## Financial Shock Transmission to Heterogeneous Firms: The Earnings-Based Borrowing Constraint Channel — Working Paper No. WP/2023/196 (content unit: wpiea2023196-print-pdf)

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### Key empirical findings on bond pricing and shock transmission
- A large share of the response in corporate bond spreads is driven by their non-fundamental component, the “excess bond premium” (EBP), following the decomposition into an expected default risk component and EBP (Gilchrist and Zakrajšek (2012)).
- Impact of identified shocks on funding costs and default probabilities across firms is persistent for both:
  - monetary policy shocks, and
  - global risk shocks,
  with the stronger impact observed for global risk shocks.
- Monetary policy shocks trigger stronger responses of excess bond returns for risky, low-rated corporate bonds; heterogeneous responses in bond excess returns are driven more by news about (non-fundamental) risk premia than about cash flows (Guo et al. (2020)).
- Contrary to much of the literature:
  - firms’ funding costs respond rather homogeneously to monetary policy shocks, and
  - firms’ funding costs respond heterogeneously to global risk shocks,
  with the differential response attributable to heterogeneity in the tightness of firms’ earnings.

### BVAR model: specification, identification, and validation
- Model form:
  - Structural daily Bayesian vector autoregression (BVAR) in structural form: Ay_t = c + sum_{l=0}^p B_l y_{t-l} + ε_t, with lag length p set to 4.
- Endogenous variables:
  - 3-month US government bond benchmark yield,
  - 10-year US government bond benchmark yield,
  - cyclically-adjusted price to earnings ratio (CAPE),
  - US nominal effective exchange rate,
  - corporate spreads (ICE Bank Of America 15+ Year BBB United States Corporate Index minus US 10-year Government Benchmark Bid Yield).
- Data transformations:
  - yields and corporate spreads in plain differences;
  - CAPE, exchange rate, and other endogenous variables in first differences of the logarithm.
- Identified structural shocks simultaneously within the model:
  - US monetary policy shock,
  - global risk shock,
  - US macro risk shock,
  - foreign monetary policy shock,
  - foreign macro risk shock.
- Identification via:
  - sign restrictions,
  - relative magnitude restrictions,
  - narrative restrictions (e.g., Lehman collapse as adverse global risk shock).
- Estimation and validation:
  - Estimated January 1995 to October 2022 at daily frequency.
  - Bayesian estimation with a normal-inverse-Wishart prior; structural shocks used in firm heterogeneity analysis are based on the median over 10,000 draws satisfying restrictions.
  - BVAR monetary policy shock series correlates closely with high-frequency Fed monetary policy surprises (Jarociński and Karadi (2020)); global risk shock co-moves with the US VIX and spikes on major global-risk events.
  - Forecast error variance decomposition (20-day ahead median FEVD, averaged over endogenous variables): US monetary policy and global risk shocks together explain about a third of total variability in US financial conditions over the sample; variable-specific FEVD ranges between 22-46 percent.

### Data, samples, and descriptive statistics
- Firm-level data:
  - Sample: listed companies included in the S&P 500 between January 2000 and May 2021.
  - Initial sample size: 436 firms; final sample statistics: Number of bonds: 7,674; Number of firms: 407; Number of bond-week observations: 2,274,822 (sample period 2000/01/07 – 2021/12/17; trimmed per Appendix Table B.1).
  - Key firm-level measures:
    - Leverage (LEV): debt-to-equity ratio,
    - Expected earnings per share (EPSE): 12-month forward EPS,
    - Interest coverage ratio (ICR): EBIT-to-interest expense,
    - Expected default frequencies (EDFs) from Moody’s KMV CreditEdge,
    - CDS spreads (5-year) from Bloomberg.
- Bond-level data and selection:
  - Source: Bloomberg; initial bond sample: 12,996 bonds.
  - Selection criteria included USD denomination, non-financial issuers, fixed coupon, remaining maturity 1–30 years, volume between USD 1 mn and USD 5 bn.
  - Final bond sample used in analysis: 7,364 bonds (10,679 bonds after weekly OAS/duration availability reduced to 7,364 after cleaning).
  - Bond-level series: option-adjusted spreads (OAS) and option-adjusted bond duration; Bloomberg Composite Credit Rating used.
- Descriptive highlights (Table 2; trimmed sample):
  - No. of bonds per firm/week: Mean 38.24; SD 82.29; P25 6.00; Median 12.00; P75 23.00.
  - Bond volume (mil): Mean 640.72; SD 636.10; P25 250.00; Median 500.00; P75 800.00.
  - Maturity at issue (years): Mean 15.73; SD 10.02; P25 9.50; Median 10.03; P75 29.98.
  - Term to maturity (years): Mean 10.49; SD 8.61; P25 3.93; Median 7.31; P75 16.43.
  - BB Composite Bond Rating: Median BBB+.
  - OAS spread (bsp): Mean 174.25; SD 167.40; P25 85.56; Median 138.24; P75 209.36.
  - Duration (years): Mean 6.91; SD 4.53; P25 3.29; Median 5.91; P75 10.09.
  - Coupon rate (pct): Mean 5.18; SD 1.89; P25 3.75; Median 5.05; P75 6.62.
  - Bond options (pct): 0.46.
  - Firm-level (selected):
    - EDF 1-Year (%): Mean 0.41; SD 1.95; P25 0.03; Median 0.05; P75 0.19.
    - Leverage ratio: Mean 47.68; SD 38.77; P25 30.70; Median 42.46; P75 57.51.
    - Expected earnings per share: Mean 4.52; SD 9.91; P25 1.69; Median 2.94; P75 5.03.
    - Interest coverage ratio: Mean 12.92; SD 46.56; P25 3.45; Median 7.25; P75 13.72.
    - S&P Issuer Rating: Median BBB+.
  - Median bond: volume USD 500 mn, 10-year tenor, BBB+ composite rating, trades at a 138 basis point spread.
  - About 46% of bonds feature embedded options.
  - OAS distribution skew: P25 85.56 basis points; P75 209.36 basis points; some values above 1500 basis points in the right tail.

### Decomposing credit spreads into fundamentals and EBP
- Objective:
  - Decompose corporate bond spreads into: fitted fundamental component based on EDFs and bond characteristics, and non-fundamental component EBP (pricing error).
- Linear spread model (bond-level):
  - s_{j,t}[k] = a_j + β_j EDF_{j,t} + γ_k X_{j,t}[k] + u_{j,t}[k] where u_{j,t}[k] denotes pricing error.
- Bond characteristics X include:
  - option-adjusted duration, coupon rate, age since issuance, bond volume, callable indicator.
- Aggregation to firm level:
  - Predicted spread \hat{s}_{j,t} = Σ_k w_{j,t}[k] \hat{s}_{j,t}[k] with w_{j,t}[k] = 1/N_{j,t}.
  - Firm-level EBP: EBP_{j,t} ≡ \hat{u}_{j,t} = Σ_k w_{j,t}[k] \hat{u}_{j,t}[k].
- Estimation notes:
  - No log transform of spreads to retain negative OAS observations; robustness checks confirm conclusions unchanged by log specification.
  - Table D.1 coefficients (full sample, dependent variable OAS): EDF_j,t: 59.396*** / 9.207 ; Duration_j,t: 3.316*** / 0.448 ; Coupon: 27.350*** / 2.312 ; Age: -1.986*** / 0.565 ; Observations: 2,207,373; Adjusted R^2: 0.424 / 0.430.

### Estimating heterogeneous responses to shocks — methodology and calibration
- Method:
  - Panel local projections (Jordà (2005)) to estimate dynamic multipliers of asset-price responses to identified shocks.
  - Shocks from the structural BVAR: US monetary policy shock ("m_t") and global risk shock ("r_t").
  - Firms dynamically sorted into quantile buckets by z_{j,t} ∈ {LEV, ICR, EPSE} computed over roughly five-year subperiods.
  - Tail indicators: bottom and top ⌧th quantiles q ∈ {⌧, 1−⌧} with benchmark ⌧ = 0.2 (20th and 80th percentiles).
  - Controls X_{j,t−1}: four lags of the VIX, 2-year US Treasury yield, Citigroup Economic Surprise Index (CESI), crisis dummies for GFC and Covid-19 peak weeks, and industry fixed effects.
  - Estimation with pooled OLS and industry fixed effects.
- Shock calibration:
  - Shocks calibrated to a 10 basis point negative (positive) impact on long-term Treasury yields over 5 days for the global risk shock (monetary policy tightening shock).
- Sample and observations:
  - Sample period: 2000/01/07 – 2021/12/17.
  - Observations reported: 222,060 (Spread), 219,513 (EBP), 220,710 (EDF), 220,964 (ln(PI)).

### Baseline impact responses at h = 0 (impact calibrated to a 10 basis point move in the 10-year US Treasury yield)
- Monetary policy shock ("m_t", 10 basis point increase):
  - Spread (full sample): 7.395*** (basis points).
  - EBP (full sample): 5.889** (basis points).
  - EDF (full sample): 0.028* (percentage points).
  - ln(PI) (equity prices): -0.035*** (log points; interpreted as a -3.5 percent fall).
  - Notes:
    - Most of the spread increase driven by EBP (~6 basis points).
    - Unexpected monetary tightening raises firms’ probability of default on average by about 0.03 percentage points.
- Global risk shock ("r_t", 10 basis point decrease i.e., spike in global risk aversion):
  - Spread (full sample): 18.628*** (basis points).
  - EBP (full sample): 15.472*** (basis points).
  - EDF (full sample): 0.056* (percentage points).
  - ln(PI) (equity prices): -0.069*** (log points; interpreted as a -6.9 percent fall).
  - Responses are about twice as large in magnitude compared to the monetary policy shock.

### Heterogeneous responses by firm risk profiles (tail interactions; benchmark ⌧ = 0.2)
- Monetary policy shock:
  - Interaction terms with tail dummies largely insignificant — monetary tightening does not transmit disproportionately to funding conditions of strong or weak firms.
  - Examples:
    - LowLEV×"m_t": -1.167 (Spread), -1.277 (EBP), -0.003 (EDF), 0.000 (ln(PI)) — not statistically significant.
    - LowEPSE×"m_t": 1.861 (Spread), -0.652 (EBP), 0.048* (EDF), -0.004* (ln(PI)) — modest significance on EDF and ln(PI).
- Global risk shock:
  - Weak (least profitable) firms are hit disproportionately more by global risk shocks.
  - Additional credit spread cost for weak firms can amount to 15 to 19 basis points relative to peers.
  - Examples:
    - LowEPSE×"r_t": 15.194*** (Spread), 8.416*** (EBP), 0.126** (EDF), -0.019*** (ln(PI)).
    - LowICR×"r_t": 18.773** (Spread), 9.504** (EBP), 0.176* (EDF), -0.022* (ln(PI)).
    - HighICR×"r_t": -3.616** (Spread), -2.995* (EBP), -0.011* (EDF), 0.002 (ln(PI)) — strong firms pay on average 4 basis points less relative to average firm upon impact.
  - LEV interactions largely insignificant, indicating earnings-based measures show stronger heterogeneity than asset-based leverage.

### Dynamics and persistence (12-week horizon)
- Initial jumps at impact:
  - Credit spreads jump by 7 basis points (monetary) and 19 basis points (global risk) upon impact.
- Further dynamics:
  - Spreads rise further to 15 basis points (monetary) and 35 basis points (global risk) during the first weeks after shocks.
  - Spreads remain persistently elevated for at least 12 weeks.
- Components and asset classes:
  - EBP remains persistently elevated at longer horizons even when fitted spread and EDF decline, indicating non-fundamental sentiment effects linger.
  - Equity prices fall sharply at impact but recover faster; pessimistic sentiment in equity markets halves within three months, whereas EBP persistence is longer.
- Overall implication:
  - Corporate funding becomes particularly strained in debt markets due to persistent non-fundamental risk premia.

### Robustness checks and extensions
- Robustness checks performed include:
  - Shortening sample to 2005–2021 (Table F.3).
  - Including lagged dependent variables (4 lags) (Table F.4).
  - Adding week fixed effects (Table F.5) and week×industry fixed effects (Table F.6).
  - Using alternative measures of firm profitability (Table F.7), sorting into 15th percentiles, resorting every 2 years.
  - Re-running analysis at bond-level with bond, firm, and industry fixed effects (Table G.1) — results broadly in line with firm-level.
  - Augmenting spread decomposition with leverage and profitability — neither significance nor core results materially change.
  - Additional checks: interact regressors with CALL_{j,t}[k], include firm fixed effects, restrict to senior unsecured bonds — results remain robust.
- Caveats:
  - Estimation on subsamples (tails) suffers from lack of power due to smaller sample sizes.
  - Sample limited to S&P 500 non-financial firms; limits external validity for smaller corporations.

### Main conclusions and implications
- Earnings-based borrowing constraint supported:
  - Empirical evidence strongly supports the earnings-based borrowing constraint hypothesis: global risk shocks have stronger, persistent, and more heterogeneous effects on corporate funding costs that depend on firms’ position within the earnings distribution.
- Comparative findings:
  - Monetary policy shocks transmit through the non-fundamental component (EBP) to funding conditions broadly across firms, without pronounced heterogeneity across firm tails.
  - Global risk shocks disproportionately affect least profitable firms (low EPSE, low ICR), raising their funding costs substantially and increasing their default risk.
  - Leverage (LEV) is generally less informative for heterogeneous sensitivity than earnings-based measures; investors do not differentially price highly versus weakly levered firms as consistently.
- Economic interpretation:
  - Both shocks move investor sentiment beyond fundamentals, but global risk shocks tilt investor sentiment away from weak, risky firms more strongly.
  - Persistent elevation of EBP suggests financial shocks impair risk-bearing capacity of intermediaries and investor sentiment, straining corporate debt financing for an extended period.

*Source: wpiea2023196-print-pdf*

### 3.6 percentage points on average relative to a monetary policy shock.

### 3.6 percentage points on average relative to a monetary policy shock.

### Key empirical findings on bond pricing and shock transmission
- A large share of the response in corporate bond spreads is driven by their non-fundamental component, the “excess bond premium” (EBP), following the decomposition into an expected default risk component and EBP (Gilchrist and Zakrajšek (2012)).
- Using panel local projections (following Jordà (2005)), the impact of the identified shocks on funding costs and default probabilities across firms is persistent for both:
  - monetary policy shocks, and
  - global risk shocks,
  with the stronger impact observed for global risk shocks.
- Granular evidence from bond prices shows monetary policy shocks trigger stronger responses of excess bond returns for risky, low-rated corporate bonds. Heterogeneous responses to monetary policy shocks in bond excess returns are driven more by news about (non-fundamental) risk premia than about cash flows (Guo et al. (2020)).
- In contrast to much of the literature, this paper finds:
  - firms’ funding costs respond rather homogeneously to monetary policy shocks, and
  - firms’ funding costs respond heterogeneously to global risk shocks,
  with the differential response attributable to heterogeneity in the tightness of firms’ earnings.

### Relation to literature and conceptual contribution
- The paper sits at the intersection of:
  - identification of shocks using sign restrictions (Arias et al., 2018) and narrative restrictions (Antolín-Díaz & Rubio-Ramírez, 2018), and
  - the literature on firm heterogeneity in transmission of shocks to funding costs and real outcomes.
- The identification approach combines sign, narrative, and relative magnitude restrictions and builds on the concept of “financial conditions” (in particular Brandt et al. (2021)).
- Compared to high-frequency event-window identification of monetary policy shocks, this approach:
  - generates a continuous daily shock series that does not depend on overlap of event dates, and
  - does not rely on the strength of an external instrument such as changes in the price of gold around narrative events.
- The findings contribute to the emerging literature emphasizing the role of firms’ earnings and earnings-based borrowing constraints (Greenwald, 2019; Lian & Ma, 2020), noting that for large US non-financial firms only 20% of debt by value is collateralized by physical assets whereas 80% is based predominantly on cash flows.

### BVAR model: variables, frequency, and identification strategy
- Model form and lag structure:
  - Structural daily Bayesian vector autoregression (BVAR) in structural form: Ay_t = c + sum_{l=0}^p B_l y_{t-l} + ε_t, with lag length p set to 4.
- Endogenous variables included to capture financial conditions for firms:
  - 3-month US government bond benchmark yield,
  - 10-year US government bond benchmark yield,
  - cyclically-adjusted price to earnings ratio (CAPE) as a measure of equity prices,
  - US nominal effective exchange rate,
  - corporate spreads (spread between ICE Bank Of America 15+ Year BBB United States Corporate Index and US 10-year Government Benchmark Bid Yield).
- Data transformations:
  - yields and corporate spreads expressed in plain differences;
  - CAPE, exchange rate, and other endogenous variables expressed in first differences of the logarithm.
- Identified structural shocks (simultaneously within the model):
  - US monetary policy shock,
  - global risk shock,
  - US macro risk shock,
  - foreign monetary policy shock,
  - foreign macro risk shock.
- Identification implemented via a combination of:
  - sign restrictions,
  - relative magnitude restrictions,
  - narrative restrictions (e.g., Lehman Brothers collapse imposed as an adverse global risk shock that was the largest driver of the fall in US equities on that day).
- Practical estimation details:
  - Estimated over the period January 1995 to October 2022 at daily frequency.
  - Bayesian estimation with a normal-inverse-Wishart prior over reduced-form parameters.
  - Structural shocks used in firm heterogeneity analysis are based on the median over 10,000 draws that satisfy the full set of imposed restrictions.
- Lag and robustness notes:
  - Results are robust to choosing a smaller or larger number of lags (see Table A.1 referenced in text).
  - Only identifying the US monetary policy and global risk shock produces median shock series highly correlated with those from the fully identified model.

### Sign and narrative restrictions (impact)
- US monetary policy shock:
  - drives up US short-term and long-term yields,
  - depresses equity prices (CAPE),
  - appreciates the US dollar,
  - restriction that long-term yields react more strongly for US monetary policy than for foreign monetary policy.
- Global risk shock:
  - captures flight-to-safety dynamics: risk asset prices fall, demand for safe US dollar-denominated assets rises, US dollar appreciates,
  - narrative restriction: Lehman collapse (2008) characterized as an adverse global risk sentiment shock that was the largest relative driver of the fall in US equities on that day.
- US macro risk shock:
  - positive shift in macro risk sentiment supports long-term yields, equity prices, and the US dollar, while compressing corporate spreads;
  - US macro risk shocks are assumed to have a stronger effect on US equity prices than foreign macro risk shocks.
- Foreign shocks:
  - foreign monetary policy and foreign macro risk shocks are identified with similar co-movements in yields and equity prices as domestic counterparts but with opposite effects on the exchange rate (since the shock originates abroad).
- Restriction on global risk having a stronger impact on the US dollar than foreign macro risk reflects the US dollar’s role as a safe haven; robustness checks indicate shocks are very robust to leaving this restriction out.

### Model validation and illustrative results
- The BVAR-generated daily monetary policy shock series correlates closely with high-frequency Fed monetary policy surprises around FOMC meetings (Jarociński and Karadi (2020)), while the BVAR captures a wider set of monetary policy shocks arising from changes in investor perception and Fed communication outside FOMC windows.
- The identified global risk shock co-moves well with the US VIX and spikes on days associated with large shocks to global risk sentiment (e.g., September 11 attacks, onset of the COVID-19 pandemic).
- Forecast error variance decomposition (20-day ahead median FEVD, averaged over endogenous variables as proxy for financial conditions FEVD):
  - US monetary policy and global risk shocks together explain about a third of the total variability in US financial conditions over the sample.
  - Variable-specific FEVD ranges between 22-46 percent.
- Illustration of recent drivers:
  - During the first weeks of the COVID-19 pandemic, US financial conditions tightened substantially due to a combination of a worsening macro outlook and adverse global risk sentiment.
  - Subsequent Fed stimulus and improving global risk sentiment loosened financial conditions to levels looser than pre-pandemic conditions.
  - In 2022, the Fed’s monetary policy tightening tightened financial conditions again.

### Firm heterogeneity analysis setup (overview)
- After identifying shocks in the BVAR, a firm-level regression framework is used to analyze heterogeneous responses of:
  - firms’ funding costs (bond spreads),
  - equity prices,
  - default prospects,
  using rich firm- and bond-level data for a sample of large US corporates.
- When testing for firm heterogeneity, the daily shocks are aggregated to match the weekly frequency of the US corporate dataset.

*Source: wpiea2023196-print-pdf*

### 3.1  Data and descriptive statistics

### 3.1  Data and descriptive statistics

### Firm-level data
- Sample universe: listed companies included in the S&P 500 index, including both current and historical constituents between January 2000 and May 2021.
- Initial sample size: 436 firms.
- Rationale for S&P 500 focus:
  - S&P 500 firms account for a large share of business cycle activity and are “granular” (Gabaix,2011).
  - These firms are exposed to monetary policy and global risk shocks through international activities.
  - Limiting to firms obtaining a substantial share of external financing through capital markets helps abstract from substitution effects between market- and bank-based financing.
  - Limits external validity for smaller corporations with potentially less liquid bonds.
- Quarterly balance sheet indicators from Thomson Reuters Datastream used to capture firm heterogeneity.
- Proxies and indicators:
  - Leverage (LEV): debt-to-equity ratio used as proxy for collateral-based constraints; debt-to-equity and debt-to-assets are highly correlated (see FigureC.1).
  - Expected earnings per share (EPSE): 12-month forward EPS used as indicator of the tightness of a firm’s EBC (earnings-based constraint).
  - Interest coverage ratio (ICR): EBIT-to-interest expense ratio used as a hybrid indicator between asset-based and earnings-based borrowing constraints.
  - Equity prices: weekly data collected from Thompson Reuters Datastream.
  - Expected default frequencies (EDFs): from Moody’s KMV CreditEdge database, aggregated from daily to weekly averages to proxy fundamental default risk.
  - CDS spreads (5-year tenor): retrieved from Bloomberg as a model-free complementary measure of firm-level credit risk.
- Notes on proxies:
  - Leverage reflects creditors’ claims on assets in liquidation; acknowledged as imperfect proxy for collateral-based borrowing.
  - EPSE facilitates comparability across firms by normalizing by shares outstanding; alternatives like ROE are backward looking and reflect book values.
  - ICR combines earnings and outstanding debt obligations and may add information beyond EPSE and LEV.
- Data frequency and coverage: firm fundamentals at quarterly frequency; market measures at weekly frequency.

### Bond-level data
- Source: Bloomberg.
- Bond selection criteria:
  - (i) active or matured, traded on any day between 7 January 2000 and 17 December 2021,
  - (ii) issued by non-financial firms,
  - (iii) denominated in USD,
  - (iv) excluding private placements,
  - (v) subject to a fixed coupon schedule,
  - (vii) remaining time to maturity between one and 30 years,
  - (viii) minimum volume of USD 1 mn and maximum volume of USD 5 bn.
- Initial bond sample from criteria (i)-(iv): 12,996 bonds.
- Bond-level series obtained: option-adjusted spreads (OAS) and option-adjusted bond duration; cross-sectional bond characteristics.
- OAS:
  - Model-based measure of a bond’s credit risk above and beyond the maturity-matched risk-free rate (zero-coupon US Treasury yield).
  - Embedded options (e.g., early redemption) accounted for in the spread model; controls for contingent cash flow risk and makes bonds with different characteristics more comparable.
- Composite credit ratings: Bloomberg Composite Credit Rating (equally weighted average of Moody’s, Standard & Poor’s, Fitch, and DBRS) retrieved as additional bond-level credit risk measure.
- Data cleaning and final sample:
  - Limited availability of weekly OAS and duration reduces sample to 10,679 bonds.
  - Additional cleaning to remove stale bonds and filtering by criteria (v)-(viii) further reduces sample to 7,364 bonds used in analysis.
  - Despite reductions, bond-week observations remain sufficient and well-distributed across the credit risk distribution (see Appendix FigureC.2).
- Notes:
  - OAS is not the transaction price; it reflects net present value of bond cash flows once state-contingent claims are taken into account.
  - OAS computation can produce negative spreads; authors refrain from log-transforming spreads to retain negative observations (robustness checks confirm results are not changed by log specification).

### Descriptive statistics and sample features
- Table 2 summary statistics (Sample period: 2000/01/07 – 2021/12/17; Number of bond-week observations: 2,274,822; Number of bonds: 7,674; Number of firms: 407). Sample statistics are based on trimmed data following Appendix TableB.1 trimming procedure.
- (a) Bond characteristics (Mean, SD, P25, Median, P75):
  - No. of bonds per firm/week: Mean 38.24, SD 82.29, P25 6.00, Median 12.00, P75 23.00
  - Bond volume (mil): Mean 640.72, SD 636.10, P25 250.00, Median 500.00, P75 800.00
  - Maturity at issue (years): Mean 15.73, SD 10.02, P25 9.50, Median 10.03, P75 29.98
  - Term to maturity (years): Mean 10.49, SD 8.61, P25 3.93, Median 7.31, P75 16.43
  - BB Composite Bond Rating: Median BBB+
  - OAS spread (bsp): Mean 174.25, SD 167.40, P25 85.56, Median 138.24, P75 209.36
  - Duration (years): Mean 6.91, SD 4.53, P25 3.29, Median 5.91, P75 10.09
  - Coupon rate (pct): Mean 5.18, SD 1.89, P25 3.75, Median 5.05, P75 6.62
  - Bond options (pct): 0.46
- (b) Firm characteristics (Mean, SD, P25, Median, P75):
  - EDF 1-Year (%): Mean 0.41, SD 1.95, P25 0.03, Median 0.05, P75 0.19
  - Leverage ratio: Mean 47.68, SD 38.77, P25 30.70, Median 42.46, P75 57.51
  - Realized earnings per share: Mean 4.04, SD 8.68, P25 1.51, Median 2.68, P75 4.60
  - Expected earnings per share: Mean 4.52, SD 9.91, P25 1.69, Median 2.94, P75 5.03
  - Interest coverage ratio: Mean 12.92, SD 46.56, P25 3.45, Median 7.25, P75 13.72
  - S&P Issuer Rating: Median BBB+
- Additional descriptive points:
  - Median bond: volume USD 500 mn, 10-year tenor, BBB+ composite rating, trades at a 138 basis point spread.
  - Median firm: 12 bonds outstanding in an average week; some firms trade more than 23 bonds in a given week.
  - About 46% of bonds feature embedded options.
  - OAS distribution is skewed: P25 85.56 basis points, P75 209.36 basis points, with some values above 1500 basis points in the right tail (partly mechanical due to OAS pricing model and reflecting a skew in default risk).
  - EDF distribution also reflects skew towards a tail of very risky firms.
- Heterogeneity across measures:
  - Distributions of LEV, EPSE, and ICR differ and do not overlap perfectly: firms at the top of the leverage distribution are not necessarily at the bottom of the earnings distribution.
  - Figure 2 plots quantiles of EPSE against quantiles of LEV and ICR; panel (ii) shows stronger bunching along the 45-degree line, supporting ICR as a hybrid indicator.
- Time-series patterns in spreads:
  - Figure 3 shows OAS across leverage (left) and earnings (right) distributions.
  - Up until the Great Recession, highly levered and cash-flow constrained firms paid a multiple of safer firms’ credit spreads.
  - The decade following the GFC exhibits a much less pronounced difference in credit spreads across firms with strong versus weak fundamentals — particularly during monetary policy normalization when investors demanded little compensation for highly levered firms’ credit risk.
  - Investors continued to price risk across the earnings distribution during the past decade; sensitivity of indebted firms’ cash flows and debt servicing costs to changes in interest rates is a potential reason for greater attention to profitability measures.

### 3.2  Decomposing Credit Spreads into Fundamental and Excess Bond Premium Components
- Objective: Decompose corporate bond spreads into a fundamental component (expected default risk based on firm fundamentals) and a non-fundamental component (excess bond premium, EBP).
- Interpretation:
  - EBP: compensation required by investors beyond risk of default; narrowly interpretable as investor risk sentiment, and related to liquidity constraints faced by financial intermediaries in bond intermediation (Gilchrist & Zakrajˇsek,2012).
- Spread model (linear specification):
  - s_{j,t}[k] = a_j + β_j EDF_{j,t} + γ_k X_{j,t}[k] + u_{j,t}[k]
  - where u_{j,t}[k] denotes the pricing error.
- Bond characteristics vector X_{j,t}[k] includes:
  - option-adjusted bond duration,
  - coupon rate,
  - age of the traded bond since issuance,
  - bond volume,
  - indicator for bonds with underlying options.
- Estimation notes:
  - Appendix D reports estimation results and deviations from Gilchrist and Zakrajˇsek (2012).
  - Natural logarithm of spreads is not used to avoid eliminating negative spread observations; robustness checks confirm conclusions are unchanged when using log specification.
- Aggregation to firm-level predicted spread and EBP:
  - Predicted spread at firm-level: \hat{s}_{j,t} = Σ_k w_{j,t}[k] \hat{s}_{j,t}[k]
  - Firm-level EBP: EBP_{j,t} ≡ \hat{u}_{j,t} = Σ_k w_{j,t}[k] \hat{u}_{j,t}[k]
  - Weights: w_{j,t}[k] = 1/N_{j,t} (simple average over all bonds of firm j).
  - Firm-level definitions enable studying heterogeneous responses of spread components to financial shocks depending on firms’ risk profiles.

*Italic: Source: wpiea2023196-print-pdf - 3.1  Data and descriptive statistics*

### 3.3  Estimating Heterogeneous Responses to Risk and Monetary Policy Shocks

### 3.3  Estimating Heterogeneous Responses to Risk and Monetary Policy Shocks

### Methodology
- Framework:
  - Panel local projections following Jordà (2005) to estimate dynamic multipliers of asset-price responses to identified shocks.
  - Shocks: identified US monetary policy shock ("
m
t
") and global risk shock ("
r
t
") from a structural BVAR based on financial conditions.
  - Horizon of interest for reported impact results: h = 0 (upon impact); impulse responses also traced over a 12-week horizon (h = 12).
- Firm sorting and interaction:
  - Firms dynamically sorted into quantile buckets using firm-level metrics z
j,t
∈ {LEV, ICR, EPSE} computed over roughly five-year subperiods between January 2000 and December 2021.
  - Tail indicators defined for the bottom and top ⌧th quantiles q ∈ {⌧, 1−⌧}; benchmark uses ⌧ = 0.2 (20th and 80th percentiles).
  - Interaction terms of shocks with tail dummies z,⌧,t and z,1−⌧,t capture heterogeneous sensitivities.
- Controls and estimation:
  - X
j,t−1
includes four lags of the VIX, the 2-year US Treasury yield, the Citigroup Economic Surprise Index (CESI), crisis dummies for peak weeks of the Global Financial Crisis and Covid-19 pandemic, and industry fixed effects.
  - Specification estimated with pooled OLS and industry fixed effects.
- Calibration of shocks:
  - Shocks calibrated to a 10 basis point negative (positive) impact on long-term Treasury yields over 5 days for the global risk shock (monetary policy tightening shock).
- Sample:
  - Sample period covers 2000/01/07 – 2021/12/17.
  - Observations reported: 222,060 (Spread), 219,513 (EBP), 220,710 (EDF), 220,964 (ln(PI)).

### Baseline (impact) responses — key statistics at h = 0
- Monetary policy shock (panel (a), impact calibrated to a 10 basis point increase in the 10-year US Treasury yield):
  - Spread (full sample): 7.395*** (basis points)
  - EBP (full sample): 5.889** (basis points)
  - EDF (full sample): 0.028* (percentage points)
  - ln(PI) (equity prices): -0.035*** (log points; interpreted as a -3.5 percent fall)
  - Notes:
    - Most of the spread increase driven by non-fundamental component EBP (~6 basis points).
    - Unexpected monetary tightening raises firms’ probability of default on average by about 0.03 percentage points (little statistical significance).
    - Equity prices drop significantly: a 10 basis point equivalent increase in US yields leads to a fall in a firm’s equity price by 3.5 percent.
- Global risk shock (panel (b), impact calibrated to a 10 basis point decrease in the 10-year US Treasury yield — i.e., spike in global risk aversion):
  - Spread (full sample): 18.628*** (basis points)
  - EBP (full sample): 15.472*** (basis points)
  - EDF (full sample): 0.056* (percentage points)
  - ln(PI) (equity prices): -0.069*** (log points; interpreted as a -6.9 percent fall)
  - Responses are about twice as large in magnitude compared to the monetary policy shock.

### Heterogeneous responses by firm risk profiles (tail interactions)
- Tail definitions used in Table 3: bottom and top 20th percentiles (⌧ = 0.2) of LEV (debt-to-equity), ICR (interest coverage ratio), EPSE (expected earnings per share).
- Main patterns:
  - Monetary policy shock:
    - Interaction terms with tail dummies largely insignificant → monetary tightening does not transmit disproportionately to funding conditions of strong or weak firms.
    - Examples from Table 3 (panel (a), impact estimates):
      - LowLEV×"m
t
: -1.167 (Spread), -1.277 (EBP), -0.003 (EDF), 0.000 (ln(PI)) — not statistically significant.
      - LowEPSE×"m
t
: 1.861 (Spread), -0.652 (EBP), 0.048* (EDF), -0.004* (ln(PI)) — modest significance on EDF and ln(PI).
  - Global risk shock:
    - Weak (least profitable) firms are hit disproportionately more by global risk shocks.
    - Additional credit spread cost for weak firms can amount to 15 to 19 basis points relative to peers.
    - Examples from Table 3 (panel (b), impact estimates):
      - LowEPSE×"r
t
: 15.194*** (Spread), 8.416*** (EBP), 0.126** (EDF), -0.019*** (ln(PI)).
      - LowICR×"r
t
: 18.773** (Spread), 9.504** (EBP), 0.176* (EDF), -0.022* (ln(PI)).
      - HighICR×"r
t
: -3.616** (Spread), -2.995* (EBP), -0.011* (EDF), 0.002 (ln(PI)) — strong firms with high ICR pay on average 4 basis points less relative to average firm upon impact.
    - LEV interactions largely insignificant:
      - LowLEV×"r
t
: -4.942 (Spread), -5.107** (EBP), -0.006 (EDF), -0.003 (ln(PI)).
      - HighLEV×"r
t
: 10.456 (Spread), 5.000* (EBP), 0.099 (EDF), -0.002 (ln(PI)).
    - Interpretation: earnings-based measures (EPSE, ICR) show stronger heterogeneity than asset-based leverage (LEV).
- EDF (expected default probability):
  - Significant sensitivity of EDF to shocks primarily when allowing for heterogeneous responses — effect concentrated in tails of weak firms.

### Dynamics and persistence (12-week horizon)
- Cumulative responses (Figure 4 summary):
  - Initial jumps at impact:
    - Credit spreads jump by 7 basis points (monetary) and 19 basis points (global risk) upon impact.
  - Further dynamics:
    - Spreads rise further to 15 basis points (monetary) and 35 basis points (global risk) during the first weeks after shocks.
    - Spreads remain persistently elevated for at least 12 weeks.
  - Components:
    - EBP remains persistently elevated at longer horizons even when fitted spread and EDF decline, indicating non-fundamental sentiment effects linger in corporate bond markets.
  - Equity:
    - Equity prices fall sharply at impact but recover somewhat faster; pessimistic sentiment in equity markets halves within three months, whereas EBP persistence is longer.
  - Overall implication: corporate funding becomes particularly strained in debt markets due to persistent non-fundamental risk premia.

### Robustness and extensions
- Robustness checks that broadly preserve baseline results:
  - Shortening sample to 2005-2021 (Table F.3).
  - Including lagged dependent variables to account for autocorrelation (Table F.4).
  - Adding week fixed effects (Table F.5) and week-industry fixed effects (Table F.6).
  - Using alternative measures of firm profitability (Table F.7).
  - Sorting into 15th percentiles and resorting every 2 years (qualitatively similar but reduced statistical power).
  - Re-running analysis at bond-level (Table G.1) including bond, firm, and industry fixed effects → results broadly in line with firm-level.
  - Augmenting spread decomposition model with leverage and profitability → neither significance nor core results materially change.
  - Additional checks: interact regressors with CALL
j,t
[k], augment spread model with additional balance-sheet indicators, include firm fixed effects, restrict to senior unsecured bonds — results remain robust.
- Caveats noted:
  - Estimation on subsamples (tails) suffers from lack of power due to smaller sample sizes.
  - Sample limited to S&P 500 non-financial firms; chosen to ensure large firms and heterogeneity needed to test earnings-based borrowing constraint hypothesis.

### Main conclusions and implications
- Earnings-based borrowing constraint supported:
  - Empirical evidence strongly supports the earnings-based borrowing constraint hypothesis: global risk shocks have stronger, persistent, and more heterogeneous effects on corporate funding costs that depend on firms’ position within the earnings distribution.
- Comparative findings:
  - Monetary policy shocks transmit through the non-fundamental component (EBP) to funding conditions broadly across firms, but without pronounced heterogeneity across firm tails.
  - Global risk shocks disproportionately affect least profitable firms (low EPSE, low ICR), raising their funding costs substantially and increasing their default risk.
  - Leverage (LEV) is generally less informative for heterogeneous sensitivity than earnings-based measures; investors do not differentially price highly versus weakly levered firms as consistently.
- Economic interpretation:
  - Both shocks move investor sentiment beyond fundamentals, but global risk shocks tilt investor sentiment away from weak, risky firms more strongly.
  - Persistent elevation of EBP suggests financial shocks impair risk-bearing capacity of intermediaries and investor sentiment, straining corporate debt financing for an extended period.

*Italic: Source — Section 3.3, "Estimating Heterogeneous Responses to Risk and Monetary Policy Shocks", wpiea2023196-print-pdf (sample period 2000/01/07 – 2021/12/17).*

### References

### wpiea2023196-print-pdf - References

### BVAR Model Validation
- Figure A.1: Comparison BVAR monetary policy shocks versus high-frequency approach
  - Left panel: shows correlation between US monetary policy shocks identified in the BVAR and high-frequency shocks on days of FOMC meetings (Jarociński and Karadi (2020)), using contribution of the US monetary policy shocks to the 10-year interest rate of the BVAR model on the day of the FOMC meeting and the 10-year interest rate instrument for the high-frequency shocks.
  - Scatter plot excludes the monetary policy shock linked to the strong reaction of the Fed in the wake of the global financial crisis (an outlier in magnitude), which is very similarly identified in both approaches and would make the correlation stronger than depicted.
  - Right panel: compares histogram of the daily US monetary policy shock contribution to 10-year yields of the BVAR with that of the high-frequency shocks on FOMC dates using the 10-year rate as instrument.
- Table A.1: Robustness BVAR: shock correlations (correlation between benchmark BVAR shocks and alternative versions)
  - US monetary policy shock / global risk shock correlations by test:
    - Test 1: no rel. restriction on US NEER — 0.9993 / 0.9910
    - Test 2: corp. spread not restricted after US macro — 0.9944 / 0.9865
    - Test 3: US policy and global risk shock only — 0.9634 / 0.9671
    - Test 4: 1 lag — 0.9972 / 0.9792
    - Test 5: 2 lags — 0.9991 / 0.9817
    - Test 6: 3 lags — 0.9988 / 0.9838
    - Test 7: 5 lags — 0.9979 / 0.9834
    - Test 8: 6 lags — 0.9973 / 0.9838
  - Notes: Test 1 omits the relative magnitude restriction on US NEER; Test 2 omits sign restriction on corporate bond spreads after a US macro risk shock; Test 3 identifies only US monetary policy and global risk shocks; Tests 4–8 vary lag lengths of endogenous variables.

- Figure A.2: Comparison global risk shocks series with VIX
  - Chart: 60-day moving average of the global risk shock from the daily BVAR, the CBOE volatility index (VIX), and selected narrative events.

- Figure A.3: Comparison global risk shocks with global uncertainty measure
  - Chart: 9-month moving average of the global risk shock from the daily BVAR and the measure of global uncertainty by Bobasu et al. (2023).

### Details of Bond- and Firm-Level Data
- Table B.1: Reduction in OAS bond-week observations for each data trimming step
  - No. OAS observations before trimming: 2,272,931
  - (i) Drop volume < 1mil and volume > 5bn: 2,262,348
  - (ii) Drop term-to-maturity < 1 year and > 30 years: 2,194,404
  - (iii) Drop OAS < -500 and OAS > 4,500: 2,186,060
  - (iv) Drop OAS if illiquid > 26 weeks in a row: 2,186,060
  - (v) Drop bond if there exist < 26 consecutive bond-week obs.: 2,185,478
  - No. OAS observations after trimming: 2,185,478
  - Note: Cut-offs in (i)-(ii) calibrated with Gilchrist and Zakrajšek (2012). Cut-offs in (iii)-(v) chosen to remove extreme outliers and stale observations while preserving tail characteristics.

- Table B.2: Industry coverage of estimation sample (Unique bonds / Unique firms)
  - Basic Industry — 314 / 20
  - Capital Goods — 1,200 / 54
  - Communications — 779 / 28
  - Consumer Cyclical — 914 / 64
  - Consumer Non-Cyclical — 1,913 / 88
  - Electric — 388 / 23
  - Energy — 639 / 39
  - Insurance — 188 / 6
  - Natural Gas — 70 / 4
  - Other Industrial — 42 / —
  - Technology — 726 / 62
  - Transportation — 383 / 13
  - Note: Estimation sample is an unbalanced panel at the bond-firm level; counts present unique number of bonds and firms by industry used in the credit spread decomposition.

### Additional Descriptive Statistics
- Figure C.1: Distribution of balance sheet proxies for financial leverage
  - Chart: median (solid line) and 20th and 80th percentiles (shaded area) of debt-to-equity and debt-to-asset ratios across the sample of S&P 500 firms.
- Figure C.2: Count of bond-week observations by rating category and distribution of option-adjusted spreads (OAS) across ratings
  - Left panel: count of bond-week observations by Bloomberg composite bond rating categories.
  - Right panel: average OAS across the same rating category subsets.

### Spread Decomposition
- D.1 Comparison with GZ spread model — methodological differences and sample choices
  - Sample and frequency differences:
    - This study: S&P500 firms; weekly observations from January 2000 to December 2021; week-end credit spreads; include all bonds issued before 28 May 2021 with remaining term to maturity ≤ 30 years.
    - Gilchrist and Zakrajšek (2012) (GZ): broader set of firms; monthly data from 1973 to 2010; month-end credit spreads; monthly frequency.
  - Spread and credit-risk measures:
    - This study: option-adjusted spread (OAS); credit risk based on Moody’s EDFs; trimmed spreads range from -500 bsp to 4500 bsp.
    - GZ: synthetic GZ spread (mimicking cash flows per Gürkaynak, Sack and Wright, 2007); distance to default from a Merton-type model; GZ spreads range from 5 bsp to 3500 bsp.
  - Model specification differences:
    - GZ: use bond characteristics plus interaction terms of callable bond indicator variables with bond characteristics; control for liquidity premia via interactions with slope, level, curvature of the yield curve; include firm-level ratings fixed effects (S&P rating) and three-digit NAICs industry fixed effects.
    - This study: use only bond characteristics (OAS corrects for embedded option pricing and liquidity premia); refrain from log-spread estimation due to presence of negative OAS values; use Bloomberg’s BICS industry classification for industry fixed effects; in some specifications include bond-level ratings fixed effects based on Bloomberg’s composite bond rating.
  - Robustness:
    - Panel LP exercise results remain virtually invariant to augmenting spread model with additional interaction terms.
    - Excluding bonds with negative OAS values does not materially affect results.
    - Aggregate-level EBP remains highly correlated with GZ-EBP even without firm fixed effects.

- D.2 Estimation results of spread model — credit spread decomposition
  - Table D.1: Credit spread decomposition based on the full sample (sample period covers 2000/01/07 – 2021/12/17; dependent variable OAS)
    - Columns (1) and (2) report estimates and standard errors (Est. / SE)
    - Coefficients (Est.*** indicates significance; clustered SEs in firm and time dimension):
      - EDF_j,t: 59.396*** / 9.207 ; 54.617*** / 17.333
      - Duration_j,t [k]: 3.316*** / 0.448 ; 4.680*** / 0.681
      - Coupon_j [k]: 27.350*** / 2.312 ; 20.905*** / 2.901
      - Age_j,t [k]: -1.986*** / 0.565 ; -0.684 / 0.601
      - Volume_j [k]: -5.979 / 4.838 ; -9.527 / 6.120
      - CALL_j [k]: 3.599 / 4.657 ; -34.402** / 13.505
      - EDF_j,t x CALL_j [k]: 7.258 / 16.264
      - Duration_j,t [k] x CALL_j [k]: -2.257*** / 0.674
      - Coupon_j [k] x CALL_j [k]: 12.778*** / 2.881
      - Age_j,t [k] x CALL_j [k]: -4.463*** / 0.871
      - Volume_j [k] x CALL_j [k]: 7.611 / 5.961
    - Industry FE: YES
    - Observations: 2,207,373
    - Adjusted R^2: 0.424 / 0.430
    - Notes: Daily EDFs at 1-year horizon converted into weekly averages. CALL_j[k] equals one for bonds with any type of underlying call option. Industry fixed effects based on BICS industry level 3.

  - Table D.2: Credit spread decomposition based on a restricted sample of only senior unsecured bonds (sample period covers 2000/01/07 – 2021/12/17; dependent variable OAS)
    - Columns (1) and (2) report estimates and standard errors (Est. / SE)
      - EDF_j,t: 55.651*** / 12.542 ; 47.456*** / 16.470
      - Duration_j,t [k]: 3.131*** / 0.561 ; 3.715*** / 0.940
      - Coupon_j [k]: 26.266*** / 2.879 ; 22.747*** / 3.744
      - Age_j,t [k]: -1.598*** / 0.559 ; -0.849 / 0.582
      - Volume_j [k]: -9.948** / 4.963 ; -13.050** / 6.178
      - CALL_j [k]: -3.497 / 4.620 ; -31.098** / 13.678
      - EDF_j,t x CALL_j [k]: 17.568 / 14.931
      - Duration_j,t [k] x CALL_j [k]: -0.875 / 0.910
      - Coupon_j [k] x CALL_j [k]: 7.545** / 3.498
      - Age_j,t [k] x CALL_j [k]: -2.783*** / 0.911
      - Volume_j [k] x CALL_j [k]: 7.070 / 5.979
    - Industry FE: YES
    - Observations: 1,776,736
    - Adjusted R^2: 0.403 / 0.411
    - Notes: Standard errors clustered in firm and time dimension. Daily EDFs at 1-year horizon converted into weekly averages. CALL_j[k] equals one for bonds with any type of underlying call option. Industry fixed effects based on BICS industry level 3.

*wpiea2023196-print-pdf - References (selected appendices and tables).*

### Appendix E  Supplementary results: firm-level local projections

### Appendix E  Supplementary results: firm-level local projections

### E.1 Responses to shocks across weak and strong firms
- Figures E.3–E.5 present cumulative impulse responses of asset pricing variables to:
  - monetary policy shock s_m_t calibrated to a 10 basis point increase (panel (a)) and decrease (panel (b)) in the 10-year US Treasury yield;
  - global risk shock r_t calibrated similarly.
- Responses obtained from estimating model (6) over a 12-week horizon h= 12 for the sample period 01/2000-12/2021.
- Excess bond premium and fitted corporate spread obtained from a decomposition following Gilchrist and Zakrajˇsek (2012), estimated over 01/2000-12/2021.
- Shaded areas in figures denote 95% and 68% confidence bands.
- Stratifications shown:
  - by leverage (LEV) — Figure E.3;
  - by interest coverage ratio (ICR) — Figure E.4;
  - by expected earnings per share (EPSE) — Figure E.5.

### E.2 Asymmetric responses to tightening and easing shocks
- Figure E.6 presents cumulative responses to identified tightening and easing shocks:
  - monetary policy tightening (+) and easing (−) shocks ε_m and global risk tightening (−) and easing (+) shocks ε_r.
- Responses obtained from model (6) over h= 12, sample 01/2000-12/2021.
- Shocks calibrated to a 10 basis point increase (panel (a)) and decrease (panel (b)) in the 10-year US Treasury yield.
- Excess bond premium and fitted spread from Gilchrist and Zakrajˇsek (2012) decomposition (01/2000-12/2021).
- Shaded areas denote 95% and 68% confidence bands.

### Appendix F  Robustness: firm-level panel regressions

### F.1 Baseline results: Extended set of estimates of asset price reactions (Table F.1)
- Estimated impact at horizon h=0 (initial impact) of:
  - monetary policy shock "m_t (panel (a)) calibrated to a 10 basis point increase;
  - global risk shock "r_t (panel (b)) calibrated to a 10 basis point decrease.
- Dependent variables in columns: Spread (column 1), Fitted Spread (column 2), Excess Bond Premium (EBP) (column 3), CDS (column 4), ln(PI) (equity prices) (column 5), EDF (default probabilities) (column 6).
- Key coefficients (panel (a): monetary policy shock "m_t):
  - "m_t: 7.395*** ; 1.547* ; 5.889** ; 3.118*** ; 0.028* ; -0.035***
  - alternative spec: "m_t: 7.261*** ; 1.106** ; 6.220*** ; 2.932*** ; 0.020** ; -0.035***
  - LowLEV × "m_t: -1.167 ; -0.136 ; -1.277 ; -0.431** ; -0.003 ; 0.000
  - HighLEV × "m_t: 1.842 ; 2.462 ; -0.537 ; 1.351 ; 0.045 ; -0.002
  - LowICR × "m_t: 2.670 ; 4.182 ; -1.178 ; 2.494 ; 0.073 ; -0.007*
  - HighICR × "m_t: -0.358 ; -0.219* ; -0.126 ; -0.722** ; -0.005** ; 0.001
  - LowEPSE × "m_t: 1.861 ; 2.715* ; -0.652 ; 1.544* ; 0.048* ; -0.004*
  - HighEPSE × "m_t: 0.034 ; -0.385 ; 0.468 ; -0.149 ; -0.006 ; -0.001*
- Key coefficients (panel (b): global risk shock "r_t):
  - "r_t: 18.628*** ; 3.200* ; 15.472*** ; 6.615*** ; 0.056* ; -0.069***
  - alternative spec: "r_t: 17.502*** ; 2.246** ; 15.406*** ; 6.125*** ; 0.039** ; -0.068***
  - LowLEV × "r_t: -4.942 ; -0.357 ; -5.107** ; -1.195* ; -0.006 ; -0.003
  - HighLEV × "r_t: 10.456 ; 5.370 ; 5.000* ; 3.643 ; 0.099 ; -0.002
  - LowICR × "r_t: 18.773** ; 9.965* ; 9.504** ; 7.758* ; 0.176 ; -0.022*
  - HighICR × "r_t: -3.616** ; -0.628* ; -2.995* ; -2.036*** ; -0.011* ; 0.002
  - LowEPSE × "r_t: 15.194*** ; 7.041** ; 8.416*** ; 5.022** ; 0.126** ; -0.019***
  - HighEPSE × "r_t: -1.695 ; -0.700 ; -0.788 ; -0.603 ; -0.013 ; -0.005
- Industry fixed effects: YES for all columns.
- Observations: 222,060 ; 219,575 ; 219,513 ; 219,821 ; 220,710 ; 220,964.
- Note: sample period 2000/01/07 – 2021/12/17. Standard errors and controls omitted. Asterisks denote significance (*** p<0.01, ** p<0.05, * p<0.1).

### F.1 Baseline results normalized to 1 standard deviation (Table F.2)
- Estimates of model (6) at h=0 normalized to a 1 standard deviation adverse shock.
- Key normalized coefficients (panel (a): monetary policy shock "m_t):
  - "m_t: 1.989*** ; 0.416* ; 1.584** ; 0.839*** ; 0.008* ; -0.009***
  - "m_t alt: 1.953*** ; 0.298** ; 1.673*** ; 0.789*** ; 0.005** ; -0.009***
  - LowLEV × "m_t: -0.314 ; -0.037 ; -0.343 ; -0.116** ; -0.001 ; 0.000
  - HighLEV × "m_t: 0.495 ; 0.662 ; -0.145 ; 0.363 ; 0.012 ; -0.001
  - LowICR × "m_t: 0.718 ; 1.125 ; -0.317 ; 0.671 ; 0.020 ; -0.002*
  - HighICR × "m_t: -0.096 ; -0.059* ; -0.034 ; -0.194** ; -0.001** ; 0.000
  - LowEPSE × "m_t: 0.501 ; 0.730* ; -0.175 ; 0.415* ; 0.013 ; -0.001*
  - HighEPSE × "m_t: 0.009 ; -0.104 ; 0.126 ; -0.040 ; -0.002 ; -0.000*
- Key normalized coefficients (panel (b): global risk shock "r_t):
  - "r_t: 2.643*** ; 0.454* ; 2.195*** ; 0.939*** ; 0.008* ; -0.010***
  - "r_t alt: 2.483*** ; 0.319** ; 2.186*** ; 0.869*** ; 0.005** ; -0.010***
  - LowLEV × "r_t: -0.701 ; -0.051 ; -0.725** ; -0.170* ; -0.001 ; -0.000
  - HighLEV × "r_t: 1.484 ; 0.762 ; 0.709* ; 0.517 ; 0.014 ; -0.000
  - LowICR × "r_t: 2.664** ; 1.414* ; 1.348** ; 1.101* ; 0.025 ; -0.003*
  - HighICR × "r_t: -0.513** ; -0.089* ; -0.425* ; -0.289*** ; -0.002* ; 0.000
  - LowEPSE × "r_t: 2.156*** ; 0.999** ; 1.194*** ; 0.713** ; 0.018** ; -0.003***
  - HighEPSE × "r_t: -0.240 ; -0.099 ; -0.112 ; -0.085 ; -0.002 ; -0.001
- Observations: 222,060 ; 219,575 ; 219,513 ; 219,821 ; 220,710 ; 220,964.

### F.2 Shorter sample period 2005–2021 (Table F.3)
- Estimates of model (6) at h=0 for sample period 2005/01/07 – 2021/12/17.
- Panel (a) monetary policy shock "m_t:
  - "m_t: 7.507*** ; 1.563* ; 5.985** ; 3.195*** ; 0.028* ; -0.035***
  - alternative spec: "m_t: 7.362*** ; 1.110** ; 6.321*** ; 2.994*** ; 0.020** ; -0.035***
  - LowLEV × "m_t: -1.297 ; -0.139 ; -1.432 ; -0.468** ; -0.003 ; 0.000
  - HighLEV × "m_t: 2.002 ; 2.528 ; -0.433 ; 1.461 ; 0.043 ; -0.002
  - LowICR × "m_t: 2.910 ; 4.309 ; -1.035 ; 2.660 ; 0.072 ; -0.007*
  - HighICR × "m_t: -0.369 ; -0.253* ; -0.107 ; -0.796*** ; -0.005** ; 0.001
  - LowEPSE × "m_t: 2.060 ; 2.928* ; -0.646 ; 1.705* ; 0.049* ; -0.004*
  - HighEPSE × "m_t: 0.041 ; -0.370 ; 0.457 ; -0.186 ; -0.006 ; -0.001
- Panel (b) global risk shock "r_t:
  - "r_t: 18.886*** ; 3.249* ; 15.684*** ; 6.724*** ; 0.056* ; -0.069***
  - alternative spec: "r_t: 17.767*** ; 2.308** ; 15.610*** ; 6.225*** ; 0.039** ; -0.069***
  - LowLEV × "r_t: -5.054 ; -0.370 ; -5.211** ; -1.176 ; -0.007 ; -0.003
  - HighLEV × "r_t: 10.520 ; 5.316 ; 5.136* ; 3.676 ; 0.095 ; -0.002
  - LowICR × "r_t: 18.983** ; 9.962 ; 9.783** ; 7.791* ; 0.172 ; -0.022*
  - HighICR × "r_t: -3.717** ; -0.615 ; -3.099* ; -2.065*** ; -0.011* ; 0.002
  - LowEPSE × "r_t: 15.674*** ; 7.260** ; 8.705*** ; 5.187** ; 0.125** ; -0.019***
  - HighEPSE × "r_t: -1.736 ; -0.657 ; -0.880 ; -0.582 ; -0.012 ; -0.005
- Observations: 204,863 ; 202,558 ; 202,521 ; 202,654 ; 203,245 ; 203,608.

### F.3 Baseline model augmented with lagged dependent variable (Table F.4)
- Model (6) augmented with 4 lags of the dependent variable; reports initial impact at h=0. Sample 2000/01/07 – 2021/12/17.
- Panel (a) monetary policy shock "m_t:
  - "m_t: 7.228*** ; 1.567* ; 5.718** ; 3.166*** ; 0.029* ; -0.035***
  - alternative spec: "m_t: 7.109*** ; 1.160** ; 6.046** ; 2.994*** ; 0.021** ; -0.035***
  - LowLEV × "m_t: -1.065 ; -0.146 ; -1.100 ; -0.420** ; -0.003 ; 0.000
  - HighLEV × "m_t: 1.666 ; 2.297 ; -0.674 ; 1.268 ; 0.043 ; -0.002
  - LowICR × "m_t: 2.628 ; 4.031 ; -1.289 ; 2.431 ; 0.072 ; -0.007*
  - HighICR × "m_t: -0.197 ; -0.230* ; 0.034 ; -0.726** ; -0.005** ; 0.001
  - LowEPSE × "m_t: 1.822 ; 2.691* ; -0.670 ; 1.545* ; 0.049* ; -0.004*
  - HighEPSE × "m_t: -0.040 ; -0.366 ; 0.399 ; -0.151 ; -0.005 ; -0.001
- Panel (b) global risk shock "r_t:
  - "r_t: 18.189*** ; 3.235* ; 15.093*** ; 6.634*** ; 0.058* ; -0.069***
  - alternative spec: "r_t: 17.030*** ; 2.344** ; 14.970*** ; 6.175*** ; 0.040** ; -0.068***
  - LowLEV × "r_t: -4.825 ; -0.377 ; -4.924** ; -1.176 ; -0.007 ; -0.003
  - HighLEV × "r_t: 10.482 ; 5.067 ; 5.106* ; 3.456 ; 0.097 ; -0.002
  - LowICR × "r_t: 19.565** ; 9.533* ; 10.146** ; 7.486* ; 0.171 ; -0.022*
  - HighICR × "r_t: -3.413* ; -0.616** ; -2.866* ; -1.983*** ; -0.010** ; 0.002
  - LowEPSE × "r_t: 15.778*** ; 6.875** ; 9.011*** ; 4.950** ; 0.125** ; -0.019***
  - HighEPSE × "r_t: -1.974 ; -0.641 ; -1.056 ; -0.562 ; -0.012 ; -0.005
- Observations: 222,060 ; 219,575 ; 219,513 ; 219,821 ; 220,710 ; 220,964.

### F.4 Results with additional fixed effects (Tables F.5 and F.6)
- Table F.5: week fixed effects added; Industry FE = YES; Week FE = YES.
  - Panel (a) monetary policy (selected tail interactions):
    - LowLEV × "m_t: -0.450 ; -0.188 ; -0.385 ; -0.592** ; -0.004 ; 0.000
    - HighLEV × "m_t: 2.203 ; 2.447 ; -0.200 ; 1.302 ; 0.044 ; -0.002
    - LowICR × "m_t: 2.466 ; 4.174 ; -1.518 ; 2.458* ; 0.072 ; -0.007*
    - LowEPSE × "m_t: 1.986 ; 2.730* ; -0.597 ; 1.529* ; 0.048* ; -0.004*
  - Panel (b) global risk (selected tail interactions):
    - LowLEV × "r_t: -3.329 ; -0.429 ; -3.173 ; -1.611* ; -0.008 ; -0.004
    - HighLEV × "r_t: 11.232* ; 5.351 ; 5.759** ; 3.503 ; 0.099 ; -0.003
    - LowICR × "r_t: 18.292** ; 9.950* ; 8.821*** ; 7.715* ; 0.175 ; -0.021*
    - LowEPSE × "r_t: 15.542*** ; 7.078** ; 8.675*** ; 4.944** ; 0.126** ; -0.019***
  - Observations: 222,060 ; 219,575 ; 219,513 ; 219,821 ; 220,710 ; 220,964.
- Table F.6: week × industry fixed effects; Industry FE = NO; Week × Industry FE = YES.
  - Panel (a) monetary policy (selected tail interactions):
    - LowLEV × "m_t: -1.297 ; -0.928* ; -0.587 ; -0.718** ; -0.016* ; 0.001
    - HighLEV × "m_t: 2.325 ; 2.500 ; -0.128 ; 1.199 ; 0.045 ; -0.003***
    - LowICR × "m_t: 2.151 ; 4.535* ; -2.200 ; 2.217 ; 0.078 ; -0.007**
    - LowEPSE × "m_t: 1.335 ; 2.177* ; -0.701 ; 1.253** ; 0.039 ; -0.004**
  - Panel (b) global risk (selected tail interactions):
    - LowLEV × "r_t: -7.243** ; -2.449** ; -5.258** ; -2.676** ; -0.043** ; 0.004
    - HighLEV × "r_t: 11.432* ; 5.606 ; 5.707** ; 3.357* ; 0.102 ; -0.006
    - LowICR × "r_t: 18.221** ; 10.680* ; 8.157*** ; 7.063* ; 0.185* ; -0.023***
    - HighICR × "r_t: -6.708*** ; -1.642*** ; -5.031** ; -2.065*** ; -0.029*** ; 0.009***
    - LowEPSE × "r_t: 12.797** ; 5.602* ; 7.400*** ; 3.528** ; 0.100* ; -0.015**
  - Observations: 221,914 ; 219,429 ; 219,367 ; 219,675 ; 220,564 ; 220,818.

### F.5 Results with alternative earnings-based measures (Table F.7)
- Earnings-based tails: ROE (return on equity), PE (price-earnings ratio), EPSEgrowth (y-o-y % change in expected EPS), EPSTgrowth (y-o-y % change in realized EPS).
- Panel (a) monetary policy shock s_m_t:
  - s_m_t: 7.007*** ; 1.048* ; 5.982*** ; 2.790*** ; 0.019** ; -0.035***
  - LowROE × s_m_t: 2.026 ; 3.227** ; -0.988 ; 2.531* ; 0.057** ; -0.004*
  - HighROE × s_m_t: 0.351 ; -0.037 ; 0.367 ; -0.427 ; 0.000 ; 0.002*
  - s_m_t alt: 6.838*** ; 0.782** ; 6.018*** ; 2.770*** ; 0.014** ; -0.034***
  - LowPE × s_m_t: 4.269* ; 4.455** ; 0.018 ; 2.281 ; 0.076** ; -0.009**
  - LowEPSEgrowth × s_m_t: 3.275 ; 3.080** ; -0.084 ; 3.196* ; 0.052*** ; -0.007*
  - HighEPSEgrowth × s_m_t: 1.229 ; 2.412* ; -1.385 ; 1.075 ; 0.044* ; -0.008***
  - LowEPSTgrowth × s_m_t: 5.016* ; 1.915** ; 2.947 ; 1.972* ; 0.032** ; -0.005*
  - HighEPSTgrowth × s_m_t: 0.357 ; 1.086 ; -0.818 ; 0.886 ; 0.016* ; -0.006***
- Panel (b) global risk shock s_r_t:
  - s_r_t: 16.414*** ; 1.979* ; 14.521*** ; 5.686*** ; 0.035* ; -0.068***
  - LowROE × s_r_t: 15.342*** ; 7.769*** ; 8.024** ; 7.423** ; 0.135*** ; -0.015***
  - HighROE × s_r_t: -1.553 ; -0.028 ; -1.568 ; -1.543* ; 0.003 ; 0.010*
  - s_r_t alt: 14.898*** ; 1.294** ; 13.516*** ; 5.329*** ; 0.023** ; -0.064***
  - LowPE × s_r_t: 25.218** ; 11.454*** ; 14.385** ; 8.297** ; 0.194*** ; -0.036***
  - LowEPSEgrowth × s_r_t: 18.337*** ; 7.637*** ; 10.039** ; 8.501*** ; 0.128*** ; -0.025***
  - HighEPSEgrowth × s_r_t: 6.455 ; 5.267* ; 0.889 ; 3.607 ; 0.093* ; -0.020**
  - LowEPSTgrowth × s_r_t: 15.756*** ; 2.447* ; 13.431*** ; 5.810*** ; 0.044* ; -0.065***
  - LowEPSTgrowth × s_m_t (panel labeling retained from source): 21.520*** ; 5.583*** ; 15.593** ; 6.133*** ; 0.093*** ; -0.028***
  - HighEPSTgrowth × s_m_t: 9.726* ; 2.656 ; 6.816* ; 2.673 ; 0.041 ; -0.018***
- Industry FE: YES for all columns.
- Observations: 222,060 ; 219,575 ; 219,513 ; 219,821 ; 220,710 ; 220,964.
- Note: sample period 2000/01/07 – 2021/12/17. Asterisks denote significance (*** p<0.01, ** p<0.05, * p<0.1).

*Source: Appendix E–F, “Supplementary results: firm-level local projections” (wpiea2023196-print-pdf).*

### Appendix G  Robustness: Bond-level Results of Shock Impact

### Appendix G  Robustness: Bond-level Results of Shock Impact

### Impact on contemporaneous change in corporate and CDS spreads (Table G.1)
- Dependent variables (columns): (1) Spread t,t1, (2) Pred. Spread t,t1, (3) EBP t,t1, (4) CDS t,t1.
- Panel (a): Monetary policy shock (shock calibrated to a 10 basis point increase in the 10-year US Treasury yield)
  - "m_t" coefficients: 9.835*** 1.832** 7.977*** 3.020***
  - Alternative specification: "m_t": 9.231*** 1.022** 8.232*** 2.750***
  - LowLEV×"m_t": -2.187** -0.186 -2.270** -0.285
  - HighLEV×"m_t": 0.338 0.835 -0.466 0.639
  - "m_t" (third block): 8.394*** 0.687*** 7.676*** 2.507***
  - LowICR×"m_t": 3.404* 2.765* 0.863 2.151*
  - HighICR×"m_t": -0.079 -0.325** 0.264 -0.542***
  - "m_t" (fourth block): 9.109*** 0.935** 8.152*** 2.709***
  - LowEPSE×"m_t": 0.939 1.709 -0.699 1.214
  - HighEPSE×"m_t": -0.631 -0.180 -0.489 -0.203
- Panel (b): Global risk shock (shock calibrated to a 10 basis point decrease in the 10-year US Treasury yield)
  - "r_t" coefficients: 23.454*** 3.918** 19.461*** 6.487***
  - Alternative specification: "r_t": 20.378*** 2.093** 18.296*** 5.541***
  - LowLEV×"r_t": -6.105*** -0.350 -6.266*** -0.485
  - HighLEV×"r_t": 6.542** 1.682 4.870*** 2.351*
  - "r_t" (third block): 18.037*** 1.191*** 16.829*** 4.962***
  - LowICR×"r_t": 18.623*** 6.769** 12.086*** 6.638**
  - HighICR×"r_t": -2.925* -0.806** -2.080 -1.779***
  - "r_t" (fourth block): 19.308*** 1.624** 17.626*** 5.313***
  - LowEPSE×"r_t": 14.909*** 4.837* 10.169** 4.950**
  - HighEPSE×"r_t": -2.646 -0.224 -2.453 -0.613
- Fixed effects: Bond FE YES, Firm FE YES, Industry FE YES.
- Observations: 1,895,150; 1,875,950; 1,875,269; 1,884,174 (corresponding to columns (1)-(4)).
- Note highlights:
  - Estimates are bond-level regressions for monetary policy shock "m_t" (panel (a)) and global risk shock "r_t" (panel (b)).
  - Indicator variables for tails of firms (20th and 80th percentiles) computed as outlined in (4)-(5).
  - Sample period: 2000/01/07 – 2021/12/17.
  - Shocks calibrated to a 10 basis point increase (panel (a)) and decrease (panel (b)) in the 10-year US Treasury yield.
  - Excess bond premium (EBP) and fitted spread obtained from decomposition following Gilchrist and Zakrajˇsek (2012), estimated over the sample period.
  - Asterisks denote statistical significance (*** for p<0.01, ** for p<0.05, * for p<0.1).

### Impact on one-period-ahead change in corporate and CDS spreads (Table G.2)
- Dependent variables (columns): (1) Spread t+1,t1, (2) Pred. Spread t+1,t1, (3) EBP t+1,t1, (4) CDS t+1,t1.
- Panel (a): Monetary policy shock (shock calibrated to a 10 basis point increase in the 10-year US Treasury yield)
  - "m_t" coefficients: 12.213*** 2.018** 10.232*** 3.591***
  - Alternative specification: "m_t": 11.233*** 1.085** 10.161*** 3.252***
  - LowLEV×"m_t": -2.237** -0.163 -2.288** -0.271
  - HighLEV×"m_t": 1.359 1.077 0.316 0.747
  - "m_t" (third block): 10.380*** 0.742*** 9.608*** 2.968***
  - LowICR×"m_t": 5.197 3.162 2.269 2.560*
  - HighICR×"m_t": -0.771 -0.371** -0.385 -0.676***
  - "m_t" (fourth block): 11.332*** 1.148** 10.160*** 3.255***
  - LowEPSE×"m_t": 1.848 1.474 0.449 1.178
  - HighEPSE×"m_t": -1.206 -0.318 -0.937 -0.211
- Panel (b): Global risk shock (shock calibrated to a 10 basis point decrease in the 10-year US Treasury yield)
  - "r_t" coefficients: 29.829*** 4.158** 25.737*** 7.553***
  - Alternative specification: "r_t": 25.581*** 2.000* 23.608*** 6.434***
  - LowLEV×"r_t": -6.134*** -0.477 -6.051*** -0.097
  - HighLEV×"r_t": 8.289 1.820 6.418* 2.663
  - "r_t" (third block): 21.985*** 0.827** 21.159*** 5.778***
  - LowICR×"r_t": 27.560*** 8.234** 19.666*** 7.729**
  - HighICR×"r_t": -4.556** -0.944** -3.581** -2.078***
  - "r_t" (fourth block): 23.504*** 1.371** 22.089*** 6.164***
  - LowEPSE×"r_t": 23.012** 5.840* 17.337*** 5.681**
  - HighEPSE×"r_t": -3.307 -0.298 -3.121 -0.533
- Fixed effects: Bond FE YES, Firm FE YES, Industry FE YES.
- Observations: 1,888,147; 1,868,980; 1,868,306; 1,877,258 (corresponding to columns (1)-(4)).
- Note highlights:
  - Estimates are bond-level regressions for monetary policy shock "m_t" (panel (a)) and global risk shock "r_t" (panel (b)).
  - Indicator variables for tails of firms (20th and 80th percentiles) computed as outlined in (4)-(5).
  - Sample period: 2000/01/07 – 2021/12/17.
  - Shocks calibrated to a 10 basis point increase (panel (a)) and decrease (panel (b)) in the 10-year US Treasury yield.
  - Excess bond premium (EBP) and fitted spread obtained from decomposition following Gilchrist and Zakrajˇsek (2012), estimated over the sample period.
  - Asterisks denote statistical significance (*** for p<0.01, ** for p<0.05, * for p<0.1).

*Financial Shock Transmission to Heterogeneous Firms: The Earnings-Based Borrowing Constraint Channel — Working Paper No. WP/2023/196*

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_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023196-print-pdf.pdf_