# Presentation: 546033

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

Robert DeYoung
Federal Reserve Bank of Chicago *
Dennis Glennon
Office of the Comptroller of the Currency *
Peter Nigro
Bryant University

presented at
FDIC/JFSR annual conference
Arlington, VA — September 22, 2005

- Robert DeYoung
- Federal Reserve Bank of Chicago *
- Dennis Glennon
- Office of the Comptroller of the Currency *
- Peter Nigro
- Bryant University
- _presented at_
- FDIC/JFSR annual conference
- Arlington, VA — September 22, 2005

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

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

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

- _Motivation_

## 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.  

- 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.

- _Motivation_

## 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.

- 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.

- _Motivation_

## We adapt a theory model from Heiner (1983, 1985, 1986).
Lenders have imperfect information about the creditworthiness of loan applicants (i.e., standard risky loan outcomes).
Borrower-lender distance is our proxy for information imperfection. 
Lenders have imperfect ability to make the correct accept/reject decision (i.e., they make both Type I and Type II errors).
Credit scoring is our proxy for decision-making ability.  

- Lenders have _imperfect information_ about the creditworthiness of loan applicants (i.e., standard risky loan outcomes).
- _Borrower-lender distance_ is our proxy for information imperfection.
- Lenders have _imperfect ability_ to make the correct accept/reject decision (i.e., they make both Type I and Type II errors).
- _Credit scoring_ is our proxy for decision-making ability.

- _Motivation_

## We adapt a theory model from Heiner (1983, 1985, 1986).
Lenders have imperfect information about the creditworthiness of loan applicants (i.e., standard risky loan outcomes).
Borrower-lender distance is our proxy for information imperfection. 
Lenders have imperfect ability to make the correct accept/reject decision (i.e., they make both Type I and Type II errors).
Credit scoring is our proxy for decision-making ability.  
Theory predicts that loan default increases with loan subsidies and geographic distance -- and perhaps with credit scoring.
We find empirical support for these predictions in the data.

- Lenders have _imperfect information_ about the creditworthiness of loan applicants (i.e., standard risky loan outcomes).
- _Borrower-lender distance_ is our proxy for information imperfection.
- Lenders have _imperfect ability_ to make the correct accept/reject decision (i.e., they make both Type I and Type II errors).
- _Credit scoring_ is our proxy for decision-making ability.
- Theory predicts that loan default increases with loan subsidies and geographic distance -- and perhaps with credit scoring.
- We find empirical support for these predictions in the data.

- _Motivation_

##  S represents states of nature regarding loan performance.
 X represents information available to lender about S.

-  X represents information available to lender about S.

- _Theory_

- S

- X

- S

- 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.

-  X represents information available to lender about S.
-  Actions  and  indicate loan approval and denial, respectively.

- _Theory_

- S

- X

- S

- 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:
g is the gain from correctly choosing .
l is the loss from incorrectly choosing .
ps is the unconditional probability that  is correct choice.

-  X represents information available to lender about S.
-  Actions  and  indicate loan approval and denial, respectively.
-  Lender knows the following:
- g is the gain from correctly choosing .
- l is the loss from _in_correctly choosing .
- ps is the unconditional probability that  is correct choice.

- _Theory_

- S

- X

- S

- A( or )

- Imperfect Information

- Imperfect Decision-Making

## Theory

- Lender selects  if  expected gain  >  expected loss:
- 			ps  rXB  g   >   (1-ps)  wXB  l
- 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.

## Theory

- Lender selects  if  expected gain  >  expected loss:
- 			ps  rXB  g   >   (1-ps)  wXB  l
- 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  if:
- 		      	rXB / wXB   >   (l)(1-ps) / (g)(ps)
-    	       (Joint Reliability Ratio)   >   (Minimum Performance Bound)

## Theory: Predictions 

## Theory: Predictions 

## 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 pro rata with lender. (Banks have incentives to 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.

- _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 *pro rata* with lender. (Banks have incentives to 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 sources_

**Notes:**
We have a random sample of over 32,000 loans made through the SBA’s flagship 7a program.

The 7a program is the primary policy tool in the U.S. for addressing the credit availability concerns of small business
Firms obtaining guarantees must meet the SBA definition of small which varies by SIC code.

  - banks find the borrowers and initiate SBA involvement

Loan guarantees are provided to eligible small firms through SBA qualified lenders.  

We have over 5,500 bank lenders in our sample over the 1984 – 2001.
These lenders select the firms to receive loans, initiate SBA involvement, underwrite the loans within SBA guideines, and monitor/service the ;loans on an ongoing basis.   They report performance back ot the SBA on a quarterly basis. 

In the event of default – lenders and the SBA share losses on a pro rata basis based on the outstanding balance at the time of defualt.  The guarantee can be exercised on any loan in arrears 60 days or more. 
Should note here the SBA is not in a first loss position. 

And tha there is a lot of insitutional detail that we discuss in the paper – including types of SBA approaved lenders and othe runuqie aspects of the program which we don’t have itme to get into detaliu here – but I refer you to the paper.

Historically the guarantee program has been funded by U.S. govt appropriations

## Loan default: Lenders can exercise the SBA guarantee when a 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. 

- _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 variables_

## Distance increased during late 1990s

- 1996

- _Distance increased during late 1990s_

## Increased distance associated with credit-scoring lenders

- _Increased 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.

- ....but this _does not_ appear to be driving increased distance, as the average SBA 7(a) subsidy rate declined in recent years.

- _SBA 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.

- Pr[Di(t)=1]   =   **F** { SBA%i,  lnDISTANCEi,  SCORERij,
- 				   lnDISTANCEi*SCORERij,  **Z **}   +   **e**i
- 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 model_

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

- SAVE THE DATE!May 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.)

- 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)_

**Notes:**
Results from our empirical model are presented in Table 3 and 4 

Consisitent with theory model that bob outlined
1. 

Although loan defaults increase with borrower-lender distance, the adoption of credit-scoring models dampens this relationship.

Transition

## 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 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 probability.

- _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.

- 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...._

## 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? 

- 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 Implications_

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

Robert DeYoung
Federal Reserve Bank of Chicago *
Dennis Glennon
Office of the Comptroller of the Currency *
Peter Nigro
Bryant University

presented at
FDIC/JFSR annual conference
Arlington, VA — September 22, 2005

- Robert DeYoung
- Federal Reserve Bank of Chicago *
- Dennis Glennon
- Office of the Comptroller of the Currency *
- Peter Nigro
- Bryant University
- _presented at_
- FDIC/JFSR annual conference
- Arlington, VA — September 22, 2005

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