## _wp1023

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---

### Introduction and research question
- Central question: How do financial shocks propagate through the real economy and affect total factor productivity (TFP)?
- Standard framing: increases in funding costs depress investment and consumption; most specifications treat TFP as exogenous to financial conditions.
- Empirical strategy preview: use a stylized model with sectoral dependence on external finance as an identifying device; test whether changes in the cost of funds affect sectoral TFP growth using panel data for manufacturing industries in the United States and Canada between 1991 and 2007.

### Key theoretical insights (model summary)
- Setup and primitives:
  - S industries, each with N firms; industry output Y_s is a CES aggregator of firm outputs Y_si.
  - Firm production: Y_si = A_si K_si^α_s L_si^(1-α_s) (Cobb-Douglas).
  - A fraction φ of production costs must be paid up front (working capital requirement); φ varies across sectors but is identical within a sector.
  - Cost of working capital: τ_si = τ + τ_s + τ_si (common component τ, sector-specific τ_s, idiosyncratic τ_si with cross-sectional mean zero).
- Proposition 1 (industry TFP expression):
  - Industry TFP A_s = [ (1/N) ∑_i A_si^((σ-1)/σ) γ_si ]^(σ/(σ-1)), where γ_si depends explicitly on A_si, σ, φ, and τ components.
- Corollary and mechanism:
  - If cost of external funds is identical across firms within an industry (τ_i = 0 for all i), sectoral TFP depends only on technological elements A_si and is unaffected by financial shocks.
  - Financial shocks affect sectoral TFP through reshuffling of weights γ_si (reallocation of factors across firms).
- Two polar financial-shock types and predicted effects:
  - Increase in common component τ: moves relative financial distortions closer to 1, potentially boosting sectoral TFP; gains larger for sectors with higher φ.
  - Increase in dispersion of idiosyncratic τ_si: increases wedges, decreasing sectoral TFP; negative effects larger for higher φ.
- Relation to literature:
  - Connects to creative-destruction/“cleansing” and reverse-liquidationist views; common channel is reallocation across heterogeneous firms, sign of effect depends on whether reallocation improves efficiency.

### Empirical strategy and data construction
- Dependence on external finance:
  - Use Rajan and Zingales (1998) index modified to NAICS as MRZ.
- Sectoral TFP measurement:
  - Sector production function: Y_s = A_s K_s^α_s L_s^(1-α_s), α_s estimated from U.S. data (1 minus average compensation share in value added during 1997–2007); Canadian industries assumed to share α_s.
  - Sample: 16 manufacturing industries in the United States and 15 in Canada, 1990–2007 (capital stock unavailable for NAICS 336 in Canada; that industry excluded); panel emphasis 1991–2007.
  - Data sources and choices:
    - U.S. Y_s: BEA value added (chained 2000 dollars).
    - U.S. K_s: BLS capital services series × Federal Reserve capacity utilization index.
    - U.S. L_s: actual average hours worked × number of employees (BLS).
    - Rationale: use actual hours and capacity utilization adjustment to control for capital hoarding.
- Cost-of-funds proxies:
  - Baseline: yields on long-term corporate bonds (U.S.: Moody’s Aaa series; Canada: Scotia Capital series).
  - Alternative (U.S. only): industry-specific cost of issuing equity — industry betas interacted with market dividend yield (CAPM logic).

### Estimation approach
- Baseline panel regression:
  - %Δ V_st = α + γ (MRZ_s × cost_s,t) + sector fixed effects + time dummies + ε_st
  - V_st includes sectoral TFP growth and alternative outcomes (industry GDP, capital-labor ratio, labor size, capacity utilization).
  - γ captures differential impact of changes in cost of finance across industries with different MRZ.

### Main empirical findings (baseline regressions and magnitudes)
- Baseline TFP effect:
  - Estimated γ = -0.96 (reported).
  - Interpretation: a one-standard deviation increase in yields on long-term corporate bonds reduced TFP growth in sectors with average dependence on external finance by 0.25 percentage point more than in a benchmark sector without dependence on external finance.
- Industry GDP and other margins (Table 4 summary):
  - GDP: Estimated -2.12*** — Std. Dev. 0.43 — Probability 0.00
    - Interpreted: a 100 basis point increase in the cost of funds reduces GDP growth in a sector with average dependence by around 0.6 percentage point relative to a sector with no external finance dependence (contextual interpretation in text).
  - Labor: Estimated -0.49** — Std. Dev. 0.20 — Probability 0.02
  - Capacity: Estimated -0.90*** — Std. Dev. 0.06 — Probability 0.00
  - K/L: Estimated 0.07 — Std. Dev. 0.12 — Probability 0.57 (no significant effect)
- Equity-based cost-of-funds (U.S. only):
  - Equity γ: Estimate -1.66*** — Std. Dev. 0.10 — Probability 0.00 (Table 6)
  - Using dividend-yield proxy: a one-standard deviation increase reduces annual TFP growth in sectors with average MRZ by approximately 0.46 percentage point relative to a benchmark nondependent sector; after controlling for K/L growth and labor growth the implied decline is roughly 0.6 percentage point.
- Comparative benchmark:
  - Average annual growth rate of aggregate TFP for the U.S. between 1948 and 2000 is 1.18 percent (contextual reference).
  - The 0.25 percentage point or 0.46–0.6 percentage point impacts are economically meaningful relative to these benchmarks.

### Robustness checks and alternative specifications
- Returns to scale and scale-bias control:
  - Under generalized production function with returns-to-scale parameter ρ, measured TFP growth may be biased; regression (4) includes growth in K/L and growth in labor.
  - Result: negative impact preserved but magnitude reduced:
    - A one standard-deviation increase in yields reduces annual TFP growth in an average-dependence sector by 0.16 percentage point more than in a benchmark nondependent sector.
  - Table 5:
    - Γ: Estimate -0.58*** — Std. Dev. 0.17 — Probability 0.00
    - b0: Estimate 0.25*** — Std. Dev. 0.03 — Probability 0.00
    - b1: Estimate 0.02 — Std. Dev. 0.02 — Probability 0.51
- Cost-of-equity vs. cost-of-debt:
  - Table 6 shows Equity γ = -1.66*** and Bonds γ = 0.73***; Table 7 (cost of equity with returns to scale) shows γ = -2.04***, b0 = 0.41***, b1 = -0.18***.
- Sensitivity:
  - Sequential exclusion of individual industries does not overturn main conclusions.
  - Excluding U.S. petroleum industry (NAICS 324) does not overturn results; effect can be stronger once returns to scale are controlled.
- Endogeneity considerations:
  - Reverse causality would bias γ upward; observed negative γ is not explained away by that bias.
  - Aggregate time-variation in bond and dividend yields limits simple reverse-causality interpretations concentrated in finance-dependent sectors.

### Interpretation, mechanism, and policy-relevant implications
- Mechanism emphasized by authors:
  - Financial shocks impair TFP via misallocation of factors across heterogeneous firms within industries; magnitude increases with sectoral dependence on external finance φ.
- Policy implications:
  - Policymakers should consider effects of financial shocks on aggregate supply (TFP), not only on aggregate demand and unemployment.
  - Severe financial crises that impair financial intermediation can generate distortions in allocation of capital and production, harming sectoral efficiency.
  - Misallocation within sectors is a relevant policy concern alongside industry-level resource shortfalls.
- Future research directions suggested:
  - Firm-level analysis to detect misallocations from financial shocks.
  - Disentangle whether distortions arise from shifts in firm scale or from distortions in factor composition.

### Selected empirical magnitudes and sample facts (preserved numbers)
- Sample period: United States and Canada, 1991 to 2007 (TFP data sometimes constructed for 1990–2007).
- Baseline TFP coefficient: γ = -0.96.
- GDP interaction coefficient: Estimated -2.12*** — Std. Dev. 0.43 — Probability 0.00.
- TFP (Table 4): Estimated -0.96*** — Std. Dev. 0.35 — Probability 0.01.
- TFP effect using equity proxy (Table 6): Equity γ = -1.66*** — Std. Dev. 0.10 — Probability 0.00.
- TFP with equity and returns to scale (Table 7): γ = -2.04*** — Std. Dev. 0.05 — Probability 0.00; b0 = 0.41*** — Std. Dev. 0.01 — Probability 0.00; b1 = -0.18*** — Std. Dev. 0.01 — Probability 0.00.
- Descriptive statistics (Table 2 highlights):
  - TFP: Mean 1.59, Std. Dev. 5.99, Min -29.32, Max 30.50, Obs 527
  - GDP: Mean 1.28, Std. Dev. 7.5, Min -24.18, Max 35.98, Obs 527
  - Labor: Mean -1.06, Std. Dev. 4.87, Min -15.65, Max 23.38, Obs 527
  - Capital-Labor Ratio: Mean 1.82, Std. Dev. 5.02, Min -22.04, Max 18.24, Obs 527
  - Capacity Utilization: Mean 0.01, Std. Dev. 4.25, Min -19.28, Max 14.48, Obs 527
  - Yields: Mean 7.18, Std. Dev. 1.47, Min 5.24, Max 11.32, Obs 527
  - RZ: Mean 0.28, Std. Dev. 0.26, Min -0.08, Max 0.96, Obs 527

### Appendices — key tables, figures, and calibration parameters
- Appendix A — Index of Dependence on External Finance (selected MRZ values, Table 1):
  - Examples: Food, Beverage and Tobacco (311-312) MRZ 0.08; Petroleum (324) MRZ 0.33; Machinery (333) MRZ 0.45; Electrical Appl. And Comp. (335) MRZ 0.96; Plastic (326) MRZ 0.69; Transportation (336) MRZ 0.39.
- Appendix B — Figures:
  - Figure 1: horizontal axis Dependence on External Source of Funding (0.0 to 0.9); vertical Percent change in TFP (0 to 0.4).
  - Figure 2: same horizontal axis; vertical Percent Change in TFP from -0.45 to 0.
  - Figure 3: panels of NAICS industry TFP percent change for US and CA, years 1991–2005; y-axis in panels ranges from -40 to 40 percent change.
- Appendix C — Calibration parameters:
  - σ = 1.2.
  - Sectoral component sτ normalized to 0.
  - Firm-specific TFP siA uniformly distributed over [0.5,1] with 100 observations per industry.
  - Dependence on external finance sφ uniformly distributed over [0,1] with 100 different industries.
  - Exercise 1: idiosyncratic siτ uniformly distributed over [-0.15,0.15]; common τ increased from 0 to 0.4.
  - Exercise 2: common component = 0.1; increase dispersion of idiosyncratic term from no dispersion to uniform over [-0.15,0.15].
  - Diagrams assume independence of firm-specific TFP and idiosyncratic cost-of-funds; perfect positive/negative correlation cases yield virtually identical TFP-growth results.

*Source: _wp1023 - APPENDIX A–TABLES*

### Appendix A–Tables ......................................................................................................

### _wp1023 - Appendix A–Tables ......................................................................................................

### Appendix A–Tables
- Appendix A–Tables .................................................................................................................28

### Appendix B–Figures
- Appendix B–Figures ................................................................................................................31

### Appendix C–Calibration
- Appendix C–Calibration ..........................................................................................................33

*Source: _wp1023 - Appendix A–Tables ......................................................................................................*

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

### _wp1023 - References .............................................................................................................

### Introduction and research question
- Central question: How do financial shocks propagate through the real economy and affect total factor productivity (TFP)?
- Standard neoclassical view: increases in funding costs depress investment and consumption, reducing aggregate demand and future capital accumulation; most specifications treat TFP as exogenous to financial conditions.
- Motivation: TFP behavior is central to macroeconomics and growth theory (references to Kydland and Prescott (1982), Kehoe and Prescott (2007), Solow model).
- Theoretical inspiration: Chari et al. (2007) — distortions from taxes or frictions can be represented as wedges; shocks to financial frictions can be isomorphic to TFP shocks in a frictionless model.
- Empirical strategy preview: use a stylized model with sectoral dependence on external finance as an identifying device; test whether changes in the cost of funds affect sectoral TFP growth, using panel data for manufacturing industries in the United States and Canada between 1991 and 2007.

### Key theoretical insights (summary of the model)
- Setup:
  - S industries, each with N firms; industry output Y_s is a CES aggregator of firm outputs Y_si.
  - Firm production: Y_si = A_si K_si^α_s L_si^(1-α_s) (Cobb-Douglas).
  - A fraction φ of production costs must be paid up front (working capital requirement); φ varies across sectors but is identical within a sector.
  - Cost of working capital for firm i in sector s: τ_si = τ + τ_s + τ_si (common component τ, sector-specific τ_s, idiosyncratic τ_si with cross-sectional mean zero).
- Optimality conditions yield:
  - Common capital-labor ratio within a sector (equation (1) form).
  - Firm labor allocation condition (equation (2) form) that depends on A_si and φ, τ terms.
- Proposition 1 (industry TFP expression):
  - Industry TFP A_s is a weighted aggregate of firm-level productivity A_si with weights γ_si that depend on firm-level costs of external funds:
    - A_s = [ (1/N) ∑_i A_si^( (σ-1)/σ ) γ_si ]^( σ/(σ-1) )  (as presented in the text)
  - Definition of γ_si depends explicitly on A_si, σ, φ, and τ components (preserved in the model).
- Corollary:
  - If the cost of external funds is identical across firms within an industry (τ_i = 0 for all i), sectoral TFP depends only on technological elements A_si and is unaffected by financial shocks.
- Mechanism and testable predictions:
  - Financial shocks affect sectoral TFP only through reshuffling of weights γ_si (i.e., factor allocation across firms).
  - Two polar financial-shock types:
    - Increase in common component τ: moves relative financial distortions closer to 1, reducing wedges, potentially boosting sectoral TFP; gains are larger for sectors with higher dependence on external finance φ.
    - Increase in dispersion of idiosyncratic τ_si: increases wedges, decreasing sectoral TFP; negative effects larger for higher φ.
  - Net effect of real-world shocks depends on mixture of these two characteristics; differential impact across industries (based on dependence on external finance) permits identification.
- Relation to creative-destruction/“cleansing” literature:
  - Liquidationist prediction: higher funding costs accelerate exit of unproductive firms, raising average productivity, more so in externally-dependent sectors.
  - Reverse-liquidationist view (Caballero and Hammour (2005)): crises can freeze restructuring; crises can reduce productivity growth or cause decay in externally-dependent sectors.
  - Both views and the present model emphasize reallocation of factors across firms; main difference is whether reallocation raises or lowers TFP.

### Empirical strategy and data construction
- Dependence on external finance:
  - Use Rajan and Zingales (1998) index (RZ) of dependence on external finance (fraction of capital expenditures not financed with cash-flow) for median firm in 36 U.S. manufacturing industries during the 1980s.
  - Modified RZ index to match NAICS classification where needed; denoted MRZ.
  - MRZ treated as reasonably exogenous to TFP and inputs (assumption underlying RZ).
- Measuring sectoral TFP:
  - Sector production function: Y_s = A_s K_s^α_s L_s^(1-α_s), with α_s allowed to vary by sector.
  - Data:
    - 16 manufacturing industries in the United States and 15 industries in Canada, 1990–2007 (note: capital stock unavailable for NAICS 336 in Canada; that industry excluded).
    - U.S. Y_s: BEA value added by industry (chained 2000 dollars).
    - U.S. K_s: BLS capital services series × Federal Reserve capacity utilization index.
    - U.S. L_s: actual average hours worked × number of employees (BLS).
    - α_s estimated using U.S. data as 1 minus average fraction of value added paid as compensation to employees during 1997–2007 (BEA compensation data). Canadian industries assumed to share α_s.
  - Rationale for variable choices: use actual hours (better measure of labor services) and capacity utilization adjustment (controls for capital hoarding); sample limited by availability of hours worked at 3-digit NAICS since 1990.
- Cost of funds proxies:
  - Baseline: yields on long-term corporate bonds.
    - U.S.: Moody’s series on Aaa long-term corporate bond yields.
    - Canada: Scotia Capital INC. series of yields on long-term bonds (from Canadian Central Bank).
  - Caveats: bond yields vary only over time (no industry-level yields), may reflect large-corporation financing costs more than small firms’, and include non-manufacturing firms.
  - Alternative (U.S. only, Section 5): industry-specific cost of issuing equity — estimated via industry betas interacted with proxy for expected market return (market dividend yield) under CAPM logic. This equity-based cost of funds varies over time and across industries.

### Estimation approach
- Baseline panel regression (equation (3) in text):
  - %Δ V_st = α + γ (MRZ_s × cost_s,t) + sector fixed effects + time dummies + ε_st
  - V_st denotes alternative dependent variables (focus on sectoral TFP growth; also industry GDP, capital-labor ratio, labor size, capacity utilization).
  - γ captures the differential impact of changes in the cost of finance on growth of V across industries with different MRZ.

### Main empirical findings (baseline regressions)
- Industry GDP:
  - Estimated coefficient for interaction implies: a 100 basis point increase in the cost of funds reduces GDP growth in a sector with average dependence on external finance by around 0.6 percentage point relative to a sector with no external finance dependence (coefficient reported as -2.12 in text; interpretation given in context).
  - Authors note potential upward bias due to demand-side channels and use of long-term yields.
- Labor and capacity utilization:
  - Higher dependence on external finance makes labor and capacity utilization more sensitive to financial shocks.
- Capital-labor ratio:
  - No significant effect of cost of funds on capital-labor ratio — sectors scale back but do not change factor shares.
- Total factor productivity (TFP) growth:
  - Baseline result: γ = -0.96 (as reported in text for the TFP regression).
  - Interpretation: a one-standard deviation increase in yields on long-term corporate bonds reduced TFP growth in sectors with average dependence on external finance by 0.25 percentage point more than in a benchmark sector without dependence on external finance.
  - Authors emphasize economic significance: 0.25 percentage point is almost half of the average growth rate of aggregate TFP for the U.S. economy in the last 20 years (contextual numbers referenced below).
- Robustness / alternative cost-of-funds measure (equity-based, U.S. only):
  - Negative link between TFP growth and the cost of funds is stronger when using industry-specific expected return on equity.
  - Quantified effect: a one-standard deviation increase in the equity-based cost-of-funds measure reduces annual TFP growth in sectors with average dependence on external finance by 0.5 percentage point relative to a benchmark sector with no external dependence.

### Interpretation and policy-relevant implications
- Mechanism: financial shocks can impair TFP through misallocation of factors across firms within an industry when heterogeneity in firms’ cost of funds changes; effect magnitude is increasing in sectoral dependence on external finance φ.
- Implication for crises:
  - Severe financial crises that undermine the financial system can generate distortions in allocation of capital and production, harming sectoral efficiency.
  - Empirical results suggest distortions across firms within industries are relevant — policy concern should include misallocation within sectors, not only inadequate expansion of particular industries.
- Measurement and identification strengths:
  - Focusing on sectoral TFP at business-cycle frequency helps separate allocation-efficiency effects from aggregate-demand-driven fluctuations that also affect output, capital, and labor.
  - Use of MRZ interaction with time-varying cost measures exploits cross-sectional heterogeneity in dependence on external finance for identification.
- Caveats noted by authors:
  - Long-term bond yields may imperfectly capture cost of capital for smaller firms.
  - Potential biases from demand-channel feedbacks and from using aggregate yield series that include non-manufacturing firms.
  - Data limitations: sample period and industry coverage constrained by availability of hours worked and capital services at 3-digit NAICS.

### Empirical magnitudes and sample facts (select numbers preserved)
- Sample period for main panel: United States and Canada, 1991 to 2007 (earlier mention: TFP data constructed for 1990–2007 for some elements; panel emphasis 1991–2007).
- Baseline TFP effect: γ = -0.96 (reported), interpreted as:
  - 100 basis points increase in corporate bond yields → TFP growth in sectors with average dependence on external finance falls roughly 0.25 percentage point relative to a benchmark non-dependent sector.
- Equity-based cost of funds (U.S. only): one-standard deviation increase → reduces annual TFP growth by 0.5 percentage point for sectors with average dependence on external finance (relative to a non-dependent benchmark).
- Comparative benchmark: average annual growth rate of aggregate TFP for the U.S. between 1948 and 2000 is 1.18 percent (contextual reference for economic significance).

*Source: Excerpt from the provided IMF working paper content (sections I–IV and model exposition).*

### 0.53 percent from the 1970’s until 2000.

### _wp1023 - 0.53 percent from the 1970’s until 2000.

### Main empirical finding
- Financial shocks have a statistically significant and economically meaningful impact on TFP growth: sectors more dependent on external finance suffer larger productivity declines when the cost of capital rises.
- To the extent that dependence on finance is relatively exogenous to factors or productivity, the relation is more than pure co-movement between variables.
- Conclusion: the cost of funds is an important determinant of total factor productivity growth at the business cycle frequency.

### Robustness checks (returns to scale, sector composition, outliers)
- Concern: measured sectoral TFP was calculated assuming a Cobb-Douglas production function with constant returns to scale; if technology displays non-constant returns to scale, measured TFP growth may be biased by changes in scale (labor) and the capital-labor ratio.
- Under a generalized production function Ys = As~ Ks^ψ Ls^(1-ψ) with returns-to-scale parameter ρ, measured TFP growth equals true technological growth plus a bias that depends on the capital-labor ratio, returns to scale, and labor growth.
- Regression (4) augments the baseline with growth in the capital-labor ratio and growth in labor to control for scale effects.
- Result: the negative impact of the cost of funds on TFP growth is preserved though magnitude is reduced. Specifically:
  - A one standard-deviation increase in yields on corporate bonds reduces annual TFP growth in a sector with average dependence on external finance by 0.16 percentage point more than in a benchmark nondependent sector.
- The coefficient on labor growth (b1) provides evidence about returns to scale; estimates indicate industries display fairly constant returns to scale.
- Sequential exclusion of individual industries in both countries leaves basic conclusions unchanged.
- Excluding the U.S. petroleum industry (NAICS code 324) does not overturn results; shocks to funding costs remain statistically significant and the effect can be stronger once returns to scale are controlled for.

### Changes in the cost of equity and TFP growth (U.S. analysis)
- Motivation: firms may substitute between debt and equity; examine robustness using a proxy for the cost of equity (U.S. only).
- Cost-of-equity measurement:
  - Expected returns for firm i in sector s assumed generated by CAPM: E[Ri] = Rf + βi (Rmkt − Rf).
  - Industry betas (βs) are estimated using Fama and French returns on industry portfolios (annual returns, 1969–2008 after discarding first 40 years).
  - Expected market return proxied by the dividend yield on the market portfolio (average of 4th and 5th decile portfolios); normalized to zero mean and standard deviation 1; multiplied by βs to obtain sector-level proxy for expected return on equity.
- Empirical results:
  - Baseline regression using either yields on corporate bonds or the equity cost proxy shows strong evidence that increases in the cost of funds reduce TFP growth.
  - The effect is much stronger using the expected-return-on-equity proxy: the estimated γ is more than twice the coefficient estimated using yields on corporate bonds.
  - Quantitatively: a one-standard deviation increase in the dividend-yield on the market portfolio predicts a decline in annual TFP growth of a sector with an average dependence on external finance of approximately 0.46 percentage point more than in a benchmark sector.
  - After controlling for capital-labor ratio growth and labor growth, the estimated γ increases to over 2. This implies:
    - A one-standard deviation increase in the dividend-yield on the market reduces annual TFP growth for a sector with average dependence on external finance by roughly 0.6 percentage point more than a benchmark sector (noted as almost half the average growth rate for the manufacturing sector as whole in the sample).

### Discussion: interpretation and endogeneity concerns
- Endogeneity concerns:
  - Reverse causality (positive productivity shocks raising demand for funds and interest rates) would bias γ upward; thus the observed negative γ would be even stronger if that bias were present.
  - A potential alternative is that financial intermediaries anticipate industry-specific productivity shocks and tighten credit to affected sectors; but aggregate time-variation in bond yields and dividend yields implies the reverse-causality explanation must account for why aggregate cost-of-funds rises precisely when finance-dependent sectors have low productivity.
- Theoretical reconciliation:
  - The basic neoclassical model suggests symmetric increases in cost of funds could improve factor allocation and raise TFP; for empirical TFP to decline, shocks must increase dispersion of firm-specific financing distortions.
  - The “reverse-liquidationist” view (Caballero and Hammour): tighter credit conditions impede creative destruction, allowing inefficient plants to survive longer and reducing factor productivity.
- Common root: both perspectives implicate reallocation of factors across firms with different efficiencies as the channel linking financial shocks and TFP; whether via creative destruction or scale changes is secondary for business-cycle frequency events.

### Conclusion and policy implications
- Core result: tighter credit conditions have a negative effect on factor productivity, contrary to “cleansing effect” theories.
- Mechanism: misallocation of factors across firms reduces industry-wide productivity.
- Policy relevance:
  - Policymakers should consider effects of financial shocks on aggregate supply (TFP), not only on aggregate demand and unemployment, when managing macroeconomic policy.
  - Reductions in TFP diminish the magnitude of the output gap, with implications for monetary and fiscal policy calibration.
  - For economic depressions, if these are initiated or followed by severe financial crises, resulting misallocation can impair efficiency and contribute to declines in production and income; an open question is whether this efficiency effect can explain the magnitude and persistence of contractions.
- Future research directions:
  - Firm-level analysis to detect misallocations from financial shocks.
  - Determine whether distortions arise from shifts in firm scale or from distortions in factor composition.

*Source: _wp1023 - 0.53 percent from the 1970’s until 2000.*

### APPENDIX A–TABLES

### APPENDIX A–TABLES

### Index of Dependence on External Finance (Table 1)
- Industry mappings (NAICS — Index MRZ — Corresponding Industry — Rajan and Zingales ISIC):
  - Food, Beverage and Tobacco: 311-312 — 0.08 — Average of Industries* — 314,313,311
  - Apparel and Leather: 315-316 — 0.06 — Average of Industries* — 323,322
  - Primary Metal: 331 — 0.05 — Average of Industries* — 371,372
  - Mineral: 327 — 0.06 — Nonmetal — 369
  - Paper: 322 — 0.18 — Paper — 341
  - Printing: 323 — 0.20 — Printing and Publishing — 324
  - Chemical: 325 — 0.21 — Average of Industries* — 35,113,513,352
  - Fabricated Metal Products: 332 — 0.24 — Metal — 381
  - Furniture: 337 — 0.24 — Furniture — 332
  - Wood: 321 — 0.28 — Wood — 331
  - Petroleum: 324 — 0.33 — Petroleum and Coal — 354
  - Transportation: 336 — 0.39 — Motor Vehicle — 3843
  - Textile: 313-314 — 0.40 — Textile — 321
  - Machinery: 333 — 0.45 — Machinery — 382
  - Plastic: 326 — 0.69 — Average of Industries* — 356,355
  - Electrical Appl. And Comp.: 335 — 0.96 — Average of Industries* — 38,253,833,832
- Note: "* Arithmetic average of RZ's index of dependence on external finance for the industries in the ISIC column."

### Descriptive Statistics (Table 2)
- Variables (Annual percent change, except Yields and RZ, which are in levels):
  - TFP: Mean 1.59, Std. Dev. 5.99, Min -29.32, Max 30.50, Obs 527
  - GDP: Mean 1.28, Std. Dev. 7.5, Min -24.18, Max 35.98, Obs 527
  - Labor: Mean -1.06, Std. Dev. 4.87, Min -15.65, Max 23.38, Obs 527
  - Capital-Labor Ratio: Mean 1.82, Std. Dev. 5.02, Min -22.04, Max 18.24, Obs 527
  - Capacity Utilization: Mean 0.01, Std. Dev. 4.25, Min -19.28, Max 14.48, Obs 527
  - Yields: Mean 7.18, Std. Dev. 1.47, Min 5.24, Max 11.32, Obs 527
  - RZ: Mean 0.28, Std. Dev. 0.26, Min -0.08, Max 0.96, Obs 527

### Baseline Regressions (Table 3)
- Summary line (header): γ Variable — Mean Std. Dev. Min Max Obs (see Descriptive Statistics for values above)

### TFP Growth: The Canadian Dummy (Table 4)
- Coefficients and inference:
  - γ0: Estimate -1.20*** — Std. Dev. 0.44 — Probability 0.01
  - γ1: Estimate 0.17 — Std. Dev. 0.94 — Probability 0.85
- Regression notes:
  - "The regression allows for heteroskedasticity and panel-specific autocorrelation of the residuals."
  - Significance notation:
    - *Significant at the 10% confidence level.
    - **Significant at the 5% confidence level.
    - ***Significant at the 1% confidence level.
- Dependent Variable Growth Rates (Estimated / Std. Dev. / Probability):
  - GDP: Estimated -2.12*** — Std. Dev. 0.43 — Probability 0.00
  - TFP: Estimated -0.96*** — Std. Dev. 0.35 — Probability 0.01
  - K/L: Estimated 0.07 — Std. Dev. 0.12 — Probability 0.57
  - Labor: Estimated -0.49** — Std. Dev. 0.20 — Probability 0.02
  - Capacity: Estimated -0.90*** — Std. Dev. 0.06 — Probability 0.00
- Note: "All regressions allow for heteroskedasticity and autocorrelation of the residuals."

### TFP Growth: Returns to Scale (Table 5)
- Coefficients:
  - Γ: Estimate -0.58*** — Std. Dev. 0.17 — Probability 0.00
  - b0: Estimate 0.25*** — Std. Dev. 0.03 — Probability 0.00
  - b1: Estimate 0.02 — Std. Dev. 0.02 — Probability 0.51
- Regression note: "The regressions allow for heteroskedasticity and panel-specific autocorrelation of the residuals."
- Significance notation repeated as above.

### TFP Growth: Cost of Debt vs. Cost of Equity (Table 6)
- Coefficients:
  - Equity γ: Estimate -1.66*** — Std. Dev. 0.10 — Probability 0.00
  - Bonds γ: Estimate 0.73*** — Std. Dev. 0.06 — Probability 0.00
- Regression note: "The regressions allow for heteroskedasticity and panel-specific autocorrelation of the residuals."
- Significance notation repeated as above.

### TFP Growth: Cost of Equity and Returns to Scale (Table 7)
- Coefficients:
  - γ: Estimate -2.04*** — Std. Dev. 0.05 — Probability 0.00
  - b0: Estimate 0.41*** — Std. Dev. 0.01 — Probability 0.00
  - b1: Estimate -0.18*** — Std. Dev. 0.01 — Probability 0.00
- Regression note: "The regressions allow for heteroskedasticity and panel-specific autocorrelation of the residuals."
- Significance notation repeated as above.

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### APPENDIX B–FIGURES

### Increase in the Cost of Finance and TFP (Figure 1)
- Axes and labels:
  - Horizontal axis: "Dependence on External Source of Funding" with ticks from 0 to 0.9 (0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9)
  - Vertical axis: "Percent change in TFP" with values from 0 to 0.4 in increments shown: 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4

### Increase in Heterogeneity and TFP (Figure 2)
- Axes and labels:
  - Horizontal axis: "Dependence on External Source of Funding" with ticks from 0 to 0.9 (0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9)
  - Vertical axis: "Percent Change in TFP" with values from -0.45 to 0 in increments shown: -0.45, -0.4, -0.35, -0.3, -0.25, -0.2, -0.15, -0.1, -0.05, 0

### US and Canada TFP Growth, 1991-2007 (Figure 3)
- Display: Multiple time-series panels for NAICS industries comparing US and CA percent change in TFP over the period 1991–2005 (labelled "1991 2005" across panels)
- Panels listed (each panel shows percent change in TFP, LH axis, tick range -40 to 40):
  - NAICS 321 US
  - NAICS 327 US
  - NAICS 331 US
  - NAICS 332 US
  - NAICS 333 US
  - NAICS 335 US
  - NAICS 336 US
  - NAICS 337 US
  - NAICS 311 - 312 US
  - NAICS 313-314 US
  - NAICS 315-316 US
  - NAICS 322 US
  - NAICS 323 US
  - NAICS 324 US
  - NAICS 325 US
  - NAICS 326 US
  - NAICS 321 CA
  - NAICS 327 CA
  - NAICS 331 CA
  - NAICS 332 CA
  - NAICS 333 CA
  - NAICS 335 CA
  - NAICS 337 CA
  - NAICS 311-312 CA
  - NAICS 313-314 CA
  - NAICS 315-316 CA
  - NAICS 322 CA
  - NAICS 323 CA
  - NAICS 324 CA
  - NAICS 325 CA
  - NAICS 326 CA
- Note: Each panel y-axis ranges from -40 to 40 percent change in TFP; years shown as 1991–2005 on axis.

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### APPENDIX C–CALIBRATION
- Parameter values and distributions used in comparative static exercises:
  - Elasticity of substitution across goods σ is set to 1.2.
  - Sectoral component of interest rates sτ is normalized to 0.
  - Firm-specific TFP siA is uniformly distributed over the [0.5,1] interval with 100 observations per industry.
  - Parameter of dependence on external finance sφ is uniformly distributed over the [0,1] interval, with 100 different industries.
- Exercise 1 (common component increase):
  - Idiosyncratic component siτ is uniformly distributed over the [-0.15,0.15] interval for the 100 firms in each industry.
  - Common component of the cost of funds τ increased from 0 to 0.4.
- Exercise 2 (dispersion increase):
  - Common component set equal to 0.1.
  - Increase dispersion of idiosyncratic term from no dispersion to uniform dispersion over the interval [-0.15,0.15].
- Additional note:
  - Diagrams assume distribution of firm-specific TFP is independent from distribution of the idiosyncratic component of the cost of funds.
  - Cases of perfect positive and perfect negative correlation between the two variables were also considered, with virtually identical results in terms of TFP growth.

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*Source: _wp1023 - APPENDIX A–TABLES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1023.pdf_