Borrower-Lender Distance, Credit-Scoring, and the Borrower-Lender Distance, Credit-Scoring, and the Performance of Small Business LoansPerformance of Small Business Loans

Robert DeYoungRobert DeYoungFederal Reserve Bank of Chicago *Federal Reserve Bank of Chicago *

Dennis GlennonDennis GlennonOffice of the Comptroller of the Currency *Office of the Comptroller of the Currency *

Peter NigroPeter NigroBryant UniversityBryant University

presented atpresented atFDIC/JFSR annual conferenceFDIC/JFSR annual conference

Arlington, VA — September 22, 2005Arlington, VA — September 22, 2005

* * The views expressed here are those of the authors, and are not necessarily those The views expressed here are those of the authors, and are not necessarily those of the Federal Reserve Bank of Chicago, the Federal Reserve System, the Office of the Federal Reserve Bank of Chicago, the Federal Reserve System, the Office

of the Comptroller of the Currency, or the U.S. Treasury Department.of the Comptroller of the Currency, or the U.S. Treasury Department.

Average Distance between Borrower-Lender(SBA 7(a) Loans)

0

100

200

300

400

1983 1986 1989 1992 1995 1998 2001

year originated

mil

es (

mea

n)

The distance between small business borrowers and their lenders has increased substantially in the past decade.

MotivationMotivation

The distance between small business borrowers and their lenders has increased substantially in the past decade.

– Is increased distance anathema to relationship lending?

– Does increased distance require new lending technologies?

– Does increased distance affect loan performance?

A growing literature: Cyrnak and Hannan (2000), Stein (2001), Petersen and Rajan (2002), Brevoort and Hannan (2004), Dell-Ariccia and Marquez (2005), Berger, Frame, and Miller (2005), etc.

MotivationMotivation

The distance between small business borrowers and their lenders has increased substantially in the past decade.

– Is increased distance anathema to relationship lending?

– Does increased distance require new lending technologies?

– Does increased distance affect loan performance?

A growing literature: Cyrnak and Hannan (2000), Stein (2001), Petersen and Rajan (2002), Brevoort and Hannan (2004), Dell-Ariccia and Marquez (2005), Berger, Frame, and Miller (2005), etc.

We construct a theoretical model of how borrower distance and lending technology affects loan supply and loan performance.

We test empirically the loan performance predictions using data on 29,577 SBA 7(a) loans originated in 1984-2001.

MotivationMotivation

We adapt a theory model from Heiner (1983, 1985, 1986).We adapt a theory model from Heiner (1983, 1985, 1986).

Lenders have Lenders have imperfect informationimperfect information about the creditworthiness about the creditworthiness of loan applicants (i.e., standard risky loan outcomes).of loan applicants (i.e., standard risky loan outcomes).

— Borrower-lender distanceBorrower-lender distance is our proxy for information imperfection. is our proxy for information imperfection.

Lenders have Lenders have imperfect abilityimperfect ability to make the correct accept/reject to make the correct accept/reject decision (i.e., they make both Type I and Type II errors).decision (i.e., they make both Type I and Type II errors).

— Credit scoringCredit scoring is our proxy for decision-making ability. is our proxy for decision-making ability.

MotivationMotivation

We adapt a theory model from Heiner (1983, 1985, 1986).We adapt a theory model from Heiner (1983, 1985, 1986).

Lenders have Lenders have imperfect informationimperfect information about the creditworthiness about the creditworthiness of loan applicants (i.e., standard risky loan outcomes).of loan applicants (i.e., standard risky loan outcomes).

— Borrower-lender distanceBorrower-lender distance is our proxy for information imperfection. is our proxy for information imperfection.

Lenders have Lenders have imperfect abilityimperfect ability to make the correct accept/reject to make the correct accept/reject decision (i.e., they make both Type I and Type II errors).decision (i.e., they make both Type I and Type II errors).

— Credit scoringCredit scoring is our proxy for decision-making ability. is our proxy for decision-making ability.

Theory predicts that loan default increases with loan subsidies Theory predicts that loan default increases with loan subsidies and geographic distance -- and perhaps with credit scoring.and geographic distance -- and perhaps with credit scoring.

We find empirical support for these predictions in the data.We find empirical support for these predictions in the data.

MotivationMotivation

S represents states of nature regarding loan performance.

X represents information available to lender about S.

TheoryTheory

S XS

Imperfect Information

S represents states of nature regarding loan performance.

X represents information available to lender about S.

Actions and indicate loan approval and denial, respectively.

TheoryTheory

S XS A( or )

Imperfect Information Imperfect Decision-Making

S represents states of nature regarding loan performance.

X represents information available to lender about S.

Actions and indicate loan approval and denial, respectively.

Lender knows the following:Lender knows the following:

– gg is the gain from correctly choosing is the gain from correctly choosing ..

– ll is the loss from is the loss from inincorrectly choosing correctly choosing ..

– ppss is the unconditional probability that is the unconditional probability that is correct choice. is correct choice.

TheoryTheory

S XS A( or )

Imperfect Information Imperfect Decision-Making

TheoryTheory

Lender selects Lender selects if expected gain > expected loss: if expected gain > expected loss:

ppss rXB

gg > (1-p > (1-pss) ) wXB

ll

Where:

– rXB is the joint probability that the lender makes the right choice given

the imperfect information in her possession.

– wXB is the joint probability that the lender makes the wrong choice

given the imperfect information in her possession.

TheoryTheory

Lender selects Lender selects if expected gain > expected loss: if expected gain > expected loss:

ppss rXB

gg > (1-p > (1-pss) ) wXB

ll

Where:

– rXB is the joint probability that the lender makes the right choice given

the imperfect information in her possession.

– wXB is the joint probability that the lender makes the wrong choice

given the imperfect information in her possession.

Rearranging, a lender selects Rearranging, a lender selects if: if:

rrXBXB // wwXBXB

> (l> (l)(1-p)(1-pss) / (g) / (g)(p)(pss

) )

(Joint Reliability Ratio) > (Minimum Performance Bound)(Joint Reliability Ratio) > (Minimum Performance Bound)

TheoryTheory: Predictions: Predictions

loan supply default rate

for a singlelender

Better expected profits(e.g., subsidies or scale economies)

+ +

Greater information uncertainty(e.g., borrower-lender distance)

— 0

Improved decision-making ability(e.g., credit scoring)

+ 0

TheoryTheory: Predictions: Predictions

loan supply default rate

for a singlelender

for a cross-sectionof lenders

Better expected profits(e.g., subsidies or scale economies)

+ + +

Greater information uncertainty(e.g., borrower-lender distance)

— 0 +

Improved decision-making ability(e.g., credit scoring)

+ 0 —

SBA loans: Random sample of 29,577 SBA 7(a) loans originated by 5,535 unique lenders between 1984 and 2001:

– Firms are “small” and unable to access financing through other means at similar terms.

– Lenders must find the borrowers and underwrite, monitor and service the loans within SBA program guidelines.

– SBA shares losses losses pro ratapro rata with lender. (Banks have incentives to with lender. (Banks have incentives to screen for creditworthiness and set appropriate rates and terms.) screen for creditworthiness and set appropriate rates and terms.)

– Fairly active secondary market for guaranteed portions.

Credit scoring data: Atlanta Fed survey of 200 largest U.S. bank holding companies taken in 1998.

Other data: Call Report; Summary of Deposits; Haver.

Data sourcesData sources

Loan default: Lenders can exercise the SBA guarantee when a Lenders can exercise the SBA guarantee when a loan is in arrears for 60 days or more.loan is in arrears for 60 days or more.

Borrower-lender distance is the straight-line distance between borrower address and lending office address.

Credit-scoring is a dummy variable equal to one if lender was an affiliate of a credit-scoring institution, based on Atlanta Fed survey data. (See Frame, Srinivasan, and Woosley, 2001).

Government subsidy is the percent SBA guarantee rate which varies over time and across loans.

Four main variablesFour main variables

Average Distance between Borrower-Lender(SBA 7(a) Loans)

0

100

200

300

400

1983 1986 1989 1992 1995 1998 2001

year originated

mil

es (

mea

n)

1996

Distance increased during late 1990sDistance increased during late 1990s

Median borrower-lender distance for SBA 7(a)small business loans originated in each year.

Banks that credit-scored small

business loans

Non-scoringbanks

1995 11.96 miles 8.25 miles1996 15.88 8.811997 18.80 9.551998 57.64 9.361999 40.48 10.772000 103.37 10.662001 142.34 12.03

Increased distance associated with credit-scoring lendersIncreased distance associated with credit-scoring lenders

Government policy can provide incentives for lenders to make riskier loans at the margin....

....but this does not appear to be driving increased distance, as the average SBA 7(a) subsidy rate declined in recent years.

Average SBA guarantee %1995 86.3%1997 77.7%1999 70.7%2001 69.7%

SBA subsidies declined during late 1990sSBA subsidies declined during late 1990s

A discrete time hazard model (“stacked logit”) of loan default:

Pr[Di(t)=1] = F { SBA%i, lnDISTANCEi, SCORERij,

lnDISTANCEi*SCORERij, Z } + ei

– Di(t)=1 indicates loan i defaults at time t.

– SBA% = percent of loan i principal guaranteed by SBA.

– lnDISTANCE = the log of borrower-lender distance (miles).

– SCORER = 1 if lending bank j uses scoring models.

– Z = controls: lender, borrower, and loan characteristics; macroeconomic conditions; and competitive factors.

– F is the logistic cumulative distribution function.

Empirical modelEmpirical model

SAVE THE DATE!SAVE THE DATE!May 17-19, 2006May 17-19, 2006

Defaults increase with loan guarantees. (Expected profits increase, so banks approve marginal loan applications.)

Defaults increase with distance. (Increased information uncertainty.)

Defaults increase with credit scoring. (Distance held constant, the dominant effect of credit scoring is enhanced lender profit functions.)

Scoring mitigates distance effects. (SCORER*lnDISTANCE < 0.)

Results consistent with theory (Table 3, column 1)Results consistent with theory (Table 3, column 1)

Coeff. Chi Sq.

SBA% 0.5633 0.0055

lnDISTANCE 0.0413 0.0001

SCORER 0.3409 0.0003

lnDISTANCE*SCORER -0.0544 0.0184

a 10 percentage point increase in %SBA 5.6% increase in loan default probability.

a doubling of distance (for non-scoring banks) 2.8% increase in loan default probability.

a doubling of distance (for scoring banks) 1.1% decrease in loan default probability.

adopting credit scoring 22.1% increase in loan default increase in loan default probabilityprobability..

Economic effects are non-trivial (marginals)Economic effects are non-trivial (marginals)

Alternative definitions of SCORER and DISTANCE.

Sub-sampling by time period, loan size, and lender size.

Robust standard errors that allow for intra-group correlations or “clusters” (e.g., across loans or lenders).

Some results worth mentioning:– Impact of DISTANCE declines over time.

– Impact of SBA guarantee is weaker at small lenders.

– Impact of SBA guarantee is stronger for small loans.

Results are robust to the following tests....Results are robust to the following tests....

Theoretical model: Substantial empirical support for theoretical predictions for loan default. (Hypotheses for loan supply are not tested here.)

Distance: More distant borrowers are more difficult to screen and monitor.

Continued role for local banks and/or “local banking.”

Credit scoring: Helps offset distance problems, but primary effect may be on the profit function. (Implied) expanded loan supply. Higher default rates are inconsistent with relationship lending.

Government loan guarantees: (Implied) expanded loan supply, but are higher default rates efficient? As SBA moves off-budget, can it remain viable (e.g., use scoring to reduce expenses) but keep serving “opaque” small firms?

Conclusions and ImplicationsConclusions and Implications

Borrower-Lender Distance, Credit-Scoring, and the Borrower-Lender Distance, Credit-Scoring, and the Performance of Small Business LoansPerformance of Small Business Loans

Robert DeYoungRobert DeYoungFederal Reserve Bank of Chicago *Federal Reserve Bank of Chicago *

Dennis GlennonDennis GlennonOffice of the Comptroller of the Currency *Office of the Comptroller of the Currency *

Peter NigroPeter NigroBryant UniversityBryant University

presented atpresented atFDIC/JFSR annual conferenceFDIC/JFSR annual conference

Arlington, VA — September 22, 2005Arlington, VA — September 22, 2005

* * The views expressed here are those of the authors, and are not necessarily those The views expressed here are those of the authors, and are not necessarily those of the Federal Reserve Bank of Chicago, the Federal Reserve System, the Office of the Federal Reserve Bank of Chicago, the Federal Reserve System, the Office

of the Comptroller of the Currency, or the U.S. Treasury Department.of the Comptroller of the Currency, or the U.S. Treasury Department.