## wp17188

## Source details

**Canonical URL:** [wp17188](https://www.imf.org/-/media/files/publications/wp/2017/wp17188.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2017/wp17188.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2017/wp17188.pdf.json)

---

### Model and key assumptions
- Framework: two-period overlapping generations (OLG) dynamic general equilibrium model with heterogeneous savers (lenders) and investors (entrepreneurs); one period = 10 calendar years; time indexed t = 0,1,2,...
- Agents and technology:
  - Exogenous fraction θ of risk-neutral entrepreneurs and fraction 1−θ of risk-averse households.
  - Representative firm Cobb-Douglas production: Y_t = K_t^β, β ∈ (0,1).
  - Private investment technology: k_{t+1} = x_{t+1} i_t with x_{t+1} ~ F(x), mean μ, variance σ^2; ln(x) ~ N(μ_x, σ_x^2) in calibration.
  - Capital fully depreciates in second period; no government or money; labor supply inelastic.
- Three exogenous distortion parameters describing bankruptcy technology and business environment:
  - cost of resolving bankruptcy / monitoring cost ω (also denoted κ in some calibrations);
  - degree of creditor protection χ (also denoted ξ in calibrations);
  - non-factor cost of running a business ζ (also denoted τ in calibrations).
- Contracting environment:
  - Banks use a modified standard debt contract (modified SDC) in a costly state verification framework.
  - Verification/monitoring cost ω per unit of capital verified; χ(x) denotes bank recoveries in bankruptcy states with χ(x) ≥ ω and x − χ(x) ≥ 0.
  - Solvency cutoff μ_x and project scale i_t characterize optimal contract; leverage ϕ_{t+1} ≡ R_{t+1}^D / ( R_{t+1}^D − Q_{t+1} R_B(μ_x_t) ), with ϕ_{t+1} ≥ 1.

### Key quantitative findings and calibrated experiments
- Baseline calibration: benchmark roughly mimics the U.S. economy; parameter table selected entries exactly reproduced:
  - Capital income share α 0.40
  - Fraction of entrepreneurs η 0.15
  - Risk aversion coefficient γ 0.50
  - Discount factor β 0.80
  - Mean return of capital projects μ 1.60
  - Volatility of returns σ 0.80
  - Mean of the normal distribution μ_x 0.35
  - Standard deviation of the normal σ_x 0.47
  - Cost of running a business τ 0.10
  - Bankruptcy cost κ 0.20
  - Creditor protection ξ 1.00
- Baseline model statistics:
  - Leverage ratio ≈ 3:5
  - Entrepreneurial share of capital income = 33percent
  - Lending spread roughly matches spread between prime lending rate and return on 6-month certificate of deposit
- Long-run output and welfare effects of reducing distortions to U.S. levels (illustrative country examples given in the text):
  - Reducing costs of doing business in countries at the top quartile (examples: Cambodia, CÙte díIvoire) could reduce their income gap relative to the U.S. by as much as 20 percent over the long run.
  - Increasing creditor protection in countries at the bottom quartile (examples: Phillipines and Egypt) could yield similar output gains (as much as 20 percent).
  - Reducing bankruptcy costs to U.S. levels yields gains up to 7 percent for countries like Ukraine and Venezuela.
  - Welfare gains are double-digit (referenced: Figure 7) and can be comparable to or exceed gains from radical policy reforms such as reducing to zero the capital income tax in the U.S.
- Quantitative sensitivities:
  - Reducing ζ (τ) to U.S. levels can increase long-run output per capita up to 30percent depending on country position relative to U.S.
  - Countries with κ close to one (Ukraine, Venezuela) could increase income per capita by as much as 8percent by reaching U.S. levels.
  - Creditor protection improvements for countries with ξ around :2 - :3 could yield double-digit output gains.

### Mechanisms, comparative statics and non-linearities
- Key mechanism channels:
  - Price-of-capital channel: effective capital cost (1+ζ)Q_t; larger ζ raises price of capital and reduces demand.
  - Net-worth channel: entrepreneurs pay upfront fee ζ so disposable income = (1−ζ)W_t; larger ζ reduces entrepreneurial equity and tends to raise leverage.
  - Monitoring/bankruptcy costs ω (κ) and weaker creditor protection χ (ξ) amplify expected bankruptcy costs and can induce credit rationing or market collapse.
- Contractual responses:
  - R_E'(μ_x) = −χ [1 − F(μ_x)] < 0 and R_E''(μ_x) = χ f(μ_x) > 0 (entrepreneur payoff decreasing and convex in cutoff).
  - R_B(μ_x) is strictly concave on [0, x̄] and attains global maximum at x̄ where x̄ h(x̄) = χ/ω.
  - μ_x decreases with higher deposit rate R_{t+1}^D and increases with higher price of capital Q_{t+1}.
  - Leverage ϕ_{t+1} increases with Q_{t+1} and satisfies ϕ_{t+1} ≥ 1; ∂ϕ/∂W_t < 0.
- Non-linearities and counterintuitive outcomes:
  - Lending spreads S_{t+1}^L = χ μ_x_t R_B(μ_x_t) / R_{t+1}^D − R_{t+1}^D are highly non-linear and can exhibit inverted-U shapes with respect to ξ and κ.
  - Very low creditor protection combined with moderate-to-large bankruptcy costs can lead to lower lending spreads than when bankruptcy costs are small; low spreads may therefore mask severe distortions.
  - Spreads sharply increase as ζ approaches 1 (net-worth channel dominance).
  - Creditor protection below :2 typically violates bank limited liability constraint in the baseline calibration.

### Deposit supply sensitivity and alternative equilibrium regimes
- If households have an autarkic alternative with fixed real return R_A:
  - Financial intermediation collapses if R_{t+1}^D < R_A or if bank limited liability is violated; economy can be trapped in a self-finance (autarkic) equilibrium.
  - In autarky: I_t = η (1 − τ) W_t; R_{t+1}^E = μ Q_{t+1}; K_{t+1} = η μ (1 − τ) (1 − α) K_t^α (equations (26)–(28)).
- Policy-simulation notes:
  - Imposing a floor on deposit rates can attenuate deposit supply collapse but does not eliminate large economic costs and leaves underlying distortions unaddressed (Figure 10).
  - The sign of gains from improved bankruptcy technology depends on the slope of loan supply parameter ζ_s: with upward-sloping supply (baseline ζ_s = 0:5) improvements unambiguously raise output; with downward-sloping supply (very high depositor risk aversion) an upward shift in loan demand can reduce equilibrium credit if demand is more elastic than supply (Figure 11).

### Interactions between distortions and policy experiments
- Parameter ranges used for joint experiments constrained to preserve intermediation equilibria:
  - τ in [:1;:5]
  - κ in [:2;:6]
  - ξ in [:6;1]
  - Midpoint shifts: τ = :3, κ = :4, ξ = :8
- Combined effects:
  - Output and credit: interactions tend to be additive/parallel in many simulations (no large amplifying/dampening effect), so multiple simultaneous distortions can double or triple income gaps compared to single distortions (example: a country with ξ = :6 and τ three times U.S. and κ twice U.S. can see income gap double from 10percent to 20percent).
  - Lending spreads: interactions can be highly non-linear and perverse; weak creditor protection interacting with bankruptcy cost can reduce spreads in some regimes.
- Identification challenge: observed low spreads can reflect equilibrium responses to severe distortions; empirical diagnosis must account for general-equilibrium and non-linear interaction effects.

### Policy implications and recommendations
- Structural reforms prioritized:
  - Reduce non-factor costs of running a business (red tape, bureaucratic burdens) — parameter τ (ζ).
  - Improve creditor protection (limit asset diversion, enforce APR and reduce legal exemptions) — parameter ξ (χ).
  - Lower bankruptcy resolution costs and speed insolvency procedures — parameter κ (ω).
- Reform design:
  - Coordinated reforms addressing multiple distortions likely yield amplified payoffs in countries with simultaneous weaknesses.
  - Pricing/regulatory intervention (e.g., a floor on deposit rates) may prevent deposit runs but does not solve core distortions.
- Identification caution for policymakers:
  - Low observed lending spreads do not necessarily imply sound financial fundamentals; they may reflect equilibrium responses to distortions.

### Empirical regularities and cross-country evidence (selected illustrative facts)
- Doing Business indicators (selected entries reproduced exactly):
  - Starting a business: Bottom quartile 0.21, Median 0.87, Top quartile 2.17
  - Getting electricity: Bottom quartile 1.39, Median 6.46, Top quartile 16.85
  - All five combined 2/: Bottom quartile 9.67, Median 17.22, Top quartile 34.92
- Bankruptcy cost (cost of resolving insolvency 3/): Bottom quartile 0.09, Median 0.15, Top quartile 0.21
- Creditor protection (recovery rate 4/): Bottom quartile 0.27, Median 0.37, Top quartile 0.50
- Cross-country correlations (Figure 1):
  - Income per capita and private credit/GDP are negatively correlated with costs of running a business and resolving insolvency, and positively correlated with lending spreads.
  - Correlations with creditor protection move in the opposite direction.
- Examples cited:
  - Cost to comply with procedures for permanent electricity connection: Solomon Islands cost is over 100 times larger than in Australia.
  - Cost of insolvency proceedings: Venezuela about 10 times larger than Belgium.
  - Secured creditors recoup loans: secured recovery in United States is 10 times likelier than in Liberia.

*Source: wp17188 - 11. Sensitivity to the Deposit Supply Function; Sections 3.1–3.6; 5.3 (IMF Working Paper, wp17188).*

### 1. Introduction..................................................................................... 3

### wp17188 - 1. Introduction..................................................................................... 3

### Document structure and major sections
- 1. Introduction..................................................................................... 3
- 2. Related Literature.............................................................................. 6
- 3. Model............................................................................................. 8
  - 3.1. Overview................................................................................... 8
  - 3.2. Households................................................................................. 9
  - 3.3. Entrepreneurs.............................................................................. 10
  - 3.4. Banks and Loan Contract................................................................ 11
  - 3.5. Credit Market Outcomes and Supply of Capital...................................... 14
  - 3.6. Equilibrium with Financial Intermediation............................................ 15
  - 3.7. Self-Finance Equilibrium................................................................ 16
  - 3.8. Steady State and Welfare................................................................ 17
- 4. Functional Forms and Parameters............................................................ 18
- 5. Results........................................................................................... 20
  - 5.1. Marginal Effects........................................................................... 20
  - 5.2. Welfare Implications..................................................................... 22
  - 5.3. Perverse Interactions..................................................................... 22
  - 5.4. Bankruptcy Technology and Capital Flight........................................... 23
- 6. Conclusion....................................................................................... 24

### Appendix contents
- Appendix........................................................................................... 25
  - A. Modified SDC.............................................................................. 25
  - B. Properties of the Loan Contract........................................................... 27
  - C. Properties of the Capital Supply Correspondence...................................... 28
  - D. Alternative Deposit Supply Function.................................................... 30

### References and supporting lists
- References.......................................................................................... 31

### Tables (listed)
- 1. Cost of Doing Business and Bankruptcy Technology Across Countries........... 35
- 2. Baseline Parameters........................................................................... 35

### Figures (listed)
- 1. Cost of Doing Business, Bankruptcy Technology and Economic Outcomes...... 36
- 2. Sequence of Events for Time-t Young Cohorts........................................ 36
- 3. Payment Function of the Bank........................................................... 37
- 4. Expected Payoffs (case of unit investment)............................................ 37
- 5. Credit Market Equilibrium (case of unit wage rate)................................... 37
- 6. Marginal Effects of the Cost of Running a Project (τ), Bankruptcy Cost (κ), and Creditor Protection (ξ) on Output, Credit and Spread.................................... 38
- 7. Welfare Effects............................................................................. 38
- 8. Interactions................................................................................. 39
- 9. Equilibrium with Alternative Savings Instruments.................................... 39
- 10. Equilibrium with a “Floor” on the Deposit Rate..................................... 40

*Source: wp17188 - 1. Introduction..................................................................................... 3 (canonical source PDF filename as provided).*

### 11. Sensitivity to the Deposit Supply Function...........................................

### 11. Sensitivity to the Deposit Supply Function

### Introduction and model setup
- Framework: two-period overlapping generations (OLG) dynamic general equilibrium model with heterogeneous savers (lenders) and investors (entrepreneurs).
- Financial intermediation: a bank allocates funds between savers and entrepreneurs through a debt contract (standard debt contract, SDC). A "modified SDC" is used to capture partial creditor protection.
- Three exogenous parameters describe the bankruptcy technology and business environment:
  - cost of resolving bankruptcy (affects net value of assets of a distressed project);
  - degree of creditor protection (parameter describing how assets are distributed between stakeholders; proxy for legal exemptions, deviations from APR, asset diversion by insiders);
  - non-factor cost of running a business (enters like a distortionary tax on entrepreneurial savings and use of capital).
- Monitoring and bankruptcy resolution costs are treated as the same in the contracting problem; liquidation costs may include direct (legal fees, court expenses) and indirect (loss of asset value while in court) components.
- Entrepreneurs have private information about project returns; banks can learn returns at a cost. SDC remains optimal but partial creditor protection weakens debt's bonding role and raises strategic default.

### Key quantitative findings and calibrated experiments
- Baseline calibration: benchmark roughly mimics the U.S. economy.
- Long-run output and welfare effects of reducing distortions to U.S. levels:
  - Reducing costs of doing business in countries at the top quartile (examples: Cambodia, CÙte díIvoire) could reduce their income gap relative to the U.S. by as much as 20 percent over the long run.
  - Increasing creditor protection in countries at the bottom quartile (examples: Phillipines and Egypt) could yield similar output gains (as much as 20 percent).
  - Reducing bankruptcy costs to U.S. levels yields gains up to 7 percent for countries like Ukraine and Venezuela.
  - Reforms also produce higher levels of financial intermediation and lower borrowing costs (referenced: Figure 6).
  - Welfare gains are double-digit (referenced: Figure 7) and can be comparable to or exceed gains from radical policy reforms such as reducing to zero the capital income tax in the U.S.
- Interaction effects:
  - Interactions between distortions tend to amplify individual effects, doubling or even tripling them depending on distortion sizes.
  - Interactions often work non-linearly (examples in Figures 8–11).

### Interactions and non-linearities (illustrative outcomes)
- Large bankruptcy costs combined with moderate creditor protection may lead to disproportionately larger lending interest spreads (Figure 8).
- Counterintuitive case: very low creditor protection combined with moderate-to-large bankruptcy costs may lead to lower lending spreads than when bankruptcy costs are small. Mechanism:
  - Low protection has a direct effect lowering lending spreads.
  - Simultaneously, low protection raises the minimum return consistent with entrepreneurial solvency and the bank break-even condition, which, because minimum return is positively correlated with default, tends to push spreads up.
  - When protection is sufficiently low, the direct effect dominates and spreads fall. Implication: low spreads do not always signal strong fundamentals; they may reflect general equilibrium responses to severe market distortions.
- Deposit supply sensitivity and equilibrium regimes:
  - If savers have an alternative savings instrument (e.g., a risk-free asset abroad) and distortions depress the return on bank deposits below the return on that alternative, the supply of credit would collapse and financial intermediation would halt (Figure 9).
  - In that case investment is financed by internal funds only and the economy can be trapped in an autarkic equilibrium.
  - Imposing a floor on deposit rates could mitigate negative spillovers on financial intermediation but would not solve underlying problems nor eliminate large economic costs (Figure 10).
  - The impact of distortions on output and intermediation depends on the slope of the loan supply:
    - With an upward-sloping loan supply (assumed in baseline), improvement in bankruptcy technology shifts up loan demand, increases equilibrium credit, and unambiguously raises output and welfare.
    - If loan supply is downward-sloping (depositors have very high risk aversion), gains from improved bankruptcy technology on output and welfare become less obvious—an upward shift in loan demand could reduce equilibrium credit if demand is more elastic than supply (Figure 11). Whether this scenario is empirically relevant is left open.

### Policy implications and recommendations
- Structural reforms targeting:
  - reducing non-factor costs of running a business (red tape, bureaucratic burdens),
  - improving creditor protection (closer adherence to APR, limiting asset diversion and legal exemptions),
  - lowering bankruptcy resolution costs and speeding insolvency procedures,
  can generate sizable long-run output, financial intermediation, and welfare gains.
- Coordinated reforms may yield amplified payoffs because countries that perform poorly tend to have multiple simultaneous distortions; joint implementation can produce larger-than-marginal effects.
- Pricing and regulatory responses:
  - A floor on deposit rates can attenuate collapse of deposit supply in extreme cases but does not address fundamental distortions and leaves large costs in place.
- Identification caution for policymakers and empirical researchers:
  - Observed low lending spreads may hide severe market distortions; disentangling direct and general-equilibrium effects of reforms poses identification challenges.

### Empirical regularities and country examples from cross-country data
- Large cross-country variation in costs and creditor protection (Table 1 examples):
  - Cost to comply with procedures for permanent electricity connection and supply: Solomon Islands cost is over 100 times larger than in Australia.
  - Cost of insolvency proceedings: Venezuela about 10 times larger than Belgium.
  - Secured creditors recoup loans: secured recovery in United States is 10 times likelier than in Liberia.
- Correlations (Figure 1):
  - Income per capita and private credit/GDP are negatively correlated with costs of running a business and resolving insolvency, and positively correlated with lending spreads.
  - Correlations with creditor protection move in the opposite direction.

### Relation to literature and robustness
- Builds on and synthesizes previous work (Bernanke and Gertler (1989); Townsend (1979); Gale and Hellwig (1985); Longhofer (1997); Castro et al. (2004); Cooley et al. (2003); Azariadis and Chakraborty (1999); Antunes et al. (2010); Krasa et al. (2008); Rodriguez-Delgado (2010); Barseghyan (2008); Haidar (2012); Divanbeigi and Ramalho (2015); others).
- Novelty: separates bankruptcy resolution cost from creditor protection, embeds modified SDC in a dynamic GE model, and highlights non-linear interactions and sensitivity to deposit/loan supply slopes.
- Empirical and case-study corroboration: examples include U.S. state-level homestead exemption results (Berkowitz and White (2004)), Brazil’s 2005 corporate bankruptcy reform and firm-level borrowing capacity (Araujo et al. (2012)), and cross-country evidence linking entry costs and business regulations to productivity and growth (Klapper et al. (2006); Kaplan et al. (2011); Monteiro and Assuncao (2011); Ciccone and Papaioannou (2007)).

*Source: wp17188 - 11. Sensitivity to the Deposit Supply Function (excerpt).*

### 3.1  Overview

### 3.1 Overview

### Model structure and key assumptions
- Overlapping generations (OLG) model with young and old generations; planning horizon is two periods; time indexed by t = 0,1,2,...; one period = 10 calendar years.
- Closed economy with no government or money; labor supply is inelastic; no entry decision into entrepreneurial or financial activities.
- No aggregate uncertainty; perfect foresight at the macro level.
- Heterogeneity: within and across cohorts; each generation normalized to size one; an exogenous fraction θ of risk-neutral entrepreneurs and fraction 1−θ of risk-averse households.
- Two goods: consumption and capital.
  - Consumption good produced by representative firm with Cobb-Douglas technology: Y_t = K_t^β, where β ∈ (0,1).
  - Capital production carried out by entrepreneurs via a private investment technology (described in 3.3).
- Capital fully depreciates in the second period; no sales of undepreciated capital between agents.
- Nonfactor cost of running a project parameterized by ζ ∈ [0,1); effective cost of capital incorporates (1+ζ)Q_t (deadweight loss, not a tax).

### Timing and notation
- Lower-case letters for individual variables; capital letters for aggregate variables.
- Generation index suppressed for simplicity.
- Units and aggregation: one unit of labor endowment for young agents (households and entrepreneurs).

### Two channels through which project costs enter the model
- Price-of-capital channel: each unit of capital sold incorporates a cost ζ ∈ [0,1), effective capital cost (1+ζ)Q_t.
- Net-worth channel: entrepreneurs pay an upfront fee proportional to entrepreneurial income equal to ζ, so entrepreneurial disposable income = (1−ζ)W_t.

---

### 3.2 Households — preferences and savings
- Preferences: CRRA utility u(c_t^H) = c_t^H^(1−1/ψ), where ψ > 0 is inverse of intertemporal elasticity of substitution.
  - Savings behavior: independent of interest rate if ψ = 1; increasing if ψ < 1; decreasing if ψ > 1.
  - Baseline assumes ψ < 1 to obtain upward-sloping loan supply, monotonicity and uniqueness of capital policy function; numerical simulations also consider alternative ψ.
- Lifecycle: young households supply one unit of labor in period t, can save in bank deposits and receive gross real return R_t+1^D in t+1, then consume and exit.
- Household savings problem and optimal savings function:
  - s_H(R_t+1^D, W_t) = arg max_{s_H_t} { u(W_t − s_H_t) + β u(R_t+1^D s_H_t) }.
  - Given homogeneity of utility, s_H(R_t+1^D, W_t) = d_t = s_H(R_t+1^D) W_t, where
    s_H(R_t+1^D) = β^{1/(1−ψ)} (R_t+1^D)^{1/(1−ψ)} / (1 + β^{1/(1−ψ)} (R_t+1^D)^{1/(1−ψ)}) is the marginal propensity to save.
- Autarkic alternative: households may invest in a risk-free asset with fixed real return R_A (informal savings arrangement or storage technology that does not contribute to capital accumulation).

---

### 3.3 Entrepreneurs — technology, net worth, and incentives
- Young entrepreneurs: one unit of labor supplied inelastically; pay upfront fee proportional to income equal to ζ, so disposable income = (1−ζ)W_t.
- Entrepreneurial savings problem:
  - s_E(R_t+1^E, W_t) = arg max_{s_E_t} { (1−ζ)W_t − s_E_t + β u(R_t+1^E s_E_t) }.
  - s_E(R_t+1^E, W_t) = s_E(R_t+1^E)(1−ζ)W_t.
  - Marginal propensity s_E(R_t+1^E) = 0 if R_t+1^E < 1/β and = 1 if R_t+1^E ≥ 1/β.
- Focus on equilibria with maximum equity participation (entrepreneur invests full disposable income when R_t+1^E ≥ 1/β).
  - Entrepreneurial net worth (contribution to project) s_E = 0 if R_t+1^E < 1/β; s_E = (1−ζ)W_t if R_t+1^E ≥ 1/β.
- Private investment technology (linear, iid returns):
  - k_t+1 = x_t+1 i_t, where i_t is project scale and x_t+1 ~ F(x) iid across time and entrepreneurs, with mean μ and variance σ^2. Density f(x), hazard h(x)=f(x)/[1−F(x)] twice continuously differentiable.
  - Technical assumption: ∂(x h(x))/∂x > 0 (holds for many distributions including normal and lognormal).
- Financing: entrepreneurs use net worth and loans from households via banks; if realized x_t+1 is high enough repay loan, else declare bankruptcy and receive bankruptcy-court transfer.

---

### 3.4 Banks and loan contract — costly state verification framework
- Banks are financial intermediaries receiving deposits from households and making one-period loans to entrepreneurs; use law of large numbers to eliminate idiosyncratic risk and offer sure return to depositors (depositors effectively risk-neutral).
- Verification cost: to learn x_t+1 bank pays verification cost ω ∈ [0,1] per unit of capital verified; total verification cost ω x_t+1 i_t. Monitoring/verification deterministic; incurred only when project fails (interpreted as bankruptcy costs).
- Distinct frictions:
  - ζ: nonfactor cost of running project (deadweight loss borne partly by entrepreneurs and households via higher price of capital).
  - ω: bankruptcy/monitoring cost (falls on banks).
  - ϕ(x) (denoted as χ(x) in text): function describing amount bank recovers in bankruptcy states; constraints: χ(x) ≥ ω and x − χ(x) ≥ 0 for all x.
- Optimal contract: modified standard debt contract (modified SDC) where solvency cutoff μ_x_t (lowest project return above which entrepreneur is solvent) and project scale i_t characterize the contract.
- Expected payoffs under modified SDC (Appendix A results summarized):
  - R_E(μ_x_t) = μ − χ B(μ_x_t) − χ μ_x_t (1 − F(μ_x_t)).
  - R_B(μ_x_t) = (χ − ω) B(μ_x_t) + χ μ_x_t (1 − F(μ_x_t)).
  - Where ω B(μ_x_t) = ω ∫_0^{μ_x_t} x_{t+1} F(dx_{t+1}) is total expected bankruptcy cost; μ_x_t is solvency cutoff.
- Properties:
  - R_E'(μ_x) = −χ [1 − F(μ_x)] < 0; R_E''(μ_x) = χ f(μ_x) > 0 → R_E(μ_x) decreasing and convex.
  - R_B'(μ_x) = χ [1 − F(μ_x)] [1 − (ω/χ) μ_x h(μ_x)] ? 0 for μ_x < x̄ where x̄ satisfies x̄ h(x̄) = χ/ω; R_B(μ_x) strictly concave on [0, x̄] and attains global maximum at x̄.
  - Bounds: (1−χ) μ < R_E(μ_x) < μ and 0 < R_B(μ_x) < (χ − ω) μ.
- Distortions and equilibrium functioning:
  - Large ω (high bankruptcy cost) or small χ (weak creditor protection) can violate bank limited-liability and collapse intermediation.
  - Large ζ makes it harder to meet bank break-even condition (distorting financing and investment).
- Relationship between returns, solvency cutoff, leverage, and prices:
  - First-order conditions for optimal contract (μ_x_t, i_t):
    - Q_{t+1} [ ω R_B(μ_x_t) + (1 − ω) χ μ_x_t h(μ_x_t) R_E(μ_x_t) ] = R_t+1^D.  (Equation (8) pins down μ_x_t.)
    - i_t = ϕ_{t+1} (1−ζ) W_t, where ϕ_{t+1} is leverage ratio. (Equation (9))
  - Leverage ratio ϕ_{t+1} defined as ϕ_{t+1} ≡ ( R_t+1^D / ( R_t+1^D − Q_{t+1} R_B(μ_x_t) ) ).
  - Appendix B results: μ_x_t is decreasing in R_t+1^D and increasing in Q_{t+1}; ϕ_{t+1} ≥ 1, ∂ϕ/∂W_t < 0, ∂ϕ/∂Q_{t+1} > 0.

---

### 3.5 Credit market outcomes and supply of capital
- Entrepreneurial rate of return (from participation constraint and (9)):
  - R_t+1^E = Q_{t+1} R_E(μ_x_t) ϕ_{t+1}.  (Equation (11))
  - R_t+1^E is decreasing in deposit rate and increasing in price of capital if leverage ratio is sufficiently large (see Appendix B).
- Gross lending rate and lending spread:
  - Gross lending rate R_t+1^L defined as repayment to bank in solvency states scaled by loan size:
    - R_t+1^L ≡ Q_{t+1} R_K_{t+1} = χ μ_x_t R_B(μ_x_t) / R_t+1^D.  (Equation (12))
  - Lending interest spread S_t+1^L ≡ R_t+1^L − R_t+1^D = χ μ_x_t R_B(μ_x_t) / R_t+1^D − R_t+1^D.  (Equation (13))
    - S_t+1^L ≥ 0 and increases in the cutoff μ_x_t.
  - Lending rate increases in price of capital; total effect of deposit rate is ambiguous (depends on elasticity of μ_x_t).
- Bank credit (loan size) as function of leverage ratio and entrepreneurial income:
  - l_t = ( ϕ_{t+1} − 1 ) (1−ζ) W_t.  (Equation (14))
  - Bank credit inherits properties of leverage ratio.
- Supply of capital by typical entrepreneur:
  - k_t+1 = [ μ − ω B(μ_x_t) ] i_t.  (Equation (15))
    - The term in square brackets is average productivity in capital good sector and is strictly less than μ due to frictions (ζ, ω, χ).

---

### Key mechanisms and comparative statics (qualitative)
- Larger ζ (entry/operating costs) reduces entrepreneurial disposable income and makes it more difficult to satisfy bank break-even, lowering capital income and affecting general equilibrium via higher price of capital.
- Larger ω (bankruptcy/monitoring costs) directly reduces bank payoffs and can impede intermediation; amplifies expected bankruptcy costs when creditor protection is weak.
- Smaller χ (weaker creditor protection) enlarges bankruptcy region, increases expected bankruptcy costs, reduces bank recoveries, and can induce credit rationing or market collapse.
- μ_x_t (solvency cutoff) decreases with higher deposit rate R_t+1^D and increases with higher price of capital Q_{t+1} (Appendix B).
- Leverage ϕ_{t+1} ≥ 1 and increases with Q_{t+1}; affects loan supply, lending spreads, and equilibrium investment scale.

*Source: IMF Working Paper — wp17188, Section 3.1 Overview (and following subsections 3.2–3.5).*

### 3.6  Equilibrium with Financial Intermediation

### wp17188 - 3.6 Equilibrium with Financial Intermediation

### Equilibrium with financial intermediation: structure and key relations
- Aggregate capital stock K is the only state variable; input prices reflect marginal products:
  - (1 + )Q_t =  K_t^(-1)  (equation (16))
  - W_t = (1 - ) K_t^  (equation (17))
- Aggregate savings and investment:
  - S_t = [ (1 - ) + (1 - ) s_H(R_D_{t+1}) ] W_t  (equation (18))
  - I_t =  (R_D_{t+1}; Q_{t+1}) (1 - ) W_t  (equation (19))
- Aggregate consumption:
  - C_t =  R_E_t (1 - ) W_{t-1} + (1 - ) [ s_H(R_D_t) R_D_t W_{t-1} + (1 - s_H(R_D_{t+1})) W_t ]  (equation (20))
- Law of motion for aggregate capital:
  - K_{t+1} = [  -  B( x_t) ] [  (1 - ) + (1 - ) s_H(R_D_{t+1}) ] (1 - ) K_t^  (equation (21))
- Loan market clearing:
  - Loan demand: L_t = ( (R_D_{t+1}; Q_{t+1})^{-1} ) (1 - ) W_t  (equation (22))
  - Loan supply (deposits): D_t = (1 - ) s_H(R_D_{t+1}) W_t  (equation (23))
  - Deposit rate pinned down by: s_H(R_D_{t+1}) (R_D_{t+1}; Q_{t+1})^{-1} =  (1 - ) / (1 - )  (equation (24))
- Credit-to-GDP ratio (dividing (22) by output):
  - L/Y_{t+1} =  (1 - ) (1 - ) [ ( R_D_{t+1} / Q_{t+1} )^{-1} ]  (equation (25))
- Comparative statics notes:
  - Loan demand is unambiguously decreasing in the deposit rate.
  - Loan supply slope depends on parameter
: increasing if
 < 1, decreasing if
 > 1, independent if
 = 1 (in which case R_D_{t+1} = 1/).

### Self-finance equilibrium: conditions and dynamics
- Arises when:
  - Expected deposit rate lower than storage return: R_D_{t+1} < R_A, or bank limited liability constraint violated (collapse of credit supply); or
  - Entrepreneurial expected return under loan contract lower than time discount factor: R_E_{t+1} < 1/, or cost of running a project too large (collapse of credit demand).
- Investment determined by entrepreneurial equity:
  - I_t =  (1 - ) W_t  (equation (26))
- Entrepreneurial expected return becomes linear in price of capital:
  - R_E_{t+1} =  Q_{t+1}  (equation (27))
- Aggregate capital evolution under self-finance:
  - K_{t+1} =   (1 - ) (1 - ) K_t^  (equation (28))
- Comparative effect:
  - Distortions () hurt investment and capital accumulation more in autarky than under financial intermediation; first-order effect on capital-to-output ratio in autarky is -  (1 - ), larger in absolute value than under intermediation - [ -  B( x_t)] (1 - ).
- Aggregate consumption analogous to equation (20) but household savings determined by constant return R_A.

### Steady state and welfare: non-linearities and special cases
- Distortions (bankruptcy costs, partial creditor protection) produce two complications:
  - Shape and dynamics of law of motion (equation (21)) depend on preferences, technology, and distortions.
  - Financial contract (solvency cutoff  x_t) conveys information about future capital beyond price and interest signals.
- Log-utility special case: solvency cutoff as function of Q and R_D:
  -  x = R_B^{-1} [ (1 - )  / (  (1 - ) + (1 -  )  ) (R_D / Q) ]  (equation (29))
- Substitution into (21) yields highly non-linear capital correspondence:
  - K = [  -  B( R_B^{-1} [ ... ] ) ] [ (1 - )  + (1 -  )  / (1 + ) ] (1 - ) K^  (equation (30))
  - Multiple steady states possible; existence of at least one positive, locally stable steady state discussed in Appendix C.
- When distortions negligible (payoffs proportional to contributions), Modigliani-Miller like indeterminacy:
  - Rates equalize: R_D = R_E = R_L =  Q, lending spread and equity premium converge to unity.
  - Law of motion simplifies: K_{t+1} = J(Q_{t+1}) (1 - ) K_t^  (equation (31))
  - Logarithmic preferences lead to unique globally stable steady state:
    - K = [  / (  +  / (1 + ) ) (1 - ) ]^{1/(1-)}  (equation (32))
- Self-finance steady state closed form:
  - K = [   (1 - ) (1 - ) ]^{1/(1-)}  (equation (33))
  - Q =  / [   (1 - ) (1 - ^2) ]  (equation (34))
  - High  destroys capital accumulation and increases price of capital similar to a distortionary tax.
- Welfare (long-run, no transition dynamics, additive across agents by population weights):
  - Welfare = 1/(1 - ) [  u_E(R_E; W) + (1 - ) u_H(R_D; W) ]  (equation (35))
  - Welfare gains in simulations measured as consumption equivalents.

### Functional forms and baseline calibration
- Benchmark: U.S. economy treated as reference.
- Parameter baseline values:
  - Capital income share  = 0:4
  - Fraction of entrepreneurs  = 0:15
  - Loan-supply slope parameter 
 = 0:5 (upward-sloping deposit supply)
  - Median risk aversion ≈ 1.7 (from Chiappori and Paiella (2011)); alternative considered 
 = 2 and logarithmic preferences.
  - Discount factor  chosen so deposit rate matches real return on 6-month certificate of deposit in U.S. since WWII (decennial terms).
- Bankruptcy and productivity stochastic process:
  - F(x) is lognormal with parameters _x and _x; ln(x) ~ N(_x, _x^2).
  - Closed forms for expected capital income to entrepreneur and bank:
    - R_E( x) = (1 - ) [  (1 - ) B( z) -   x (1 - ( z)) ]
    - R_B( x) = (1 - ) [  ( - ) B( z) +   x (1 - ( z)) ]
    - where  B( z) =  ( z - _x), (:) is standard normal c.d.f., and  z = (ln( x) - _x)/_x.
- Calibration targets and choices:
  - Average productivity  chosen to match entrepreneurial rate of return to S&P 500 post-WWII.
  - Volatility parameter  chosen to match decennial business bankruptcy rate; chosen  implies bankruptcy rate around 35percent.
  - Matching triple (; ; ) via Doing Business Indicators produces rounded figures (:1; :2; 1) for the U.S. (as empirical counterparts of (; ; )).
- Baseline model statistics generated:
  - Leverage ratio ≈ 3:5
  - Entrepreneurial share of capital income = 33percent
  - Lending spread roughly matches spread between prime lending rate and return on 6-month certificate of deposit
  - Limited liability and participation constraints satisfied.

### Quantitative results and policy-relevant comparative statics (steady state focus)
- Analysis focuses on steady-state marginal effects of each distortion holding others at baseline and assuming depositors do not use storage technology.
- Cost of running a project ():
  - Acts through cost of capital and net worth channels (analogous to non-lump sum tax on capital and labor).
  - Reducing  to U.S. levels can increase long-run output per capita up to 30percent depending on country position relative to U.S.
  - Effects on credit and spreads:
    - Cost-of-capital channel → lower demand for capital → lower credit and lower lending spreads.
    - Net-worth channel → lower entrepreneurial equity → higher leverage → more credit and larger lending spreads.
    - Baseline: cost-of-capital channel dominates credit volume effect (lower credit), net-worth channel dominates price effect (larger spreads).
  - Example: Bringing  from high levels (around :6 - :8) to U.S. levels could reduce income gaps by as much as 20percent for countries like Cambodia or CÙte díIvoire.
- Bankruptcy resolution cost ():
  - Higher  flattens bank payoff, raises optimal solvency cutoff  x, increases default rate and borrowing costs → lower investment and output.
  - Countries with  close to one (Ukraine, Venezuela) could increase income per capita by as much as 8percent by reaching U.S. levels.
- Creditor protection ():
  - Improving  benefits growth and financial intermediation: reduces strategic default, steepens bank payoff, reduces  x, economizes monitoring, increases expected capital output.
  - Results: higher expected returns to depositors, higher price of capital, higher corporate leverage, and relatively low lending spreads.
  - Countries at bottom quartile for creditor protection ( around :2 - :3) could see double-digit output gains by improving  to U.S. levels.
- Nonlinearities in spreads:
  - Response of output and credit roughly linear; lending spreads highly non-linear.
  - Spreads sharply increase as  approaches 1 (net-worth channel).
  - Spread response to  shows inverted-U shape; very large  can prompt banks to engineer reductions in spreads via reducing  x.
  - Spread response to  is inverted-U, peaking near  = :5:
    - For  < :5 direct effect on spreads dominates (spreads fall below peak).
    - For  > :5 indirect effect via reduced  x and lower expected bankruptcy costs reduces spreads significantly.
  - Creditor protection below :2 typically violates bank limited liability constraint in baseline calibration.
- Welfare implications (long-run consumption equivalents):
  - Reforms reducing  or improving  and  can yield large welfare gains, sometimes double-digit consumption-equivalent increases.
  - Examples:
    - Cambodia and CÙte díIvoire reducing  to U.S. levels → steady-state welfare gain ≈ 20percent consumption equivalent.
    - Philippines and Egypt improving  → similar double-digit gains.
    - Ukraine and Venezuela reducing  → welfare gains up to 10percent of long-run consumption.
  - These long-run gains are larger than many prior estimates in the literature; comparable to large reform exercises (e.g., zero capital income taxation or tax system adoption comparisons).
- Qualitative conclusion:
  - Obstacles to entrepreneurship and financial intermediation (high , high , low ) are major impediments to improving living standards in developing countries; poorly designed policies and institutions help explain slow convergence.

*Source: wp17188 - 3.6 Equilibrium with Financial Intermediation (IMF Working Paper)*

### 5.3  Perverse Interactions

### 5.3  Perverse Interactions

### Combined policy experiments and design
- The section assesses net e§ect of policies that tackle more than one distortion at a time, using the same three variables of interest and deviations from the benchmark as before.
- Parameter ranges are constrained to narrower intervals to preserve equilibria with Önancial intermediation:
  -  in [:1;:5]
  -  in [:2;:6]
  -  in [:6;1]
- Each panel in Figure 8 shows three lines:
  - Solid line: change in only one parameter while keeping others at baseline.
  - Dashed line: shift in the second parameter while keeping the third at baseline.
  - Dotted line: shift in the second and third parameters.
- Parameter shifts are to midpoints of the ranges:
  -  = :3
  -  = :4
  -  = :8

### Key findings on output and credit
- The Figure 8 results do not reveal any signiÖcant amplifying or dampening e§ect for output and credit, as illustrated by parallel shifts in the curves.
- The exercise shows combined e§ect of the three distortions and allows decomposition of individual e§ects:
  - A country resembling the U.S. except for lower creditor protection (say :6) would have an income gap of 10percent.
  - If in addition its costs of doing business are three times larger than in the U.S. and its bankruptcy costs are twice as large, its income gap would double to 20percent (top right panel).
- Policy implication: countries with poor performance on all three dimensions should address the distortions simultaneously to fully reap reform beneÖts.

### Non-linear and counterintuitive effects on lending spreads
- Combined impact of the three distortions on lending spreads is substantial and non-linear.
- Interaction between cost of doing business and bankruptcy cost:
  - Does not seem to matter much (bottom left and bottom middle panels), reflecting that even large changes in bankruptcy costs have modest impact on lending spreads (see Figure 6).
- Interaction between weak creditor protection and the other two distortions:
  - Leads to non-linear and often unexpected e§ects on spreads.
  - Example: combination of weak creditor protection and rising bankruptcy costs may reduce lending spreads if protection is already su¢ ciently low (dotted line in bottom right panel).
  - Interpretation: two opposing forces under the loan contract — direct impact of weakening protection can dominate the indirect e§ect through the solvency cuto§-x.
- Central message: low spreads do not always signal strong fundamentals; they may reáect general equilibrium reactions to severe distortions in output and Önancial markets.

### Identification challenges
- The simulation highlights identiÖcation challenges for empirical researchers and policy makers when disentangling marginal impacts of individual distortions on the Önancial sector.
- Empirical and policy diagnosis must account for potential perverse interactions and non-linearities among:
  - creditor protection ()
  - bankruptcy costs ()
  - costs of doing business ()

*Source: wp17188 - 5.3  Perverse Interactions*

### References

### References

### Cited Literature
- Acharya, V. and K. Subramanian (2009) Bankruptcy Codes and Innovation.The Review of Financial Studies,Vol. 22, Issue 12, pp. 4949-4988.
- Antunes, A. and T. Cavalcanti, A. Villamil (2010) Intermediation Costs and Welfare.Center for Growth & Business Cycle Research Discussion Paper Series,No. 142.
- Araujo, A. and B. Funchal (2005) Past and Future of the Bankruptcy Law in Brazil and Latin America.Ensaios Economicos,No. 599.
- Araujo, A. and R. Ferreira, B. Funchal, (2012) The Brazilian Bankruptcy Law Experience. Journal of Corporate Finance,Vol. 18, Issue 4, pp. 994-1004.
- Azariadis, C. and S. Chakraborty (1999) Agency Costs in Dynamic Economic Models.The Economic Journal,109, pp. 222-241.
- Barseghyan, L. (2008) Entry Costs and Cross-Country Di§erences in Productivity and Output. Journal of Economic Growth,Vol. 13, Issue 2, pp. 145.167.
- Bebchuck, L.A. (2002) Ex-Ante Costs of Violating Absolute Priority Rule in Bankruptcy.The Journal of Finance,Vol. 57, No. 1, pp. 445-460.
- Beck, T. and R. Levine (2005) Legal Institutions and Financial Development. In C. Menarde and M. Shirley (eds.),Handbook of New Institutional Economics,pp. 251-278. Springer.
- Bergoeing, R. and P. Kehoe, T. Kehoe, R. Soto (2002) A Decade Lost and Found: Mexico and Chile in the 1980s.Review of Economic Dynamics, Vol. 5, Issue 1, pp. 166-205.
- Berkowitz, J. and M.J. White (2004) Bankruptcy and Small FirmsíAccess to Credit.RAND Journal of Economics, Vol. 35, No. 1, pp. 69-84.
- Bernanke, B. and M. Gertler (1989) Agency Costs, Net Worth, and Business Fluctuations. The American Economic Review,Vol. 79, No. 1, pp. 14-31.
- Bernanke, B. and M. Gertler, S. Gilchrist (1999) The Financial Accelerator in a Quantitative Business Framework. In J. B. Taylor and M. Woodford (eds.),Handbook of Macroeconomics, Edition 1, Vol. 1, No. 1, Ch. 1, pp. 1341-1393. Elsevier.
- Boyd, J. and B. Smith (1994) How Good Are Standard Debt Contracts?  Stochastic Versus Nonstochastic Monitoring in a Costly State VeriÖcation Environment.The Journal of Business, Vol. 67, No. 4, pp. 539-561.
- Carlstrom, C. and T. Fuerst (1997) Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis.The American Economic Review,Vol. 87, No. 5, pp. 893-910.
- Castro, R. and G.L. Clementi, G. MacDonald (2004) Investor Protection, Optimal Incentives, and Economic Growth.The Quarterly Journal of Economics,Vol. 119, Issue 3, pp. 1131-1175.
- Chatterjee, S. and D. Corbae, N. Nakajima, J. RÌos-Rull (2007) A Quantitative Theory of Unsecured Consumer Credit with Risk of Default.Econometrica,Vol. 75, No. 6, pp. 1525-1589.
- Chiappori, P-A. and M. Paiella (2011) Relative Risk Aversion is Constant: Evidence from Panel Data.Journal of European Economic Association,Vol. 9, Issue 6, pp. 1021-1052.
- Christiansen, L. and M. Schindler, T. Tressel (2013) Growth and Structural Reforms: A New Assessment.Journal of International Economics,89, pp. 347-356.
- Ciccone, A. and E. Papaioannou (2007) Red Tape and Delayed Entry.Journal of the European Economic Association,Vol. 5, Issue 2-3, pp. 444-458.
- Claessens, S. and S. Djankov, T. Nenova (2000) Corporate Risk Around the World.World Bank Policy Research Working Paper,No. 2271.
- Cooley, T. and R. Marimon, V. Quadrini (2003) Aggregate Consequences of Limited Contract Enforceability.NBER Working Paper,No. 10132.
- Dabla-Norris, E. and G. Ho, K. Kochhar, A. Kyobe, R. Tchaidze (2013) Anchoring Growth: The Importance of Productivity-Enhancing Reforms in Emerging Market and Developing Economies.IMF Sta§ Discussion Note, SDN/13/08.
- Divanbeigi, R. and R. Ramalho (2015) Business Regulations and Growth.World Bank Policy Research Working Paper,No. 7299.
- Djankov, S. and C. McLiesh, A. Shleifer (2007) Private Credit in 129 Countries.Journal of Financial Economics, 89, pp. 299-329.
- Doing Business 2017 Equal Opportunity for All. World Bank, Washington D.C.
- Dreher, A. and T. Herzfeld (2005) The Economic Costs of Corruption: A Survey and New Evidence. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=734184.
- Dubey, P. and J. Geanakoplos, M. Shubik (2005) Default and Punishment in General Equilibrium.Econometrica, Vol. 73, No. 1, pp. 1-37.
- Galor, O. and H. Ryder (1989) Existence, Uniqueness, and Stability of Equilibrium in a Overlapping-Generations Model with Productive Capital.Journal of Economic Theory, Vol. 49, Issue 2, pp. 360-375.
- Gale, D. and M. Hellwig (1985) Incentive-Compatible Debt Contracts: The One-Period Problem.The Review of Economic Studies, Vol. 52, No. 4, pp. 647-663.
- Gentry, W. and G. Hubbard (2004) Entrepreneurship and Household Saving.Advances in Economic Analysis & Policy, Vol. 4, Issue 1, Article 8.
- Gitlin, R. and B. House (2015) Just Enough, Just in Time Improving Sovereign Debt Restructuring for Creditors, Debtors and Citizens Special Report. Centre for International Governance Innovation.
- Haidar, J. (2012) The Impact of Business Regulatory Reform on Economic Growth.Journal of the Japanese and International Economies,Vol. 26, Issue 3, pp. 285-307.
- Hart, O. (1995)Firms, Contracts, and Financial Structure. Oxford University Press.
- Headd, B. (2003) RedeÖning Business Success: Distinguishing Between Closure and Failure. Small Business Economics, Vol. 21, No. 1, pp. 51-61.
- International Monetary Fund (2013) Sovereign Debt Restructuringó Recent Developments and Implications for the Fundís Legal and Policy Framework. Washington, D.C., April 2013.
- International Monetary Fund (2014) The Fundís Lending Framework and Sovereign Debtñ Preliminary Considerations. Washington, D.C., June 2014.
- International Monetary Fund (2015) Reforming the Fundís Policy on Non-Toleration of Arrears to O¢ cial. Washington, D.C., December 2015.
- International Monetary Fund (2016) The Fundís Lending Framework and Sovereign Debtñ Further Considerations. Washington, D.C., January 2016.
- Japelli, T. and M. Pagano, M. Bianco (2005) Courts and Banks: E§ects of Judicial Enforcement on Credit Markets.Journal of Money, Credit and Banking, Vol. 37, No. 2, pp. 223-244.
- Kaplan, S. and A. Schoar (2005) Private Equity Performance: Returns, Persistence, and Capital Flows.The Journal of Finance, Vol. 60, No.4, pp. 1791-1823.
- Kaplan, D. and E. Piedra, E. Seira (2011) Entry Regulation and Business Start-Ups: Evidence from Mexico. Journal of Public Economics, Vol. 95, Issues 11-12, pp. 1501-1515.
- Klapper, L. and L. Laeven, R. Rajan, (2006) Entry Regulation as a Barrier to Entrepreneurship.Journal of Financial Economics,Vol. 83, Issue 3, pp. 591-629.
- Krasa, S. and T. Sharma, A. Villamil (2008) Bankruptcy and Firm Finance.Economic Theory,Vol. 36, Issue 2, pp. 239-266.
- Krueger, A. (2002) A New Approach to Sovereign Debt Restructuring. International Monetary Fund, Washington, D.C., April 2002.
- Levine, R. (2005) Finance and Growth: Theory and Evidence. In P. Aghion and S. Durlauf (eds.),Handbook of Economic Growth,Volume 1A, Chapter 12, pp. 865-934. North Holland.
- Longhofer, S. (1997) Absolute Priority Rule Violations, Credit Rationing, and E¢ ciency. Journal of Financial Intermediation,6, pp. 249-267.
- Longhofer, S. and C. Carlstrom (1997) Absolute Priority Rule Violations in Bankruptcy. Federal Reserve Bank of Cleveland Economic Review,Issue Q IV, pp. 21-30.
- Lucas, R. (2003) Macroeconomic Priorities.The American Economic Review,Vol. 93, Issue 1, pp. 1-14.
- Monteiro, J. and J. Assuncao (2011) Coming Out of the Shadows? Estimating the Impact of Bureaucracy SimpliÖcation and Tax Cut on Formality in Brazilian Microenterprises.Journal of Development Economics,Vol. 99, Issue 1, pp. 105-115.
- Moskowitz, T. and A. Vissing-Jorgensen (2002) The Returns to Entrepreneurial Investment: A Private Equity Premium Puzzle?The American Economic Review,Vol. 92, No. 4, pp. 745-778.
- Phillips, B. and B. Kirchho§ (1989) Formation, Growth and Survival; Small Firm Dynamics in the U.S. Economy.Small Business Economics, Vol. 1, No. 1, pp. 65-74.
- Prescott, E. (2002) Prosperity and Depression.The American Economic Review,Vol. 92, Issue 1, pp. 1-15.
- Rodriguez-Delgado, J. D. (2010) Bankruptcy and Firm Dynamics: The Case of the Missing Firms.IMF Working Paper,No. 10/41.
- Singer, S. and J. Amoros, D. Arreola (2014)Global Entrepreneurship Monitorñ2014 Global Report.
- Souza-Sobrinho, N. (2010) Macroeconomic of Bank Interest Spreads: Evidence from Brazil. Annals of Finance, Vo. 6, Issue 1, pp. 1-32.
- Townsend, R. (1979) Optimal Contracts and Competitive Markets with Costly State VeriÖcation.Journal of Economic Theory, 21, pp. 265-291.

### Tables and Figures Referenced in the Unit
- Table 1. Cost of Doing Business and Bankruptcy Technology Across Countries
  - Source: World Bank’s Doing Business 2015-2017, sample of 124 countries. See http://www.doingbusiness.org/.
  - Notes: 1/ Each component is expressed in percent of the business’ value. 2/ Expressed in percent of the business’ assets. 3/ Sum of the five components of Doing Business, properly adjusted as a fraction of enterprise’s value. 4/ Used in the paper as proxy for creditor protection. It is defined as cents on the dollar recouped by secured creditors through reorganization, liquidation or debt enforcement proceedings.
- Table 2. Baseline Parameters
  - Note: Discount factor, average returns and standard deviations are consistent with decennial data.
  - Selected entries reproduced exactly:
    - Running a Business 1/
      - Starting a business: Bottom quartile 0.21, Median 0.87, Top quartile 2.17
      - Dealing with construction permits: Bottom quartile 0.76, Median 2.00, Top quartile 5.48
      - Getting electricity: Bottom quartile 1.39, Median 6.46, Top quartile 16.85
      - Registering property: Bottom quartile 2.59, Median 5.00, Top quartile 7.60
      - Enforcing contracts: Bottom quartile 0.88, Median 1.16, Top quartile 1.49
      - All five combined 2/: Bottom quartile 9.67, Median 17.22, Top quartile 34.92
    - Bankruptcy Cost
      - Cost of resolving insolvency 3/: Bottom quartile 0.09, Median 0.15, Top quartile 0.21
    - Creditor Protection
      - Recovery rate 4/: Bottom quartile 0.27, Median 0.37, Top quartile 0.50
    - Parameter table (Symbol / Value)
      - Capital income share α 0.40
      - Fraction of entrepreneurs η 0.15
      - Risk aversion coefficient γ 0.50
      - Discount factor β 0.80
      - Mean return of capital projects μ 1.60
      - Volatility of returns σ 0.80
      - Mean of the normal distribution μ_x 0.35
      - Standard deviation of the normal σ_x 0.47
      - Cost of running a business τ 0.10
      - Bankruptcy cost κ 0.20
      - Creditor protection ξ 1.00
- Figure 1. Cost of Doing Business, Bankruptcy Technology and Economic Outcomes
  - Sources: Doing Business, Global Financial Development, World Development Indicators, International Financial Statistics; and author’s calculations. Macro data are averages for 2010-15, and business indicators are averages for the three latest available years, and cover 124 countries with available data, after eliminating outliers.
  - Note: Scatterplot associations between costs of running a business, costs of resolving bankruptcy, creditor rights, and macro indicators: real GDP per capita (logs, PPP, 2011 international dollars), domestic credit to private sector (percent of GDP), and lending interest spread (ratio between lending rate and deposit rate). Solid lines are linear fitting curves.
- Figure 2. Sequence of Events for Time-t Young Cohorts
  - Labels and axes shown in source (country codes AFG, ALB, ..., ZMB) and numerical axes markers preserved as in original.
- Figures 3–11. Model diagrams and simulation results
  - Figure 3. Payment Function of the Bank
  - Figure 4. Expected Payoffs (case of unit investment)
  - Figure 5. Credit Market Equilibrium (case of unit wage rate)
  - Figure 6. Marginal Effects of the Cost of Running a Project (τ), Bankruptcy Cost (κ), and Creditor Protection (ξ) on Output, Credit and Spread (deviations from benchmark)
  - Figure 7. Welfare Effects (deviations from benchmark)
  - Figure 8. Interactions (deviations from benchmark)
  - Figure 9. Equilibrium with Alternative Savings Instrument (deviation from benchmark)
    - Note: The simulation for bankruptcy cost assumes: τ = 0.1 and ξ = 1; for creditor protection: τ = 0.1 and κ = 0.2; and for both R_A = 1.0.
  - Figure 10. Equilibrium with a “Floor” on the Deposit Rate (deviation from benchmark)
    - Note: The simulation for bankruptcy cost assumes: τ = 0.1 and ξ = 1; for creditor protection: τ = 0.1 and κ = 0.2; and for both R_A = 1.0.
  - Figure 11. Sensitivity to the Deposit Supply Function (deviation from benchmark)

*Source: wp17188 - References (wp17188 - References).*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17188.pdf_