Principles of Banking (II): Microeconomics of Banking (4 ...
Transcript of Principles of Banking (II): Microeconomics of Banking (4 ...
IntroductionCredit Rationing in Market Equilibrium
Principles of Banking (II): Microeconomics ofBanking (4) Credit Market
Jin Cao(Norges Bank Research, Oslo & CESifo, Munchen)
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Outline
1 Introduction
2 Credit Rationing in Market EquilibriumAdverse selection and credit demandCredit supply and credit rationing
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Disclaimer
(If they care about what I say,) the views expressed inthis manuscript are those of the author’s and shouldnot be attributed to Norges Bank.
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Bank-borrower relationship
So far we have focused mostly on liability side frictions
Uncertainty in depositors’ liquidity preference leads toliquidity risk , and principal-agent problems imply thatcapital is needed to align banks’ incentives;With a little touch on asset side: liquid assets needed tobuffer liquidity shocks;
However, main problem on asset side is banks’ decision onrisky loans, or bank-borrower relationship
Obviously plagued by uncertainty and asymmetricinformation;Which lead to credit risks in banking.
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Loanable funds and credit rationing
A result of such frictions is the puzzling credit rationingphenomenon
Borrowers’ demand for credit is higher than available loansprovided by banks (“unsatisfied fringe of borrowers”,Keynes, 1930);Some borrowers’ demand is turned down even if they arewilling to pay higher interest rate for loans;
Is it consistent with basic demand and supply analysis
Given that banks are profit-maximizing?Any implication on banks’ risk-taking incentives?
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Credit rationing in equilibrium and disequilibrium
Credit rationing obviously happens in temporary marketdisequilibrium: e.g., frictions that prevent market fromquickly adjusting to shocks;
Credit rationing can emerge as a permanent phenomenonin equilibrium: increasing loan rate leads to
Higher interest income from loans, butRiskier projects chosen by borrowers due to adverseselection;Profit-maximizing loan supply balances these two effects,with implied loan rate lower than market clearing rate;
We’ll focus on the second type of credit rationing.
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Agents, technology and information
There are many risk-neutral entrepreneurs in theeconomy, each
Has a project which needs initial investment k;Has wealth W < k: needs to borrow L = k −W to start theproject;Has an outside option: deposit in banks with safe return δ;
Projects are identical in rate of return, but different in risk.For entrepreneur i ’s project:
Returns Ri if successful, with probability pi (withprobability density function f (pi )); zero otherwise;Expected return R0 = Ripi is identical for all projects;Likelihood of success pi is entrepreneur’s privateinformation.
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Agents, technology and information (cont’d)
There are risk-neutral banks in the economy
Issue loan L to each entrepreneur who wants to startprojects;Do not know pi of each entrepreneur;Compete in deposit market, maximizing gross return todepositors;Charge uniform loan rate r to maximize gross return.Assume Ri > (1 + r)L for all entrepreneurs: loans are fullypaid when projects are successful; zero otherwise.
There are depositors (not explicitly modelled), whoseaggregate supply of deposit d (δ) is an increasing functionof deposit rate δ.
J. C. Microeconomics of Banking: Credit Market
institution-logo-filenameO
IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Credit demand
The expected return to individual entrepreneur is
E [πi ] = pi [Ri − (1 + r) L] = R0 − pi (1 + r) L ≥ (1 + δ)W ;
pi ≤R0 − (1 + δ)W
(1 + r) L= p (r) ;
The participation constraint implies
Only risky entrepreneurs with pi ≤ p (r) will borrow;
And dp(r)dr < 0 implies higher loan rate increases the
riskiness of loans: adverse selection.
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Credit demand (cont’d)
The aggregate demand of loans is decreasing with r , andwith dp(r)
dr < 0 this gives the demand curve for loans:
D (r) = L
∫ p(r)
0f (pi ) dpi ,
𝑓𝑓(𝑝𝑝)
𝑝𝑝 ��𝑝(𝑟𝑟)
ℓ
𝑟𝑟
𝐷𝐷
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Equilibrium loan rate and credit supply
The banks’ decision problem is
maxr
E [πb] = (1 + r) L
∫ p(r)
0
pi f (pi ) dpi ;
The effect of increasing loan rate is
dE [πb]
dr= L
∫ p(r)
0
pi f (pi ) dpi︸ ︷︷ ︸(A)
+dp (r)
dr(1 + r) Lp (r) f (p (r))︸ ︷︷ ︸
(B)
;
Two diverting effects:
(A) > 0: r ↑ increases profit from the borrowers;(B) < 0: r ↑ decreases the threshold of borrowers, less butriskier borrowers: lower quality for the pool of loans.
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Equilibrium loan rate and credit supply (cont’d)
The equilibrium loan rate r∗ is determined by
dE [πb]
dr= 0;
And the deposit rate δ is determined by zero profitcondition
E [πb] = (1 + r) L
∫ p(r)
0pi f (pi ) dpi︸ ︷︷ ︸
gross profit
= (1 + δ) L
∫ p(r)
0f (pi ) dpi︸ ︷︷ ︸
gross cost
,
1 + δ =(1 + r)
∫ p(r)0 pi f (pi ) dpi∫ p(r)
0 f (pi ) dpi
.
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Equilibrium loan rate and credit supply (cont’d)
The relationship between deposit and loan rates is
dδ
dr=
∫ p(r)0 pi f (pi ) dpi∫ p(r)
0 f (pi ) dpi
−(1 + r)
∫ p(r)0 pi f (pi ) dpi p
′ (r) f (p)[∫ p(r)0 f (pi ) dpi
]2
︸ ︷︷ ︸(A)
+(1 + r) p′ (r) pf (p)∫ p(r)
0 f (pi ) dpi︸ ︷︷ ︸(B)
>< 0;
Two diverting effects on δ:
(A) > 0 (remember p′ (r) < 0): r ↑ increases gross profit,more return to depositors;(B) < 0: r ↑ attracts only riskier borrowers, more projectsfail, less return.
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Equilibrium loan rate and credit supply (cont’d)
Banks’ loanable funds, or loan supply, is determined bydeposits they collect, d (δ), an increasing function of δ
δ may increase with r (when r is small) or decrease with r(when r is large);Implies banks’ loan supply is a hump-shaped curve.
ℓ
𝑟𝑟
𝑆𝑆
J. C. Microeconomics of Banking: Credit Market
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IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Credit rationing
The equilibrium (r∗, `∗) implies credit rationing: excessdemand for loans Z = ˜− `∗.
ℓ
𝑟𝑟
𝑆𝑆
𝐷𝐷
��𝑟 𝑟𝑟∗
ℓ� ℓ∗
𝑍𝑍
ℓ�
Banks would never choose ˆ — which implies market clearing rate r —since profit is not maximized under ˆ: r would attract too many risky projects andincrease the likelihood of failure.
J. C. Microeconomics of Banking: Credit Market
institution-logo-filenameO
IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
Conclusion
Bank-borrower relationship is heavily plagued byasymmetric information: strong implication for banks’ riskmanagement and credit supply
Borrowers may behave improperly, pocketing private benefitand leaving too much risk to banks;Banks have to take this into account when issuing loans: toinduce borrowers to behave as desired, and cut back creditsupply to minimize losses from risky loans;
Credit rationing happens in equilibrium, so that someborrowers’ credit demand has to be rejected
Lower loan rate than market clearing rate, avoidingattracting too many risky projects;Credit rationing is optimal, as long as adverse selectionproblem exists.
J. C. Microeconomics of Banking: Credit Market
institution-logo-filenameO
IntroductionCredit Rationing in Market Equilibrium
Adverse selection and credit demandCredit supply and credit rationing
References
(F: Recommemded reading)
Freixas, X. and Rochet, J.-C. (2008), Microeconomics of Banking (2ndEdition), MIT Press, Chapter 4&5.
F Matthews, K. and Thompson, J. (2014), The Economics of Banking (3rdEdition), Wiley, Chapter 8.
Stiglitz, J. E. and Weiss, A. (1981), Credit rationing in markets withimperfect information, American Economic Review 71, 393-410.
J. C. Microeconomics of Banking: Credit Market