## 1. Estimation Result of the Error Correction Model

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### Theoretical model and key propositions
- Framework: extension of the Monti‑Klein deposit‑financed credit intermediation model with L + B = D + W + E and profit decomposition including (R_L – R_M – k) L, (R_M – R_D) D, and R_M E.
- Functional forms preserved:
  - L = A_L (R_L/g)^(–B_L), A_L > 0, B_L > 0.
  - D = A_D (R_D/R_M)^(B_D), A_D > 0, B_D > 0.
  - Market rate scenario: R_M = g (steady‑state natural rate); focus on economies with a zero lower bound (ZLB) on deposit rates.
- Propositions (as stated):
  - Proposition 1. Equilibrium bank profitability experiences a negligible decrease if equilibrium market interest rates fall with a decline in the steady state rate of economic growth (no ZLB constraint).
  - Proposition 2. When deposit rates are constrained by the ZLB, lower equilibrium market interest rates that reflect a decrease in the steady state growth rate of the economy translate into a negative impact on bank profitability that is larger than when deposit rates are not so constrained.
  - Proposition 3. When R_M is constrained by the ZLB, a decline in g exerts an additional negative effect on the bank’s profit through the decline in lending volume.
  - Proposition 4. If the bank has an opportunity to invest in a foreign lending market, the bank can mitigate the negative effects of a decline in g by extending the loans in foreign markets.
- Nonlinear channels emphasized:
  - No ZLB: lending and deposit spreads and volumes approximately constant; equity excess return independent of R_M.
  - With ZLB on deposit rates: deposit supply becomes relatively more attractive; deposit volumes increase as market rates fall; loan‑to‑deposit ratio and NIM decline; bank leverage rises.
  - If R_M constrained by ZLB (R_M ≥ 1): lending volumes decline with g and profits fall further.
  - Geographic diversification cushions NIM and profit compression via foreign lending opportunities.

### Numerical calibration and threshold behavior (simulation details)
- Calibration parameters used (Figure 1 notes):
  - A_L = 10, B_L = 150, A_D = 2, B_D = 150, k = 0.015, ϕ = 0.15, A_F = 2, B_F = 120, g^F = 0.7%.
- Thresholds and qualitative outcomes:
  - When steady state growth g is higher than around 0.7 percent, equilibrium deposit rate is positive and NIMs are almost constant.
  - When g falls below around 0.7 percent, deposit rates are constrained by the ZLB, producing sharp NIM and profit compression.
  - When g falls below zero and R_M is constrained by the ZLB, lending volumes fall while deposit stock remains constant, producing further decreases in loan‑to‑deposit ratio, NIM, and bank profits.

### Empirical testing — Japan (ECM estimates and stylized facts)
- Data and setup:
  - Japan used for ECM estimation: panel period 1989–2014 for ECM estimation; descriptive testing extends to 1989–2017.
  - Market rate proxy: five‑year government bond zero coupon yield.
  - Low regime defined when r_m,t ≤ r_m^threshold with cut‑off at 0.9 percent (robust to nearby cut‑offs).
- Long‑run and short‑run coefficient summary (reported coefficients and standard errors as in source):
  - Asset return: 0.838***  0.030  0.864***  ‐0.431*** 0.420*** ‐0.160***  
    (0.006)  (0.024)  (0.014)   (0.006)  (0.005)  (0.015)
  - Funding cost: 0.853*** ‐0.743*** 0.082***  ‐0.544*** 0.446*** ‐0.386***  
    (0.004)  (0.017)  (0.004)   (0.007)  (0.004)  (0.014)
  - Significance notation: *** p<0.01, ** p<0.05, * p<0.1
- Key ECM findings (consistent with model):
  - Long‑run sensitivities ϑ_1,asset and ϑ_1,liability ≈ 0.85, implying NIM almost independent of market interest rates in normal regime.
  - Short‑run sensitivity for liabilities in the Low regime, ϑ_2,liability = ‑0.74 (reported as ‑0.743***), indicating funding spreads compressed as market rates decline at the ZLB.
  - Short‑run sensitivity for assets in the Low regime, ϑ_2,asset, is small and statistically insignificant — asset returns do not adjust much at the ZLB.
  - Impulse responses: in the normal regime (market rates in the 1–2 percent interval), NIM nearly independent of bond rates; once liabilities hit ZLB (0.9), further market‑rate decreases compress funding spreads and sharply compress NIM in short and long run.
- Observed bank responses in Japan:
  - Small deposit‑funded banks (Regional, Shinkin): increase bond portfolio duration; deposits constitute over 90 percent of nonequity financing; branch rationalization and cost cutting.
  - Large internationally active banks: expand foreign lending and securities, increase noninterest income and fee businesses, source about one‑third of funding from capital markets; operating cost ratios nearly flat over two decades.
  - Risk tradeoffs: small banks increase interest‑rate duration risk; large banks increase cross‑border market and counterparty risk and wholesale foreign‑currency funding exposure.

### Cross‑country panel evidence — impact of prolonged low rates on bank profits
- Sample and definitions:
  - Almost 17,000 banks in 8 advanced economies (Canada, Finland, France, Germany, Japan, Netherlands, United Kingdom, United States), annual data from the 1990s to 2015.
  - "Periods of prolonged low rates": double‑threshold — three‑month treasury bill rate below 1 percent AND on‑the‑run 10‑year nominal government bond yield lower than the historical average of short‑term policy rates (Japan long‑rate threshold set at 2 percent).
- Main empirical findings on ROE:
  - Normal periods: "a one percent drop in the interest rate leads to around 0.3 percent increase in the ROE."
  - Prolonged low interest rate periods: "ROE drops following a fall in interest rates." A decrease of the same magnitude results in "an almost one percent drop in profit," a significantly larger and opposite response.
  - Term premium: lower term premiums tend to reduce bank profits in normal times (statistically significant in baseline and LDV specifications).
- Bank characteristics and heterogeneous effects (selected coefficients preserved):
  - Low*3‑month interest rate: 0.0126*** (0.00369) in baseline; other specifications up to 0.0605*** (0.0166).
  - Size: 0.0102*** (0.000922); Low*size: ‑0.00155*** (0.000308).
  - Leverage: 0.000154** (6.26e‑05); Low*leverage: ‑0.000249*** (9.60e‑05).
  - Deposit funding: ‑0.0134*** (0.00434); Low*depositfunding: ‑0.0148*** (0.00386).
  - Trading asset ratio: 0.0567*** (0.00807); Low*tradingassets: ‑0.0651*** (0.00610).
- Business model clustering (selected group averages from Table 2):
  - Business Model 1 (Wholesale funded, diversified): Average Size: 42 (billions of U.S. dollars); Average Loan‑to‑Asset Ratio: 47 (percent); Average Deposit Funding Ratio: 25 (percent); Average Share of Foreign Income: 17 (percent) — subset data.
  - Business Model 2 (Deposit funded domestic): Average Size: 32 (billions of U.S. dollars); Average Loan‑to‑Asset Ratio: 73 (percent); Average Deposit Funding Ratio: 88 (percent); Average Share of Foreign Income: 24 (percent) — subset data.
  - Clustering results: large, internationally diversified wholesale‑funded banks tend to outperform deposit‑funded domestic banks in low‑for‑long periods; estimated average profit is 0.7 percentage points higher than deposit‑funded domestic banks with small lending portfolios.
- Robustness: results robust to alternative bank characteristics, alternative low‑rate definitions, lagged business model characteristics, concentration controls, and various GMM estimators (Arellano‑Bover/Blundell‑Bond and Arellano‑Bond).

### Impact of expectation shifts (forward‑rate surprises) on bank equity returns
- Data and setup:
  - Daily data 2000–2016 for 16 advanced economies; forward‑rate surprise measured as change in country‑specific 9‑year‑ahead, one‑year‑forward rate; equity prices from Bloomberg; sample restricted to frequently traded banks.
- Key results and magnitudes (selected coefficients preserved):
  - Market return: 0.491*** (0.0179) in baseline all‑banks column.
  - Surprise (9y forward): 0.00237*** (0.000334) in baseline.
  - surprise(9y forward)*MP in normal(2 pc): ‑0.0110*** (0.00187) in baseline.
  - surprise(9y forward)*MP in low(2 pc): 0.00200*** (0.000693) in baseline.
- Interpretation:
  - On average, decreases in forward rates have a negative effect on bank equity returns.
  - Monetary easing surprises on monetary policy meeting dates: during prolonged low‑rate periods, they negatively impact bank equity returns with magnitude more than twice that in other periods; during normal periods, monetary easing surprises boost bank equity returns.
  - Figure 4 illustrates the estimated impact of a one percentage point surprise decrease in forward rates on daily bank equity returns relative to the sample average during normal periods (only statistically significant impacts shown).
- Business model heterogeneity:
  - Larger, more diversified, wholesale‑funded banks are less sensitive to monetary policy news during prolonged low‑rate periods.
  - Deposit‑funded domestic intermediaries show greater sensitivity of equity returns to monetary easing surprises in prolonged low‑rate periods.
- Robustness: endogeneity of surprises addressed by orthogonalization to market return and event‑study regressions; main results robust.

### Business‑model adjustments, systemic implications, and long‑run dynamics
- Stylized adaptation strategies:
  - Small, deposit‑funded, domestically oriented banks: lengthen bond portfolio duration, focus on urban loan growth, cut operating costs via branch rationalization; deposits > 90 percent of nonequity financing.
  - Mid/large internationally active banks: expand foreign lending and securities, increase fee businesses and noninterest income, rely more on wholesale funding (about one‑third from capital markets).
- Anticipated sectoral shifts:
  - Aggregate domestic credit demand likely decreases where population aging and slower productivity growth dominate; demand for transaction and fee‑based services rises.
  - Domestic bank lending likely to shrink and concentrate more on small businesses; consolidation pressures for smaller banks.
  - Tail risk increases: duration mismatches for small banks; foreign‑currency and counterparty risk for large banks expanding abroad.
- Consolidation tradeoffs:
  - Policy challenge: balance facilitating smooth consolidation with limiting excessive risk taking and preventing a worsening of the too‑big‑to‑fail problem.
  - Macroprudential and prudential focus needed to contain incentives for wider maturity mismatches, higher leverage, and more wholesale funding.

### Policy implications and recommendations
- Overarching objective: enable smooth adjustment of financial institutions’ business models in a low‑rate, low‑growth steady state while containing financial stability risks.
- Specific policy foci (as stated in source):
  - Contain incentives to increase exposure to tail risk from widening maturity mismatches, higher wholesale funding, and foreign‑currency exposures.
  - Reap benefits from banks’ higher engagement in emerging market economies while containing new financial stability risks in home and host countries.
  - Legal and regulatory frameworks should facilitate consolidation where desirable for efficiency and stability while enforcing risk constraints and effective resolution regimes.
  - Prudential authorities should monitor and limit behaviors that raise tail risk: wider maturity mismatches, higher leverage, more wholesale funding.
- Additional considerations:
  - Macroprudential regulation (lag) shown to have a statistically significant negative effect on ROE in baseline (e.g., ‑0.0165*** (0.00569)), implying tradeoffs between resilience and near‑term profitability.
  - Policymakers should weigh benefits of consolidation and scale efficiencies against integration risks, potential market power effects, and implications for financial stability.

*Italic: Source — wp18192 — "1. Estimation Result of the Error Correction Model" (IMF staff analysis and empirical results).*

### 1. Estimation Result of the Error Correction Model ................................................................18

### 1. Estimation Result of the Error Correction Model ................................................................18

### Section listings and major themes
- 1. Estimation Result of the Error Correction Model ................................................................18
- 2. Classification of Bank Business Model ...............................................................................24
- 3. Impact of Low-for-long Episodes on Bank Profits: Main Results ......................................26
- 4. Impact of Low-for-long Episodes on Bank Profits: Robustness Check ..............................27
- 5. Impact of Changes in Expectations Regarding a Low-for-Long Scenarios on Bank    
  Equity Price Return ..................................................................................................................31

### Figures referenced in this content unit
- Figure 1. Banking Under Low-for-Long Steady State ........................................................................15
- Figure 2. Japan: Evolution of NIMs in Normal and ZLB Equilibria ..................................................19
- Figure 3. Japan: Banks’ Adaptation to the Deposit Rate Lower Bound Period ..................................20
- Figure 4. Impact of Forward Rate Surprises on Bank Equity Returns ................................................30

*Source: wp18192 - 1. Estimation Result of the Error Correction Model (page listings and figures) from the provided PDF content.*

### References .............................................................................................................

### wp18192 - References

### III. I. INTRODUCTION — Context and central question
- Advanced economies have experienced: insipid growth; low asset returns; low levels, and volatility, of interest rates; and flatter yield curves.
- Structural drivers highlighted: population aging, slower labor force growth, slower productivity growth, rising savings, and growing demand for advanced-economy financial assets from emerging market economies.
- Central research question: What are the long-term consequences for financial intermediation, particularly banking, of a steady state with low growth and low interest rates (a "low-for-long" steady state)?

### Major mechanisms and hypotheses
- Low steady-state growth can generate lower long-term nominal and real interest rates and a significantly flatter yield curve.
- A flatter yield curve reduces bank profits from maturity transformation and can incentivize "search-for-yield" behavior (widening balance-sheet mismatches, higher exposure to higher risk–higher return activities).
- Differential impact by bank business model:
  - Smaller, geographically undiversified, deposit-funded banks suffer the greatest erosion in earnings once deposit rates hit a floor.
  - Larger, internationally active banks can seek higher returns abroad and rely more on wholesale funding.

### II. THEORETICAL MODEL — Setup and comparative statics
- Model framework: extension of the Monti-Klein model of deposit-financed credit intermediation with loan (L) and bond (B) assets; financing via deposits (D), wholesale funding (W), and equity (E): L + B = D + W + E.
- Profit decomposition (symbols preserved as in source): profit comprises lending revenue (R_L – R_M – k) L, deposit revenue (R_M – R_D) D, and R_M E from equity financing effects.
- Functional forms:
  - Loan demand: L = A_L (R_L/g)^(–B_L), with A_L > 0 and B_L > 0.
  - Deposit supply: D = A_D (R_D/R_M)^(B_D), with A_D > 0 and B_D > 0.
  - R denotes gross rate of interest; g represents the equilibrium rate of economic growth (natural rate).
- Key modeling scenario: market rate R_M = g (steady-state natural rate), with a focus on economies subject to a zero lower bound (ZLB) on deposit rates.

### Key analytical results (Propositions)
- Proposition 1. Equilibrium bank profitability experiences a negligible decrease if equilibrium market interest rates fall with a decline in the steady state rate of economic growth (no ZLB constraint).
- Proposition 2. When deposit rates are constrained by the ZLB, lower equilibrium market interest rates that reflect a decrease in the steady state growth rate of the economy translate into a negative impact on bank profitability that is larger than when deposit rates are not so constrained.
- Proposition 3. When R_M is constrained by the ZLB, a decline in g exerts an additional negative effect on the bank’s profit through the decline in lending volume.
- Proposition 4. If the bank has an opportunity to invest in a foreign lending market, the bank can mitigate the negative effects of a decline in g by extending the loans in foreign markets.

### Nonlinearities and channels emphasized
- When deposit rates are free (no ZLB), lending and deposit spreads and volumes are (approximately) constant and bank profit sensitivity to R_M is limited; equilibrium excess return on bank equity is independent of R_M.
- When deposit rates hit the ZLB:
  - Deposit supply becomes more attractive relative to bonds; deposit volumes increase as market interest rates fall.
  - Loan-to-deposit ratio and NIM decline as R_M falls further below the threshold where R_D = 1 (deposit gross rate equals 1).
  - Bank leverage increases due to greater deposit inflows and constrained deposit remuneration.
- If market rate R_M itself is constrained by the ZLB (R_M ≥ 1):
  - Lending volumes decline with g because borrowing costs cannot adjust; profits fall further.
- Geographic diversification: the ability to expand foreign lending (at domestic bank’s R_F and foreign steady-state growth g^F) cushions average NIM declines and profit compression; larger banks are better placed to exploit this.

### Numerical calibration and illustrative thresholds
- Numerical calibration (Figure 1 notes): values used in simulation:
  - A_L = 10, B_L = 150, A_D = 2, B_D = 150, k = 0.015, ϕ = 0.15, A_F = 2, B_F = 120, g^F = 0.7%.
- Threshold behavior highlighted:
  - When steady state growth g is higher than around 0.7 percent, equilibrium deposit rate is positive and NIMs are almost constant.
  - When g falls below around 0.7 percent, deposit rates are constrained by the ZLB, producing sharp NIM and profit compression.
  - When g falls below zero and R_M is constrained by the ZLB, lending volumes fall while deposit stock remains constant, producing further decreases in loan-to-deposit ratio, NIM, and bank profits.

### III. EMPIRICAL TESTING — Japan (1989–2017 and panel 1989–2014)
- Rationale for Japan: Japan’s demographics, growth, asset returns, and long-running near-zero interest rate environment approximate the low-for-long steady state.
- Empirical strategy:
  - Error correction model (ECM) estimated on a panel of Japanese banks.
  - Periods: panel used 1989 through 2014 for ECM estimation; broader descriptive testing covers 1989–2017 for product-pricing patterns.
  - Proxy for market rate: five-year government bond zero coupon yield.
  - Low regime (Low_t = 1) defined when market rate r_m,t ≤ r_m^threshold; cut-off chosen at 0.9 percent (results robust to nearby cut-offs).
- Main empirical findings (consistent with model):
  - Estimated long-run sensitivities ϑ_1,asset and ϑ_1,liability are approximately 0.85, implying NIM is almost independent of market interest rates in the normal regime.
  - Estimated short-run sensitivity for liabilities in the Low regime, ϑ_2,liability, is estimated at -0.74, indicating funding spreads are compressed as market rates decline at the ZLB.
  - Estimated short-run sensitivity for assets in the Low regime, ϑ_2,asset, is small and statistically insignificant — asset returns do not adjust much at the ZLB.
  - Impulse responses: in the normal regime (market rates in the 1–2 percent interval), NIM is almost independent of bond interest rates; once liability returns hit their ZLB (0.9), further decreases in market rates compress funding spreads and sharply compress NIMs in both short and long run.

### Observed bank responses and business-model adjustments (Japan and cross-country panel)
- Typical adaptation strategies by bank type:
  - Small, deposit-funded, domestic banks: increase interest-rate risk by lengthening duration of bond portfolios (raising tail risk from duration mismatches).
  - Mid-size and large banks: expand foreign lending (notably to emerging market economies) and increase reliance on wholesale funding (raising counterparty and market risks and potential too-big-to-fail concerns).
- Long-run sectoral shifts anticipated:
  - Aggregate demand for credit likely decreases where population aging and slower productivity growth are dominant forces; demand for transaction and fee-based services rises.
  - Domestic bank lending likely to shrink and concentrate more on small businesses rather than households and large firms.
  - Consolidation pressures: smaller banks with unviable business models pressured toward mergers; scale efficiencies incentivize consolidation and wholesale funding adoption by larger banks.
  - Tail risk increases: interest rate volatility hits duration-mismatched small banks; foreign expansion increases foreign-currency and counterparty risk for large banks.

### Policy implications and recommended balance of objectives
- Policy challenge: balance facilitating smooth consolidation with limiting excessive risk taking and preventing a worsening of the too-big-to-fail problem.
- Key policy foci:
  - Contain incentives to increase exposure to tail risk from widening maturity mismatches, higher wholesale funding, and foreign-currency exposures.
  - Reap benefits from banks’ higher engagement in emerging market economies while containing potential, new financial stability risks in both home and host countries.
  - Legal and regulatory frameworks should facilitate consolidation while enforcing risk constraints and effective resolution regimes.

*Source: IMF Staff analysis and empirical work presented in the document.*

### 1. Long‐term equilibrium2. Short‐term dynamics

### wp18192 - 1. Long‐term equilibrium2. Short‐term dynamics

### Long‐term / short‐term coefficient summary
- Reported coefficients for the model (Standard errors in parentheses):
  - Asset return: 0.838***  0.030  0.864***  ‐0.431*** 0.420*** ‐0.160***  
    (0.006)  (0.024)  (0.014)   (0.006)  (0.005)  (0.015)
  - Funding cost: 0.853*** ‐0.743*** 0.082***  ‐0.544*** 0.446*** ‐0.386***  
    (0.004)  (0.017)  (0.004)   (0.007)  (0.004)  (0.014)
- Significance notation: *** p<0.01, ** p<0.05, * p<0.1

### Japan: bank business models and adaptation to ZLB / low‐for‐long
- Stylized outcomes:
  - Resilience to the low-for-long steady state improves with diversification.
  - Regional and Shinkin banks (smaller, domestically oriented, deposit-dependent):
    - Countered NIM compression primarily through expansion or adjustment of domestic balance sheets; when benefits declined they engaged in cost cutting and consolidation.
    - Focused on growing loan portfolios in urban centers (Regional) and expanding maturity of sovereign bond portfolios (Regional and Shinkin).
    - Deposits constitute over 90 percent of their nonequity financing.
    - Cut operating costs substantially via branch rationalization.
  - Large internationally active banks:
    - Expanded international loans and securities via foreign branches and M&A.
    - Expanded fee businesses outside Japan (including emerging markets and syndicated loans).
    - Increased noninterest income through cross-product customer connections (investment trusts, life insurance).
    - Source about one-third of funding from capital markets; operating cost ratios have been almost flat for the past two decades.
- Risk implications of strategies:
  - Large banks: maintained stable NIMs and profitability at the cost of higher cross-border market and counterparty risk; growing share of wholesale foreign currency funding increases vulnerability to tightening in those markets.
  - Shinkin banks: increased interest rate risk by extending average maturity of domestic bonds; risk-adjusted returns increased only modestly given unusually low inflation and interest rate volatility.

### Cross‐country empirical framework and definitions
- Sample and data:
  - Almost 17,000 banks in 8 advanced economies (Canada, Finland, France, Germany, Japan, Netherlands, United Kingdom, and United States), annual data from the 1990s to 2015.
  - Data sources: Fitch Connect; International Financial Statistics; Haver analytics; Thomson Reuters Datastream.
- Definition of "periods of prolonged low rates":
  - Bank profitability analysis: double-threshold — short-term yield (three-month treasury bill rate) below one percent AND the “on-the-run,” 10-year nominal government bond yield lower than the historical average of short-term policy interest rates (for Japan the long-rate threshold set at two percent).
  - Equity valuation analysis: period of prolonged low rates defined as 10-year government bond yield below two percent (double threshold not used because high-frequency short-term rates are volatile).
- Regression for ROE (Profit): includes Low dummy, short-rate (3-month), term premium (TP), Macro controls (CPI inflation, credit growth, GDP growth), Policy (lagged macroprudential), Bankch/businessmodel (size, leverage, deposit funding ratio, loans-to-assets, trading assets share), time- and bank-fixed effects, and specifications with and without lagged dependent variable and GMM robustness.

### Impact of low‐for‐long episodes on bank profits — main empirical findings
- Aggregate effects:
  - In normal periods: "a one percent drop in the interest rate leads to around 0.3 percent increase in the ROE."
  - In periods with prolonged low interest rates: "ROE drops following a fall in interest rates." A decrease of the same magnitude results in "an almost one percent drop in profit," a significantly larger and opposite response relative to normal periods.
  - Sub-sample GMM estimates confirm an even larger difference in sensitivity of profits to interest rates between normal and low-for-long periods.
- Term premium:
  - Lower term premiums tend to reduce bank profits in normal times (statistically significant in baseline and LDV specifications), though not always supported across specifications with bank characteristics.
- Bank characteristics and business models:
  - Banks that are more leveraged, rely more on deposit funding, and have more trading assets experience a significantly bigger dent in profits in prolonged low-rate periods.
  - Example effects from Table 3 (selected coefficients; standard errors in parentheses):
    - Low*3‑month interest rate: 0.0126*** (0.00369) in baseline; other specifications report Low*3‑month interest rate up to 0.0605*** (0.0166) in one column.
    - Low*term premium: 0.000836 (0.00168) in baseline; variation across specifications.
    - Size: 0.0102*** (0.000922); Low*size: ‐0.00155*** (0.000308).
    - Leverage: 0.000154** (6.26e‑05); Low*leverage: ‐0.000249*** (9.60e‑05).
    - Deposit funding: ‐0.0134*** (0.00434); Low*depositfunding: ‐0.0148*** (0.00386).
    - Trading asset ratio: 0.0567*** (0.00807); Low*tradingassets: ‐0.0651*** (0.00610).
  - Clustering into three business models (Table 2):
    - Business Model 1: Wholesale funded, diversified geographically and by business line.
      - Average Size (billions of U.S. dollars): 42
      - Average Loan-to-Asset Ratio (percent): 47
      - Average Deposit Funding Ratio (percent): 25
      - Average Share of Foreign Income (percent): 17 (data for smaller subset)
    - Business Model 2: Deposit funded domestic credit intermediary.
      - Average Size (billions of U.S. dollars): 32
      - Average Loan-to-Asset Ratio (percent): 73
      - Average Deposit Funding Ratio (percent): 88
      - Average Share of Foreign Income (percent): 24 (data for smaller subset)
    - Business Model 3: Deposit funded, diversified by business line, domestic bank.
      - Average Size (billions of U.S. dollars): ?
      - (Table shows three groups/types; full numeric entries presented in source.)
  - Clustering results: Large, internationally diversified wholesale-funded banks tend to outperform deposit-funded domestic banks in low-for-long periods; estimated average profit is 0.7 percentage points higher than deposit-funded domestic banks with small lending portfolios.
- Other controls:
  - MacroPrudential Regulation (lag) has a statistically significant negative effect on ROE (e.g., ‐0.0165*** in baseline (0.00569)), indicating that more intense macroprudential policy leads to profit reductions down the line.
- Robustness:
  - Baseline results robust to alternative bank characteristics, alternative definitions of prolonged low rates, lagging business model characteristics, controlling for concentration, and various GMM estimators (Arellano‑Bover/Blundell‑Bond and Arellano‑Bond).

### Impact of changes in expectations about low‐for‐long on bank equity values
- Data and setup:
  - Daily data 2000-2016 for 16 advanced economies; equity prices from Bloomberg; sample restricted to frequently traded banks; forward-rate surprises measured as change in country-specific 9-year-ahead, one-year-forward rate.
  - Model includes market return, surprise, interactions for monetary policy announcement dates in normal vs low periods (MP_normaltime, MP_low), conditioning variables (VIX, oil price), firm fixed effects; orthogonalized surprise measures and event-study robustness checks performed.
- Key empirical results and magnitudes (Table 5 highlights):
  - On average, decreases in forward rates have a negative effect on bank equity returns.
  - Monetary easing surprises on monetary policy meeting dates:
    - During prolonged low interest rate periods: negatively impact bank equity returns, with magnitude more than twice that of such surprises in other periods.
    - During normal periods: monetary easing surprises boost bank equity returns.
  - Selected coefficients (Table 5, baseline columns):
    - Market return: 0.491*** (0.0179) in baseline all-banks column.
    - Surprise (9y forward): 0.00237*** (0.000334) in baseline.
    - surprise(9y forward)*MP in normal(2 pc): ‑0.0110*** (0.00187) in baseline.
    - surprise(9y forward)*MP in low(2 pc): 0.00200*** (0.000693) in baseline.
  - Figure 4 interpretation:
    - Depicts estimated impact of a one percentage point surprise decrease in forward interest rates on daily equity returns of banks relative to the sample-average impact during normal periods; only statistically significant impacts shown.
  - Business model differences:
    - Larger, more diversified, wholesale-funded banks are less sensitive to monetary policy news during prolonged low-rate periods.
    - Deposit-funded domestic intermediaries show greater sensitivity of equity returns to monetary easing surprises in prolonged low-rate periods.
- Robustness:
  - Addressed potential endogeneity of surprises by orthogonalizing the surprise to market return and by event-study regressions; main results are robust.

### Discussion — implications and likely medium/long‑term outcomes
- Structural drivers and difficulty of exit:
  - Demographic changes and lower total factor productivity growth may produce a steady state of low growth and low asset returns; longer-term decline in real interest rates since the mid-1980s suggests natural rates may have fallen.
- Industry structure and consolidation:
  - In a low natural rate scenario, consolidation is likely in the long run.
  - Small deposit-funded, less internationally diversified banks suffer the largest profitability hit and may merge or exit; industry concentration could rise.
  - Possible outcomes of consolidation: lower operational costs, greater diversification, greater market power, potentially less incentive to take excessive risks; but integration risks and potential efficiency losses may remain.
- Tail risk and funding composition:
  - Tail risk exposure expected to increase: banks may seek longer asset maturities (raising interest rate risk) and increase share of wholesale funding (more volatile than retail deposits).
  - Large banks may increase capital-market financing for international expansion, raising cross-border stability considerations.
- Business-line shifts:
  - Aging population and low income growth: demand for household loans falls, deposits tend to rise; demand for transaction services increases.
  - Financial technology advances may erode banks' role in payment services.
  - Lending prospects to domestic companies likely modest due to shrinking population and low productivity.

*Italic: Source — IMF staff estimates and analysis from the chapter "1. Long‐term equilibrium 2. Short‐term dynamics" (wp18192).*

### Chapter 2 of the April 2015 GFSR.

### Chapter 2 of the April 2015 GFSR

### Financial-sector business model implications of low interest rates
- Low interest rates can reduce banks’ loan demand and profitability, potentially causing banks to lose market share in debt financing of larger companies if financial technology allows nonbanks to price corporate credit risk and low rates drive large firms to seek bond market funding.
- Business models of banks active in advanced economies may evolve toward fee-based and utility banking services.
- Fewer domestic lending opportunities may motivate larger, internationally active banks to increase their exposure abroad, especially to emerging market economies.

### Policy recommendations for a low-rate, low-growth scenario
- Policymakers must help enable a smooth adjustment of financial institutions’ business models in a scenario of low interest rates and low growth.
- Where desirable from efficiency and financial stability perspectives, policy should not hinder—and should, where feasible, actively facilitate—consolidation for smaller institutions and liquidation of nonviable businesses.
- Prudential authorities need to contain incentives arising in a low-for-long steady-state that may increase exposure to tail risk. Specific bank responses to these incentives could include:
  - wider maturity mismatches,
  - higher leverage, or
  - more wholesale funding.

### Key variable definitions and data sources (Appendix Table)
- Low: Dummy for period with low interest rates; defined as the time when the 10-year government bond yield and the three-month short rate are below their corresponding thresholds. The threshold for the 10-year government bond yield of all countries except Japan is set to be the historical average of the country-specific policy rates (for Japan, it is set to be 2 percent) when the real rate adjusted by the inflation target is at zero. The threshold for the three-month interest rates is set to be 1 percent. Source: Thomson Reuters Datastream and IMF staff calculations.
- Surprise (9-year forward): Daily change in the forward rate of the one-year government bond yield, based on a no-arbitrage assumption and the spot rate of the 10-year and 9-year government bond yield (from yield curve values for constant maturity). Source: Thomson Reuters Datastream and IMF staff calculations.
- Surprise (9-year-forward orthogonal): Surprise that is orthogonal to market return, measured by the residual of the regression of surprise on market return. Source: IMF staff calculations.
- Monetary Policy in Low (2 percent): Dummy for period in low period and with monetary policy announcements. The low period is defined as a period when the 10-year government bond yield is below 2 percent. Sources: Thomson Reuters Datastream, central bank websites, and IMF staff calculations.
- Monetary Policy in Normal (2 percent): Dummy for period in non-low period and with monetary policy announcements. The low period is defined as a period when the 10-year government bond yield is below 2 percent. Sources: Thomson Reuters Datastream, central bank websites, and IMF staff calculations.

- Bank Characteristics (source: Fitch Connect):
  - Return on Equity: Earnings before interest and taxation divided by equity
  - Size: Logarithm of banks' total assets
  - Loan-to-Asset Ratio: Loan before impairment divided by total assets
  - Deposit Funding Ratio: Customer deposit divided by total liability
  - Trading Asset: Asset held for trading plus asset held at fair value
  - Trading Asset Ratio: Trading asset divided by total asset
  - Leverage Ratio: Total asset divided by equity

- Macroeconomic variables and sources:
  - Consumer Price Index Inflation: Year-on-year growth of consumer price index, percent — IMF, International Financial Statistics database
  - Credit-to-GDP Ratio: Private-sector credit in percent of GDP — Bank for International Settlements
  - Real GDP Growth: Year-over-year growth of GDP, constant prices — IMF, World Economic Outlook database
  - Three-Month Interest Rate: Typically central bank bill/treasury bill yield or interbank offered rate — Haver Analytics
  - Term Premium: Term premium estimated based on Wright (2011) — IMF, Global Financial Stability Report, October 2016
  - Ten-Year Government Bond Yield: On-the-run 10-year government bond yield (from yield curve values for constant maturity) — Thomson Reuters Datastream
  - Monetary Policy Rates: Short-term interest rates represent the monetary policy stance in a country — Haver Analytics

- Financial market variables and sources:
  - Equity Price Return: Log difference of equity prices
  - Market Return: Difference of overall country-specific equity price indices
  - VIX: Chicago Board Options Exchange Market Volatility Index — Bloomberg L.P.
  - Oil Price: Crude oil-West Texas Intermediate spot price — Bloomberg L.P.

*Source: IMF staff.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18192.pdf_