Credit Market Problems January 2011 () Credit Markets January - PowerPoint PPT Presentation

Credit Market Problems January 2011 () Credit Markets January 2011 1 / 17

Should Governments Intervene in Credit Markets Moneylenders historically viewed as exploitive: high interest rates , ! BUT displacing them may remove valuable/unique services , ! and interest rates may re‡ect high costs (Aleem, 1990 and Steel et. al. 1997) Two main rationales for intervention , ! E¢ciency: are productive investments not being undertaken? , ! Distribution: is access to credit equitable? , ! there need not be a trade-o¤ () Credit Markets January 2011 2 / 17

Agency Problems Reasons for absence of formal institutions in village economies A result of limited liability (lack of collateral) and asymmetric information Even when titled land is available, formal banks may not accept it as collateral () Credit Markets January 2011 3 / 17

Adverse Selection Example Investment requires $1, but borrowers have no wealth A fraction q of borrowers are “safe”: earn certain output y A fraction 1 � q of borrowers are “risky”: � ¯ y with probability p Output = 0 with probability 1 � p Bank cannot distinguish borrower types Equal expected return: p ¯ y = y . Gross cost to bank per $1 lent = k , where y > k Bank charges gross (interest plus principle) lending rate = R () Credit Markets January 2011 4 / 17

How does the bank’s expected pro…t vary with R? Given R , the bank’s expected return per dollar lent is [ q + ( 1 � q ) p ] R De…ne the “break-even” value of R as R b [ q + ( 1 � q ) p ] R b = k k R b = q + ( 1 � q ) p k + ( 1 � q )( 1 � p ) k = R b q + ( 1 � q ) p = k + A R b Bank’s expected pro…t: � [ q + ( 1 � q ) p ] R � k if R < y π = ¯ pR � k if R > y () Credit Markets January 2011 5 / 17

π 0 R y y/p k k/p k+A () Credit Markets January 2011 6 / 17

π 0 R y k+A k/p y/p k () Credit Markets January 2011 7 / 17

Implications Raising interest rates need not increase pro…ts linearly If p falls, the bank may not be able to break even at a rate low enough for safe borrowers ) Banks will only serve risky borrowers , ! this is ine¢cient (since y > k ) and inequitable , ! credit rationing () Credit Markets January 2011 8 / 17

Moral Hazard Example (Ghosh, Mookherjee and Ray 2000) Indivisible project requires funds L All agents risk neutral Likelihood of high output depend on non-contractible e¤ort e : � Q if good harvest with prob. p ( e ) Output = 0 if crop failure with prob. 1 � p ( e ) where p 0 ( e ) > 0 , p 00 ( e ) < 0 () Credit Markets January 2011 9 / 17

Case 1: Self–…nanced farmer (benchmark) Farmer chooses e to solve max p ( e ) . Q � e � L e , ! FOC p 0 ( e � ) = 1 Q where e � = …rst–best (e¢cient) e¤ort level () Credit Markets January 2011 10 / 17

Case 2: Debt–…nanced farmer Total debt: R = ( 1 + i ) L Limited Liability: In case of default can only lose collateral, w < L Farmer chooses e to solve max p ( e ) . ( Q � R ) + ( 1 � p ( e )) . ( � w ) � e e , ! FOC yields the incentive curve: 1 p 0 ( ˆ e ) = (IC) Q + w � R , ! ˆ e ( w , R ) is decreasing in R and increasing in w , ! if R > L > w , it follows that e < e � ˆ () Credit Markets January 2011 11 / 17

Lender’s pro…t: π = p ( e ) R + [ 1 � p ( e )] w � L Competitive lending (Figure 1) ) π = 0 : R = L � w p ( e ) + w = L � ( 1 � p ( e )) w (ZP) p ( e ) , ! equilibrium: determined by intersection of (IC) and (ZP) Monopoly lending ) maximize pro…ts subject to IC (Figure 2) ! if max pro…t is π M then isopro…t line is , R = L � π M � ( 1 � p ( e )) w (MP) p ( e ) () Credit Markets January 2011 12 / 17

R Isoprofit Curve Incentive Curve E ^ R ^ e e* e Figure 1: Equilibrium Debt and Effort in the Credit Market. the lender’s market power (although that certainly exacerbates the problem), but

R Isoprofit Curve Incentive Curve E' ^ E R ^ e e* e Figure 2: Effect of an Increase in the Lender’s Profit. The observation that borrower-friendly equilibria are more efficient has broad

An increase in collateral, w (Figure 3) , ! fall in the equilibrium interest rate and debt, and an increase in the e¤ort level. , ! for a …xed π , the borrower’s income increases ) interest rate dispersion, even in competitive credit markets ) exaccerbates pre-existing inequality () Credit Markets January 2011 13 / 17

R E Isoprofit Curve E' Incentive Curve e Figure 3: Effect of Higher Borrower Wealth (Collateral).

Enforcement Problems (Ex Post Moral Hazard) Example (Ghosh, Mookherjee and Ray 2000) In…nite horizon lending–borrowing game with no saving and discount factor δ Borrower’s production technology is F ( L ) where F 0 ( L ) > 0 and F 00 ( L ) < 0 r = bank rate of interest (opportunity cost of funds) Self–…nanced farmer (benchmark): max F ( L ) � ( 1 + r ) L L , ! FOC: F 0 ( L � ) = 1 + r () Credit Markets January 2011 14 / 17

Partial Equilibrium: Single Lender Assume that a defaulting borrower goes into “autarky” and receives v (exogenous for now) Borrower’s incentive constraint: δ 1 F ( L ) + 1 � δ v � 1 � δ [ F ( L ) � R ] (IC) Optimal contract solves max F ( L ) � R L , R subject to R � δ [ F ( L ) � v ] (IC) z = R � ( 1 + r ) L (PC) where z is lender’s minimum pro…t () Credit Markets January 2011 15 / 17

Two types of solution: (1) if indi¤erence curves are tangent to isopro…t curve between A and B at L � , this is the solution and IC is not binding (2) if not, both constraints are binding and solution ˆ L ( v , z ) is at corner B , ! in general, the constrained optimal level of lending is � � ˜ L � , ˆ L ( v , z ) = min L ( v , z ) () Credit Markets January 2011 16 / 17

R Borrower's indifference curve ~ B R Incentive constraint Isoprofit line A ~ L * L L Figure 4: Optimal Solution to the Enforcement Problem. subject to the constraints

Some Implications Increase in lender’s pro…t z ! PC shifts up (Figure 5) , ! reduced lending, L , ! increase in interest rate, R / L Increase in value of outside option, v ! IC shifts down (Figure 6) , ! reduced lending, L , ! increase in interest rate, R / L Can credit rationing arise in equilibrium ? , ! yes: if z or v become high enough there is no combination of L and R that satis…es both (IC) and (PC) () Credit Markets January 2011 17 / 17

R Incentive constraint Isoprofit line L Figure 5: Effect of an Increase in Lender’s Profit. leads to the conclusion:

Isoprofit Line R Incentive Constraint B B' L Figure 6: Effect of an Increase in Borrower’s Outside Option.