediation shows slight upward trend over time
Pandemic Effects:
Modest changes during 2020 compared to fragility measure
Reflects compositional adjustments in funding structure
Economic Interpretation:
Higher reliance ratios indicate greater dependence on bank funding
According to amplification condition (κn < ρn), Credit Intermediation and Other Financial Investment sectors most prone to amplification effects
These high-reliance sectors account for substantial share of bank-NBFI exposures (per Figure 4)
Systemic Risk Implications:
Sectors with elevated ρn more likely to transmit losses to banking system when liquidation capacity limited
Concentration of reliance in specific sectors creates potential vulnerability points
Figure 8: Bank convexity \(\gamma_b\)
over time based on committed amounts. In the computation of \(\gamma_b = (r -c)/X_b\), \(r\) and \(c\) are expressed as percentages and \(X_b\) in billions of dollars.
Source: Authors’ calculation based on Y-14 dataset, Z.1
Financial Accounts (see Appendix B2), FRED
10Y rate (DGS10), FRED cpi (CPIAUCSL), and Bloomberg Finance LP,
Bloomberg Per Security Data License.
Type: Time series line chart Time Period: 2015 Q1 to 2026 Q1 Y-axis: Gamma (γb) ranging from 0.0010 to 0.0030
Comparison to Figure 2 (Utilized Amounts):
Scale: Much lower values (approximately 1/3 to 1/4 of utilized amounts)
Interpretation: Committed exposures include unused credit lines, diluting the marginal cost measure
Patterns: Similar temporal dynamics maintained
Key Observations:
GSIBs remain below non-GSIBs
COVID-19 dip still visible but less pronounced
Post-2021 increase still evident
Overall correlation with utilized amounts version is high
Figure 9: NBFI fragility \(\eta_n\)
by sector over time based on committed amounts. Source:
Authors’ calculation based on Y-14 dataset, Z.1 Financial Accounts (see
Appendix B2), FRED 10Y rate (DGS10), FRED cpi
(CPIAUCSL), and Bloomberg Finance LP, Bloomberg Per Security Data
License.
Type: Time series line chart Time Period: 2015 Q1 to 2026 Q1 Y-axis: NBFI Fragility (ηn) ranging from 0.0 to 7.5
Comparison to Figure 3 (Utilized Amounts):
Scale: Dramatically lower (7.5 vs 150 maximum)
Sectoral Rankings: Generally preserved
Volatility: Substantially reduced, especially pandemic spike
Key Patterns:
Insurance sector still shows highest fragility
Much smoother time series overall
Less dramatic pandemic effects
Suggests committed amounts smooth out short-term funding stress
Figure 10: Bank exposures to NBFI sectors over time. The figure plots
aggregate funding volumes \(f_{bn}\)
from banks to NBFI sectors at the quarterly frequency based on committed
amounts. Source: Y-14 dataset.
Type: Stacked area chart Time Period: 2015 Q1 to 2025 Q1 Y-axis: Billions of dollars (ranging from $0B to $2,500B)
Comparison to Figure 4 (Utilized Amounts):
Scale: Approximately 3-4 times larger
Ratio Interpretation: Reflects substantial unused committed capacity
Sectoral Composition: Similar proportions maintained
Key Observations:
Total committed exposures reach nearly $2.5 trillion by 2025
Implies significant available but unutilized credit lines
Similar growth trajectory and pandemic expansion
Real estate remains dominant sector
Figure 11: Heatmap of bank lending to NBFI sectors over time,
separately for GSIBs and non-GSIBs, based on committed amounts.
Source: Y-14 dataset.
Type: Dual-panel heatmap Structure: Same as Figure 5
Color Scales:
NBFI Flow: 1e+05 to 2e+05
Non-NBFI Flow: 1,500,000 to 2,500,000
Key Differences from Figure 5:
Approximately 2-3x higher magnitude across all cells
Similar relative patterns between sectors and bank types
Darker overall coloring reflecting larger committed amounts
Temporal evolution qualitatively similar
Figure 12: Decomposition of changes in NBFI funding from banks based on
committed amounts. Panel A shows the decomposition of funding changes
into capacity and reliance channels, as derived in Section 3.6. Panel B further decomposes these
changes into underlying drivers. Source: Authors’ calculation
based on Y-14 dataset, Z.1 Financial Accounts (see Appendix B2), FRED 10Y rate (DGS10), FRED cpi
(CPIAUCSL), and Bloomberg Finance LP, Bloomberg Per Security Data
License.
Type: Two-panel decomposition (same structure as Figure 6)
Panel A: Capacity vs Reliance
Similar qualitative patterns to utilized amounts
Reliance channel still dominates
Slightly different magnitude of fluctuations
Panel B: Underlying Drivers
NBFI fragility (η) remains dominant driver
Other drivers show similar relative importance
Pandemic period dynamics qualitatively similar
Validates robustness of decomposition results
Interpretation: Confirms main empirical findings are not sensitive to choice between utilized and committed exposures.
Figure 13: NBFI reliance levels \(\rho_n\) for the different NBFI sectors.
Source: Authors’ calculation based on Y-14 dataset and Z.1
Financial Accounts (see Appendix B2.)
Type: Time series line chart Time Period: 2015 Q1 to 2026 Q1 Y-axis: NBFI Reliance (ρn) ranging from 0.0 to 0.9
Comparison to Figure 7 (Utilized Amounts):
Scale: Higher maximum (0.9 vs 0.4)
Credit Intermediation: Reaches 0.8-0.9 levels (double the utilized rate)
Interpretation: Committed funding shows higher apparent reliance
Sectoral Rankings: Preserved from utilized amounts
Key Observations:
Credit Intermediation dramatically elevated
Other Financial Investment also shows higher committed reliance
Insurance and Real Estate remain low
Greater spread between high and low reliance sectors
Systemic Risk Interpretation:
Even higher values suggest greater vulnerability under committed basis
But reflects potential rather than actual funding stress
Amplification condition (κn < ρn) more easily satisfied