## wp1703 — sections 2.1, 3.3, 4.2, 4.4 (selected excerpts)

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### Credit rating, firm size and hedging (Section 2.1)

- Empirical findings: pre-hedging exposure
  - Firms with poorer credit ratings and smaller firms have more floating-rate debt, both as a fraction of debt and as a fraction of assets.
  - Regressions (Panel A of Table 3) use three outcome variables: floating-rate debt as a fraction of debt, the debt to assets ratio, and floating-rate debt as a fraction of assets.
  - Relative to investment grade firms (omitted category), high yield and unrated firm-years have more floating-rate exposure both as a fraction of debt and as a fraction of assets.
  - Smaller firms (three size categories) similarly exhibit greater floating-rate exposure.
  - Visual evidence (Figure 2, Panels A and B) shows a noticeable jump in exposure at the investment grade/high yield cutoff.
  - Firms with the best credit ratings have exposure primarily through commercial paper.
  - Panel B of Table 3 (sample restricted to BBB- and BB+ firm-years): relative to BBB- firms (omitted), BB+ firms have more floating debt as a fraction of debt and as a fraction of assets, and also have more leverage.
  - Regressions include industry and year fixed effects; patterns are consistent across year and industry.
  - Interpretation: institutions such as insurance companies and pension funds have requirements or strong preferences to invest in investment grade bonds, contributing to the observed jump at the cutoff.

- Empirical findings: post-hedging exposure and hedging behavior
  - Firms hedge partially with interest-rate derivatives (primarily interest-rate swaps), but hedging is incomplete.
  - Table 4 regressions report five outcome variables: the floating fraction of debt, net pay-fixed interest-rate swaps as a fraction of debt, post-hedging floating fraction of debt, the debt to assets ratio, and post-hedging floating debt as a fraction of assets.
  - Panel A of Table 4: high yield and unrated firms retain more exposure to interest rates post-hedging via a combination of more floating debt, partial hedging, and (for high yield firms) greater leverage.
  - Investment grade firms use swaps to increase their exposure to interest rates.
  - Comparison of Panels A of Tables 3 and 4: the post-hedging difference in net floating-rate debt as a fraction of assets is roughly half the pre-hedging difference.
  - Panel B of Table 4: smaller firms also have more exposure to interest rates than large firms post-hedging.
  - Figure 3 (Panels A and B): firms hedge toward the exposure levels of better rated firms but only partially; a noticeable jump in post-hedging exposure remains at the investment grade/high yield cutoff.
  - Manual collection: usage of interest-rate swaps from SEC filings for about 40 percent of the relevant sample.

- Synthesis
  - Bank-dependent firms (poor credit ratings and small firms) have more floating-rate bank debt.
  - These firms partially hedge with interest-rate swaps but remain more exposed to floating rates than firms with better access to capital markets.
  - The exposure appears driven by a need for bank financing: it consists primarily of bank debt and is not matched by greater cash-flow sensitivity to interest rates.

### Theoretical framework and model primitives (Section 2.1 summary)

- Purpose and three main points
  - Explain why banks pass interest-rate risk on to firms and derive testable implications about bank balance sheets.
  - Three main points:
    - Banks with more floating-rate liabilities should make more floating loans.
    - Banks’ securities holdings can rule out the idea that banks simply match with firms demanding floating-rate loans (supply-driven vs demand-driven view).
    - Collateral costs prevent firms and banks from hedging fully with derivatives.

- Model setup — primitives and interpretation
  - Banks fund loans and securities with deposit liabilities and internal wealth; deposits are short-term and therefore floating, but cheap because deposit pass-through is partial.
  - Key primitives for uncertainty in future short-term interest rate r:
    - E[r] = ̄r
    - V ar[r] = σ^2
  - Deposit interest expense is αr, where α < 1 (deposit pass-through is not complete).
  - Term premium δ > 0 (same for loans and securities).
  - Securities interest rate r_S has the same mean and variance as r and correlation ρ with r.
  - Collateral for swaps: for each unit of derivatives the bank posts ̄q ∈ (0,1) units of collateral; the opportunity cost of collateral is modeled as (q/2) H_Bank^2 where q = ̄q^2.
  - Banks and firms are modeled with mean-variance preferences (effective risk aversion captured by γ for banks).

- Key equations and objects (as presented)
  - Interest rate received on the loan portfolio:
    (1−f_L)( ̄r+δ) + f_L r + μ^*(f_L)      (Equation 1)
  - Interest rate received on the securities portfolio:
    (1−f_S)( ̄r+δ) + f_S r_S               (Equation 2)
  - Net income (NI):
    NI = L((1−f_L)( ̄r+δ) + f_L r + μ^*(f_L)) + S((1−f_S)( ̄r+δ) + f_L r_S) + H_Bank(r−( ̄r+δ)) − Dαr − (q/2) H_Bank^2     (Equation 3)
  - Bank objective:
    Ω_Bank = E[NI] − (γ/2) V ar[NI]       (Equation 4)
  - First-order conditions (expressed as in the text):
    - H_Bank = (γσ^2 q + γσ^2(Dα − f_L L − ρ f_S S) − δ) / (q + γσ^2)     (Equation 5)
    - f_L L = Dα − ρ f_S S − H_Bank + ∂μ(f_L)/∂f_L − δ/(γσ^2)             (Equation 6)
    - f_S S = ρ(Dα − f_L L − H_Bank) − δ/(γσ^2)                           (Equation 7)

- Implications from first-order conditions
  - Collateral requirements (q > 0) discourage full hedging.
  - A positive term premium δ also discourages hedging.
  - Increasing the floating fraction of loans reduces the loan spread (∂μ(f_L)/∂f_L appears in first-order condition).
  - The securities optimality condition incorporates ρ, the correlation between r_S and r.

- Model interpretation and testable implication
  - Banks optimally choose floating fractions f_L and f_S and hedging H_Bank subject to collateral costs and risk aversion.
  - Main testable implication: banks with more floating liabilities should extend more floating-rate loans.
  - Allowing banks to adjust securities portfolios separates supply-driven explanations from demand-driven ones.
  - Collateral costs create convex costs of hedging, preventing complete pass-through of interest-rate risk to financial markets.

### Bank-dependent firms: model setup and lemmas (Section 3.3)

- Model setup for bank-dependent firms
  - Baseline includes only bank-dependent firms that must finance some of their investment with bank debt.
  - Firms:
    - Invest amount I (fixed-scale investment).
    - Produce output AI + C r, where C captures potential co-movement of output with interest rates (extent to which floating interest rates are an economic hedge).
    - Borrow amount B in bank debt and finance remainder I − B with bonds; bond cost is ̄r + δ (term premium δ).
    - Have mean-variance preferences and access to interest-rate swaps subject to collateral costs q (same as banks). A positive unit of the swap contract is in the pay-fixed direction.
  - Net income of bank-dependent firms:
    - NI_BD = AI + C r − (1 + ̄r + δ)(I − B) − (1 + f_L r + (1 − f_L)(̄r + δ) + μ) B + (r − (̄r + δ)) H_BD − q/2 H_BD^2  (equation (8))
  - Objective (mean-variance):
    - Ω_BD = E[NI_BD] − γ/2 Var[NI_BD]  (equation (9))
  - Firms assumed to have the same effective risk aversion γ as banks.
  - Solution approach: find optimal hedging demand, substitute into objective, derive firm credit demand via FOC with respect to bank credit, then find equilibrium loan spread μ at which firms demand fixed quantity L of bank credit while banks vary floating fraction f_L.

- Lemma on spread responsiveness
  - Lemma 1: The equilibrium spread responds to the floating fraction of lending as follows:
    - ∂μ*(f_L)/∂f_L = q((C − 2 f_L L) γ σ^2 + δ) / (q + γ σ^2)  (equation (10))
  - Interpretation:
    - The derivative has a decreasing component: banks must accept a lower loan spread to increase the floating fraction f_L.
    - Attenuating factors:
      - Large C (cyclical output) makes floating-rate loans an economic hedge for firms.
      - Term premium δ makes fixed-rate debt more expensive.
      - Firms hedge partially; cost depends on collateral requirement q.

- Testable predictions and propositions
  - Key mechanism: floating-rate liabilities push banks to lend at floating rates; banks with more floating liabilities should make more floating-rate loans.
  - Proposition 1:
    - Banks with more floating-rate liabilities (greater deposit pass-through) should make more floating-rate loans:
      - ∂f*_L/∂α > 0  (equation (11))
    - α represents degree of deposit pass-through.
  - Identification concern:
    - Alternative explanation: banks may make more floating loans because they match with firms that demand floating debt (firms with higher C).
  - Distinguishing supply vs demand via securities holdings:
    - Supply-driven view: banks with greater deposit pass-through should make more floating loans and hold more floating-rate securities.
    - Borrower-demand view: banks that make floating loans due to borrower demand should hold fewer floating-rate securities because fixed-rate securities also reduce interest-rate risk.
  - Proposition 2:
    - Banks with more floating-rate liabilities should make more floating-rate loans and hold more floating-rate securities:
      - ∂f*_L/∂α > 0,  ∂f*_S/∂α > 0  (equation (12))
    - Contrast (demand-driven):
      - ∂f*_L/∂C > 0,  ∂f*_S/∂C < 0  (equation (13))
  - Extensions that preserve main results:
    - Endogenize swap price beyond term premium; include investment grade firms that borrow only with fixed-rate corporate bonds; introduce risk-neutral institutions that face collateral costs. Collateral costs prevent full hedging; bank-dependent firms hedge only partially, investment grade firms may bear some interest-rate risk with derivatives. Propositions 1 and 2 continue to hold.

- Empirical implications summary
  - Banks with more floating liabilities (greater deposit pass-through α) should:
    - Make more floating-rate loans (higher f_L).
    - Hold more floating-rate securities (higher f_S).
    - Quote lower prices for adjustable-rate mortgages (ARMs) relative to fixed-rate mortgages (FRMs).
  - Use of securities holdings as a test:
    - Supply-driven prediction: floating fractions of loans and securities are positively correlated with deposit pass-through.
    - Demand-driven prediction: floating fraction of securities would move in opposite direction to loans if driven by borrower demand (variation in C).

### Deposit pass-through, competition and size (Section 4.2)

- Competition and deposit pass-through
  - Deposit pass-through is partly driven by geographic variation in deposit competition.
  - Competition is measured at the bank level as a deposit-weighted average of county-level Herfindahl Indices of deposit concentration.
  - Banks operating in counties with a Herfindahl Index (HHI) higher by 0.1 (one standard deviation) have deposit pass-through lower by one percentage point.
  - HHI is higher in counties with more deposit concentration, where the market for bank deposits is less competitive.

- Bank size and pass-through
  - Bigger banks have more deposit pass-through.
  - Summary statistics in the bank holding company sample reaffirm that larger banks have greater deposit pass-through and more floating-rate assets.

- Instrumental-variable evidence: competition as an instrument for pass-through
  - Competition is used as an instrument for deposit pass-through to address endogeneity concerns.
  - Panel B regressions using competition as an instrument show positive relationships between deposit pass-through and the floating fraction of bank assets (loans and securities), including non-residential loans and non-residential securities.
  - IV (2SLS) estimates display magnitudes somewhat stronger than OLS estimates.
  - The finding that securities are affected as well reduces the concern that competition is merely capturing loan opportunities.
  - The first stage (competition → pass-through) is reported as statistically strong (F-statistic reported in the source tables).

- Interpretation: liabilities versus assets
  - Evidence argues against the view that the composition of banks’ liabilities shifts endogenously to match the characteristics of banks’ assets.
  - Instead, banks match the interest-rate exposure of their assets with that of their liabilities; deposit competition and bank size act as external forces shaping pass-through.
  - If banks could reduce pass-through to match asset characteristics, they would likely have already done so; similarly, banks could hold more long-term fixed-rate securities to accommodate floating-rate borrower demand.

- Time series analysis (overview)
  - Bank holding company data (form FR-Y9C) used for time series analysis covering 1986Q3-2014Q4 (about 80,000 bank quarters for close to 2,000 banks).
  - Floating fraction defined as fraction of assets with remaining maturity or repricing frequency less than one year.
  - Deposit pass-through estimated in the time series for each bank using lagged data for 8-20 quarters, as available.
  - Panel A (Table 10) shows floating fraction of banks’ assets is positively related with deposit pass-through in the sample back to the late 1980s.
  - Regressions with both quarter and bank fixed effects provide evidence that within-bank variation in deposit pass-through also helps explain the interest-rate exposure of bank assets.
  - Unreported analyses find similar results using an alternative measure: the floating fraction of liabilities.

- Robustness and additional points
  - IV regressions may yield larger magnitudes if deposit pass-through is estimated with error (instrumenting can reduce attenuation bias).
  - Unreported regressions show the component of bank liabilities explained by variation in competition also helps explain the extent to which banks with higher pass-through quote higher FRM-ARM spreads.
  - Results apply to aggregate loans and specifically to C&I lending.

### Historical analysis (Section 4.4)

- Evidence on bank liabilities and loan-rate sensitivity
  - Prior to about 1970, deposits were largely non-interest-bearing and effectively fixed-rate liabilities.
  - Interest-bearing deposits were subject to (binding) rate ceilings below market rates beginning in 1966.
  - After June 1970, at least some types of time deposits in excess of $100,000 were exempt from Regulation Q ceilings on interest rates.
  - There is substantially more volatility in both deposit rates and loan rates after about 1970.
  - Inferred realized interest rates on bank loans are computed by dividing interest income on loans and leases by net outstanding loans and leases.
  - The short-term interest-rate proxy used is the yield on three month T-Bills (from the Federal Reserve).

- Regression framework and results
  - Regression specification (changes):
    - ∆y_t = α + β ∆r_t + ρ ∆y_{t−1}
  - Interpretation:
    - If loans are made at floating rates, realized loan rates should strongly co-move with short-term interest rates.
    - If loans are made at fixed rates, realized loan rates should not co-move strongly with short-term rates.
  - Estimated responsiveness of loan rates to short-term rates:
    - Prior to 1970:
      - Loan rates rose about 20 basis points for a 100 basis point increase in short-term rates.
      - Long-term response, β/(1−ρ), was about 40 basis points.
      - R^2 = 27%.
    - After 1970:
      - Loan rates rose almost 50 basis points for a 100 basis point increase in short-term rates.
      - Long-term response was almost 70 basis points.
      - R^2 = 79%.
  - Robustness:
    - The year 1970 is chosen as the cutoff because this is approximately when the majority of bank liabilities became interest bearing; results are similar using any year from 1965-1975.

- Inferred floating-rate lending shares and interpretation
  - Simulations imply:
    - About 10% of loans were floating-rate before 1970.
    - Around 25-40% of loans were floating-rate subsequently.
  - Interpretation:
    - When bank liabilities were predominantly fixed-rate (pre-1970), loans were effectively made at fixed rates despite contractual floating-rate language, supporting a supply-driven view in which the structure of bank liabilities determines the interest-rate exposure of bank lending.

- Implications for monetary transmission and firm balance sheets
  - Banks with more floating-rate liabilities make more floating-rate loans and hold more floating-rate securities.
  - Cross-sectional relationships (higher quantities and lower prices for ARMs vs FRMs at banks with greater deposit pass-through) point to supply variation rather than firm demand for floating-rate debt.
  - Bank-dependent firms:
    - Obtain two thirds of their debt finance from banks, largely at floating rates.
    - Firms with better access to capital markets obtain one sixth of their debt from banks.
    - Within the derivatives data subsample, bank-dependent firms have twice as much floating-rate debt as a fraction of assets after taking hedging into account.
  - Consequence for monetary transmission:
    - Floating-rate bank lending is interpreted as a component of the Bernanke & Gertler (1995) balance-sheet channel: as interest rates rise, firms’ financial health deteriorates because interest expense rises and cash flows fall.
    - Bank-dependent firms’ interest coverage ratios are more sensitive to short-term interest rates than those of firms with better access to capital markets.
    - Using investment cash-flow sensitivity methods, the author imputes that cash-flow shocks from floating-rate debt can account for a significant portion of the greater interest-rate sensitivity of bank-dependent firms’ investment.

- Summary findings and regulatory implication
  - Historical and cross-sectional evidence supports the supply-driven view that banks’ floating-rate liabilities drive floating-rate bank lending to firms.
  - The structure of banks’ funding has important implications for interest-rate mismatch on banks’ balance sheets and for the contracts used by non-financial firms.
  - The results suggest that tighter regulation of banks’ exposure to interest rates might lead banks to pass on more interest-rate risk to firms.

*IMF Working Paper — section 2.1, "Credit rating, firm size and hedging"; sections 3.3, 4.2, 4.4 (wp1703).*

### 2.1    Credit rating, firm size and hedging

### 2.1    Credit rating, firm size and hedging

### Empirical findings: pre-hedging exposure
- Firms with poorer credit ratings and smaller firms have more floating-rate debt, both as a fraction of debt and as a fraction of assets.
- Regressions (Panel A of Table 3) use three outcome variables: floating-rate debt as a fraction of debt, the debt to assets ratio, and floating-rate debt as a fraction of assets.
- Relative to investment grade firms (omitted category), high yield and unrated firm-years have more floating-rate exposure both as a fraction of debt and as a fraction of assets.
- Smaller firms (three size categories) similarly exhibit greater floating-rate exposure.
- Visual evidence (Figure 2, Panels A and B) shows a noticeable jump in exposure at the investment grade/high yield cutoff.
- Firms with the best credit ratings have exposure primarily through commercial paper.
- Panel B of Table 3 (sample restricted to BBB- and BB+ firm-years): relative to BBB- firms (omitted), BB+ firms have more floating debt as a fraction of debt and as a fraction of assets, and also have more leverage.
- Regressions include industry and year fixed effects; patterns are consistent across year and industry.
- Interpretation: institutions such as insurance companies and pension funds have requirements or strong preferences to invest in investment grade bonds, contributing to the observed jump at the cutoff.

### Empirical findings: post-hedging exposure and hedging behavior
- Firms hedge partially with interest-rate derivatives (primarily interest-rate swaps), but hedging is incomplete.
- Table 4 regressions report five outcome variables: the floating fraction of debt, net pay-fixed interest-rate swaps as a fraction of debt, post-hedging floating fraction of debt, the debt to assets ratio, and post-hedging floating debt as a fraction of assets.
- Panel A of Table 4: high yield and unrated firms retain more exposure to interest rates post-hedging via a combination of more floating debt, partial hedging, and (for high yield firms) greater leverage.
- Investment grade firms use swaps to increase their exposure to interest rates.
- Comparison of Panels A of Tables 3 and 4: the post-hedging difference in net floating-rate debt as a fraction of assets is roughly half the pre-hedging difference.
- Panel B of Table 4: smaller firms also have more exposure to interest rates than large firms post-hedging.
- Figure 3 (Panels A and B): firms hedge toward the exposure levels of better rated firms but only partially; a noticeable jump in post-hedging exposure remains at the investment grade/high yield cutoff.
- Manual collection: usage of interest-rate swaps from SEC filings for about 40 percent of the relevant sample.

### Synthesis of empirical evidence
- Bank-dependent firms (poor credit ratings and small firms) have more floating-rate bank debt.
- These firms partially hedge with interest-rate swaps but remain more exposed to floating rates than firms with better access to capital markets.
- The exposure appears driven by a need for bank financing: it consists primarily of bank debt and is not matched by greater cash-flow sensitivity to interest rates.

### Theoretical framework: objectives and three main points
- Purpose: explain why banks pass interest-rate risk on to firms and derive testable implications about bank balance sheets.
- Three main points:
  - Banks with more floating-rate liabilities should make more floating loans.
  - Banks’ securities holdings can rule out the idea that banks simply match with firms demanding floating-rate loans (supply-driven vs demand-driven view).
  - Collateral costs prevent firms and banks from hedging fully with derivatives.

### Model setup: primitives and interpretation
- Banks fund loans and securities with deposit liabilities and internal wealth; deposits are short-term and therefore floating, but cheap because deposit pass-through is partial.
- Key economic intuition: mismatch between banks’ short-term floating liabilities and long-term lending creates interest-rate exposure when future interest rates are uncertain.
- Uncertainty in future short-term interest rate r:
  - E[r] = ̄r
  - V ar[r] = σ^2
- Deposit interest expense is αr, where α < 1 (deposit pass-through is not complete).
- Term premium δ > 0 (same for loans and securities).
- Securities interest rate r_S has the same mean and variance as r and correlation ρ with r.
- Collateral for swaps: for each unit of derivatives the bank posts ̄q ∈ (0,1) units of collateral; the opportunity cost of collateral is modeled as (q/2) H_Bank^2 where q = ̄q^2.
- Banks and firms are modeled with mean-variance preferences (effective risk aversion captured by γ for banks).

### Key equations and objects (as presented)
- Interest rate received on the loan portfolio:
  (1−f_L)( ̄r+δ) + f_L r + μ^*(f_L)      (Equation 1)
- Interest rate received on the securities portfolio:
  (1−f_S)( ̄r+δ) + f_S r_S               (Equation 2)
- Net income (NI):
  NI = L((1−f_L)( ̄r+δ) + f_L r + μ^*(f_L)) + S((1−f_S)( ̄r+δ) + f_L r_S) + H_Bank(r−( ̄r+δ)) − Dαr − (q/2) H_Bank^2     (Equation 3)
- Bank objective:
  Ω_Bank = E[NI] − (γ/2) V ar[NI]       (Equation 4)
- First-order conditions (expressed as in the text):
  - H_Bank = (γσ^2 q + γσ^2(Dα − f_L L − ρ f_S S) − δ) / (q + γσ^2)     (Equation 5)
  - f_L L = Dα − ρ f_S S − H_Bank + ∂μ(f_L)/∂f_L − δ/(γσ^2)             (Equation 6)
  - f_S S = ρ(Dα − f_L L − H_Bank) − δ/(γσ^2)                           (Equation 7)
- Implications from these conditions:
  - Collateral requirements (q > 0) discourage full hedging.
  - A positive term premium δ also discourages hedging.
  - Increasing the floating fraction of loans reduces the loan spread (∂μ(f_L)/∂f_L appears in first-order condition).
  - The securities optimality condition incorporates ρ, the correlation between r_S and r.

### Model interpretation and testable implications
- Banks optimally choose floating fractions of loan and securities portfolios (f_L and f_S) and hedging H_Bank subject to collateral costs and risk aversion.
- Main testable implication: banks with more floating liabilities should extend more floating-rate loans.
- By allowing banks to adjust securities portfolios, the model separates supply-driven explanations (banks driving floating lending) from demand-driven explanations (firms demanding floating loans).
- Collateral costs create convex costs of hedging, preventing complete pass-through of interest-rate risk to financial markets.

### Additional notes from the source
- Term loans constitute much of observed floating-rate bank lending to firms; effective maturity of bank loans reported elsewhere ranges from 2-4 years (Mian & Santos).
- Hedging in practice is concentrated in interest-rate swaps; collateral costs influence banks’ derivative usage (Rampini et al. evidence cited).

*Italic source attribution: IMF Working Paper — section 2.1, "Credit rating, firm size and hedging" (wp1703).*

### Section 3.3. I now turn to the set up for firms.

### Section 3.3. I now turn to the set up for firms.

### Model setup: bank-dependent firms
- Baseline includes only bank-dependent firms that must finance some of their investment with bank debt.
- Firms:
  - Invest amount I (fixed-scale investment).
  - Produce output AI + C r, where C captures potential co-movement of output with interest rates (extent to which floating interest rates are an economic hedge).
  - Borrow amount B in bank debt and finance remainder I − B with bonds; bond cost is ̄r + δ (term premium δ).
  - Have mean-variance preferences and access to interest-rate swaps subject to collateral costs q (same as banks). A positive unit of the swap contract is in the pay-fixed direction.
- Net income of bank-dependent firms:
  - NI_BD = AI + C r − (1 + ̄r + δ)(I − B) − (1 + f_L r + (1 − f_L)(̄r + δ) + μ) B + (r − (̄r + δ)) H_BD − q/2 H_BD^2  (equation (8))
- Objective (mean-variance):
  - Ω_BD = E[NI_BD] − γ/2 Var[NI_BD]  (equation (9))
- Firms assumed to have the same effective risk aversion γ as banks.
- Solution approach:
  - Find optimal hedging demand, substitute into objective, derive firm credit demand via FOC with respect to bank credit, then find equilibrium loan spread μ at which firms demand fixed quantity L of bank credit while banks vary floating fraction f_L.

### Lemma on spread responsiveness
- Lemma 1: The equilibrium spread responds to the floating fraction of lending as follows:
  - ∂μ*(f_L)/∂f_L = q((C − 2 f_L L) γ σ^2 + δ) / (q + γ σ^2)  (equation (10))
- Interpretation:
  - The derivative has a decreasing component: banks must accept a lower loan spread to increase the floating fraction f_L.
  - Attenuating factors:
    - Large C (cyclical output) makes floating-rate loans an economic hedge for firms.
    - Term premium δ makes fixed-rate debt more expensive.
    - Firms hedge partially; cost depends on collateral requirement q.

### Testable predictions (theoretical implications)
- Key mechanism: floating-rate liabilities push banks to lend at floating rates; banks with more floating liabilities should make more floating-rate loans.
- Proposition 1:
  - Banks with more floating-rate liabilities (greater deposit pass-through) should make more floating-rate loans:
    - ∂f*_L/∂α > 0  (equation (11))
  - α represents degree of deposit pass-through.
- Identification concern:
  - Alternative explanation: banks may make more floating loans because they match with firms that demand floating debt (firms with higher C).
- Distinguishing supply vs demand via securities holdings:
  - Under supply-driven view: banks with greater deposit pass-through should make more floating loans and hold more floating-rate securities.
  - Under borrower-demand view: banks that make floating loans due to borrower demand should hold fewer floating-rate securities because fixed-rate securities also reduce interest-rate risk.
- Proposition 2:
  - Banks with more floating-rate liabilities should make more floating-rate loans and hold more floating-rate securities:
    - ∂f*_L/∂α > 0,  ∂f*_S/∂α > 0  (equation (12))
- Contrast (demand-driven):
  - ∂f*_L/∂C > 0,  ∂f*_S/∂C < 0  (equation (13))
- Extensions that preserve main results:
  - Endogenize swap price beyond term premium; include investment grade firms that borrow only with fixed-rate corporate bonds; introduce risk-neutral institutions (e.g., hedge funds) that face collateral costs. Collateral costs prevent full hedging; bank-dependent firms hedge only partially, investment grade firms may bear some interest-rate risk with derivatives. Propositions 1 and 2 continue to hold.

### Empirical implications and summary of main predictions
- Main empirical implication: banks with more floating liabilities (greater deposit pass-through α) should:
  - Make more floating-rate loans (higher f_L).
  - Hold more floating-rate securities (higher f_S).
  - Quote lower prices for adjustable-rate mortgages (ARMs) relative to fixed-rate mortgages (FRMs).
- Use of securities holdings as a test:
  - Supply-driven prediction: floating fractions of loans and securities are positively correlated with deposit pass-through.
  - Demand-driven prediction: floating fraction of securities would move in opposite direction to loans if driven by borrower demand (variation in C).
- Model-driven additional predictions:
  - Cross-sectional correlation between floating fractions of loans and securities is informative about relative importance of supply versus demand (see Internet Appendix B.2).
  - Full model matches relative levels of interest-rate risk and derivatives use across bank-dependent and investment grade firms (Internet Appendix B.3).

*Source: wp1703 - Section 3.3. I now turn to the set up for firms.*

### 4.2    Deposit pass-through, competition and size

### 4.2    Deposit pass-through, competition and size

### Competition and deposit pass-through
- Deposit pass-through is partly driven by geographic variation in deposit competition.
- Competition is measured at the bank level as a deposit-weighted average of county-level Herfindahl Indices of deposit concentration.
- Banks operating in counties with a Herfindahl Index (HHI) higher by 0.1 (one standard deviation) have deposit pass-through lower by one percentage point.
- HHI is higher in counties with more deposit concentration, where the market for bank deposits is less competitive.

### Bank size and pass-through
- Bigger banks have more deposit pass-through.
- Summary statistics in the bank holding company sample reaffirm that larger banks have greater deposit pass-through and more floating-rate assets.

### Instrumental-variable evidence: competition as an instrument for pass-through
- Competition is used as an instrument for deposit pass-through to address endogeneity concerns.
- Panel B regressions using competition as an instrument show positive relationships between deposit pass-through and the floating fraction of bank assets (loans and securities), including non-residential loans and non-residential securities.
- IV (2SLS) estimates display magnitudes somewhat stronger than OLS estimates.
- The finding that securities are affected as well reduces the concern that competition is merely capturing loan opportunities.
- The first stage (competition → pass-through) is reported as statistically strong (F-statistic reported in the source tables).

### Interpretation: liabilities versus assets
- Evidence argues against the view that the composition of banks’ liabilities shifts endogenously to match the characteristics of banks’ assets.
- Instead, banks match the interest-rate exposure of their assets with that of their liabilities; deposit competition and bank size act as external forces shaping pass-through.
- If banks could reduce pass-through to match asset characteristics, they would likely have already done so; similarly, banks could hold more long-term fixed-rate securities to accommodate floating-rate borrower demand.

### Time series analysis (Section 4.3)
- Bank holding company data (form FR-Y9C) are used for time series analysis covering 1986Q3-2014Q4.
- The sample is aggregated pro-forma by present ownership, adjusted for mergers, restricted to holding companies that meet quarterly reporting requirements, and consists of about 80,000 bank quarters for close to 2,000 banks.
- The floating fraction is defined as the fraction of assets with remaining maturity or repricing frequency less than one year; for loans and securities this is estimated by progressively adjusting for federal funds and repo assets, and floating securities.
- Deposit pass-through is estimated in the time series for each bank using lagged data for 8-20 quarters, as available.
- Panel A (Table 10) shows that the floating fraction of banks’ assets is positively related with deposit pass-through in the sample back to the late 1980s.
- Regressions with both quarter and bank fixed effects provide evidence that within-bank variation in deposit pass-through also helps explain the interest-rate exposure of bank assets.
- Unreported analyses find similar results using an alternative measure: the floating fraction of liabilities.
- Additional evidence (Internet Appendix) shows that the time series response of banks’ liabilities to market conditions is not consistent with liabilities adjusting to match shifts in assets; for example, when term spreads are high, banks tend to have a smaller fraction of deposits maturing or repricing in less than one year.

### Robustness and additional points
- IV regressions may yield larger magnitudes if deposit pass-through is estimated with error (instrumenting can reduce attenuation bias).
- Unreported regressions show the component of bank liabilities explained by variation in competition also helps explain the extent to which banks with higher pass-through quote higher FRM-ARM spreads.
- Results apply to aggregate loans and specifically to C&I lending (referenced in Internet Appendix).

*wp1703 - 4.2    Deposit pass-through, competition and size*

### 4.4    Historical analysis

### 4.4    Historical analysis

### Evidence on bank liabilities and loan-rate sensitivity
- Prior to about 1970, deposits were largely non-interest-bearing and effectively fixed-rate liabilities.
- Interest-bearing deposits were subject to (binding) rate ceilings below market rates beginning in 1966.
- After June 1970, at least some types of time deposits in excess of $100,000 were exempt from Regulation Q ceilings on interest rates.
- There is substantially more volatility in both deposit rates and loan rates after about 1970.
- Inferred realized interest rates on bank loans are computed by dividing interest income on loans and leases by net outstanding loans and leases.
- The short-term interest-rate proxy used is the yield on three month T-Bills (from the Federal Reserve).

### Regression framework and results
- Regression specification (changes):
  - ∆y_t = α + β ∆r_t + ρ ∆y_{t−1}
- Interpretation:
  - If loans are made at floating rates, realized loan rates should strongly co-move with short-term interest rates.
  - If loans are made at fixed rates, realized loan rates should not co-move strongly with short-term rates.
- Estimated responsiveness of loan rates to short-term rates:
  - Prior to 1970:
    - Loan rates rose about 20 basis points for a 100 basis point increase in short-term rates.
    - Long-term response, β/(1−ρ), was about 40 basis points.
    - R^2 = 27%.
  - After 1970:
    - Loan rates rose almost 50 basis points for a 100 basis point increase in short-term rates.
    - Long-term response was almost 70 basis points.
    - R^2 = 79%.
- Robustness:
  - The year 1970 is chosen as the cutoff because this is approximately when the majority of bank liabilities became interest bearing; results are similar using any year from 1965-1975.

### Inferred floating-rate lending shares and historical interpretation
- Simulations imply:
  - About 10% of loans were floating-rate before 1970.
  - Around 25-40% of loans were floating-rate subsequently.
- Interpretation:
  - When bank liabilities were predominantly fixed-rate (pre-1970), loans were effectively made at fixed rates despite contractual floating-rate language, supporting a supply-driven view in which the structure of bank liabilities determines the interest-rate exposure of bank lending.

### Implications for monetary transmission and firm balance sheets
- Banks with more floating-rate liabilities make more floating-rate loans and hold more floating-rate securities.
- The cross-sectional relationships (higher quantities and lower prices for ARMs vs FRMs at banks with greater deposit pass-through) point to supply variation rather than firm demand for floating-rate debt.
- Bank-dependent firms:
  - Obtain two thirds of their debt finance from banks, largely at floating rates.
  - Firms with better access to capital markets obtain one sixth of their debt from banks.
  - Within the derivatives data subsample, bank-dependent firms have twice as much floating-rate debt as a fraction of assets after taking hedging into account.
- Consequence for monetary transmission:
  - Floating-rate bank lending is interpreted as a component of the Bernanke & Gertler (1995) balance-sheet channel: as interest rates rise, firms’ financial health deteriorates because interest expense rises and cash flows fall.
  - Bank-dependent firms’ interest coverage ratios are more sensitive to short-term interest rates than those of firms with better access to capital markets.
  - Using investment cash-flow sensitivity methods, the author imputes that cash-flow shocks from floating-rate debt can account for a significant portion of the greater interest-rate sensitivity of bank-dependent firms’ investment.

### Summary findings and regulatory implication
- Historical and cross-sectional evidence supports the supply-driven view that banks’ floating-rate liabilities drive floating-rate bank lending to firms.
- The structure of banks’ funding has important implications for interest-rate mismatch on banks’ balance sheets and for the contracts used by non-financial firms.
- The results suggest that tighter regulation of banks’ exposure to interest rates might lead banks to pass on more interest-rate risk to firms.

*Source: 4.4 Historical analysis (wp1703)*

### References

### wp1703 - References

### Major referenced works
- Auclert, A. (2015), ‘Monetary policy and the redistribution channel’.
- Baker, M., Stein, J. C. & Wurgler, J. (2003), ‘When does the market matter? stock prices and the investment of equity-dependent firms’, Quarterly Journal of Economics 118(3), 969–1005.
- Bernanke, B. S. & Gertler, M. (1995), ‘Inside the black box: The credit channel of monetary policy transmission’, Journal of Economic Perspectives 9(4), 27–48.
- Diamond, D. W. & Dybvig, P. H. (1983), ‘Bank runs, deposit insurance, and liquidity’, Journal of Political Economy 91(3), 401–419.
- Gorton, G. B. (2010), Slapped by the invisible hand: The panic of 2007, Oxford University Press.
- Holmström, B. & Tirole, J. (1998), ‘Private and public supply of liquidity’, Journal of Political Economy 106(1), 1–40.
- Keys, B. J., Piskorski, T., Seru, A. & Yao, V. (2014), Mortgage rates, household balance sheets, and the real economy, Technical report, National Bureau of Economic Research.
- Krishnamurthy, A. & Vissing-Jorgensen, A. (2015), ‘The impact of treasury supply on financial sector lending and stability’, Journal of Financial Economics 118(3), 571–600.
- Stein, J. C. (2012), ‘Monetary policy as financial stability regulation’, Quarterly Journal of Economics 127(1), 57–95.
- Tirole, J. (2006), The Theory of Corporate Finance, Princeton University Press.
- (Full list of references contained in the source PDF.)

### Summary of Appendix A — Tables and Figures: key sample definitions and measures
- Table 1: Summary statistics for sample of firms (annual data, 2003-2013; excludes financial firms and utilities).
  - Panel A: Full sample (Firm-Years 13,400; Firms 2,186)
    - Assets (MM): Median 976.0, Mean 4,567.2, Std. Dev. 23,936.6
    - Floating Fraction: Median 30.3, Mean 38.3, Std. Dev. 34.6
    - Bank Fraction: Median 36.2, Mean 42.7, Std. Dev. 37.5
    - Debt/Assets: Median 29.5, Mean 33.1, Std. Dev. 21.6
    - LTD/Debt: Median 93.9, Mean 80.9, Std. Dev. 27.9
    - CAPX/Assets: Median 3.4, Mean 5.8, Std. Dev. 7.0
    - RD/Assets: Median 0.0, Mean 2.1, Std. Dev. 5.2
    - CF Beta: Median 0.1, Mean 0.2, Std. Dev. 3.0
  - Panel B: Derivatives sub-sample (Firm-Years 4,846; Firms 571)
    - Assets (MM): Median 1,526.8, Mean 4,325.6, Std. Dev. 10,490.5
    - Floating Fraction: Median 26.9, Mean 34.9, Std. Dev. 32.2
    - Bank Fraction: Median 30.4, Mean 38.2, Std. Dev. 35.2
    - Net Pay Fixed: Median 0.0, Mean 6.1, Std. Dev. 22.3
    - Post-Hedge Floating: Median 22.9, Mean 28.8, Std. Dev. 31.1
    - Post-Hedge Floating/Assets: Median 6.7, Mean 10.2, Std. Dev. 12.9

- Figure 1: Debt structure by rating and size (annual data, 2003-2013)
  - Shows types of debt (revolving loans, term loans, commercial paper and floating-rate bonds) as a fraction of debt (value weighted). Term loans are separated into fixed and floating rate. Remainder primarily fixed-rate bonds.
  - Panel A: capital structure by rating. Panel B: capital structure by size tercile by year.

### Key empirical regressions and findings (tables 2–4, 6–10, 11)
- Table 2: Determinants of floating debt (annual data, 2003-2013; outcome = fraction of debt that is floating)
  - Bank Fraction coefficient examples: 0.60 (t = 46.13), 0.57 (t = 38.98), 0.73 (t = 42.47), 0.71 (t = 39.82)
  - Debt rated: -4.53 (t = -3.23); -3.12 (t = -2.25)
  - Debt/Assets: 2.21 (t = 4.27); -0.03 (t = -0.05)
  - Swap Spread: 0.56 (t = 2.88)
  - Term Spread: -0.32 (t = -1.57)
  - R2 ranges: 0.49, 0.51, 0.74, 0.75
  - Firm-Years: 13,400; Firms in specifications: 2,186 and 1,404

- Table 3: Risky, small firms bear more interest-rate risk (annual data, 2003-2013)
  - Panel A (examples):
    - Constant for V/D: 18.33 (t = 10.52)
    - High Yield coefficient for V/D: 14.43 (t = 8.23)
    - Small coefficient for V/D: 23.81 (t = 15.46)
    - R2 examples: 0.11, 0.15, 0.06
    - Firm-Years: 13,400; Firms: 2,186
  - Panel B (restricted to BBB- and BB+):
    - BB+ coefficient examples: V/D 7.28 (t = 2.79); D/A 3.78 (t = 2.45); V/A 3.15 (t = 3.35)
    - R2 examples: 0.07, 0.05, 0.08
    - Firm-Years: 1,057; Firms: 273

- Table 4: Risky, small firms bear more interest-rate risk post-hedging (derivatives sub-sample, 2003-2013)
  - Panel A (by rating):
    - Constant V/D 18.28 (t = 10.77); NPF/D -5.07 (t = -3.43); (V-NPF)/D 23.35 (t = 9.70)
    - High Yield NPF/D 13.74 (t = 8.58)
    - Firm-Years: 4,846; Firms: 571
  - Panel B (by size):
    - Constant V/D 25.22 (t = 13.08); NPF/D 1.38 (t = 0.87); (V-NPF)/D 23.83 (t = 13.78)
    - Small (V-NPF)/D 11.14 (t = 5.69)
    - Firm-Years: 4,846; Firms: 571

- Table 6: Floating fraction of bank assets and deposit pass-through (commercial bank data, 2001Q1-2014Q4)
  - Panel A: Deposit PT coefficients on floating fractions (collapsed to bank means):
    - Loans, Sec: 0.48 (t = 14.40)
    - NR Loans: 0.47 (t = 11.88)
    - For 2009Q2-2014Q4: Loans, Sec 0.39 (t = 9.33); NR Loans 0.38 (t = 7.28)
    - R2 examples: 0.12, 0.09, 0.08, 0.05
    - Bank-Quarters: 57,224; Banks: 1,483
  - Panel B: NR Securities regression:
    - Deposit PT 0.13 (t = 4.72)
    - NR Loans (floating fraction) 0.16 (t = 10.05)
    - R2 examples: 0.01, 0.06

- Table 7: Relationship of FRM-ARM spread to deposit pass-through (bank-level, end-2014 branch data; spreads in basis points)
  - Panel A: 15 year FRM minus ARMs
    - Deposit PT coefficients: FRM - ARM 0.77 (t = 0.82); FRM - ARM 3/1 0.93 (t = 2.11); FRM - ARM 5/1 0.65 (t = 1.80); FRM - ARM 7/1 0.45 (t = 1.51)
    - Banks in regressions: 104, 265, 419, 296
    - Frac deposits (%) examples: 42, 26, 56, 3
  - Panel B: 30 year FRM minus ARMs
    - Deposit PT coefficients: FRM - ARM 0.46 (t = 0.50); FRM - ARM 3/1 0.76 (t = 1.76); FRM - ARM 5/1 0.67 (t = 1.94); FRM - ARM 7/1 0.43 (t = 1.44)
    - Banks and Frac deposits (%) same as Panel A

- Table 8: Bank competition, pass-through and asset mix (commercial bank data, 2001Q1-2014Q4)
  - Panel A: HHI and Deposit PT relationships
    - HHI coefficient on Deposit PT (Collapsed cross section): -10.30 (t = -4.77)
    - HHI coefficient in Panel regressions: -8.77 (t = -4.02)
    - Log(Assets) coefficient (Collapsed): 0.79 (t = 4.01)
    - Interaction ∆FF×HHI: -0.12 (t = -4.80); ∆FF×Log(Assets): 0.02 (t = 5.55)
    - Bank-Quarters: examples 57,224; Banks: 1,483
  - Panel B: HHI as instrument for Deposit PT (2SLS)
    - OLS Deposit PT → Loans, Sec: 0.48 (t = 14.40)
    - First stage: HHI → Deposit PT: -10.30 (t = -4.77); F-stat = 22.77
    - IV (examples): Loans, Sec IV coefficient 1.79 (t = 4.63); NR Loans IV 0.99 (t = 2.92); NR Securities IV 1.36 (t = 4.01)

- Table 9: Summary statistics for Bank Holding Company (BHC) data (1986Q3-2014Q4)
  - Full Sample (BHC-Quarters 78,160; BHCs 1,912)
    - Assets (BN): Median 4.2, Mean 1.25, Std. Dev. 1.82, Large Banks Std. Dev. 3.1 (table reports Full Sample/Small Banks/Large Banks with Std. Dev.)
    - Total≤1Yr (%): Median 43.3, Mean 42.9, Std. Dev. 49.7, Std. Dev. 16.0
    - Loans≤1Yr (%): Median 50.9, Mean 50.2, Std. Dev. 61.2, Std. Dev. 25.4
    - Implied Deposit Rate: Median 2.6, Mean 2.6, Std. Dev. 2.5, Std. Dev. 1.5
    - Deposit PT: Median 26.9, Mean 26.5, Std. Dev. 33.7, Std. Dev. 21.5

- Table 10: Floating mix of bank assets and deposit pass-through (BHC data, 1986Q3-2014Q4)
  - Panel A (within Quarter and Bank variation):
    - Deposit PT coefficients:
      - All (total assets ≤1yr): 0.10 (t = 6.75)
      - Loans, Sec: 0.10 (t = 6.75)
      - Loans: 0.13 (t = 5.82)
    - R2 examples: 0.15, 0.17, 0.11
    - BHC-Quarters: 78,160; BHCs: 1,912
  - Panel B (Deposit pass-through and bank size):
    - Log(Assets) coefficients on Deposit PT: 1.61 (t = 6.57); 1.57 (t = 1.42)
    - R2 examples: 0.17, 0.46

- Table 11: Sensitivity of implied loan rates to short-term interest rates (FDIC aggregate commercial bank data, 1934-2013)
  - Regression ∆y_t = α + β ∆r_t + ρ ∆y_{t−1}
    - Sample 1934-1969: ∆r_t coefficient 0.24 (t = 3.08); ∆y_{t−1} coefficient 0.37 (t = 3.14); long-run β/(1−ρ) = 0.37; R2 = 0.27; N = 344
    - Sample 1970-2013: ∆r_t coefficient 0.47 (t = 11.25); ∆y_{t−1} coefficient 0.30 (t = 4.17); long-run β/(1−ρ) = 0.67; R2 = 0.79; N = 44
    - t-statistics use Newey-West standard errors allowing autocorrelation up to five lags

*Source: wp1703 - References (appendix tables and figures and bibliography).*

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_Source: https://www.imf.org/-/media/files/publications/wp/wp1703.pdf_