Jhr 0302 Quercia 12

Journal of Housing Research • Volume 3, Issue 2 341

Residential Mortgage Default:A Review of the Literature*

Roberto G. Quercia and Michael A. Stegman**

Abstract

For nearly 30 years, the subject of mortgage default has claimed the attentionof scholars, policy analysts, and government officials. During this time, theprincipal purposes of these inquires, their theoretical underpinnings, empiri-cal estimation techniques, and data sources have undergone substantialchange. This article traces our evolving understanding of residential mortgagedefault risk from the early studies to the current literature. Default studiesare divided into three groups: first-, second-, and third-generation studies.The studies vary in three respects. First, each study chooses a perspective fromwhich mortgage risk is analyzed: lender, borrower, or institutional. A secondaspect is the different measures studies use to determine mortgage risk:mortgage interest rate premiums, default rates, delinquency rates, or ex-pected mortgage losses. Finally, studies follow one of two primary researchapproaches, that is, they make either a theoretical or an empirical contribu-tion to the literature. The last section of this article presents an overalldiscussion of the state of residential mortgage default literature and suggestsdirections for future research.

Introduction

Increasing opportunities for homeownership has been a long-term goalin the United States. Today we are a nation of homeowners, with anownership rate of about 64 percent (Apgar 1989). Both governmentagencies and private lenders have played significant roles in helpingfamilies achieve this ideal by making available the necessary mortgagefinancing. Unfortunately, not all mortgages are repaid. Failure to repaymortgage financing (default) varies substantially with the type of loanand borrower (Simons 1990). A desire to gain an accurate understandingof the risk of default represented by loan and borrower characteristics isat the core of the residential mortgage default literature. This article

*The research reported here was carried out with funding from Fannie Mae.

**Roberto G. Quercia is an assistant professor at the School of Urban and Public Affairs,University of Texas at Arlington. Michael A. Stegman is Cary C. Boshamer Professor andchairman of the Department of City and Regional Planning and chairman of Ph.D. curriculumin public policy analysis, University of North Carolina at Chapel Hill.

342 Roberto G. Quercia and Michael A. Stegman

traces our evolving understanding of residential mortgage default riskfrom the early studies to the current literature.

For nearly 30 years, the subject of mortgage default has claimed theattention of scholars, policy analysts, and government officials. Defaultis costly to everybody involved. On the one hand, mortgage default iscostly to lenders and to the federal institutions that guarantee andinsure home mortgages.l Costs to lenders and institutions are incurredwhen the net cash recouped from foreclosure proceedings is less thanthe value of the financial asset. Another cost to lenders is associatedwith the restrictions imposed by regulatory authorities when a historyof loan losses impairs the soundness of those institutions (Giliberto andHouston 1989, p. 56).

On the other hand, default is also costly to borrowers. On an individuallevel, a borrower who defaults is penalized with a lower credit rating,fewer opportunities for future home purchase, and sometimes, evenreduced future employment or advancement opportunities (Gilibertoand Houston 1989). There are also intangible costs to individual borrow-ers, such as emotional distress experienced when they decide to default.Default is also costly to borrowers collectively. When default risks arenot properly understood, lenders charge mortgage interest rate premi-ums to compensate for the above-normal risk represented by borrowerswith certain characteristics.2 In extreme situations, borrowers may bedenied loans altogether because they are residents of areas consideredrisky, regardless of their individual creditworthiness. All of thesesituations make credit more expensive and more difficult to obtain formany families considering a home purchase. A desire to minimizedefault costs to both borrowers and lenders is central in default studies.

Studies have focused on several distinct aspects of the default decision,a fact that reflects the complexity of the mortgage process for bothborrowers and lenders. Typically, borrowers purchase homes withcertain characteristics and in a location to meet their preferences. Homeprices commonly represent several years of annual income, so borrowersput down some fraction of the price in cash in the form of a down paymentand finance the rest by borrowing against future earnings. Smalldifferences in loan characteristics become significant in the resulting

1The Federal Housing Administration provides loan guarantees for residential mortgages.Federal mortgage insurance can be direct, such as that offered by the Department of VeteransAffairs, or indirect, such as that funded by insured deposits or agency securities such as thoseoffered by Fannie Mae, Freddie Mac, and the Government National Mortgage Association.

2This mortgage interest rate premium is the rate of interest above the normal rate; it is chargedto borrowers considered risky.

Residential Mortgage Default: A Review of the Literature 343

mortgage payment. This significant difference entices borrowers to shopamong lenders for the right combination of down payment, mortgageinterest rate, length of loan, and other factors. Borrowers repay themortgage principal, plus the corresponding interest payment, for anumber of years after home purchase. At each payment time, borrowershave three choices. They can choose to make the scheduled mortgagepayment, not to make the payment, or to pay the balance of the loanthrough refinancing or sale of the property.

When scheduled payments are not made, lenders cannot know whetherborrowers are only delaying payment temporarily or stopping mortgagepayments altogether. In practice, when payments are first missed, thelender considers that the borrower is only delaying payment temporarilywith the intention of renewing payment in the future (delinquency). Ifpayments are not met for a number of periods (typically three), thelender considers that the borrower has decided to stop payment com-pletely (default).3 The number of nonpayment periods for which borrow-ers are considered to be delinquent varies from lender to lender and withthe lender’s willingness to work with nonpaying borrowers and renego-tiate the loan terms. This willingness, in turn, is based on the value ofthe outstanding debt and the costs of foreclosure.4

Lenders will choose on the basis of expected losses associated with eachoutcome either to renegotiate the loan terms or to foreclose.5 If lendersdecide that foreclosure is the least cost option, they foreclose and disposeof the mortgaged property to recover the unpaid mortgage principal,interests, and costs. In effect, although it is the borrower who stopspayments, it is the lender who decides if default has occurred by choosingwhether to work with the borrower or to foreclose.

When payments are first missed, it is not possible to know whether theborrower has defaulted or is just delinquent. It is possible retroactivelyto identify those delinquent loans that were later cured (mortgage

3Consistent with Giliberto and Houston (1989), default is considered the “transfer of the legalownership of the property from the borrower to the lender either through the execution offoreclosure proceedings or the acceptance of a deed in lieu of foreclosure.” This is the definitionused commonly in default studies. This definition should be distinguished from “technicaldefault.” Legally, any nonpayment of a scheduled mortgage payment places a mortgage intechnical default (Giliberto and Houston 1989, p. 56).

4In addition to the value of the debt and the costs of foreclosure, that is, the legal act thatextinguishes the borrower’s right of redeeming the mortgage property, lenders also considerwhether or not the loan has been securitized. As an anonymous referee correctly pointed out,“the ability of the lender to forbear or restructure the loan is generally eliminated if the loanhas been securitized.”

5In states where nonjudicial foreclosure is available, lenders may accept a deed in lieu offoreclosure as a means of minimizing losses.


payment was restarted) and those that ended up in default (foreclosureoccurred). If foreclosure does occur, the timing of default can be setretroactively to the first payment missed. This assumption has allowedresearchers to analyze the behavior of defaulting borrowers in a largenumber of published studies.

The number of default studies is also largely attributable to the availabil-ity of public aggregate and disaggregate loan data on residential borrow-ing and default (Simons 1990). Unfortunately, the available informationis collected by lenders at the time of loan origination (ex-ante data) andis not the more desirable information contemporaneous with (at the timeof) the default decision (ex-post data). Data contemporaneous with thedefault decision have been estimated through the use of proxy and othermeasures.6

In this article, default studies are divided into three groups: first-,second-, and third-generation studies. The studies vary in three respects.First, each study chooses a perspective from which mortgage risk isanalyzed: lender, borrower, or institutional. A second aspect is thedifferent measures studies use to determine mortgage risk: mortgageinterest rate premiums, default rates, delinquency rates, or expectedmortgage losses. Finally, studies follow one of two primary researchapproaches, that is, they make either a theoretical or an empiricalcontribution to the literature.7 The last section of this article presents anoverall discussion of the state of residential mortgage default literatureand suggests directions for future research.

First-Generation Studies: the Lender’s Perspective

An important stream of literature, beginning in the 1960s and extendingthrough the present, addresses default principally from the perspectiveof the individual mortgage lender. Relatively light on formal theory,these empirical studies attempt to identify the characteristics of bothmortgages and borrowers at the time of loan origination that could behighly correlated with mortgage default later in the loan term. The early

6The use of the expressions ex-ante and ex-post is not fully adequate. These expressions mean,literally, “out of what came before” and “out of what came afterward,” respectively. Thesemeanings do not capture the nature of data at time of loan origination or contemporaneous withthe default decision. Better terms are needed. To be consistent with the literature, bothexpressions will be used in this article.

7The inclusion of individual studies in a given generation is advanced for presentationpurposes only. Although every study has innovations that could place it in any of thegenerations, the central aspects of studies were used to group them into the three generations.Ultimately, the evolution of default studies over the last three decades has been a continuum,with each new study expanding our previous understanding of mortgage risk, in general, andthe default decision, in particular.


works of Jung (1962), Page (1964), and von Furstenberg (1969), amongothers, evaluated the relationships between mortgage risk and charac-teristics of the mortgage loan, including the loan-to-value ratio, interestrate, and mortgage term. Subsequent research extended this analysis ofmortgage risk to include an array of borrower (von Furstenberg 1969;Herzog and Earley 1970; Sandor and Sosin 1975) and property (vonFurstenberg and Green 1974) characteristics. (See table 1 for a summaryof these early studies.)

The Role of Loan Characteristics

The first predictive studies of default evaluated the default expectationsthat lenders assign to mortgage risk as represented by loan characteris-tics, especially mortgage interest rate premiums charged for loansconsidered risky.8 The basic premise of these studies was that becauseinterest rates charged to borrowers reflect the expectations that lendershold toward mortgage risk, and because the risk of default increases witha higher loan-to-value ratio, interest rates should have a positive corre-lation with the loan-to-value ratio at the time of origination (Jung 1962).

Page (1964) provided empirical support for this premise as well as thecontention that interest rates also vary with other terms of financing.9The term of the loan and property value were found to be negativelycorrelated with mortgage interest rate. The inverse relationship be-tween mortgage interest rate and property value may indicate that onlymore stable and better borrowers can purchase high-value propertiesand are therefore considered to be low risk by lenders (Sandor and Sosin

8Four early studies, descriptive in nature, examined the default and/or delinquency decisions.These studies were the U.S. Veterans Administration’s Report on Loan Service and ClaimsStudy (1962), the U.S. Federal Housing Administration’s FHA Experience with MortgageForeclosures and Property Acquisitions (1963), the U.S. Housing and Home Finance Agency’sMortgage Foreclosures in Six Metropolitan Areas (1963), and the U.S. Savings and LoanLeague’s Anatomy of the Residential Mortgage (1964). These studies suggested that delin-quency and foreclosure rates vary directly with loan-to-value ratio, mortgage interest rate,housing expense-to-income ratio, and number of dependents, and inversely with age of theloan, home equity, purchase price, age of borrower, and borrower’s occupational skill level.Also, these studies indicated that loans involving junior financing or refinancing are riskierthan other loans. Unfortunately, none of these studies performed tests of statistical signifi-cance, and thus “no basis exists for determining whether the relationships observed have anyreal meaning or whether they largely reflect random variation” (Herzog and Earley 1970,pp. 39–40).

9Using aggregate data from 31 savings and loans institutions, Jung (1962) had shown alreadythat interest rate and loan-to-value ratio were positively correlated, but given the small samplesize, he was unable to perform tests of statistical significance. Using multivariate regressionanalysis, Page (1964) found the debt-to-equity ratio (purchase price to purchase price minusloan amount) to be a better predictor of mortgage interest rate premiums than the comparable,but somewhat different, initial loan-to-value ratio used by Jung. Sandor and Sosin (1975)found both measures to be good predictors of mortgage interest rate premiums.

Tab

le 1

. Res

iden

tia

l M

ort

ga

ge

Def

au

lt: F

irst

-Gen

era

tio

n S

tud

ies


Mea

sure

of

Mor

tgag

e R

isk

Dat

aM

eth

odol

ogy

Var

iabl

es*

Jun

g (1

962)

Pag

e (1

964)1

von

Fu

rste

nbe

rg(1

969)

von

Fu

rste

nbe

rg(1

970a

)

von

Fu

rste

nbe

rg(1

970b

)

Her

zog

and

Ear

ley

(197

0)

Del

inqu

ency

and

fore

clos

ure

von

Fu

rste

nbe

rgan

d G

reen

(197

4)

Inte

rest

rat

epr

emiu

mA

ggre

gate

, loa

ns

orig

inat

ed b

y 31

S&

Ls

Inte

rest

rat

e

prem

ium

Agg

rega

te

Def

ault

rat

eA

ggre

gate

, FH

A

Def

ault

rat

e

Def

ault

rat

e

Agg

rega

te b

y st

ate,

FH

A-V

A l

oan

sor

igin

ated

195

3–67

Agg

rega

te, V

A lo

ans

orig

inat

ed 1

953–

67

Dis

aggr

egat

e,

of M

utu

al S

avin

gs B

anks

12,5

81 F

HA

, VA

loan

s or

igin

ated

in

1963

U.S

. Sav

ings

&L

oan

s L

eagu

e,M

ortg

age

Ban

kers

Ass

ocia

tion

,N

atio

nal

Ass

ocia

tion

Del

inqu

ency

rate

(del

inqu

ency

affe

cted

by

sam

e f

acto

rsth

at a

ffec

ted

defa

ult

)

Agg

rega

te f

rom

disa

ggre

gate

,7,

600

loan

sor

igin

ated

196

1–72

by a

n S

&L

inP

itts

burg

h

Cor

rela

tion

(n

o st

atis

tica

l

te

st d

ue

to s

mal

l nu

mbe

r)M

ortg

age

rate

Loa

n-t

o-va

lue

rate

Mor

tgag

e ra

te (

DV

)D

ebt-

to-e

quit

y ra

tlo

(+)

P

rope

rty

valu

e (–

)C

ontr

act

mat

uri

ty (

–)

Reg

ress

ion

Reg

ress

ion

Reg

ress

ion

Def

ault

rat

e (D

V)

Init

ial l

oan

-to-

valu

e ra

tio

(–)

Reg

ress

ion

an

alys

is a

nd

wei

ghte

d re

gres

sion

Reg

ress

ion

(wit

h 0

/1 d

epen

den

tva

riab

le)

Age

of

mor

tgag

e (+

)A

ge o

f m

ortg

age

squ

are

(–)

Def

ault

rat

e (D

V)

Init

ial

1 m

inu

s lo

an-t

o-va

lue

rati

o (–

)

Vac

ancy

rat

e (+

)N

o. h

omes

for

sal

e, 1

960

cen

sus

(+)

Def

ault

rat

e (D

V)

Init

ial 1

min

us

loan

-to-

valu

e ra

tio

(–)

Age

of

mor

tgag

e (+

)A

ge o

f m

ortg

age

squ

are

(–)

Del

inqu

ency

(D

V)

& D

efau

lt (

DV

)

Init

ial l

oan

-to-

valu

e ra

tio

(–)

No.

of

depe

nde

nts

(N

S)

If ju

nio

r fi

nan

cin

g (+

)P

aym

ent-

to-i

nco

me

rati

o (N

S)

Ter

m t

o m

atu

rity

,(N

S)

If p

rofe

ssio

nal

occ

upa

tion

(–)

If s

elf-

empl

oyed

/sal

esm

an (

+)

Mar

ital

sta

tus

(NS

)

Coh

ort

anal

ysis

use

d to

con

stru

ct d

elin

quen

cyra

te, r

egre

ssio

n a

nal

ysis

Del

inqu

ency

rat

e (D

V)

Init

ial 1

min

us

loan

-to-

valu

e ra

tio

(–)

Age

of

mor

tgag

e (+

)A

ge o

f m

ortg

age

squ

ared

(–)

Bor

row

er i

nco

me

(–)

If e

xist

ing

un

ity

(+)

If in

side

met

ro a

rea

(+)

Tab

le 1

. Res

iden

tia

l M

ort

ga

ge

Def

au

lt: F

irst

-Gen

era

tio

n S

tud

ies

(con

tin

ued

)


Mea

sure

of

Mor

tgag

e R

isk

Dat

a M

eth

odol

ogy

Var

iabl

es*

Wil

liam

s,B

eran

ek, a

nd

Ken

kel (

1974

)

Def

ault

rat

e1,

530

urb

an lo

ans

Reg

ress

ion

an

alys

isor

igin

ated

196

2–72

(w

ith

0/1

dep

ende

nt

by S

&L

in P

itts

burg

hva

riab

le)

Wh

eth

er d

efau

lt (

DV

)If

FH

A in

sure

d (–

)If

ref

inan

ced

(+)

If ju

nio

r f

inan

cin

g (+

)If

age

of

mor

tgag

or >

50

yr (

+)

If in

itia

l loa

n-t

o-va

lue

rati

o >

90

(+)

Init

ial p

aym

ent-

to-i

nco

me

rati

o >

30

(+)

No.

yr

wit

h e

mpl

oyer

at

orig

inat

ion

(–)

If s

elf-

empl

oyed

, far

mer

, un

skil

led

at o

rigi

nat

ion

(+

)U

nem

ploy

men

t r

ate

(+)

San

dor

an

dS

osin

(19

75)

Mor

ton

(19

75)

Van

dell

(19

78)

Mor

tgag

e ri

skpr

emiu

mD

isag

greg

ate,

556

loan

s (s

ingl

e-fa

mil

yu

nit

s) o

rigi

nat

ed19

67–7

1 by

S&

L in

Cal

ifor

nia

Def

ault

rat

e an

dde

lin

quen

cyra

te

Agg

rega

te, 5

45 lo

ans

orig

inat

ed b

y 24

inst

itu

tion

s in

Con

nec

ticu

t

Def

ault

rat

e(e

xpan

ded

defa

ult

an

alys

isto

oth

erm

ortg

age

inst

rum

ents

:F

RM

, VR

M,

GR

M, P

LA

M)

Reg

ress

ion

an

alys

isR

isk

prem

ium

(ef

fect

ive

con

trac

t ra

tem

inu

s ef

fect

ive

prim

e ra

te a

t or

igin

atio

n (

DV

)In

itia

l lo

an-t

o-va

lue

rat

io (

+)

Age

of

mor

tgag

e (+

)L

oan

siz

e (+

)If

sec

onda

ry f

inan

cin

g (+

)In

itia

l pay

men

t-to

-in

com

e ra

tio

(NS

)In

itia

l nei

ghbo

rhoo

d co

ndi

tion

(N

S)

Ste

pwis

e d

iscr

imin

ant

fun

ctio

n a

nal

ysis

: th

ree

(Sig

nif

ican

t in

all

th

ree

fun

ctio

ns)

Init

ial l

oan

-to-

valu

e ra

tio

(+)

sepa

rate

fu

nct

ion

sco

mpa

rin

g(1

) go

od v

s. b

ad lo

ans

(def

ault

an

d de

lin

quen

t)(2

) d

efau

lt v

s. n

onde

fau

lt(3

) g

ood

vs.

deli

nqu

ent

vs.

defa

ult

ed lo

ans

Sim

ula

ted,

bas

ed o

nvo

n F

urs

ten

berg

(197

0);

un

it a

nd

inco

me

appr

ecia

tion

over

tim

e es

tim

ated

Reg

ress

ion

an

alys

is

Non

-rea

l est

ate

debt

(+

)If

jun

ior

fin

anci

ng

(+)

If t

hre

e-fa

mil

y u

nit

(+

)If

fiv

e pl

us

depe

nde

nts

(+

)If

pro

fess

ion

al o

ccu

pati

on (

–)If

un

skil

led

labo

r (+

)

Def

ault

rat

e (D

V)

Loa

n-t

o-va

lue

rati

o (+

)A

ge o

f m

ortg

age

(+)

Init

ial m

ortg

age

rate

(+

)

Tab

le 1

. Res

iden

tia

l M

ort

ga

ge

Def

au

lt: F

irst

-Gen

era

tio

n S

tud

ies

(con

tin

ued

)

Mea

sure

of

Mor

tgag

e R

isk

Dat

a M

eth

odol

ogy

Var

iabl

es*

Web

b (1

982)

P

oten

tial

deli

nqu

ency

(bas

ed o

nan

alys

is o

fin

com

e va

ribi

lity

; al

so F

RM

, VR

M,

GR

M, P

LA

M,

oth

er)

Dis

aggr

egat

e, P

anel

Stu

dy o

f In

com

eD

ynam

ics

(Su

rvey

Res

earc

h C

ente

r,U

niv

. of

Mic

hig

an,

Tob

it a

nal

ysis

, fou

r eq

uat

ion

s S

ever

ity

of p

oten

tial

(D

V)

est

imat

ed o

n t

he

basi

s of

Hou

seh

old

char

acte

rist

ics

sev

erit

y of

pot

enti

al

Sou

rces

of

inco

me

Not

e: S

&L

= s

avin

gs a

nd

loan

; FH

A =

Fed

eral

Hou

sin

g A

dmin

istr

atio

n; V

A =

Dep

artm

ent

of V

eter

ans

Aff

airs

(fo

rmer

ly t

he

Vet

eran

s A

dmin

istr

atio

n);

F

RM

= f

ixed

-rat

e m

ortg

age;

VR

M =

var

iabl

e-ra

te m

ortg

age;

GR

M =

gra

duat

ed-p

aym

ents

mor

tgag

e; P

LA

M =

pri

ce-l

evel

-adj

ust

ed m

ortg

age.

*D

V =

dep

ende

nt

vari

able

, + =

sig

nif

ican

t po

siti

ve e

ffec

t, –

= s

ign

ific

ant

neg

ativ

e ef

fect

, NS

= n

o si

gnif

ican

t ef

fect

.

348 Reberto G. Quercia and Micheal A. Stegman


1975). In these first studies, mortgage risk, as it translates into mortgageinterest rate premiums, was considered exclusively as a characteristic ofthe loan.10 The first studies on actual default were undertaken in the late1960s and early 1970s. In these studies, rational homeowners who haveto move are assumed to contemplate the default option if they expecttheir equity in the home to be negative, net of costs such as salescommission, and are prepared to suffer a lower credit rating and thestigma of “immorality” of default (von Furstenberg 1969).

Evidence of the importance of home equity to actual default behavior ispresent in these early studies. Using aggregate data from a sample ofFederal Housing Administration (FHA) and Veterans Administration(VA; now the Department of Veterans Affairs) mortgages, von Furstenberg(1969, 1970a, 1970b) found that home equity at the time of originationwas the most important predictor of default risk. For instance, whenloan-to-value ratios are raised from 90 to 97 percent, default rates fornew homes increase sevenfold.

Other loan characteristics were also found to be important determinantsof mortgage risk. Mortgage risk increases with the term of the loan11 andwith the age of the mortgage up to year 3 or 4 after origination, afterwhich it declines (von Furstenberg 1969). Finally, the presence ofsecondary or junior financing is also an important determinant ofdelinquent loans (Herzog and Earley 1970).12

The Role of Borrower-Related Factors

Compared with loan characteristics, borrower-related factors do notpresent such a clear-cut measure for default. For instance, althoughdefault rates rise rapidly as mortgagor income falls, it can also be shownthat loan-to-value ratio rises as income falls (typically, low-incomefamilies can afford only minimal down payments). Thus, when vonFurstenberg (1969) found household income to have a significant effect

10Page (1964) also included one property characteristic in his study: whether the unit was newor existing. He estimated his model for both new and existing homes with similar results.

11Von Furstenberg (1969) found, for instance, that a 30-year mortgage on a new home is eighttimes as risky as a comparable 20-year mortgage. In contrast, Herzog and Earley (1970) foundthat once the effects of other variables are removed, the term of the mortgage has little or nosignificance as a determinant of delinquent loans.

12Herzog and Earley (1970) found the presence of secondary or junior financing the mostimportant factor in explaining mortgage default and delinquency. Consistent with priorwork, the authors found loan-to-value ratio and loan purpose to have significant effects ondefault and delinquency. In contrast, term of the mortgage was found to have an effect ondefault but not on delinquency, while region of the country was found to have an effect ondelinquency but not on default.


on default, he believed that the effect was actually capturing the effect ofloan-to-value ratio on default.13

In their analysis of mortgage delinquency, Herzog and Earley (1970)examined the role of other borrower-related factors on delinquency.Neither borrower age, marital status, nor number of dependents wasfound to have an effect on delinquency or default.14 Also, mortgagepayment-to-income ratio at the time of origination was not found to besignificant, a finding confirmed by Morton (1975) and Sandor and Sosin (1975). This fact can be attributed to lending practices that watch thisratio very carefully and deny loans that exceed some critical threshold attime of origination (Herzog and Earley 1970).15

In contrast to the continuous measure considered in prior work,Williams, Beranek, and Kenkel (1974) included payment-to-income ratioinformation in categorical form in their analysis of the default decision.In this form, borrowers with an initial payment-to-income ratio higherthan 30 percent were significantly more likely to default than were otherborrowers.

Unlike other borrower-related factors, the variability of household in-come shows a consistent effect on mortgage default and delinquency. Intheir analysis of mortgage delinquency, Herzog and Earley (1970) exam-ined the impact of income variability, captured by the proxy measure ofoccupation, on troubled loans. Borrowers in occupations with greaterincome variability at the time of loan origination were found to be morelikely to be delinquent than other borrowers. For instance, self-employedpeople and salespeople, whose incomes exhibit the greatest variability(Webb 1982), are more likely to be delinquent than are professionalpeople and executives, whose income is less variable.

The Role of Property Characteristics

In addition to confirming the importance of loan characteristics andsuggesting a number of borrower-related factors for further analysis,

13In comparing the effects of loan and borrower characteristics on default, von Furstenberg(1969) concluded that loan-to-value ratio explains 32 percent of the total variation in annualdefault rates, while household income, by itself, explains less than 10 percent (p. 477).

14In contrast, in his discriminant analysis of the delinquency and default decisions, Morton(1975) found the presence of five or more dependents to have a significant and positiveeffect on both delinquency and default.

15This fact would limit the variance in this continuous variable to such a narrow range thatit would likely minimize its significance in a regression model. However, the use ofalternative payment-to-income measures could lead to different conclusions.


later studies assessed local real estate markets and property conditions asfactors in default risk. Loans made in suburban locations were found to beless risky than those made in central-city locations (von Furstenberg andGreen 1974).16 Areas with high unemployment rates were found likely tohave higher loan default rates (Williams, Beranek, and Kenkel 1974).17

Finally, good condition of property and neighborhood were negativelycorrelated with mortgage interest rate premiums (Sandor and Sosin 1975).

Extension of Early Study Findings

Their contributions to the identification of important loan, borrower,and property characteristics aside, most first-generation studies suf-fered from three limitations. With the primary focus of identifying riskyloans at the time of loan origination, researchers did not consider theactual time frame of default and the importance of factors existing whenthe default decision was made. Second, because of data limitations,researchers relied on the use of proxy measures, such as occupation forincome variability, to capture the effect of factors believed to affect ahousehold’s ability to pay and its equity position. Finally, researchersfocused on the default decision of borrowers holding fixed-rate mort-gages (FRMs) exclusively, because this was the only type of mortgageinstrument available at that time.

Vandell (1978), Webb (1982), Zorn and Lea (1989), and Cunningham andCapone (1980) extended the default analysis to other mortgage instru-ments. Vandell (1978) also considered the timing of default and the effectof contemporaneous net equity—the ratio of contemporaneous bookvalue of the loan to contemporaneous value of the property—on thedefault decision. He contended that borrower-related effects are alsoimportant, especially events such as loss of employment, death, anddivorce.18 Overall, Vandell found support for his theories, except for the

16In their cohort analysis of 7,609 loans originated by a Pittsburgh, Pennsylvania, mortgagelender, von Furstenberg and Green (1974) found that a suburban location reduces delinquencyrisks significantly (by as much as 47 percent) compared with an urban location.

17In their comparative analysis of default among seven lending institutions in Pittsburgh,Williams, Beranek, and Kenkel (1974) found that the unemployment rate has a significantpositive effect on default. In contrast, they found that area crime, captured with the proxymeasure “per capita changes in crimes against property,” had no effect on default rates.

18Specifically, Vandell (1978) contended that borrower-related effects include the “level ofborrower consciousness towards repayments or the likelihood of occurrence of a seriouslydestabilizing incident such as unemployment, death, and divorce, which would render defaultmore likely” (p. 1285). Vandell used the proxy measure household income to capture theseeffects. He also included a transient time term designed to capture the borrower’s initial effortto make mortgage payments. He believed this time term to be a function of borrowercharacteristics, especially the level of liquid assets at the time of loan origination.


importance of borrower-related effects on default.19 The estimation ofcontemporaneous borrower information from ex-ante data may explainthis lack of borrower effect, as the national and regional indices used inthis estimation may not have captured the individual circumstances ofborrowers who default.

On the basis of his findings, Vandell simulated the default risk underalternative mortgage instruments.20 Under normal circumstances, suchas a 20 percent down payment and a unit that was appreciating in valueand located in a stable neighborhood, all instruments performed aboutthe same. Under worse conditions, such as a low down payment or no unitappreciation, mortgage risk increased under all instruments, includingFRMs. Increases in risk, however, were found to be particularly severeunder the price-level-adjusted mortgage (PLAM) and graduated-pay-ment mortgage (GPM).

Unlike Vandell (1978), who used simulations, Zorn and Lea (1989)estimated a model of mortgage borrower behavior using actual indi-vidual loan data aon Canadian borrowers with rollover mortgages, a formof adjustable-rate mortgage (ARM). Their multinomial logit estimationconfirmed the implicit assumption of previous studies: The defaultbehavior of FRM and ARM borrowers is similarly motivated. Given theimportance of equity and mortgage interest rate in the default decision,Zorn and Lea inferred that the default risk of ARMs in the United Statesis likely to be higher than that of FRMs because “mortgage-relatedcapital gains are less likely with frequently adjusting ARMs,” and that,by design, ARMs have the potential for higher real mortgage interestrates (p. 131).21

The only study of the default experience among U.S. borrowers hold-ing alternative mortgage instruments is a recent one by Cunninghamand Capone (1990). The authors analyzed the mortgage termination

19Using ex-ante data to estimate the necessary ex-post information, Vandell (1978)respecified the default model developed by von Furstenberg (1969,1970a, 1970b). Vandell’sfindings are consistent with those of prior work. He found contemporaneous net equity tobe of great importance in affecting default risk. Also consistent with von Furstenberg,Vandell found household income to be statistically not significant, thus giving no supportto the importance of borrower-related effects.

20A later study by Webb (1982) also used simulation methodology to analyze potentialdelinquency under different mortgage instruments.

21In their analysis, Zorn and Lea (1989) estimated the concurrent probabilities of thecontinue payment, prepay, become delinquent, and default alternatives that borrowershave each payment period.


experience of a sample of ARM and FRM borrowers.22 Expanding on priorwork, they included a set of ARM-specific determinants to isolate uniquemortgage termination behavior under ARMs. Large lifetime caps werefound to be positively related to default under ARMs, whereas longadjustment periods were found to be inversely related. When interestrate movements exceeded lifetime cap limits, caps were also found tohave a secondary effect on default probabilities, because ARMs with lowcaps become more desirable when interest rates rise substantially abovethe cap limit.23 Using mean-based simulation analysis, the authorsconcluded that ARMs are more sensitive to variable changes and have,overall, a greater default risk than FRMs.24

In summary, the first-generation studies offer the first insights onresidential mortgage default risk. They provide evidence of the impor-tance of loan characteristics, such as equity, on default, and they suggesta need to examine further the role of borrower-related factors in default.They also suggest that loan and borrower information should be collectedand considered at the time of mortgage default and not just at loanorigination. Overall, these early studies have one common purpose: toassist lenders in predicting the default decisions of borrowers. Generally,no attempt is made to provide a theoretical basis for borrower behaviorat the time of default. In contrast, the second-generation studies seek toexplain borrowed behavior through a structured model.

Second-Generation Studies: the Borrower's Perspective

Beginning in the late 1970s, a second generation of empirical defaultstudies, rooted in the economic theory of consumer behavior, emerged.Rather than informing the lender about loan and borrower characteris-tics associated with default, such studies model the behavior of indi-vidual households that, in the course of maximizing their utility (and netwealth) over time, rationally decide whether it is in their best interest tocontinue making payments on their mortgage loans. This research alsoviews the default decision within a broader framework, a borrowerpayment model that includes the simultaneity of mortgage paymentdecisions. (See table 2 for summary of this research.)

22Using data from 879 loans from a mortgage banking firm in Houston, Texas, and amultinomial logit estimation, Cunningham and Capone analyzed the concurrent defaultand prepayment decision of 411 borrowers holding ARMs and 469 borrowers holdingFRMs.

23Likewise, when rates fall substantially borrowers terminate more quickly [prepay] toavoid cap restrictions” (Cunningham and Capone 1990, p. 1697).

24Cunningham and Capone found the reverse to be true for prepayment. For instance,interest rate expectations were found to have a stronger effect on FRM than on ARMprepayment behavior.

Tab

le 2

. Res

iden

tia

l M

ort

ga

ge

Def

au

lt: S

eco

nd

-Gen

era

tio

n S

tud

ies

Mea

sure

of

Mor

tgag

e R

isk

Dat

aM

eth

odol

ogy

Var

iabl

es*

Jack

son

an

dK

asse

rman

(198

0)

Def

ault

rat

e(f

orm

al a

nal

ysis

of c

ompe

tin

gh

ypot

hes

es,

equ

ity

and

abil

ity

to p

ay)

Cam

pbel

l an

dD

ietr

ich

(19

83)

Def

ault

rat

e(m

ult

iper

iod

mod

el lo

ante

rmin

atio

n b

yde

fau

lt,

prep

aym

ent,

can

cell

atio

n)

Fos

ter

and

Van

Ord

er(1

984)

Epp

erso

n, K

au,

Kee

nan

, an

dM

ull

er (

1985

)

Van

dell

an

dT

hib

odea

u(1

985)

Def

ault

rat

e(o

ptio

n-b

ased

defa

ult

)

Def

ault

rat

e(c

urr

ent

valu

eof

th

e m

ortg

age

affe

cted

by

opti

on t

ode

fau

lt in

the

futu

re)

Def

ault

defa

ult

; in

clu

des

com

para

tive

stat

isti

cs f

orde

fau

lt,

deli

nqu

ency

,pr

epay

men

t,an

d co

nti

nu

edpa

ymen

top

tion

s)

Dis

aggr

egat

e a

nd

Reg

ress

ion

(O

LS

) a

nd

aggr

egat

e, 1

,735

pr

obit

(di

sagg

rega

teF

HA

203

(b)

loan

s da

ta),

an

d O

LS

an

d G

LS

orig

inat

ed 1

969–

79

(agg

rega

te d

ata)

Agg

rega

te, l

oan

sor

igin

ated

196

0–80

.

Mor

tgag

e G

uar

anty

Insu

ran

ce C

orp.

,an

d ec

onom

ic t

ime

seri

es d

ata

Agg

rega

te, F

HA

203

(b)

loan

s or

igin

ated

19

60-7

8

Sim

ula

tion

Dis

aggr

egat

e, 4

50F

RM

loan

s(s

ingl

e-fa

mil

y u

nit

s)or

igin

ated

197

2–83

by S

&L

in D

alla

s

Reg

ress

ion

an

alys

is;

se

para

te d

efau

lt,

prep

aym

ent,

an

dca

nce

llat

ion

equ

atio

ns

Reg

ress

ion

an

alys

is

Par

tial

dif

fere

nti

al

equ

atio

ns,

rec

urs

ive

mod

el(b

ecau

se f

utu

re v

alu

e of

opti

on a

ffec

ts v

alu

e of

opti

on t

oday

)

Log

it

Wh

eth

er d

efau

lted

(D

V)

un

der

all m

odel

s es

tim

ated

: L

oan

-to-

valu

e ra

tio

(+)

Con

trac

t ra

te (

+)

Con

trac

t lif

e of

mor

tgag

e (+

)(s

upp

orts

equ

ity

hyp

oth

esis

)

Pro

babi

lity

of

defa

ult

(D

V)

(or

prep

aym

ent

or c

ance

llat

ion

) M

ean

init

ial l

oan

-to-

valu

e ra

tio

(+)

Mea

n p

aym

ent-

to-i

nco

me

rati

o (+

)U

nem

ploy

men

t ra

te (

+)

Rat

e of

ret

urn

(–)

Age

of

loan

(+

), a

ge s

quar

ed (

–)

If e

xist

ing

un

it (

+)

Def

ault

rat

e (D

V)

Con

tem

pora

neo

us

equ

ity-

to-l

oan

rat

io (

–)

(un

it a

ppre

ciat

ion

est

imat

ed)

Tra

nsa

ctio

n c

osts

(+

)

NA

Wh

eth

er d

efau

lted

(D

V)

Con

tem

pora

neo

us

real

aft

er-t

axpa

ymen

t-to

-in

com

e ra

tio

(–)

Exp

ecte

d lo

an-t

o-va

lue

rati

o (+

) by

S&

L in

Dal

las

% D

iffe

ren

ce b

etw

een

mar

ket

valu

e an

d pa

r va

lue

ofm

ortg

age

(–)

Wh

eth

er s

elf-

empl

oyed

(+

) L

engt

h in

job

at o

rigi

nat

ion

(–)

In

com

e fr

om c

omm

issi

on (

+)

Non

hou

sin

g w

ealt

h (

–)

Nei

ghbo

rhoo

d ra

tin

g (–

)

mod

el o

f

(opt

ion

-bas

edm

odel

of


Tab

le 2

. Res

iden

tia

l M

ort

ga

ge

Def

au

lt: S

eco

nd

-Gen

era

tio

n S

tud

ies

(con

tin

ued

)

Mea

sure

of

Mor

tgag

e R

isk

Dat

a M

eth

odol

ogy

Var

iabl

es*

Zor

n a

nd

Lea

(198

9)

Cu

nn

ingh

aman

d C

apon

e ( 1

990)

Def

ault

,de

lin

quen

tpr

epay

an

dm

ake

paym

ent

(an

alys

is o

fC

anad

ian

borr

ower

s wit

hro

llov

erm

ortg

ages

, aty

pe o

f A

RM

)

Def

ault

, pre

paid

,se

rvic

ed lo

anA

RM

s an

dF

RM

s

Dis

aggr

egat

e,C

anad

ian

bor

row

ers

wit

h r

ollo

ver

mor

tgag

es

Mu

ltin

omia

l log

it

Wh

eth

er d

efau

lted

, del

inqu

ent,

prep

aid,

ser

vice

d lo

an (

DV

) E

ffec

t on

def

ault

dec

isio

n:

Con

tem

pora

neo

us

age

of b

orro

wer

(–)

In

itia

l no.

of

depe

nde

nts

(+

)

Con

tem

pora

neo

us

net

equ

ity

(–)

Dis

aggr

egat

e, 8

79lo

ans

orig

inat

ed

1962

–85

(411

AR

Ms

an

d 46

8 F

RM

s)

Mu

ltin

omia

l log

it

Wh

eth

er d

efau

lted

, pre

paid

ser

vice

d lo

an (

DV

)

Eff

ect

on d

efau

lt d

ecis

ion

: C

onte

mpo

ran

eou

s lo

an-t

o-va

lue

rati

o (+

) A

ge o

f lo

an (

–)

Rat

e sp

read

(m

arke

t &

not

e) (

–)

Bor

row

er's

age

(+

) C

onte

mpo

ran

eou

s pa

ymen

t-to

-in

com

e ra

tio

(–)

Net

wor

th a

t or

igin

atio

n (

+)

R

ente

r at

ori

gin

atio

n (

+)

Y

r. e

mpl

oyed

at

orig

inat

ion

(–)

Reg

ion

al u

nem

ploy

men

t ra

te (

–)

Inte

rest

rat

e ex

pect

atio

ns

(+)

Y

r. b

etw

een

AR

M a

dju

stm

ents

(–)

M

axim

um

life

tim

e ca

p (+

)C

urr

ent

not

e ra

te a

nd

orig

inal

rat

e as

% o

f

life

tim

e ca

p (–

)

Not

e: O

LS

= o

rdin

ary

leas

t sq

uar

es; G

LS

= g

ener

aliz

ed le

ast

squ

ares

. *D

V =

dep

ende

nt

vari

able

; + s

ign

ific

ant

posi

tive

eff

ect,

– =

sig

nif

ican

t n

egat

ive

effe

ct, N

A =

not

app

lica

ble.

-



Borrower Payment Model

The borrower payment model used in most second-generation studies ofdefault is an optimization model of borrower choice. At each paymentperiod during the life of the mortgage, borrowers have four choices. Theycan make the scheduled mortgage payment, delay payment (becomedelinquent), stop payment altogether (default), or prepay the mortgagethrough refinancing or the sale of the property. Borrowers are assumedto assess the utility derived from each of the four alternatives separatelyand to choose the outcome that maximizes their utility over time, giventheir circumstances. A central aspect of this model is the simultaneity ofmortgage payment decisions.25

25In technical terms, a borrower is assumed to maximize a utility function defined overa vector of mutually exclusive qualitative choices, S, and a vector of exogenous statevariables, X. It is assumed that the utility-maximizing choice can be represented as aprobability function of the other state variables, P(si |X) = fi (X ), where the sum of theprobabilities of all n elements in S for a given X is equal to unity (Campbell and Dietrich1983). McFadden’s (1973) variation on random utility models has been used to derive theseprobabilities (e.g., Campbell and Dietrich 1983; Zorn and Lea 1989). Given that theborrower can choose among continuing payment, delaying payment, defaulting, orprepaying, a multinomial logit estimation, in which the default decision is viewed as aparticular form of mortgage payment outcome (Zorn and Lea 1989; Cunningham andCapone 1990), is ideal. Borrowers are expected to default if this outcome maximizes theirafter-tax real wealth in the terminal period. For instance, the payoff function if borrowerschoose to default can be expressed as follows (Vandell and Thibodeau 1985, pp. 295–296):

The payoff function if borrowers choose to continue payment can be expressed as follows:

where

W D = payoff function if borrower defaults;

WC = payoff function if borrower continues payment;Y = real annual after-tax household income;

R = required real nondiscretionary expenditures (other than housing);

Qr = required real rent on new unit (gross rent plus utilities, etc.);

i

r = expected real return on nonhousing investments; W = current real nonhousing wealth;

Q = required real after-tax payment on mortgage (plus taxes, insurance, and otherownership costs);

r0 = expected opportunity cost of borrowing or return on lending(r0 = ri if Y – R – Q ≥ 0 or r 0 = rb if Y – R – Q < 0);

VT = expected real market value of current home; and

LT = expected real outstanding loan balance on current mortgage.

Borrowers are expected to choose to default rather than continue payment if WD is greaterthan WC

.

(1)


Optimization model of default. Jackson and Kasserman (1980) were thefirst to test and confirm the adequacy of an optimization model ofconsumer choice in the analysis of default decisions. The authors explic-itly formulated and tested two competing hypotheses: the net equityapproach, based on an optimizing mode of behavior; and the ability to pay(i.e., cash flow) approach. In the first approach, borrowers base theirdefault decision on a rational comparison of the financial costs andreturns involved in continuing or terminating mortgage payments. Ifhome equity is negative after all costs and benefits are considered,borrowers will choose to default. In the second approach, borrowersdefault if their income flow becomes insufficient to meet the periodicpayments without undue financial burden. Jackson and Kassermanhypothesized that loan-to-value ratios and the mortgage interest rate arepositively related to default in both scenarios, whereas the term of themortgage is positively related to default only under the net equityapproach. Using ex-ante data from 1,736 FHA Section 203(b) loans, theauthors found support for the net-equity-maximization model of defaultover the ability-to-pay model.

In their multiperiod model of consumer choice, Campbell and Dietrich(1983) extended Jackson and Kasserman’s work on the importance of netequity in the borrower’s decision to default. Both original and contempo-raneous loan-to-value ratios were found to have significant positiveeffects on the default decision, providing evidence of the importance ofhome equity level at the time of the default decision.26 One borrower-relatedfactor, income variability, captured by the proxy measure regional unem-ployment rate, was found to have a significant positive effect on default.27

Option-based model of default. In the mid-1980s a narrower concept-ualization of the default decision was proposed in the form of an option-based model of default. This model views default as a put option, allowingthe borrower to sell the house to the lender for the value of the mortgageat the beginning of each payment period (Foster and Van Order 1984).28

In assessing whether or not to exercise the option, borrowers consider the

26Consistent with prior work, Campbell and Dietrich (1983) also established that loanson new homes are riskier than loans on existing homes. Also, age of mortgage was foundto have a nonlinear relationship with default. Yet the authors cautioned about interpret-ing the effect of age of mortgage directly. They contended that the underlying determi-nants of default cannot be measured with adequate precision today because of datalimitations that impede isolation of any independent age effect.

27Campbell and Dietrich (1983) found that the initial mortgage payment-to-income ratioexhibited too little variation up front to be included in the model. The authors attributedthis lack of variation to the fact that lenders review this ratio carefully at the time of loanorigination, denying loans that exceed a certain critical threshold. The use of an aggregateincome index to estimate contemporaneous, ex-post information from ex-ante data mayalso reduce variability of this ratio over time.

28Similarly, prepayment can be viewed as a call option, allowing the borrower to exchangea sum of money for the mortgage instrument.


market value of the mortgage and the equity they have in the home,which is a crude measure of the extent to which the put option is “in themoney” (Quigley and Van Order 1991). From this perspective, default isseen as a purely financial matter, in which borrower characteristics suchas income and employment status do not matter.

Ideally, borrowers will exercise this option, and thus default, wheneverthe value of the house plus any costs of exercising the option falls belowthe mortgage value (Foster and Van Order 1984). However, because thedefault option has intrinsic value and the current value of the mortgageis affected by the option to default in the future, some borrowers withnegative equity may not default because they would forfeit the option ofdefaulting later (Epperson et al. 1985). This factor makes it difficult tocompute the value of the option.

A second issue that makes this computation complex is the problem ofestimating the costs of exercising the default option. Borrowers areassumed to consider costs such as transaction costs, moving costs, andthe value of the borrower’s reputation and credit rating, which are alsoaffected by default (Quigley and Van Order 1991).

Foster and Van Order (1984) were the first to apply option theoryformally to the field of mortgage default by significantly extendingCampbell and Dietrich’s work. Using data on FHA 203(b) default ratesfrom 1960 through 1978, Foster and Van Order (1984) estimated loan-to-value ratios over time and used this information to create a numberof variables that represented the percentage of loans with negativeequity for each year in the study period. These equity variables wereincluded in the regression model in current and lagged form. Overall, theoption-based model of default worked remarkably well: It explained over90 percent of the variance using just the equity variables.

The significance of the lagged equity terms indicates that the defaultoption is not exercised immediately. Given a borrower with negative netequity, Foster and Van Order (1984) contended, an event such as adivorce or loss of employment may be needed to trigger a default. Therewas no empirical support for this contention.29 Ultimately, Foster andVan Order attributed the imperfect exercise of the option to the impor-tance of transaction costs, which were captured inadequately in theirstudy. Foster and Van Order (1985) later found that borrowers do not

29In trying to explain this imperfect exercise of the default option, Foster and Van Order(1984) reestimated their model with a number of variables suggested by prior work:divorce rate, unemployment rate, expected inflation, age of loan, and mortgage payment-to-income ratio. Overall, none of these variables contributed much to the model.


exercise the default option consistently, even under zero transaction costsor with negative equity.30

The Role of Transaction Costs, Crisis Events, and Expectations

Vandell and Thibodeau (1985) also addressed the issue of transactioncosts and crisis events. The authors extended Campbell and Dietrich’s(1983) and Foster and Van Order’s (1984) models of consumer choice,using option-based modeling to include local market conditions thataffect property values: the occurrence of crisis events and transactioncosts.31 Unlike the previous authors, Vandell and Thibodeau also consid-ered the importance of the contemporaneous market value of the loan, asopposed to its contemporaneous book value, and used individual loanhistory data in their analysis. They also considered the role of expectationin the default decision by modeling expected home values with a weightedindex of backward-looking adaptive factors (Simons 1990).32

30Foster and Van Order (1985) also acknowledged what they called the simultaneityproblem. Specifically, they stated that “an owner with negative equity with a mortgageevaluated at par might not default because he forfeits the option of defaulting later, whichis to say he is getting more insurance than he is paying for, and he may choose to keepgetting the cheap insurance” (p. 280). This simultaneity is difficult to estimate. Fortu-nately, the use of FHA loans in their analysis allowed the authors to control for this effect,because FHA charges the same price for all insurance, subject to a minimum downpayment, “Hence the excess value of insurance is approximately the new, minimumdownpayment that would have to be made on the house, assuming the defaulter simplyrepurchases a similar house after default.” Foster and Van Order took the value of themortgage to be the present value of remaining payments, given a standard prepaymentassumption, and they included the minimum down payment as a part of the cost of default(p. 280).

31Because of data limitations, Vandell and Thibodeau (1985) used a number of proxymeasures to capture the significance of transaction costs and the occurrence of crisisevents that may trigger, delay, or eliminate the need to exercise the default option.

32Vandell and Thibodeau (1985) considered the role of borrower expectations on the defaultdecision in a manner consistent with prior work. For example, Jackson and Kasserman (1980)indicated that borrowers considered future expected property values when assessing theirequity position in their multiperiod optimization model. When expectations are considered,a borrower’s equity position can be captured with a measure of expected net equity (NETEQ).At time t, this measure can be expressed as the following function (Simons 1990, p. 135–136):

E[NETEQ]t = E[MVP – CT – SC – LI – OPB – PAR]t

whereMVP = expected market value of the property at time t;CT = capital gains tax on sale of the property at time t;SC = sales commission to an outside agent;

LI = reduction of borrower equity attributable to recognition of all outstandingnonmortgage liens against the property;

OPB = outstanding principal balance of the mortgage; and

PAR = expected financial value to the borrower of the current difference between thecontracted mortgage rate and the prevailing mortgage rate, weighted by theoutstanding principal balance.


Using economic theory, Vandell and Thibodeau (1985) formally devel-oped a two-period maximization model of consumer choice that includedborrower’s expectations. At each payment period, the borrower is as-sumed to choose one of five outcomes: to default on the mortgage, tobecome delinquent, to prepay through refinancing, to repay through sale,or to make the scheduled payment. Borrowers are expected to choose theoutcome that maximizes after-tax real wealth in the terminal period. Forinstance, borrowers are expected to choose to default rather than con-tinue payment if their real after-tax wealth in the terminal period will begreater if they default.

In their empirical analysis, Vandell and Thibodeau analyzed the defaultdecision exclusively.33 Consistent with the contentions of their model,the authors found contemporaneous net equity to have a significantpositive effect on default, whereas the difference between market and parvalue of the mortgage exhibited a significant negative effect.

These two variables, however, have a smaller effect on default than do thevariables representing source of income. Vandell and Thibodeau (1985)found that an increase in initial loan-to-value ratio from 75 to 95 percenthas an effect on default risk that is only about 1/14 as large as the effectof being self-employed. Similarly, they found that reducing the differencebetween market value and the par value of the mortgage to zero hasan effect only 1/10 as large as the effect of being self-employed (p. 312).On the basis of these results, Vandell and Thibodeau simulated defaultrates under different risk scenarios. Under normal circumstances, theyestimated that the probability of default in the presence of a 10 percentexpected negative net equity at year 5 after origination was only1.75 percent.34 Contrary to the contention of the option-based model ofdefault, nonequity factors seem to play an important role in the defaultdecision.

33To our knowledge, only two studies have estimated the concurrent continue payment,prepay, or default decision confronted by borrowers at each payment period. Cunningham andCapone (1990) used a multinomial logit estimation to analyze the concurrent loan terminationexperience of borrowers holding FRMs and ARMs, and Zorn and Lea (1989) undertook a similaranalysis on a sample of Canadian borrowers holding rollover mortgages, a form of adjustable-rate mortgage. Zorn and Lea also analyzed the delinquency decision.

34Vandell and Thibodeau (1985) found that several borrower-related factors significantlyaffect default. Variables such as self-employment, sources of income from commission andinvestment, a short length of employment, and low nonhousing wealth at time of loanorigination (i.e., variables capturing low permanent income), were associated with riskierloans. Surprisingly, payment burden had a negative effect on default. The authors suggestedthat this effect might be due to stricter appraisal standards or underwriting practices thatpermitted high payment-to-income-ratio loans only to those borrowers with ample additionalresources to overcome default (p. 313). Neighborhood quality also had a significant negativeeffect on default.


Overall, the theoretical premises set forth by Vandell and Thibodeau(1985) and other second-generation studies constitute the basis for thecurrent state of theory. The examination of the default decision as anoption and the central role of net equity constitute the dominant view inall recent default studies. Second-generation studies also provide someevidence about the importance of transaction costs and borrower-relatedfactors such as borrower’s expectations and occupation. Finally, al-though there are conceptual justifications for the relevance of crisisevents on the default decision, second-generation studies provide littledirect empirical correlation. This and other issues were further consid-ered in the third generation of research.

Third-Generation Studies: the Institutional Perspective

The high rates of default on mortgage loans originated in the late 1970sand early 1980s stimulated the birth of a third generation of research onmortgage defaults, which viewed default mainly from an institutionalperspective. Because of the large loan volumes involved in FHA, FannieMae, and Freddie Mac operations and the need to price mortgage creditto anticipate losses from default, this research is more concerned withestimating the probability that a particular fraction of a large loan poolwill default than it is with modeling individual borrowers’ defaultdecisions. The contribution of most third-generation studies is in largepart methodological, both in terms of examining measures of default riskthat better reflect institutional concerns and in the use of sophisticatedestimation techniques, such as proportional hazard estimation of defaultprobabilities. (See table 3 for a summary of third-generation studies.)

Expected Losses and Default Rates

From the perspective of lenders and investors (both of which can beinstitutions), default rates are not an adequate measure of mortgagerisk. For instance, default rate is an inappropriate measure of risk if thepurpose of the analysis is to establish a premium for mortgage defaultinsurance, to estimate the costs of default on a government subsidyprogram, or to establish a mortgage interest rate premium on a categoryof loans (Evans, Maris, and Weinstein 1985). This is because the propor-tion of dollars loaned that become losses in default varies by loan, a factthat is not captured when default rates are considered.35 Thus, ameasure of expected mortgage loss is a better indicator of mortgage riskthan are default rates.

35Thus there are significant differences in risk even among defaulted loans.

Tab

le 3

. Res

iden

tia

l M

ort

ga

ge

Def

au

lt: T

hir

d-G

ener

ati

on

Stu

die

s

Mea

sure

of

Mor

tgag

e R

isk

Dat

a M

eth

odol

ogy

Var

iabl

es*

Exp

ecte

d lo

ssan

d de

fau

lt r

ate

(ris

k an

alys

is,

po

rtfo

lio

anal

ysis

)

Gre

en a

nd

Sh

oven

(19

86)

Mor

tgag

epr

epay

men

t(s

ensi

tivi

ty t

opr

evai

lin

gin

tere

st r

ates

)

Qu

igle

y (1

987)

Mor

tgag

epr

epay

men

t(m

odel

of

resi

den

tial

mob

ilit

yin

corp

orat

esow

ner

ship

of

mor

tgag

e w

ith

favo

rabl

e ra

tein

th

epr

epay

men

tde

cisi

on)

Cla

ure

tie

(198

7)

F

orec

losu

re(a

dd le

nde

rs'

pers

pect

ive)

Gil

bert

o an

dH

oust

on (

1989

)D

efau

lt a

nd

relo

cati

onop

port

un

itie

s(t

heo

reti

cal

mod

el)

Agg

rega

te, F

HA

loan

sD

efau

lt r

ates

esti

mat

ed f

orca

tego

ries

su

ch a

sra

ce, l

oan

siz

e, v

alu

e,in

ner

cit

y/su

burb

s

Dis

aggr

egat

e, 3

,938

loan

s by

S&

L in

Cal

ifor

nia

Dis

aggr

egat

e, P

anel

Pro

port

ion

al h

azar

d m

odel

Stu

dy o

f In

com

e

al

so c

ompa

red

wit

hD

ynam

ics

(Su

rvey

n

onpr

opor

tion

al m

odel

,R

esea

rch

Cen

ter,

o

ne

equ

atio

n e

stim

ated

Un

iv. o

f M

ich

igan

)

f

or e

ach

yea

r, 1

979–

81

Agg

rega

te, 1

976–

85,

MB

A a

nd

1976

–83,

FH

LB

B F

HA

,co

nve

nti

onal

FR

MV

A

NA

Reg

ress

ion

an

alys

is, t

wo

ques

tion

s, o

ne

for

each

depe

nde

nt

vari

able

,se

vera

l mea

sure

s of

disp

ersi

on (

e.g.

,se

miv

aria

nce

)

Pro

port

ion

al h

azar

d m

odel

(max

imu

m li

keli

hoo

des

tim

atio

n)

Est

imat

ed lo

ck-i

n m

easu

rean

nu

ally

197

5–78

an

d19

79–8

2

Def

ault

rat

e (D

V)

Exp

ecte

d lo

ss (

DV

) L

oan

/val

ue

> 9

5 (–

bot

h e

quat

ion

s)

Loa

n s

ize

> $

20,7

50 (

– ex

pect

ed lo

ss)

If

wh

ite,

(–

both

equ

atio

ns)

D

own

tow

n u

nit

(N

S b

oth

equ

atio

ns)

On

e lo

ck-in

var

iabl

e (f

ace

valu

em

inu

s m

arke

t va

lue

ofm

ortg

age)

div

ided

by

rem

ain

ing

real

bal

ance

(+

)

Wh

eth

er m

oved

(D

V),

sign

ific

ant

all

yea

rs:

Pre

sen

t va

lue

of m

ortg

age

at c

ontr

act

rate

&th

e pr

esen

t va

lue

of t

he

mor

tgag

e at

mar

ket

rate

(–)

Incr

ease

in f

amil

y si

ze (

+)

Ch

ange

in f

amil

y h

ead

(+)

Oth

er v

aria

bles

Reg

ress

ion

an

alys

is (

two

esti

mat

ion

s, o

ne

per

data

set,

per

mor

tgag

e ty

pe)

For

eclo

sure

rat

e in

sta

te (

DV

) C

osts

of

fore

clos

ure

(+

)C

urr

ent-

to-c

ontr

act

rate

(va

lue

of

mor

tgag

e )

(+

)U

nit

app

reci

atio

n (–

)

NA

NA


Tab

le 3

. Res

iden

tia

l M

ort

ga

ge

Def

au

lt: T

hir

d-G

ener

ati

on

Stu

die

s (c

onti

nu

ed)

Mea

sure

of

Mor

tgag

e R

isk

Dat

aM

eth

odol

ogy

Var

iabl

es*

Pri

ceW

ater

hou

se(1

990)

Con

tin

gen

cycl

aim

an

alys

isof

FH

A-M

utu

alM

ortg

age

Insu

ran

ce F

un

d

Agg

rega

te f

rom

indi

vidu

al F

HA

loan

s, p

ooli

ng

tim

ese

ries

of

loan

perf

orm

ance

ove

r19

75–8

9

Con

tin

gen

cy c

laim

rat

em

odel

, GL

S, o

ne

equ

atio

n f

or e

ach

of

seve

n

leve

ls o

f lo

an-t

o-va

lue

rati

o

Cla

im t

erm

inat

ion

(D

V)

Net

equ

ity

(–)

Un

empl

oym

ent

rate

(+

)H

ouse

pri

ce d

ispe

rsio

n (

+)

Van

Ord

er (

1990

)

Qu

igle

y an

dV

an O

rder

(199

1)

Kau

, Kee

nan

,an

d K

im (

1991

)

Qu

igle

y an

dV

an O

rder

(199

2)

Def

ault

(def

ault

cos

tsan

d m

ortg

age

pric

ing)

725,

000

sin

gle-

fam

ily

fixe

d-ra

te lo

ans

1976

–83,

bou

ght

byF

redd

ie M

ac

Pro

port

ion

al h

azar

d m

odel

,es

tim

atio

n o

f de

fau

ltco

sts

and

mor

tgag

epr

icin

g

Def

ault

(D

V)

Loa

n-t

o-va

lue

rati

o (+

) (y

ear

of o

rigi

nat

ion

, eff

ect

vari

es)

Def

ault

(cap

ital

requ

irem

ents

for

savi

ngs

inst

itu

tion

s)

Def

ault

(sol

ved

nu

mer

ical

lyop

tion

-bas

edth

eore

tica

lm

odel

)

Def

ault

(eff

icie

ncy

insi

ngl

e-fa

mil

ydw

elli

ng

mar

ket,

tran

sact

ion

cost

s co

nsi

dere

da

mar

ket

impe

rfec

tion

)

300,

000

loan

s19

76–8

0,

bou

ght

byF

redd

ie M

ac

NA

Pro

port

ion

al h

azar

d m

odel

,es

tim

atio

n o

f m

ean

retu

rns,

var

ian

ces,

an

dco

vari

ance

s o

f va

riou

slo

an-t

o-va

lue

and

geog

raph

ic g

rou

ps; c

apit

alre

quir

emen

ts a

rees

tim

ated

fro

m r

esu

lts

NA

Def

ault

haz

ard

(D

V)

Loa

n-t

o-va

lue

rate

(+

) G

eogr

aph

ic d

iver

sifi

cati

on (

–)

NA

Fre

ddie

Mac

Haz

ard

mod

el o

f de

fau

ltre

gres

sion

(lo

ss s

ever

ity)

,se

vera

l spe

cifi

cati

ons

Def

ault

haz

ard

(DV

) S

ever

al n

egat

ive

equ

ity

leve

ls (

+)

Los

s se

veri

ty (

DV

) L

oan

-to-

valu

e ra

tio

(+)

Age

of

loan

(+

) A

ge o

f lo

an s

quar

ed (

+)

Cou

pon

min

us

curr

ent

rate

(+

)C

oupo

n m

inu

s cu

rren

t ra

te s

quar

ed (

+)

Tex

as d

um

my

(+)

Not

e: M

BA

= M

ortg

age

Ban

kers

Ass

ocia

tion

; FH

LB

B =

Fed

eral

Hom

e L

oan

Ban

k B

oard

. *D

V =

dep

ende

nt

vari

able

, + =

sig

nif

ican

t p

osit

ive

effe

ct, –

= s

ign

ific

ant

neg

ativ

e ef

fect

, NS

= n

o si

gnif

ican

t e

ffec

t, N

A =

not

app

lica

ble.



One study has analyzed the determinants of both mortgage loss anddefault rates. Evans, Maris, and Weinstein (1985) found high initial loan-to-value ratios riskier in terms of both default rates and expectedlosses.36 In contrast, loan amount had no effect on default rates but didhave a significant negative effect on expected loss. Similarly, althoughloans made to African-American borrowers were found to be riskier thanthose made to other borrowers on both measures, the magnitude of thedifference was smaller on expected loss than on default rates. Loansmade to African-American borrowers had 7.47 percent more defaultsthan those made to other borrowers, yet the expected loss differenceamong these borrowers was only 2.35 percent.37 These findings suggestthat from an institutional perspective, expected losses may be a bettermeasure of default risk than default rates, because expected lossesprovide a more accurate basis for estimating mortgage insurance premi-ums, mortgage interest rate premiums, and the potential default costs ofa government subsidy program.

Foreclosure: the Lender' Decision to Minimize Losses

The foreclosure costs faced by lenders are an important consideration inestimating the expected loss resulting from mortgage default. Foreclo-sure costs are affected by several factors.38 First, foreclosure costs arelower in states where there is nonjudicial foreclosure, such as power-of-sale foreclosure, foreclosure by advertisement, or a trustee’s sale (Clauretie1987). Where nonjudicial foreclosure is available, a third party such asa lawyer or a foreclosing service conducts the sale of the foreclosedproperty. In these states, lenders can avoid the more costly court-supervised foreclosure. Also, costs are lower where there is an absence ofstatutory right of redemption, which allows borrowers to redeem theirproperties after the foreclosure sale for the amount paid at the sale. Costsare also lower where deficient judgment is allowed, which permitslenders to recover directly against the borrower’s personal assets.Finally, foreclosure costs decrease in states with shorter foreclosure and

36In a recent study, Clauretie (1990) also found that the loss rate on defaulted loansincreases with loan-to-value ratio. Clauretie contended that an adequate measure ofmortgage risk is the dollar loss per amount originated. This dollar loss is the product ofthe default rate and the loss rate on defaulted loans (p. 203).

37Evans, Maris, and Weinstein (1985) performed a risk-return analysis considering factorssuch as loan characteristics, borrower’s race, and location. Using information from theFHA Mortgage Cross Reference File, the authors found that the magnitude of the effectsof loan characteristics and race on expected loss and default rate was distinct amonggroups of loans. However, in contrast to prior studies of default rates, they found suburbanand urban location (other than central city) to have no effect on either default rates orexpected loss.

38The presentation in this section follows Clauretie (1987).


redemption periods (i.e., the period of time borrowers have to exercisetheir right of redemption). Foreclosure costs are important to the lender’sdecision to foreclose rather than renegotiate a loan.

In his analysis of the foreclosure decision by lenders, Clauretie (1987)found that foreclosure is more likely in states where costs are lower.39 Instates where legal costs are high, lenders appear more willing to work withslow or delinquent borrowers. In such cases, however, lenders may also incurlosses as a result of the negotiation. Thus, Clauretie concluded, interstateforeclosure rates “reflect the choice of the least-cost method of limitinglosses” by lenders when dealing with slow or delinquent loans (p. 165).

Default Risk and Capital Requirements

An estimation of expected losses and mortgage risk is indispensable inassessing the capital requirements of lenders and the institutionsinsuring these mortgages. Erosion of reserves in the FHA MutualMortgage Insurance Fund in the late 1980s prompted an actuarialanalysis of the fund, which was conducted by Price Waterhouse (1990).Given that defaulted loans make claims on the reserve fund, PriceWaterhouse developed economic models to explain the probability ofclaim and nonclaim loan terminations and to forecast future claims onthe fund by analyzing the default experience of FHA loans.40

The results of Price Waterhouse’s contingency claims analysis wereconsistent with those of prior work. The level of home equity, capturedwith loan-to-value ratio, was found to have a significant effect on claimrates. This effect, however, varied across loan-to-value ratios. As loan-to-value ratio increased, the negative effect of equity also increased. There

39Clauretie (1987) also found that in states with high foreclosure costs, lenders are morelikely to make loans on risky properties only if they are underwritten by federal agencies.In his analysis, Clauretie used foreclosure data on conventional FHA and VA loans, bystate, from the member institutions of the Mortgage Bankers Association (1976–1985) andthe Federal Home Loan Bank System (1976–1983).

40Using a framework similar to the one proposed by Vandell and Thibodeau (1985), PriceWaterhouse estimated claim rates due to loan termination through default. Default rateswere expressed as a function of the level of equity (loan-to-value) and a number of economicconditions. Consistent with prior work, default is expected to occur with high initialmortgage loan-to-property-value ratio because a high ratio provides little cushion againstdefault when property values decline. Similarly, risk increases when the value of themortgage rises above the remaining mortgage balance, which occurs when the currentinterest rate falls below the original contract rate. Thus, both a sharp decline in propertyvalue and prevailing interest rates below the contract rate could lead to default. Borrowersmay also consider the default decision if they desire or are forced to move by events suchas divorce or loss of employment. Data from a pool of FHA-insured 30-year fixed-rate loansoriginated between 1975 and 1989 were used in the analysis. Price Waterhouse alsoestimated and analyzed claim rates due to loan termination through prepayment.


was a pronounced increase in claims when loan-to-value ratio was above90 percent, and even a further escalation when it exceeded 95 percent.Conversely, loan size was found to have a significant but negative effecton claims. That is, smaller loans were found to be riskier than biggerloans, reflecting the fact that only high-income borrowers may qualify forlarge loans.41

Thus, the characteristics of loans are crucial in estimating risk of lossesin loan pools. In assessing the effectiveness of the estimates, PriceWaterhouse found that 96 percent of the actual number of FHA claimterminations from 1979 to 1987 were predicted accurately. Consistently,the pattern of claims forecast for the period from 1988 to 1990 was easilyexplained by differences in loan composition. The sharp increase inpredicted claim terminations in 1988 and 1989 was attributable to themove toward higher loan-to-value ratio on FHA loans. The decline inpredicted claims in 1990 was attributable to the fact that the simulationused a larger loan amount, which, by law, requires a lower initial loan-to-value ratio.42

The risk of losses in large loan pools and the resulting capital require-ments for lenders were also examined by Quigley and Van Order (1991).43

Loan-to-value ratio and geographic diversification were found to havesignificant effects on risk. Institutions holding loans with initial loan-to-value ratios between 81 and 90 percent required one-third of the capitalrequired by institutions holding loans with ratios between 91 and 95percent.44 Similarly, a nationally diversified lender was found to needonly one-half of the capital required of a regionally based lender (p. 354).This disparity suggests that capital requirements for lending institu-tions need to be set by loan characteristics such as loan-to-value ratio andby geographical diversification.

41Other variables considered in the claim analysis were also found to have a positiveimpact on loan termination through default. For instance, unemployment rate, lagged oneyear, had a positive impact on claims. As was the case with home equity, the effect ofunemployment rate on claims increased with loan-to-value ratio. Also, age of mortgagewas found to have a nonlinear effect on claims. Consistent with prior work, claims causedby default peaked in the fourth year after origination and declined afterward (PriceWaterhouse 1990).

42The larger loan amount used in the 1990 simulation is the result of an expanded ceilingallowed for loans originated that year.

43Using data from 300,000 conventional loans originated from 1976 through 1980 andbought by Freddie Mac, Quigley and Van Order estimated mean returns and theirvariances and covariances, that is, the risk associated with the return, for various loan-to-value and geographical groups.

44In assessing the adequacy of the 3 percent capital requirement for 30-year FRMs withlow loan-to-value ratios, Quigley and Van Order (1991) concluded that this requirementis excessive and that, based on the experience of loans originated between 1976 and 1980,premiums of 2 to 22 basis points are adequate, given the predicted risk (p. 367).


The Proportional Hazard Estimation of Default Probabilities

Proportional hazard estimation is the state-of-the-art methodology indefault studies. Quigley and Van Order (1991) used a proportionalhazard model to estimate the probability of default.45 The use of thismethodology is consistent with the continued application of innovativestatistical methods developed throughout the past three decades to studydefault. Prior applications include the use of regression analysis (Page1964; von Furstenberg 1969), multivariate discriminant analysis (Herzogand Earley 1970), stepwise discriminant analysis (Morton 1975), cohortanalysis (von Furstenberg and Green 1974), tobit estimation (Webb1982), logit estimation (Vandell and Thibodeau 1985), and multinomiallogit estimation (Zorn and Lea 1989; Cunningham and Capone 1990).

Hazard methodology is ideally suited to analyze default risks in loanpools.46 If we define hazard as a chance event (i.e., default) and hazardrate as the probability that this event will occur in a particular periodgiven that it did not occur at the beginning of the period (i.e., the mortgageis current at the beginning of the period), then a hazard model can be usedto estimate the probability of default in the first year, second year, andso on. A hazard model can also be used to analyze the factors that affect thehazard rate each year, for example, the equity in the home and the differencebetween par and market value of the mortgage. By statistically estimatinghazard functions, we can measure the effects of these factors on theoccurrence of default.47 In turn, the results of this statistical estimation

45The proportional hazard model was first used in the loan termination literature toanalyze mortgage prepayment behavior. See, for example, Green and Shoven (1986) andQuigley (1987). Other recent studies on residential default and delinquency that have usedproportional hazard methodology include Harmon (1989) (cited in Vandell et al. 1991) andVan Order (1990). Vandell et al. (1991) used this methodology in their study of commercialreal estate default.

46The presentation in this paragraph follows the general presentation of the hazardmodels in Van Order (1990).

47In technical terms, on the basis of proportional hazard methodology, the probability ofdefault (a), given the exogenous factors x1,..,x n at time t, can be divided into twomultiplicative factors:

Prob = λ(a) * π(x1,..., xn ),

where

λ(a) is the baseline hazard, which is the proportion of the population that would defaulteven under completely stationary or homogenous conditions. The baseline hazard givesthe normal time profile of conditional default rates (the probability of default in year 1,year 2, etc., of a loan with a given loan-to-value ratio [Van Order 1990]); and

π(x1,.,xn ) are the exogenous factors that make default more or less likely.

The proportionality assumption refers to the fact that if the factors xl,..,xn make turnovermore likely at one age, they also have an “equiproportional impact at all ages” (Green and


can be used in different types of analysis, such as mortgage pricing, or toanswer questions like this: “How much greater is the chance of default fora 95 percent loan-to-value loan versus a 75 percent loan-to-value loan?”Van Order 1990, p. 29).

Van Order (1990) presented an example of the use of this methodology toestimate mortgage pricing.48 He found that a loan with a loan-to-valueratio of 80 percent or less originated in 1980 had about a 1.4 percentchance of defaulting in the first ten years. Given that the loss on defaultis about 25 cents on the dollar for an 80 percent loan-to-value-ratio loan,an upfront charge of .25 × 1.4 percent, or .35 percent (an annual chargeof about 8 basis points) would cover the expected losses (p. 30).49 As theuse of the proportional hazard methodology becomes widespread, otheraspects of the default experience may be better understood.

Recent Developments

The contribution of most third-generation studies is largely methodologi-cal, both in terms of advancing better measures of mortgage risk andusing of sophisticated estimation techniques. Conceptually, the basicpremises postulated by second-generation studies have not been revised.There is consensus among analysts about viewing default as an option inwhich net equity has the dominant role. However, the issue of whetheror not this option is exercised ruthlessly—that is with no consideration

Shoven 1986, p. 45). The effect of these factors on default is also assumed to be time- separable, that is, past and future attributes of the environment are assumed to have noeffect on turnover in the present (Green and Shoven 1986, p. 45). Assuming an exponential functional form (Green and Shoven 1986; Quigley 1987; Van Order 1990), the hazardrate of default after t years (h[t]) can then be expressed as (Van Order 1990, p. 31)

h(t) = λ(t)ebx,

where

λ(t) is a series of dummy coefficients given the baseline hazard rate for each year afterorigination;

e is the exponential function;

b are the coefficients to be estimated that measure the effect of x on the hazard function;and

x are the explanatory, exogenous factors l...n.

48For a comprehensive review of the option literature on mortgage pricing, pricing of bothprepayment and default risks, refer to Hendershott and Van Order (1987).

49In his analysis, Van Order (1990) used data from about 725,000 single-family fixed-rateconventional loans originated from 1976 through 1983 and purchased by Freddie Mac.


for transaction costs and crisis events that may delay, expedite, oreliminate the need to exercise the default option—remains open todebate.

The role of transaction and other costs in the default decision has beenthe subject of several recent studies. For instance, Kau, Keenan, and Kim(1991, p. 8) developed an intertemporal optimization model of the defaultdecision and contended that a borrower defaults not when the value of theequity falls below the unpaid principal or the present value of payments,but when it falls below the value of the mortgage to the lender (the costto the borrower). Consistent with Epperson et al. (1985), the authorsshowed that this value includes both the value of exercising the optionnow and the value of terminating the option in the future. Usingsimulation analysis, the authors found support for their model. Specifi-cally, they found that the value of the house must fall by substantiallymore than the value of the mortgage’s termination option at the point ofzero equity before it is in fact rational for a borrower to default. Theauthors concluded that the amounts involved can be mistaken fortransaction costs when in reality transaction costs play little or no role inthe default decision (p. 9).50

Quigley and Van Order (1992) disagreed; they contended that transac-tion costs, moving costs, reputation costs, and capital constraints makethe exercise of the default option on residential mortgages less ruthlessthan in other “frictionless financial” markets (p. 2). In response to Kau,Keenan, and Kim (1991), Quigley and Van Order (1992) acknowledgedthat although the notion of a ruthless exercise of the default option isconsistent with observed default data, it does not explain three inconsis-tencies: (1) peaks in average default rates over time for various initialloan-to-value ratios are more similar than predicted by Kau, Keenan, andKim (1991); (2) loss severity increases significantly as a function of initialloan-to-value ratio, contrary to theory; and (3) the spread betweendefault rates for high and low loan-to-value-ratio loans is less significantthan predicted by Kau, Keenan, and Kim (1991).

Quigley and Van Order (1992) found support for their contention in datafrom Freddie Mac loans.51 Although they acknowledged that transaction

50In other words, Kau, Keenan, and Kim (1991) concluded that the default option isexercised “ruthlessly.”

51In their study of the efficiency of the single-family housing market and the role thattransaction costs (a market imperfection) have in this market, Quigley and Van Order(1992) undertook two types of analysis. First, using data on the default experience byFreddie Mac, the authors estimated several specifications for a proportional hazard modelof default, using different measures of home equity. Second, the authors estimated severalspecifications of a model of mortgage loss severity due to default. In general, the findingsof these analyses with regard to the significance of loan-to-value ratio, equity, and age ofthe mortgage are consistent with those of prior work (the authors included only thesefinancial variables in their analyses).


costs by themselves do not explain the discrepancies either, they claimedthat transaction costs, especially reputation costs, coupled with a ran-dom—rather than deterministic-—mortgage term are indeed consistentwith the observed default behavior. The term of the mortgage becomesrandom because borrowers move for random reasons “and the holders ofnon-assumable mortgages pay off at par,” not market value, when theymove (p. 29).52 The authors did not test this contention empirically.

In a recent study, Giliberto and Houston (1989) further examined the roleof crisis events and costs on default in their presentation of a theoreticalmodel of default that explicitly considered moving opportunities. Theauthors contended that borrowers purchase homes and mortgages thatare optimal at the time of loan origination. These homes and mortgages,however, become suboptimal over time because of life-cycle and economicevents. Life-cycle events include marriage, divorce, death, and change injob or transfer of job location. Economic events that may make homes andmortgages suboptimal include a decline in value or a loss of job or incomeand an increase in housing costs, which make the mortgage paymentsexcessively burdensome.

When a home, mortgage, or both become suboptimal, borrowers are saidto consider relocation and the default option. Giliberto and Houston(1989) contend that a range of book equity exists within which borrowerswho are about to relocate could default (but would not necessarily doso).53 Within this range, both the equity and the value of relocationopportunities associated with moving interact to determine default.54

Factors affecting relocation opportunities include the present value ofthe incremental income effects associated with moving, the current valueof the mortgage to the borrower, the current principal balance of themortgage, the difference between the market value and the value of theproperty to the owners, and the costs of refinancing and moving. Gilibertoand Houston did not test their model empirically.

52A particularly important random move is one forced by exogenous reasons, for example, jobloss or divorce. “Under these circumstances, the term of the mortgage may be short and thevalue of keeping the option alive may be negligible” (Quigley and Van Order 1992, pp. 29–30).

53Thus, both the presence of negative equity and the inability to meet mortgage paymentsare considered necessary but not sufficient conditions for default.

54Giliberto and Houston (1989) considered their model consistent with prior work.Although there is widespread acceptance that default is primarily driven by equity, thereis also some indication in the literature that default conditions can be modified whenborrowers have to move (Hendershott 1985, cited in Giliberto and Houston 1989). Forinstance, inability to meet mortgage payments is one reason people have to move. Gilibertoand Houston considered highly beneficial relocation opportunities as reasons that peoplehave to move.


The Delinquency Decision in the Default Process

Related to but distinct from the borrower’s decision to default is thedecision to delay making one or more scheduled loan payments. Accord-ing to the premises of the borrower payment model discussed earlier,another mortgage payment choice borrowers have every payment periodis to become delinquent.55 Yet compared with the widespread interest indefault, the number of studies on delinquency is rather limited.56 Thereare two main reasons for this lack of research. First, default is consideredmore serious and costly than delinquency. Borrowers who default give upthe title to their homes for the value of the mortgage, whereas borrowerswho become delinquent have every intention of keeping the title to theproperty and continuing mortgage payments at some future time. Delin-quency appears to be less severe than default.

Second, the delinquency decision is difficult to model. From the borrower’sperspective, delinquency can be considered a cash flow problem: Borrow-ers who experience a decline in income or an unexpected increase inexpenditures are forced to choose between mortgage delinquency and areduction of nonmortgage expenditures. Thus, delinquency cannot easilybe framed within the prevailing option-based approach.57

Given these difficulties and the fact that default is considered the mostserious and costly termination of the mortgage contract, the emphasis ondefault is easily understood.

However, delinquency is costly to both borrowers and lenders. Forborrowers, delinquency costs include penalty charges, a lower creditrating, and emotional distress borrowers may associate with the decisionto delay mortgage payments. For lenders, slow loans—those loans thatare chronically delinquent—may be almost as troublesome and costly asloans that reach foreclosure (Sandor and Sosin 1975). This fact aloneshould warrant a more widespread interest in the study of delinquency.

In addition, not all aspects of mortgage risk can be addressed adequatelyin the study of default. For instance, Webb (1982) contended that an

55Actually, borrowers’ payment choices are not as clearly defined as the model suggests. Inpractice, a loan is considered delinquent before default. When payments are first missed, itis not possible to know whether the borrower has defaulted or is just delinquent, but it ispossible retrospectively to identify those delinquent loans that were later cured (mortgagepayment restarted) and those that ended up in default (foreclosure occurred).

56Similarly, the number of studies on delinquency is small compared with the number ofstudies on prepayment, which is the other mortgage payment choice borrowers have.

57As an anonymous referee correctly pointed out, “If we believe the models which underlie themodern option theory of default, then the right model is some form of competing risks modelwith time-varying covariates. At a minimum, the time varying covariates include thedifference between the present discounted value of the mortgage at coupon and at currentinterest rates, and the current equity in the house. The competing risks are mortgagetermination through default and prepayment, which are clearly related.”


analysis of delinquency, not default, was needed to assess whetherdifferent mortgage risks exist among different segments of the popula-tion, because the determinants of default are related to property and loancharacteristics, and these have only a marginal relationship to borrowercharacteristics.

Nonetheless, delinquency has received little attention, and most studiesare based on the assumption that delinquency is triggered by the samefactors as default. Delinquency has, however, been analyzed from boththe lender and the borrower perspectives.

The Lender Perspective

The earlier studies of delinquency attempted to identify the factorsknown to lenders at the time of loan origination that were associated withsubsequent delinquent loans. Consistent with findings of the defaultstudies, three loan factors had a consistent and positive effect on delin-quency: loan-to-value ratio, the presence of junior financing (Herzog andEarley 1970; von Furstenberg and Green 1974), and the age of themortgage (von Furstenberg and Green 1974).58 Similarly, two borrower-related factors, borrower occupation and household income, had signifi-cant effects on the decision to delay mortgage payment.59 Because amajority of delinquencies are cured, these early studies showed thatvariables capturing home equity and a borrower’s ability to pay are lesssystematically related to delinquency than to default (von Furstenbergand Green 1974; Morton 1975).60

58In their multivariate regression analysis, Herzog and Earley (1970) found initial loan-to-value ratio to be significantly related to the delinquency decision. The presence of juniorfinancing was found to be the most important loan characteristic affecting this decision.Loan purpose, such as construction, was also found to be a significant predictor ofdelinquency. In contrast, the authors found term of loan to have no effect on delinquency.In their analysis of 7,609 loans originated by one lender in Pittsburgh, Pennsylvania, vonFurstenberg and Green (1974) found that if the initial loan-to-value ratio is raised from80 percent to 90 percent, delinquency rates will increase by over two-thirds, ceterisparibus. The authors also found that delinquency rates peak four years after loanorigination and fall to about one-third of their initial level by year 15, thus exhibiting anage pattern similar to that of default rates.

59In their analysis of borrower characteristics, Herzog and Earley (1970) found borrower’soccupation, a proxy measure for the stability of income, to be highly significant. Incontrast, mortgage-payment-to-income ratio at the time of origination was found not to besignificant. In their analysis, von Furstenberg and Green (1974) found income to besignificant and negatively related to delinquency. An increase in income from $5,000 to$10,000 lowered the expected delinquency rate by 31 percent (p. 1547).

60For instance, in comparing default with delinquency, von Furstenberg and Green (1974)found that the delinquency elasticities with respect to home equity and family income wereonly half as large in absolute value as the corresponding default elasticities. In hisdiscriminant analysis of loans originated from 24 financial institutions in Connecticut,Morton (1975) arrived at similar conclusions. In addition, he found that borrowers withfive or more dependents and those living in properties with three or more units were morelikely to be delinquent in their payments than were other borrowers.


The Borrower Perspective

In contrast to the early works, later studies analyzed the delinquencydecision from the borrower perspective. The decision to delay mortgagepayment may be made when borrowers are faced with a decline inincome and are forced to choose between mortgage delinquency and areduction of nonmortgage expenditures. In his study of potential delin-quency under alternative mortgage instruments (AMIs), Webb (1982)examined such a premise with data from the Panel Study of IncomeDynamics (Survey Research Center, University of Michigan).

Defining potential delinquency as increases in mortgage payment-to-income ratio over time (housing burden), Webb (1982) found that borrowercharacteristics play a role in explaining simulated potential delinquencies.Households headed by older persons, minorities, or persons in occupationswith high income variability were more likely to experience increases inhousing burden. In turn, mortgages with a high degree of variability inpayments and with a relatively slow rate of payment growth, such as ARMs,or with a steady but slow rate of growth, such GRMs, were less risky thanmortgages with payments that increase steadily but at a relatively high rateof growth, such as PLAMs. In assessing the relative contribution of incomeand mortgage payment variability to potential delinquency, Webb foundthat high-risk borrowers were consistently more likely to be delinquentthan were other borrowers, regardless of the degree of variability inmortgage payments. The severity and duration of potential delinquencywere also related to borrower characteristics. However, AMIs with the mostvariability in payments exhibit the highest risk of delinquency, regardlessof borrower characteristics.

Although empirically substantive, early studies of delinquency lack aformal theoretical treatment. In their study of the default decision,Vandell and Thibodeau (1985) also considered the delinquency option intheir two-period maximization model of consumer choice.61 However,

61Vandell and Thibodeau (1985, pp. 295–296) expressed the payoff function if borrowerschoose to become delinquent as

W Del = (Y – R)(1 + ri +(VT –LT) + W(1 + r

i) – Q(1 + rd)

where

WDel = payoff function if borrower chooses to become delinquent;

Y = real annual after-tax household income;

R = required real nondiscretionary expenditures (other than housing);

ri = expected real return on nonhousing investments;

VT = expected real market value of the property;

LT = expected real outstanding loan balance on mortgage;

W = current real nonhousing wealth;


their empirical analysis examined the default option exclusively; they didnot test the delinquency decision. In a recent study, Harmon (1989) usedproportional hazard methodology to examine the delinquency decision.6262

Compared with the thoroughness of default studies, little is known aboutthe delinquency decision. Recent developments in the default literaturesuggest that crisis events (e.g., Vandell and Thibodeau 1985) and thedesire or need to move (e.g., Foster and Van Order 1984; Giliberto andHouston 1989) may play an important role in the borrower’s decision todefault. Given that these events are only marginally related to loancharacteristics and fully related to borrower characteristics, an analysisof the default decision within a framework that incorporates the delin-quency decision may be more appropriate. Ultimately, a better under-standing of the delinquency decision may lead to a reassessment of theborrower payment model and its analytical assumption that delinquencyand default decisions are distinct and may suggest instead that thesedecisions are sequential and related.63

Residential Mortgage Default: What is Known and What isUnknown

The review of the literature presented here indicates a continuedinterest in the subject of mortgage default. Today, most studies viewdefault from the option perspective, in which a borrower’s home equityhas the dominant effect. There is also some evidence of the importanceof transaction costs and borrower expectations in affecting the exerciseof the default option. In contrast, the role of other borrower-relatedfactors in the default decision is not so well understood. For instance,household income and mortgage payment have been found both to havean effect and to have no effect on default. A major reason for these mixed

Q = required real after-tax payment on mortgage (plus taxes and insurance and otherownership costs); and

rd = expected real cost of delinquent payment, including interest and penalties.62Cited in Vandell et al. (1991).

63To our knowledge, only one study has ever examined this contention. In their study ofmortgage delinquency and foreclosure, Herzog and Earley (1970) estimated the determi-nants of conditional foreclosure risk, that is, the risk that loans already delinquent will beforeclosed. The authors found that significant effects on conditional foreclosure risk weresimilar to those affecting delinquency, with three exceptions. First, term of the loan wasfound to be negatively related to delinquency but directly related to conditional risk.Second, while borrower occupation at time of loan origination was found to have asignificant effect on delinquency, it was found to have no consistent and significant effecton conditional risk. Finally, while only loans made for refinancing purposes exhibited ahigher risk of delinquency, loans made for both refinancing and new construction had ahigh conditional risk.


findings has been a lack of adequate panel data with relevant borrower,property, and loan information over time. This problem could be solvedby the construction and maintenance of a widely accessible longitudinaldatabase of borrowers who are representative of U.S. home buyers.

What is Known: the Role of Loan Characteristics

Consistently, home equity, or the related measure of loan-to-value ratio,has been found to influence the default decision. There is a consensus inmost recent default studies that the correct measure of a borrower’s netequity is the contemporaneous market value of property less the contem-poraneous market value of the loan, a measure that also incorporatesborrower expectations. Default probabilities estimated using this mea-sure indicate the importance of equity in the default decision. However,they also indicate the importance of transaction costs and the complexityof estimating the value of the default option, because there is value inkeeping the default option viable. For instance, simulations indicatethat the probability of default in the presence of a 10 percent negativeequity in year 5 after origination is only 1.75 percent (Vandell andThibodeau 1985).

What is Unknown: the Role of Transaction Costs and Borrower-Related Factors

The role of transaction costs and borrower-related factors in the defaultdecision is less well understood. The debate over the importance oftransaction costs on the exercise of the default option, exemplified by theworks of Kau, Keenan, and Kim (1991) and Quigley and Van Order(1992), remains unresolved. Kau, Keenan, and Kim (1991) have solvednumerically an option-based theoretical model of default that indicatesthat transaction costs play little or no role in the exercise of the option;therefore, they conclude that the option is exercised ruthlessly. Quigleyand Van Order (1992), however, have identified a number of inconsisten-cies between the theoretical premises of the ruthless model and observeddefault behavior. Quigley and Van Order suggest that reputation costs(one form of transaction cost), along with a random term of the mortgage,can explain observed default behavior, especially among borrowers withnonassumable mortgages who want or have to move. This premise,however, remains to be tested empirically.

Similarly, the role that borrower-related factors have in the defaultdecision needs to be addressed in future research. The lack of consistentfindings in this area is most likely due to the fact that all borrowerinformation at the time of default is estimated from ex-ante information,

376 Roberto G. Quercia and Michael A. Stegnan

using national, regional, or local indices that may not reflect events orchanges in the individual circumstances of borrowers who default.When new panel data with the necessary borrower, loan, and propertyinformation become available, a more comprehensive analysis of theeffects of borrower factors on default will be possible.

A better understanding of the role of borrower-related factors in defaultis of crucial importance for practical and theoretical reasons. Forpractical reasons, a better understanding can be used, for instance, toextend homeownership opportunities to borrowers now considered risky.If the effects of factors such as self-employment on default are proxies forincome variability, then it should be possible to minimize mortgage riskby designing AMIs to address them. If, conversely, these effects are areflection of lower permanent incomes among some borrowers, thendefault risks cannot be minimized through the use of AMIs (Vandell andThibodeau 1985). Lenders and loan-insuring institutions could also usethis information to set mortgage interest rate premiums and to pricemortgages more in line with the real risk represented by borrowers withcertain characteristics.

Understanding borrower-related effects is also important for theoreticalreasons. The notion that the desire or need to move may lead to thedecision to default has long been recognized (von Furstenberg 1969; vonFurstenberg and Green 1974; Giliberto and Houston 1989; PriceWaterhouse 1990) but has never been tested empirically. Ex-post infor-mation is needed to analyze whether borrower factors such as crisisevents are indeed driving forces underlying the default decision and toanalyze how the decision to move relates to the equity position. Thenotion suggests a possible bridge between the mobility and defaultdecision (Giliberto and Houston 1989).

The need to understand the effect of borrower-related factors alsosuggests another area of further research. A weakness in the defaultliterature reviewed is the lack of analysis of the default experience ofborrowers holding AMIs such as ARMS. Only two studies, those of Zornand Lea (1989) and Cunningham and Capone (1990), have examinedARM default rates, and both studies have limited applicability. As ananonymous reviewer stressed, “Not only is more work needed on defaultexperience with these instruments, but it may reveal stronger relation-ships between borrower characteristics and mortgage default than thefixed-rate mortgage experience.”

In conclusion, the current state of the literature indicates that defaultdepends clearly on loan characteristics, mainly home equity. Less cer-tain, however, is the role that transaction costs and borrower-relatedfactors play in the default decision. While the analysis of the default


decision of borrowers holding nonassumable mortgages may clarify theimportance of transaction costs, the development of an expanded defaultmodel, which includes considerations commonly associated with delin-quency, may clarify the role of borrower-related factors. Similarly, thedevelopment of an expanded model needs to incorporate the mobilitydecision.

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