Credit Market Problems in Developing Countries

Transcription

1 Credit Market Problems in Developing Countries September 2007 () Credit Market Problems September / 17

2 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?,! need not be a trade-o () Credit Market Problems September / 17

3 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 Market Problems September / 17

4 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 : ȳ with probability p Output = 0 with probability 1 p Bank cannot distinguish borrower types Equal expected return: pȳ =y. Gross cost to bank per $1 lent = k, where y > k Bank charges gross (interest plus principle) lending rate = R () Credit Market Problems September / 17

5 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 R b = k q + (1 q)p (1 q)(1 p)k R b = k + q + (1 q)p R b = k + A Bank s expected pro t: [q + (1 q)p] R k if R < y π = pr k if R > y () Credit Market Problems September / 17

6 π 0 k k+a y k/p y/p R () Credit Market Problems September / 17

7 π 0 k y k+a k/p y/p R () Credit Market Problems September / 17

8 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 Market Problems September / 17

9 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 Market Problems September / 17

10 Case 1: Self nanced farmer (benchmark) Farmer chooses e to solve max e p(e).q e L,! FOC p 0 (e ) = 1 Q where e = rst best (e cient) e ort level () Credit Market Problems September / 17

11 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 e,! FOC yields the incentive curve: p(e).(q R) + (1 p(e)).( w) e p 0 (ê) = 1 Q + w,! ê(w, R) is decreasing in R and increasing in w,! if R > L > w, it follows that R (IC) ê < e () Credit Market Problems September / 17

12 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 p(e) (ZP),! 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 πm (1 p(e))w p(e) (MP) () Credit Market Problems September / 17

13 R Isoprofit Curve Incentive Curve R^ E e^ e* e Figure 1: Equilibrium Debt and Effort in the Credit Market.

14 R Isoprofit Curve Incentive Curve E' R^ E e^ e* e Figure 2: Effect of an Increase in the Lender s Profit.

15 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 Market Problems September / 17

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

17 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 L F (L) (1 + r)l,! FOC: F 0 (L ) = 1 + r () Credit Market Problems September / 17

18 Partial Equilibrium: Single Lender Assume that a defaulting borrower goes into autarky and receives v (exogenous for now) Borrower s incentive constraint: F (L) + Optimal contract solves δ 1 δ v 1 [F (L) R] (IC) 1 δ max L,R F (L) R subject to where z is lender s minimum pro t R δ [F (L) v] (IC) z = R (1 + r)l (PC) () Credit Market Problems September / 17

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

20 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 ˆL(v, z) is at corner B,! in general, the constrained optimal level of lending is L(v, z) = min L, ˆL(v, z) () Credit Market Problems September / 17

21 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 Market Problems September / 17

22 R Incentive constraint Isoprofit line L Figure 5: Effect of an Increase in Lender s Profit.

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