## 1. The Effect of the Interaction Between Firing Costs and Liquidity Requirements

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### Main mechanism and conceptual contribution
- Introduces labor’s "liquidity service": when there is a time gap between production and associated revenues, firing can be used as a liquidity-adjustment tool to increase short-term net working capital (net liquidity is created by firing).
- Liquidity-service effect of firing costs: firing costs reduce the value of labor’s liquidity service, which lowers firms’ demand for liquidity and reduces firms’ demand for inputs (a downward scaling effect).
- Adds a third independent channel to established channels (efficiency cost from keeping low-productivity workers; bargaining effects): a channel driven by financial restrictions and demand for liquidity.
- Key qualitative prediction: interaction between firing costs and financial restrictions yields a negative effect of firing costs on production/efficiency that is unambiguous (contrasting with ambiguous effects in Bentolila and Bertola 1990 and Lazear 1990).

### Empirical evidence and stylized facts
- Null hypothesis tested: the effect of firing costs does not depend on the presence of financial restrictions; this null is rejected in favor of a relatively stronger negative effect of firing costs on output (value added) when financial restrictions are present.
- Panel findings:
  - Country-industry (manufacturing) panel: industries with higher liquidity requirements display a relatively stronger negative effect of firing costs on value added.
  - Country-sectoral (retail and wholesale trade) panel with firm-size disaggregation: small firms show a relatively stronger negative effect of firing costs on output (value added).
- Stylized facts cited:
  - "in the USA, small firms with 10-249 employees represent approximately 30% of total employment, and small firms with 20-99 employees represent approximately 22% of total gross job creation"
  - Smaller firms tend to have significantly less, and more pro-cyclical, credit access than larger firms (Gilchrist and Gertler 1994).
- Employment Protection Legislation (EPL) observation: the OECD ELP index shown for selected countries; "the average value for the late 1980’s is 2.2 and for 2003 is 2.1."

### Theoretical model — setting and core elements
- 3-period model (investment, production, output) with Leontief technology and constant returns to scale.
- Entrepreneur starts with initial wealth W and chooses project scale H (maximum H̄). H workers hired initially; may fire to L ≤ H before production.
- Period-2 stochastic liquidity shock Z ∼ U[Z, Z̄] affects disposable wealth W − eH − Z; Z is private information (entrepreneur faces financial restriction and limited access to external finance).
- Labor-related period-2 cash outflow: ωL + ψ(H − L), where ψ ≥ 0 denotes firing costs.
- Production in period 3: F(L) = A L.
- Liquidation decision It: It = 1 if entrepreneur liquidates in period 2; otherwise It = 0.

### Entrepreneur’s optimization (key expressions and constraints)
- Objective:
  - V(W) = max_{H,I(·),L(·)} − e H + E( F(L) − ω L − ψ(H−L) ) (1−I)
- Constraints:
  - H ≤ H̄; L ≤ H; W − eH − Z ≥ ωL + (H − L) ψ if I = 0; W ≥ eH
- Period-2 optimal labor policy L(W,H) characterized by three regions (hire H; reduce to interior L; liquidation) with thresholds:
  - Z_F(W,H) = min{ W − eH − ω H, Z̄ }
  - Z_L(W,H) = min{ W − eH − ψ θ H, Z̄ } where θ ≡ A / (A − ω + ψ)
- Reformulation yields an integral expression for V(W) and a first-order condition (equation 5) decomposing marginal benefit and marginal expected restructuring cost of expanding H.

### Optimal scale results and comparative statics (closed-form and signs)
- First-best scale is H̄ when capital markets are perfect or entrepreneur has sufficient wealth.
- Minimum wealth for first-best: W̄ (explicit expression in text).
- Closed-form solution for H*(W) with three cases:
  - H*(W) = H̄, if W ≥ W̄;
  - interior expression for W_B ≤ W ≤ W̄;
  - interior expression for W ≤ W_B.
- Monotonicity:
  - ∂ H* / ∂ W ≥ 0 (optimal scale increases with initial wealth).
  - Response of H* to W is larger when W > W_B.
- Effect of firing costs:
  - ∂ H* / ∂ ψ < 0, if W ≤ W̄;
  - ∂ H* / ∂ ψ = 0, if W > W̄.
  - Interpretation: firing costs reduce optimal scale for financially constrained entrepreneurs; unconstrained (well-funded) entrepreneurs unaffected.

### Mechanisms through which firing costs operate (intuition and limits)
- Two opposing impacts of ψ:
  - Higher ψ makes restructuring more costly: for each excess worker fired, the firm must fire e+ψ over (ω − ψ) additional workers (numerator e+ψ is liquidity used by each excess worker; denominator ω − ψ is net liquidity raised by firing a worker).
  - Higher ψ increases risk of liquidation and reduces region of feasible restructuring (especially for entrepreneurs with W ≤ W_B).
- In the limit ψ → ω, labor becomes a fully fixed production factor and Z_L → Z_F.
- Net effect: higher ψ induces a more conservative initial investment/employment policy (downward scaling effect).

### Creation-destruction dynamics and expected labor in period 2
- Expected value of labor in period 2:
  - EL* = ∫_{Z_F}^{Z̄} H* dG(z) + ∫_{Z_L}^{Z_F} L(H*) dG(z)
  - Represented as EL* = Λ(H*(ψ), ψ), with total derivative:
    - ∂ EL* / ∂ ψ = (∂ Λ / ∂ H*) · (∂ H* / ∂ ψ) + ∂ Λ / ∂ ψ
  - In the model, ∂ Λ / ∂ H* > 0 and the reduction in H* dominates any reduction in destruction due to smaller H*, so higher ψ unambiguously lowers EL*.
- Comparison with Bentolila and Bertola (1990): whereas higher firing costs reduce both creation and destruction incentives (leading there to ambiguous steady-state employment effect), interaction with financial constraints here yields an unambiguous negative effect of firing costs on production levels for constrained firms.

### Welfare and macroeconomic implications
- Liquidity-service channel creates a direct pathway through which firing costs affect capital accumulation via firms’ cash-flow constraints (beyond employment’s effect on capital productivity).
- Aggregate implications:
  - Affected medium-run growth rates and transitional dynamics.
  - Distorted speed of employment recovery after recessions, especially because small firms account for a large share of employment and have more constrained credit access.
- Policy-relevant insight: interaction between firing costs and firms’ financial restrictions matters for micro outcomes (firm scale, liquidation risk) and macro outcomes (aggregate production, employment dynamics).

### Appendix 2 — effects of firing costs on EL∗ (synthesis)
- Established: ∂H∗/∂ψ < 0, so the indirect effect of firing costs on EL∗ is negative.
- Direct effect for given H∗: an increase in firing costs increases destruction in the second period, reinforcing the negative effect.
- Combined total derivative (equation 11):
  - ∂EL∗/∂ψ = ∂Λ(H∗,ψ)/∂H∗ · ∂H∗/∂ψ + ∂Λ(H∗,ψ)/∂ψ < 0
- Interpretation:
  - Increase in firing costs reduces initial investment/employment.
  - Expected production in period 2 is reduced.
  - Effective creation level associated to EL∗ responds negatively to an increase in firing costs.

### Appendix 3 — when initial labor L− > H∗: incentives and FOC adjustment
- Scenario L− > H∗ can create an incentive to reduce destruction (as in standard models) but:
  - Incentive to reduce destruction is smaller than in standard models without financial restrictions.
  - For some parameters, L− > H∗ can become an incentive to increase destruction.
- Entrepreneur’s problem with L− > H∗ (equation 12) adjusts constraints to include ψ[L− − H]+.
- First-order condition (FOC) when Z_L < Z̄ has an additional term when L− > H (equation 13); qualitatively:
  - Term ψ1_{ {L− > H} } is the standard incentive to reduce firing.
  - Term −ψ(A − ω)(L− − H)(Z̄ − Z)1_{ {L− > H} } represents cost from worsening liquidity; if sufficiently negative, it can overturn the standard incentive.
- Summary of outcomes:
  - Financially unrestricted firms (W ≥ W̄): firing costs reduce destruction (standard).
  - Financially restricted firms: L− > H∗ can i) create a reduced incentive to cut destruction, or ii) create an incentive to increase destruction.
  - Differentiated effect—stronger downward scaling for financially restricted firms—applies at both creation and destruction margins.
- Special cases:
  - When Z_L = Z̄, the additional term reduces to (ψ − ψ(A−ω)(e+ω)(L−−H)((ω−ψ)(Z̄−Z)))1_{ {L−>H} }.
  - When Z_F = Z̄, the additional term is ψ1_{ {L−>H} }.

### Empirical objective and strategies
- Main theoretical conclusion tested: firing costs have a stronger negative effect on production when financial restrictions are present.
- Null hypothesis tested: the effect of firing costs does not depend on presence of financial restrictions (controlling for individual effects).
- Two empirical strategies:
  1. Industry-level (country-industry manufacturing) tests using cross-industry differences in liquidity requirements and country legal firing costs.
  2. Country-sectoral (retail vs wholesale) panel tests using firm size as proxy for external finance access and a difference-in-differences contrast between labor intensive (retail) and labor un-intensive (wholesale) sectors.

### Empirical strategy 1 — liquidity requirements (industry-level) details
- Reduced-form regression (equation 14):
  - Y_{i j} = α_i + α_j + β_1 FC_j · LR_i + β_2 Z_{i j} + η_{i j}
    - FC_j: firing costs in country j (weeks of pay).
    - LR_i: degree of liquidity requirements implied by industry i’s technology.
    - Z_{i j}: controls; α_j and α_i: country and industry fixed effects.
  - β_1 measures differential effect of firing costs across industries with different liquidity requirements.
- Measures of liquidity requirements:
  - External Financial Dependence (EFD): median across US listed firms in industry of (capital expenditures − cash flow from operations) / capital expenditures, period 1980-89.
  - Cash Conversion Cycle (CCC): days in inventories + days in receivables − days in payables (period 1980-89); correlation between EFD and CCC is 0.08.
- Data and estimation:
  - Sample: 40 countries and 28 manufacturing industries; all countries have per capita GDP higher than $1000 in 1985 (1985 dollars).
  - Dependent variable Y_{i j}: industry i’s share of total value added in country j’s manufacturing sector; median observation within 1986-1995 (UNIDO Rev2).
  - FC_j from Botero et al. (03): severance and penalty payments in weeks of pay for economic dismissals.
  - Controls Z_{i j} include interactions between country financial development and EFD/CCC; financial development measured as domestic credit provided by banking sector (fraction of GDP in 1985).
  - Correlation between firing costs and financial development: -0.10.
  - Estimation: panel with country and industry fixed effects; robust to heteroscedastic errors.

### Industry-level main empirical results and magnitudes
- Estimated coefficient ˆβ_1 on FC · LR is negative and significant for both EFD and CCC.
  - Negative ˆβ_1 implies an increase in firing costs has a relatively stronger negative effect in industries with higher liquidity requirements.
  - If financial markets worked perfectly, expected ˆβ_1 would be zero.
- Nested estimation (both interactive terms and financial controls included) suggests EFD and CCC capture different dimensions of financial restrictions.
- Economic magnitude (from nested estimation):
  - A one week reduction in firing costs is associated with a 0.86% (EFD) and 1.14% (CCC) growth differential between an industry more affected by the liquidity-service effect and an industry less affected.
    - Distance between more and less affected industry computed as one standard deviation in the corresponding liquidity requirement variable.
- Controls show industries with higher financial needs benefit more from financial development (consistent with Rajan and Zingales 1998).

### Industry-level robustness checks
- Added controls: industries’ labor intensity interaction and countries’ rule of law interaction.
  - Labor intensity: median ratio of number of employees in US industry i to gross fixed capital formation in US industry i (1986-1995); correlations:
    - labor intensity with EFD: -0.22
    - labor intensity with CCC: 0.37
  - Rule of law (Knack and Keefer 1995): correlations:
    - rule of law with firing costs: -0.31
    - rule of law with financial development: 0.25
- Results:
  - Negative coefficient on interaction between firing costs and liquidity requirements remains.
  - Interaction between firing costs and labor intensity is negative and significant when using EFD, but not when using CCC (possible explanation: positive correlation between CCC and labor intensity).
  - Interaction between firing costs and rule of law is positive and significant only when using EFD.

### Asset collateralization alternative (TAN) and findings
- Tangibility index (TAN) from Braun (2003): net property, plant, and equipment / total assets, industry median using US firms.
  - Correlations:
    - TAN with EFD: 0.01
    - TAN with CCC: -0.77
    - TAN with labor intensity: -0.51
- Due to high correlation between TAN and CCC, CCC excluded from this set.
- Results:
  - Positive and significant coefficient on interaction implies industries with lower asset collateralization (lower TAN) experience a relatively stronger negative effect of firing costs.
  - Robustness checks replicate main conclusions.

### Empirical strategy 2 — small firms (retail vs wholesale) details
- Regression (equation 15):
  - S_{i j} = α_i + α_j + θ_1 FC_j · D_i + μ_{i j}
    - S_{i j}: share of small firms’ value added in sector i of country j.
    - FC_j: firing costs in country j.
    - D_i: dummy = 1 for labor intensive sector (retail), 0 for wholesale.
    - θ_1: differential effect of firing costs on small firms’ value added.
- Identification and choices:
  - Small firm: fewer than 250 employees (robustness with 20-249; separate check 1-9 employees).
  - Retail vs wholesale chosen because average labor to capital ratio in US retail (1990-1999) is 4.4 times that in US wholesale; both belong to same supply chain.
  - Exclusions: sales and maintenance and repair of motor vehicles excluded from both sectors.
- Sector liquidity differences (Rajan and Zingales methodology):
  - Wholesale minus retail differences: -0.18 for EFD and 0.06 for CCC (expressed as shares of the max-min range among manufacturing industries for EFD and CCC).

### Small firms data, correlations, and regression magnitudes
- Sample: 12 EU-15 countries with sectoral data on aggregate value added by firm size; Eurostat Structural Business Statistics, period 1996-2001.
- Aggregate context: across 12 countries in sample, value added in wholesale sector in 1999 represented 5.6% of total GDP, retail represented 4.6%.
- Figure evidence: plot of S_Rj − S_Wj against country firing costs for 1999 shows correlation -0.69.
- Regression results (Table 4 fragment):
  - Columns correspond to small-firm definitions: 10-249, 10-249, 20-249, 20-249, 1-9, 1-9.
  - Coefficient point estimates: -0.009, -0.008, -0.006, -0.005, 0.008, 0.009
  - Standard errors (in parentheses): (0.003)**, (0.003)**, (0.002)**, (0.003)**, (0.003)**, (0.003)**
  - N: 2498 for all columns.
  - R: 0.9714, 0.9479, 0.9768, 0.9582, 0.9333, 0.9308
  - Countries: 12; Years: 16
  - Notes: Robust standard errors in parentheses; * significant at 10%, ** significant at 5%. Fixed effects control for sector, country, and year. Standard errors clustered at country level for multi-year estimates.
- Interpretation:
  - Firing costs associated with relatively stronger negative effect on small firms’ market participation (share of small firms’ value added in retail vs wholesale).
  - Clustered SE estimation: a one week reduction in firing costs is associated with a 0.8% increase in the share of small firms’ value added in retail sector (relative to wholesale).
  - Robust to redefining small firms as 20-249 employees.
  - Firms with 1-9 employees show a positive instead of negative effect of firing costs, consistent with typical exemptions of micro-firms from layoff costs and with size/sector selection to avoid labor-law costs.

### Policy-relevant conclusions and implications
- Mechanism summary: firing costs reduce the ability to generate net liquidity through firing and decrease value of labor’s liquidity service; produces relatively stronger negative effect on financially restricted firms at both creation and destruction margins.
- Empirical confirmation: controlling for individual effects, the null that the effect of firing costs does not depend on financial restrictions is rejected.
- Evidence:
  - Country-industry (manufacturing) panel: stronger negative effect of firing costs on value added in industries with higher liquidity requirements.
  - Country-sectoral (retail and wholesale) panel with firm-size disaggregation: stronger negative effect on small firms’ value added.
- Policy takeaways:
  - Reductions in dismissal costs could have heterogeneous effects across firm types depending on relevance of financial restrictions.
  - Countries with less developed financial sectors could, ceteris paribus, benefit more from reducing firing costs—this is in addition to standard efficiency gains from lower firing costs.
  - Within-country, financially constrained firms could benefit more from reductions in firing costs.
  - A heterogeneous labor policy that sets lower firing costs for financially restricted firms could, without changing average job turnover, increase allocation of capital and labor based on productivity rather than financial constraints.
  - Existing exemptions of smaller firms from employment protection measures can be interpreted, in the model, as justified by limited access to credit markets.

### Analytical appendices — concise technical summaries
- Appendix I: threshold characterization for W_B and conditions for Z_L relative to Z̄; uniqueness of solution for each W; for W < W_B solution implies Z_L < Z̄; for W ≥ W_B, Z_L = Z̄.
- Appendix II: expression for EL* by cases (equation 22) and differentiation (equation 23) showing ∂EL*/∂H* > 0 in both W ≥ W_B and W < W_B cases.
- Appendix III: FOC adjustment when L^− > 0 (equations 24–25); FOC identical to original except for additional first term when L^− > 0.
- Appendix IV: composition of samples (manufacturing sample: Total1066 observations across many countries; EU-15 sample: Total98 observations).

*Source: _wp07120 - 1. The Effect of the Interaction Between Firing Costs and Liquidity Requirements*

### 1. The Effect of the Interaction Between Firing Costs and Liquidity Requirements:

### 1. The Effect of the Interaction Between Firing Costs and Liquidity Requirements

### Main mechanism and conceptual contribution
- Introduces labor’s "liquidity service": when there is a time gap between production and associated revenues, firing can be used as a liquidity-adjustment tool to increase short-term net working capital (net liquidity is created by firing).
- Liquidity service effect of firing costs: firing costs reduce the value of labor’s liquidity service, which lowers firms’ demand for liquidity and reduces firms’ demand for inputs (a downward scaling effect).
- Distinction from prior literature: builds on two established channels (efficiency cost from keeping low-productivity workers; bargaining effects) and adds a third independent channel driven by financial restrictions and demand for liquidity.
- Key qualitative prediction: interaction between firing costs and financial restrictions yields a negative effect of firing costs on production/efficiency that is unambiguous (in contrast to ambiguous effects in Bentolila and Bertola 1990 and Lazear 1990).

### Empirical evidence and stylized facts reported
- Tests the null hypothesis that the effect of firing costs does not depend on the presence of financial restrictions and rejects it in favor of a relatively stronger negative effect of firing costs on output (value added) when financial restrictions are present.
- Panel results:
  - Country-industry (manufacturing) panel: industries with higher liquidity requirements display a relatively stronger negative effect of firing costs on value added.
  - Country-sectoral (retail and wholesale trade) panel with firm-size disaggregation: small firms show a relatively stronger negative effect of firing costs on output (value added).
- Stylized labor-market and credit facts cited:
  - "in the USA, small firms with 10-249 employees represent approximately 30% of total employment, and small firms with 20-99 employees represent approximately 22% of total gross job creation"
  - Smaller firms tend to have significantly less, and more pro-cyclical, credit access than larger firms (cited: Gilchrist and Gertler 1994).
- Employment Protection Legislation (EPL) observations:
  - OECD ELP index shown for selected countries; "the average value for the late 1980’s is 2.2 and for 2003 is 2.1."

### Theoretical model — setting and core elements
- 3-period model (investment, production, output) with Leontief technology and constant returns to scale.
- Entrepreneur starts period 1 with initial wealth W and chooses project scale H (maximum size H̄). H workers hired initially; may fire to L ≤ H before production period.
- Period-2 stochastic liquidity shock Z ∼ U[Z, Z̄] affects disposable wealth W − eH − Z; Z is private information (entrepreneur faces financial restriction and limited access to external finance because outcome in period 3 is not verifiable).
- Labor-related period-2 cash outflow: ωL + ψ(H − L), where ψ ≥ 0 denotes firing costs.
- Production in period 3: F(L) = A L.
- Liquidation decision It: It = 1 if entrepreneur liquidates in period 2; otherwise It = 0.

### Entrepreneur’s optimization formulation (as presented)
- Objective function:
  - V(W) = max_{H,I(·),L(·)} − e H + E( F(L) − ω L − ψ(H−L) ) (1−I)
- Constraints:
  - H ≤ H̄; L ≤ H; W − eH − Z ≥ ωL + (H − L) ψ if I = 0; W ≥ eH
- Period-2 optimal labor policy L(W,H) characterized by three regions (hire H; reduce to interior L; liquidation) with thresholds Z_F(W,H) and Z_L(W,H) given by:
  - Z_F(W,H) = min{ W − eH − ω H, Z̄ }
  - Z_L(W,H) = min{ W − eH − ψ θ H, Z̄ } where θ ≡ A / (A − ω + ψ)
- Reformulation of V(W) (integral expression) and first-order condition (equation 5) that decomposes the marginal benefit and marginal expected restructuring cost of expanding H.

### Optimal scale results and comparative statics
- First-best scale is H̄ (when capital markets are perfect or entrepreneur has sufficient wealth).
- Definition of minimum wealth for first-best: W̄ (explicit expression provided in text).
- Closed-form solution for optimal scale H*(W) provided with three cases:
  - H*(W) = H̄, if W ≥ W̄;
  - interior expression for W_B ≤ W ≤ W̄;
  - interior expression for W ≤ W_B.
- Monotonicity:
  - ∂ H* / ∂ W ≥ 0 (optimal scale increases with initial wealth).
  - Response of H* to W is larger when W > W_B.
- Effect of firing costs on optimal scale:
  - ∂ H* / ∂ ψ < 0, if W ≤ W̄;
  - ∂ H* / ∂ ψ = 0, if W > W̄.
  - Interpretation: firing costs reduce optimal scale for financially constrained entrepreneurs; firing costs do not affect unconstrained (well-funded) entrepreneurs.

### Mechanisms through which firing costs operate
- Two opposing impacts of ψ:
  - Higher ψ makes restructuring more costly: for each excess worker fired, the firm must fire e+ψ over (ω − ψ) additional workers (numerator e+ψ is liquidity used by each excess worker; denominator ω − ψ is net liquidity raised by firing a worker).
  - Higher ψ increases risk of liquidation and reduces region of feasible restructuring (particularly for entrepreneurs with W ≤ W_B).
- In the limit ψ → ω, labor becomes a fully fixed production factor and Z_L → Z_F.
- Net effect: higher ψ induces a more conservative initial investment/employment policy (downward scaling effect).

### Creation-destruction dynamics and expected labor in period 2
- Comparison with Bentolila and Bertola (1990): while higher firing costs reduce both creation and destruction incentives (leading there to an ambiguous steady-state employment effect), in this model the interaction with financial constraints yields an unambiguous negative effect of firing costs on production levels for constrained firms.
- Expected value of labor in period 2:
  - EL* = ∫_{Z_F}^{Z̄} H* dG(z) + ∫_{Z_L}^{Z_F} L(H*) dG(z)
  - Represented as EL* = Λ(H*(ψ), ψ), with total derivative:
    - ∂ EL* / ∂ ψ = (∂ Λ / ∂ H*) · (∂ H* / ∂ ψ) + ∂ Λ / ∂ ψ
  - The first term captures the indirect effect via the optimal scale; the second term captures the direct effect of ψ on destruction for a given H*.
  - In the model, ∂ Λ / ∂ H* > 0 and reduction in H* dominates any reduction in destruction due to smaller H*, so higher ψ unambiguously lowers EL*.

### Welfare and macroeconomic implications
- Introducing the liquidity service effect creates a direct channel through which firing costs affect capital accumulation via firms’ cash-flow constraints (beyond the indirect channel of employment affecting capital productivity).
- Potential aggregate implications:
  - Affected medium-run growth rates and transitional dynamics.
  - Distorted speed of employment recovery after recessions, particularly because small firms both account for a large share of employment and have more constrained credit access.
- Policy-relevant insight: the interaction between firing costs and firms’ financial restrictions matters for both micro outcomes (firm scale, liquidation risk) and macro outcomes (aggregate production, employment dynamics).

*Source: _wp07120 - 1. The Effect of the Interaction Between Firing Costs and Liquidity Requirements*

### Appendix 2 shows the details of this derivation. We already know that

### _wp07120 - Appendix 2 shows the details of this derivation. We already know that

### Effects of firing costs on EL∗
- It is established that ∂H∗/∂ψ <0, so the indirect effect of firing costs on EL∗ is also negative.
- The direct effect for a given level of H∗: an increase in firing costs increases the level of destruction in the second period, reinforcing the result implied by equation 10.
- Combined total derivative (equation 11):
  - ∂EL∗/∂ψ = ∂Λ(H∗,ψ)/∂H∗ · ∂H∗/∂ψ + ∂Λ(H∗,ψ)/∂ψ <0
- Interpretation:
  - An increase in firing costs reduces the firm’s initial investment/employment decision.
  - The expected level of production in period 2 is reduced.
  - The effective creation level associated to EL∗ responds negatively to an increase in firing costs.

### Optimal scale and firing in period 1 (case L− > H∗)
- Question addressed: How does the optimal scale H∗ change if the firm starts period 1 with a labor force of size L− > H∗?
- Qualitative findings:
  - This scenario creates an incentive to reduce destruction, similar to models with no financial restrictions (e.g., Bentolila and Bertola 1990).
  - However, the incentive to reduce destruction is smaller than in standard models of firing costs.
  - For certain parameter values, L− > H∗ can become an incentive to increase, rather than reduce, destruction.

### Entrepreneur’s problem when L− > H∗
- Given W and L−, the entrepreneur maximizes the value of the firm:
  - V(W,L−) = max_{H,I(·),L(·)} − eH − ψ[L− − H]+ + E( F(L) − ωL − (H − L)ψ )(1 − I)  (equation 12)
- Subject to:
  - H ≤  ̄H
  - L ≤ H
  - W − eH − ψ[L− − H]+ − Z ≥ ωL + (H − L)ψ if I = 0
  - W ≥ eH + ψ[L− − H]+  (equation 13)
- Control variable:
  - I takes the value of 1 if the entrepreneur liquidates the firm in period 2 and 0 if she does not liquidate.

### First-order condition (FOC) with additional term when L− > H∗
- The FOC is similar to the FOC of the original problem (equation 5), but with an additional first term that appears when L− > H.
- For the case when Z_L <  ̄Z the FOC is given as:
  - 0 = ( ψ − ψ(A − ω)(L− − H)( ̄Z − Z ) ) 1_{ {L− > H} } − e + (A − ω) ∫_{Z}^{ ̄Z } F_Z dG(z) + ∫_{Z}^{Z_L} F [ (A − ω) − (e + ψ) ω − ψ − ψ( 1 − −(e + ψ) ω − ψ ) ] dG(z)  (equation 13)

*Italic: Source: _wp07120 - Appendix 2 shows the details of this derivation. We already know that*

### Appendix 3 shows the details of this derivation.

### _wp07120 - Appendix 3 shows the details of this derivation.

### Theoretical mechanism: firing costs, financial restrictions, and incentives
- The term ψ1{L−>H} represents the standard incentive to reduce firing created by the presence of firing costs.
- If the entrepreneur has a strong financial position (W≥ ̄W), the presence of firing costs has the standard effect: adding a positive term to the FOC implies that H∗ has to increase to balance the FOC.
- When financial restrictions are present, ψ1{L−>H} is counter-balanced by the term −ψ(A−ω)(L−−H)( ̄Z−Z)1{L−>H}, which represents the cost associated to the worsening of the firm’s liquidity position.
  - If this last term is sufficiently negative, the incentive to reduce firing can become an incentive to increase firing.
- Summary of outcomes:
  - For financially unrestricted firms: firing costs reduce destruction (standard argument).
  - For financially restricted firms:
    - L−>H∗ can i) create an incentive to reduce destruction, but with less intensity than for unrestricted firms, or ii) become an incentive to increase destruction.
  - The differentiated effect of firing costs on financially restricted firms—a relatively stronger downward scaling effect compared to financially unrestricted firms—is present at both the creation margin and the destruction margin.
- Special cases:
  - When ZL = ̄Z, the additional term is (ψ − ψ(A−ω)(e+ω)(L−−H)((ω−ψ)( ̄Z−Z)))1{L−>H}.
  - When ZF = ̄Z, the additional term is ψ1{L−>H}.

### Empirical objective and hypothesis
- Main theoretical conclusion tested: firing costs have a stronger negative effect on production levels when financial restrictions are present.
- Null hypothesis tested: the effect of firing costs does not depend on the presence of financial restrictions, controlling for the individual effects of firing costs and financial restrictions.
- Two empirical strategies employed:
  1. Industry-level (country-industry manufacturing) tests using cross-industry differences in liquidity requirements and country legal firing costs.
  2. Country-sectoral (retail and wholesale trade) panel tests using firms’ size as proxy for access to external finance and a difference-in-differences contrast between labor intensive (retail) and labor un-intensive (wholesale) sectors.

### Empirical strategy 1: liquidity requirements (industry-level)
- Regression specification (reduced form):
  - Yi j = αi + αj + β1 FCj · LRi + β2 Zi j + ηi j  (equation 14)
    - FCj: firing costs in country j (legal severance and penalty payments, in weeks of pay).
    - LRi: degree of liquidity requirements implied by industry i’s production technology.
    - Zi j: control variables; αj and αi: country and industry fixed effects.
  - Interpretation: β1 = differential effect of firing costs across industries with different liquidity requirements. β1 = 0 implies no differential effect.
- Measures of liquidity requirements:
  - External Financial Dependence (EFD): median across US listed firms in industry of (capital expenditures − cash flow from operations) / capital expenditures, period 1980-89.
  - Cash Conversion Cycle (CCC): days in inventories + days in receivables − days in payables, where:
    - days in inventories = total inventories·365 / cost of goods sold
    - days in receivables = total receivables·365 / sales
    - days in payables = total payables·365 / cost of goods sold
    - Period 1980-89.
  - Correlation between EFD and CCC is 0.08.
- Data and estimation details:
  - Sample: 40 countries and 28 manufacturing industries.
  - All countries have per capita GDP higher than $1000 in 1985 (1985 dollars).
  - Dependent variable Yi j: industry i’s share of total value added in country j’s manufacturing sector, computed as the median observation within 1986-1995 (UNIDO Industrial Statistics Database, Rev2).
  - FCj from Botero et al. (03): level of severance and penalty payments, in weeks of pay, for economic dismissals.
  - Controls Zi j include interactions between each country’s financial development and EFD/CCC:
    - Financial development measured as domestic credit provided by the banking sector (fraction of GDP in 1985, World Development Indicators).
    - Correlation between firing costs and financial development is -0.10.
  - Estimation: panel data with country and industry fixed effects; robust to heteroscedastic errors.

### Industry-level main empirical results
- Main finding: estimated coefficient ˆβ1 on FC · LR is negative and significant for both EFD and CCC measures.
  - Negative ˆβ1 indicates that an increase in firing costs has a relatively stronger negative effect in industries with higher liquidity requirements.
  - If financial markets worked perfectly (no demand for liquidity for insurance), expected ˆβ1 would be zero.
- Nested estimation (both interactive terms and financial controls included) suggests EFD and CCC capture different dimensions of financial restrictions.
- Economic magnitude (from nested estimation):
  - A one week reduction in firing costs is associated with a 0.86% (EFD) and 1.14% (CCC) growth differential between an industry more affected by the liquidity service effect and an industry less affected.
    - Distance between more and less affected industry computed as one standard deviation in the corresponding liquidity requirement variable.
- Controls in Zi j show industries with higher financial needs benefit more from financial development (consistent with Rajan and Zingales 1998).

### Robustness checks (industry-level)
- Controls added: industries’ labor intensity interaction and countries’ rule of law interaction.
  - Labor intensity constructed as median ratio of number of employees in US industry i to gross fixed capital formation in US industry i (period 1986-1995), with gross fixed capital formation deflated by US nonresident gross private domestic investment deflator.
  - Correlations:
    - labor intensity with EFD: -0.22
    - labor intensity with CCC: 0.37
  - Rule of law variable (Knack and Keefer 1995) used to control for institutional enforcement heterogeneity:
    - Correlations: rule of law with firing costs: -0.31; rule of law with financial development: 0.25.
- Results:
  - Negative coefficient on interaction between firing costs and liquidity requirements remains, confirming the main result and rejecting the hypothesis that liquidity requirement variables proxy only for labor intensity.
  - Interaction between firing costs and labor intensity is negative and significant when using EFD, but not when using CCC (possible explanation: positive correlation between CCC and labor intensity).
  - Interaction between firing costs and rule of law is positive and significant only when using EFD.

### Asset collateralization alternative measure
- Tangibility index (TAN) from Braun (2003): net property, plant, and equipment / total assets, computed using US listed firms (industry median).
  - Correlations:
    - TAN with EFD: 0.01
    - TAN with CCC: -0.77
    - TAN with labor intensity: -0.51
- Due to high correlation between TAN and CCC, CCC excluded from this set.
- Results (Table 3):
  - Positive and significant coefficient on interaction implies industries with lower asset collateralization (lower TAN) experience a relatively stronger negative effect of firing costs.
  - Robustness checks replicate main conclusions.

### Empirical strategy 2: small firms (retail vs wholesale sectors)
- Objective: test whether firing costs have a differential effect on small firms’ value added, using firm size as proxy for difficulty in accessing external finance; contrast labor intensive sector (retail) with labor un-intensive sector (wholesale).
- Regression specification:
  - Si j = αi + αj + θ1 FCj · Di + μi j  (equation 15)
    - Si j: share of small firms’ value added in sector i of country j.
    - FCj: firing costs in country j.
    - Di: dummy = 1 for labor intensive sector (retail), 0 otherwise (wholesale).
    - θ1: differentiated effect of firing costs on small firms’ value added, controlling for country effects via sector contrast.
- Definition and identification:
  - Small firm defined as employing fewer than 250 employees.
  - Retail and wholesale selected because:
    - Average labor to capital ratio in US retail (1990-1999) is 4.4 times higher than in US wholesale.
    - Both sectors are important and belong to the same supply chain.
  - Exclusions: sales and maintenance and repair of motor vehicles excluded from both sectors.
- Consideration of sector liquidity requirements:
  - Using Rajan and Zingales methodology, wholesale has lower EFD and higher CCC than retail.
  - Differences (whole sector minus retail): -0.18 for EFD and 0.06 for CCC (expressed as shares of the max-min range observed among manufacturing industries for EFD and CCC, respectively).

### Small firms data and sample
- Sample: 12 EU-15 countries with available sectoral data on aggregate value added by firm size (size measured by number of employees).
- Note: Aggregated note on retail and wholesale importance (from earlier context):
  - Aggregating 12 countries in sample (see next section in source), value added in wholesale sector in 1999 represented 5.6% of total GDP, and value added in retail sector represented 4.6%.

*Source: _wp07120 - Appendix 3 shows the details of this derivation.*

### Appendix 4 for the composition of the sample).  The data is obtained from Eurostat’s Structural Business

### Appendix 4 and subsequent appendices (composition of the sample; robustness; analytical appendices)

### Definition and sample construction
- Small firms are defined as firms employing between 10 and 249 employees.
- Robustness checks use an alternative small-firm range of 20 to 249 employees.
- A separate robustness check studies firms employing between 1 and 9 employees (labor laws typically exempt these firms from layoff costs).
- Data is obtained from Eurostat’s Structural Business Statistics and covers the period 1996-2001.
- Manufacturing sample: Total1066 observations (see Table A2).
- EU-15 sample: Total98 observations (see Table A3).

### Empirical patterns and main findings
- Figure evidence: plots differences S_Rj − S_Wj against country firing costs for year 1999 (the only year with data for all 12 countries) and suggests that the impact of firing costs is relatively stronger in more financially restricted firms. If financial restrictions played no role, no correlation would be expected.
- Observed simple correlation in Figure 2: -0.69.
- Main regression conclusions (Table 4 summary):
  - Firing costs are associated with a relatively stronger negative effect on small firms’ market participation (small firms’ value added share in sector i over total value added in sector i; i = Retail, Wholesale).
  - The estimate of parameter θ in equation 15 confirms the negative correlation.
  - Using the estimation with clustered standard errors, a one week reduction in firing costs is associated with a 0.8% increase in the share of small firms’ value added in the retail sector (relative to the observed change in the wholesale sector).
- Results are robust to redefining small firms as 20 to 249 employees (Columns 3 and 4 replicate Columns 1 and 2 with similar results).
- Firms with 1-9 employees show a positive instead of negative effect of firing costs in the corresponding estimations (Columns 5 and 6), consistent with the expectation that exempted micro-firms do not experience the negative liquidity-channel effect, and suggesting size and/or sector selection among small firms to avoid labor-law costs.

### Regression fragment (as presented)
- Coefficient values (fragment from Table 4):
  - Columns labeled (1) through (6) associated with definitions 10-249, 10-249, 20-249, 20-249, 1-9, 1-9.
  - Coefficient point estimates: -0.009, -0.008, -0.006, -0.005, 0.008, 0.009
  - Standard errors (in parentheses): (0.003)**, (0.003)**, (0.002)**, (0.003)**, (0.003)**, (0.003)**
  - N: 2498, 2498, 2498, 2498, 2498, 2498
  - R: 0.9714, 0.9479, 0.9768, 0.9582, 0.9333, 0.9308
  - Countries: 12, 12, 12, 12, 12, 12
  - Years: 16, 16, 16
- Notes: Robust standard errors in parentheses; * significant at 10%, ** significant at 5%. Fixed effects control for sector, country, and year unobserved characteristics. Standard errors are clustered at the country level for estimates with more than one year of data.

### Economic and policy implications highlighted in conclusion
- Mechanism: Firing costs reduce the ability to generate net liquidity through firing and decrease the value of labor’s liquidity service; this produces a relatively stronger negative effect on financially restricted firms at both creation and destruction margins.
- Empirical confirmation: Controlling for individual effects of firing costs and financial restrictions, the null that the effect of firing costs does not depend on financial restrictions is rejected.
- Sectoral and firm-size evidence:
  - Country-industry (manufacturing) panel: stronger negative effect of firing costs on value added in industries with higher liquidity requirements.
  - Country-sectoral (retail and wholesale) panel with firm-size disaggregation: stronger negative effect on small firms’ value added.
- Policy takeaways:
  - Reductions in dismissal costs could have heterogeneous effects across firm types depending on the relevance of financial restrictions.
  - Countries with less developed financial sectors, where firms more likely face limited credit access, could, ceteris paribus, benefit more from reducing firing costs—this is an effect in addition to standard efficiency gains from lower firing costs.
  - Within-country, financially constrained firms could, ceteris paribus, benefit more from reductions in firing costs.
  - A heterogeneous labor policy that sets lower firing costs for financially restricted firms could, without changing the average level of job turnover, increase allocation of capital and labor based on productivity rather than financial constraints.
  - Existing exemptions of smaller firms from employment protection measures can be interpreted through the model as justified by their limited access to credit markets.

### Analytical appendices — concise summaries
- Appendix I: Threshold characterization for W_B
  - Derived H* solutions under two cases:
    - Case A: Z_L ≤ Z̄. H* given by equation (16). Consistency requires inequality (17), which yields condition W ≤ Z̄ + (A−ω−e)(Ae−ωe+ψe+Aψ)/((A−ω+ψ)(e+ω)(A−ω)) (Z̄ − Z) = W_B (equation 18). Strong inequality implies W < W_B.
    - Case B: Z_L = Z̄. H* given by equation (19). Consistency requires inequality (20), which yields condition W ≥ Z̄ + (A−ω−e)(Ae−ωe+ψe+Aψ)/((A−ω+ψ)(e+ω)(A−ω)) (Z̄ − Z) = W_B (equation 21).
  - Conclusion: there is only one solution for each W. For all values W < W_B, the solution implies Z_L < Z̄; for all values W ≥ W_B, Z_L = Z̄.
- Appendix II: Effect of optimal scale on expected value of labor in period 2 (∂EL*/∂H*)
  - EL* expression by cases (equation 22):
    - If W ≥ W_B: EL* = H* − (Z̄ − Z_F)^2 / [2(ω − ψ)(Z̄ − Z)]
    - If W < W_B: EL* given by the more complex expression in equation 22 (function of H*, e, A, ω, ψ, θ).
  - Differentiation (equation 23) shows ∂EL*/∂H* > 0 in both cases:
    - For W ≥ W_B: 1 − (e + ω)(Z̄ − Z_F)/[(ω − ψ)(Z̄ − Z)] > 0.
    - For W < W_B: derivative expression is positive given A > ω, ω ≥ ψ θ, and (A−ω)^2/(2(A−ω+ψ)) < 1.
  - Conclusion: an increase in the initial optimal scale H* increases production in period 2.
- Appendix III: First-order condition adjustment when L^− > 0
  - The FOC for Z_L < Z̄ is given in integral form (equation 24), which can be rearranged into equation 25.
  - The FOC in equation 25 is identical to the original FOC (equation 5) except for an additional first term arising when L^− > 0.
  - When Z_L(W) = Z̄ an equivalent derivation applies.
- Appendix IV: Composition of samples (selected counts)
  - Manufacturing sample: country-level counts include Argentina28, Australia28, Austria28, Belgium19, Brazil18, Canada28, Chile28, Colombia28, Denmark28, Ecuador28, Finland28, France26, Greece28, Hungary28, Ireland27, Israel28, Italy28, Japan28, Jordan28, Korea28, Malaysia28, Mexico26, Netherlands27, New Zealand26, Norway28, Panama25, Poland28, Portugal28, Romania27, Singapore26, South Africa28, Spain28, Sweden28, Switzerland13, Tunisia22, Turkey28, United Kingdom28, United States28, Uruguay28, Venezuela28. Total1066.
  - Manufacturing sample by ISIC industry counts (Table A2): examples include 311 Food products40, 313 Beverages39, 314 Tobacco39, 321 Textiles40, 322 Wearing apparel, except footwear40, 323 Leather products37, 324 Footwear, except rubber or plastic36, … Total1066.
  - EU-15 sample country counts (Table A3): Austria10, Belgium12, Denmark6, Finland8, France10, Ireland2, Italy12, Netherlands6, Portugal10, Spain6, Sweden8, United Kingdom8. Total98.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07120.pdf*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07120.pdf_