## Section 3.1–3.4: Construction of shocks and full specification

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### Estimating and filtering shocks (Section 3.1)
- Two-step shock estimation:
  - Decompose firm revenue growth into a sectoral term and an idiosyncratic residual à la di Giovanni, Levchenko, and Mejean (2014).
  - Define industry upturns and downturns as large changes in the sectoral component and convert them into binary dummies.
- Decomposition details:
  - Year-over-year revenue growth:
    - γi,t = ln( Salesi,t / Salesi,t−4 ) × 100 (Equation 3.2)
  - Nominal sales growth decomposition:
    - γi,t = δn,t + εi,t (Equation 3.3)
      - δn,t is the macro sectoral component specific to industry n.
      - εi,t is the firm-specific idiosyncratic component.
  - Data handling and sample:
    - Winsorize sales growth at the 2.5th and 97.5th percentiles.
    - Require at least 10 firms per industry; on average, 57 firms per industry in the regression sample.
    - Table A.2 documents properties and persistence; size-dependent bias is evident when including a size factor.
- Filtering and binary shock indicators:
  - Remove a linear time trend from δn,t by OLS.
  - Define downturns and upturns using detrended δn,t percentiles:
    - δ−n,t = 1 if δdetrendedn,t < 25th
    - δ+n,t = 1 if δdetrendedn,t > 75th (Equation 3.4)
  - Convert upturns and downturns into binary dummies to avoid imposing linearity and mitigate size-dependent bias.
  - Normalize εi,t so that interpretation is an idiosyncratic shock of one standard deviation.

### Variable definitions (Table 1 selected entries)
- Text-based financial constraints:
  - Text-based indexi,t Numeric: The “Delay Investment Score” from Hoberg and Maksimovic (2015)
  - Unconstrained firmi,t Dummy: Text-based index < −0.062 (25th percentile)
  - Constrained firmi,t Dummy: Text-based index ≥ +0.036 (75th percentile)
  - Unconstrained industryi,t Dummy: Over 47% (75th percentile) of firms are above the medium score
  - Constrained industryi,t Dummy: Below 27% (25th percentile) of firms are above the medium score
- Leverage:
  - Firm leveragei,t Numeric: Debti,t / Assetsi,t ×100 if Assetsi,t > 0, winsorized between [0, 100]
  - Peer leveragei,t Numeric: Average leverage of competitors
  - Low leveragei,t Dummy: Firm leverage < Peer leverage − 13.7 (25th percentile)
  - High leveragei,t Dummy: Firm leverage ≥ Peer leverage + 9.9 (75th percentile)
- Interest coverage ratio (ICR):
  - ICRi,t Numeric: EBITi,t / Interest expensei,t if interest expensei,t > 0, ICRi,t = +∞ if interest expensei,t ≤ 0
  - Low ICRi,t Dummy: ICR < 1
  - High ICR industryi,t Dummy: Over 80% (75th percentile) of firms have ICR ≥ 1
  - Low ICR industryi,t Dummy: Below 56% (25th percentile) of firms have ICR ≥ 1
- Other variables:
  - Capital expenditurei,t Numeric: CAPXi,t / Assetsi,t−1 ×100 for firms with Assetsi,t−1 > 0
  - Productivityi,t Numeric: ln(Salesi,t / Employeesi,t) for firms with Employeesi,t > 0
  - High productivityi,t Dummy: Productivity ≥ Peer average + 0.4 (75th percentile)
  - Market sharei,t Numeric: Nominal sales share in the industry
  - Tobin’s qi,t Numeric: (Assetsi,t + Market Equityi,t − Book Equityi,t) / Assetsi,t
- Notes:
  - In Compustat, EBITi,t = Interest expensei,t + Pre-tax incomei,t.
  - For text-based index, if a firm has at least one non-missing value in the database, then its missing observations (if any) are treated as neither constrained nor unconstrained when computing the dummies.

### Full empirical specification (Section 3.2)
- Basic pooled regression (all regressors have three additional lags):
  - yi,t+h = β1 · δ−n,t · FCi,t−1 · FCpeern,t−1
    + β2 · δ−n,t · FCi,t−1
    + β′1 · δ+n,t · FCi,t−1 · FCpeern,t−1
    + β′2 · δ+n,t · FCi,t−1
    + ˜β1 · εi,t · FCi,t−1 · FCpeern,t−1
    + ˜β2 · εi,t · FCi,t−1
    + ˜β3 · εi,t · FCpeern,t−1
    + ˜β4 · εi,t
    + β5 · FCi,t−1 · FCpeern,t−1
    + β6 · FCi,t−1
    + Full interaction controlsi,t
    + Other controlsi,t−1
    + Lags
    + Firm FEi
    + Time FEt
    + FIC Industry x Time FEn,t
    + ζi,t (Equation 3.5)
- Dependent variable — investment channel:
  - yi,t+h is firm i’s future capital expenditure (CAPX), either cumulative or quarterly.
  - Cumulative CAPX:
    - ycumi,t+h = Σh k=1 CAPXi,t+k / Assetsi,t−1
  - Quarterly CAPX:
    - yi,t+h = CAPXi,t+h / Assetsi,t−1
- Right-hand side:
  - Shock terms: δ−i,t, δ+i,t, εi,t as defined above.
  - FCi,t−1 and FCpeern,t−1 summarize lagged financial constraints of firm i and its competitors (measures in Section 3.3).
  - Full interaction controls and other controls described in Section 3.4.
  - Standard errors clustered by industry, firm, and time.

### Measures of financial constraints (Section 3.3)
- FCi,t−1 and FCpeern,t−1 are binary dummies unless noted otherwise.
- Main measure: text-based financial constraint measure (Hoberg and Maksimovic, 2015).
- Additional robustness measures:
  - Plain-vanilla leverage.
  - Size-Age (SA) index by Hadlock and Pierce (2010).
  - Whited-Wu (WW) index by Whited and Wu (2006).
  - Interest coverage ratio (ICR).
- Fixed effects absorption (percent variation absorbed by industry–time and firm fixed effects):
  - WW and SA indices: 74–82% and 77–86% of the variation is absorbed, respectively.
  - Text-based measure, leverage, and the ICR: fixed effects account for only 47–48%, 55–59%, and 47–50%, respectively.
  - Conclusion: WW and SA indices are far less informative after fixed effects; text-based, leverage, and ICR remain more informative.
- Use text-based measure at both firm and industry levels and compare text-based and leverage for firm-level unconstrained classification; compare text-based and ICR for industry-level unconstrained classification.

### Control variables and baseline specification (Section 3.4 and Section 4)
- Controls aligned with literature (e.g., Rauh, 2006; Hoberg and Maksimovic, 2015; Grieser and Liu, 2019).
- Full interactions with shock terms and peers’ financial constraints are included for important controls.
- Productivity:
  - Labor productivity relative to peer average.
  - Categorical productivity ladder with 5 categories (very low to very high) defined by the 5th, 10th, 90th, and 95th percentiles; reference group = 10th–90th percentiles.
  - Annual frequency → lagged by one year (Productivity ladderi,t−4).
  - Full productivity controls include triple interaction:
    - Productivity interactionsi,t = Shocksi,t × Productivity ladderi,t−4 × FCpeern,t−1 + ···
- Lumpy investments:
  - Categorical variable dividing lagged CAPX at the 90th and 95th percentiles; reference group = below the 90th percentile.
  - Use triple interaction and associated terms to control for lumpy investments.
- Market share controls (baseline specification):
  - Categorical market share using the 90th and 95th percentiles as thresholds; reference group = firms with non-extraordinary market share.
  - Triple interaction and all associated terms included to control for extraordinary market share.
- Tobin’s q:
  - Partitioned at the 5th, 10th, 90th, and 95th percentiles; reference group = middle category.
  - Full interactions with this categorical variable are added.
- Other non-interacted controls: lagged CAPX, peers’ average CAPX, and leverage.
- Interacted controls: triple interaction terms for firm–industry channels and extraordinary market share.

### Empirical estimation details
- Standard errors clustered by industry, firm, and quarter.
- Significance notation: *p<0.1, **p<0.05, ***p<0.01.

### Baseline empirical results on firm interactions (summary)
- Baseline dependent variable: 6-quarter ahead cumulative CAPX, ycum_i,t+6.
- Key interaction: financially unconstrained firms × financially constrained industries (coefficient β1).
- Measures used:
  - Industry-level: text-based "unconstrained industry" dummy.
  - Firm-level: "low leverage" dummy (columns (1)–(4)) and text-based "unconstrained firm" dummy (columns (5)–(8)).
- Estimated β1 (Downturn × Dummy × Constrained peers) across Table 2 columns:
  - Columns (1)–(4) (Leverage dummy): 1.21**, 1.72**, 1.51**, 1.43**
  - Columns (5)–(8) (Text-based dummy): 0.53, 1.06***, 1.25***, 1.16***
  - Text summary: Under both measures β1 is 1.1-1.5 after 6 quarters and remains significant after fixed effects, industry size filter, and full interaction controls.
- Selected coefficients (Table 2):
  - Idiosyncratic shocks — ˜β4:
    - (1) 0.73*** (0.09)
    - (2) 0.74*** (0.10)
    - (3) 0.62*** (0.08)
    - (4) 0.63*** (0.07)
    - (5) 0.74*** (0.09)
    - (6) 0.75*** (0.09)
    - (7) 0.60*** (0.08)
    - (8) 0.65*** (0.07)
  - Idiosyncratic shocks × Constrained peers — ˜β3:
    - (1) -0.36*** (0.09)
    - (2) -0.41*** (0.11)
    - (3) -0.23** (0.09)
    - (4) -0.23** (0.09)
    - (5) -0.33*** (0.12)
    - (6) -0.36*** (0.13)
    - (7) -0.18 (0.11)
    - (8) -0.23** (0.11)
- Fit and sample (Table 2):
  - R2: 0.737, 0.707, 0.722, 0.713, 0.736, 0.705, 0.721, 0.712
  - Within R2: 0.086, 0.079, 0.121, 0.124, 0.085, 0.078, 0.121, 0.124
  - N (observations): 125,241; 98,602; 95,112; 112,990; 122,133; 96,173; 92,869; 110,455
  - Firms: 4,625; 4,312; 4,208; 4,272; 4,440; 4,147; 4,052; 4,111
  - FIC industries: 124; 95; 95; 96; 123; 95; 95; 96

### Dynamic/local projection evidence
- β1 dynamics (Figure 3 summary):
  - β1 stabilizes at 1-1.5% of pre-shock assets after 8 quarters.
  - Results with the text-based measure are more significant.
  - This magnitude ≈ two times as large as the effect of a one-standard-deviation idiosyncratic shock (˜β4).
- Industry upturns: firm interactions are not sizable during upturns.
- Competitors’ financial constraints matter:
  - ˜β3 is often large and significant, implying competitors affect a firm’s response to idiosyncratic shocks.

### Medium-term sales gains (Section 4.2)
- Dependent variable:
  - y∆sales_i,t+h = (Cum. Sales_i,t+h − Cum. Sales_i,t−1) / Assets_i,t−1
  - Cum. Sales_i,t = Σ_{k=0}^{3} Sales_i,t−k
- Sample restrictions:
  - Focus on small and medium unconstrained firms: market share below the 75th percentile (2.5% of industrywide sales).
  - Restrict to firms with non-missing sales in 16 quarters (y∆sales_i,t+16 ≠ NA).
  - Dependent variable winsorized at 5 and 95 percentiles.
- Sales dynamics (Figure 4/local projections):
  - Sales begin to rise marginally about 2 years after a downturn.
  - Sales increase stabilizes at 10% of pre-shock assets after 4 years.
  - The 10% increase is quantitatively similar to the effect of an idiosyncratic shock of one standard deviation (Table A.6).
  - The increase is significant at the 10% level in 16 quarters.
  - Timing consistent with most investment occurring in the second year after a downturn.

### Firm and industry heterogeneity (Section 4.3)
- Market share:
  - Firms split into extraordinarily large (>75th percentile, 2.5% of industrywide sales) and small/medium (≤75th percentile).
  - For small and medium firms, β1 is larger and more significant.
  - For extraordinarily large firms, the β1 effect disappears.
  - Interpretation: firm interactions are almost entirely driven by small and medium firms.
- Product similarity (Hoberg and Phillips (2016) similarity score):
  - Firms with product similarity ≤25th percentile: β1 small and insignificant.
  - Firms with higher product similarity: β1 remains larger and significant.
  - Interpretation: greater product similarity → larger firm interactions.
- Industry concentration (TNIC HHI):
  - In high-HHI industries (above 75th percentile), β1 is much smaller and insignificant.
  - Interpretation: weaker countercyclical effects of firm interactions in highly concentrated industries.
- Note: market share and concentration measures are endogenous; causal mechanisms are not identified here.

### Equilibrium implications and hypothesis testing (Section 5)
- Competing interpretations of β1:
  - Competitive interaction channel: unconstrained firms increase investment during downturns to substitute for constrained firms’ reduced investment, raising investment and sales for unconstrained firms.
  - Strategic crowding-out channel: unconstrained firms overinvest strategically to lower rivals’ marginal benefit and push constrained rivals into inaction.
- Theoretical setup:
  - MB curve shared across firms; MC curves differ by financial constraint (more convex for constrained firms).
  - Nonconvex adjustment costs and substitutability of investment across firms allow deterrence/crowding-out via MB shifts and inaction regimes.
- Hypotheses (model terms):
  - Hypothesis 5.1 (no crowding out): β1|Highly constrained = β1|Less constrained = 0 ≪ β1|Unconstrained
  - Hypothesis 5.2 (crowding out): β1|Highly constrained ≪ β1|Less constrained ≤ 0 ≪ β1|Unconstrained
- Empirical test (FE-DiD):
  - Replace FCi,t−1 with categorical variable; estimate relative effects βFE_1|i = β1|i − β1|0.
  - Test ordering consistent with Hypothesis 5.1 versus crowding out ordering.
- Empirical findings (Section 5.3 and Figure 8):
  - Using text-based categorical FCi,t−1 and h=6.
  - In constrained industries, highly constrained firms show no evidence of being worse off than less constrained firms.
  - Example (Panel (b) summary): the average of two unconstrained categories is higher than the "high" category by 1.11 (p=0.041) and the "less high" category by 1.33 (p=0.011).
  - Regressions in unconstrained industries and high ICR industries show no evidence that highly constrained firms are negatively affected.
  - Split by firm size: results unchanged for small and medium firms.
  - Conclusion: results reject the crowding-out hypothesis and support the competitive interaction interpretation.

### Main conclusions (Section 6)
- During industry downturns, financially unconstrained competitors significantly increase capital expenditure to substitute for depressed investment by constrained firms.
- Investment increase strongest among unconstrained firms with low or medium market share and leads to substantial sales gains in 3–4 years (sales gains stabilize at 10% of pre-shock assets after 4 years for small and medium firms).
- Aggregate effects of financial heterogeneity are substantially mitigated by firm interactions during downturns; competition during negative idiosyncratic shocks is more intensive than competition during industry downturns.
- Findings are robust to replacing the financial constraint measure with leverage.
- Open questions for future research:
  - Why extraordinarily large firms are unresponsive during downturns (possible roles: industry concentration and strategic differences).
  - Origins and implications of the sizeable dispersion of financial constraints for building full-scale quantitative models.

### Appendix highlights — summary statistics and shock decomposition
- Table A.1 (selected statistics, regression-sample with industry size filter):
  - Sectoral component: Count 126,889; Mean 7.43; SD 14.04; Min -62.50; p25 2.34; p50 8.26; p75 14.32; Max 98.23
  - Idiosyncratic component: Count 126,889; Mean -0.893; SD 2.97; Min -189.65; p25 -12.57; p50 -1.16; p75 11.05; Max 168.32
  - Capital expenditure: Count 126,697; Mean 1.32; SD 1.49; Min 0.00; p25 0.35; p50 0.82; p75 1.69; Max 9.96
  - Market share: Count 126,889; Mean 2.73; SD 6.00; Min 0.00; p25 0.10; p50 0.50; p75 2.17; Max 44.99
  - Leverage: Count 126,762; Mean 22.78; SD 22.39; Min 0.00; p25 1.56; p50 18.79; p75 35.74; Max 100.00
  - Productivity: Count 123,712; Mean 5.44; SD 1.01; Min -3.09; p25 4.93; p50 5.43; p75 5.97; Max 11.01
  - Notes: Tradable sectors include 2-digit NAICS industries: 11, 21, 31, 32, 33, 51. The idiosyncratic component is not standardized. Neither the sectoral nor idiosyncratic component is winsorized because sales growth input is winsorized at 2.5 and 97.5 percentiles.
- Table A.2 (properties of δn,t and εi,t, 1988-2019 panel):
  - Sectoral and idiosyncratic AR(1) and size interactions reported; examples:
    - Sectoral: 0.99*** (0.01); -0.01** (0.01); 0.79*** (0.00)
    - Sectoral × Large: 0.90*** (0.01); -0.10*** (0.01)
    - Idiosyncratic: 0.57*** (0.00)
  - Observations: up to 221,255; Firms: up to 5,418; FIC industries: up to 142.
- Appendix B — Shock decomposition implications:
  - Under CES and monopolistic competition, ln(pf,t yf,t) decomposes into macro, sectoral, and firm-level idiosyncratic factors; time fixed effects can absorb macro factors (Equations B.1–B.8).
  - Under imperfect competition, real market share Γf is endogenous and responds to sectoral demand φj; in industries with uneven market shares Γf’s dependence on φj biases additive decompositions and leads larger firms to have different revenue elasticities to sectoral demand shocks (Equations B.9–B.19).

*Source: wpiea2023110-print-pdf — Sections 3.1–3.4 from the provided PDF content.*

### Section 3.1 explains the construction of the shocks.  Section 3.2 lays out the full specification.

### Section 3.1–3.2: Construction of shocks and full specification

### 3.1 Estimating shocks
- Two-step shock estimation:
  - Decompose revenue growth into a sectoral term and an idiosyncratic residual à la di Giovanni, Levchenko, and Mejean (2014).
  - Define industry upturns and downturns as large changes in the sectoral component and convert them into binary dummies.
- Decomposition:
  - Let γi,t be the year-over-year revenue growth of firm i:
    - γi,t = ln( Salesi,t / Salesi,t−4 ) × 100 (Equation 3.2)
  - Decompose nominal sales growth:
    - γi,t = δn,t + εi,t (Equation 3.3)
    - δn,t is the macro sectoral component specific to industry n where firm i operates.
    - εi,t is the firm-specific idiosyncratic component.
  - Notes:
    - Winsorize sales growth at the 2.5th and 97.5th percentiles.
    - Require at least 10 firms per industry; on average, 57 firms per industry in the regression sample.
    - Table A.2 (referenced) shows properties and persistence of estimated components; size-dependent bias is evident when including size factor.
- Filtering shocks:
  - Remove a linear time trend from δn,t by OLS.
  - Define downturns and upturns using detrended δn,t percentiles:
    - δ−n,t = 1 if δdetrendedn,t < 25th
    - δ+n,t = 1 if δdetrendedn,t > 75th (Equation 3.4)
  - Convert upturns and downturns into binary dummies to avoid imposing linearity and to mitigate size-dependent bias.
  - Normalize εi,t so that interpretation is an idiosyncratic shock of one standard deviation.
- Table 1: Definitions of key variables (selected entries preserved exactly)
  - Text-based financial constraints
    - Text-based indexi,t Numeric: The “Delay Investment Score” from Hoberg and Maksimovic (2015)
    - Unconstrained firmi,t Dummy: Text-based index < −0.062 (25th percentile)
    - Constrained firmi,t Dummy: Text-based index ≥ +0.036 (75th percentile)
    - Unconstrained industryi,t Dummy: Over 47% (75th percentile) of firms are above the medium score
    - Constrained industryi,t Dummy: Below 27% (25th percentile) of firms are above the medium score
  - Leverage
    - Firm leveragei,t Numeric: Debti,t / Assetsi,t ×100 if Assetsi,t > 0, winsorized between [0, 100]
    - Peer leveragei,t Numeric: Average leverage of competitors
    - Low leveragei,t Dummy: Firm leverage < Peer leverage − 13.7 (25th percentile)
    - High leveragei,t Dummy: Firm leverage ≥ Peer leverage + 9.9 (75th percentile)
  - Interest coverage ratio (ICR)
    - ICRi,t Numeric: EBITi,t / Interest expensei,t if interest expensei,t > 0, ICRi,t = +∞ if interest expensei,t ≤ 0
    - Low ICRi,t Dummy: ICR < 1
    - High ICR industryi,t Dummy: Over 80% (75th percentile) of firms have ICR ≥ 1
    - Low ICR industryi,t Dummy: Below 56% (25th percentile) of firms have ICR ≥ 1
  - Other variables
    - Capital expenditurei,t Numeric: CAPXi,t / Assetsi,t−1 ×100 for firms with Assetsi,t−1 > 0
    - Productivityi,t Numeric: ln(Salesi,t / Employeesi,t) for firms with Employeesi,t > 0
    - High productivityi,t Dummy: Productivity ≥ Peer average + 0.4 (75th percentile)
    - Market sharei,t Numeric: Nominal sales share in the industry
    - Tobin’s qi,t Numeric: (Assetsi,t + Market Equityi,t − Book Equityi,t) / Assetsi,t
  - Notes: In Compustat, EBITi,t is calculated as Interest expensei,t + Pre-tax incomei,t. For text-based index, if a firm has at least one non-missing value in the database, then its missing observations (if any) are treated as neither constrained nor unconstrained when computing the dummies.

### 3.2 Specification
- Basic pooled specification (all regressors have three additional lags, not spelled out):
  - yi,t+h = β1 · δ−n,t · FCi,t−1 · FCpeern,t−1
    + β2 · δ−n,t · FCi,t−1
    + β′1 · δ+n,t · FCi,t−1 · FCpeern,t−1
    + β′2 · δ+n,t · FCi,t−1
    + ˜β1 · εi,t · FCi,t−1 · FCpeern,t−1
    + ˜β2 · εi,t · FCi,t−1
    + ˜β3 · εi,t · FCpeern,t−1
    + ˜β4 · εi,t
    + β5 · FCi,t−1 · FCpeern,t−1
    + β6 · FCi,t−1
    + Full interaction controlsi,t
    + Other controlsi,t−1
    + Lags
    + Firm FEi
    + Time FEt
    + FIC Industry x Time FEn,t
    + ζi,t (Equation 3.5)
- Dependent variable (investment channel):
  - yi,t+h is firm i’s future capital expenditure (CAPX), either cumulative or quarterly.
  - Cumulative CAPX:
    - ycumi,t+h = Σh k=1 CAPXi,t+k / Assetsi,t−1
  - Quarterly CAPX:
    - yi,t+h = CAPXi,t+h / Assetsi,t−1
- Right-hand side variables:
  - Shock terms: δ−i,t, δ+i,t, εi,t as defined above.
  - FCi,t−1 and FCpeern,t−1 summarize lagged financial constraints of firm i and its competitors, respectively (measures discussed in Section 3.3).
  - Full interaction controls and other controls are described in Section 3.4.
  - Standard errors clustered by industry, firm, and time.

### 3.3 Measures of financial constraints
- Both FCi,t−1 and FCpeern,t−1 are binary dummies unless otherwise noted.
- Main measure: text-based financial constraint measure by Hoberg and Maksimovic (2015).
- Additional measures for robustness:
  - Plain-vanilla leverage.
  - Size-Age (SA) index by Hadlock and Pierce (2010).
  - Whited-Wu (WW) index by Whited and Wu (2006).
  - Interest coverage ratio (ICR).
- Fixed effects absorption (percentages of variation absorbed by industry–time and firm fixed effects, depending on threshold):
  - WW and SA indices: 74–82% and 77–86% of the variation is absorbed, respectively.
  - Text-based measure, leverage, and the ICR: fixed effects account for only 47–48%, 55–59%, and 47–50%, respectively.
  - Conclusion: WW and SA indices are far less informative after fixed effects; text-based, leverage, and ICR are more informative.
- Dummies based on text-based measure, leverage, and the ICR are defined in Table 1.
- Use text-based measure at both firm and industry levels.
  - For financially unconstrained firms, compare results using text-based measure and leverage in parallel.
  - For financially unconstrained industries, compare text-based measure and the ICR in parallel.

### 3.4 Control variables
- Controls broadly in line with the literature (e.g., Rauh, 2006; Hoberg and Maksimovic, 2015; Grieser and Liu, 2019).
- Full interactions with shock terms and peers’ financial constraints are included for important controls.
- Productivity:
  - Measure: labor productivity relative to peer average.
  - Use categorical productivity ladder with 5 categories from very low to very high defined by the 5th, 10th, 90th, and 95th percentiles; reference group is 10th–90th percentiles.
  - Productivity is annual frequency and thus lagged by one year (i.e., Productivity ladderi,t−4).
  - Full productivity controls include triple interaction:
    - Productivity interactionsi,t = Shocksi,t × Productivity ladderi,t−4 × FCpeern,t−1 + ···
- Lumpy investments:
  - Categorical variable using lagged CAPX that divides lagged CAPX at the 90th and 95th percentiles.
  - Reference group: below the 90th percentile.
  - Use triple interaction and associated terms to control for lumpy investments.
- Extraordinary market share:
  - Firms with extraordinary size relative to the industry may behave differently; this is explored later in the text (Section referenced).

*Source: wpiea2023110-print-pdf — Sections 3.1–3.4 from the provided PDF content.*

### 4. In the baseline specification, I include a triple interaction and all associated terms to control

### 4. In the baseline specification, I include a triple interaction and all associated terms to control for extraordinary market share.  The categorical variable for market share again uses the 90th and  95th  percentiles  as  thresholds,  and  the  reference  group  is  the  group  of  firms  with  non-extraordinary market share.

### Baseline specification and controls
- Market share: categorical variable with thresholds at the 90th and 95th percentiles; reference group = firms with non-extraordinary market share.
- Tobin’s q: partitioned at the 5th, 10th, 90th, and 95th percentiles; reference group = middle category (firms with normal Tobin’s q). Full interactions with this categorical variable are added to control for Tobin’s q.
- Other non-interacted controls included: lagged CAPX, peers’ average CAPX, and leverage.
- Interacted controls: triple interaction terms included to control for firm–industry interaction channels and extraordinary market share.

### Empirical results on firm interactions (summary)
- Dependent variable in baseline regressions: 6-quarter ahead cumulative CAPX, ycum_i,t+6.
- Key interaction: financially unconstrained firms × financially constrained industries captures firm interactions (coefficient denoted β1).
- Measures of financial constraints:
  - Industry-level: text-based "unconstrained industry" dummy.
  - Firm-level: "low leverage" dummy (columns (1)–(4)) and text-based "unconstrained firm" dummy (columns (5)–(8)).
- Estimated β1 (Downturn × Dummy × Constrained peers) across Table 2 columns:
  - Columns (1)–(4) (Leverage dummy): 1.21**, 1.72**, 1.51**, 1.43**
  - Columns (5)–(8) (Text-based dummy): 0.53, 1.06***, 1.25***, 1.16***
  - Text summary: Under both measures β1 is 1.1-1.5 after 6 quarters and remains significant after fixed effects, industry size filter, and full interaction controls.
- Dynamic/local projection evidence (Figure 3):
  - β1 stabilizes at 1-1.5% of pre-shock assets after 8 quarters.
  - Results using the text-based measure are more significant.
  - This magnitude is approximately two times as large as the effect of a one-standard-deviation idiosyncratic shock (β̃4).
- Industry upturns: firm interactions are not sizable during upturns.
- Idiosyncratic shocks:
  - Idiosyncratic shocks coefficient β̃4 is large and significant.
  - Competitors’ financial constraints interaction (β̃3) is large and significant in many specifications, implying competitors affect a firm’s response to idiosyncratic shocks.

### Selected coefficients and statistics from baseline regressions (Table 2)
- Industry downturns — Downturn × Dummy × Constrained peers (β1):
  - (1) 1.21** (0.47)
  - (2) 1.72** (0.67)
  - (3) 1.51** (0.68)
  - (4) 1.43** (0.69)
  - (5) 0.53 (0.37)
  - (6) 1.06*** (0.38)
  - (7) 1.25*** (0.43)
  - (8) 1.16*** (0.38)
- Idiosyncratic shocks — β̃4:
  - (1) 0.73*** (0.09)
  - (2) 0.74*** (0.10)
  - (3) 0.62*** (0.08)
  - (4) 0.63*** (0.07)
  - (5) 0.74*** (0.09)
  - (6) 0.75*** (0.09)
  - (7) 0.60*** (0.08)
  - (8) 0.65*** (0.07)
- Idiosyncratic shocks × Constrained peers — β̃3:
  - (1) -0.36*** (0.09)
  - (2) -0.41*** (0.11)
  - (3) -0.23** (0.09)
  - (4) -0.23** (0.09)
  - (5) -0.33*** (0.12)
  - (6) -0.36*** (0.13)
  - (7) -0.18 (0.11)
  - (8) -0.23** (0.11)
- Goodness-of-fit and sample:
  - R2: 0.737, 0.707, 0.722, 0.713, 0.736, 0.705, 0.721, 0.712 (columns (1)–(8))
  - Within R2: 0.086, 0.079, 0.121, 0.124, 0.085, 0.078, 0.121, 0.124
  - N (observations): 125,241; 98,602; 95,112; 112,990; 122,133; 96,173; 92,869; 110,455
  - Firms: 4,625; 4,312; 4,208; 4,272; 4,440; 4,147; 4,052; 4,111
  - FIC industries: 124; 95; 95; 96; 123; 95; 95; 96
- Standard errors clustered by industry, firm, and quarter.
- Significance notation: *p<0.1, **p<0.05, ***p<0.01.

### Medium-term gains in sales (Section 4.2)
- Dependent variable: change in future rolling cumulative sales normalized by pre-shock assets:
  - y∆sales_i,t+h = (Cum. Sales_i,t+h − Cum. Sales_i,t−1) / Assets_i,t−1
  - Cum. Sales_i,t = Σ_{k=0}^{3} Sales_i,t−k
- Sample restrictions:
  - Focus on small and medium unconstrained firms: market share below the 75th percentile (2.5% of industrywide sales).
  - Restrict to firms with non-missing sales in 16 quarters (i.e., y∆sales_i,t+16 ≠ NA) to eliminate firm exit composition effects.
  - Dependent variable winsorized at 5 and 95 percentiles.
- Sales dynamics (Figure 4/local projections):
  - Sales begin to rise marginally about 2 years after a downturn.
  - Sales increase stabilizes at 10% of pre-shock assets after 4 years.
  - The 10% increase is quantitatively similar to the effect of an idiosyncratic shock of one standard deviation (see Table A.6).
  - Despite long horizon, the increase is significant at the 10% level in 16 quarters.
  - Timing consistent with most investment occurring in the second year after a downturn.

### Firm and industry heterogeneity (Section 4.3)
- Market share:
  - Firms split into extraordinarily large (market share > 75th percentile, 2.5% of industrywide sales) and small/medium (≤75th percentile).
  - For small and medium firms, β1 is larger and more significant.
  - For extraordinarily large firms, the β1 effect disappears completely.
  - Interpretation: firm interactions are almost entirely driven by small and medium firms.
- Product similarity (Hoberg and Phillips (2016) similarity score):
  - Firms with product similarity ≤25th percentile: β1 small and insignificant.
  - Firms with higher product similarity: β1 remains unchanged (i.e., larger and significant).
  - Interpretation: greater product similarity → larger firm interactions.
- Industry concentration (TNIC Herfindahl-Hirschman Index (HHI)):
  - In high-HHI industries (above 75th percentile), β1 is much smaller and insignificant.
  - Interpretation: weaker countercyclical effects of firm interactions in highly concentrated industries.
- Note: market share and concentration measures are endogenous; causal mechanisms not identified in this paper.

### Equilibrium implications and hypothesis testing (Section 5)
- Competing interpretations of β1:
  - Competitive interaction channel: unconstrained firms increase investment during downturns to substitute for constrained firms’ reduced investment, leading to higher investment and sales for unconstrained firms.
  - Strategic crowding-out channel: unconstrained firms overinvest strategically to lower rivals’ marginal benefit and push constrained rivals into inaction; potentially reduces constrained firms’ investment.
- Theoretical setup:
  - MB (marginal benefit) curve shared across firms; MC (marginal cost) curves differ by financial constraint (more convex for constrained firms).
  - Nonconvex adjustment costs and substitutability of investment across firms allow deterrence/crowding-out via MB shifts and inaction regimes.
- Hypotheses (expressed in model terms):
  - Hypothesis 5.1 (no crowding out): β1|Highly constrained = β1|Less constrained = 0 ≪ β1|Unconstrained
  - Hypothesis 5.2 (crowding out): β1|Highly constrained ≪ β1|Less constrained ≤ 0 ≪ β1|Unconstrained
- Empirical test via FE-DiD:
  - Replace FC_i,t−1 with categorical variable (n categories); estimate relative effects βFE_1|i = β1|i − β1|0.
  - Testing whether βFE_1|Less constrained = 0 ≪ βFE_1|Unconstrained (consistent with Hypothesis 5.1) versus alternative ordering implied by crowding out.
- Empirical findings on crowding out (Section 5.3 and Figure 8):
  - Using text-based measure to construct categorical FC_i,t−1 and h=6.
  - In constrained industries, highly constrained firms show no evidence of being worse off than less constrained firms.
  - Example (Panel (b) summary): the average of two unconstrained categories is higher than the "high" category by 1.11 (p=0.041) and the "less high" category by 1.33 (p=0.011).
  - Regressions in unconstrained industries and high ICR industries show no evidence that highly constrained firms are negatively affected.
  - Split by firm size: results remain unchanged when focusing on small and medium firms.
  - Conclusion: results reject the crowding-out hypothesis and support the competitive interaction interpretation.

### Main conclusions (Section 6)
- During industry downturns, financially unconstrained competitors significantly increase capital expenditure to substitute for depressed investment by constrained firms.
- The investment increase is strongest among unconstrained firms with low or medium market share and leads to substantial sales gains in 3–4 years (sales gains stabilize at 10% of pre-shock assets after 4 years for small and medium firms).
- Aggregate effects of financial heterogeneity are substantially mitigated by firm interactions during downturns; competition during negative idiosyncratic shocks is more intensive than competition during industry downturns.
- Findings are robust to replacing the financial constraint measure with leverage.
- Open questions for future research highlighted by the paper:
  - Why extraordinarily large firms are unresponsive during downturns (potential role of industry concentration and strategic differences).
  - Origins and implications of the sizeable dispersion of financial constraints for building full-scale quantitative models.

*Source: Excerpt from the provided IMF working paper content unit.*

### References

### References

### Appendix A — Additional Tables and Figures (summary and key statistics)
- Figures
  - Figure A.1: Dispersion of the text-based financial constraint measure by Hoberg and Maksimovic (2015) after removing industry fixed effects.
  - Figure A.2: TNIC and NAICS industry size distribution; industry sizes based on the regression sample with the industry size filter (e.g., industry with 100 Compustat firms but 30 in regression sample is counted as 30).
  - Figure A.3: Testing crowding out (Small and Medium Firms, h=6) — panels distinguish unconstrained vs constrained industries and high ICR industries; displays β_FE_1|i for small and medium firms only.

- Table A.1: Summary Statistics (sample based on regression sample with industry size filter; definitions notes follow table)
  - Sectoral component: Count 126,889; Mean 7.43; SD 14.04; Min -62.50; p25 2.34; p50 8.26; p75 14.32; Max 98.23
  - Idiosyncratic component: Count 126,889; Mean -0.893; SD 2.97; Min -189.65; p25 -12.57; p50 -1.16; p75 11.05; Max 168.32
  - Industry downturns: Count 126,889; Mean 0.22; SD 0.41; Min 0.00; p25 0.00; p50 0.00; p75 0.00; Max 1.00
  - Industry upturns: Count 126,889; Mean 0.24; SD 0.43; Min 0.00; p25 0.00; p50 0.00; p75 0.00; Max 1.00
  - Capital expenditure: Count 126,697; Mean 1.32; SD 1.49; Min 0.00; p25 0.35; p50 0.82; p75 1.69; Max 9.96
  - Unconstrained firm (text-based): Count 123,665; Mean 0.26; SD 0.44; Min 0.00; p25 0.00; p50 0.00; p75 1.00; Max 1.00
  - Constrained firm (text-based): Count 123,665; Mean 0.26; SD 0.44; Min 0.00; p25 0.00; p50 0.00; p75 1.00; Max 1.00
  - Unconstrained industry (text-based): Count 126,889; Mean 0.26; SD 0.44; Min 0.00; p25 0.00; p50 0.00; p75 1.00; Max 1.00
  - Constrained industry (text-based): Count 126,889; Mean 0.21; SD 0.41; Min 0.00; p25 0.00; p50 0.00; p75 0.00; Max 1.00
  - Leverage: Count 126,762; Mean 22.78; SD 22.39; Min 0.00; p25 1.56; p50 18.79; p75 35.74; Max 100.00
  - Relative leverage: Count 126,762; Mean 0.12; SD 19.58; Min -58.83; p25 -12.49; p50 -4.18; p75 9.38; Max 92.72
  - Low leverage: Count 126,889; Mean 0.22; SD 0.41; Min 0.00; p25 0.00; p50 0.00; p75 0.00; Max 1.00
  - High leverage: Count 126,889; Mean 0.24; SD 0.43; Min 0.00; p25 0.00; p50 0.00; p75 0.00; Max 1.00
  - ICR below 1: Count 107,169; Mean 0.29; SD 0.45; Min 0.00; p25 0.00; p50 0.00; p75 1.00; Max 1.00
  - Low ICR industry: Count 126,889; Mean 0.24; SD 0.42; Min 0.00; p25 0.00; p50 0.00; p75 0.00; Max 1.00
  - High ICR industry: Count 126,889; Mean 0.30; SD 0.46; Min 0.00; p25 0.00; p50 0.00; p75 1.00; Max 1.00
  - Productivity: Count 123,712; Mean 5.44; SD 1.01; Min -3.09; p25 4.93; p50 5.43; p75 5.97; Max 11.01
  - Relative productivity: Count 123,712; Mean 0.03; SD 0.78; Min -7.67; p25 -0.32; p50 0.03; p75 0.40; Max 6.02
  - Market share: Count 126,889; Mean 2.73; SD 6.00; Min 0.00; p25 0.10; p50 0.50; p75 2.17; Max 44.99
  - Tradable sector: Count 126,889; Mean 0.64; SD 0.48; Min 0.00; p25 0.00; p50 1.00; p75 1.00; Max 1.00
  - Notes: Productivity refers to labor productivity. Tradable sectors include 2-digit NAICS industries: 11, 21, 31, 32, 33, 51. The idiosyncratic component is not standardized. Neither the sectoral nor idiosyncratic component is winsorized because sales growth input is winsorized at 2.5 and 97.5 percentiles.

- Table A.2: Properties of δ_{n,t} and ε_{i,t} (panel regressions; sample 1988-2019)
  - Columns report estimates for Raw Sales Growth, Idiosyncratic Component, Sectoral, AR(1), Idiosyncratic, AR(1)
  - Reported coefficients and significance:
    - Sectoral: 0.99*** (0.01); -0.01** (0.01); 0.79*** (0.00)
    - Sectoral × Non-large: 1.01*** (0.01); 0.01** (0.01)
    - Sectoral × Large: 0.90*** (0.01); -0.10*** (0.01)
    - Idiosyncratic: 0.57*** (0.00)
  - Firm FE: YYYYYY (included in columns); Size dummy YY (included where indicated)
  - R^2 values: 0.228, 0.230, 0.109, 0.111, 0.682, 0.407
  - Within R^2 values: 0.138, 0.140, 0.000, 0.000, 0.636, 0.331
  - Observations (N): 221,255; 220,425; 221,255; 220,425; 212,569; 212,569
  - Firms: 5,418; 5,414; 5,418; 5,414; 5,404; 5,404
  - FIC industries: 142; 142; 142; 142; 139; 139
  - Standard errors in parentheses; *p<0.1, **p<0.05, ***p<0.01
  - Note: Size dummy indicates firm market share > 75th percentile (2.3%).

- Tables A.3–A.6: Regression results (dependent variable cumulative CAPX in 6 quarters (h=6) for Tables A.3–A.5; Table A.6 dependent variable change in future sales at horizons h=4,8,12,16,20)
  - Common elements:
    - Regressions interact industry downturns/upturns and idiosyncratic shocks with measures of competitor financial status (text-based or leverage-based) and with high/low ICR peers.
    - Coefficients include many statistically significant interactions (e.g., negative idiosyncratic shocks coefficients routinely significant at ***).
    - R^2 values reported around 0.73–0.74 for CAPX regressions and increasing R^2 from 0.490 to 0.645 across Table A.6 horizons.
    - Samples and firm counts reported per table (e.g., N up to 112,990; Firms around 4,052–4,272; FIC industries count around 95–96).

### Appendix B — Shock Decomposition (analytical derivations and implications)
- B.1 Decomposition under CES and monopolistic competition
  - Environment and demand:
    - Utility: U_t = Π_{j=1}^J (Y_{j,t})^{φ_{j,t}} (Equation B.1)
    - Sectoral CES aggregator: Y_{j,t} = [Σ_{i ∈ S} ω_{i,t}^{1/θ} y_{i,t}^{(θ−1)/θ}]^{θ/(θ−1)} (Equation B.2)
    - Firm price p_{f,t} relates to sectoral price index P_{j,t}, firm demand shock ω_{f,t}, sectoral demand φ_{j,t}, and relative quantities (Equation B.3).
  - Production and first-order conditions:
    - Linear production y_{f,t} = A_{f,t} l_{f,t} (Equation B.4).
    - FOC (Equation B.6) leads to y_{f,t}^{1/θ} = (A_{f,t} / w_t) P_{j,t} ω_{f,t}^{1/θ} Y_{j,t}^{1/θ} [(1−1/θ)] and p_{f,t} = w_t A_{f,t}^{θ/(θ−1)} (Equation B.7).
  - Sales decomposition:
    - Firm sales p_{f,t} y_{f,t} = P_{j,t}^{θ−1} ω_{f,t} φ_{j,t} Y_t [(w_t A_{f,t} θ^{/(θ−1)})]^{1−θ} (Equation B.8).
    - ln(p_{f,t} y_{f,t}) is a linear combination of macro factors (w_t, Y_t), sectoral factors (P_{j,t}, Y_{j,t}, φ_{j,t}), and firm-level idiosyncratic factors (ω_{f,t}, A_{f,t}), making separation of sectoral and idiosyncratic components feasible when macro factors absorbed by time fixed effects.

- B.2 Decomposition under imperfect competition (limitations and bias)
  - Environment: product market j has n large firms L_{1,j},...,L_{n,j} and a synthetic fringe F_j; firms have firm-specific elasticities θ_f with θ_f > θ for fringe (Equation B.9–B.10).
  - Demand: same Cobb-Douglas form U = Π_{j=1}^J (Y_j)^{φ_j} (Equation B.11) and firm-level demand relation (Equation B.12).
  - Supply and FOC: market output dependence ∂Y_j/∂y_f ≠ 0 introduces additional terms in FOC; after manipulation supply condition can be written (Equation B.15) w_t A_f = p_f (θ_f−1)/θ_f [1 − y_f^{1−1/θ_f} / Y^{1−1/θ_j} ].
  - Definitions and implications:
    - Real market share Γ_f ≡ y_f^{1−1/θ_f} / Y^{1−1/θ_j} (Equation B.16).
    - Optimal price p_f = w_t A_f (θ_f/(θ_f−1)) (1 / (1−Γ_f)) (Equation B.17).
    - Log revenue expression ln(p_f y_f) = ln φ_j + ln Γ_f + ln(U/κ) + ln((θ_f−1)/θ_f) + ln(θ/(θ−1)) (Equation B.19).
  - Main implication: Γ_f is endogenous and responds to sectoral demand shocks φ_j; in industries with uneven market shares, Γ_f’s dependence on φ_j biases the simple decomposition that separates sectoral from idiosyncratic shocks. Larger firms (higher Γ_f) tend to have countercyclical market shares and different revenue elasticities to sectoral demand shocks, so simple additive decompositions can be empirically biased in presence of imperfect competition.

*Financial Heterogeneity, Investment, and Firm Interactions — Working Paper No. WP/2023/110S*

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