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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Outline

1 Introduction

2 Credit Rationing in Market EquilibriumAdverse selection and credit demandCredit supply and credit rationing




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.




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.




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?




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.




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.





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.





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.





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





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.





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

.






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.






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





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.





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.





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.


Principles of Banking (II): Microeconomics of Banking (4 ...

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