credit risk and credit rationing

8/6/2019 Credit Risk and Credit Rationing

1/22

Credit Risk and Credit RationingAuthor(s): Donald R. HodgmanSource: The Quarterly Journal of Economics, Vol. 74, No. 2 (May, 1960), pp. 258-278Published by: Oxford University PressStable URL: http://www.jstor.org/stable/1884253 .

Accessed: 29/07/2011 20:49

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you

may use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at .http://www.jstor.org/action/showPublisher?publisherCode=oup. .

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed

page of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

Oxford University Press is collaborating with JSTOR to digitize, preserve and extend access to The Quarterly

Journal of Economics.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=ouphttp://www.jstor.org/stable/1884253?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/action/showPublisher?publisherCode=ouphttp://www.jstor.org/action/showPublisher?publisherCode=ouphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/1884253?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=oup


2/22

CREDIT RISK AND CREDIT RATIONING*By DONALD R. HODGMAN

I. Approaches to credit rationing, 258. - II. The influence of credit riskon loan payoff, 259. - III. Implications for lender behavior and borrower accessto credit, 267. - IV. The central bank's influence, 275.

I. APPROACHES TO CREDIT RATIONINGCredit rationing is a much debated phenomenon. Althoughpractical borrowers and lenders long have regarded credit rationingas a fact of experience, economists of a more analytical persuasionhave been reluctant to accept it at face value because of their diffi-culty in providing a theoretical explanation for the phenomenon whichis consistent with the tenets of rational economic behavior. Whyshould lenders allocate credit by non-price means and thus denythemselves the advantage of higher interest income? Explanationswhich meet this difficulty are those which attribute credit rationingto sticky interest rates associated with oligopoly in credit marketsand to ceilings on interest charges imposed by usury laws. But mostcorporate borrowers are exempt from the protection of the usurystatutes, and sticky rates of interest usually rise without too muchdelay as credit conditions tighten. These considerations have ledto the apparently prevailing view that credit rationing as a generalphenomenon, while it does occur, is primarily a temporary expedientwhich lenders resort to only until they have made up their minds toraise the interest rate to a new equilibrium level following an increasein borrower demand or restrictive action by the monetary authority.This view denies to credit rationing any significant influence on creditavailability other than in the fairly short run.'Recently there have been attempts to free credit rationing from*I am deeply indebted to Professor Colin R. Blyth of the MathematicsDepartment, University of Illinois for developing my intuitive surmisesinto theexplicit mathematical reasoningof Section I. ProfessorMarvinFrankel read the

manuscriptand provIdedhelpful criticism. ProfessorThomas A. Yancey gavegenerously of his time in several prolongeddiscussionsof probability measure-ments. It is a pleasureto acknowledgethe support of The MerrillFoundationfor the Advancementof FinancialKnowledgefor the larger study from which thisarticle derives.1. For an explicit statement of this view see MonetaryPolicy and Manage-ment of the PublicDebt:Hearingsbefore heSubcommitteen GeneralCreditControland Debt Management, oint Committee on the EconomicReport, 82d Congress,2d Session,Statement of Paul Samuelson,esp. pp. 697-98.258


3/22

CREDIT RISK AND CREDIT RATIONING 259its dependence upon interest ceilings, whether voluntary or imposed,by suggesting that credit rationing is an aspect of lender attitudetoward risk. To date, so far as I am aware, these attempts have notbeen able to cope with one particular difficulty: the principle thatwhen other factors such as credit rating or maturity are less favorable,borrowers may succeed in obtaining the credit they wish by paying ahigher rate of interest to compensate lenders for the less favorablerisk features of the loan or investment.2 Once this camel's nose isunder the tent, interest appears to regain much of the authority thatthe concept of credit rationing seeks to deny to it. If a determinedborrower can always obtain funds by agreeing to a sufficiently highrate of interest, he can be denied credit only by quoting him a ratewhich he regards as prohibitive. This, however, is not credit rationingin the specific sense but traditional interest rationing.In the analysis which follows I have sought to explore further theimplications of risk for the terms upon which money is loaned. Mypurpose is to provide a more general explanation for credit rationingwhich does not rely upon oligopolistic market structure or legalmaxima to the interest rate, which is consistent with rational behavioralong the lines of economic self-interest, and which is permanentrather than temporary in its effect for so long as the general creditsituation which occasions it lasts. The implications of the analysisextend to any credit transaction. However, the institutional influ-ences which have conditioned my thinking are those of commercialbanks, so there may be some special assumptions imbedded in theapproach of which I am not aware. The reader may wish to remindhimself of this occasionally.

II. THE INFLUENCE OF CREDIT RISK ON LOAN PAYOFFThe attractiveness of a loan or investment to a lender dependsupon various factors: the interest rate, risk, possible benefits of a longterm customer relationship and so on. In this section we focus ourattention upon the interest rate and risk and their expression in aprobability distribution of possible payoffs which is logically impliedby the yield-risk features of ally loan or investment.3 We shall see2. For an otherwise suggestive treatment of credit rationing as an aspect oflenders' attitude toward risk which fails exactly at this stage in the argument seeIra 0. Scott, "The Availability Doctrine: Theoretical Underpinnings," The Reviewof Economic Studies, XXV (Oct. 1957). The dependence of Scott's solution oninterest ceilings is stated in fn. 4, p. 46.3. Note that all features of a loan including customer relationship can ulti-mately be reduced to the dimensions of a payoff distribution in an appropriatedynamic analysis. I have not attempted this in the present static analysis.However, this consideration signifies that the logic of rational lender behavior is


4/22

260 QUARTERLY JOURNAL OF ECONOMICSthat the yield and risk aspects of an investment are systematicallyinterrelated and can be varied relative to each other by the borroweronly within specific limits. In particular, given the credit rating ofthe borrower, risk of loss is an increasing function of the size of theloan while the expected value of possible gains and losses (as ameasure of yield under risky conditions) is an increasing function ofthe amount the borrower promises to repay (inclusive of interest).However, the influence of the borrower's credit rating sets an upperlimit to the expected value of the payoff while no such limit appliesto the expected loss. These conclusions follow logically from somefairly simple and intuitively reasonable stipulations concerningborrower capacity to pay.The purpose of this section is to establish the logical basis forthese conclusions. Their implications for lender behavior and forborrower access to credit are explored in Sections II and III. Areader who is prepared to accept these conclusions as intuitivelyconvincing can save time and effort by skipping at this point toSection II. The balance of the present section is for skeptics.Suppose that a lender has applied the techniques of creditanalysis to the financial affairs of a potential borrower and hassummed up his (the lender's) confidence in the borrower's capacityto pay various dollar amounts by assigning to each potential payment,(y), a number between zero and one to represent the probabilitywhich the lender associates with the event that the borrower wouldpay exactly that amount if he promised to do so. This informationon the probability of the borrower's capacity to pay various hypo-thetical sums can be summarized in the form of a mathematicalfunction. Let +(y) be the probability that the borrower will be ableto pay the amount y. Some very general restrictions on the natureof 4 can be suggested. Since it is certain that the borrower can paynothing if he makes this promise, q5(0) = 1. The consideration thatthe financial resources of a specific borrower are not unlimited implies+(y) = 0 for y sufficiently large. Moreover, it seems reasonable toassume that 4(y) is nonincreasing (the probability of repaymentshould not increase with the size of the amount promised) and con-tinuous as well as differentiable for most y. Further, for a range ofsmall y values, 4 (y) may be close to 1. There are infinitely manyfunctions having these properties. The general appearance of suchfunctions is illustrated in Figure I.morebroadlyencompassed n the presentdiscussion than might appear to be thecase in view of the omission of customerrelations, maturities and other dynamicconsiderations.


5/22

CREDIT RISK AND CREDIT RATIONING 261For any y on Figure I we can read off the probability that thelender attaches to the event that the borrower would pay exactlythat y should he promise to do so.4 Let s be the amount that theborrower promises to pay. The lender's attention will be confinedexclusively to s only if ?>(s) = 1. For ?>(s) < 1 the actual payoff

0 ( m y )

I .00

? FIGURE Imay be less than s. Assume that the borrower pays s if he is ableand otherwise pays the greatest amount which he can. Let Y be theamount the borrower actually pays. This is a random variable. Thecumulative distribution function of Y is:

P(Y -< y) 1 - (y), y < s.P(Y = s) = C(s).4. The function, 0, is assumed to be independent of the size of the borrower'spromise to pay and of the size of the loan granted. There must be many instanceswhere this is reasonable, although there may be other situations for which one orboth of these assumptions would have to be dropped.


6/22

262 QUARTERLY JOURNAL OF ECONOMICSThe appearance of this distribution function is illustrated in Figure II.The probability P(Y ? y) is nondecreasing in y, and at y = s jumpsto 1 if it has not already reached 1 (since the borrower will never paymore than s).If 0(y) is almost everywhere differentiable for 0 < y < s, the

P(Yay)

1.00

I~~~

l

0 SFIGURE IIprobability distribution of Y can be given by the density -+'(y) ono < y < s, together with the non-zero probability on s:

bP(a < Y < b) = f - 4V(y)dy, 0 < a < b ? sa

P(Y = s) = c/s).The appearance of this density is shown in Figure III. Thus theprobability that Y lies between any two limits less than s and equal


7/22

CREDIT RISK AND CREDIT RATIONING 263to or greater than zero is shown by the area under the curve, whilethe probability that Y equals s is simply q>(s).To understand the reason for our next step we must pause toconsider what aspects of the payoff function associated with a borrow-er's promise to pay a particular sum the lender may regard as relevant.One way to summarize the payoff function is to calculate its expected

- 0 ' ( y )

O S y~~~~~0 FIGURE IIIs y

value. There is, however, considerable cogency to the view oftenexpressed in the literature concerned with the analysis of risky choice,that the lender (investor, gambler) faced with such a payoff distribu-tion may not be indifferent to the dispersion of the distributionaround its expected value. Frequently some such measure of dis-persion as the standard deviation or variance of the payoff distribu-tion has been utilized to illustrate the influence of dispersion on theutility of risky choices. Either of these measures is acceptable.However, to emphasize the asymmetrical influence of payoffs whichimply gains versus those which imply losses, I prefer to use a measure


8/22

264 QUARTERLY JOURNAL OF ECONOMICSof the expectedvalue of probableosses to be definedbelow. Accord-ingly, we shall proceedon the assumption that the aspects of thepayoff distribution which the lender regardsas relevant are theexpected value of the entire distributionand the expectedvalue ofthe probablelosses. The use of these measuresis intended to besuggestiverather than definitive.EY

,~~~~~~~~0 FIGUREIV

The expectedvalue of the payoff distributiondependsupon the4,function(illustrated n FigureI) and s, the promiseto pay madeby the borrower. The expectedvalue of Y iss

EY = sP(Y = s) + f - yq$'(y)dy0

8= fo(y)dy usingintegrationby parts.0


9/22

CREDIT RISK AND CREDIT RATIONING 265The derivative of the expected value with respect to s is

d EY=4+(s).dsAccordingly, for a 4 function similar to that in Figure I, the expectedvalue of the payoff increases with s at a decreasing rate and approachesa limiting value. This functional relationship between EY and s isillustrated in Figure IV.EZ

a 1

a ,a o

I ~~~~0l0 a a1

FIGURE VA loss occurs when the payoff is less than the amount of the loan

given the borrower. If the amount loaned is a and the amount paidis Y, the loss Z isZ = Oif Y > aZ = a - Yif Y


10/22

266 QUARTERLY JOURNAL OF ECONOMICSand the size of the loan (a) made by the lender. Thus,a a

EZ = f (a - y)[-4'(y)]dy =a - f 4(y)dy, a < s0 0EZ = a - f q(y)dy, a > s.

0 EYa

a~~~~~~~~~~~a

EZaFIGURE VI

Normally the lender will not make loans when a > s, but it is usefulto have EZ defined for that possibility to facilitate certain diagram-matic treatment below. It may be useful to point out that anincrease in s after s = a does not affect EZ although it does increaseEY until /(y) = 0. This is apparent from the fact that the payofffunction depends only on the 4 function and s. Thus, for any


11/22

CREDIT RISK AND CREDIT RATIONING 267specific a, say a,, EZ declines as s increases from zero to a and there-after remains constant for further increases in s as in Figure V.

III. IMPLICATIONSORLENDERBEHAVIORNDBORROWERCCESS OCREDITWe turn now to the implications of our analysis for lenderbehavior and borrower access to credit. From the relationships dis-cussed thus far it is possible to determine the various combinationsof expected value of payoff (EY) and expected loss (EZ) which con-front a lender who considers making various size loans (a) in response

to various promises to pay (s) on the part of a specific borrower.The derivation of this information is described in Figure VI. Thenortheast quadrant is identical to Figure IV except that EY for eachs has been replaced by for each s and a. Since EY increases with sauntil k(y) = 0, - increases similarly with s for each value of a. Theasoutheast quadrant of Figure VI is identical with Figure V exceptthat EZ has been replaced by EZ and possibilities for an additionalaloan (a,) have been included.5 Dividing EY and EZ by the relevant asimply serves to emphasize the relationship of expected value andexpected loss to the dollar amount of the loan. These are essentialrelationships when we come to consider the ability of the borrowerto meet competitive market terms. The northwest quadrant ofFigure VI shows the achievable combinations of EY and EZ for differ-a aent loans (a) and promises to pay (s) for a borrower whose creditrating, (/ function), has been determined. The southwest quadrantis simply a means to transfer the EZ values from the lower half of theavertical axis to the left half of the horizontal axis.To have this information on our borrower's capacity to demandin a form more convenient for purposes of relating it to the terms uponwhich the lender offers credit we shall now transfer it to Figure VIIwhich is one of the key figures in our analysis. In Figure VII combi-nations of and EZ which a particular borrower can attain by vary-a a

5. The ratio - for any a is 1 when s is zero.a


12/22

268 QUARTERLY JOURNAL OF ECONOMICSing his promise to pay (s) are shown as the locus of points along thevarious loan curves labeled aj (where j = 0 ... n). Variations in sare implied but not explicitly shown in Figure VII. However, therelevant value for s can be ascertained by inserting the EY, EZ, co-or-a a

EY va MlSI%~~~

/110A / A SEa)I i% '

EY '~~ ' 1001 EY

\a \

0 EZ aFIGURE VII

dinates of any point on Figure VII into Figure VI and reading off theresulting required values for s. The curve labeled (s = a) whichslopes downward to the right is the locus of minimum expected lossesat associated minimum values of EY for loans of different amounts.If there is any risk (4(y) < 1), the expected value at (s = a) is


13/22

CREDIT RISK AND CREDIT RATIONING 269always less than (s = a), that is EY < 1. Moreover, EY for (s = a)a adecreases as (s = a) and associated EZ increase. Therefore, thelocus of minimum EZ and associated EY values falls further belowa athe line - = 1 as (s = a) increases. The maximum - attainablea a

S-0D S2 SIa a

r2 -o .I I~~~~~~~~~~~DJ

decla0 a a2FIGURE VIII

dEYby the prospective borrower for any a occurs when ~~becomes zero.dsThis maximum ratio for -Y (shown by MM' in Figure VII) alsoadeclines as a increases.Our next step is to introduce the borrower's demand schedulewhich expresses his willingness as distinguished from his capacity tomeet the terms which the lender may require. The borrower's demandschedule appropriate to Figure VII is easily derived from a conven-


14/22

270 QUARTERLY JOURNAL OF ECONOMICStional demand schedule for loanable funds.6 Suppose our borrower'sconventional demand schedule is that shown by DD' in Figure VIII.(The reader is asked to ignore the supply schedules in Figure VIIIfor the present.) This schedule relates the size of the loan (a) whichthe borrower will want to the contract rate of interest (r) charged.But r = a . Therefore, any pair of (r, a) from the demand sched-aule of Figure VIII implies a specific value for s, the borrower's promiseto pay. Given specific values for s and a, specific values for EY andaEZ are likewise determined. Thus, the borrower's conventionalademand schedule is readily translated into terms of - and EZ anda acan be represented on Figure VII. In making the translation onerestriction must be observed. No matter how high the value forr = s a to which the borrower will agree, the upper limit to theacorresponding value for EY is determined by the borrower's creditarating (the q function). This limit is represented in Figure VII bythe curve MM'. Therefore, the borrower's effective demand cannotrise above MM'. The demand schedule of Figure VIII translatedinto terms of Figure VII is shown by the dotted curve DD'. Althoughthe borrower might well wish to take larger loans at combinations ofEY and EZ lying below and to the left of the lower end of the demanda aschedule in Figure VII, the lender will never lend at such terms(unless he is an avid gambler with little regard for odds), since theyare always inferior to holding cash for which EY = 1 and EZ = o.7a aThe terms upon which the lender is willing to lend are shown bythe supply curves (labeled S83; j = 0 ... n) in Figure VII. Onlyone such SS, curve is in effect at any one time. We shall now examinethe factors which determine the shape and position of these SiS curvesas well as which curve is operational at a particular time. Thesefactors include the subjective preferencesof the lender for yield versus

6. We shall not explore the analytical determinants of borrowerdemandunder risk and uncertainty, although this would improve the symmetry of thediscussion.7. This statement ignores price changes in the markets for goods andservices.


15/22

CREDIT RISK AND CREDIT RATIONING 271risk of loss, the terms upon which he can exchange risk of loss foryield as established by market conditions (i.e., borrower demand andcompeting supply), his total supply of investable funds, and hisliability position which must be related to his asset position beforethe implications of his asset position for yield and risk can be deter-mined. The influence of a lender's liability position has been neglectedin the formal literature of investment choice. This is not the occasionto attempt to repair this neglect. Perhaps it will be intuitively obvi-ous to the reader that two lenders with different liability structuresmay hold identical collections of assets and yet face quite differentyield-risk situations. The simplest way to handle this problem in thepresent context is to incorporate the effect of the lender's liabilitystructure in his indifference curves. This means, of course, that twolenders with identical subjective attitudes toward risk and yield arelikely to have quite different preference patterns for assets. (Differ-ences in liabilities are probably a far more important cause of differ-ences in institutional asset preferences than the subjective attitudesof institutional managers.) Once we have incorporated the influenceof liability position in the indifference curves, we are entitled to con-centrate on the available asset characteristics and combinations ofassets.The indifference curves (labeled I,, 12, etc.) in Figure IX repre-sent our lender's preference pattern for yield versus risk in his totalasset collection as conditioned by his subjective preferences and hisliability position. Note that Figure IX is intended to represent therisk-yield implications of the lender's total asset position in contra-distinction to the marginal changes in that position caused by a singleborrower as reflected in Figure VII. (Note also, that the alternativerisk-yield combinations of Figure IX do not represent the ultimaterisk-yield position of the lender. For this, the influence of the liabilityposition must be made explicit.) The influence of market conditionsand the volume of total investable resources available to the lenderare represented by what we may call "opportunity curves" labeled01, 02, etc. Only one of the opportunity curves is in effect at any onetime. For given market conditions an opportunity curve can bederived by considering the terms upon which the lender can extendcredit to the various borrowers who seek accommodation.8 On the

8. There is a problemof interdependenceamong payoff functions which Ipropose to ignore. It can be dealt with formally by replacingEZ by the varianceof the payoffdistribution (formathematicalconvenience)forindividual borrowers,introducing covariance measuresbetween different distributions, and followingmethods outlined by Harry Markowitz in "Portfolio Selection," The Journal ofFinance,March 1952.


16/22

272 QUARTERLY JOURNAL OF ECONOMICSconventional assumption that borrowers' demand curves are down-ward sloping and their credit ratings subject to deterioration as theamounts they borrow increase, the slope of the opportunity curvesmust diminish as they extend further to the right. This simplyreflects the fact that the lender must accept less favorable terms toexpand his volume of loans. Moreover, in a competitive market noborrower will pay better than the worst terms.

EEY 10 13 12- 1-'O

A

0 IEZFIGURE IX

Given the opportunity line (borrower demand) the positionsavailable to the lender depend upon the volume of investable resourcesin his possession. This magnitude is not shown explicitly in Figure IX,but its effect is indicated by the solid portion of the opportunity lines.The lender has sufficient investable resources to go out a given oppor-tunity line to the point where the line becomes dashed (- - ).At that point the lender is fully invested (that is, cash is zero) and is


17/22

CREDIT RISK AND CREDIT RATIONING 273powerless to extend additional credit. The optimum risk-yield combi-nation for the lender is shown diagrammatically as the highest indiffer-ence curve attainable (by intersection or tangency) by traveling alongthe solid portion of the existing opportunity line. The optimumpoint in Figure IX will normally be a tangency rather than an inter-section. This follows from the consideration that a lender will usuallyretain some cash for his own transactions and precautionary require-ments. Therefore, his fully invested position (cash = zero) willhave to be further out on the relevant opportunity line than hisoptimum position. But this implies a tangency optimum. However,an intersection optimum is possible if the lender is restrained fromreducing his (as he regards it) surplus cash because of a minimumcash requirement imposed by law or regulatory authority.In a competitive market our borrower must pay the going ratefor funds. Let A (where A = 2aj and j = 1 ... n) represent totalearning assets of the lender. Then ZEY at (or in the neighborhood of)~2EZthe optimum point in Figure IX are the EY terms which our borrowermust meet to qualify for a loan.The loans and terms available to the particular borrower towhich Figure VII applies are shown by the relevant SSj curve on thatdiagram. Let us suppose that the tangency optimum in Figure IXestablishes SS as the operational supply curve in Figure VII.9 Thenour borrower is able to qualify for any loan between zero and ai.Given supply curve SS, our borrower cannot qualify to borrow morethan a, because his credit rating (?>function) does not warrant alarger loan at market terms. Assuming s > a, the loan requestedcarries with it an irreducible risk of loss indicated by the location withEZrespect to the - axis of the vertical portion of the respective a curve.aThe maximum EY or EY which the borrower can generate to offsetathat irreducible risk also is a function of the q5 unction (and s). Thus,the area of effective borrower demand is bounded by the MM' curve,

9. If the optimum in Figure IX occurs at an intersection rather than atangency (due to an imposedminimum cash requirement)the relevantSS'j curvein Figure VII will intersect the vertical axis at a point where- > 1 since theamarginal utility of available additional loans will exceed the marginal utility ofcash to the lender.


18/22

274 QUARTERLY JOURNAL OF ECONOMICSthe relevantSS' curve,and the vertical axis. Clearly,as changes nthe optimumpoint on FigureIX causethe operationalSS' curveofFigure VII to rotate (or shift) northwest,our borrower's bility toqualifyfor loansis steadily andinescapablydecreased. In particular,the maximum oanforwhicha particularborrower anqualifydeclinesas the minimumqualificationsn termsof EY/a and EZ/a increase.If the borrower'swillingnesso demand allsshortof his capacity,theloan agreedupon is shown by the intersection of SS' and DD' inFigureVII.It is instructive o lookat the analogueof the supplyanddemandcurves of Figure VII in conventionalsupply and demand terms.Since we alreadyhave the demandequivalent n FigureVIII we needonly translatethe supplycurves of FigureVII into their equivalentexpression n FigureVIII. This is readilydone by translating the- and a values of points locatedon a supply curve of FigureVIIainto their interestrate and a equivalent for the particularborrower.Givena andD, the s requiredof the borrower an be readfrom theanortheastquadrantof FigureVI thus determiningr = Theaconventional upplycurvesanalogous o the two-dimensionalupplycurves SS', SS and SS' in Figure VII are identically labeledinFigure VIII. It must be emphasized hat these conventionalsupplycurvesof FigureVIII are specificto one particularborrower or, atleast, one particular4 function). Wemay note that supply curveSS'in Figure VIII is interest-elasticboth above and below its inter-section with DD'; the borrowercould obtain additionalfunds if hewerewillingto increasehis promise o pay, (s). At a2,however,SS'becomes otally interest nelastic. Theborrower's apacityto borrowhas reached ts limit. ShouldSS' replaceSS', our borrowerwouldfind himself borrowingat absolute capacity at a,. He would bepowerless o borrowmore,sincehis creditratingwouldpreventhimfrom increasingEY to compensatethe lender for the unavoidableincrease n EZ whichwouldaccompanyan increase n a. A furthershift to SS' in FigureVIII wouldfurtherreducethe maximum oanavailable to the borrowerroma, to ao. The usual interpretationofthe intersection of DD' and SS' leads to the erroneousconclusionthat the contractrate of interestfor aois rl. In fact, however,thecontractratefor a0 s r2. Therearetwo reasons orthis. Theborrowerwill receivea0eitherby promising i orr2and,hence,willpromise he


19/22

CREDIT RISK AND CREDIT RATIONING 275lesser, r2. The lender, thinking in terms of - and - for ao, willa aregard hesevalues asidentical orratesr, and r2andwillbeindifferentbetweenthe two contract rates of interest.Whenever he borrower's emandcurve ntersectswith a verticalportionof the relevantsupply curve, the particularborrowerwill beunable to obtain additionalborrowedfunds by promisingto payadditional nterest. Moreover,as the supplycurveshifts to the leftandupward, he borrowerwillencounterprogressivelymorestringentrestrictionson the supply of fundswhich he will be unableto over-come by offering o pay moreinterest. However,anotherborrowerwith a superiorcreditrating(/ function)may continueto be abletoborrowas much as he wishesand even may not be required o paymuch additionalinterest to meet the higher qualificationsmposedby the lender. The borrowerwith the inferiorcredit rating willregard"availability"as moreimportant han interestin determininghis access to borrowed unds.It is this combinationof circumstanceswhich has come to beknown as "credit rationing." Clearly, however, the "rationing"involvedhere is quite a differentphenomenon rom that associatedwitha regulatedceilingprice. Twopointsofdifferencemaybeempha-sized. First, the lenderis not denyinghimself (or being denied)anadvantage(higher nterest)which he normallyseeks,but is behavingrationallyin the face of risk. Second,the supply of loanablefundsto someborrowers emains nterest-elasticeven afterbecomingcom-pletely inelasticto others. In this connectionwe may note that thelender's ndifference urvesin Figure IX as well as the supplycurvesin Figure VII retain their elasticity even after credit is rationed.Indeed, since there is always the "unsatisfied ringe of borrowers,"to makecreditrationingdependupon nterest nelasticsupplywithoutdistinguishing among differentborrowerswould make our theorycontradict he empirical videncethat therearealways someborrow-ers who can obtain additional accommodationat higher rates ofinterest.

IV. THE CENTRAL BANK'S INFLUENCETherearenumerousopics inmonetary heorywhichcanusefullybe exploredfrom the vantage point we have now reached. In theinterests of brevity I shall confinemy remarks o establishingthatcentralbankpolicycanalterthe locationof the optimum n FigureIXand, hence, the termsavailable to the individualborrowern FigureVII or VIII. Then I shall comment on the implications of this


20/22

276 QUARTERLY JOURNAL OF ECONOMICSprocessfor the ability of the centralbank to restrictcreditwithout"excessive" ncreases n the effectiverate of intereston governmentbonds.Suppose the lender, a commercialbank, happens to be at anoptimumpoint P1 in FigureIX. Now imaginethat the centralbankraisesreserverequirements. This has no initial effect on the marketvalue of the bank's total assets (its wealth position), but it doesrequire the bank to sell some earning assets to increase its cash(includingreservebalances). Threeeffects follow: (1) the volume ofearningassets whichthe bankcan holdis reduced: t must move backalongthe opportunitycurvetoward the origin; (2) to the extent thatthe sale of bank assets to replenishits cash position reduces assetprices, nterestratesareraisedand a new opportunitycurve(say02)is created with slope higher than the original opportunitycurve;(3) to the extent that interestrates rise andassetprices all themarketvalue of the bank's total resources alls; since the value of its totalliabilities (principallydeposits) remains virtually unchanged, it isnow in a more risky position than before. In Figure IX such anincrease n risk has to be shownby an increase in the slopes of theindifference urvessuch as representedby 1o. All these effects rein-forceeach otherto producea new optimumpoint in FigureIX (sayEYat P2) forwhich the ratio E perdollarloaned orinvested s higher hanbefore. This is equivalent to moving to a highersupply curve inFigures VII and VIII and thus to requiringhigherterms from theborrower.

A similar chain of consequencesfollows central bank sale ofgovernmentsecuritiesin the open market. If our bank is typical,this actionwillboth reduce ts reservebalancesandits depositliabili-ties. The net effectwill be to reduce ts cash positionand henceitsliquidity by a greater proportionthan its liabilities and hence toincreaserisk. This will steepen the slopeof the indifference urves nFigureIX at the sametime that it reduces otal investableresources.Moreover, he sale of government ecuritiesby the centralbankwillhave raised nterest rates anddepressedasset values. This raises theslope of the opportunity ine and reinforces he declinein investable(indeed, total) resources n the hands of the bank. Onceagain theratioEY per dollar oaned orinvestedwill be higherat the new opti-mumthan at the old and termsto borrowerswill have risen.


21/22

CREDIT RISK AND CREDIT RATIONING 277What insight does this analysis permit into the ability of thecentral bank to restrict credit expansionwithout, or with only amodest,risein interestrates on government ecurities? Clearly,any

restrictiveaction by the central bank, ceterisparibus,must producesomerisein interestrates on government ecurities,althoughthe risemay be almost imperceptiblef conditionsarefavorable. The extentof the risein interestwhichmust accompanya given degreeof creditrestrictionwill depend upon the characterand compositionof aggre-gateborrower emand. Thelarger he proportionof marginalborrow-ers in the aggregatedemand (those who do not wish or are unable toraiseEY when terms increase) the more effectivelywill credit berestricted or a given rise in intereston governmentsecurities. Thelargerthe proportionof determinedprime borrowers he greater thereliancethat will have to be placedon interest rationingas opposedto credit rationingto restrict credit. Of course,the higherinterestrates go, the morenumerousare the borrowerswho becomemarginalin terms of credit rationing (risk considerations)regardlessof theirwillingnessto commit themselves to higher interest charges. Ulti-mately every borrower s limited by his capacity rather than hiswillingness. Accordinglyhe higher nterestrates go, the moreperva-sive will become the influence of credit rationing. More and moreborrowerswill findthat "availability" atherthaninterestdeterminestheir access to credit. Indirectly this will affect even the primeborrowers, ince the marketsthey sell in are dependenton effectivedemandand this may come to be stronglyinfluencedby the restric-tions that creditrationingplaces on their customers.'The rise in interestrates that accompaniescredit restriction(orincreasein borrowers'demand with money supply constant) can,of course,be restrainedby the presenceof interest ceilings, eitherthose which aredue to the oligopolistic tructureof creditmarkets orthosedue to usurylaws. Thepresenceof suchceilingswill accentuatethe non-pricerationing of credit. However, the credit rationingoccasionedby suchceilings asts only so longas the ceilingsaremain-tained. (Usury ceilingsmay be presumed o last longerthan oligopo-listic ceilings, but most corporateborrowersare exempt from usury

1. Note that if the centralbank tightens credit with memberbank reservesconstant, for example by buying short term government securities and sellinglong terms, it may exercise its influence directly on the velocityrather than thevolume of the money supply, since it may impede the transferof idle to activebalanceswhile leaving money supply unchanged.


22/22

credit risk and credit rationing

Documents