## _wp1297

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### Introduction and motivation
- Investment-cash flow sensitivity is a central empirical tool in finance for identifying firms likely to face binding financing constraints; seminal references include Fazzari, Hubbard and Petersen (1988) and subsequent literature (Allayannis and Mozumdar, 2004; Rousseau and Kim, 2009; Brown and Petersen, 2009).
- Debate exists on interpretation of investment-cash flow regressions (Kaplan and Zingales, 1997; Cleary, 1999; Fazzari, Hubbard and Petersen, 2000), but the regressions remain widely used.
- Author hypothesis: investment-cash flow sensitivity must account for the expected value of a firm’s capital usable as collateral, which differs across industries. The 2008 financial crisis provides a natural experiment that changed collateral values and thus testable implications for investment-cash flow sensitivity.
- Empirical scope: quarterly COMPUSTAT for U.S. firms, 1990–2011; baseline panel: 3,071 firms and 67,811 firm-quarter observations (selection and exclusions as described in the source).

### Model and empirical approach
- Model setup:
  - One-period representative firm chooses investment I financed by internal funds W and external funds E, with I = W + E.
  - Production: F(I, L), where L denotes collateral-capable assets (capital); external financing cost C(E, k, L) rising in E and falling in L.
  - Firms differ by L; empirical proxy: capital-to-assets ratio (K/A) using "Property, Plant, and Equipment-Total".
- Comparative statics and key theoretical implication:
  - ∂I/∂W > 0: Higher internal funds increase investment.
  - ∂I/∂L > 0: Higher collateral value increases investment by lowering external financing costs.
  - Under additional assumptions, ∂(∂I/∂W)/∂L > 0: investment is more sensitive to internal funds when collateral value L is higher.
  - Implication: cross-industry differences in collateral generate differing tightness of financial constraints and differing investment–cash flow sensitivities.
- Empirical identification:
  - Use 2008 crisis as shock that lowered expected collateral values.
  - Regression framework includes K/A and interactions Cash flow * (K/A) and Crisis * (K/A) * Cash flow (Crisis dummy starts 2008:Q4).
  - Main estimation methods: IV, GMM-IV (preferred; Baum, Schaffer and Stillman (2011) procedure), FE, RE. Robust standard errors clustered by industry 4-digit SIC code.
  - Variables: Investment = capital expenditures; Cash flow = earnings before extraordinary items plus depreciation; Q proxied by ratio of market to book value of firm financial obligations. All balance-sheet items except capital expressed as ratios to beginning-period capital. All variables except Q are in logs; coefficients interpretable as elasticities.

### Data highlights (selected exact values from summary tables)
- Sample observations by year (examples): 1990: 2,175; 2000: 10,039; 2008: 13,795; 2009: 14,346.
- Baseline panel observation counts reported in regressions: IV: Observations 69,811; Number of firms 3,071. GMM-IV: Observations 60,674; Number of firms 2,856. FE and RE: Observations 89,644; Number of firms 3,718.
- Selected means (examples):
  - CF ($m) mean examples: 1990: 66.6; 2000: 73.2; 2008: 92.8; 2010: 144.5.
  - Investment ($m) mean examples: 1990: 102.0; 2000: 81.4; 2008: 155.7; 2010: 123.7.
  - Capital/Assets examples: 1990: 55.33%; 2000: 43.50%; 2008: 46.51%; 2009: 52.49%.
- Distribution of firm assets (percentiles): 1% .32; 5% 2.6; 10% 6.6; 25% 29.9; 50% 189.56; 75% 1139; 90% 5251; 95% 13586.

### Key estimation results (selected exact coefficients and statistics)
- From Table III (dependent variable: log(Investment)):
  - Cash flow (β_cf):
    - IV: 0.0902** (std. err. -0.0369)
    - GMM-IV: 0.428*** (std. err. -0.0241)
    - FE: 0.448*** (std. err. -0.00851)
    - RE: 0.440*** (std. err. -0.00808)
  - Share of capital in assets (β_k):
    - IV: -0.472*** (std. err. -0.11)
    - GMM-IV: -0.475*** (std. err. -0.0685)
    - FE: 0.0409 (std. err. -0.036)
    - RE: 0.0699** (std. err. -0.028)
  - Share of capital in assets * Cash flow (β_kcf):
    - IV: 0.270*** (std. err. -0.0518)
    - GMM-IV: 0.00251 (std. err. -0.0343)
    - FE: 0.0381*** (std. err. -0.00767)
    - RE: 0.0380*** (std. err. -0.00695)
  - Crisis * K/A * Cash flow (β_crisis_kcf):
    - IV: -1.499*** (std. err. -0.224)
    - GMM-IV: -0.291** (std. err. -0.125)
    - FE: -0.0748*** (std. err. -0.00949)
    - RE: -0.0729*** (std. err. -0.00903)
  - Q (β_q):
    - IV: 0.192*** (std. err. -0.0572)
    - GMM-IV: -0.112*** (std. err. -0.037)
    - FE: -0.00441 (std. err. -0.0204)
    - RE: 0.00749 (std. err. -0.019)
- Cumulative elasticity of investment by K/A * Cash flow during the crisis (β_kcf + β_crisis_kcf):
  - IV: -1.179
  - GMM-IV: -0.2884
  - FE: -0.0367
  - RE: -0.0349
- GMM-IV preferred aggregate and size results (Table IV, selected):
  - Aggregate pre-crisis cash flow elasticity: 0.167*** (std. err. -0.016); Observations: 71,096; R-squared: 0.173; Number of groups: 3,134.
  - Size subsamples (cash flow elasticity):
    - Small firms (assets less $50m): 0.301*** (std. err. -0.0356)
    - Medium firms ($50-500m): 0.256*** (std. err. -0.0296)
    - Large firms ($500-1000m): 0.601*** (std. err. -0.0324)
    - The largest firms (assets >$1000m): 0.0926*** (std. err. -0.0248)

### Sectoral and size heterogeneity (selected exact coefficients and interpretation)
- Industry-specific GMM-IV crisis marginal elasticities (selected from column (1) All firms):
  - Division A: Agriculture, Forestry, and Fishing: 0.121*** (std. err. -0.044)
  - Division B: Mining: 0.0804*** (std. err. -0.0163)
  - Division C: Construction: 0.153** (std. err. -0.0761)
  - Division D: Manufacturing: 0.141*** (std. err. -0.00922)
  - Division F: Wholesale Trade: 0.205*** (std. err. -0.0417)
  - Division G: Retail Trade: 0.203*** (std. err. -0.0195)
  - Division I: Services: 0.160*** (std. err. -0.0173)
- FE and RE pre-crisis cash flow elasticities (selected):
  - FE All firms: 0.418*** (std. err. -0.0113)
  - RE All firms: 0.407*** (std. err. -0.0121)
  - Note: FE and RE estimates are larger than GMM-IV and may overestimate cash flow influence due to endogeneity concerns; GMM-IV is preferred.
- Interpretation:
  - The 2008 crisis increased liquidity constraints and the sensitivity of investment to cash flow (β_crisis positive and significant across sectors in sectoral specifications).
  - The increase in sensitivity was particularly pronounced in wholesale trade, retail trade, construction, manufacturing, and services—where elasticity of investment by cash flow nearly doubled in value according to the sectoral analysis.
  - Size heterogeneity: GMM-IV shows a bell-shaped distribution of cash flow elasticities across firm sizes (≈0.3 for small/medium, ≈0.6 for large, ≈0.1 for largest firms).

### Main empirical conclusions (compact)
- Theoretical and empirical evidence in the paper support that higher collateral value (higher share of physical capital in assets) increases pre-crisis investment–cash flow sensitivity.
- The 2008 financial crisis lowered expected collateral values and increased borrowing discounts, changing investment–cash flow relationships: firms with larger capital holdings experienced sizable reductions in cash-flow sensitivity during the crisis (cumulative interaction elasticities during crisis negative in Table III).
- Aggregate GMM-IV estimate: an increase in cash flow by 1 percent increases investment by 0.17 percent on average (pre-crisis).
- Size- and industry-specific effects are substantial; crisis-induced increases in cash-flow sensitivity concentrate in wholesale trade, retail trade, construction, manufacturing, and services.
- Estimation strategy and robustness: GMM-IV preferred to address endogeneity; FE and RE produce larger elasticities but may be biased.

*Source: _wp1297 (IMF working paper content unit)._

### INTRODUCTION

### _wp1297 - INTRODUCTION

### Role of investment-cash flow sensitivity in literature
- Investment-cash flow sensitivity is a central empirical tool in finance; many papers find that investment is more sensitive to cash flow among firms more likely to face binding financing constraints (Fazzari, Hubbard and Petersen, 1988; Allayannis and Mozumdar, 2004; Rousseau and Kim, 2009; Brown and Petersen, 2009).
- There is disagreement on interpretation of these findings (Kaplan and Zingales, 1997; Cleary, 1999), but investment-cash flow regressions remain widely used.

### Traditional viewpoint and empirical evidence
- Fazzari, Hubbard and Petersen (1988) argue that “most constrained” firms should have investment expenditures that are more sensitive to internal cash flows and the stock of liquidity than “least constrained” firms.
- Their empirical tests show substantially higher sensitivity of investment to cash flow and liquidity for firms that retain nearly all of their income.
- Many empirical studies, following Fazzari, Hubbard and Petersen (1988), find greater cash-flow sensitivity for initially identified financially more constrained firms.
- Counterevidence: Kaplan and Zingales (1997) argue the empirical approach is not well-grounded in theory and provide evidence in apparent conflict with Fazzari, Hubbard and Petersen (1988); debate continued (response by Fazzari, Hubbard and Petersen, 2000).

### Theoretical models and predictions
- Kaplan and Zingales (1997): constrained firms should be sensitive to internal cash flow, while unconstrained firms should not; magnitude of sensitivity need not increase monotonically with degree of financing constraints.
- Cleary, Povel and Raith (2007): firm’s optimal investment is a U-shaped function of its internal funds; increased information asymmetry raises sensitivity of investment to internal funds.
- Pratap (2003): a dynamic model with liquidity constraints and non-convex capital adjustment costs can explain high sensitivity, with firms needing a threshold level of financial resources before increasing investment.
- Abel and Eberly (2011): closed-form solution for Tobin’s Q in a stochastic dynamic framework shows investment positively related to Tobin’s Q and cash flow even without adjustment costs or financing frictions; cash flow has larger effects for smaller and faster-growing firms.

### Critiques of conventional regressions and econometric issues
- Recent critiques target omission of cash-flow endogeneity and external financing possibilities.
- Alti (2003) and Moyen (2004): calibrate models where debt substitutes for internal financing and show OLS on simulated data can generate investment-cash flow sensitivities without financing frictions.
- Gatchev, Pulvino and Tarhan (2010): dynamic multiequation model where financing and investment decisions are simultaneous; static models produce inconsistent coefficient estimates and the positive relationship between investment and cash flow disappears when allowing for lagged-current decision connections.
- Econometric obstacles include endogeneity; many recent papers use the GMM estimator developed by Arellano and Bond (1991) to address endogeneity (examples: Rousseau and Kim, 2009; Brown and Petersen, 2009).

### Using the 2008 financial crisis as an experiment
- The 2008 crisis constituted a severe credit-supply shock that affected firms’ investment decisions and created conditions to test investment-cash flow sensitivity more directly.
- Campello, Graham and Harvey (2009): survey of 1,050 CFOs in the U.S., Europe, and Asia finds constrained firms experienced deeper cuts in tech spending, employment, and capital spending; burned more cash; drew more heavily on lines of credit; and sold more assets.
- Campello, Giambonam, Graham and Harvey (2010): study of liquidity management during 2008 crisis indicates an important role for internal and external liquidity in driving spending; constrained firms drew more heavily on credit lines and were more likely to face difficulties renewing or initiating lines of credit.

### Author’s hypothesis and empirical approach
- Hypothesis: investment-cash flow sensitivity must be measured taking into account the expected value of a firm’s capital that can be used as collateral and is different across industries.
- Rationale: before the crisis, expected continued real estate appreciation led banks to lend more easily to firms with higher physical capital and in construction-connected sectors because expected collateral values would increase; thus investment-cash flow sensitivity in these industries was less pronounced.
- Theoretical contribution: construct a simple model showing tightness of financial constraints depends on value of a firm’s capital and differs across sectors.
- Empirical approach: use the financial crisis of 2008 as a natural experiment that changed the value of firms’ assets; use quarterly data for U.S. firms from 1990 to 2011 from COMPUSTAT to estimate changes in investment-cash flow sensitivity.

### Key empirical findings reported
- Investment is negatively dependent on the share of capital in assets.
- Firms with relatively higher level of capital have higher investment-cash flow sensitivity during the pre-crisis period.
- After the crisis, firms with higher amounts of capital experienced less financial constraints and became less sensitive to cash flow when deciding to invest.
- The financial crisis of 2008 increased liquidity constraints among firms and nearly doubled the sensitivity of investment to cash flow.
- The author attributes the observed asymmetry to different collateral-intensity dependence across industries.

### Paper structure
- Section 2: simple theoretical model showing tightness of financial constraints depends on firm collateral value.
- Section 3: data discussion.
- Section 4: empirical results.
- Final section: concluding remarks and findings summarized.

*Source: _wp1297 - INTRODUCTION*

### 2. MODEL

### _wp1297 - 2. MODEL

### Model setup and assumptions
- One-period representative firm maximizes profits from investment.  
- Investment I financed by internal funds W and external funds E, with I = W + E.  
- Return on investment and collateral-capable assets (capital) L given by production function F(I, L).  
- External financing entails additional costs represented by C(E, k, L), where k measures the wedge between internal and external costs and L reduces external financing costs.  
- Standard assumptions: cost of external funds rises with E and information problems, and falls with L; marginal cost of external financing is decreasing in L and convex in E.  
- Firms differ by L (interpreted as market value of non-tradable assets such as land, machinery, housing); in empirical work capital-to-assets ratio used as proxy.

### First-order condition and comparative statics
- Firm chooses I to maximize profits subject to financing constraint; first-order condition equates marginal product of investment to marginal cost of external financing net of internal funds.  
- Implicit differentiation yields:
  - ∂I/∂W > 0: Higher internal funds increase investment.  
  - ∂I/∂L > 0: Higher collateral value L reduces external financing cost and increases investment.  
- Sensitivity of investment to internal funds varies with L:
  - Under additional assumptions (convex marginal cost of external financing, certain third-derivative and cross-partial derivative restrictions), ∂(∂I/∂W)/∂L > 0.  
  - Key implication: investment is more sensitive to internal funds when collateral value is higher — higher L lowers external financing costs and raises relative importance of internal funds, increasing investment–cash flow sensitivity.  
- Model implication: cross-industry differences in collateral (L) generate differing tightness of financial constraints and differing investment–cash flow sensitivities.

### Empirical approach (testing model using 2008 crisis as shock)
- Use 2008 financial crisis as a natural experiment that lowered expected value of firms' collateral (L) via banks' re-evaluation and higher collateral discounts.  
- Two empirical dimensions:
  1. Include physical capital-to-assets ratio in investment–cash flow sensitivity regressions.  
  2. Decompose investment–cash flow sensitivity by firms' assets and estimate industry-specific crisis effects.  
- Data: Quarterly COMPUSTAT for U.S. firms, 1990–2011. Exclude Finance, Insurance, Real Estate, and Public Administration divisions. Require firms to exist at least five subsequent quarters after the beginning of the crisis (since end of 2008). Baseline panel: 3,071 firms and 67,811 firm-quarter observations.

### Data and variable definitions
- Investment measured as capital expenditures; cash flow measured as earnings before extraordinary items plus depreciation.  
- Proxy for Tobin's Q: ratio of market to book value of a firm's financial obligations.  
- All balance-sheet items other than capital expressed as ratios to firm capital at beginning of period.  
- Capital-to-assets ratio uses "Property, Plant, and Equipment-Total" as capital.  
- Summary dynamics (selected from Table I):
  - Obs counts by year (examples): 1990: 2,175; 2000: 10,039; 2008: 13,795; 2009: 14,346; baseline panel total observations reported as 69,811 in some regressions.  
  - CF ($m) mean examples: 1990: 66.6; 2000: 73.2; 2008: 92.8; 2010: 144.5.  
  - Investment ($m) mean examples: 1990: 102.0; 2000: 81.4; 2008: 155.7; 2010: 123.7.  
  - Capital/Assets examples: 1990: 55.33%; 2000: 43.50%; 2008: 46.51%; 2009: 52.49%.  
- Distribution of firm assets (Table II percentiles): 1% .32; 5% 2.6; 10% 6.6; 25% 29.9; 50% 189.56; 75% 1139; 90% 5251; 95% 13586.

### Estimation strategy
- Baseline regression specification: log(Investment) on log(Cash flow), log(Q), and controls; variables scaled by capital at beginning of period.  
- To capture collateral effects and crisis:
  - Equation (11): includes share of capital in assets (K/A), interaction Cash flow * (K/A), and a Crisis dummy starting 2008:Q4 and its triple interaction Crisis * (K/A) * Cash flow. All variables except Q are in logs; coefficients interpretable as elasticities.  
  - Estimation methods: IV, GMM-IV (Baum, Schaffer and Stillman (2011) procedure with lagged independent variables and sales as instruments), FE, RE. Robust standard errors clustered by industry 4-digit SIC code.

### Key estimation results — investment–cash flow sensitivity with capital (Table III)
- Coefficients (selected) — dependent variable: log of Investment:
  - Cash flow (β_cf):
    - IV: 0.0902** (std. err. -0.0369)
    - GMM-IV: 0.428*** (std. err. -0.0241)
    - FE: 0.448*** (std. err. -0.00851)
    - RE: 0.440*** (std. err. -0.00808)
  - Share of capital in assets (β_k):
    - IV: -0.472*** (std. err. -0.11)
    - GMM-IV: -0.475*** (std. err. -0.0685)
    - FE: 0.0409 (std. err. -0.036)
    - RE: 0.0699** (std. err. -0.028)
  - Share of capital in assets * Cash flow (β_kcf):
    - IV: 0.270*** (std. err. -0.0518)
    - GMM-IV: 0.00251 (std. err. -0.0343)
    - FE: 0.0381*** (std. err. -0.00767)
    - RE: 0.0380*** (std. err. -0.00695)
  - Crisis dummy * Share of capital in assets * Cash flow (β_crisis_kcf):
    - IV: -1.499*** (std. err. -0.224)
    - GMM-IV: -0.291** (std. err. -0.125)
    - FE: -0.0748*** (std. err. -0.00949)
    - RE: -0.0729*** (std. err. -0.00903)
  - Q (β_q):
    - IV: 0.192*** (std. err. -0.0572)
    - GMM-IV: -0.112*** (std. err. -0.037)
    - FE: -0.00441 (std. err. -0.0204)
    - RE: 0.00749 (std. err. -0.019)
- Observations and firms:
  - IV: Observations 69,811; Number of firms 3,071.
  - GMM-IV: Observations 60,674; Number of firms 2,856.
  - FE and RE: Observations 89,644; Number of firms 3,718.
- Cumulative elasticity of investment by share of capital in assets * cash flow during the crisis (β_kcf + β_crisis_kcf):
  - IV: -1.179
  - GMM-IV: -0.2884
  - FE: -0.0367
  - RE: -0.0349

Interpretation and empirical findings from Table III:
- Elasticity of investment to cash flow positive and statistically significant across models: about 0.1 (IV) and about 0.43 (GMM-IV, FE, RE).  
- Share of capital in assets has negative elasticity (~ -0.47) in IV and GMM-IV, consistent with diminishing marginal returns on investment; near zero in FE/RE.  
- Pre-crisis interaction (K/A * Cash flow) positive in most models: firms with higher capital shares are more sensitive to cash flow.  
- Crisis interaction (Crisis * K/A * Cash flow) negative and statistically significant in all regressions: after the crisis, firms with higher capital experienced less sensitivity to cash flow (cumulative K/A*Cash flow elasticity during crisis becomes negative), consistent with banks re-evaluating asset values and higher collateral discounts.

### Sectoral asymmetries — estimation results (Tables IV–VII)
- Specification (12): log(Investment) on log(Cash flow), Q, and sector-specific crisis interaction terms to capture industry k marginal elasticities during crisis. All variables in logs except Q; GMM-IV preferred.

Selected GMM-IV results (Table IV) — dependent variable: log of Investment
- Aggregate (All firms):
  - Pre-crisis elasticity of investment by cash flow: 0.167*** (std. err. -0.016)
  - Q coefficient: 0.316*** (std. err. -0.0292)
  - Observations: 71,096; R-squared: 0.173; Number of groups: 3,134.
- Size subsamples (cash flow elasticity):
  - Small firms (assets less $50m): 0.301*** (std. err. -0.0356)
  - Medium firms ($50-500m): 0.256*** (std. err. -0.0296)
  - Large firms ($500-1000m): 0.601*** (std. err. -0.0324)
  - The largest firms (assets >$1000m): 0.0926*** (std. err. -0.0248)
- Industry-specific crisis effects (β_k,t for crisis marginal elasticity increases; selected coefficients from column (1) All firms):
  - Division A: Agriculture, Forestry, and Fishing: 0.121*** (std. err. -0.044)
  - Division B: Mining: 0.0804*** (std. err. -0.0163)
  - Division C: Construction: 0.153** (std. err. -0.0761)
  - Division D: Manufacturing: 0.141*** (std. err. -0.00922)
  - Division F: Wholesale Trade: 0.205*** (std. err. -0.0417)
  - Division G: Retail Trade: 0.203*** (std. err. -0.0195)
  - Division I: Services: 0.160*** (std. err. -0.0173)

Selected IV results (Table V) mirror GMM-IV magnitudes:
- All firms cash flow elasticity: 0.168*** (std. err. -0.016)
- Size subsamples and industry-specific crisis effects broadly similar to GMM-IV.

FE and RE models (Tables VI and VII) — alternative specifications
- FE (Table VI) — pre-crisis cash flow elasticity:
  - All firms: 0.418*** (std. err. -0.0113)
  - Small firms: 0.353***; Medium: 0.417***; Large: 0.478***; Largest: 0.478***.
- RE (Table VII) — pre-crisis cash flow elasticity:
  - All firms: 0.407*** (std. err. -0.0121)
  - Small: 0.339***; Medium: 0.395***; Large: 0.453***; Largest: 0.469***.
- Note: FE and RE may overestimate cash flow influence due to endogeneity concerns; GMM-IV preferred.

Interpretation of sectoral and size heterogeneity
- Aggregate finding: crisis of 2008 increased liquidity constraints and the sensitivity of investment to cash flow (β_crisis positive and significant across sectors).  
- The increase in sensitivity was particularly pronounced in wholesale trade, retail trade, construction, manufacturing, and services — elasticity of investment by cash flow nearly doubled in these sectors.  
- Size heterogeneity:
  - Elasticities vary by firm size: small- and medium-size firms show elasticities ~0.3; large firms ~0.6; the very largest firms ~0.1 (GMM-IV).  
  - In construction, smaller firms did not experience significantly higher cash flow dependence, but bigger and the largest firms experienced tighter constraints consistent with higher non-tradable asset exposure.  
  - In wholesale trade and services, larger firms experienced smaller crisis influence relative to smaller peers.

### Overall empirical conclusions
- Evidence supports model prediction that higher collateral (capital share) increases pre-crisis investment–cash flow sensitivity.  
- The 2008 financial crisis reduced expected collateral values and increased borrowing discounts, changing the investment–cash flow relationship: firms with larger capital holdings experienced sizable changes in sensitivity (cumulative interaction elasticities during crisis negative in Table III).  
- Sectoral and size heterogeneities are substantial: certain industries (wholesale, retail, construction, manufacturing, services) and firm-size categories exhibited larger crisis-induced increases in cash flow sensitivity.  
- GMM-IV estimates (preferred for endogeneity) show average pre-crisis cash flow elasticity about 0.167 (All firms), with pronounced variation by firm size and industry.

*Italic: Source — _wp1297 - 2. MODEL (IMF working paper content unit).*

### CONCLUSIONS

### CONCLUSIONS

### Theoretical framework and empirical approach
- A simple theoretical model shows that the tightness of financial constraints depends on the value of a firm‟s collateral and differs by sector.
- Under general assumptions higher collateral value increases the sensitivity of investment to cash flow.
- Empirical strategy: quarterly data for U.S. firms from 1990 to 2011 from COMPUSTAT; investment-cash flow sensitivity estimated using the IV and GMM-IV methods.

### Key empirical findings on investment-cash flow sensitivity
- Elasticity of investment by cash flow:
  - about 0.1 in the case of the IV model.
  - about 0.43 in the case of the GMM-IV, FE, and RE models.
- The share of physical capital in assets strongly influences investment and investment-cash flow sensitivity:
  - The elasticity of investment by the share of capital in assets is about -0.47 in the GMM-IV and IV cases.
  - Investment is negatively dependent on the share of capital in assets, consistent with diminishing marginal returns on investment.
- Firms with higher share of physical capital in assets have higher investment-cash flow sensitivity on average.
- Pre-crisis, firms with higher levels of capital had higher investment-cash flow sensitivity; after the crisis, firms with higher amounts of capital experienced less financial constraints and became less sensitive to cash flow when investing.
  - As banks changed expectations about the value of firms‟ assets, the cumulative elasticity of investment by the interaction of capital and cash flow for the crisis period was found to be negative in all models.

### Size- and industry-specific heterogeneity
- Aggregate and size-specific effects:
  - An increase in cash flow by 1 percent increases investment by 0.17 percent on average.
  - Pre-crisis elasticity of investment by cash flow by size:
    - about 0.3 for small- and medium-size firms.
    - about 0.6 for larger firms.
    - about 0.1 for the largest firms.
  - The distribution across sizes is bell-shaped.
- Crisis effects and industry heterogeneity:
  - The financial crisis increased liquidity constraints and almost doubled the sensitivity of investment to cash flow.
  - Negative effects (higher dependence of investment on cash flow) were experienced most strongly in the wholesale trade, retail trade, construction, manufacturing, and services sectors, where the elasticity of investment by cash flow almost doubled in value.
  - Firms with higher levels of assets experienced a lower increase in investment-cash flow sensitivity in most industries.

### Estimation notes and robustness
- Models reported include GMM-FD and BETWEEN estimations (tables and coefficients presented in the source), with sample splits by firm size:
  - Small firms (assets less than $50m)
  - Medium firms (assets $50-500m)
  - Large firms (assets $500-1000m)
  - The largest firms (assets >$1000m)
- All variables but Q are in logs. Balance sheet item variables are scaled by total capital at the beginning of the period.
- Significance indicators reported: *** p<0.01, ** p<0.05, * p<0.1. Standard errors are shown in italics in the source tables.

*Source: _wp1297 - CONCLUSIONS*

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