## _wp09233

## Source details

**Canonical URL:** [_wp09233](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09233.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09233.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09233.pdf.json)

---

### I. Introduction
- Financial crisis beginning in 2007 highlighted excesses in lending, leverage, and risk-taking, and large scale government interventions (“bailouts”).
- Central questions addressed:
  - Is there a connection between actions amounting to bailouts of lenders and the excesses in lending/borrowing and risk-taking that led to the crisis?
  - Can bailing out lenders validate moral hazard and help recreate similar behaviors in the future?
  - Does the need to salvage the financial system necessarily imply that lenders must be bailed out and that reinforcement of moral hazard is unavoidable?
- Empirical characterizations emphasized:
  - Excessive buildup of debt preceded the crisis.
  - Parallel increase in leverage (debt grew faster than equity).
  - Lenders charged particularly low interest rates; spreads were compressed.
  - Excessive risk-taking accompanied the buildup of debt.
- Approach and scope:
  - Presents a simple analytical framework with rational agents and adequate information (probability distributions) to analyze effects of lenders’ perceptions that they may be bailed out by a third party.
  - Applies to bank and non-bank (“shadow” banking) lending relationships.
  - Does not claim uniqueness as an explanation nor attempt to explain precipitation, propagation, or severity of the crisis.

### II. The analytical framework — setup and mechanisms
- Core assumptions:
  - Project output price X is non-negative random variable: X = q(L) Y, with q′(L) > 0 and q′′(L) < 0; Y ∈ [0, m] with distribution F(Y); price per unit set equal to 1.
  - Single source of finance (credit) initially; debtor repays RL if project return > X̂ = q(L)Ŷ = RL; if Y < Ŷ borrower remits all returns.
  - Third party intervenes with probability π when Y < Ŷ and pays RL − q(L)Y.
  - Lender and debtor-investor are risk neutral; lender subject to zero profit condition due to competition. Cost of loanable funds to lender is I.
- Borrower optimization and first-order conditions:
  - Borrower’s problem expressed by integrals over Y with threshold Ŷ; first-order and second-order conditions derived (equations (1)–(4) in source).
  - For second-order condition to be negative require e < 1 and hazard rate properties (H′(Ŷ) < 0; [1 − F(Y)]/f(Y) increasing in Y).
- Lender’s zero-profit condition with bailout probability π:
  - 0 = ∫_{Ŷ}^{m} P q(L) Y f(Y) dY − R L F(Ŷ) + π [R L − ∫_{0}^{Ŷ} q(L) Y f(Y) dY] − I L  (equation (7) as presented).
  - π is perceived probability of third-party intervention paying RL − q(L)Y when Y < Ŷ.

### III. Main analytical results and comparative statics (key propositions)
- Credit demand and isoprofit properties:
  - Slope of implied credit demand curve: dR/dL = (∂^2 B / ∂L^2) / (∂^2 B / ∂L ∂R)  (equation (5)).
  - Proposition 1: Under stated technical conditions, L decreases as R increases.
  - Proposition 2: Isoprofit curves R(L,B) have a unique turning point L*(B) and specific curvature and comparative-statics signs (properties i–iii in source).
- Lender zero-profit line and effect of bailout probability:
  - Proposition 3: If e(L) < 1, zero profit line per borrower has non-negative slope for all L ≥ 0; dR/dL > 0 under stated conditions (equations (8)–(10)).
  - Proposition 4: An increase in perceived probability π of bailout reduces the slope of the zero-profit line; 0 > ∂(dR/dL)/∂π.
  - Corollary: If π = 1, the zero-profit line is infinitely elastic at R = I; as π → 1 spread collapses to zero (limit profit expression given as equation (16)).
- Overborrowing/overlending:
  - With π > 0, interest rate at which lender is willing to lend a given amount will not fully reflect credit risk; spread between that interest rate and cost of funds is compressed.
  - Graphical equilibrium: equilibrium lies where zero-profit line is tangent to borrower’s best feasible isoprofit curve; amount borrowed is larger when π > 0 (distance L*L** in source figure denotes overlent amount).
  - Proposition 5: If Pareto-efficient allocation given by q′(L) E(Y) = I, then allocation when π > 0 is inefficient with capital invested larger than Pareto-optimal amount; deviation (overlending) increases with π and is zero when π = 0.
- Risk aversion remark:
  - Introducing risk-averse borrower reduces credit demanded at each interest rate and preserves concave isoprofit lines and unique maximum; main conclusions remain.
- Leverage and project choice:
  - Proposition 6: If borrower-investors are risk-neutral and π = 0, debt-equity ratio is indeterminate; if π > 0, no equity will be used and project is completely debt financed.
  - Proposition 7: For project riskiness parameter Θ, if π = 0 project risk choice is indeterminate; if π > 0 the riskiest project Θm is undertaken.
  - Proposition 10: If π = 0, an increase in project riskiness (mean-preserving spread) leaves L unaffected; if π > 0, an increase in project riskiness causes L to rise.
- Cost of loanable funds and sensitivity:
  - Proposition 8: Increase in I causes decrease in L for 0 ≤ π < 1; an increase in I causes unambiguous increase in R only when π = 1.
  - Proposition 9: Larger π renders amount lent less sensitive to changes in I; desensitization increases with π (policy implication: bailout expectations reduce effectiveness of monetary policy on credit supply).
- Interest-rate behavior as π increases:
  - As π → 1, interest rates charged unambiguously decline and spread to cost of funds decreases to zero.
  - For 0 < π < 1 net effect on R is indeterminate: rising π reduces perceived credit risk (tending to lower R) but increases amount lent (raising endogenous default probability and tending to raise R).

### IV. Mechanisms summarized (compact)
- Positive perceived bailout probability π:
  - Raises amount lent L above social optimum (overlending); overlending increases with π.
  - Compresses observed spreads between lending rates and cost of funds for a given loan amount.
  - Encourages full debt financing (no equity) in risk-neutral setting.
  - Drives selection of riskiest available projects.
  - Makes credit supply less responsive to changes in cost of funds I.

### V. Policy implications and recommended design
- Two broad policy options to offset effects of bailout expectations:
  - (i) Tax lending to offset bailout expectations (calibrate tax so amount lent ≤ social optimum).
    - Practical issues: Estimation of needed tax is complex and controversial; implementing contract-level taxes is overwhelming; uniform taxes produce distortions (coexistence of overlending and underlending).
    - Positive aspect: affects current lending behavior.
  - (ii) Commit that owners of a lending institution will not receive more than implied by return to investments; any assistance should be capital injections that dilute existing owners.
    - Advantages: Readily implemented, promotes market discipline and rule of law, avoids reinforcing future bailout expectations, aligns shareholders’ incentives for governance.
    - Practical concerns:
      - Government may become majority owner if recapitalization occurs; addressable via pre-established divestment framework that prevents transfers to prior owners upon reprivatization.
      - Impact on lending behaviour may be lagged; requires stern implementation and a “track record” and can be supplemented by regulation and stronger supervision.
- Operational guidance when project outcome Y < Ŷ (shortfall):
  - Loss RL − q(L)Y equals amount by which lending institution capital would decline absent bailout.
  - Under option (ii) government capital injection should be limited to at most that loss and should dilute existing owners.
  - Capital injection should be accompanied by prohibition on dividend payouts to existing shareholders; government should acquire voting rights commensurate with its capital injection to enforce penalties on management and appropriate incentives.
  - Regulators should set capital requirements high enough to cover potential losses; failure increases probability that transfers to owners arise via prior dividend payments.
- Government asset-purchase approaches on default:
  - Purchase asset at full RL → full bailout of owners (capital intact).
  - Purchase at discount equal to shortfall → lending institution bears losses and may be allowed to fail or be recapitalized with existing owners wiped out.
  - Continuum of intermediate discounts yield partial bailout degrees.
- Market valuation caution:
  - Introducing market valuation into discount setting or capital calculations can incorporate market functioning and probability of government intervention beyond borrower repayment capacity.
  - Supervisory-guided balance sheet valuation tailored to solvency perspective suggested; detailed treatment beyond paper’s focus.

### VI. Conclusion — main findings and implications
- A perceived positive probability of bailout of the creditor by a third party leads to greater amounts lent (and capital invested) than the social optimum; overlending increases as π rises.
- If π > 0, the interest rate a lender charges for a given loan will not fully reflect associated credit risk; spreads between that interest rate and cost of funds will be compressed for a given loan amount.
- With risk-neutral borrowers who can use own capital:
  - Debt-to-equity mix indeterminate when π = 0.
  - When π > 0 the project is financed entirely with debt (no equity).
- With projects of varying mean-preserving riskiness:
  - Choice among projects indeterminate when π = 0.
  - When π > 0, borrowers and lenders choose the riskiest project available.
- Greater project riskiness leads to greater amounts lent by risk-neutral creditors to risk-neutral borrowers when π > 0; no change in L when π = 0.
- Increase in cost of loanable funds I causes a decrease in L for any π, but expectation of bailout desensitizes L to changes in I; desensitization increases with π.
- Policy recommendation emphasized as most productive in the long run:
  - Ensure lending institutions do not receive more than implied by returns to their investments; any government assistance to maintain solvency should take the form of capital injections that dilute existing owners’ equity.

*Source: _wp09233 - conclusions in any significant way.*

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

### _wp09233 - References.......................................................................................................................

### I. INTRODUCTION
- The financial crisis that began in 2007 highlighted excesses in lending, leverage, and risk-taking, alongside large scale government interventions often referred to as bailouts.
- Broad questions addressed:
  - Is there a possible connection between actions that could amount to the bailout of lenders and the excesses in lending/borrowing and risk-taking that led to the crisis?
  - Can bailing out lenders validate a moral hazard that may have been one of the causes of the recent crisis and thus help recreate similar behaviors in the future?
  - Does the need to salvage the financial system necessarily imply that lenders must be bailed out and that reinforcement of moral hazard is unavoidable?
- Key empirical characterizations of the crisis:
  - The crisis was preceded by an excessive buildup of debt.
  - There was a parallel increase in leverage (as debt grew faster than equity).
  - The buildup of excessive debt took place with lenders charging particularly low interest rates; spreads were compressed.
  - Excessive risk-taking accompanied the buildup of excessive debt.
- Approach and scope:
  - Presents a simple analytical framework based on rational agents with adequate information (probability distributions) to analyze effects of lenders’ perceptions that they may be bailed out by a third party.
  - Does not rely on irrationality or informational opaqueness to explain lending and risk-taking excesses, though such factors may have also played roles.
  - Applies to both bank and non-bank (“shadow” banking) lending relationships as a relatively generic lending model.
  - Does not claim uniqueness as an explanation nor attempt to explain precipitation, propagation, or severity of the crisis.

### II. THE ANALYTICAL FRAMEWORK
A. The Basic Model — assumptions and setup
- Model lineage: belongs to class of models developed by Jaffee and Modigliani (1969), Smith (1972), Jaffee and Russell (1976), Milde and Riley (1984), Clemenz (1986).
- Emphasizes creditor assignment of a positive probability to ex post involvement by a third party in a formally two-party contract.
- Assumptions:
  (i) Project output price X is non-negative random variable: X = q(L)Y, where q is quantity produced with input L, and L is funds invested. Price per unit output set equal to 1. Y ∈ [0, m] with distribution F(Y). q′(L) > 0 and q′′(L) < 0 for all L.
  (ii) For the moment only one source of finance: credit.
  (iii) Debtor repays amount borrowed times R (R = 1 + interest rate) if project return > X̂, where X̂ = q(L)Ŷ = RL. If Y < Ŷ (i.e., X < X̂), borrower remits all returns of the project.
  (iv) When Y < Ŷ, a third party intervenes with probability π and bails out the lender by paying RL – q(L)Y.
  (v) Both lender and debtor-investor are risk neutral (maximize expected returns).
  (vi) Lender is restricted by zero profit condition due to competition of alternative lenders.

B. Borrower’s problem and first-order conditions
- Borrower’s optimization written as:
  - max_B ∫_{Ŷ}^{m} B q(L) Y f(Y) dY – R L [1 – F(Ŷ)]  (equation (1) as presented)
- Rewritten as:
  - max_B ∫_{Ŷ}^{m} q(L) Y [1 – F(Y)] dY {…} – R L F(Ŷ)  (equation (2) as presented)
- First order condition:
  - (1) ˆ'( ) ( ) 1 () 0  B Req LHYFY L  = − + − =  (equation (3) as presented)
  - Definitions: ˆ(1( )) and ˆ() etc. (as in source).
- Second order condition and sufficient conditions:
  - Second order condition expression given as equation (4).
  - For second order condition negative, require e < 1, which implies certain derivatives constraints and hazard rate properties (H′(Ŷ) < 0; hazard rate [1 − F(Y)]/f(Y) should be increasing in Y).
  - Under these conditions 0 = ∂L_B/∂? defines maximum.

C. Credit demand curve slope
- Slope of implied credit demand curve:
  - dR/dL = (∂^2 B / ∂L^2) / (∂^2 B / ∂L ∂R)  (equation (5))
- Expression for ∂^2 B / ∂L ∂R given (equation (6)).
- Given ˆ0,1 and '( ) 0 etc., it holds that ∂^2 B / ∂L ∂R < 0.
- Proposition 1:
  - If ()()() 1,0 and 1( eL f Y eL LF ∂ < = ∂−)Y increases with Y, then L decreases as R increases. (Preserves source notation and conditions verbatim.)

D. Isoprofit curve properties (Proposition 2)
- Under same conditions as Proposition 1:
  - (i) Each isoprofit curve R(L,B) has unique turning point at L*(B) with sign conditions on second derivatives: 0 for* ( ) and0 for* ( ) RR LLBLLB LL ∂∂ > < < > ∂∂
  - (ii) * 0 L B ∂ > ∂
  - (iii) [ ] *( ) 0 RL  B B ∂ < ∂
  - (Proof reference to Clemenz (1986), p. 134).

E. Lender’s zero-profit condition with bailout probability π
- Zero profit condition of lender:
  - 0 = ∫_{Ŷ}^{m} P q(L) Y f(Y) dY − R L F(Ŷ) + π [R L − ∫_{0}^{Ŷ} q(L) Y f(Y) dY] − I L  (equation (7) as presented)
  - Explanation: π is lender’s perceived probability that third party will intervene and pay RL − q(L)Y when Y < Ŷ. Per unit cost of loanable funds to lender is I.

Proposition 3:
- If e(L) < 1, then the zero profit line per borrower of a given lender has a non-negative slope for all L ≥ 0.
- Slope of zero-profit line:
  - dR/dL = − (∂P/∂L) / (∂P/∂R)  (equation (8))
- Expressions for partial derivatives given in equations (9) and (10).
- It follows that dR/dL > 0 under stated conditions.

Proposition 4:
- An increase in perceived probability π of bailout reduces the slope of the zero-profit line of the lender.
- Change in slope for change in π given by expression (11).
- Supporting inequalities and expressions provided (equations (12)–(15)).
- Conclusion: 0 > ∂(dR/dL)/∂π ; increase in π lowers the slope.

Corollary:
- If perceived probability π = 1, the zero-profit line is infinitely elastic at R = I.
- Proof: limit of bank’s profit function as π → 1 given (equation (16)); in limit profit per borrower equals RL − IL; with zero profit, R = I, implying spread collapses to zero.

F. Comparative statics and overborrowing
- With π > 0, interest rate at which lender is willing to lend a given amount will not fully reflect associated credit risk; spread between that interest rate and cost of funds is compressed for given loan amount.
- Graphical characterization (referenced Figure 1 in source):
  - Equilibrium lies on lender’s zero-profit line; equilibrium occurs where zero-profit line tangent to borrower’s best feasible isoprofit curve.
  - Comparing equilibria for π > 0 vs π = 0: amount borrowed is larger when π > 0.
  - Distance L*L** in Figure 1 is amount overlent (overborrowed) due to expectations of bailout.

G. Formal equilibrium conditions
- Equilibrium as constrained maximization: maximize B(R,L) + λ P(R,L) (equation (17)).
- First order conditions provided (equations (18) and (19)).
- Equilibrium conditions summarized (equations (20) and (21)).
- Pareto-efficient allocation of capital: q′(L) E(Y) = I (maximizing E(X) − I L).
- Proposition 5:
  - If Pareto-efficient allocation given by q′(L) E(Y) = I, then allocation when π > 0 is inefficient and amount of capital invested is larger than Pareto-optimal amount.
  - Deviation from socially optimal amount is overlending/overborrowing, which increases with π and is zero when π = 0.

H. Remarks on risk aversion (footnote summary)
- Model can be reformulated with risk-averse borrower:
  - Quantity of credit demanded at each interest rate will be smaller than when borrower is risk neutral.
  - Quantity of credit demanded at each interest rate declines as degree of relative risk aversion increases.
  - Introduction of risk-averse borrowers preserves concave isoprofit lines and existence of unique maximum; does not alter main conclusions of model.

_Italic source attribution line._

### conclusions in any significant way.

### _wp09233 - conclusions in any significant way.

### Proof sketch and key mathematical results
- Equation (22) (rewriting of (20)) shows:
  - When π > 0, q′(L)EY < I and, since q′′(L) < 0, the amount borrowed when π > 0 is greater than the socially optimal amount.
  - The deviation from the socially optimal amount depends on the magnitude of the term ()ˆ1(1  )()FY
    
    
    
    
    
    in expression (22); this term reduces to zero when π = 0.
  - (23) shows (   )
     increases as π increases, since 2
    ˆ
    ()1   ()
    0
    ˆ
    1(1   )()
    FY
    FY
    
    
    
    
    
    
    
    
    .

- Interest-rate behavior as π increases:
  - Interest rates charged to borrowers may not monotonically decline as π increases.
  - As π → 1, interest rates charged will unambiguously decline and the spread between these interest rates and the cost of funds will decrease towards zero.
  - For 0 < π < 1, two opposing effects operate:
    - Rising π reduces perceived credit risk and tends to lower R.
    - Rising π increases the amount lent, which increases the endogenous probability of default ˆF(Y) (since 0. Y L   ), warranting a higher R.
  - Net effect on R for 0 < π < 1 is indeterminate without specific parameter values.

### A. Overlending and spreads
- If the probability of default does not increase too rapidly as L increases, then:
  - As π becomes positive and rises, amounts of credit provided increase while interest rates charged fall, compressing observed spreads between lending rates and cost of funds.
  - Cost of funds to creditors can be expected to closely track the rate of return on benchmark government paper, so rising π is associated with increasingly compressed spreads between effectively riskless government paper and risky credits.
  - Observed spreads lose signaling content as π increases.

### B. Different sources of finance (Proposition 6)
- Setup: borrower-investor can have equity K ≤ W0 and opportunity cost of equity IK.
- Proposition 6:
  - If borrower-investors are risk-neutral and π = 0, then the debt-equity ratio of the project is indeterminate.
  - If π > 0, no equity will be used and the project will be completely debt financed.
- Intuition and implication:
  - Positive π leads to substitution of debt for equity (increase in leverage); in the risk-neutral model, projects end up being financed solely by issuing debt when π > 0.

### C. Choice of project riskiness (Proposition 7)
- Setup: borrower chooses projects with riskiness Θ ∈ [Θ0, Θm]; larger Θ = mean-preserving increase in risk; F(Y, Θ), f(Y, Θ) = F′(Y, Θ). Conditions (24) and (25) hold:
  - ˆ0ˆ(, )0for0. Y FYdYY       (24)
  - ˆˆ(, )0for. m Y FYdYY m      (25)
- Proposition 7:
  - (i) If π = 0, the riskiness of the project undertaken in equilibrium is not determinate.
  - (ii) If π > 0, the riskiness of the project undertaken in equilibrium is determinate, and the riskiest project available (Θm) is undertaken.
- Intuition:
  - With risk neutrality and π = 0, expected returns to borrower-lender unaffected by Θ → indeterminate choice.
  - With π > 0, higher Θ increases probability that third party intervenes, increasing expected value to borrower-lender → both parties prefer riskiest project.
- Implication: Positive π not only causes overlending but increases project riskiness chosen.

### D. Change in the cost of loanable funds (Proposition 8 and 9)
- Change in I shifts zero-profit line of lender:
  - Vertical shift: 1 1for ˆ1(1  )() dR LL dI FY    (26)
  - For 0 ≤ π < 1 the shift is not parallel; the zero-profit line rotates counterclockwise as I increases. For π = 1 the zero-profit line is infinitely elastic and undergoes only a parallel upward shift equal to the change in I.
- Proposition 8:
  - An increase in I will cause a decrease in the amount lent for 0 ≤ π < 1.
  - An increase in I will cause an unambiguous increase in the loan interest rate only when π = 1.
  - Heuristic reasoning: For π = 0 equilibrium satisfies q′(L)EY = I plus zero-profit condition; solving total differentials shows dL/dI < 0 but dR/dI ambiguous for π < 1. For π = 1, R = I so dR/dI = 1.
- Proposition 9:
  - A larger probability of bailout π renders the amount lent less sensitive to changes in I.
  - For a given change in I, the change in L becomes smaller as π increases; shift of zero-profit line for a given ΔI is smaller for larger π at any given L̅. Shift is smallest when π = 1 and largest when π = 0.
  - Policy implication: Positive π desensitizes supply of credit to monetary policy actions (changes in policy rates).

### E. Changes in the probability distribution function of the debt-financed project (Proposition 10)
- Proposition 10:
  - If π = 0, an increase in project riskiness (mean-preserving spread) leaves L unaffected.
  - If π > 0, an increase in project riskiness will cause L to rise.
- Rationale:
  - When π = 0 the second term in expression (22) is zero and remaining components unaffected by Θ → L unchanged.
  - When π > 0 the second term is negative and its absolute value increases with Θ (using (24) and (25)), so q′(L)EY becomes increasingly smaller than I; with q′′(L) < 0 this implies L rises above the socially optimal amount as Θ rises.
  - Intuition: With positive π, greater Θ raises probability of third-party intervention, increasing expected return to borrower-lender and inducing larger loans.

### III. Some thoughts on policy implications
- Two broad policy options to offset effects of bailout expectations:
  - (i) Recognize bailout expectations and tax lending, calibrating tax to prevent amount lent exceeding socially optimal amount.
    - Practical issues: Estimating needed tax is complex and controversial (government estimating lender’s expectation of its own bailout probability). Implementing contract-level taxes is overwhelming. Uniform taxes across categories likely produce distortions (coexistence of overlending and underlending). Positive aspect: affects current lending behavior.
  - (ii) Commit that owners of a lending institution will not receive more than implied by return to investments; any assistance to maintain solvency should take form of capital injections that dilute equity of existing owners.
    - Advantages: Readily implemented, promotes market discipline and rule of law, avoids reinforcing future bailout expectations, aligns shareholders’ incentives for corporate governance.
    - Practical concerns:
      - Government could become majority owner if recapitalization occurs; addressed by pre-established divestment framework (footnote: framework should prevent owners receiving transfers upon reprivatization).
      - Impact on lending behavior may be lagged—requires stern implementation and a “track record” (supplement with regulation and stronger supervision).
- When project outcome Y < Ŷ (debt service shortfall):
  - Loss RL – q(L)Y is amount by which lending institution capital would decline absent bailout.
  - Under option (ii), government capital injection should be limited to at most that loss and should dilute existing owners.
  - Capital injection should be accompanied by prohibition on dividend payouts to existing shareholders; government should acquire voting rights commensurate with its capital injection to enforce penalties on management and appropriate incentives.
  - Regulators should set capital requirements high enough to cover potential losses; failure to do so increases probability that even after owners’ capital is wiped out, transfers to them arise via prior dividend payments.
- Government asset-purchase options if project fails to cover debt:
  - Purchase asset at full RL → full bailout of owners (capital intact).
  - Purchase at discount equal to shortfall → lending institution bears losses and may be allowed to go bankrupt or be recapitalized with existing owners wiped out.
  - Continuum of intermediate discounts yields partial bailout degrees.
- Market valuation issues:
  - Introducing market valuation into discount setting or capital calculations can bring in factors beyond actual borrower repayment capacity (market functioning, probability of government intervention).
  - Author suggests supervisory-guided balance sheet valuation tailored to solvency perspective; detailed treatment beyond paper’s focus.

### IV. Conclusion — main findings and implications (bulleted)
- A perceived positive probability of bailout of the creditor by a third party leads to greater amounts lent (and capital invested) than the social optimum; overlending increases as π rises.
- If π > 0, the interest rate a lender charges for a given loan will not fully reflect associated credit risk; spreads between that interest rate and cost of funds will be compressed for a given loan amount.
- With risk-neutral borrowers who can use own capital:
  - Debt-to-equity mix is indeterminate when π = 0.
  - When π > 0 the project is financed entirely with debt (no equity).
- With projects of varying mean-preserving riskiness:
  - Choice among projects is indeterminate when π = 0.
  - When π > 0, borrowers and lenders choose the riskiest project available.
- Greater project riskiness leads to greater amounts lent by risk-neutral creditors to risk-neutral borrowers when π > 0; no change in L when π = 0.
- Increase in cost of loanable funds I causes a decrease in L for any π, but expectation of bailout desensitizes L to changes in I; this desensitization increases with π.
- Policy recommendation emphasized as most productive in the long run:
  - Ensure lending institutions do not receive more than implied by returns to their investments.
  - Any government assistance to maintain solvency should take the form of capital injections that dilute existing owners’ equity.

*Italic: Source: _wp09233 - conclusions in any significant way.*

### References

### References

### Bibliographic entries
- Clemenz, Gerhard, (1986), Credit Markets With Asymmetric Information, (Berlin: Springer-Verlag).
- Jaffee, Dwight M. and Franco Modigliani, (1969), “A Theory and Test of Credit Rationing,” American Economic Review, No. 59, pp. 850-72.
- Jaffee, Dwight M. and Thomas Russell, (1976), “Imperfect Information, Uncertainty, and Credit Rationing,” The Quarterly Journal of Economics, MIT press, No. 90 Vol. 4, pp. 651-66.
- Georgiou, Andreas, (1989), Essays in Overlending and Capital Flight, Ph. D. Dissertation, The University of Michigan, (Michigan: Ann Arbor).
- Milde, H. and J. G. Riley, (1984), “Signaling in Credit Markets,” Diskussionsbeitrage, Series No. 185, (Germany: University of Konstanz).
- Rothchild, M and J. E. Stiglitz (1970), “Increasing Risk: A Definition,” Journal of Economic Theory, 2, 225-43.
- Sjaastad, Larry A. (1983), The international debt quagmire: to whom do we owe it?, Graduate papers in international economics, No. 8302, (Genève: Institut universitarie de hautes études internationals).

*Source: _wp09233 - References (PDF).*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp09233.pdf_