## _wp1522 - 3.1 Individuals

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---

### Model structure and key mechanisms
- Agents heterogeneous by wealth and talent (talent denoted z); each agent lives for two periods.
- First-period decisions: credit participation, occupational choice (entrepreneur or worker), and investment. Second period: wage or business profit, consumption, and bequest.
- Occupational choice:
  - Entrepreneurs use technology with capital and labor; only sufficiently talented and wealthy agents become entrepreneurs.
  - Untalented or wealth-constrained (including talented-but-poor) individuals choose wage employment.
- Two financial regimes:
  - Savings regime: agents can save (deposit) to transfer wealth; participation is free but borrowing unavailable.
  - Credit regime: agents can borrow after paying fixed participation cost ψ; borrowing further constrained by limited commitment (collateral) and asymmetric information (monitoring/intermediation costs).
- Three modeled financial frictions:
  - Fixed credit participation cost ψ: captures fixed transactions costs, high annual fees, documentation requirements, and access barriers.
  - Limited commitment / collateral constraint parameterized by λ: imperfect enforceability requires collateral; bank lends at most λ ∆ if ∆ posted.
  - Asymmetric information / monitoring costs χ: banks monitor highly-leveraged firms at cost proportional to scale, χ k; monitoring occurs when η(1 − δ) k + (1 + r_d)(b − ψ) < Ω.
- Borrowing contract primitives: (Φ, ∆, Ω) where Φ = amount borrowed, ∆ = collateral value, Ω = face value to be repaid; lending rate r_l = Ω / Φ − 1; leverage λ̃ = Φ / ∆.
- Bank zero-profit condition (Equation 3.8):
  - (1 − p) Ω + p min(Ω, η(1 − δ) k + (1 + r_d)(b − ψ)) = (1 + r_d) k + p χ k · 1{η(1 − δ) k + (1 + r_d)(b − ψ) < Ω}.

### Calibration, data, and empirical anchors
- Micro data: World Bank Enterprise Surveys; supplemented with World Development Indicators.
- Calibration targets include:
  - percent of firms with credit,
  - firm employment distribution,
  - economy-wide non-performing loan ratio (NPL),
  - interest rate spread.
- Six country calibrations (country and survey year):
  - Low-income: Uganda in 2005, Kenya in 2006, Mozambique in 2006.
  - Emerging markets: Malaysia in 2006, Philippines in 2007, Egypt in 2007.
- Specific empirical numbers (preserved from source):
  - "51 percent of firms in advanced economies use a bank loan or line of credit as compared with 34 percent in developing economies (World Bank, 2014)."
  - "In developing economies, 35 percent of small firms report that access to finance is a major obstacle..., compared with 25 percent of large firms in developing economies and 8 percent of large firms in advanced economies (World Bank, 2014)."
  - "The collateral requirement in the Philippines is 238.4% of the loan amount."
- Cross-section firm counts: Uganda 563, Kenya 781, Mozambique 599, Malaysia 1115, Philippines 1326, Egypt 996.
- Fixed parameters from literature:
  - δ = 0.06, v = 0.21, α = 0.33, γ = 0.894.
- Country-specific η values used for identification:
  - η = 0.37 for Uganda, Kenya, Malaysia.
  - η = 0.54 for Mozambique.
  - η = 0.29 for Philippines.
  - η = 0.44 for Egypt.
- Selected empirical moments (Table 1 values):
  - Savings (% of GDP): Uganda 8, Kenya 15.4, Mozambique 7.1, Malaysia 39, Philippines 25.7, Egypt 24.5
  - Collateral (% of loan): Uganda 173, Kenya 120.8, Mozambique 120.8, Malaysia 64.6, Philippines 238.4, Egypt 85.5
  - Firms with credit (%): Uganda 17.2, Kenya 25.4, Mozambique 14.2, Malaysia 60.4, Philippines 33.2, Egypt 17.4
  - Non-performing loan (%): Uganda 2.3, Kenya 10.6, Mozambique 3.1, Malaysia 8.5, Philippines 4.5, Egypt 19.3
  - Interest rate spread: Uganda 10.9, Kenya 8.5, Mozambique 8.2, Malaysia 3.3, Philippines 4.3, Egypt 6.1
  - Employment share (top 5%): Uganda 53.8, Kenya 54.1, Mozambique 41.3, Malaysia 29.5, Philippines 52.7, Egypt 58.4

### Main quantitative and qualitative findings
- Two principal channels by which greater financial inclusion affects GDP and inequality:
  - Reallocation channel: funds flow to more talented entrepreneurs, increasing aggregate output and TFP because talented entrepreneurs scale up disproportionately.
  - Friction-reduction channel: more efficient financial contracts reduce waste from participation and monitoring costs, raising GDP.
- Aggregate and distributional outcomes:
  - Financial inclusion unambiguously raises total factor productivity (TFP) as constraints ease and talented entrepreneurs expand.
  - Reducing participation cost ψ:
    - GDP increases via higher investment and improved capital allocation.
    - Interest rate spread: ambiguous — can decrease or increase depending on wealth and entry effects.
    - Inequality: in low-income calibrations Gini first increases then decreases as ψ falls (Kuznets-type); in emerging markets Gini unambiguously falls as ψ decreases (example: Malaysia).
  - Relaxing borrowing constraint λ:
    - GDP increases in all countries; low-income countries' GDP more responsive due to low savings.
    - Interest rate spread generally increases with λ after a threshold because leverage and NPLs rise.
    - Inequality: possible Kuznets pattern — Gini may rise initially as talented entrepreneurs gain, then fall as higher interest rates compress profits.
  - Decreasing intermediation cost χ:
    - TFP increases slightly; GDP response varies by country — in Uganda, Mozambique, Philippines GDP may be unresponsive because only few highly-leveraged firms benefit.
    - Interest rate spread: "monotonically declines in Kenya and Malaysia, but displays an inverted V-curve in other countries."
    - Gini typically increases because efficient intermediation disproportionately benefits highly leveraged, higher-income firms; Gini may decline only marginally at very low χ.
- Numerical marginal-response table (change when credit-to-investment ratio increased by 1 percentage point) — selected entries preserved:
  - Uganda: ψ → GDP 0.39% | TFP 0.34% | Gini -0.00060; λ → GDP 0.35% | TFP 0.25% | Gini 0.00080; χ → GDP 0.12% | TFP 0.23% | Gini -0.0004
  - Kenya: ψ → GDP 0.63% | TFP 0.39% | Gini 0.00300; λ → GDP 0.47% | TFP 0.35% | Gini 0.00041; χ → GDP 1.17%* | TFP 0.36%* | Gini 0.0065* (note: * cases report changes when χ is reduced to zero)
  - Philippines: ψ → GDP 0.29% | TFP 0.17% | Gini 0.00060; λ → GDP 0.26% | TFP 0.18% | Gini 0.00030; χ → GDP 0.41% | TFP 0.33% | Gini 0.0002
- Frontier experiments (move parameter to world-best: ψ=0, λ=3, or χ=0) — selected entries preserved:
  - Uganda: ψ frontier → GDP 5.79% | TFP 5.76% | Gini -0.0210; λ frontier → GDP 18.05% | TFP 11.01% | Gini -0.00290; χ frontier → GDP 0.69% | TFP 0.33% | Gini 0.0014
  - Philippines: ψ frontier → GDP 2.69% | TFP 3.52% | Gini -0.0170; λ frontier → GDP 21.17% | TFP 16.38% | Gini -0.0337; χ frontier → GDP 0.92% | TFP 0.38% | Gini 0.0023
- Occupational-choice maps and contract effects:
  - Savings regime map identifies unconstrained workers, constrained workers, constrained entrepreneurs, unconstrained entrepreneurs.
  - Credit access (ψ = 0, χ = 0 illustration) expands unconstrained-entrepreneur region, shrinks constrained-worker region, and partitions constrained entrepreneurs into low-leverage (no monitoring; lending rate = r_d) and high-leverage (monitoring; higher lending rate) regions.
- Leverage and monitoring numerical illustration parameters:
  - r_d = 0.05, η = 0.35, δ = 0.06, p = 0.15, χ = 0.3.
  - Threshold leverage ratio = 1.69: below monitoring probability is zero; above threshold monitoring probability equals p; cost of capital when monitored equals r_d + p χ.

### Welfare heterogeneity and general-equilibrium effects
- General-equilibrium factor-price adjustments (wages and interest rates) create winners and losers across wealth and talent types — partial equilibrium (fixed w, r_d) would make all agents better off with more inclusion.
- Reducing ψ:
  - Biggest winners: poor but very talented agents who gain credit access.
  - Some wealthier agents can lose due to higher wages and interest rates.
  - Threshold wealth level for losers is non-monotonic in talent.
- Relaxing λ:
  - Biggest winners: talented and wealthy agents because credit expands proportionally with wealth.
  - Losers: untalented entrepreneurs with low credit demand who face higher factor prices.
- Decreasing χ:
  - Biggest winners: most talented agents with moderate wealth who use more capital.
  - Wealthiest agents may not gain much because they self-finance.
  - Some talented-poor agents can lose due to higher wages outweighing small capital-cost gains.

### Policy implications and recommendations
- Diagnose country-specific binding constraints before prioritizing reforms — the most effective policy differs across countries.
  - If collateral requirements bind (e.g., Uganda calibration), prioritize relaxing borrowing/collateral constraints (increase λ, improve collateral frameworks).
  - If fixed participation costs bind (e.g., Malaysia calibration), prioritize lowering participation costs ψ (reduce documentation burdens, fees, and fixed transaction costs; expand branch presence and low-fee accounts).
- Consider distributional consequences:
  - Reducing ψ tends to benefit poorer and talented agents and can reduce inequality.
  - Relaxing λ can disproportionately benefit wealthy and talented agents and can increase inequality initially.
- Account for interactions and sequencing:
  - Reducing χ amplifies the effectiveness of relaxing λ; if χ is high, relaxing λ may be ineffective because entrepreneurs avoid leverage to avoid monitoring costs.
  - Reducing ψ and relaxing λ can be partially substitutable; evaluate combined packages to exploit complementarities and avoid wasted reforms.
- Policy tools and institutional recommendations:
  - Improve collateral frameworks, creditor rights enforcement, registries for movable collateral.
  - Alleviate information asymmetries via credit bureaus, timely borrower data, leveraging trade-credit relationships.
  - Strengthen insolvency regimes.
  - Increase banking penetration with simplified accounts, reduced fees, and non-financial services to improve record keeping.
  - Recognize challenges and risks of direct credit-market interventions (directed lending, risk-sharing) especially in weak-institution environments.
- Use microdata (firm-level surveys) to jointly calibrate structural models to match moments (percent of firms with credit, firm employment distribution, NPL ratio, interest spread) to inform tailored policy advice.

### Model contributions and literature positioning
- Extends occupational-choice frameworks (Banerjee and Newman; Lloyd-Ellis and Bernhardt; Cagetti and Nardi) by incorporating multiple dimensions of financial inclusion — fixed participation costs, limited commitment (collateral constraints), and asymmetric information (monitoring/intermediation costs) — in a unified general-equilibrium model.
- Provides a quantitative, calibrated framework to evaluate aggregate and distributional impacts of targeted financial inclusion policies and their interactions, complementing empirical cross-sectional results on financial deepening and growth by identifying channels and general-equilibrium feedbacks.

*Italic: Source — _wp1522 - 3.1 Individuals......................................................................................*

### 3.1 Individuals ......................................................................................

### _wp1522 - 3.1 Individuals ......................................................................................

### Model structure and key mechanisms
- Agents are heterogeneous by wealth and talent (talent denoted z).  
- Each agent lives for two periods: first period decisions include credit participation, occupational choice, and investment; second period realizations determine wage or business profit, consumption, and bequest.  
- Occupational choice: individuals choose between entrepreneurship (use technology with capital and labor) or supplying labor for a wage. Only sufficiently talented and wealthy individuals become entrepreneurs; untalented or wealth-constrained (including talented-but-poor) individuals choose wage employment.  
- Two financial regimes:
  - Savings regime: agents can save (deposit to transfer wealth over time); participation is free but borrowing is not available.
  - Credit regime: agents can borrow after paying a participation cost. Borrowing availability is further constrained by two frictions: endogenous collateral constraints (limited commitment) and asymmetric information (monitoring/intermediation costs).
- Three financial frictions modeled:
  - Fixed credit participation cost: captures fixed transactions costs, high annual fees, documentation requirements, and other access barriers to borrowing.
  - Limited commitment / collateral constraints: imperfect enforceability of contracts requires entrepreneurs to post collateral; collateral size/value determines borrowing capacity.
  - Asymmetric information / monitoring costs: interest rates must cover monitoring costs for highly-leveraged firms; more productive and poorer agents are more likely to be highly leveraged and therefore face higher intermediation costs; only highly-leveraged firms are monitored, creating differential costs of capital and potential non-participation despite credit availability.

### Calibration, data, and empirical anchors
- Main micro data source: World Bank Enterprise Surveys, supplemented with World Development Indicators. Enterprise Surveys cover firm-level access to finance, corruption, infrastructure, crime, competition, and performance.  
- Calibration targets include:
  - percent of firms with credit,
  - firm employment distribution,
  - economy-wide non-performing loan ratio,
  - interest rate spread.
- Six developing-country calibrations (country and survey year):
  - Low-income countries: Uganda in 2005, Kenya in 2006, Mozambique in 2006.
  - Emerging markets: Malaysia in 2006, Philippines in 2007, Egypt in 2007.
- Specific empirical numbers preserved from the source:
  - 51 percent of firms in advanced economies use a bank loan or line of credit as compared with 34 percent in developing economies (World Bank, 2014).
  - In developing economies, 35 percent of small firms report that access to finance is a major obstacle to their operations, compared with 25 percent of large firms in developing economies and 8 percent of large firms in advanced economies (World Bank, 2014).
  - The collateral requirement in the Philippines is 238.4% of the loan amount (compared with lower requirements in Uganda, Kenya, and Mozambique).

### Main quantitative and qualitative findings
- Two principal channels through which greater financial inclusion affects GDP and inequality:
  - Reallocation channel: better inclusion channels funds to more talented entrepreneurs, increasing aggregate output and aggregate TFP because talented entrepreneurs scale up disproportionately.
  - Friction-reduction channel: more efficient financial contracts reduce waste from participation and monitoring costs, raising GDP.
- Distributional effects and trade-offs:
  - Increased allocation to talented entrepreneurs can raise income inequality because talented entrepreneurs already earn higher incomes.
  - Reducing credit participation costs can crowd-in relatively untalented agents, reducing income inequality.
  - Relaxing borrowing/collateral constraints can have an ambiguous effect on inequality: inequality may initially increase and then decline — a Kuznets-type response is possible.
  - In general equilibrium, changes in interest rates and wages can produce winners and losers across wealth and talent types (partial equilibrium analyses can mask these effects).
- Country-specific responsiveness (model simulation highlights):
  - Uganda’s GDP is most responsive to a relaxation of borrowing/collateral constraints because high collateral requirements strongly bind firms in Uganda; reducing intermediation costs benefits only a small number of highly-leveraged firms in such a context.
  - Malaysia is most affected by high fixed participation costs; reducing participation costs is particularly important for increasing access there.
- Aggregate productivity:
  - Different dimensions of financial inclusion unambiguously increase the economy’s total factor productivity (TFP) because talented entrepreneurs expand output more when constraints are eased.
- Policy interactions:
  - Policies that target different financial frictions can interact nonlinearly: joint implementation can yield larger GDP gains for some parameter ranges.
  - To the extent policies are substitutes, implementing one reform can reduce the marginal effectiveness of another in boosting GDP.

### Policy implications and recommendations (derived from model simulations)
- Diagnose country-specific binding constraints before prioritizing reforms: the most effective policy differs across countries depending on which friction most tightly constrains financial inclusion.
  - If collateral requirements are the binding constraint (e.g., Uganda calibration), prioritize reforms that relax borrowing/collateral constraints.
  - If fixed participation costs are the binding constraint (e.g., Malaysia calibration), prioritize lowering participation costs (reducing documentation burdens, fees, and fixed transaction costs).
- Consider distributional consequences when designing financial inclusion policies:
  - Policies that reduce participation costs tend to benefit poorer and talented agents and can reduce inequality.
  - Policies that deepen credit (relax borrowing constraints) may benefit wealthy and talented agents disproportionately and can increase inequality, at least initially.
- Account for interactions across reforms: evaluate combined policy packages because complementarities or substitutability across participation cost reductions, collateral relaxations, and intermediation-cost reductions will determine overall effectiveness in raising GDP and affecting inequality.
- Use microdata (firm-level surveys) to jointly calibrate structural models to match moments such as percent of firms with credit, firm employment distribution, non-performing loan ratio, and interest rate spread to inform tailored policy advice.

### Model contributions and positioning in the literature
- Extends occupational-choice frameworks (Banerjee and Newman, Lloyd-Ellis and Bernhardt, Cagetti and Nardi) by incorporating multiple dimensions of financial inclusion within a unified general equilibrium model: fixed participation costs, limited commitment (collateral constraints), and asymmetric information (monitoring/intermediation costs).  
- Provides a quantitative, calibrated framework to evaluate the aggregate and distributional impacts of targeted financial inclusion policies and their interactions, complementing empirical cross-sectional results on financial deepening and growth by identifying channels and general-equilibrium feedbacks.

*Italic: Source — _wp1522 - 3.1 Individuals......................................................................................*

### 3.1    Individuals

### 3.1    Individuals

### Utility, bequest motive, and period structure
- Utility is generated only in the second period through consumption (c) and a bequest to offspring (b′).
- Utility function: u(c,b′) = c^{1−ω} b′^{ω} (Cobb-Douglas).
- The Cobb-Douglas form implies the optimal bequest rate is ω.
- As a result u(c,b′) is a linear function of end-of-period wealth (W) and the agent is risk neutral; maximizing expected utility is equivalent to maximizing expected second-period wealth.
- First-period decisions (financial participation, occupation, investment) therefore maximize expected income that determines W.
- Bequest motive transfers wealth across periods and endogenously determines the economy’s wealth distribution; a higher ω implies ceteris paribus a higher level of wealth transferred to the next period.

### First-period choices and occupational structure
- Occupational choice: each agent chooses to be a worker or an entrepreneur.
  - Worker: supplies one unit of labor; first-period income equals the equilibrium wage, w.
  - Entrepreneur: invests capital and labor and obtains income through business profit.
- Workers do not invest and therefore do not demand external credit; entrepreneurs may borrow to expand firm scale and profits.

### Talent, inheritance, and distributional assumptions
- Talent z is drawn from a Pareto distribution μ(z) with tail parameter θ.
- Offspring inherits the talent of her parents (or former self) with probability γ; otherwise a new talent is drawn from μ(z).

### Production technology and profit realization
- Entrepreneur production function: f(k,l) = z (k^{α} l^{1−α})^{1−ν}
  - 1−ν is the Lucas span-of-control parameter (share of output accruing to variable factors).
  - A fraction α of variable-factor output goes to capital; 1−α goes to labor.
  - Production exhibits diminishing returns to scale, with ν > 0.
- Capital depreciates by δ after use.
- Production fails with probability p; if production fails output is zero and the agent recovers only a fraction η < 1 of installed capital, net of depreciation, in the second period.
- To simplify calculation, workers are assumed to be paid only when production is successful; thus each worker earns a wage with probability 1−p.

### Financial participation, credit regimes, and fixed entry cost
- All agents can make deposits in a financial institution to transfer income and initial wealth within period for consumption and bequest.
- Agents must pay a fixed credit participation cost ψ to obtain a borrowing contract from financial institutions.
  - If an agent pays ψ they live in a "credit" regime and can borrow.
  - If an agent does not pay ψ they live in a "savings" regime and can only save.
- The cost ψ can be interpreted as a contractual fee or a bargaining cost with financial institutions.
- In equilibrium the fixed entry cost ψ is more likely to exclude poor entrepreneurs from financial markets because it represents a larger fraction of their initial wealth.

*Source: _wp1522 - 3.1    Individuals*

### section illustrates the structure of the borrowing contract in detail.

### _wp1522 - section illustrates the structure of the borrowing contract in detail.

### Overview of decision problem and solution strategy
- Agents of type (b,z) choose occupation and credit participation to maximize expected income, solved in two steps:
  - Step 1: choose occupation conditional on current regime (savings or credit).
  - Step 2: choose regime by comparing expected incomes across regimes.
- Both wage w and deposit interest rate r_d are potentially time-varying and determined endogenously by labor and capital market clearing conditions.
- Agents are risk-neutral; occupational choice equates to comparing end-of-period wealth outcomes.

### Savings regime: structure and entrepreneur problem
- End-of-period wealth in savings regime, W^S, is:
  - (1 + r_d) b + (1 − p) w for workers
  - π^S(b,z) for entrepreneurs
  - Hence W^S = max{(1 + r_d) b + (1 − p) w, π^S(b,z)}. (Equation 3.3)
- Entrepreneur expected end-of-period wealth π^S(b,z) solves:
  - π^S(b,z) = max_{k,l} {(1 − p)[z(k^α l^{1−α})^{1−ν} − w l − δ k + k] + p η (1 − δ) k + (1 + r_d)(b − k)} (Equation 3.4)
  - Subject to k ≤ b (Equation 3.5).
- Interpretation of terms:
  - With probability 1 − p production succeeds: entrepreneur receives revenues minus wage and depreciation plus working capital k.
  - With probability p production fails: entrepreneur recovers fraction η of depreciated working capital.
  - Constraint k ≤ b reflects financing capital exclusively from own wealth in savings regime.
- Note: diminishing returns imply an unconstrained optimal capital scale k̃_S(z); entrepreneurs never optimally choose larger scale.

### Credit regime: contract primitives and constraints
- Financial contract characterized by (Φ, ∆, Ω):
  - Φ = amount borrowed.
  - ∆ = collateral value (assumed interest-bearing at r_d).
  - Ω = face value to be repaid if no default.
- Implied lending interest rate r_l defined as:
  - r_l = Ω / Φ − 1 (Equation 3.6).
- Leverage ratio defined as:
  - λ̃ = Φ / ∆ (Equation 3.7).
- Default outcome:
  - If production fails entrepreneur may not repay Ω; bank seizes (1 + r_d) ∆ and η (1 − δ) k.
- Two financial frictions considered:
  - Limited commitment: bank lends at most λ ∆ if ∆ posted; λ ≥ 1 parameterizes degree of limited commitment. λ = 1 implies no borrowing.
  - Asymmetric information: entrepreneurs privately observe production outcome; banks can monitor at cost proportional to scale, χ k, to verify outcome and legally enforce full repayment.
- Monitoring and incentive logic:
  - Banks monitor reported failures only when contract is highly leveraged and entrepreneur cannot cover Ω from recovered assets.
  - Monitoring occurs with probability p when η(1 − δ) Φ + (1 + r_d) ∆ < Ω, zero otherwise.
  - Monitoring cost is borne by entrepreneurs through contract design because banks make zero profits in equilibrium.

### Optimal contract design and zero-profit condition
- Entrepreneurs optimally post collateral ∆ = b − ψ (ψ = upfront credit participation cost) and borrow amount equal to capital used Φ = k(b,z).
- Optimal contract reduces to (k(b,z), b − ψ, Ω(k(b,z), b)) with Ω pinned down by the bank zero-profit condition:
  - (1 − p) Ω + p min(Ω, η(1 − δ) k + (1 + r_d)(b − ψ)) = (1 + r_d) k + p χ k · 1{η(1 − δ) k + (1 + r_d)(b − ψ) < Ω} (Equation 3.8).
- Entrepreneur problem under credit regime:
  - π^C(b,z) = max_{k,l} {(1 − p)[z(k^α l^{1−α})^{1−ν} − w l + (1 − δ) k − Ω + (1 + r_d)(b − ψ)]
    + p max(0, η(1 − δ) k + (1 + r_d)(b − ψ) − Ω)} (Equation 3.9)
  - Subject to k ≤ λ (b − ψ).
- Monitoring occurs only when η(1 − δ) k + (1 + r_d)(b − ψ) < Ω; otherwise entrepreneur retains positive end-of-period wealth when production succeeds and monitoring is not triggered.
- Dividing zero-profit equation by k yields:
  - (1 − p) (Ω / k) + p min(Ω / k, η(1 − δ) + (1 + r_d) (b − ψ) / k) = (1 + r_d) + p χ · 1{η(1 − δ) + (1 + r_d) (b − ψ) / k < Ω / k} (Equation 3.11).
- Key implication: implied gross lending rate Ω / k depends on inverse leverage ratio (b − ψ) / k but not directly on talent z; hence incentive compatibility across talent types follows because leverage is observable.

### Leverage, monitoring, and interest-rate profiles (numerical illustration)
- Figure 1 description: lending interest rate, monitoring frequency, and cost of capital as functions of leverage ratio.
- Numerical parameter values used to plot Figure 1:
  - r_d = 0.05, η = 0.35, δ = 0.06, p = 0.15, χ = 0.3.
- Quantitative features highlighted:
  - Threshold leverage ratio = 1.69: below this monitoring probability is zero; lending interest rate and cost of capital equal deposit rate r_d.
  - For leverage above threshold monitoring probability equals p.
  - Cost of capital when monitored equals r_d + p χ (constant in leverage when monitored under model assumptions).
  - Implied lending interest rate increases strictly with leverage once leverage exceeds threshold.

### Occupational choice maps and effects of credit access
- Occupation map in savings regime (left panel of Figure 2) identifies four agent categories:
  - Unconstrained workers
  - Constrained workers
  - Constrained entrepreneurs
  - Unconstrained entrepreneurs
- Talent threshold in savings regime: talent below 1.3 → always prefer wage work (unconstrained workers).
- In savings regime:
  - Left region: talented but insufficient wealth → constrained workers.
  - Middle region: sufficient wealth for profitable firm but scale constrained → constrained entrepreneurs.
  - Right region: operate at unconstrained scale with marginal return of capital = r_d → unconstrained entrepreneurs.
- Credit regime occupation map (right panel of Figure 2) assumptions for illustration:
  - ψ = 0, χ = 0, and same w and r_d to highlight partial equilibrium effects.
  - Parameters used for Figure 2 plotting:
    - r_d = 0.05, w = 0.6, η = 0.35, δ = 0.06, ν = 0.21, p = 0.15, α = 0.33, λ = 2.5, ψ = 0, χ = 0.
- Effects of credit access:
  - Area of constrained workers shrinks; area of unconstrained entrepreneurs expands.
  - The constrained-entrepreneur region is partitioned into low-leverage and high-leverage subregions:
    - Low-leverage: face value repayable even if production fails → no monitoring → lending rate = r_d.
    - High-leverage: default occurs on failure → banks monitor and seize recovered assets and collateral.
  - High-leverage region lies to the left of low-leverage region: entrepreneurs with low wealth prefer higher leverage to exploit high marginal returns.

### Aggregate implications and policy leverages
- Micro-level occupational and contract adjustments induced by credit access alter aggregate outcomes (GDP and income inequality).
- Policy interventions considered later (section 5) move the boundaries in the occupation map and alter relative incomes across agent types, thereby impacting aggregate GDP and inequality.

*Source: _wp1522 - section illustrates the structure of the borrowing contract in detail.*

### 3.2    Competitive Equilibrium

### 3.2    Competitive Equilibrium

### Definition of competitive equilibrium
- Given an initial joint probability density distribution of wealth and talent H0(b,z), a competitive equilibrium consists of:
  - Allocations {ct(b,z), kt(b,z), lt(b,z)}∞t=0.
  - Sequences of joint distributions of wealth and talent {Ht(b,z)}∞t=1.
  - Prices {rd(t), w(t)}t.
- Conditions:
  - (1) Agent of type (b,z) optimally chooses the underlying regime, occupation, ct(b,z), kt(b,z), lt(b,z) to maximize utility at t ≥ 0.
  - (2) Capital market clears at all t ≥ 0:
    - ∫∫(b,z)∈E(t) kt(b,z) Ht(b,z) db dz = ∫∫(b,z) b Ht(b,z) db dz − ψ ∫∫(b,z)∈Fin(t) Ht(b,z) db dz
    - where E(t) is the set of types who choose to be entrepreneurs at time t; Fin(t) is the set of types who are in the credit regime.
  - (3) Labor market clears at all t ≥ 0:
    - ∫∫(b,z)∈E(t) lt(b,z) Ht(b,z) db dz = ∫∫(b,z)/∈E(t) Ht(b,z) db dz
  - (4) {Ht(b,z)}∞t=1 evolves according to the equilibrium mapping:
    - Ht+1( ̄b, ̄z) db = γ μ( ̄z) ∫z1 {b′ = ̄b} Ht(b,z) db dz + (1 − γ) ∫b1 {b′ = ̄b} Ht(b, ̄z) db
    - where b′ is the bequest for agent of type (b,z), and 1{b′ = ̄b} is an indicator equal to 1 if b′ = ̄b, and 0 otherwise.
- Steady state:
  - The steady-state joint distribution H(b,z) is defined as H(b,z) = limt→∞ Ht(b,z).

### Calibration: data and parameter strategy
- Countries calibrated: 6 total — low-income: Uganda (2005), Kenya (2006), Mozambique (2006); emerging markets: Malaysia (2007), Philippines (2008), Egypt (2007).
- Data sources: World Bank Enterprise Surveys (firm-level cross-section) and World Development Indicators (gross savings, non-performing loans, interest rate spread).
- Cross-section firm counts: Uganda 563, Kenya 781, Mozambique 599, Malaysia 1115, Philippines 1326, Egypt 996.
- Fixed parameter choices from literature:
  - Depreciation rate δ = 0.06.
  - Share of output to variable factors v = 0.21; share of capital α = 0.33.
  - Probability offspring inherits talent γ = 0.894.
- Calibration targets and methods:
  - Each generation = one year.
  - Gross savings rate matched to calibrate bequest rate ω.
  - Average collateral as % of loan used to calibrate λ (tightness of borrowing constraint).
  - Jointly calibrate ψ (financial participation cost), χ (intermediation cost), p (probability of project failure), θ (parameter for talent distribution) to match:
    - Percent of firms with a line of credit.
    - Non-performing loans (NPLs) as % of total loans.
    - Interest rate spreads.
    - Employment share distribution (top 5% / 10% / 20% / 40%).
  - Parameter η set close to but below (λ − 1)(1 + rd) / (λ(1 − δ)) to aid identification; country values:
    - η = 0.37 for Uganda, Kenya, Malaysia.
    - η = 0.54 for Mozambique.
    - η = 0.29 for Philippines.
    - η = 0.44 for Egypt.
- Notable calibration departures:
  - Myopic savings assumption (constant bequest rate) leads to calibrating λ from average collateral instead of credit-to-GDP.
  - Model generates lower credit-to-GDP ratios by about 10%−40% compared with data.
  - Calibrated ω directly from gross savings rate (following Gine and Townsend (2004)).
  - Model fails to match deposit interest rate due to myopic-agent specification; trend of Gini under policy evaluation remains informative.

### Key empirical moments and calibrated parameter outcomes (selected)
- Table 1 (selected country statistics from data):
  - Savings (% of GDP): Uganda 8, Kenya 15.4, Mozambique 7.1, Malaysia 39, Philippines 25.7, Egypt 24.5
  - Collateral (% of loan): Uganda 173, Kenya 120.8, Mozambique 120.8, Malaysia 64.6, Philippines 238.4, Egypt 85.5
  - Firms with credit (%): Uganda 17.2, Kenya 25.4, Mozambique 14.2, Malaysia 60.4, Philippines 33.2, Egypt 17.4
  - Non-performing loan (%): Uganda 2.3, Kenya 10.6, Mozambique 3.1, Malaysia 8.5, Philippines 4.5, Egypt 19.3
  - Interest rate spread: Uganda 10.9, Kenya 8.5, Mozambique 8.2, Malaysia 3.3, Philippines 4.3, Egypt 6.1
  - Employment share (top 5%): Uganda 53.8, Kenya 54.1, Mozambique 41.3, Malaysia 29.5, Philippines 52.7, Egypt 58.4
- Table 2 (examples of calibration targets and fitted parameters):
  - Uganda: Savings (% of GDP) target 8 → ω = 0.0815 (model 5.4); Collateral target 173 → λ = 1.58; Firms with credit 17.2% → ψ = 0.03; NPL 2.3% → p = 0.15; Interest spread 10.9 → χ = 0.85; Top 5% emp. share 53.8 → θ = 4.80.
  - Malaysia: Savings target 39 → ω = 0.39 (model 25.7); Collateral 64.6 → λ = 2.56; Firms with credit 60.4% → ψ = 0.13; NPL 8.5% → p = 0.12; Interest spread 3.3 → χ = 0.11; Top 5% emp. share 29.5 → θ = 6.80.
  - (Full table contains analogous rows for Kenya, Mozambique, Philippines, Egypt with exact numeric entries.)

### Model performance and interpretation
- Model replicates percent of firms with credit for all six countries nearly exactly.
- NPL ratio and interest rate spread matched reasonably, with heterogeneity:
  - Examples: Malaysia and Egypt have low NPL ratios but relatively low interest rate spreads; Uganda and Mozambique have high NPL ratios and high spreads.
- Employment share distribution captured qualitatively; model tends to generate more larger firms (higher top 5% employment share, lower 40% share) than data.
- Cross-country comparative insight:
  - Low-income countries generally face more constrained financial inclusion: higher collateral requirements, lower share of firms with credit, higher borrowing costs.
  - Within-group heterogeneity exists (e.g., Mozambique lower firms-with-credit despite lower collateral and spreads).
  - Calibrated ψ can be lower in low-income countries despite lower financial inclusion because higher λ and lower χ in emerging markets increase participation cost in relative terms; higher ω (savings) in emerging markets makes ψ a smaller proportion of wealth.

### Policy dimensions and interpretation in the model
- Financial inclusion in model captured by three parameters:
  - ψ — credit participation cost (direct measure of difficulty obtaining credit). A decrease in ψ indicates greater inclusion.
  - λ — borrowing constraint (maximum leverage ratio). An increase in λ indicates lower collateral requirements (greater inclusion).
  - χ — cost of state verification / intermediation efficiency. A decrease in χ indicates increased efficiency of financial intermediation (greater inclusion).
- Empirical policy analogues:
  - Reducing ψ: policies promoting branch openings in rural/unbanked areas, reducing distance to bank (evidence: Assuncao et al. (2012) and Alem and Townsend (2013)).
  - Increasing λ: widening acceptable securities as collateral during crises to boost lending.
  - Decreasing χ: financial liberalization and competition leading to investment in computerization and lower average cost of funds (example: Thai banking sector 1985–1994 reduced cost of raising funds from 14.40% to 5.61% for large banks).

### Steady-state comparative-static results: reducing participation cost (ψ)
- Experiment: vary ψ from 0.15 to 0 (move left to right).
- Aggregate effects:
  - GDP increases due to higher investment: more firms access credit and less wasted funds on contracting.
  - Model-implied TFP increases as capital allocation among entrepreneurs improves.
- Interest rate spread:
  - Stable when ψ is high; eventually decreases in some countries (Uganda, Mozambique, Philippines) and increases slightly in others (Kenya, Malaysia).
  - Two countervailing effects when ψ decreases:
    - Wealth effect: entrepreneurs become richer, deleverage → lower average spread.
    - Entry effect: previously constrained workers become entrepreneurs, choose high leverage → higher average spread.
  - First effect dominates when borrowing constraint is tighter (smaller λ).
- Inequality (Gini coefficient):
  - Low-income countries: Gini first increases then decreases as ψ falls — consistent with Kuznets’ hypothesis.
    - Reason: Initial decreases in ψ mainly benefit incumbent entrepreneurs (raising inequality); further reductions disproportionately help constrained poorer agents, reducing inequality.
  - Emerging markets: no Kuznets pattern; decrease in ψ unambiguously lowers Gini (e.g., Malaysia).
    - At ψ = 0.15, financial systems in emerging markets are already relatively developed; reductions in ψ benefit poorer entrepreneurs proportionally more.
  - Examples from figures:
    - At ψ = 0.15, percent of firms with credit ≈ 50% in Malaysia and close to 0 in Uganda.

### Steady-state comparative-static results: relaxing collateral constraints (λ)
- Experiment: vary λ from 1 to 3.
- Aggregate effects:
  - Aggregate GDP increases in all countries following relaxation of borrowing constraint.
  - Responsiveness depends on saving rates:
    - Low-income countries: GDP more responsive due to reliance on external financing (low savings).
    - Philippines: strong GDP response because moderate financial access combined with low spreads and high savings.
  - TFP increases as resource allocation improves; talented entrepreneurs expand scale more when λ increases.
- Interest rate spread:
  - Spread increases with λ after a threshold:
    - At low λ, spread = 0 because low leverage avoids defaults.
    - As λ increases, leverage and NPL share increase, raising spreads.
  - Low-income countries generally have higher spreads due to higher intermediation costs.
- Inequality (Gini coefficient):
  - Kuznets pattern observed in low-income countries:
    - As λ increases, talented entrepreneurs initially gain disproportionately, raising Gini.
    - For large λ, higher interest rates shrink entrepreneurs’ profits, reducing Gini.
- Financial participation and NPLs:
  - Relaxing λ induces more entrepreneurs to join financial regime (once they pay ψ), increasing percent of firms with credit.
  - NPLs increase because new small entrants tend to be more leveraged.

*Source: IMF working paper section 3.2 Competitive Equilibrium and subsequent calibration and policy evaluation material from the same chapter.*

### 5.3    Increasing intermediation efficiency

### _wp1522 - 5.3    Increasing intermediation efficiency

### Comparative statics and channels
- The exercise varies the financial monitoring cost χ from 1.2 to 0 to reflect deepening from an intermediation efficiency angle.
- When χ decreases:
  - GDP responses vary across countries: in some countries (Uganda, Mozambique and Philippines), GDP is not responsive as lower intermediation costs only benefit highly leveraged firms which are few (due to the low financial access ratio and tight borrowing constraints).
  - TFP increases (but only slightly) as the lower intermediation cost facilitates the allocation of capital to efficient entrepreneurs.
  - The interest rate spread:
    - "monotonically declines in Kenya and Malaysia, but displays an inverted V-curve in other countries."
    - Two opposing forces drive the spread outcome:
      - Decline in net borrowing rate induces entrepreneurs to leverage more, pushing up the share of non-performing loans and tending to increase the endogenous interest rate spread.
      - Lower χ directly decreases the interest spread because the spread is a direct function of the intermediation cost.
    - Whether the spread increases or decreases depends on which effect dominates.
  - The Gini coefficient increases because efficient intermediation disproportionately benefits highly leveraged firms (who already have higher income than workers). General equilibrium effects on wages and interest rates prevent smaller firms from entering the financial system; lower intermediation costs induce more agents to borrow, increasing the percent of firms with credit. The Gini coefficient only declines marginally at very low parameter values.
- Note: The actual intermediation cost is pχ as stated in Equation 3.8.

### Interactions among three financial parameters (λ, ψ, χ)
- Experiment: For the Philippines, relax the borrowing constraint λ by 20% and measure the relative increase in GDP for different levels of credit participation cost ψ and intermediation cost χ.
- Key interaction findings:
  - When χ increases, the GDP gain from relaxing λ becomes smaller for all ψ because high intermediation costs partially block the channel through which relaxing λ boosts entrepreneur borrowing.
  - If χ is too high, relaxing borrowing constraints can be futile as entrepreneurs prefer low leverage to avoid monitoring costs.
  - The change in GDP as ψ increases is non-monotonic:
    - Almost constant for low ψ (ψ <0.03).
    - Increasing in ψ when ψ is between 0.03 and 0.04.
    - Decreasing for ψ >0.04.
  - Mechanisms: relaxing λ affects GDP via an intensive margin (agents in credit regime borrow more) and an extensive margin (more agents join the credit regime). The relative gains on these margins depend on the fraction of agents already in the credit regime.
  - When ψ decreases, financial inclusion increases gains on the intensive margin but may reduce extensive-margin gains if the financial access ratio is already high (financial access ratio ~100% when ψ <0.03 in the Philippines calibration).
- Policy interaction implication: reducing intermediation costs not only directly boosts GDP but also amplifies the effect of relaxing borrowing constraints. Simultaneously reducing participation costs and relaxing borrowing constraints may be partially substitutable because both increase financial access. The optimal policy mix depends on underlying financial sector parameters and country characteristics.

### Numerical comparisons and country responses (marginal responses)
- Table 3: Change when country’s credit to investment ratio is increased by 1 percentage point (differences between current state and eventual steady state). Numbers shown as (GDP(%), TFP(%), Gini).
  - Uganda:
    - Participation cost ψ: GDP 0.39% | TFP 0.34% | Gini -0.00060
    - Borrowing constraint λ: GDP 0.35% | TFP 0.25% | Gini 0.00080
    - Intermediation cost χ: GDP 0.12% | TFP 0.23% | Gini -0.0004
  - Kenya:
    - Participation cost ψ: GDP 0.63% | TFP 0.39% | Gini 0.00300
    - Borrowing constraint λ: GDP 0.47% | TFP 0.35% | Gini 0.00041
    - Intermediation cost χ: GDP 1.17%* | TFP 0.36%* | Gini 0.0065*
      - Note: Cases marked with * report changes when χ is reduced to zero because even if χ is reduced to zero, the increase in credit to investment ratio is still less than 1%.
  - Mozambique:
    - Participation cost ψ: GDP 0.39% | TFP 0.28% | Gini 0.00020
    - Borrowing constraint λ: GDP 0.47% | TFP 0.21% | Gini 0.00170
    - Intermediation cost χ: GDP 0.60% | TFP 0.24% | Gini 0.0021
  - Malaysia:
    - Participation cost ψ: GDP 0.43% | TFP 0.21% | Gini -0.00050
    - Borrowing constraint λ: GDP 0.51% | TFP 0.33% | Gini 0.00100
    - Intermediation cost χ: GDP 0.86%* | TFP 0.23%* | Gini 0.0007*
  - Philippines:
    - Participation cost ψ: GDP 0.29% | TFP 0.17% | Gini 0.00060
    - Borrowing constraint λ: GDP 0.26% | TFP 0.18% | Gini 0.00030
    - Intermediation cost χ: GDP 0.41% | TFP 0.33% | Gini 0.0002
  - Egypt:
    - Participation cost ψ: GDP 0.19% | TFP 1.45% | Gini -0.01100
    - Borrowing constraint λ: GDP 0.46% | TFP 0.37% | Gini 0.00040
    - Intermediation cost χ: GDP 0.42%* | TFP 0.19%* | Gini 0.0021*
- Summary insights:
  - Financial inclusion increases GDP and TFP in all cases, but its impact on inequality varies depending on the source of friction and country characteristics.
  - Uganda’s GDP responds more to reductions in participation costs; Egypt’s GDP responds more to relaxing the borrowing constraint; other countries respond more to lower intermediation costs.
  - Adopting the world-best intermediation technology (χ = 0) does not always bring a sizable GDP boost in isolation because interactions with other parameters matter.

- Table 4: Change when country moves to world financial sector frontier in one parameter (ψ=0, λ=3 as best, or χ=0). Numbers shown as (GDP(%), TFP(%), Gini).
  - Uganda:
    - ψ frontier: GDP 5.79% | TFP 5.76% | Gini -0.0210
    - λ frontier: GDP 18.05% | TFP 11.01% | Gini -0.00290
    - χ frontier: GDP 0.69% | TFP 0.33% | Gini 0.0014
  - Kenya:
    - ψ frontier: GDP 5.76% | TFP 7.99% | Gini -0.0324
    - λ frontier: GDP 13.02% | TFP 9.39% | Gini -0.0155
    - χ frontier: GDP 1.17% | TFP 0.36% | Gini 0.0065
  - Mozambique:
    - ψ frontier: GDP 12.73% | TFP 11.53% | Gini -0.0292
    - λ frontier: GDP 10.40% | TFP 4.97% | Gini 0.0206
    - χ frontier: GDP 0.62% | TFP 0.25% | Gini 0.0023
  - Malaysia:
    - ψ frontier: GDP 8.74% | TFP 10.69% | Gini -0.0713
    - λ frontier: GDP 4.51% | TFP 2.97% | Gini 0.0060
    - χ frontier: GDP 0.86% | TFP 0.23% | Gini 0.0007
  - Philippines:
    - ψ frontier: GDP 2.69% | TFP 3.52% | Gini -0.0170
    - λ frontier: GDP 21.17% | TFP 16.38% | Gini -0.0337
    - χ frontier: GDP 0.92% | TFP 0.38% | Gini 0.0023
  - Egypt:
    - ψ frontier: GDP 6.81% | TFP 11.80% | Gini -0.0630
    - λ frontier: GDP 7.90% | TFP 6.66% | Gini 0.0031
    - χ frontier: GDP 0.42% | TFP 0.19% | Gini 0.0021
- Interpretation:
  - Largest GDP gains from moving to frontier depend on country: relaxing borrowing constraints yields largest GDP increases in Uganda, Kenya, and the Philippines, indicating disproportionately higher collateral requirements; decreasing participation costs yields largest GDP increases in Mozambique, Malaysia, and Egypt, indicating limited credit availability or low financial access.
  - Reducing credit participation costs tends to uniformly increase TFP and decrease the Gini coefficient across countries; relaxing borrowing constraints increases TFP but has ambiguous effects on inequality.
  - Inefficient intermediation (high χ) dampens responsiveness of GDP to lower ψ and relaxed λ, and can block those channels.

### Welfare redistribution effects (heterogeneous agents)
- Method: quantify income change for agents with different wealth and talent when one financial parameter changes. Present partial equilibrium (interest rate and wage fixed) and general equilibrium (interest rate and wage endogenous) separately.
- Findings by policy:
  - Reducing participation cost ψ:
    - Some agents (white areas) lose income in general equilibrium because lower ψ enables more entrepreneurs to borrow, raising equilibrium wages and interest rates.
    - Wealthier agents tend to lose as they benefit less from lower ψ and suffer more from higher wages and interest rates.
    - The threshold wealth level beyond which agents lose is non-monotonic in talent: increases with talent for talent <1.5, then decreases for talent >1.5. Explanation relates to whether agents can self-finance and how talent affects labor versus capital demand.
    - Biggest winners are poor but very talented agents (upper-left corner): they gain access to external credit and expand production.
  - Relaxing borrowing constraint λ:
    - Losers are untalented entrepreneurs with low credit demand who suffer from increased wages and interest rates.
    - Biggest winners are talented and wealthy agents because credit is proportional to wealth; relaxing λ enables wealthier agents to receive more funds and increase profits.
    - If talented and wealthy agents were not financially constrained, these agents could lose due to general equilibrium effects; but calibration assumes severe credit constraints for almost all agents.
  - Decreasing intermediation cost χ:
    - Biggest winners are the most talented agents with moderate wealth because talented agents employ more capital and benefit more from lower cost of capital.
    - Wealthiest agents do not necessarily gain most because they already self-finance and have low demand for credit.
    - Some agents lose for distinct reasons:
      - Upper-left white area: talented but poor agents operating at maximum leverage benefit less from lower χ than they suffer from higher wages because their demand for capital is low.
      - Lower-right white area: agents with low leverage (not monitored) receive no benefit from lower χ but suffer from increased labor costs.
- Partial vs general equilibrium: if wages and interest rates were fixed (partial equilibrium), all agents would gain from financial inclusion; the general equilibrium reallocation of factor prices creates winners and losers.

### Policy implications and recommendations
- Country-specific characteristics are central in determining impacts, interactions, and trade-offs between macro aggregates and financial policies; therefore policy prescriptions must be tailored to the specific binding financial frictions of each country.
- Policy levers and their targeted frictions:
  - Improve collateral frameworks and creditor rights enforcement to alleviate borrowing constraints and reduce intermediation costs (examples cited: registries for movable collateral).
  - Alleviate information asymmetries via credit bureaus and registries (public or private), timely borrower data, and leveraging buyer-supplier trade credit relationships.
  - Strengthen insolvency regimes to regulate exit and recovery processes.
  - Direct interventions to increase banking penetration (low-fee accounts, simplified documentation, non-financial services to improve record keeping, improving competition) can reduce participation costs ψ.
  - Direct credit market interventions (directed lending, risk-sharing) can increase firm access, particularly for SMEs, but design and management are challenging and risks are magnified in weak-institution environments.
- Strategic complementarities and substitutes:
  - Reducing χ amplifies effectiveness of relaxing λ; hence sequencing and combinations matter.
  - Reducing ψ and relaxing λ can be partially substitutable because both increase financial access; optimal mixes depend on country parameters.

*Source: _wp1522 - 5.3    Increasing intermediation efficiency.*

### References

### _wp1522 - References

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*References list as provided in the source PDF.*

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