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An economic analysis of the home mortgage default insurance market with emphasis on the decline of FHA

Material Information

Title:
An economic analysis of the home mortgage default insurance market with emphasis on the decline of FHA
Creator:
Kaserman, David Lynn, 1947-
Publication Date:
Language:
English
Physical Description:
xii, 196 leaves : ill. ; 28 cm.

Subjects

Subjects / Keywords:
Default insurance ( jstor )
Housing ( jstor )
Insurance ( jstor )
Insurance policies ( jstor )
Insurance risks ( jstor )
Lenders ( jstor )
Loan defaults ( jstor )
Mathematical variables ( jstor )
Mortgage loans ( jstor )
Supply ( jstor )
Dissertations, Academic -- Economics -- UF
Economics thesis Ph. D
Homeowner's insurance -- United States ( lcsh )
Mortgage guarantee insurance -- United States ( lcsh )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 182-195.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by David L. Kaserman.

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Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
Copyright [name of dissertation author]. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Resource Identifier:
025637537 ( ALEPH )
03122543 ( OCLC )
AAU5145 ( NOTIS )

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AN ECONOMIC ANALYSIS OF THE HOME MORTGAGE
DEFAULT INSURANCE MARKET WITH EMPHASIS
ON THE DECLINE OF FHA
















By


DAVID L.


KASERMAN


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY


































"However,


just


as pressing


is the need


to reappraise


in the comprehensive manner


the entire


program


and to determine


housing


its future


needs --Wright


role


Patman,


in serving


Congress4ional


national

Record,


August


1974.















ACKNOWLEDGEMENTS


This study has benefited from the helpful contributions of many


people.


First,


the dissertation committee,


consisting of Roger Blair,


Max Langham,


Jerome Milliman, and Dean Taylor,


has been invaluable in


making suggestions for basic improvements in both the organization and


content of


the final product.


They have also provided a continual


source of encouragement throughout this effort.


This cooperation and


guidance has been particularly valuable because of my absence from the


university during the entire period of research.


This absence has


created considerable problems of communication that a less dedicated


or less understanding committee would not have tolerated.


cularly grateful to Dr.


I am parti-


Milliman for his willingness to serve on this


committee without previous contact with me in the classroom and for


the valuable advice that he has provided at every stage of


the research


effort.


Finally,


the greatest debt of appreciation is owed to Dr.


Blair


for providing both a counsel and an example for the last three years of

graduate study.

And second, a considerable amount of help and encouragement has

been provided by various colleagues at the Department of Housing and

Urban Development where the research for this dissertation took place.


John Morrall


was influential in providing the initial opportunity to









useful


comments


and has been


extremely


patient


in allowing


a more


tensive


effort


than


that


which


was


originally


envisioned.


Olsen


provided


careful


and extremely valuable


advice


on earlier


drafts


this


study.


And finally,


John


Ermisch


contributed


an unmeasurable


degree


through


both


extensive


discussions


and written


comments


every


stage.


ex-
















TABLE


OF CONTENTS


Page


ACKNOWLEDGEMENTS


LIST OF


LIST


TABLES


OF FIGURES


vill


. .a a S a .ix


ABSTRACT


CHAPTERS


INTRODUCTION


* a C a a S S 1


HISTORY
PROGRAM


Depressio
Section 2
Later Ent
The Volum


ENVIRONMENT


n Conditions and
03's Major Objec
rants into the D
e of Insurance u


OF THE FHA SECTION


Federal Response


tives
'efault
under S


Insurance
section 20


e Market


LITERATURE REVIEW


S C 34


The S
Studi
Aaron


carcity of Relevant Liter
es of Default Behavior by
's Analysis of the Contra


Mortga


ge Loans


nature
von
cting


Furs
Pro


tenberg


cess


A THEORETICAL MODEL
INSURANCE .


OF DEFAULT


RISK


AND DEFAULT


Introduction a
Default Probab
Individual M
The Demand for
The SuDolv of


Summary:


asi


nd Ov
ility


erview of the Theoretical Model
and Expected Default Loss on


mortgage
Default
Default
c Theory


Loans
Insurance
Insurance C
of Decline


Covera
overage


* a S C
a .


THE EMPIRICAL MODEL:


SPECIFICATION


92









TABLE


OF CONTENTS


(Continued)


Page


Equation
Equation


Private
Section


Mortgage


Insurance


203 Insurance


Volume


Volume


on New


Units


Supply


Constraints


on Alternative


sources


Default
Relative


erage


erms


Available


on Section


203 Insur


Loans


Other


Factors


Section


that


erve


203 Insurance


to Diff
Service


erentiate


FHA mortgage limit
FHA processing time


reorganize


. .
* a S S .


tion


Secondar


market


activity


FHA i


nsure


loans


proc


Housing


essing
starts


requirements


as a proxy


for overall


housi


mortgage


market


activity


Equation


Section


Insurance


Volume


on Existing


Units


Equation
Equation


Proc


essi


Time


FHA Subsid


FHA Appli


grams


cations


Identity


ummary


EMPIRICAL MODEL:


ESTIMATION


AND INTERPRETATION


Data


Employed


timation


Techniques


Qualifications


Estimation


Result


and Interpretation


Equation
Equation
Equation
Equation


Total
VA In


Private


tion


surance


surance


Volume


Volume


Insurance


Volume


203 Insurance


Volume


on New


Units


Equation
Existing
Equation


tion


203 Insurance


Volume


Units


FHA Pro


cess


Time


An Empirical


Test


Joint


Cream


-Skimmin


Hypothesis








TABLE OF


CONTENTS


(Continued)


Contributions


Study


to the Exi


stin


Economic


Literature


Areas for Future


Need


Governme


for a B


not's


Rese


asic


arch
Chan


Role in


in the Federal
Home Mortgage D


fault


Insurance


Market


APEND ICES


APPENDIX


Hypoth


esis


ests


for Re


gress


Coeffi


clients


APPENDIX


Variable


finitions


and Data


sources


BIBLIOGRAPHY


Books


Journal
Working


Arti


Papers,


government


Public


nations


and Unpubl


Memoranda


BIOGRAPHICAL


SKETCH


Page
















LIST OF TABLES


Table


Page


Privately Owned Housing Units Started under the FHA
Section 203(b) Mortgage Insurance Program Compared


with Total Housing Starts


in the U.S.;


1935-69


Regressions of Default Rates on the Age


(t) and Loan-


Value


(L/V) of Mort


gages


Grouped by


Terms


S. S S S 43


Al. 1


Regression Results for Total Insurance Volume


Equation,


Dependent Variable:


TOT/ORIG


A1.2


Regression Results for VA Insurance Volume Equation


Dependent Variable:


A1.3


Regression Results for Private Insurance Volume


Equation,


A1.4


Dependent Variable:


Regression Results for Section 203 New Units Insurance


Volume Equation,


Dependent Variable:


FHAN


Al.5


Regression Results for Section 203 Existing Units


Insurance Volume Equation, Dependent Variable:


A1.6


FHAE


Regression Results for FHA Single-Family Processing


Time Equation, Dependent Variable:


PROC
















LIST OF FIGURES


Figure


Page


Relationship Between the Provision of Insurance,


Supply of Mortgage Funds


and the Demand for Housing


Number of New Single-Family Dwelling Units


under the Section 203 Mortgage
1960:1-1974:2


Insured


Insurance Program;


Number of Existing Single-Family Dwelling Units
Insured under the FHA Section 203 Mortgage Insurance


Program;


1960:1-1974:2


. 30


Share of the Default
by the FHA Section 2
1960:1-1974:2


Insurance Market Accounted for
03 Mortgage Insurance Program;


Time Path of Defaults on Home Mortgages


Lender and Borrower
,and Downpayments


Tradeoffs Between Interest Rates


Utility of Profits Function for a Risk Averse Lender


Supply Curves of Individual Default Insurance Market


Participants


S .81


The Relationship Between Private Market Supply
Constraints and Section 203 Demand in the Default


Insurance Market


85








Abstract


of D


issertation


Presented


to the Graduate


Council


of the University


Florida


in Partial


Fulfillment


of the Requirements


for the Degree


AN ECONOMIC


Doctor


ANALYSIS


Philosophy


OF THE HOME MORTGAGE


DEFAULT


INSURANCE


MARKET


WITH


EMPHASIS


ON THE


DECLINE


OF FHA


David


L. Kaserman


March,


1976


Chairman:


Major


Roger


Department:


D. Blair
Economics


home


mortgage


Administration


(FHA)


default


have


insurance


experienced


programs


of the Federal


a precipitous


decline


Hous-


in the


volume


contracts


written


recent


years.


This


decline


in insurance


activity


considerable


been a

burden


accompanied


increasing


on the insurance


funds


claims


that


that


support


have

these


placed


programs.


The major


program


providing


unsubsidized


(actuarially


sound)


coverage


for mortgages


Section


written


203 program which


on single-family


has been


housing


severely


units


affected


has been


the declining


volume


of insurance


activity.


The fundamental


decline

gram in


question


in FHA insurance


efficiencies


addressed


activity


or increasing


in this


has been th

competitive


study


e result

pressure


is whether

of internal


S


from


this

pro-


the pri-


vate


firms


in the market.


This


is the crucial


issue


that


should


determine


the primary


thrust


of the federal


government


s future


poli-


cies


in this


area.


In nttamnti no


t-n adrlr r


hani r


1R 11 .


this


studv


develops


-


1hi r









mortgagor,


mortgagee,


and the supplier


of default


insurance


coverage.

viewed as

loss unce


The first


Sa competiti


!rtainty


two sets

ve mortga


to determine


of these p

ge market

the market


participants


under c

demand


interact


conditions


in what


of default


for mortgage


default


insurance.


Thus,


this


demand


seen


as being


derived


in nature,


with


its primary


source


found


in the demand


for and supply


mortgage


funds.


The last


set of market


participants


(the


suppliers


of default


coverage)


is composed


of four major


actors:


the FHA Section


program,


the FHA


subsidized


housing


mortgage


insurance


programs,


the Veterans


Administration


home


loan


guarantee


program


and the private


mortgage


insurance


industry.


Of these


four


actors,


the last


three


are viewed


subject


to supply


constraints


an institutional


nature


which


result


in their


services


being


rationed.


The notion


that


these


con-


strains


remain


effective


a fundamental


maintained


hypothesis


throughout


the analysis.


Finally,


coverage


supplied


the various


actors


in the market


is considered


to be non-homogeneous


substitutable.


This


result


in the overall


mortgage


default


insurance


market


being


determined


from


the operations


occurring


in four


inter-


related


sub-markets


(one


for each


supplier


of coverage).


This

partially


theoretical

simultaneous


model is t

equations


hen


that


used


to specify


depicts


a system of


the important


relation-


ships


that


determine


total


insurance market


activity


and the individual


insurance


activities


in each


of the four


sub-markets.


Estimation


this


model


using


quarterly


time


series


data


that


cover


postwar


1.


a ~


.. 9 0


bein


r *1 -


*


-t I









of the various


factors


that


have


led to the decline


in insurance


activity


under


Section


203.


There


are a number


of conclusions


that


are drawn


from


this


model


concerning


the overall


functioning


of the home mortgage


default


insur-


ance


market.


most


significant


result


for policy


purposes,


however,


is the finding


that


insurance


volume


losses


experienced


FHA have


been


primarily


determined


by market-oriented


opposed


program-


oriented)


influences.


important


implication


of this


finding


that


policy


actions


that


are intended


to rejuvenate


s activity


this market


should


be avoided.
















CHAPTER


INTRODUCTION


The home


mortgage


default


insurance


programs


of the Federal


Hous-


Administration


have


helped


serve


the nation


s housing needs


the last


forty-one


years.


During


this


period,


the basic


service


that


has been


coverage


rendered


against


these


default


programs


loss


has been


on individual


the provision


mortgages


insurance


originated


private


lenders.


It is generally


felt


that


such


insurance


encour-


aged


a larger


supply


mortgage


funds


on more


liberal


financing


terms


than


would


have


been


forthcoming


in the absence of


these


programs.


is also


felt


that


these


funds


have,


turn,


increased


the effective


demand


for housing


services


as the feasibility


of home


ownership


been


expanded


a larger


segment


of the overall


population.


The public


purpose


served


the FHA insurance


programs


is now


being


called


into


question,


and a fundamental


reexamination


of the


federal


government's


role


in the market


appears


to be imminent.


need


some


basic


revisions


seems


to have


been


created


an evolu-


tionary


process


that


has brought


forth


fundamental


structural


institutional


changes


in the


mortgage


lending


and default


insurance


markets


over


the last


decade.


Partly


as a result


of these


long


chan


and partly


as a result


of specific


operational


inadequacies,


thp PF A c


in l p


fmil v


- r n-t


1-' r -.


ornamme av


exneri enced


increase inr


difficulties


run









activity and in achieving the Congressional objective of actuarial


soundness.


These difficulties are now providing the catalyst for major policy

decisions that will determine the future role of FHA in the insurance


of home mortgage default risk.


Such decisions should be based upon the


most complete information that can reasonably be made available in

order to ensure that short run reactions to the existing situation do

not result in the design of policies or programs that will have unde-


sirable long run effects.


The likelihood that such effects will be


generated may be reduced with each additional piece of relevant informa-


tion provided to decision makers.


It is the purpose of this study to


provide such information in the form of an economic model of the home

mortgage default insurance market.

The model that has been derived for this purpose determines both


the volume of insurance written by the total market and


the individual


volumes of insurance written by the various supply-side participants in


that market over time.


In so doing,


the model contributes to the exist-


ing economic literature relating to the theory of mortgagor default


behavior,


the mortgage origination process, and the overall operation


of the default insurance market.


At the same time,


the model can be


used to provide a detailed explanation of the causal events that have


led to the current problems of FHA and,


thereby,


serve


as an important


input to the decision-making process.


Thus,


the study has two broad


objectives:


to contribute to the literature providing an economic


S- I C. 1i








and to provide an explanation of the process that has led FHA to its

current situation.


With regard to


FHA,


the study will be seen to give particular at-


tension to the insurance volume and claims experience of the Section


203 program.


This program is the oldest and by far the largest of the


single-family programs, accounting for almost 80 percent of the cumula-


tive insurance written by units and nearly 77 percent of the estimated

insurance in force in dollars at the end of June, 1973 (Sammawry of Mott-


gage InluAance Operations and Contract Autho itu


, 1973,


Section 203 program has been the mainstay of the general insurance op-

erations of FHA since its origination in 1934, and it has been the con-

tinuing loss of business being carried out under this program in recent

years that has created the great concern of both the administrators in

charge of these insurance operations and the decision makers involved

in federal housing policy.

A clear understanding of the causes of this decline is essential

in the design of future policies relating to the operation of the


program.


Completely different approaches are warranted by different


causes of decline.


For example,


if the Section 203 insurance program


has declined because of identifiable changes in the program's opera-


tions that have generated internal inefficiencies which have,

led to the neglect of basic default insurance market needs, t


in turn,


:hen a


corrective approach would appear to be appropriate.


But,


on the other


hand,


if the declining insurance volume has been primarily generated


4-1, fl n n .n .4 t% 4n n an a- 4 4- 4 an 4 n 41 a A a Cr, i-wi e -4 ii t r nn n n inn rl, ~ 4- n ^ f~









whether


there


exists


a public


need


for continuation


of the


program.


Hopefully


the findings


of this


study will


provide


information


for the


design


future


policies


relating


to the provision


of home


mortgage


default


insurance


on the


part


of the federal


government.


The study


itself


is divided


into


seven


chapters.


Following


this


brief


introductory


the default


insurance


chapter,


market


the history


are


presented


and institutions


in Chapter


relevant


II along with


detailed


documentation


of the decline


in insurance


activity under


Section


program.


Then,


a brief


review


some


economic


literature


that


is relevant


to the default


insurance


market


given


in Chapter


III.


Chapter


IV is devoted


to the development


a theoretical


model


of de-


fault


risk


and the default


insurance market


that


explains


the mechanisms


involved


in the determination


the individual


insurance


of total


activities


market


insurance


of the various


activity


suppliers


of default


coverage


in that


market.


This


model


is then


employed


in Chapter


specify


an empirical


model


of the default


insurance


market


that


can be


used


to estimate


the marginal


influence


of each


of the causal


factors


that


are implied


the theoretical


considerations


of the preceding


chapter.


The estimation


results


obtained


from


this


empirical


model


their


interpretations


are given


in Chapter


And finally,


the basic


conclusions


relating


to both


overall


default


insurance


market


operations


and the decline


of Section


are drawn


in Chapter


VII.


Additionally,


this


final


chapter


contains


a summary


of the study


and a discussion


some


promising


areas


for future


research.
















CHAPTER


HISTORY


ENVIRONMENT


OF THE


FHA SECTION


203 PROGRAM


Depression


Conditions


and Federal


Response


The Federal


Housing Administration's


basic


programs


providing


fault


insurance


conceived


eral


during


government


on private

the Great


financed


Depression


to the depressed


mortgage co

as a direct


conditions


of the


ntracts were


response

economy


originally

the fed-


in general


and the building


and construction


trades


sector


in particular.


state


of the


economy


at that


time


was such


that


the flow


of funds


through


the nation's


mort


gage


markets


had been


reduced


a trickle,


and residential


construction


activity


had virtually


ceased.


The produc-


tion


percent


new


homes


of the number


had dropped


built


to 93.000 units


in 1925),


in 1933


and on-site


(less


than


construction


employed


only


150,000


people


throughout


the entire


economy


R. Report


No. 897,


81st


gress,


56-67).


Harry


L. Hopkins,


the Federal


Emergency


Relief


Administrator,


testimony


before


the Housing


Banking


and Cur-


rency


Committee


on May


, 1934,


stated


The building


trades


erica


repres


ent b


all odds


largest


single


unit


our unemployment.


Prob


more


than


one-third


indir
1973,


ectl


all the unemploy


with


the building


are identified


trades.


..(Foard


, directly
and Frantz


. III, 3).


In addition


aonroximatelv


a


one half


of all home


mortgages


were


in de-










response


the federal


government


to these


serious


conditions


consisted


an array


of housing


mortgage


related


programs


that


were


created


over


six


year


period


from


1932


to 1938.


Among


these


were t

family


he basic


FHA mortgage


unsubsidized


Section


insurance


programs,


203 program with


whi


including

ch this s


the single-


tudy


concern

it will


Prior


be useful


to describing


to list


this


and briefly


program

describe


in some

e some


detail,


however,


of the other


impor-


tant


institutions


created


in this


period


that


relate


to the housing


mortgage markets.


This


will


give


the reader


an indication


of the


degree


of attention


that


was devoted


to this


sector


of the


economy


this


time and


provide


a rough


description


of the institutional


environ-


ment


surrounding


the Section


program.


The Federal


Home


Loan


Bank


Board


was created


under


authority


of the Federal


Home


Loan


Bank


Board


Act of 1932


in order


organize,


incorporate,

associations.


examine,


and regulate


The primary


a system


objective


this


of federal s

institution


savings


was


and loan

encour-


the development


of local mutual


thrift


institutions


in which


dividuals


could


safely


invest


funds


in order


to provide


for the


financing


of home


purchases


(Foard


and Frantz,


1973,


11).


The Home


Owners


Loan


Corporation


was


created


under


authority


of the Home


Owners'


Loan Act


of 1933


with


the obj


ective


of refinancing


home


mortgages


that


were


in default


or process


foreclosure.


addition,


this


institution


was


given


the authority


to originate


direct


loans


to permit


former


homeowners


recover


properties


that


had been


I









lost


through


foreclosure


or forced


sale


(Foard


and Frantz,


1973,


10).


The Federal


Savings


and Loan


Insurance


Corporation was


created


under a

tention


authority


of the National


encouraging


addition


Housing A

1 deposit


ct of 193

inflows


with


at savin


the basic


and loan


associations


removing


the risk


of loss


through


association


insolvency.


service


provided


to the savings


and loan


association


this


institution


is analogous


to that


provided


to the commercial


banking


system


the Federal


Deposit


Insurance


Corporation


(Foard


Frantz,


1973,


13-14).


The Reconstruction


Finance


Corporation


Mort


gage


Company was


created


Housing


under


authority


Act of 1934


a 1935


(Public


Law 1,


amendment


74th


of Title


Congress).


III of the


purpose


National


of this


institution


was


to assist


in the re-establishment


a nationwide mort-


gage


market


investing


in many


types


mortgage


instruments,


both


residential


and commercial,


where


such


funds


were


not obtainable


reasonable


rates


from


private


sources.


Purchases


this


institution


however,


primarily


consisted


of FHA-insured


(and,


later,


VA-guaranteed)


mortgages


that


had been


originated


private


lenders.


The Corporation


was dissolved


act of Congress


in 1948


(Public


Law 132,


80th


Congress)


(Foard


and Frantz,


1973,


8-9).


The Federal


National


Mortgage


Association


(FNMA)


was


created


under


authority


Act of 1934


a 1938


(Public


amendment


424,


75th


of Title


Congress).


III of the National


The objective


Housing


behind


n --'#*4. 4 .- -' 4- 4- 1-


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be traded


as financial investment assets.


Such a market,


it was felt,


would encourage inter-regional arbitrage operations that would reduce

the wide variations that existed in mortgage financing availability and


interest rates across the country.


Also,


it was felt that the added


liquidity given to the mortgage


instrument by the functioning of an


active secondary market would increase the willingness of institutional


investors to commit funds to this kind of long-term instrument


(Foard


and Frantz,


1973,


9-10).


While various other programs and policies that were designed to

stimulate the depressed mortgage and housing sectors were adopted at


all levels of government during this period,


the above list,


with the


obvious exclusion of the FHA mortgage insurance programs,


provides


adequate documentation of the degree of effort that was expended at the


federal level.


2
We turn,


now,


to a somewhat detailed description of


the major single-family program excluded from the above list--the FHA

Section 203 mortgage insurance program.

The enabling legislation for this insurance program was the


National Housing Act of 1934.


This act laid out the administrative


framework within which FHA was to operate and indicated what the vari-

ous constraints that were to be placed on the program were to be.

Section 203 of Title II of this act provided for the insurance of ap-

proved private lenders against losses arising from mortgagor defaults

on first mortgage loans originated on single-family properties.


2
It is of interest to note that all of the above programs


(and the


- -r~ e~ r -i t-- i*









This


legislation


placed


ceilings


twenty


years


on the


term


to maturity


and 80


percent


on the loan-to-value


ratio


on insured


loans


and limited


the size


of the eligible mortgage


to $16,000


or less.


The interest


rate


allowed


on insured


loans was


limited


to 5


percent


annum


on the


outstanding


balance


and the


property


securing


the loan was


required


be "economically


sound.


" The settlement


insurance


claims


in the


event


that


the loan


was foreclosed


required


that


the lender


convey


property

receive


and all relevant


return:


claims


debentures


against


guaranteed


to FHA for which


the U.S.


we would


government


equal


to the outstanding


balance


on the loan


plus


certain


other


allow-


ances


with


these


debentures


maturing


three


years


after


contract


maturity


on the


mortgage


obligation


carrying


an interest


rate


fixed


FHA with


consent


of the U.S.


Treasury


based


upon


current


yields


.S. bonds


(later


was


given


the option


of paying


this


insurance


claim


in cash)


and (2)


a certificate of


claim


redeemable


in cash


equal


to the earned


but unpaid


interest


of the loan


plus


partial


reimbursal


of foreclosure


costs,


with


these


items


payable


only


to the


extent


that


FHA realized


net proceeds


from handling


property


(Foard


and Frantz,


1973


, pp.


III,


4-5;


Bartke,


1967,


654).


With


regard


to the financing


of FHA'


Section


program,


the in-


tent


of Congress


was that,


after


an initial


period


negative


returns


during which


start-up


costs


would


be absorb


insurance


reserves


accumulated,


the program would


become


self-financing


(i.e. ,


actuarially


sound).


The legi


station,


therefore,


required


that


an insurance


premium


k a 1r r nr.4 r


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was authorized


the actual


premium--this


range


being


one-half


percent


annum


of the outstanding mortgage


balance.


While


of the other


contract


term


limits


placed


on FHA-insured


loans


(the


lowable


term


to maturity,


loan-to-value


ratio,


mortgage amount,


interest


rate)


have


been altered


from


time


to time


in order


least


partially,


reflect


market


developments,


the insurance


premium


charged


for FHA


coverage


has remained


fixed


at one-half


percent


for all


loans


insured


under


Section


since


1934.


This


has been


an important


feature


of the Section


program


to which


we will


return


several


times


in this


study.


Section


203's


Major


Objectives


As with


the majority


of federal


programs


created


at that


time,


immediate


objective


of the FHA


Section


203 insurance


program was


to in-


crease


employment,


with


its initial


impact,


obviously,


directed


toward


the building


and construction


trades


sector.


Also,


the long


term


objec-


tive


increasing


in terms

a general


of both


improvement


the nation's


quantity


overall


and quality


in the financing


consumption

of the uni


terms


availab


of housing

ts consume

le in the


services

d through

mortgage


market


was made


clear


in the hearings


leading


to the actual


legislation.


The House


Committee


Report


stated


the intent


improve


.. to
ment,


Nation-wide


and stimulate


housing


industry;


standards,


improve


provide


conditions


employ-


with


respect
excess
necessi


Repr


to home-mortgage


new-mortgage


for costly


esentatives


Repor


financing,


investment,


second-mortgage
t No. 1922, 73rd


to prevent


speculative


and to eliminate


financing
Congress


(House


2nd Session,


I 2. I'


one


I









of homeownership


among


lower


income


families,


have


generally


been


tacked


the creation


of additional


programs


within


the FHA


insurance


system.


The basic


concept


of providing mortgage


lenders with


default


insur-


ance


protection


was not without


precedent.


A private mortgage


insurance


industry


the title


existed


insurance


prior to


business


the creation


in the late


of FHA,


1800


having


s and early


grown


1900's.


out of


There


were,


however,


almost


no regulatory


constraints


placed


on the firms


this


industry


either


the federal


government


or by


various


states


in which


they


operated


(primarily


New York).


a result,


there


veloped


a great


deal


of fraud


and misrepresentation


in the industry,


and the contingency


reserves


held


these


firms


were


dangerously


in the late

the State o


1920


s and early


f New York


in 1934,


L930's.

George


a report


Alger,


to the


a special


governor


commissioner


appointed


to investigate


the operations


private mortgage


Insur-


ance


industry,


stated


The value


of it.
issuing
The need
tionship


These
these


a guaranty
companies
guarantees


some


between


depends,


were


safeguard


capital


course


growing


in continually


the law


guarantees


eaps


incr


on what


back


and bounds


easing


requiring


seems


volume.


a fixed


rela-


obvious.


York,
limit


where


upon


a company might


the bulk


amount c
assume.


this


siness


contingent


Without


was done,


obli


a limit


nations
on the


placed
which
amount


such


guarantees


in the


assumed,


amount


only


required


protection


capital


investors


and in


the saf


would
uards


plac
were


upon


their


similarly


investments.


unprote


cted


(Alger,


these
1934,


respects


investors


In addition


mental


to this


contradiction


basic


weakness,


of sound


the indus


insurance


practice


exhibited

in that t


a funda-


he majority


at-









of its contingency


reserves


were


held


in mortgage


obligations,


which


were


subject


to the


same


risks


tha t


they were


being


held


to offset.


With


the crash


of 1929


and the ensuing


flood


of foreclosure


activity


and,


hence,


insurance


claims,


the private


mortgage


insurance


industry


failed.

biguous

losses


The actual

accounting

as the firms


collapse was


practices


postponed


and actual


in the industry


for a brief


falsification


attempted


to delay


period


am-


of insurance

the inevitable


result

value


in the hope


of their


that


declining


an early

reserves


economic


recovery would


reverse


the downwar


bolster

d trend


premium


and investment


income.


But,


the end of March,


1933,


firms


in the industry were


bankrupt.


response


to this


event,


most


states


enacted


legislation


forbidding


private


firms


from


selling mort-


gage


insurance within


their


boundaries,


many


of these


states


pro-


hibitions


have


remained


in effect


until


very


recently.


4
Consequently,


a major


impetus


for the federal


government


adopting


the role


mortgage


insurance


supplier was


that


a private


market


for this


type


coverage


simply


not exist


at that


time.


The theoretical mechanisms


through


which


the provision


of default


insurance


protection


was to stimulate


employment


in the residential


construction

enabling leg


sector were


isolation


hinted


at in various


and the hearings


places


proceeding


that


throughout


legislation.


Many


general


references


were


made


which


indicated


that


insurance


cover-


would


increase


investment


in home


mortgages


and,


thereby,


increase


housing


and construction


activity.


But,


the theoretical


links


through








which


this


effect


would


take


place were


not laid


out.


can,


however,


trace


through


the likely


effects


of default


insurance


protection


deduce


the probable


impact


on the mortgage


market


and housing


industry


employing


markets.


a highly


From


simplified


the standard


model


macroeconomic


of the housing


assumptions,


mortgage


one should


able


to derive


the individual's


demand


function


for housing


services,


with


the typical


result


that


quantity


of housing


demanded


will


bear


a functional


relation


to the price


of housing


services


the individual


income,


and the


prices


of related


goods.


Then,


the individual


s demand


function


could


be written as


F (PH'
H,


. .,


where


(where


is the quantity


this


of housing


quantity measure


services


incorporates


demanded


all structural,


the individual

locational,


and neighborhood


characteristics


of the unit--see


Olsen


, 1969)


the real


price


of housing


services,


is the individual's


real


income,


aDh


and PI,

and, if


.. a


are real


Shousin


prices


a normal


of related


good,


goods.


We know


that


> 0.


Since


most


individuals


are not financially


able


cash


a house,


a mortgage


is generally


required


for homeownership


The


skeletal


model


outlined


here


is not taken


directly


from any


existing
synthesis


housing


many


eration


a great


or mortgage market


treatments


these
deal


models


of the subject


markets.


of the work


my view,


in this


but,


instead,


own


represents


views


the theoretical


area


are extremely


concerning
underpin-


weak


an ad


nature.


the interactions


At this time,


that


take


place


a truly
between


rigorous


the housing


theoretical


model


market,


mortgage market,


and the default


insurance


market


does


not exist.









Consequently,


the demand


for mortgage


funds


a derived


demand,


having


as its direct


source


demand


for housing services.


Because


of this,


the mortgage


loan may


conveniently


viewed


as a good


that


is comple-


mentary


to the consumption


of housing


services.


Being


complementary


we know


that


cross


price


elasticity


of demand


between


housing


services


and mortgages will


active.


Letting


mortgage


be de-


noted


as good


interest


we know


on mortgage


D,
that Dh
P.
7 J
loans.


where


P. is the effective
J


rate


raphical


terms,


we could


translate


the above


demand


function


into


an individual


demand


schedule


for housing


services


with


the price


of housing


services


on the ordinate


and the quantity


demanded


on the


abscissa.


Then,


a change


in the


price


mortgage


funds


would


result


in a shift


in the demand


schedule


for housing


services--with,


course,


a reduction


in the price


of these


funds


resulting


an increase


in the


quantity

duction


of housing

in the price


services


demanded


mortgage


credit


any given


(the


price.


effective


Thus


interest


a re-

rate)


results


in an


increase


in the individual'


demand


schedule


for housing


services.

obtain th


Summing


te market


these

demand


individual

schedule f


demand


or housing


hedules ho

services,


irizontally,


given


which


will


exhibit


similar


qualitative


relationships


to the price


housing


services


and the price


mortgage


funds.


The introduction


mortgage


insurance


would


have


the effect


reducing


the effective


price


mortgage


funds,


and thereby,


shift


housing


service


For those individual


s opting


for homeownership,


1


f -


~~


*









the market


duction


demand


in P


schedule


.is brought


for housing


about


services


an increase


to the right.


in the supply


This


re-


mortgage


funds


stimulated


instrument


the reduction


as an investment


in the relative


alternative.


Mortgage


risk


investors


mortgage

(suppliers


mortgage


funds)


will,


if they


are risk


averse,


adjust


their


portfo-


lios

funds


as the risk


held


on the


in mortgage


asset


is reduced


obligations.


As this


increasing

occurs, t


amount


he quantity


mortgage

creased


funds

and, w


supplied


ith


a downward


rate


sloping


of effective


demand


interest


schedule


will


for mort


be in-


funds,


the effective


interest


rate


on mortgage


obligations


will


be bid down


until


decrease


risk


is compensated


for by


a decreased


rate


turn


and the adjustment


process


is complete.


The resulting model


demand


schedule


for mortgage


is depicted


funds;


in Figure


S(I)
J


Here,


is the supply


. is the

mortgage


funds


expressed


as being


dependent


upon


provision


of default


insur-


ance,


is the demand


schedule


for housing


services


expressed


as a decrease


function


of the price


of housing,


and the price


mortgage


funds,


and SH


is the supply


schedule


for housing


services.


The provision


default


Insurance,


a change


from


to I


1
results


an increased


supply


mortgage


funds,


a reduction


in the effective


rate


of interest


from


1
to Pl


an increase


in the demand


for housing


services


from


to DH


a consequent


increase


in the


quantity


of housing


services


produced


and consumed.


In addition


to the effect


generated


the direct


reduction


in de-


faut t


ri.Se


on Tnnrtrnn


1 nan


hrnio'ht


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SIV


t-hp i nr1ir'nnc


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17


provided by FHA, several related occurances were taking place simulta-

neously that exerted an upward pressure on the demand for housing


services at that time.


First,


the development of a national secondary


mortgage market operated to increase the liquidity of


the mortgage in-


strument


as a financial


asset


and attract new sources of investment


funds into the mortgage market.


This development was facilitated by:


the trading activities of the Federal National Mortgage Association;

the application of FHA's Minimum Property Standards to insured


loans


(Foard and Frantz,


1973,


16);


(3) competent,


objective


appraisals of the properties securing insured loans; and


the trend


toward standardization of the mortgage instrument.


Also,


the liberal-


ization of mortgage financing terms made possible by the provision of


default insurance cover


ments


ge served to reduce the downpayment require-


(through increased loan-to-value ratios) and/or monthly payments


(through increased terms to maturity) necessary to obtain and


fully retire a mortgage contract.


sketched above,


success-


In the highly simplified model


this effect would have to be translated into a reduc-


tion in the effective interest rate required on mortgage loans where

the effective rate would be defined to incorporate the financing terms


of the loan


(Cassidy,


1972).


Both of these developments operated to


increase further the demand for housing services,


thereby supporting


the pure insurance effect of FHA.


Given this increase in the demand for housing services,


some in-


crease in the quantity of housing produced and consumed should be


ex-


norton i-n h uol hn fnrrhrmi4 nO (irni nec nE rniu rr-cnn nnl


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schedule


exibited


a price


elasticity


equal


to zero).


Such


an in-


crease


could


only


be accomplished


through


an increase


in employment


the residential


construction


sector.


Therefore,


we conclude


that


Section


203 insurance


program


should,


on theoretical


grounds,


have


been


successful


in generating


increased


employment


in this


sector


of the


economy


and in


increasing


the nation's


overall


consumption


of housing


services.


Later


Entrants


into


the Default


Insurance


Market


For the first


decade


following


its origination,


the FHA


Section


program


remained


the sole


supplier


of default


insurance


coverage


for home


mortgages.


During


that


period,


any potential


mortgagor


quiring


preferring)


a high


ratio


, long maturity


loan


turned


to FHA


for the


insurance


protection


that


mortgagee was


likely


require


on such a


loan.


Since


that


time,


however,


several


alternative


sup-


pliers


mortgage


default


insurance


have


entered


the market


exerting


varying


Such


degrees


pressure


of competitive


has been


provided


pressure


on the Section


the creation


programs.


of the Veterans


Administration


program


providing


home


loan


guarantees


to eligible


veterans;


surance


re-emergence


industry;


and growth


the introduction


the private


of subsidized


mortgage


single-family


housing


mortgage


insurance


programs


within


the FHA


system.


creation


and growth


of these


three


basic


alternative


sources


of default


For


a review


id evaluation


of the current


state


knowledge


re-


I


1 .


_1









insurance


coverage


have


greatly


affected


post-war


evolution


of the


mortgage

perience


insurance market.


of the Section


Consequently,

program over


they

this


have i

period.


influenced


now discuss


each


of these


later


entrants.


With


the intention


of aidin


post-war


adjustment


of returning


veterans

distance


to civilian


the Cong


life


ress,


through


in 1944,


the provision


enacted


housing


the Servicemen's


credit


as-


Readj ustment


Act.


This


act authorized


the Veterans


Administration


to guarantee


lenders


against


default


loss


on home mortgages


made


to eligible


veterans.


These


insurance


guarantees


coverage- -they


serve e

reduce


essentially


the default


same


risk


purpose


on the


as the


mortgage


, thereby,


encourage


lenders


increase


the supply


mortgage


funds.


There


are,


however,


several


features


that


distinguish


the VA


home


loan


guarantee


from


FHA mortgage


insurance.


First


the VA


guar-


antee


is only


available


to eligible


veterans,


where


eligibility


defined


legislative


decree.


requirements


imposed


for such


eli-


gibility


have


been altered


several


times


over


years


in order


admit

which


purchase


veterans


of later


the individual


a home


conflicts


veteran


under


remains


program.


and to prolong


eligible


The number


the period


to exercise


of individuals


during


his option


having


the option


to insure


thier


loans


under


VA guarantee


program


has,


therefore,


fluctuated


over


time with


variations


in the number


per-


sons


leaving


the armed


services


and with


variations


in the eligibility


requirements


of the


program.


Second,


coverage


provided


to the


mnr tan o-


nntrjpr


rhP VA


cynntrnt-on


nrnor-rn


ic 1 occ


rhbn 1 nn


nPrr-nt


ex-


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provided


for in the


act,


however,


stipulates


that


the Veterans


Adminis-


traction absorb


the lesser


of 50 percent


(later


raised


to 60 percent)


the outstanding


balance


on the loan


or $


2,000


(raised


to $


000 the


following


year


and increased


several


times


hence)


before


lender


begins


experience


a loss.


Thus,


providing


coverage


on the


portion


of the loan


opposed


a deductible


or a percentage


loss


sharing)


VA guarantee


does


provide


complete


Insurance


coverage


unless


property


securing


the loan


experiences


a very


severe


depre-


citation


in value.


Consequently,


coverage


provided


exposes


lender


very


little


actual


risk.


Third,


the Veterans


Administra-


tion


collects


no insurance


premium


for the


guarantee


service


(although


for a three


year


period


in the late


1960


s a single


origination


fee of


one-half


one percent


of the loan


was


levied).


Therefore,


the VA


form


of default


insurance


is subsidized


, being


provided


zero


cost


the eligible


mortgagor.


Fourth,


the financing


terms


available


on the


VA-guaranteed


loan are


generally


more


liberal


than


those


on FHA-insured


mortgages.


Loan-to-value


ratios


are quite


high,


often


approaching


percent


(indeed,


some


instances


they


have


exceeded


percent


the actual


value


of the


property


and have


allowed


the mortgagor


borrow most


of the real


estate


closing


costs


sometimes


placing


little


as .$200


equity


in the loan).


Also,


there


no ceiling


placed


on the size


limitation


of the mortgage


placed


eligible


on the size


for the


the potential


guarantee


insurance


(although


claim


Coverage


percent


mortgage


loan


vir-


4 -v -


-9 -. a-*t


-t -


*r f -V I









discourages


lenders


from


originating


extremely


large


mortgages


under


this

mum


program).


rate


Like


of interest


FHA,

that


the VA guarantee

may be charged


program


stipulates


on the mortgages


that


maxi-


they


insure,


and these


rates


are altered


from


time


to time


to reflect


market


conditions


(although,


at times,


these


rates


have


departed


considerably


from


those


charged


on uninsured


mortgages).


The second


Section


source


program


of competitive


has been


pressure


re-emergence


exerted


on the FHA


of the private


mortgage


insurance


industry.


The first


firm


to enter


this


industry


since


collapse


in the early


1930's


was the Mortgage Guaranty


Insurance


Corporation


which


began


operations


in 1957


in the


state


of Wisconsin.


Since


that


time,


the volume


of insurance written


private


mort-


gage


insurance


entered,


industry


insurance


has increased


reserves


have


dramatically


accumulated, and


as new


as state


firms

laws


have

forbid-


ding


operation


of private mortgage


insurance


companies


have


been


relaxed


to allow


these


firms


to expand


their


market


(the


final


state


relaxing


prohibitions


against


the activities


of these


firms


York


in 1973).


The number


single-


family


units


insured


mem-


bers


of this


industry


moved


from


12,484


in 1960


to 64,850


in 1965,


157,760 in 1971,


and 505,180


in 1973.


A few declines


have


occurred


in the volume


of insurance


written by


these


firms


over


this


period,


such


declines


have


generally


coincided


with


declines


in overall


housing


mortgage


lending


activity.


Presently,


the number


of companies


11Fur their


information


concerning


the VA


system


of home


loan


guar-


. -


nfl r fl C' r~ .n n 4 n Prt n n A r. ~ -4- n n


/1 fl'7')


was


-- ^,,t T"* c*


.1


nn


n


II


rI Tl -/- -^f- nt









this


industry


is approximately


having


declined


somewhat


in the last


two years


through


merger


activity


that


occurred


in the early


1970's


(Little,


1975,


121).


percent


of the private market


accounted


for by


the Mortgage Guaranty


Insurance


Corporation


(the


largest


firm


the industry)


been


steadily


eroded


over


years.


It stood


at 100


percent


from


1957


until


1961;


then,


in the latter


year,


it declined


93.76


percent.


1965


it had fallen


to 75.97


percent,


and b


1970


was down


to 65.18


percent


(Little,


1975,


122).


This


trend


con-


tinued


into


the 1970's


with


the 1972


market


share


falling


to 60.00


per-


cent


and declining


further


in 1973


and 1974.


Although


there


have


been


no comprehensive


studies


carried


out to


determine


the existing


entry


conditions


in the private


mortgage


insur-


ance


industry,


a recent


examination


that


was designed


to determine


adequacy


of the contingency


reserves


of the major


firms


in this


indus-


concluded


that


entry


barriers


were


low (Little,


1975).


This


infer-


ence was


regarding


made


paid


primarily


in capital


from


an examination


and contingency


state


reserve


regulations


requirements;


and,


therefore


the conclusion


relates


only


to absolute


barriers


to entry


(Bain,


1956).


Given


recent


growth


experience


in the number


firms


in this


industry


however,


one must


suspect


that


this


conclusion


accurate


of overall


barriers


to entry


also


(such


as economies


scale,


etc.).


The industry


thus


be described


as a relatively young


one that


has been


characterized


rather


steady


growth


in both


size


of the market


and the competitive


structure


exhibited.









this


outstanding


balance.


Thus,


both


coverage


provided


and the


price


charged


on these


contracts


are lower


than


those


under


the Section


program;


and,


like


the FHA program,


neither


coverage


nor the


price

much


has varied


risk


measurably


the lender


over


is exposed


time.


to under


Again,


such


it is


a plan.


not clear


some


how

loans,


coverage


lent

ance


of the


to complete

contracts w


percent


coverage


written


(see


be considered


footnote


the firms


10 above).


in this


industry


as virtually


Finally,

place n


equiva-


the insur-


1o ceilings


on the size


of the


mortgage


nor on the interest


rate


that


be applied


to the loan.


The third


and final


major


entrant


into


the default


insurance


market


was the single-family


subsidized


housing


mortgage


insurance


pro-


grams


that


were


incorporated


in the FHA


system


the National


Housing


Act of 1968.


The largest


of these


has been


the Section


program


which


combined


direct


housing


subsidies


with


default


insurance


in order


to increase


homeownership


among


lower


income


households.


Although


this


program was


suspended


in January,


1973,


the volume


of activity


carried


out under


the subsidy


programs


during


the brief


period


in which


Section


235 was

occurred


active is far

in the first


from


quarter


insignificant--the


of 1972 when


largest


33,240


insurance


new and 5,354


volume

exist-


single-family


units


were


insured.


Eligibility


for participation


these


subsidy


programs


has been


limited


household


income with


ceiling


gs varying


family


size.


Like


the insurance written


under


Sec-


tion


203,


coverage


provided


under


this


program has


been


percent,









and ceilings


have


been


placed


on the


mortgage


size


and allowable


rate


of interest.


provided,


mortgage


No premiums


however,


payments


have


been


mortgagors


under


collected


rece


program


ived


(Foard


for the insurance


direct


service


subsidization


and Frantz,


1973,


Thus,


the monopoly


situation


initially


enjoyed


FHA's Section


program


has gradually


disappeared


New firms


and additional


fed-


eral


government


programs


have


entered


the default


insurance


market


over


time,


and the competitive


pressures


exerted


on this


program have


creased


accordingly.


The degree


of substitutability


between


cover-


offered


default


under


insurance


the Section


is not,


203 program and


however,


these


immediately


alternative


apparent.


sources


On an


basis,


all that


can be said


is that


some


gree


of substitu-


tion


should


exist


between


these


various


suppliers


of d


efault


Insurance


coverage.


Both


the VA


guarantee


and the subsidy


programs


of FHA


carry


explicit


eligibility


requirements


that


reduce


the direct


substitution


between


these


programs


and Section


203 insurance


coverage.


To the


extent


that


these


programs


provide


insurance


to individuals


that


would


not have


entered


the housing


mortgage


markets


(and,


hence,


the mort-


gage


insurance market)


substitutability with


Section


203 will


lowered


(though


probably


not eliminated).


In such


a case


direct


com-


petition


in the default


insurance market


not generated


but increases


in the volume


reduce


ated


of activity


the demand


in the housing


carried


for Section


and mortgage


out under


coverage


markets.


these


programs


the price


That


still


effects


the increased


ener-


demand


a ptioti








demand for Section 203 coverage.


To the extent that these programs


provide insurance coverage to individuals that would have otherwise


purchased homes under the Section 203 program, however,


substituta-


ability will be increased since direct competition in the default insur-


ance market will also be exerted


(particularly since both of these


programs provide coverage at subsidized rates).


Finally,


the degree of


substitutability between Section 203 coverage and the insurance pro-

vided by the private firms in the market is also uncertain because of


the market difference in the level of coverage offered


20 percent,


(100 percent and


respectively).


It is theoretically possible that the lower


level of coverage pro-


vided by the private mortgage insurance firms generated an overall


increase in the


size


of the default insurance market that has been


approximately equal


i.e.,


to the volume of insurance written by these firms;


it is possible that the bulk of their business has been derived


from previously uninsured loans.


As was mentioned previously, however,


it is also possible that the lower coverage provided by these firms is


regarded by


lenders as being only marginally more risky than the full


coverage provided by


FHA.


If this has been the


case,


then competition


between the private firms and Section 203 has been direct and


the sub-


stitutability between these sources of default coverage has been large.


Thus,


the degree of substitutability cannot be inferred from theoreti-


cal considerations alone.


The Volume of Insurance under Section 203









of activity


and maintaining


actuarial


soundness.


FHA-insured


housing


starts


as a percent


of total


private


housing


starts


moved


from


per-


cent


in 1935


to 16


percent


in 1936,


percent


in 1937


and 30


percent


in 1938


(Haar,


1960


Volume


activity


terms


of the number


mortgages


on new units


insured


under


the Section


program


along


with


the total


housing


starts


for the entire


country


(both


insured


non-insured)


in five


year


intervals


for the 1935-1969


period


is given


in Table


From June,


1937


, through


November


, 1957,


.003


billion


in home mortgage


insurance


on new units


and $13


527 billion


on existing


units


been


written


under


the Section


program.


This


volume


insured


mortgages


financed


a total


600,345


new


and 1,980


783 exist-


housing


units


(Haar,


1960,


Table


2.1.


Privately


Owned


Housing


Units


Starte


under


FHA S


section


203(b)


Mortgage


insurance


gram


Compar
1935-6


with


Total


Hous


Starts


Section


203(b)


Years


Total


Section


203(b)


as percent


total


1935-39

1940-44


1945-49


1950-54


1955-59


1960-64


710.000


772.700


379.000


,708,000


935.600


160.000


353.798


388.731


406.715


1,094


156.289


894.535


20.69

21.93

7.56


14.21


16.67


12.49


n1C c


./ nnn 7nrn


rn


line r rr


n


f% 1 1U


J








The actuarial


soundness


of this


early


business


is evidenced


in the


fact


that


the initial


funds


borrowed


from


the U.S.


Treasury


in order


implement


the FHA


insurance


system were


repaid


within


a few


years


operation.


As of 1972,


FHA's


insurance


reserves


were


over


$1.6


billion


and the outstanding


insurance


in force


on Section


203 loans


amounted


almost t


$103.


billion


(Examination


Financial Statements


Ptaiyizng


to InAuannce.


OpeAationA


Federal


Housing


Administrzat.io n,


1972).


spite


of the continual


liberalization


of the financing


terms


on the


mortgages


insured,


the Section


program


has routinely


and consis-


tently met


all insurance


claims


made


against


and by


the middle


1971,


it had accumulated


million


in excess


reserves


beyond


those


required


conservative


actuarial

ly using


computatio

the period


(which,


of the 1930'


themselves,


as the base


e estimated

from which


projected


insurance


claims


are computed).


With


regard


to the


more


recent


activities


of FHA (over


the decade


of the 1960's


and the early


1970's)


no significant


change


apparent


one examines


only


the total


single-family


activity


(including


Sec-


tion


203 and the subsidy


programs).


Of the total


mortgaged


housing


starts,


FHA single-family


programs


insured


13.6


percent


in 1966


over


percent


in 1971


with


these


starts


representing


approximately


129,000


units


in 1966


more


than


300,000


in 1971


(Bur


gess,


1973,


If attention


is focused,


however,


on the unsubsidized


Section


program with


which


we are concerned


in this


study,


a different


picture


emerges.


Insurance


activity


under


this


program


has declined


considerably


over


the decade o


f the 1960's


and this


decline


has a


ecel-


.









given


in Figures


2.2 and 2.3 for


new


and existing


units


separately


the 1960


through


1974:


period.


From


these


graphs,


the decline


in Section


insurance


volume


obviously


been more


pronounced and


continuous


for policies


written


cover


mortgages


on new units.


Also,


the decline appears


to have


begun


earlier


for this


category


of insurance.


A plausible


explanation


this


observation


lies


in the


private


mortgage


insurance


firms'


tendency


to concentrate


their


activity


on the insurance


mortgages


written


new housing


units


(Semer


and Zimmerman,


1975,


155).


Such


a tendency


makes


sense


if default


risk


is generally


lower


on such


properties


since


both


coverage


provided


premium


charged


these


firms


are below


those


of the Section


program.


For the


present,


however,


this


explanation


of the observed


difference


in declines


for Section


203 in-


surance


written


on new and existing


units


must


remain


at the specula-


tive


stage.


extant


data


on the insurance


volume


of the private


firms


in the industry


not separate


activity


type


property


securing


mortgage.


This


shortcoming


is typical


of the overall


hous-


mortgage


market


data


which,


a large


extent,


are generally


unsatisfactory.


In addition


to the declining


volume


of insurance


being written


under


the Section


program,


significant


increases


have


been


14Calculated


from monthly


data


in FHA Monthly


Reportt


Operations --


Home Mortgage


P/ogrmu u


RR:301


(Homes).


Greater


attention will


be devoted


to this


issue


in Chapter


IV of


this


study.
















































































- I i II-- i i-


ttNOd)
0: p^ c( 0


t CO Ct)
V) () Un Cj


_ _t n C) u5 O o


I I


OCO


Q) O
S00


t o

r GO


1 I


Si l l


I I -













































































t O Cin-O
an o mj f-


- I I I


en tu
on
00
b0 00
C O0
*r-4 4-J
(n o

*C f


o ino
a __Lo


0 e Ln to 0
NOuiin


n 0 to O in o in
ot + O) r O (M Osi -








experienced


in the


average


insurance


loss


claim


since


1971.


If the


current


trend


continues,


the actuarial


soundness


of the


program may


become


jeopardized


at the


current


premium


level.


present


soundness


of the insurance


fund


supporting


this


program


may be largely


attributa-


to past


successes


of the Section


203 program and


interest


earnings


on past


reserves


("Actuarial


Briefing


Paper,


" 1974)


Since


FHA'


Section


program was


intended


to function


on an


actuarially


sound


basis


and since


program must


cover


certain


non-


variable


costs


(such


as the


maintenance


numerous


insuring


offices


throughout


the country)


in order


to continue


its operations,


seems


necessary


that


a certain


volume


of insurance


activity


be maintained


program


is to function


on the basis


envisioned


its enabling


legi


slation.


Therefore,


the absolute


number


mortg


ages


insured


under


the Section


program


is a crucial


factor


in the d


determination


FHA'


future


role


in the unsubsidized


single-family


default


insurance


market,


and it will


be this


measure


of FHA


activity


to which


our atten-


tion


will


be directed


throughout


this


study.


Since


this


numb er


is influenced


not only


the competitive


pres-


sures


exerted


new


growing


entrants


in the default


insurance


market,


but also


the overall


size


of that


total


market


(which,


turn,

nated)


is influenced

. it is also


the number


of interest


of houses


to trace


sold


the Section


mortgages

203 market


origi-

share


over


time.


This


given


in Figure


2.4 where


market


share


is d


efined


as Section


203 insurance


volume


divided


sum of Section


insurance,


VA insurance,


private


mortgage


insurance,


and FHA subsidized



















































































i;3 rQ i) 10 0 J)


I I 1 i I I
o a)0 of 0 o l oQ
II) s^- t^^" (f) CM' (NJ


I I
io o rnO









Clearly,


the observed


decline


in the volume


of activity


under


FHA'


Section


program


not been


generated


solely


or predomi-


nantly


decreases


in the overall


demand


mortgage


insurance--


particularly


in recent


years.


Instead,


the decline


appears


to have


resulted,


at least


partially,


from a


loss


insurance


volume


to the


competitive


suppliers


of default


coverage.


In order


to be certain


that


this


has been


case,


however,


we must


investigate


other


factors


that


have


been


significant


contributors


to this


decline.


And to do this,


we must


develop


a more


complete


theory


of the mechanisms


involved


determining


Section


203 activity


over


time.


Before


attempting


to de-


velop


such


a theory,


however,


it will


be useful


to present


a brief


review


some


recent


literature


that


will


be employed


in the


construc-


tion


of this


theory.
















CHAPTER


LITERATURE REVIEW


The Scarcity


of Relevant


Literature


There


have


been


no rigorous


studies


undertaken


to certain


factors


that


have


led to the observed


decline


in the volume


of single-


family


unsubsidized


insurance


written


FHA.


Naturally,


over


the last


several


years,


various


papers


have


emerged


that


have


examined


the de-


dine


in activity


a more


or less


logical


fashion,


usually


focusing


the reader's


attention


on one or, possibly,


two factors


that


are char-


acterized


as "the"


cause


of shrinking volume.


These


studies,


however,


typically


fail


to describe


the causal


mechanisms


through


which


hypothesized


effect


operates


(i.e.,


the theoretical


foundation


for the


conclusions


that


are reached


is either


implicit


in the


argument,


more


often,


totally


absent).


Also,


the statistical


techniques


employed


in these


presented)


studies


generally


rare


fail


instances


to allow


in which


for more


empirical


than one


evidence


explanatory


variable.


Typically


a simple


two-way


table


or g


raph


is employed


that


reveals


the time


path


of the volume


of FHA activity


and the time


path


of the hypothesized


causal


factor


(Bazan,


1974,


p. 9).


Conclusions


then


drawn


from


contemporaneous


movements


these


two paths.


,r,, ,tr /I 1- H 1 A ,


I (071


are


Rn r i> 'i


L-


f


-* -


c V ^ ^tr4


iynmTn i" I/^/-


4^ -- ^ 1- I ,1 ,, ._


1- U









There


a danger


of attributing


cause


a suprious


relationship


with


such


techniques;


and,


even


if the qualitative


nature


of the conclusion


reached

that is


correct,


crucial


the policy


in the design


maker


is denied


of effective


action.


parameter

The causa


estimate

1 factors


collectively


suggested


in these


papers,


however,


were


not ignored


the analysis


conducted


in this


study


since,


for the


most


part,


they


receive


theoretical


support


when


closely


examined.


In order


to provide


a background


of the little


economic


literature


that


exists


that


is relevant


to default


insurance,


the studies


George


von


Furstenberg


and Henry


Aaron


will


be described


and critically


evaluated


in this


chapter.


2
These


studies


are


later


employed


as a


starting


point


from which


we derive


a theory


of the demand


mortgage


insurance.


This


theor


then


provides


a framework


for the specification


an econometric


model


of the


mortgage


insurance


sector


from


which


inferences


be drawn


concerning


the causal


factors


that


underlie


observed


decline


in FHA activity.


Thus,


while


the analyses


carried


these


two authors


are not specifically


concerned


with


the fall


volume,


they


do provide


a basis


from which


our study may


proceed.


The works


of Aaron


von


Furstenberg


received


a cursory


review


a recent


Urban


paper


Institute.


Greenston


While


eQ a


criticisms


C. (1974)

revealed


that


was


in this


published


paper


are fundamen-


tally


sound,


there


exist


several


inaccuracies


and exclusions


that


tend


to detract


from


the discussion


somewhat.


These


will


be briefly men-


tioned


in this


chapter,


a great


deal


of attention


will


not be









devoted


to them.


Also,


the brevity


of the review provided


in the Urban


Institute


paper


leaves


some


confusion


with


regard


to the methodologies


employed


in these


studies


which


this


chapter will


attempt


to clarify.


Inasmuch


as the basic


conclusions


reached


in their


review


are correct,


however,


the findings


in this


chapter will


not differ


in any major


respects.


turn


now to


the studies


to be reviewed.


Studies


of Default


Behavior


by von


Furstenberg


George


von Furstenberg


has published


a number


of articles


con-


cerned


with


explaining and


predicting default


probabilities


pected


default


losses


on home


mortgages


(see


footnote


The model


developed


in each


of these


articles


is empirical


nature


with


very


little


theoretical


analysis


of the default


phenomenon.


The units


observation


employed


in the statistical


analyses


are cohorts


of FHA


insured


single-family


mortga


ges.


While


there


are some differences


vector


exogenous


variables


incorporated


in the estimating


equa-


tions


utilized


in these


studies


(which may


be attributable


to the lack


a well


developed


theory),


they


are


quite


similar


in the basic


method


employed


and the important


conclusions


reached.


Therefore,


only


first of these


studies


will


be reviewed


in detail.


This


paper,


which


appeared


in the Joutnal


Finance,


represents


one of the first


empirical


examinations


of the causal


factors


determin-


default


risk


on home


mortgages


that


utilized


multiple


regression


techniques.


purpose


of the study was


to develop


estimating


equa-


ex-








Furstenberg,


such


transfers


take


place


within


the FHA insurance


program because


non-homogeneous


risk classes


are pooled


within


Mutual


Mortgage


Insurance


Fund


of FHA and


a single


price


is charged


all purchasers


of the insurance


coverage


backed


this


fund


(i.e.,


transfers


arise


as a result


a departure


from an


actuarially


fair


pricing


scheme)


Since


since


the mortgages


the insurance


being


premiums


examined

not refl


are completely i

ect the relative


nsured


default


risks,


common


technique


inferring


the degree


of risk


on a


financial


asset


from


the relative


interest


rate


paid


cannot


be employed.


Instead,


it is


necessary


to predict


the expected


default


probability


cohort


of FHA insured


loans


(measured


percentage


loans


in the


cohort


that


entered


default


status


in a


given


year)


from


the basic


financing


characteristics


of the loans


in the cohort,


especially with


regard


loans.


to the


While


average


the actual


loan- to-value


mechanisms


ratio


through


term


which


to maturity


these


of these


characteristics


influence


default


behavior


are


not made


clear


in the article,


it is


suggested


that


their


effect


on borrower


equity


is the connecting


link.


The cohorts


utilized


in this


study


are defined


each


combination


term


to maturity,


loan-to-value


ratio,


and classification


of insured


loans


on the basis


of the


type


property


securing


the loans


(new


existing)


Then,


through


use of


the equations


that


are developed


to predict


the default


probabilities


of the individual


cohorts,


author


is able


to make


inferences


concerning


the risks


on these


loans


von









without


reliance


upon


financial


market


mechanisms (as


might


flected


in interest


rates


or insurance


premiums


in the absence of


FHA).


The discussion


carried


out by


von


Furstenberg


in the following


section


of his


paper


seems


to implicitly


contain a


loose-knit


theory


default


behavior


on home


mortgages.


There


an obvious


recognition


the importance of


borrower


equity


in determining


default


probability


and the role


of financing variables


in influencing


borrower


equity


over


time.


But,


a unified


theory


never


made


explicit


in this


paper,


does


appear


of the others.


One is tempted


to conclude


that


Furstenberg viewed


the theoretical


issues


behind


the discussion


being


too obvious


to warrant


a rigorous,


detailed


examination.


But,


when


one considers


the myriad


of factors


(financial,


economic,


demographic)


that


could,


theoretically,


affect


default


probability


(all


acting a

borrower


nd interacting


to determine


and his individual


reaction


both


to that


equity

equity


position

position)


of the

and the


logical channels


through


which


these


factors


might


operate,


the absence


a more


explicit


theoretical


treatment


must


be viewed


with


concern.


It is this


absence


a rigorous


theoretical


construct


that


detracts


from


the work


done


von Furstenberg.


And,


as mentioned


above,


apparent


inconsistencies


in the specifications


of the estimating


equa-


tions


utilized


in later


studies


probably


arise


as a result


of this


absence.


Since


defaults


on a group


mortgages


originated


a given mo-


ment


time


occur


immediately


are spread


over


time,


re-


von


nor


von









the time


tion


further


distribution


separately


separated


of defaults.


twenty,


by new


He then


twenty-five,


or existing


fits


and thirty


properties


estimating


year


securing


equa-


mortgages

the loan.


Such unpooled estimation


is appropriate


under


the hypothesis


that


structural


coefficients


of the relationship


other


than


constant


term differ


term


to maturity


property


type.


In this


situation,


a single


regression


using


the pooled


sample


that


attempts


to incorpo-


rate


these


effects


through


the addition


simple


dummy


variables


that


allow


only


for intercept


shifts


will


be clearly


misspecified.


fit-


ting


separate


equations,


the hypothesis


above


be tested,


and the


pooling decision


made


in accordance


with


the results.


For this


reason,


the approach


adopted


von Furstenberg


in fitting


the relationship


initially


using


the unpooled


samples


seems


reasonable.


This


yields


total


six regression


equations.


p4h0/u


information


concerning


the shape


of the time


path


for de-


faulting


mortgages


is employed


to determine


the functional


form of


estimating


equations.


This


shape


is generally


characterized


Figure


Defaults


as a percentage


all loans


originated


in a


given


year


tend


rise


for the first


three


or four


years


and then


fall


fairly


rapidly


and approach


zero


axis


the end of the eleventh


twelfth


year.


While


the level


of this


curve


fluctuates


with


the risk-


related


characteristics


of the loan,


this


functional


form


is consis-


tently


found


in actuarial


studies


of home


mortgages


appears


to be


quite


stable


over


time


over mortgage


characteristics


A vm C' F r nn a 17


1673\









Percentage
Defaulting


Years


Since


Loan


Origination


Figure


3.1.


Time


Path


of Defaults


on Home Mortgages


higher


loan-to-value


ratio


for the cohort


mortgages


will


shift


this


curve


upward


leaving


its functional


form unchanged.


Then,


the skewed


distribution


is represented


the natural


exponential


function


(D/E)t


a3t2


where


enter


(D/E)t

default


is the


status


percent


at t


of loans


years


after


endorsed


a given


base


year


that


endorsement;


are constants.


The variable


that


is used


to capture


the effect


of the loan-to-


value


ratio


is given


10 (1


- L/V)]


where


is the loan-to-value


ratio


on the


mortgage


contract.


therefore,


measures


ten times


percentage


down


payment


on the loan.


An explanation


of why


this


parti-


cular


transformation


is employed


not given.


corporatine


this


as a


i.


L4.









(D/E)t


a0 [10 (1


- L/VO]al


from which


he writes


his estimating equation


In (D/E)t


In a0


In [ 10 (1


- L/V)


+ a3t2


Notice


that,


in this


derivation,


the disturbance


term,


included


in the


equation


until


after


the logarithmic


transformation


has been


carried


out to characterize


the relationship


a form


that


linear


in the


parameters.


The stochastic


element


mystically


appears


an additive


fashion.


This


econometric


shell


game


is technically


unap-


pealing,


but is often


used.


Obviously,


the assumption


that


is implicit


in this


transformation


is that


equation


is actually


given


(D/E)t


10 (1


a3t2


- L/V)


where


the stochastic


part


of the relationship


(i.e.,


the distribution


of (D/E)t


for given


values


of L/V


and t)


is assumed


(implicitly)


to be


log-normally


distributed.


Also,


no evidence


is given


to demonstrate


that


the disturbance


term


in equation


is in accordance


with


the as-


sumptions


of the classical


linear


model


that


would


assure


the alleged


properties


of unbiasedness


and efficiency


from


the ordinary


least


squares


estimation


technique


that


is employed.


Another


technical


shortcoming


is found


later


in the


paper


when


Furstenberg


pools


new


and existing units


and incorporates


a dummy


variable


to capture


the effect


a different


type


property


securing


the loan.


Prior


to this


pooling,


no formal


test


a significant


dif-


ference


between


vector


of coefficients


estimated


in the


separate


von


+ al


+ a2









marked


difference which


implies


that


the effect


cannot


be characterized


a simple


shift


parameter


that


enters


additively.


If the slope


coef-


ficients


themselves


differ


between


two


groups,


merely


allowing


intercept


shift


will


not correct


properly


for the effect.


Consequently,


such


pooling may


not be warranted.


None


of these


econometric


questions


is mentioned


in the Urban


Institute


review


von


Furstenberg


s analy-


sis,


the basic


lack


an explicit


theoretical


framework


is duly


noted.


The estimates


obtained


in the unpooled


regressions


are given


Table


from


the original


paper


(von Furstenberg,


1969,


467).


Given


apparent


differences


in the structural


coefficients


in these


pooled

They a


regressions,


re reported


they


here


are (in my


only


own


to indicate


view)


the preferred


the qualitative


estimates.


impact


of the


loan- to-value


ratio


term


to maturity


on default


probabilities.


From


ties


these


on cohorts


equations,


von


of FHA-insured


Furstenberg


mortgages.


predicts


Then,


default


an attempt


probabili-


is made


transform


these


predicted


probabilities


into


expected


default


losses


utilization


a weighting


factor


that


is based


upon


assumption


that


the insurer's


loss,


given


occurrence


of default,


will


decline


with


of the


mortgage.


In all,
declines


we stipulate


with


the age


that


the insurer


of the


mortgage


s loss


in default


foreclo


sure


but less


than
(von


in proportion
Furstenberg,


to the reduction


1969


in principle


outs


standing


. 470).


This


hypothesized


relationship


between


default


loss


given


foreclosure


and time


since


origination


is primarily


founded


upon


conjecture,


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employing


individual


mortgages


as the


units


of observation and


applying


a Tobit


analysis


to predict


both


the probability


of default


pected


loss


given


default).


Incorporating


the weighting


factor


that


is postulated


on the basis


of this


assumption,


von


Furstenberg


reaches


the following


conclusions


that


are


in basic


agreement t


with


the theoretical


model


developed


in the


following


chapter


of this


study:


Expected


efault


loss


is directly


related


to the loan-to-


value


ratio


on the mortgage


contract;


Expected


default


loss


is also


directly


related


to the


term


to maturity


on the


mortgage


contract


These


qualitative


results


are strengthened


in the following


chapter


addressing


the default


probability--expected


loss


issue


from a


purely


theoretical


point


of view.


They


are then


incorporated


with


a theoreti-


cal analysis


of the loan


contracting


process


that


is developed


as an


extension


of the descriptive


treatment


provided


Aaron


in his analysis


of the effect


of default


insurance


on this


process.


Together,


these


will


provide


the basic


variables


for a demand


for FHA


insurance


equation


that


can be


more


fully


specified


the addition


of product


differentiat-


factors


and that


can be imbedded


in a


set of behavioral


equations


depicting


the market


for default


insurance


on home mortgages.


turn


a review


of Aaron's


work.


Aaron's


Analysis


of the Contracting


Process


on Mort


gage


Loans


.r -..u..


-_ A-' T A --- S- r -- -


now


* ---- --


---*t A.-


^ 1 ? _


TT ^- --.









borrower


and the lender


is contained


in his book,


Sheltet and


Subs6 idies


from


Fedeala


Housing


PolicieA


(1972).


The book


itself


deals


with


all of the major


housing-related


programs


and policies


car-


ried


out by


the federal


government


(including


incentives


provided


homeownership


adequate

portant


through


detail t

functions


the income


o provide


each,


tax system).


the reader wit

and estimates


These


are described


an understanding


of the benefits


of the im-


derived


income

major


class


are attempted


redistributive


effects.


in order


to identify


The default


the direction


insurance


and loan


of the

guaranty


operations


of FHA and


VA are


discussed


in Chapter


The first


part


of the chapter


briefly


describes


FHA'


Section


program


and the


system


of VA loan


guarantees,


providing


some


historical


perspective


for them.


The second


section


(which


is the


one of primary


interest


here)


develops


an analytical


model


of the tradeoffs


that


exist


and the negotiations


in arriving


that


a mutually


occur


between


agreeable


the mortgagee and


contract


and the influence


mortgagor


that


provision


of default


insurance


will


exert


on the


outcome.


The last


section


of the chapter


provides


estimates


of the benefits


derived


mortgage

classes


heavily


from


separate


from


the provision

ly for FHA and


the empirical


of such


insurance


VA borrowers


work


von


(thi


Furstenberg


for various

s section d


discussed


income


drawing


above).


The review


here


will


focus


on the borrower-lender


model


developed


the second


section.


The model


portrayed


in this


section


is graphical


and descriptive


in nntlir wi th


1 -tf-


r vnln ann r nn


nrnnmr n


I- I 1


Fnr t-hbc rn l f t" i nnqhii nq


Benefits


VP7 7










conclusion


of the chapter.


Nonetheless,


the description


provided


the contracting


process


provides


an intuitively


appealing


framework


from which


a more


rigorous


treatment


can be developed.


is cast


within


the framework


a two party


bargaining model


with


loan


contract


terms


(specifically,


the downpayment


and the interest


rate)


being


subjects


of negotiation.


Insurance


coverage


is entered


exogenously.


The model


used


is described


the following


graph,


adapted


from


Figure


5-1 of Aaron


s (1972,


book.


Ratio


of Equity


to Value


(E/V)1


(E/V)


Interest


Rate


Figure


3.2.


Lender
Rates


and Borrower


Tradeoffs


Between


Interest


and Downpayments


In this graph,


(E/V)


is the ratio


of borrower


equity


to property


value,


i is the


contract


a -


1 I--J


interest


rate,


a a t.a-- -


are lender


* -V. reC


a -


indifference

rTta1,, a...3 t,


jj r_.


4 ^-









increased

described


equity


decreases


as deriving


expected


increased


default


utility


loss).


from a


The borrower


reduction


in either


these


terms


as such


a reduction decreases


the required


downpayment


the price


of the borrowed


funds.


Although


Aaron


describes


the indiffer-


ence


curves


in this


graph


as representing


the utility


functions


of the


borrower


and the lender,


it is clear


that


they must,


instead,


be inter-


preted


terms


of indirect


utility


functions


since


neither


actual


profits


(for


the lender)


nor real


goods


(for


the borrower)


are captured


in the graph.

for the lender


Ideally,


one would


and a utility


of real


describe


goods


a utility

(including


of profits


future


function


goods)


function


for the borrower,


derive


indirect


utilities


as functions


loan


contract


terms,


incorporate


these


into


the bargaining model


with


which


Aaron


begins.


Also,


convexity


of the lender


and the


con-


cavity


of the borrower


indifference


curves


in Figure


are not for-


mally


defended


in Aaron' s


analysis,


but instead,


they


are merely


drawn


as exhibiting


these


properties.


Default


insurance


is introduced


arguing


that


Lenders


are willing


to accept


more


liberal


terms when


protect


tion


is available


than


when


it is


not because


enable


them


to avoid


the risk of


arge


loss


from


unusually


frequent


or costly


foreclosures.


Furthermore


loss


protection


insu-


lates
increa
downs


lenders


from 1


unemploym
economic e


losses


ent,
rowth


such unpredictable


declines
(Aaron,


in prope
1972, p.


.rty


values


events


or slow-


82).


This


curve


argument


is translated


indicates


most


terms


liberal


of Figure


combinations


asserting


of interest


that


rates


downpayment


requirements


at which


lenders


will


make


loans


no loss


nrn 4i t y f 1 rt 1- tI 4n


- ..


4 .: A 4


oss


-i^^,/ 4-U A


T^1'T-t'f/ ^t# ^-


n~lrr~rn I


CI


kn- mnn f* */Iy ^ ^ '^f


I









the implication


is that


the level


of utility


along


is equal


to the


level


of utility


along


so that


insurance


protection


is depicted


his model

regard to


as a shift


the borrower's


in the lender's


indirect


indirect


utility


utility


function,


surface.


however,


With


no shift


occurs


so that


the level


of utility


along


exceeds


the level


utility


along


negotiation


in the graph.


process


between


Thus,


the borrower


the equilibrium


and the lender


outcome


shifts


of the


from


point


to point


with


the provision


of default


insurance


with


a re-


sultant


increase


in borrower


utility


constant


lender


utility.


While


it is


not made


clear


in Aaron


s analysis,


two points


of equi-


librium


in the graph must


be viewed


as two of


an infinite


number


such


points


lying


along


contract


curve


of the negotiating


parties.


Supposedly,


some


force


is exerted


from


outside


the negotiation


process


to determine


tightness


which


of the


of these


mortgage


equilibrium


market


solutions


existing at


results--such


the time


as the


of negotiation


Insurance


coverage


also


enters


from


outside


since


it is not pictured


the graph,


it too influences


the equilibrium


outcome.


Another


point


that


should


be mentioned


that


is ignored


Aaron


that


the result


pictured


in the graph


decrease


in downpayment


increase


in interest


rate)


is solely


a result


of the actual


utility


functions


underlying


the indifference


maps


drawn.


Given


different


lender


and/or


borrower


preferences, the


post-insurance


equilibrium solu-


tion


could


easily


result


in the opposite


movement


increase


in down-


payment


and a decrease


in interest


rate),


or it could


result


in a









downpayment

a given dow


for a given


rnpayment


rate


or some


of interest

combination


or a lowe

of these,


interest


depending


rate

upon


for

the


actual


preference maps


involved.


Overall,


there


are two fundamental


weaknesses


inherent


in Aaron


analysis.


First,


the conclusions


derived


flow


from


the actual


indif-


ference


curves


drawn


and basic


underlying assumptions


remain


hidden


these


curves


(such


as risk aversion


utility


functions


for lenders).


Second,


the graphical


approach


forbids


the direct


incorporation


surance


coverage


into


the bargaining


process


and,


therefore,


leads


the complete


exclusion


of both


insurance


premium and


the lender's


risk


premium


(both


of which


are crucial


in the decision


of whether


insure


the loan).


Since


the insurance


premium


(which


just


as much


a cost


to the borrower


as higher


interest


rates


or larger


downpayments)


not incorporated


in the graph,


it would


appear


that


all borrowers


could


increase


their


utility


providing


the lender


default


insurance


on the loan,


we would


be 1


to expect


all loans


to be insured.


Also,


exclusion


of the lender's


risk


premium results


in a


mistaken


measurement


of the benefits


of the FHA insurance


program--benefits


calculated


as the difference


between


the expected


default


loss


on the


loan and


the insurance


premium


paid


with


no consideration


of lender


risk


premiums.


Thus,


many


purchasers


of FHA


insurance


are


seen as


driving negative


net benefits


from


participation


in the


program.


Since


insurance


coverage


not forced


upon


anyone,


one must


ask why


rational


consumer would


willingly


for a good


that


yielded


benefits


Trn I *10A


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Higher


income households


or those


with


loans


in relation


to value
premium
tutions


received
charged f


could


default


protection


It would


profitably


offer


such


worth


appear


less


that


borrowers


than


lending


insti-


conventional


loans


with


ventional


an interest


rate


but less


charge


than


greater
the FHA


than


premium.


current


Their


con-


failure


to do


so may


reflect


a judgment


that


in the absence


price


inflation
mortgage


and attendant


insurance


rises


would


in property


seven


rely


values,


underfinanced,


FHA home


perhaps


considerably


more


than


percent,


so that


virtually


everyone
insurance


would


(Aaron


realize


1972


a net benefit


under FHA mortgage


, p. 89).


Such


a global


view


on the


part


of lenders


is questionable.


Aaron


incorporated


the lender's


risk


premium


into


the analysis,


such


contortions would


have


been


unnecessary.


In fact,


what


Aaron


interprets


as borrowers'


net benefits


represents


only


the income


redistribution


taking


place


within


the FHA


program


because


of the non-actuarially-fair


pricing


scheme


employed


in supplying


insurance


coverage.


With all


pur-


chasers


insurance


coverage


being charged


same


premium,


it is


obvious


that


some


will


pay more


than and


some


less


than


the expected


default


loss


on their


individual


loans


if the


program


is to break


even.


Such departures


from


the actuariallyo


fair


rate


structure,


however,


not fully


necessity


represent


borrower


understate


benefits;


the real


and such


benefits


derived


an interpretation


from


must,


the insurance


purchased.


While


Aaron


does


recognize


the redistribution


that


occurs


and the


reason


its occurrence,


he mistakenly


identified


this


redis-


tribution


as the


net benefits


derived


from


the program because


risk


premiums


are


ignored.


The following


chapter


will


adopt


Aaron


s basic


approach


by viewing


mortgage


contracting


process


as a basic


choice


problem


in which









term


to maturity


on the loan


in the


contract


terms,


explicitly


con-


sidering


the lender's


risk


premium,


and deriving


the conditions


under


which


insurance will


be desirable


from


the borrower's


point


of view.
















CHAPTER


A THEORETICAL MODEL OF


DEFAULT RISK


AND DE


Introduction


FAULT


INSURANCE


and Overview


of the


Theoreti


cal Model


The theoretical


model


developed


in this


chapter


analyzes


the de-


fault


insurance


market


from


both


the demand


side and


the supply


side


order


to reach


an understanding


of the basic


mechanisms


involved


in the


determination


of the quantities


insurance


written.


It is intended


to explain


both


the overall


market


volume


of insurance


written and


individual


volumes


that


are written


various


supply-side


partici-


pants


in that


market.


The model


that


is derived


will


seen


to differ


from


the standard


microeconomic


competitive market


analysis


in three


important


respects.


First,


the model


incorporates


uncertainty


concern-


ing mortgagor


default


behavior.


Such


uncertainty


course,


basic


source


of default


insurance demand,


and it


is accounted


for in


the model


use of the state-preference


approach


to decision making


under


uncertainty.


Second,


the model


explicitly


introduces


constraints


an institutional


nature


on the supply


side


of the market.


These


constraints


have


been


particularly


influential


in the market


for de-


fault


insurance


because


of the importance


of federal


involvement


the intensity


state


regulatory


actions


in this market.


And third,









segmented


market


structure


that


requires


individual


supply-side


par-


ticipants'


behavior


to be further


constrained


the actions


of other


participants


in the market


(some


of which


exhibit


behavior


that


motivated


profit


considerations).


The model


assumes


that


the default


insurance


market


represents


sector


a larger


three


sector


system


consisting


of the housing market,


mortgage


market,


and the default


insurance markets.


Together,


these


three


sectors


determine


quantity


of houses


sold,


the quantity


mortgage


funds


loaned


and the quantity


insurance


contracts


written.


It i


further


assumed


that


the housing


mortgage


markets


are deter-


mined


simultaneously


and that


the default


insurance


market


is determined


recursively


from


outcome


of the equilibrating


process


occurring


the other


two markets.


One might


imagine


that


the demand


for and supply


of housing


services


influences


the demand


mortgage


funds


and that


the demand


for and supply


mortgage


funds


simultaneously


influences


the demand


default


for housing


insurance


services.


is determined


Then,


from


we assume


the demand


that


the demand


for and supply


mort-


gage


funds


but that


outcome


achieved


in the default


insurance


market


does


mortgage


not exert

markets.


any s

This


imultaneous


basic


feedback


assumption


effects


concerning


on the housing


structure


of the larger


three


sector


system


necessary


we are to examine


default


insurance


market


in isolation without


more


detailed


explicit


modeling of


the other


two sectors.


The model


also


assumes


that


the home


mortgage


default


insurance


ma rl -


I" rh at t 4 r'r n


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A orA n lm A


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nF n(rtrr Trn-mnrt


one


ca t -


I ^


r\









viewed


as a competitive


mortgage market


under


conditions


of default


loss


uncertainty


insurance.

the demand


Thus


to determine

the model


for default


the market


explicitly


insurance


cover


demand


recognizes

ge where t


or mortgage default

the derived nature

he primary source o


this


demand


is found


in the demand


for and supply


mortga


funds.


The relevant


behavior


of these


two participants


is explored


in the


sections


of this


chapter


that


follow


this


introductory


section.


The final


set of default


insurance


market


participants


(the


sup-


pliers


of default


coverage)


is composed


of four


major


actors:


the FHA


Section


program,


the private


mortgage


insurance


industry


Veterans


Administration


home


loan


guarantee


program


and the FHA subsi-


dized


housing


mortgage


Insurance


programs.


Of these


four


actors,


the last


three


are assumed


to be subject


to supply


constraints


institutional


nature


which


result


in their


services


being


rationed


the basis


of non-price


characteristics.


For the VA and


subsidy


programs,


the characteristics


that


are


used


to ration


the services


pro-


vided


are the prior military


service


and the family


income


of the in-


surance


applicants


of the


programs,


respectively.


For the private


mortgage


insurance


industry,


the objective


of maximizing


profits


sub-


ject


to the constraints


faced


in this


market


(regarding


both


quantity


that


legally


be written


given


state


laws


forbidding


entry


and the regulations


concerning maximum


contingent


liabilities


that


be assumed


and the price


that


practically


be charged


given


the presence of


a supply


schedule


for Section


coverage


that


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industry


implies


cream-skimming


from


the previous


customers


of the


Section


program.


Finally,


coverage


supplied


the various


actors


in the market


is considered


to be non-homogeneous


but substitutable.


This


implies


a segmented


market


structure


and results


in the overall


mortgage


fault


insurance


market


being


determined


from


the operations


four


inter-related


submarkets


(one


for each


supplier


of coverage).


And,


since


neither


cream-skimmin


nor rationing may


occur


a competitive


market


in long


run equilibrium,


the model


mus t


be interpreted


as short


run in nature.


now


derive


a theoretical


construct


that


will


allow


us to incorporate


these


complexities


our analysis


of the home


mort-


gage


default


insurance


market.


Default


Probability


and Expected


Default


Loss


on Individual


Mortgage


Loans


Since


the fundamental


purpose


mortgage


Insurance


to reduce


the lender'


exposure


to default


risk


on insured


loans,


a theoretical


analysis


of default


behavior


provides a


logical


first


step


in the


development


a comprehensive


theory


of d


efault


Insurance.


At this


preliminary


of the analysis,


we are


not concerned


with


the default


insurance


market


itself,


rather,


with


the mode


of behavior 'that


gives


rise


to the phenomenon


mortgagor


default.


An understanding


such


behavior will


prove


useful


in later


stages


of the analysis


when


the demand


side


of the default


insurance market


is approached.


factors


that


are important


in the determination


of d


efault


risk on









As pointed


out in the preceding


chapter,


the existing


body


economic


literature


contains


very


little


explicit


theoretical


analysis


mortgage


research


ment


examine


default


has been

a theory


risk,


a


conducted

of default


mortgage


default


1 though

in this


a considerable


area.


insurance,

phenomenon


amount


Therefore,


it will

from t


be usefu


of empirical


in the develop-

1 to first


he perspective


of economic


theory.


This


section


attempts


to analyze


default


behavior


from


such


perspective.


The basic


purpose


is to present


the phenomenon


of default


on home


mortgages


as the logical


outcome


a rational


decision


process


that


is influenced


certain observable


factors.


The model


of individual


default


behavior


developed


in this


section


utilizes


the following


notation:


the individual'


net assets


other


than


the mortgaged


property


in period


the individual's


income


net of consumption


expendi-


tures


in period


market
seen as


(Vt )


value of
a random


the mortgaged


variable


with


property
density


in period
function


the contractual


interest


rate


on the mortgage obliga-


tion,


constant


over


the mortgage


loan-to-value


balance


ratio


outstanding


on the mortgage


in period


at origination;


- L/V


= downpayment


on the


mortgage at


original t ion


expressed


as a percent


of the price


house;


Empirical


studies


that


deal


primarily


with


the estimation


fault


probability


equations


include:


Baza and


Kirzner


(1975);


v-1









contract


life of


mortgage


obligation


from


origination


to maturity;


probability
in period t


of default


on the


mortgage


obligation


Adopting


this


notation


and ignoring,


for the


moment


, any legal


considerations


raised


default,


we may write


the individual


s wealth


in period


t (which


we denote


+Vt -
t

* with


(1


+ r)


with


no default


default.


If V


were


non-stochastic,


it is obvious


from


this


expression


that


the individual attempting


to maximize


wealth


in period


t would


default


on the loan


if his


equity


in the mortgaged


property


became


negative,


where


equity


in period


t (which


we denote


given


- (1


t V
t


+ r)


This

defaulting

to borrow


result,

on the

funds.


however,

mortgage

Credit r


must

will


atin


be amended


have


in light


on the individual'


are based


least,


of the effect


future

some e


that


ability


xtent)


upon


past


behavior


in paying


ebts.


This


means


that


the individual


will


have


to weigh


gain


in utility


from


increased


wealth


brought


about


defaulting


a negative


equity


situation against


the loss


utility


brought


about


a decrease


in future


access


to capital


markets


that


is generated


such


behavior.


Consideration


of this


factor


means


that


+ r)


will


have


to exceed


a sufficient


amount


com-


pensate


the individual


for this


decline


in his


ability


to borrow


funds


t


Xt









to be constant


a given


individual


a given moment


in time.


doing,


we denote


dividual's


credit


this


value


rating


which


to him at


represents


period t.


Certain


the value


of the in-


demographic


char-


acteristics


found


entering


various


regression


equations


default


probability


studies


seen


to function


through


this


factor,


i.e.,


individuals with


particular


characteristics


(race,


age,


income,


etc.)


may value


credit


ratings


higher


or lower


than


others


in a


systematic


fashion.


With


still


assumed


to be known


with


certainity,


the equity/


default


probability


relationship


can be described


implies


implies


Here,


we have


the case where a


slight


decline


in V


below


+ r)


does


not result


in default


on the loan


because


the small


gain


in the


mortgagor's


wealth


position


does


not warrant


the damage


that will


done


to his credit


rating


defaulting


on the loan.


The individual


may be perfectly


willing


to suffer


negative


equities


if he places


suf-


ficient


value


on his future


access


to capital


markets.


Consideration


of the myriad


factors


that


may,.


theoretically,


influence


is beyond


scope


of this


analysis,


but it


seems


clear


that


such


factors


very


important


in determining


individual


default


behavior.


Trans


actions


costs


involved


in selling


a house would


have


oppose
a pos


ite effect


itive


equity


and could


situation


make


default


sufficiently


the optimal


large.


Assum


choice
e that


even


the in-


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however,


is not known


with


certainty.


The value


of the


mort-


gaged


property


is subject


to fluctuation


as a result


of changes


in vari-


ous factors


beyond


the control


of either


the mortgagee or


mortgagor.


For example,

containing t


borhood


construction


:he mortgaged


be re-zoned;


a new


property may


or the local


highway


through


be announced;


or national


the neighborhood


an adjoining


economy


neigh-


experience


an economic


downturn.


All of these


occurrences


will


affect


the market


demand


for the


property


securing


the loan


and,


therefore,


influence


value


of that


property.


In order


to capture


the effect


of these


various


factors


ability


ability


in the model,


density


we assume


given


distribution


of the


value


to be


Since


a random


appears


of the mortgaged


variable


likely


property


with


that


will


a proba-


the proba-


vary


over


time,


we allow


for the possibility


that


the densit


functions,


will


differ


for different


time


periods.


In particular,


chan


over


time


in the conditions


of the neighborhood


property,


or the


local


housing market


will


affect


the functional


form


ft(Vt)


now


define


as the value


of the mortgaged


property


in period


at which


plus


becomes


zero,


+ r)


Then


the individual


s expected


wealth


in period


(denoted


can be


written as


IL Lt
likely


a sufficiently


to be fairl


constant


large
over


amount.
individual


This


factor
over


, however
time.


Consequently,


we do


not incorporate


it explicitly


in the theoretical


model,


although


such


incorporation


could


be easily


adopted


if the


model


1 1 -1 1


f t


- t


- 1 1












+ It
t


+ It


+ r)


+ Vt


where the first

vidual's wealth


integral

position


on the right-hand

if the value of t


side


represents


he mortgaged


the indi-


property


becomes


sufficient


low to make


default


the optimal


(expected


wealth


maxi-


mizing)


policy


and the second


integral


represents


the individual'


wealth


position


if the value


of the


property


remains


sufficiently


high


to warrant


continuation


of the mortgage


payments.


one felt


desirable


assume


that


property values


remain


non-negative,


the lower


limit


of integration


for the first


integral


on the right-hand


side


equation


could


be replaced


with


the value


zero.


Such


an assumption,


however,


not required


our purposes


so we maintain


the more


gen-


eral


expression


above.


Maximization


of this


expected


wealth


requires


that


the individual


default


on the loan


as soon


as V


declines


to V


Given


our definition


in equation


above,


we know


that


the probability


of default


period


t is given


Pr [Vt


+ r)


Then,


definition


a cumulated


distribution


function


we know


that


e y^









This

property

ability st


expression


characteristic


udies may


reveals


the channel


variables


seen


found


through

in many


to function.


which


neighborhood


of the default


affecting


the time


proba-


path


property


values


(hence,


these


factors


influence


default


proba-


abilities


both


in the


present


period


and in future


periods.


Housing


market


disruptions


created


local


or national


recessions


can also


seen


to function


through


this


channel.


For example,


the distributions


, .,


t+i


n, may


all be shifted


to the left


(i.e.,


expectation

occurrence


of future


such


property


as the decay


values


may be reduced)


of the neighborhood


in which


an exogenous

the mortgaged


property


is located,


thus


increasing


the probability


of default


in the


present


and all future


periods.


For a given


distribution


of values


for the mortgaged


property


time


t (i.e.,


given


equation


implies


that


3iven
Given


that


default


probability


bears


such


a close


relationship


the density


function


explained


concerning


tion
the


ft(Vt)


of these futu


PtPnft


4- t-.-


property


as a divergence


in future
re values


pxnPnrtp


values,
between


periods
into th


fii tir1I


the phenomenon


lenders'


and the housing


e selling


d PrlinnCc


price


subjective
g market's
of the pr


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- hnnn


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notions
capitaliza-


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t)),


|


I


1 I,-1 I









Intuitively,


for a given


probability


distribution of


property values,


greater


the outstanding mortgage


balance,


greater


will


the probability


that


will


decline


to V


and,


as a result,


greater


will


be the probability


that


mortgagor


will


default


on the


loan,


The inequality


in expression


merely


illustrates


the ob-


vious


point


that


greater


the value


that


mortgagor


places


on his


credit


rating,


the lower


will


be the probability


default,


And,


the result


iven


in (8)


indicates


that


default


probability


will


directly


related


to the


contract


interest


rate,


This


last


finding


stems


from


the reduction


owner


equity


any given moment


in time


that


results


from higher


interest


rates.


For the


moment,


we focus


attention


on the relationship


expression


Given


the interest


rate


and the price


of the mortgaged


property


(denote


this


price


where


at t


= 0)


the important


elements


in determining


the time


path


of the outstanding mortgage


balance


percentage


downpayment,


and the


contract


life


of the


mortgage,


we ignore


interest


charges


and assume


a constant,


even


reduction


the principal


on the loan,


the outstanding


balance


in period


written as


= P (l
t


- D)


- t [P(l


- D)/T


= 0,


The first


term on


the right-hand


side


is the original mortgage


amount,


and the second


term


is the cumulative


amount


of the loan


that


has been


Today,


most


mortgage


loans


exhibit


constant,


level


payments,


which


this


formulation


does


not.


The formulation


for the


outstanding


our


are


. ,









paid


the borrower


at time


Obviously


for all


t except


last


(when


= T)


in which


case


and the


mortgage


is retired.


From


this


expression


we see that


P
=-P + t
T


= 0,


- D)


for D


= 1.


These


results


indicate


the qualitative


relationship


between


out-


standing mortga


balance


in period


and the


percentage


downpayment


expression


term


to maturity


expression


11).


given


purchase


price,


this


outstanding


balance


will


be lower


the larger


the downpayment


and the shorter


term


to maturity.


Ignoring


the special


but uninteresting


cases


t t
where D -
aD aT


we may


combine


the above


results


via the chain


rule


expression


to obtain


the results


Mgt
3M
t


that


3M

3D


gt
tM
t


These


results


stem


from


the effects


of initial


downpayment


term


= T,









(and,


a given


will


be smaller)


the smaller


is D and


larger


is T.


The inequalities


given


in expressions


and (13)


above


describe


the qualitative


relationship


between


default


probability


and loan


con-


tract


terms.


Since


the mortgagee's


actual


default


loss


the insur-


ance


claim


on 100 percent


insured


loans)


in the


event


that


default


occurs


is (ignoring


foreclosure


transactions


costs)


equal


to the


negative


equity


position


of the mortgaged


property,


expected


default


losses


will


also


be influenced


contract


terms.


we let E [


denote

period

tuate


the expectation


and adopt


of default


the simplifying


a continuous


fashion


loss


on the given


assumption


so that


that


loan


property


mortgagor


will


in the


values

default


iven

flue-

when


the value


of the mortgaged


property


equals


exactly,


we have


E [ L


- (1


+ r) M


t(Vt)


+ r) M


This


assumption


represents


an obvious


departure


from


descriptive


reality.
pression


is necessary


for expected


however


default


loss


we are to derive


under


assumption


a precise


that


ex-


mortgagors


enter


default


at precise


the optimal


point.


To the


extent


that


non-


4F:nr vnn av T\


+ Ct


+ (1


+ (1


t gt


rnrntinlr nn- f- Q


+ r) M


lth nf l l n iir>h


T~ /-\vr\ 1


ctii/llk


`t^ nh Vi '-ti nr


n-i cr*T* t-


^ i mr^ 0









Obviously,


under


the assumptions


that


mortgagor


attempts


to maxi-


mize


expected


wealth


after


taking


the value


of his credit


rating


into


account


and that


property


values


vary


continuously,


default


will


occur


as soon


as negative


equity


in the


property


(given


the difference


between


and (1


+ r)


is equal


to Ct


in absolute


value.


Then,


actual


loss


to the lender


in the


event


of default


will


always


be equal


to C


and expected


loss


is the actual


loss


times


the probability


default


occurring.


Thus,


the expected


default


loss


to the


mortgagee


depends


upon


probability

mortgagor


of default


is willing


loss


to abso


and the degree

rb to protect


of negative

his credit r


equity


eating.


that


Recall,


however,


that


this


latter


variable


also


influences


because


it is


included


our definition


of V


(expression


above


Also


recall


that


it bears


a negative


relation


t (expression


above)


so that


net effect


on E[L


becomes


ambiguous.


Intuitively,


greater


the value


that


an individual


places


on his credit


rating


the lower


will


be the probability


that


default


will


occur


but,


in the


event


that


does


occur,


the larger


the actual


loss


is likely


to be.


Such


a result


emphasizes


the inherent


weakness


of limitin


the analysis


of default


risk


to the explanation


of default


probabilities.


With


regard


to the


terms


on the


mortgage


contract,


however


it is


clear


from


the above


expression


that


Obviously,


factor


tend


been


a similar


incorporated


to increase


result


in the


the probability


would


model.


have
Here


of default


applied
, transac
but would


to Zt
tions


(ass


had this


costs


umin


would


that


rnctc


n rT 1 n TTOr"


fnr lonAnre


t-h 'n


Err inTi7,4Aiinle


hKr 0 an


J III


-hP i=









aE [Lt ]
3D

3E [Lt ]

aT




aE [Lt ]


for a given


That


expected


default


loss


is inversely


lated


to the


to-value

related


percentage


ratio),

to the c


directly


contractt


downpayment


related


rate


directly


to the


of interest


related


term to maturity

on the mortgage


to the loan-


and directly


obligation.


These are


the basic


qualitative


relationships


that


will


be employed


the following


section


of this


chapter


in examining


the individual'


decision


of whether


to borrow


on an insured


or an uninsured


basis


given


the market


receive


rate


strong


available

empirical


on the

support


two types


from


of loan.


the default


These


studies


results


von


Furstenburg


and others.


Therefore,


no attempt


is made


to replicate


these


results


in this


study,


and the reader


is referred


to the


regres-


sion


results


presented


in Chapter


III above.


The Demand


for Default


Insurance


Coverage


Recognizing


the influence


that


financing


terms


have


on default


risk


we now


consider


the impact


that


such


risk


exerts


on the indi-


vidual


lender 's


supply


mortgage


funds


and,


through


this,


the market


price


or rate


of interest)


on such


funds.


focusing attention


re-


d









(this

then


source

be in a


being


position


e lender'

to draw


aversion


inferences


to default

concerning


risk),


and we will


the important


fac-


tors


that


are likely


to determine


this


demand.


so doing,


it will


be expedient


to adopt


several


simplifying


assumptions


that


constitute


rather


drastic


departures


from


real


world


situations.

sumptions i


An extended


n the derivation


discussion


of the methodological


of theoretical


models


role


obviously,


as-

beyond


scope


that


of this


the violence


study.


that


Instead,


is done


we can merely


to descriptive


express


accuracy


the opinion


through


of these


assumptions


does


not jeopardize


the usefulness


of the conclu-


sions


that


they


enable


us to obtain.


Some


of the basic


assumptions


that


are employed


in this


section


include:


Mortgage


that
as g


markets


individual


are workable


lenders


take


competitive


prices


in the


interest


sense
rates)


iven.


Mortgage


lenders


are viewed


as suppliers


mortgage


funds


only.


Individual


mortgage


loans


are


viewed


as marginal


units


to the lender


(although,


in reality,


they


differ


size).


These


three


assumptions


represent


only


most


basic


most


obvious


departures


from


reality


that


are embodied


in the model


below.


Other


somewhat


less


brazen


assumptions


will


be adopted


as the analysis


proceeds.


The first


conceptual


difficulty


that


must


be confronted


analysis


sumption


of lender


above,


behavior


we must


is that


recognize


even within


the essential


the confines


heterogeneity


use


our


as-









individual


mortgage


loans.


Since


the financing


terms


on individual


mortgage


loans


vary


considerably


across


such


loans,


and since


these


terms


have


been


shown


to influence


default


risk,


our analysis


should


allow


us to separate


mortgages


of distinct


term-related


risk


levels.


Because


of this


risk


heterogeneity,


there


will


not exist


a single


mar-


price


for mortgage


funds


but instead,


there


will


exist


a market


price


vector


for loans


with


different


financing


terms


any given


moment


dividual


accommodate


cept


in time.


loan


this


of commodity


In this


to reflect


essential


way,


we can allow


the inherent


feature


hierarchies


default


the market


risk on


below,

to the


in the model


(Sweeney,


1974)


price


that


an in-


loan.


we apply

mortgage


the con-

market.


Specifically


we interpret


default


risk as


a quality variable


assume


k classes


loans


that


are


distinguishable


and mutually


exclusive


garding


the default


quality


(risk)


exhibited.


These


classes


are


con-


sidered


to be defined


contract


terms


of the loans


within


class;


i.e.,


all 30


year


percent


loans


are assumed


to exhibit


essentially


identi


default


risk and


are


therefore


classed


together


one quality


level.


We also


assume


that


individual


lenders


inate


a large


number


of loans


in each


quality


class


so that


the marginal


analysis


may be applied


to individual


classes


of loans.


Then,


ranking


these


loan


classes


in ascending


order


of default


risk


alternatively,


in descending


order


of loan


quality)


we may write


the market


vectors


loan


prices


and quantities


re-




















where,

that a


through


the operation


ire established


will


of the market,


increase with


we will


the default


see that


risk


the prices


exhibited,


i.e.,


for 1


Also,


assumption


each


class


quantity,


is formed


summation


loans,


each


of which


is reasonably


equivalent


with


regard


to the


default


risk


exhibited,


so that


M. = E
J i=l


and the total


quantity


of loans


originated


given


lender


in the


given


period


will


MT k
M =
j=l


Then,


the total


revenue


obtained


the lender


will


r.M .
J J


and,


obviously,


with


positive


prices


and r given


to the firm


'IU









period


referred


to in this


section


is defined


the maximum maturity


of the loans


originated


so that


r vector


will


represent


percent-


interest


Given


charges


this


over


conceptual


the life


framework,


of the various


we turn


loan


classes.


our analysis


of lender


behavior.


so doing,


we adopt


the following additional


notation


assumptions.


is the total


default


loss


to the lender


in the given


period


on all


loans


originated


in that


period.


Assuming


that


total


default


loss


increases


with


the quantity


loans


originated


and recalling


the influence


of loan


con-


tract


terms


on default


risk,


we may write


the total


default


loss


for each


class,


as a function


of the quantity


loans


originated


in that


class,


the financing


terms


that


serve


to define


the class


and a random variable,


doing,


we have


= L.


, (L/V).,
*J


zj),


where


(L/V)j


is the loan-to-value


ratio


and T.
J


term


to maturity
BL.


that


together


and from
(L.V

a(L/V).


define


class


the conclusions


and 3
aT.
j


is the total


cost of


loans.


reached

Also.


w


Obviously,


in the preceding sec
2L.
e assume that --- 2
2
aM


supplying mortgage


funds


0,

tion,

0.


that


are unrelated


to default


risk.


It includes


administrative


costs


and the


opportunity


costs


of the funds


made


available.


is seen as


an increasing


function


of the quantity









>0.


of risk,


Also,

we will


assuming

dCT
have dT
dM


that these
dC.

dM.


costs


are independent


Utilizing


this


notation,


we may


describe


the profit


function


mortgage


lending


institution


(assuming


for the


moment


that


none


the loans


originated


carry


default


insurance


coverage)


- L


- CT


where


is the total


profit


for the given


period


which


is given


sum of


the individual


profits


on each


loan


class,


Then,


we may


write


total


profits


j j=l


r. M.
J J


(M) .
J


Due to the


presence


of the random variable,


in this


equation,


lender'


profits


will


be stochastic.


Assume


that


the lender


possesses


a utility


of profits


function


that


satisfies


von


Neumann-Morgenstern axioms


(see


Horowitz,


1970,


342-351).


Let this


function


be given


and let the


function


be defined


over


profits


from


individual


loan


classes,


= U.
J


(I.).
~J


Then,


adopting


the objective


of expected


utility


maximi-


zation,


we may write


the lender


s objective


function as


= U (v


1. k -


1









Differentiating


this


expression


partially with


respect


to each


of the


lender's


control


variables


(the


M. 's)
J


aE [U


(Oj)]
.


E [U


3L.

J


dC.
-dM
dM.
3


dC.
_ dM.)]
dM.
3


(y)
3 .
Jv


9L.

3M.
J


9 ,


3U
where
an


is the lender'


marginal


utility


of profit


from


class


loans.


Setting


each


of these


expressions


equal


zero


and simplify-


ing,


we obtain


the first-order


conditions


necessary


for the maximization


of the expected


utility


of profits,


dC.
=- +
j dM.
kJ


3L.
M.j
J


rU
cov [
T J.


3L.

' 3M.
i-L, j


= 1,


Setting


this


expression


equal


zero,


we obtain


(au)
Bu.


dC.
- --)
dM.
3


Then,
equal
tween


since


the expected


to the product


these random


S. ]

value
their


- Ef[( 1U


of a product


expected


values


-L
3M.
J


two random variables


plus


the covariance


variables


3
3m.
J


-^'
- E[ ]
3


3L.
E []
3M.
]


- cov [y
anJ


3L.
---M
' M.
]


flHin rl i n ru 1i7 nn n---- l


()a
31.


S ,


dCj

dM.
J


31
JT


dC.
- L)
dM.
J


aL.
()]
3M.


'-tn t'h l, v"- oV --h'iT


c3 i t H


-i TI mntI m n x r rr




tnraQ'm









Assuming


that


the second-order


conditions


are met (i.e.,


that


lender


is indeed


maximize in


the expected


utility


of profits)


these


expressions


give


the total


interest


charges


that


the borrower


of class


loans


will


have


in order


for the lender


to be willing


originate


the marginal


loan


in that


class.


The expressions


implicitly


define


the lender


s supply


schedule


mortgage


funds


for each


of the


k loan


classes.


We know


term


assumption)


on the right-hand


the covariances


between


side


dC.
that dM
J


and E


of the expressions


the marginal


utility


> 0.


given


of profits


in (19)


The third


above


and the


are


mar-


ginal


default


loss


divided


the expectation


of the marginal


utility


of profits.


The denominators


of these


terms


are assumed


to be always


positive


(i.e.,


U is assumed


to increase


monotonically)


so the signs


depend


upon


the signs


of the covariance


terms


in the


numerators.


the lender


is risk


averse,


will


concave


as in Figure


4.1.


u (t.)
J


-1









Then,


under


the assumption


that


lenders


are risk averse,


the covariance


terms


in the expression


given


in (19)


will


be positive.


This


is be-


cause


marg


inal


utility


of profit


will,


under


this


assumption,


vary


inversely with


the level


of profit which


will


itself


vary


inversely


with marginal


default


loss.


Tha t


is, as marginal


default


loss


rises


profits


will


will,


rise.


~etVeAis


Therefore


pawtibu,


under


fall


and the marginal


the assumption


that


utility


mortgage


of profits


lenders


are


risk averse


the final


term on


the right-hand


side


of the expression


given


in (19)


above


is positive


and is added


to the other


two (positive)


terms


miums


on that


(Pratt,


side.


1964)


These


required


terms


be interpreted


by mortgage


lenders


as the risk


to originate


pre-


loans


each


the k classes.


Denoting


these


risk


premiums


equation


becomes


r.



Recall


dC.
= J +
dM.


that we ar


BL.
E [t3M1
aMJ
J


+ P.


= 1,


* S *


3L.
E [3- ]


e intrepreting


as the lender


s expecta-


tion


of default


for origination


loan.


Therefore,


loss


and dM.
dM.
J


on the individual mortgage


as the


equation


costs


states


of making


that


loan


funds


the total


being


considered


available


interest


for this


charge


on the individual


loan


in each


quality


class


must


equal


the marginal


9Note


this


result.


that


the assumption


If lenders


were


that
risk


U (j)
neutral


concave


would


, U (j )


is crucial


be linear


o U
cov [y
air


BL.
--L2
' M.
3









non-default


costs


of providing


the funds


plus


the expectation


of de-


fault


loss


on the loan


plus


some


positive


risk


premium


that


depends


upon


these


default


losses


and the lender's


degree


of risk aversion.


the absence


of default


insurance


if the borrower


is unwilling


this


amount,


then


the loan


(with


given


terms


for class


loans)


will


not be originated.


Now,


we relax


the assumption


that


default


insurance


not availa-


ble and replace


it with


the assumption


that


such


insurance


is available,


where


this


insurance


provides


the lender with


b (100)


percent


coverage


against


default


loss


price


per percentage


unit


coverage


is assumed


to be


so that


cost


of providing


(100)


percent


level


coverage


is pb (100).


Since


such


coverage


directly


reduces


the default


risk


faced


the lender,


provision


(100)


percent


level


coverage


the borrower will


reduce


the interest


charges


on a loan


of the th
of the j


class


dC.
= -J +
dM.
J


- b)


BL.
1 j]
aM.
J


- b)


And including


the insurance


cost


of providing


this


level


coverage,


we obtain


the total


price


for insured


mortgage


funds


of the jth


class


- b)


- b)


+ pb


(100)


= 1,


ThP driPniin


FnrPrl lv


hnr r nnTr


a rlnac


1n nn


i **


dC.

dM.
j


. .


+ (1


trh nntint~a


Si t


I









without

borrower


insurance co

's advantage


average and

to provide


pay r..

default


Obviously,

coverage c


it will


in the loan


to the

if10


= 1,


Substituting


equations


and (22)


into


the inequality


in (23)


gives


us the result


that


the loan will


be insured


whenever


the following


condition


(100)


3L.
E [1 ]
aM.
J


= 1,


. ,


Obviously,


if all insurance


coverage were


priced


at the actuarially


fair


rate


with no


loading


factor


(i.e.,


(100)


3L.
= E [Q ])
J


then all


loans


originated


with


risk averse


lenders


> 0)


would


insured.


As discussed


in Chapter


however,


four


sources


of default


insurance


coverage


(Section


203,


private


firms,


and FHA subsidy


programs)


provide


a fixed


coverage


a fixed


price


so that


actuarial


fairness


is not attained


under


of the available


plans.


In such


situation,


and b


are


given and


the probability


that


condition


will


met will


the precedin


depend


section


upon


of this


the size

chapter


9L.
of E [ M]
3M.


we know


tha


and Pj.
aL.
tE[
SM.
J


Since,


from


increasing


function


of the loan-to-value


ratio


term


to maturity


the marginal


loan


being


negotiated,


then


for a given


it is the


level


these


terms


that


will


determine


whether


the loan


will


be in-


sured


or not.


Higher


loan-to-value


ratios


and longer


terms


to maturity


increase


the probability


that


any given


insurance


plan,


condition


S *









will


be met.


Also,


it is obvious


from


this


condition


that


probability


that


the loan


will


be insured


will


decrease


with


increases


in the price


unit


of insurance


coverage.


Finally


if we allow


vary,


hold


and P


fixed
j


sum the individual


demands


coverage,


we obtain


the market


demand


for default


insurance.


Given


the conclusions


reached


in the previous


paragraph,


we may


expect


this


market


demand


to be
3L.


a decreasing


function


Also,


if we allow


for variations


in E [ -]
8M.
3


through


like


varia-


tions


in the loan-to-value


ratio


term


to maturity,


then


we may


expect


these


factors


to induce


shifts


in the market


demand


for default


insurance


shifts


coverage


in thi


with


demand.


increases


We turn


in these


now


terms


to the supply


leading

side o


to outward


f the default


insurance


market.


The Supply


of Default


Insurance


Coverage


Default


insurance


on home


mortgages,


like


most


service


goods


differs


from


the standard


manufa


ctured


good


in that


the product


itself


(the


insurance


contract)


is not "produced"


until


a mutually


agreeable


price


has been


settled


upon


the purchaser


and the supplier


of the


insurance


coverage.


Consequently


inventories


of insurance


contracts


cannot


exist,


and the


quantity


of insurance


produced


and consumed


must


be equal


every


period


of time.


excess


demand


in the eX ante!


sense,


however,


exist


at the quoted


premium


rate;


and,


when


this


occurs,


the service


can be expected


to be rationed


on the basis


of the


a q


F' 1 n -1


S-1s


I


4


I T_* L


~IlY~~n~


I- -


i









provision


extent


of insurance

to which it


coverage may


is being used


be used


as a rationing


as such may


be inferre


device,

d from


and

the


number


of insurance


applications


that


are denied


coverage.


amount


of rationing


that


must


take


place


through


the underwriting process,


however,


can be


seen


to depend


upon


the pricing


structure


adopted


the insurance


firm


in marketing


its product.


If this


pricing


structure


consists


multiple


premium


rates,


then


the underwriting process


be used


to classify


individual


applicants


into


various


risk


categories


for which


these


premiums


are intended.


This


combination


of pricing


and underwriting


is employed


in the


pro-


vision


many


types


insurance


(health,


auto,


life,


etc.).


With


such


a multiple


rate


premium


structure,


the underwriting


process


trans-


lates


applicants'


risks


into


premium rates


and only


serves


as a ration-


device


for those


exhibiting


risks


that


cannot


be covered


highest


existing


premium rate


rates


class.


are,


Such


thereby,


risks


are


frustrated


then


denied


in their


coverage


attempt


to obtain


insurance


non-price


rationing


of the service.


It is theoretically


possible


to eliminate


rationing


through


underwritin


process


allowing


the number


of risk


classes


enumerated


to-approach


the number


insurance


applications.


In this


situation,


the risk


that


is determined


through


underwriting


is translated


into


price


coverage


every


applicant.


The individual


applicant


then


free


to decide


whether


coverage


is worth


the price


he is


not denied


coverage


outright.


With


such


a pricing


structure,


the in-









expected


greater


claims


in the underwriting


enumeration


of risk


process


classes.


soon

some


outweighs

number of


the benefits


classes


(that


is usually


considerably


lower


than


the number


of applicants)


becomes


would


costs


cheaper


to create


generally


to ration


more


limit


the service


classes


the degree


on non-price


prices.


of risk-rating


grounds


Therefore,


that


than


information


feasible


practice.


At the opposite


extreme


, there


exist


only


one price


category


(those


deemed


eligible


for insurance)


offered


the supplier


of insurance


coverage.


As mentioned


in the preceding


section


and in


Chapter


it is this


latter


extreme


that


describes


the supply


mecha-


nism


employed


all four


participants


in the default


insurance


market.


Under


each


of the


insurance


plans


available,


a single


price


is quoted


and individual


applicants


are either


qualified


or disqualified


on the


basis


of certain


criteria.


Therefore,


under


none


of the plans


is the


individual


loan's


expected


default


loss


translated


directly


into


price


for insurance


coverage.


With


only


one category


eligible


applicants,


additional


insurance


coverage may not


be called


forth


under


of the four


plans


ineligible


applicants


are willing


higher


premium


rates.


Therefore,


the quantity


of insurance


supplies


under


of these


plans


does


not rise


with


the premium


rate,


and each


plan


s supply


schedule


will


be infinitely


price


elastic


at the quoted


rate.


Such


pricing


behavior would


not be observed


a competitive


1 C. r S


one


-


r- j


F-


.1


*









federal


government


suppliers


coverage


in this


market


attempt


maximize


profits.


The VA and


the FHA subsidy


programs


have,


as their


explicit


objective,


the subsidization


of the financing


costs


of parti-


cular


groups


mortgagors


(veterans


and low-income


families).


Section


program is


constrained


its enabling


legislation


char


a single


price


for all


coverage


provided


(Chapter


II above)


and it is intended


only


to attain actuarial


soundness


(which,


combined


with


the single


rate


premium


structure,


implies


average


cost


pricing


behavior).


Then,


private


firms


in the market,


which


must


sumed


to be profit


motivated,


are constrained


in their


pricing


supply


behavior


the activities


of these


federal


government


programs.


Specifically,


they


must


price


their


service within


the interval


between


the premium


rates


quoted


on these


programs


(0.5


percent


annum


the outstanding mortgage


balance


for the Section


203 program and


zero


for the VA and


FHA subsidy


programs).


price


equal


or below


lower


bound


of this


interval


would,


obviously,


require


that


negative


profits


be earned


(i.e.,


the insurance


service


would


require


subsidization).


And,


any price


that


is above


upper


bound


would


result


in a


zero


near-zero)


volume


of insurance


written


since


mort-


gagors


would


generally


be able


to obtain


coverage


that


the lender


requires


for a loan


program.


Within


given


this


terms


interval,


a lower


one might


price

expect


from

that


the Section

competition


among


the private


firms


themselves


would,


in the long


run,


force


some


differentiation


of risk


classes.


As noted


above


, however,


the actual


as-









individual mortgages.


Within


the relevant


price


interval,


such


separa-


tion


of risks may


insurance


industry


be extreme

is still


difficult.


in the early


Also,

stages


the private mortgage

of development, and


competitive

materialize.


pressures w

It should


within


the industry


be noted


, however,


have

that


only

some


recently

initial


begun

signs


risk


rating


within


the 0


to 0.5 premium


rate


interval


have


emerged


within


the last


few years


(Little,


1975)


But,


given


very


recent


nature


of this


development,


we may safely


ignore


price


variations


within


the private


mortgage


insurance


industry


our analysis.


In the long


run,

may


this

become


single-rate

invalid as


assumption


the industry


for the p


grows,


private firms

as intraindus


in the market

try competition


increases,


and as predictive


capabilities


are improved


through


accumu-


lated


actuarial


experience.


In this


regard,


the short


run character


the model


becomes


apparent.


Given


the prices


at which


coverage


is provided


under


the four


fault


insurance


plans,


the market


supply


curves


for the individual


participants


will


appear


as in Figure


4.2.


Price


Supply


Supply


(Section


203)


(Private)


I









The price


coverage


under


the different


insurance


plans


is given


on the ordinate:


the Section


zero


one-half


program;


for the VA and


the abscissa:


percent


one-quarter


subsidy programs


the number


dollars


annum


percent


of FHA.

insured


of the unpaid


for the private


The quantity

against defau


balance


firms;


is given


It.


Obviously,


if the four


types


coverage


were


homogeneous


and the above


supply


schedules


operative,


the VA and


FHA subsidy


programs


would


usurp


the entire


default


insurance


market.


The fact


that


this


event


been


forthcoming may


be explained


observing


that


these


programs


are operated


under


rather


severe


supply


constraints.


The VA


program


constrained


the number


of eligible


veterans


that


choose


to purchase


a house


in the given


period,


and the FHA


subsidy


programs


are con-


strained


the number


of low-income


families


choosing


to purchase


house


in the


given


period and


(probably


more


severely)


the funding


level


authorized


for the


programs.


Given


these


supply


constraints,


VA and


FHA subsidy


programs


insurance


services


must


rationed


accord-


to the prior military


service


and the family


income of


individual


applicants.


Consequently,


a condition


excess


demand


should


exist


for these


forms


of insurance


coverage


in all periods.


Also


we are dealing with


the market


for default


insurance


coverage


for the nation as


a whole,


we might


also


expect


the supply


private


mortgage


insurance


to be subject


a constraint.


This


expecta-


tion


stems


from


two basic


considerations.


First,


over


the period


with


which


we are concerned,


there


have


been


constraints


an institutional









until


1973


when


the last


state


forbidding


such


insurance


(New


York)


relaxed


its prohibition


against


these


firms;


state


regulations


that


limit


the growth


of the contingent


liabilities


of these


firms


stipu-


lation


a maximum


ratio


between


liabilities


reserves.


second,


given


the rather


narrow


interval


within


which


these


firms


forced


to price


their


insurance


services


(discussed


above),


they will


be unable


to write


coverage


profitably


on the higher


sk loans.


They


will,


therefore,


ration


their


services


on the basis


of the underwriting


risk


exhibited


individual


loans,


we may


expect


a situation


excess


demand


to exist


for the


coverage


that


they


provide.


Additionally,,


we must


recognize


that


the services


provided


under


the various


insurance


plans


that


are available


not homogeneous.


Basic


differences


coverage,


financing


terms,


mortgage


limits,


etc.,


that


were


detailed


in Chapter


serve


to differentiate


the four


kinds


insurance.


therefore,


becomes


necessary


to view


the default


surance


market


as consisting


of four


sub-markets


of substitute


insur-


ance


products,


where


three


of these


sub-markets


are characterized


conditions


excess


demand.


Then,


ignoring


the subsidy


programs


and VA for graphical


conveni-


ence


(their


treatment


would


parallel


that


of the private


firms


below),


11I
In


the long


run,


such


constraints


expec


ted to d


disappear


as the private


axed


firms


and as contingency


in the industry


reserves


lobby


to have


accumulate.


state


But,


prohibitions


over


period


the 1960'


and early


1970'


these


supply


constraints


appear


have


been


effe


active.


Mathematically,


one could


write


the profit


function


a mort-


eaae


insurance


firm


as the diff


erence


between


Doremium


income


are


CA LIJ


ex-









we can depict


the market


for default


insurance


as two inter-related


markets


as in Figure


4.3.


Then,


assuming


that


the supply


constraints


in the non-Section


203 markets


are effective,


the demand


for Section


203 insurance


(which


in the absence


of supply


constraints


under


this


program will


will


determine


be influenced


the quantity

the quantity


of Section

of default


203 insurance written)


insurance written


alternative


suppliers


of default


coverage


In Figure


4.3,


excess


demand


existing


in the private market


P
-QS)


with


the given


supply


constraint


will,


some


extent,


be channelled


into


the market


Section

market.


coverage,


If the


thereby


two forms


raising


of insurance


the level


were


of demand


perfect


in that


substitutes


if the


coverage


provided


were


homogeneous)


then


the demand


for Section


203 insurance would


be given


the horizontal


distance


AB in the graph.


They


are not,


however,


perfect


substitutes


reasons


mentioned


above; a

tionship


nd,


as a result,


between


we are unable


excess


demand


to deduce


for private


the quantitative


insurance and


rela-


the level


of demand


for Section


203.


as is obvious


from


Figure


4.3,


an in-


creased


supply


of the rationed


(constrained)


insurance will


result


a decrease


in the


excess


demand


in that


market


(holding


the level


demand


constant)


and,


mutawtA


muAan di,


a decrease


in the demand


Section


coverage.


Thus,


a partial


relaxation


of the supply


con-


strain


P
to Q
S


reduces


excess


demand


in the private


market


and the demand


for Section


203 insurance at


the existing


price


falls


P
to Q
D)















O 66
0 '
crHg 0 0

r4" J U)OJ-

O Q
T < 0

P- Cl
V3 4-*
'-- O
N

't O
0 'H
^ / en
: 0 C

,r O

/ C)
( )

A '-VQ
/ / ^


-- -- ------ -


On
o









price


of the unrationed


good


on the demand


for the rationed


good


free


market


(Tobin and


Houthakker,


1951;


Houthakker,


1961,


714-715).


This means


that


if the


two goods


are substitutes,


then an


increase


the quantity


of the rationed


good


will


reduce


the demand


for the


rationed


good,


as is pictured


in Figure


4.3.


Obviously


since


the price


insurance


coverage


under


each


of the


four sources


supply


has remained


constant


throughout


time


in both


absolute


and relative


terms,


it will


be impossible


to directly measure


own price


elasticity


of demand


or the


cross


price


elasticities


demand


for the different


types


coverage.


empirical


analysis


the default


effect


variation,


Also


insurance


own prices,

be imbedded


because


market t


but such

in the


of the effect


will,


course,


effect

constant


stated


will,

term


above,


implicitly


contain


to the complete


of the


cross


regression


price


lack of


equations.


elasticities


of demand


will


be imbedded


in the coefficients


of the rationed


quantities.


It is of


interest


to note,


however,


the effect


that


changes


in the number


related


rationed


goods


will


exert


on the own-price


sub-


stitution


effect


of the unrationed


good.


Samuelson


(1947)


has shown


that


the own-price


substitution


effect


for the unrationed


good


will


larger


in absolute


value


as the number


of rationed


goods


is reduced.


This


result


is referred


as the principle


of Le Chatelier


because


its analagous


relationship


with


the theorem


employed


in thermodynamics


(Samuelson,


1947,


footnote


13).


As Samuelson


points


out,


this


principle


I- --


provides


*I-t-- -- --I 1


an exact

A-1 -


basis


for the classic


-- --


distinction

/ET -1 1 1 .- ..-


elaborated

I nfrl


un-









effects


will


be larger.


Thus,


a given


level


consumption,


price


elasticities


of demand


will


be larger


in absolute


value


in the long


than


they


are in the short


run.


With


regard


to the Section


program,


this


result


implies


that


as rationing


in the default


insurance market


is eliminated


over


time


(through,


for example,


relaxation


of legal


con-


strains


on the private


firms


in the market)


the demand


for insurance


coverage


under


this


program


can be expected


to become


more


price


sensitive.


summarize


the important


findings


contained


in this


chapter


and relate


them


to the decline


in insurance


activity under


the Section


program.


Summary:


Basic


Theory


of Decline


The model


that


has been


developed


in the preceding


sections


con-


tains


several


theoretical


implications


that


provide


a basic


framework


for analyzing


the operation


of the default


insurance market


over


post-war


period


the decline


and particularly


in insurance


activity


for examining


under


the causal


FHA's Section


forces


prog


behind


ram.


This


framework


will


be adopted


in the


following


chapters


as the basis


an empirical


model


designed


to yield


inferences


about


causes


this


decline.


The model


will,


course,


serve


to both


test


the theo-


retical


framework and


provide


empirical


evidence


of the quantitative


impact


of the various


factors


implied


the theory.


The first


major


implication


emanating


from


the above


theory


is that


tntnl


1 fnliil t


l n clr rnr0 m nralrt


r4 tv mi' Ii iiiI'


A rtaoT-rmn nno


run


now


-3r ti i ^ iv


r 1 r i l i,-,








leads


to individual


program supply


curves


that


are infinitely price


elastic


to the point


at which


supply


constraints


become


effective.


Some


influence


on total


insurance


market


volume


may,


course


exerted


fluctuations


in the level


of these


constraints;


to the


extent


that


Section


coverage


serves


as a substitute


for the


cover-


age provided


other


(supply


constrained)


participants


in the market,


such


fluctuations


will


only


affect


the distribution


of insurance


market


activity


among


these


partic


ipants


and will


not affect


the total


volume


of insurance


written.


To the


extent,


however,


that


Section


203 does


serve


offered


as a workable


in the market,


substitute


variations


for the other


in the level


forms


of the supply


coverage


constraints


imposed

of total


on these o

insurance


their


participants


written.


But,


will


since


influence


these


the observed


constraints


quantity


are not


altered


response


to market


conditions


but,


instead,


fluctuate


with


legal


and other


institutional


changes


(such as


the number


veterans


leaving


the armed


services),


they may


be considered


as exogenous.


Therefore,


the estimation


an empirical


behavioral


relationship


with


total


insurance


volume


as the dependent


variable


will


not encounter


usual


simultaneous


equation


problems


confronted


in most


market


analyses,


and such


a relationship may


be interpreted


as a demand


equation


with


mentioned


above)


the price


term


implicit


in the


constant.


Also,


the above


theory


implies


that


total


default


insurance


market


demand


will


an increasing


function


the overall


level


activity


in the mortgage market


since


the demand


for default


coverage


is derived


from


the demand


for and supply


mortgage


funds


under


conditions




Full Text

PAGE 2

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AN ECONOMIC ANALYSIS OF THE HOME MORTGAGE
DEFAULT INSURANCE MARKET WITH EMPHASIS
ON THE DECLINE OF FHA
By
DAVID L. KASERMAN
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1976

"However, just as pressing is the need to reappraise
in the comprehensive manner the entire FHA program
and to determine its future role in serving national
housing needs"—Wright Patman, CongA£¿¿¿ona£. R&CCitid,
August 15, 1974.

ACKNOWLEDGEMENTS
This study has benefited from the helpful contributions of many
people. First, the dissertation committee, consisting of Roger Blair,
Max Langham, Jerome Milliman, and Dean Taylor, has been invaluable in
making suggestions for basic improvements in both the organization and
content of the final product. They have also provided a continual
source of encouragement throughout this effort. This cooperation and
guidance has been particularly valuable because of my absence from the
university during the entire period of research. This absence has
created considerable problems of communication that a less dedicated
or less understanding committee would not have tolerated. I am parti¬
cularly grateful to Dr. Milliman for his willingness to serve on this
committee without previous contact with me in the classroom and for
the valuable advice that he has provided at every stage of the research
effort. Finally, the greatest debt of appreciation is owed to Dr. Blair
for providing both a counsel and an example for the last three years of
graduate study.
And second, a considerable amount of help and encouragement has
been provided by various colleagues at the Department of Housing and
Urban Development where the research for this dissertation took place.
John Morrall was influential in providing the initial opportunity to
carry out this research effort and made several helpful suggestions
during the formative stages of the analysis. Fred Eggers has provided
iii

useful comments and has been extremely patient in allowing a more ex¬
tensive effort than that which was originally envisioned. Edgar Olsen
provided careful and extremely valuable advice on earlier drafts of
this study. And finally, John Ermisch contributed to an unmeasurable
degree through both extensive discussions and written comments at every
stage.
iv

TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS iii
LIST OF TABLES viii
LIST OF FIGURES ix
ABSTRACT x
CHAPTERS
I INTRODUCTION 1
IIHISTORY AND ENVIRONMENT OF THE FHA SECTION 203
PROGRAM 5
Depression Conditions and Federal Response 5
Section 203's Major Objectives 10
Later Entrants into the Default Insurance Market 18
The Volume of Insurance under Section 203 25
III LITERATURE REVIEW 34
The Scarcity of Relevant Literature 34
Studies of Default Behavior by von Furstenberg 36
Aaron's Analysis of the Contracting Process on
Mortgage Loans 44
IVA THEORETICAL MODEL OF DEFAULT RISK AND DEFAULT
INSURANCE 52
Introduction and Overview of the Theoretical Model .... 52
Default Probability and Expected Default Loss on
Individual Mortgage Loans 55
The Demand for Default Insurance Coverage 66
The Supply of Default Insurance Coverage 77
Summary: Basic Theory of Decline 87
V THE EMPIRICAL MODEL: SPECIFICATION 92
Introduction and Overview of the Empirical Model 92
Equation 1: Total Market Volume 93
Equation 2: VA Insurance Volume 97
v

TABLE OF CONTENTS (Continued)
Page
Equation 3: Private Mortgage Insurance Volume 98
Equation 4: Section 203 Insurance Volume on New
Units 101
Supply Constraints on Alternative Sources of
Default Coverage 102
Relative Terms Available on Section 203 Insured
Loans 110
Other Factors that Serve to Differentiate the
Section 203 Insurance Service 113
FHA mortgage limit 113
FHA processing time 114
HUD reorganization 116
Secondary market activity in FHA insured
loans 117
FHA processing requirements 118
Housing starts as a proxy for overall housing
and mortgage market activity 120
Equation 5: Section 203 Insurance Volume on Existing
Units 122
Equation 6: Processing Time of FHA Applications 124
Equation 7: FHA Subsidy Programs Identity 126
Summary 127
VI THE EMPIRICAL MODEL: ESTIMATION AND INTERPRETATION .... 129
Data Employed, Estimation Techniques, and
Qualifications 129
Estimation Results and Interpretation 134
Equation 1: Total Insurance Volume 137
Equation 2: VA Insurance Volume 139
Equation 3: Private Insurance Volume 139
Equation 4: Section 203 Insurance Volume on New
Units 140
Equation 5: Section 203 Insurance Volume on
Existing Units 146
Equation 6: FHA Processing Time 149
An Empirical Test of the Joint Cream-Skimming
Hypothesis 150
VII SUMMARY AND CONCLUSIONS 154
Summary of the Study's Findings 154
Limitations of the Study 160
vi

TABLE OF CONTENTS (Continued)
Page
Contributions of this Study to the Existing
Economic Literature 164
Areas for Future Research 166
The Need for a Basic Change in the Federal
Government's Role in the Home Mortgage Default
Insurance Market 170
APENDICES
APPENDIX 1: Hypothesis Tests for Regression
Coefficients 173
APPENDIX 2: Variable Definitions and Data Sources 178
BIBLIOGRAPHY
Books 182
Journal Articles 184
Working Papers, Government Publications, and Unpublished
Memoranda 191
BIOGRAPHICAL SKETCH 196
vii

LIST OF TABLES
Table Page
2.1 Privately Owned Housing Units Started under the FHA
Section 203(b) Mortgage Insurance Program Compared
with Total Housing Starts in the U.S.; 1935-69 26
3.1 Regressions of Default Rates on the Age (t) and Loan-
Value (L/V) of Mortgages Grouped by Terms 43
Al.l Regression Results for Total Insurance Volume
Equation, Dependent Variable: TOT/ORIG 174
A1.2 Regression Results for VA Insurance Volume Equation,
Dependent Variable: VA 174
A1.3 Regression Results for Private Insurance Volume
Equation, Dependent Variable: PMI 175
A1.4 Regression Results for Section 203 New Units Insurance
Volume Equation, Dependent Variable: FHAN 176
A1.5 Regression Results for Section 203 Existing Units
Insurance Volume Equation, Dependent Variable: FHAE .... 177
A1.6 Regression Results for FHA Single-Family Processing
Time Equation, Dependent Variable: PROC 177
viii

LIST OF FIGURES
Figure Page
2.1 Relationship Between the Provision of Insurance, the
Supply of Mortgage Funds, and the Demand for Housing .... 16
2.2 Number of New Single-Family Dwelling Units Insured
under the Section 203 Mortgage Insurance Program;
1960:1-1974:2 29
2.3 Number of Existing Single-Family Dwelling Units
Insured under the FHA Section 203 Mortgage Insurance
Program; 1960:1-1974:2 30
2.4 Share of the Default Insurance Market Accounted for
by the FHA Section 203 Mortgage Insurance Program;
1960:1-1974:2 32
3.1 Time Path of Defaults on Home Mortgages 40
3.2 Lender and Borrower Tradeoffs Between Interest Rates
.and Downpayments 46
4.1 Utility of Profits Function for a Risk Averse Lender .... 73
4.2 Supply Curves of Individual Default Insurance Market
Participants 81
4.3 The Relationship Between Private Market Supply
Constraints and Section 203 Demand in the Default
Insurance Market 85

Abstract of Dissertation Presented to the Graduate Council
of the University of Florida in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
AN ECONOMIC ANALYSIS OF THE HOME MORTGAGE
DEFAULT INSURANCE MARKET WITH EMPHASIS
ON THE DECLINE OF FHA
By
David L. Kaserman
March, 1976
Chairman: Roger D. Blair
Major Department: Economics
The home mortgage default insurance programs of the Federal Hous¬
ing Administration (FHA) have experienced a precipitous decline in the
volume of contracts written in recent years. This decline in insurance
activity has been accompanied by increasing claims that have placed a
considerable burden on the insurance funds that support these programs.
The major program providing unsubsidized (actuarially sound) coverage
for mortgages written on single-family housing units has been the
Section 203 program which has been severely affected by the declining
volume of insurance activity.
The fundamental question addressed in this study is whether this
decline in FHA insurance activity has been the result of internal pro¬
gram inefficiencies or increasing competitive pressures from the pri¬
vate firms in the market. This is the crucial issue that should
determine the primary thrust of the federal government's future poli¬
cies in this area.
In attempting to address this basic issue, this study develops a
theoretical model of the home mortgage default insurance market. This
market is determined by the actions of three sets of participants:
x

the mortgagor, the mortgagee, and the supplier of default insurance
coverage. The first two sets of these participants interact in what is
viewed as a competitive mortgage market under conditions of default
loss uncertainty to determine the market demand for mortgage default
insurance. Thus, this demand is seen as being derived in nature, with
its primary source found in the demand for and supply of mortgage funds.
The last set of market participants (the suppliers of default coverage)
is composed of four major actors: the FHA Section 203 program, the FHA
subsidized housing and mortgage insurance programs, the Veterans
Administration home loan guarantee program, and the private mortgage
insurance industry. Of these four actors, the last three are viewed as
being subject to supply constraints of an institutional nature which
result in their services being rationed. The notion that these con¬
straints remain effective is a fundamental maintained hypothesis
throughout the analysis. Finally, the coverage supplied by the various
actors in the market is considered to be non-homogeneous but
substitutable. This result in the overall mortgage default insurance
market being determined from the operations occurring in four inter¬
related sub-markets (one for each supplier of coverage).
This theoretical model is then used to specify a system of
partially simultaneous equations that depicts the important relation¬
ships that determine total insurance market activity and the individual
insurance activities in each of the four sub-markets. Estimation of
this model using quarterly time series data that cover the postwar
period yields results that, in general, support that theoretically
derived hypotheses concerning the causal forces at work. Such estima¬
tion also yields quantitative approximations to the marginal influences

of the various factors that have led to the decline in insurance
activity under Section 203.
There are a number of conclusions that are drawn from this model
concerning the overall functioning of the home mortgage default insur¬
ance market. The most significant result for policy purposes, however,
is the finding that insurance volume losses experienced by FHA have
been primarily determined by market-oriented (as opposed to program-
oriented) influences. The important implication of this finding is
that policy actions that are intended to rejuvenate FHA's activity in
this market should be avoided.
x i i

CHAPTER I
INTRODUCTION
The home mortgage default insurance programs of the Federal Hous¬
ing Administration have helped to serve the nation's housing needs for
the last forty-one years. During this period, the basic service that
has been rendered by these programs has been the provision of insurance
coverage against default loss on individual mortgages originated by
private lenders. It is generally felt that such insurance has encour¬
aged a larger supply of mortgage funds on more liberal financing terms
than would have been forthcoming in the absence of these programs. It
is also felt that these funds have, in turn, increased the effective
demand for housing services as the feasibility of home ownership has
been expanded to a larger segment of the overall population.
The public purpose served by the FHA insurance programs is now
being called into question, and a fundamental reexamination of the
federal government's role in the market appears to be imminent. The
need for some basic revisions seems to have been created by an evolu¬
tionary process that has brought forth fundamental structural and
institutional changes in the mortgage lending and default insurance
markets over the last decade. Partly as a result of these long run
changes and partly as a result of specific operational inadequacies,
the FHA single family programs have experienced increasing difficulties
in recent years both in maintaining an adequate volume of insurance
1

2
activity and in achieving the Congressional objective of actuarial
soundness.
These difficulties are now providing the catalyst for major policy
decisions that will determine the future role of FHA in the insurance
of home mortgage default risk. Such decisions should be based upon the
most complete information that can reasonably be made available in
order to ensure that short run reactions to the existing situation do
not result in the design of policies or programs that will have unde¬
sirable long run effects. The likelihood that such effects will be
generated may be reduced with each additional piece of relevant informa¬
tion provided to decision makers. It is the purpose of this study to
provide such information in the form of an economic model of the home
mortgage default insurance market.
The model that has been derived for this purpose determines both
the volume of insurance written by the total market and the individual
volumes of insurance written by the various supply-side participants in
that market over time. In so doing, the model contributes to the exist¬
ing economic literature relating to the theory of mortgagor default
behavior, the mortgage origination process, and the overall operation
of the default insurance market. At the same time, the model can be
used to provide a detailed explanation of the causal events that have
led to the current problems of FHA and, thereby, serve as an important
input to the decision-making process. Thus, the study has two broad
objectives: to contribute to the literature providing an economic
analysis of home mortgage default risk and the default insurance market;
^Actuarial soundness is used here to mean a non-negative reserve
accumulation net of operating expenses, i.e., a self-financing program.

3
and to provide an explanation of the process that has led FHA to its
current situation.
With regard to FHA, the study will be seen to give particular at-
tension to the insurance volume and claims experience of the Section
203 program. This program is the oldest and by far the largest of the
single-family programs, accounting for almost 80 percent of the cumula¬
tive insurance written by units and nearly 77 percent of the estimated
insurance in force in dollars at the end of June, 1973 (SummCLUy 0& Mo fit-
gage. IniuAanee OpeAattoni and Contract Authority, 1973, p. 1). The
Section 203 program has been the mainstay of the general insurance op¬
erations of FHA since its origination in 1934, and it has been the con¬
tinuing loss of business being carried out under this program in recent
years that has created the great concern of both the administrators in
charge of these insurance operations and the decision makers involved
in federal housing policy.
A clear understanding of the causes of this decline is essential
in the design of future policies relating to the operation of the
program. Completely different approaches are warranted by different
causes of decline. For example, if the Section 203 insurance program
has declined because of identifiable changes in the program's opera¬
tions that have generated internal inefficiencies which have, in turn,
led to the neglect of basic default insurance market needs, then a
corrective approach would appear to be appropriate. But, on the other
hand, if the declining insurance volume has been primarily generated
through a growth in competition in the default insurance market that
has enabled mortgagors to obtain preferred coverage from other sources,
then it would seem appropriate for federal decision makers to examine

whether there exists a public need for continuation of the program.
Hopefully, the findings of this study will provide information for the
4
design of future policies relating to the provision of home mortgage
default insurance on the part of the federal government.
The study itself is divided into seven chapters. Following this
brief introductory chapter, the history and institutions relevant to
the default insurance market are presented in Chapter II along with a
detailed documentation of the decline in insurance activity under the
Section 203 program. Then, a brief review of some economic literature
that is relevant to the default insurance market is given in Chapter III.
Chapter IV is devoted to the development of a theoretical model of de¬
fault risk and the default insurance market that explains the mechanisms
involved in the determination of total market insurance activity and
the individual insurance activities of the various suppliers of default
coverage in that market. This model is then employed in Chapter V to
specify an empirical model of the default insurance market that can be
used to estimate the marginal influence of each of the causal factors
that are implied by the theoretical considerations of the preceding
chapter. The estimation results obtained from this empirical model and
their interpretations are given in Chapter VI. And finally, the basic
conclusions relating to both overall default insurance market operations
and the decline of Section 203 are drawn in Chapter VII. Additionally,
this final chapter contains a summary of the study and a discussion of
some promising areas for future research.

CHAPTER II
HISTORY AND ENVIRONMENT OF THE
FHA SECTION 203 PROGRAM
Depression Conditions and Federal Response
The Federal Housing Administration's basic programs providing de¬
fault insurance on privately financed mortgage contracts were originally
conceived during the Great Depression as a direct response by the fed¬
eral government to the depressed conditions of the economy in general
and the building and construction trades sector in particular. The
state of the economy at that time was such that the flow of funds
through the nation's mortgage markets had been reduced to a trickle,
and residential construction activity had virtually ceased. The produc¬
tion of new homes had dropped to 93,000 units in 1933 (less than 10
percent of the number built in 1925), and on-site construction employed
only 150,000 people throughout the entire economy (H. R. Report No. 897,
81st Congress, pp. 56-67). Harry L. Hopkins, the Federal Emergency
Relief Administrator, in testimony before the Housing Banking and Cur¬
rency Committee on May 18, 1934, stated
The building trades in America represent by all odds the
largest single unit of our unemployment. Probably more than
one-third of all the unemployed are identified, directly or
indirectly, with the building trades...(Foard and Frantz,
1973, p. Ill, 3).
In addition, approximately one half of all home mortgages were in de¬
fault, and foreclosures were occurring at the phenomenal rate of over
one thousand per day (Foard and Frantz, 1973, p. II, 9).
5

6
The response by the federal government to these serious conditions
consisted of an array of housing and mortgage related programs that
were created over the six year period from 1932 to 1938. Among these
were the basic FHA mortgage insurance programs, including the single¬
family unsubsidized Section 203 program with which this study is
concerned. Prior to describing this program in some detail, however,
it will be useful to list and briefly describe some of the other impor¬
tant institutions created in this period that relate to the housing and
mortgage markets.^ This will give the reader an indication of the
degree of attention that was devoted to this sector of the economy at
this time and provide a rough description of the institutional environ¬
ment surrounding the Section 203 program.
1. The Federal Home Loan Bank Board was created under authority
of the Federal Home Loan Bank Board Act of 1932 in order to organize,
incorporate, examine, and regulate a system of federal savings and loan
associations. The primary objective of this institution was to encour¬
age the development of local mutual thrift institutions in which in¬
dividuals could safely invest funds in order to provide for the
financing of home purchases (Foard and Frantz, 1973, p. II, 11).
2. The Home Owners' Loan Corporation was created under authority
of the Home Owners' Loan Act of 1933 with the objective of refinancing
home mortgages that were in default or process of foreclosure. In
addition, this institution was given the authority to originate direct
loans to permit former homeowners to recover properties that had been
^The descriptions provided of these institutions are necessarily
brief and indicate only the most important actions taken and objectives
expressed. Those seeking a more detailed treatment of these and other
federal housing programs should see Foard and Frantz (1973).

7
lost through foreclosure or forced sale (Foard and Frantz, 1973, p. II,
10).
3. The Federal Savings and Loan Insurance Corporation was created
under authority of the National Housing Act of 1934 with the basic in¬
tention of encouraging additional deposit inflows at savings and loan
associations by removing the risk of loss through association
insolvency. The service provided to the savings and loan association
by this institution is analogous to that provided to the commercial
banking system by the Federal Deposit Insurance Corporation (Foard and
Frantz, 1973, pp. II, 13-14).
4. The Reconstruction Finance Corporation Mortgage Company was
created under authority of a 1935 amendment of Title III of the National
Housing Act of 1934 (Public Law 1, 74th Congress). The purpose of this
institution was to assist in the re-establishment of a nationwide mort¬
gage market by investing in many types of mortgage instruments, both
residential and commercial, where such funds were not obtainable at
reasonable rates from private sources. Purchases by this institution,
however, primarily consisted of FHA-insured (and, later, VA-guaranteed)
mortgages that had been originated by private lenders. The Corporation
was disolved by act of Congress in 1948 (Public Law 132, 80th Congress)
(Foard and Frantz, 1973, pp. IV, 8-9).
5. The Federal National Mortgage Association (FNMA) was created
under authority of a 1938 amendment of Title III of the National Housing
Act of 1934 (Public Law 424, 75th Congress). The objective behind the
creation of this institution was that FNMA would function alongside the
Reconstruction Finance Corporation Mortgage Company in establishing a
national secondary mortgage market in which mortgage obligations could

8
be traded as financial investment assets. Such a market, it was felt,
would encourage inter-regional arbitrage operations that would reduce
the wide variations that existed in mortgage financing availability and
interest rates across the country. Also, it was felt that the added
liquidity given to the mortgage instrument by the functioning of an
active secondary market would increase the willingness of institutional
investors to commit funds to this kind of long-term instrument (Foard
and Frantz, 1973, pp. IV, 9-10).
While various other programs and policies that were designed to
stimulate the depressed mortgage and housing sectors were adopted at
all levels of government during this period, the above list, with the
obvious exclusion of the FHA mortgage insurance programs, provides
adequate documentation of the degree of effort that was expended at the
2
federal level. We turn, now, to a somewhat detailed description of
the major single-family program excluded from the above list—the FHA
Section 203 mortgage insurance program.
The enabling legislation for this insurance program was the
National Housing Act of 1934. This act laid out the administrative
framework within which FHA was to operate and indicated what the vari¬
ous constraints that were to be placed on the program were to be.
Section 203 of Title II of this act provided for the insurance of ap¬
proved private lenders against losses arising from mortgagor defaults
on first mortgage loans originated on single-family properties.
2
It is of interest to note that all of the above programs (and the
vast majority of federal housing programs created since that time)
operate primarily through the financial (mortgage) sector rather than
directly through the real (housing) sector. This tendency has resulted
in most of the federal effort in this area having its primary impact on
the demand side of the housing market.

9
This legislation placed ceilings of twenty years on the term to maturity
and 80 percent on the loan-to-value ratio on insured loans and limited
the size of the eligible mortgage to $16,000 or less. The interest
rate allowed on insured loans was limited to 5 percent per annum on the
outstanding balance and the property securing the loan was required to
be "economically sound." The settlement of insurance claims in the
event that the loan was foreclosed required that the lender convey the
property and all relevant claims against it to FHA for which we would
receive in return: (1) debentures guaranteed by the U.S. government
equal to the outstanding balance on the loan plus certain other allow¬
ances, with these debentures maturing three years after the contract
maturity on the mortgage obligation and carrying an interest rate fixed
by FHA with the consent of the U.S. Treasury based upon current yields
of U.S. bonds (later, FHA was given the option of paying this insurance
claim in cash); and (2) a certificate of claim redeemable in cash equal
to the earned but unpaid interest of the loan plus partial reimbursal
of foreclosure costs, with these items payable only to the extent that
FHA realized net proceeds from handling the property (Foard and Frantz,
1973, pp. Ill, 4-5; Bartke, 1967, p. 654).
With regard to the financing of FHA's Section 203 program, the in¬
tent of Congress was that, after an initial period of negative returns
during which start-up costs would be absorbed and insurance reserves
accumulated, the program would become self-financing (i.e., actuarially
sound). The legislation, therefore, required that an insurance premium
be levied on the mortgagor and be collected monthly with the mortgage
installments. The exact premium rate was not stipulated by the act,
but rather, a range of allowable premium rates was set within which FHA

10
was authorized to peg the actual premium--this range being one-half to
one percent per annum of the outstanding mortgage balance. While all
of the other contract term limits placed on FHA-insured loans (the al¬
lowable term to maturity, loan-to-value ratio, mortgage amount, and
interest rate) have been altered from time to time in order to, at
least partially, reflect market developments, the insurance premium
charged for FHA coverage has remained fixed at one-half percent for all
loans insured under Section 203 since 1934. This has been an important
feature of the Section 203 program to which we will return several
times in this study.
Section 203's Major Objectives
As with the majority of federal programs created at that time, the
immediate objective of the FHA Section 203 insurance program was to in¬
crease employment, with its initial impact, obviously, directed toward
the building and construction trades sector. Also, the long term objec¬
tive of increasing the nation's overall consumption of housing services
in terms of both the quantity and quality of the units consumed through
a general improvement in the financing terms available in the mortgage
market was made clear in the hearings leading up to the actual
legislation. The House Committee Report stated the intent as
...to improve Nation-wide housing standards, provide employ¬
ment, and stimulate industry; to improve conditions with
respect to home-mortgage financing, to prevent speculative
excess in new-mortgage investment, and to eliminate the
necessity for costly second-mortgage financing (House of
Representatives Report No. 1922, 73rd Congress, 2nd Session,
1934, p. 1).
These basic objectives have remained in effect for the Section 203 pro¬
gram over the years. Additional objectives, such as the encouragement

11
of homeovnership among lower income families, have generally been at¬
tacked by the creation of additional programs within the FHA insurance
3
system.
The basic concept of providing mortgage lenders with default insur¬
ance protection was not without precedent. A private mortgage insurance
industry has existed prior to the creation of FHA, having grown out of
the title insurance business in the late 1800's and early 1900's. There
were, however, almost no regulatory constraints placed on the firms in
this industry either by the federal government or by the various states
in which they operated (primarily New York). As a result, there de¬
veloped a great deal of fraud and misrepresentation in the industry,
and the contingency reserves held by these firms were dangerously low
in the late 1920's and early 1930's. In a report to the governor of
the State of New York in 1934, George Alger, a special commissioner
appointed to investigate the operations of the private mortgage insur¬
ance industry, stated
The value of a guaranty depends, of course, on what is back
of it. These companies were growing by leaps and bounds and
issuing these guarantees in continually increasing volume.
The need of some safeguard in the law requiring a fixed rela¬
tionship between capital and guarantees seems obvious. New
York, where the bulk of this business was done, placed no
limit upon the amount of contingent obligations which such
a company might assume. Without a limit on the amount of
guarantees assumed, the only protection for investors would
be in the amount of required capital and in the safeguards
placed upon their investments. In these respects investors
were similarly unprotected (Alger, 1934, p. 15).
In addition to this basic weakness, the industry exhibited a funda¬
mental contradiction of sound insurance practice in that the majority
A discussion of the growth and evolution of FHA's housing objec¬
tives may be found in Bartke (1967).

12
of its contingency reserves were held in mortgage obligations, which
were subject to the same risks that they were being held to offset.
With the crash of 1929 and the ensuing flood of foreclosure activity
and, hence, insurance claims, the private mortgage insurance industry
failed. The actual collapse was postponed for a brief period by am¬
biguous accounting practices and actual falsification of insurance
losses as the firms in the industry attempted to delay the inevitable
result in the hope that an early economic recovery would bolster the
value of their declining reserves and reverse the downward trend in
premium and investment income. But, by the end of March, 1933, all
firms in the industry were bankrupt. In response to this event, most
states enacted legislation forbidding private firms from selling mort¬
gage insurance within their boundaries, and many of these states pro-
4
hibitions have remained in effect until very recently. Consequently,
a major impetus for the federal government adopting the role of a
mortgage insurance supplier was that a private market for this type of
coverage simply did not exist at that time.
The theoretical mechanisms through which the provision of default
insurance protection was to stimulate employment in the residential
construction sector were hinted at in various places throughout the
enabling legislation and the hearings preceeding that legislation.
Many general references were made which indicated that insurance cover¬
age would increase investment in home mortgages and, thereby, increase
housing and construction activity. But, the theoretical links through
4
Those seeking further information on the early history of the
private mortgage insurance industry should read Alger (1934), Graaskamp
(1970), Kohlhoss (1972), Rapkin (1973, 1974), and Little (1975).

13
which this effect would take place were not laid out. One can, however,
trace through the likely effects of default insurance protection and
deduce the probable impact on the mortgage market and housing industry
by employing a highly simplified model of the housing and mortgage
markets. From the standard microeconomic assumptions, one should be
able to derive the individual's demand function for housing services,
with the typical result that the quantity of housing demanded will bear
a functional relation to the price of housing services, the individual's
income, and the prices of related goods. Then, the individual's demand
function could be written as
(1)
Dh - F(Ph. y, Pr .... Pn)
where D, is the quantity of housing services demanded by the individual
h
(where this quantity measure incorporates all structural, locational,
and neighborhood characteristics of the unit—see Olsen, 1969), P is
the real price of housing services, y is the individual's real income,
3°h
and P , ..., P are real prices of related goods. We know that . < 0
1 n 3Dh 9PH
and, if housing is a normal good, -- â–  > 0.
dy
Since most individuals are not financially able to pay cash for
6
a house, a mortgage is generally required for homeownership.
The skeletal model outlined here is not taken directly from any
existing housing or mortgage market models but, instead, represents a
synthesis of many treatments of the subject and my own views concerning
the operation of these markets. In my view, the theoretical underpin¬
nings of a great deal of the work in this area are extremely weak and
of an ad hoc nature. At this time, a truly rigorous theoretical model
of the interactions that take place between the housing market, the
mortgage market, and the default insurance market does not exist.
^One can, of course, consume housing without purchasing the asset
providing the service by renting. Other factors, such as differences
in tax treatment, preferences for mobility, etc., should influence the
individual's choice concerning the ownership of the asset providing the

14
Consequently, the demand for mortgage funds is a derived demand, having
as its direct source the demand for housing services. Because of this,
the mortgage loan may be conveniently viewed as a good that is comple¬
mentary to the consumption of housing services. Being complementary,
we know that the cross price elasticity of demand between housing
services and mortgages will be negative. Letting the mortgage be de-
Dh
noted as good j, we know that p < 0, where P. is the effective rate
7 j J
of interest on mortgage loans.
In graphical terms, we could translate the above demand function
into an individual demand schedule for housing services with the price
of housing services on the ordinate and the quantity demanded on the
abscissa. Then, a change in the price of mortgage funds would result
in a shift in the demand schedule for housing services—with, of course,
a reduction in the price of these funds resulting in an increase in the
quantity of housing services demanded at any given price. Thus, a re¬
duction in the price of mortgage credit (the effective interest rate)
results in an increase in the individual's demand schedule for housing
services. Summing these individual demand schedules horizontally, we
obtain the market demand schedule for housing services, given by D ,
which will exhibit similar qualitative relationships to the price of
housing services and the price of mortgage funds.
The introduction of mortgage insurance would have the effect of
reducing the effective price of mortgage funds, P , and thereby, shift
housing service. For those individual's opting for homeownership,
however, a mortgage is generally (though not always) required.
^Present estimates of the interest rate elasticity of the demand
for single-family homes range from -0.6 to -2.8 (von Furstenberg, 1975,
p. 18).

15
the market demand schedule for housing services to the right. This re¬
duction in P_. is brought about by an increase in the supply of mortgage
funds stimulated by the reduction in the relative risk of the mortgage
g
instrument as an investment alternative. Mortgage investors (suppliers
of mortgage funds) will, if they are risk averse, adjust their portfo¬
lios as the risk on the asset is reduced by increasing the amount of
funds held in mortgage obligations. As this occurs, the quantity of
mortgage funds supplied at any rate of effective interest will be in¬
creased and, with a downward sloping demand schedule for mortgage funds,
the effective interest rate on mortgage obligations will be bid down
until the decrease risk is compensated for by a decreased rate of re¬
turn and the adjustment process is complete.
The resulting model is depicted in Figure 2.1. Here, is the
demand schedule for mortgage funds; (I) is the supply of mortgage
funds expressed as being dependent upon the provision of default insur¬
ance, I; D (P.) is the demand schedule for housing services expressed
H 3
as a decreasing function of the price of housing, P , and the price of
mortgage funds, P.; and S is the supply schedule for housing services.
1 H
The provision of default insurance, a change from I to I , results in
an increased supply of mortgage funds, a reduction in the effective
rate of interest from P^ to P^, an increase in the demand for housing
services from D (P^) to D (P^), and a consequent increase in the
H 3 H 3
quantity of housing services produced and consumed.
In addition to the effect generated by the direct reduction in de¬
fault risk on mortgage loans brought about by the insurance coverage
8
study.
This effect will be treated more rigorously in Chapter IV of this

Mortgage Market
Housing Market
Figure 2.1.
Relationship Between the Provision of Insurance, the Supply of Mortgage Funds
the Demand for Housing

17
provided by FHA, several related occurances were taking place simulta¬
neously that exerted an upward pressure on the demand for housing
services at that time. First, the development of a national secondary
mortgage market operated to increase the liquidity of the mortgage in¬
strument as a financial asset and attract new sources of investment
funds into the mortgage market. This development was facilitated by:
(1) the trading activities of the Federal National Mortgage Association
(2) the application of FHA's Minimum Property Standards to insured
loans (Foard and Frantz, 1973, p. Ill, 16); (3) competent, objective
appraisals of the properties securing insured loans; and (4) the trend
toward standardization of the mortgage instrument. Also, the liberal¬
ization of mortgage financing terms made possible by the provision of
default insurance coverage served to reduce the downpayment require¬
ments (through increased loan-to-value ratios) and/or monthly payments
(through increased terms to maturity) necessary to obtain and success¬
fully retire a mortgage contract. In the highly simplified model
sketched above, this effect would have to be translated into a reduc¬
tion in the effective interest rate required on mortgage loans where
the effective rate would be defined to incorporate the financing terms
of the loan (Cassidy, 1972). Both of these developments operated to
increase further the demand for housing services, thereby supporting
the pure insurance effect of FHA.
Given this increase in the demand for housing services, some in¬
crease in the quantity of housing produced and consumed should be ex¬
pected to have been forthcoming (unless, of course, the housing supply

18
schedule exibited a price elasticity equal to zero). Such an in¬
crease could only be accomplished through an increase in employment in
the residential construction sector. Therefore, we conclude that the
Section 203 insurance program should, on theoretical grounds, have been
successful in generating increased employment in this sector of the
economy and in increasing the nation's overall consumption of housing
services.
Later Entrants into the Default Insurance Market
For the first decade following its origination, the FHA Section
203 program remained the sole supplier of default insurance coverage
for home mortgages. During that period, any potential mortgagor re¬
quiring (or preferring) a high ratio, long maturity loan turned to FHA
for the insurance protection that the mortgagee was likely to require
on such a loan. Since that time, however, several alternative sup¬
pliers of mortgage default insurance have entered the market exerting
varying degrees of competitive pressure on the Section 203 programs.
Such pressure has been provided by: (1) the creation of the Veterans
Administration program providing home loan guarantees to eligible
veterans; (2) the re-emergence and growth of the private mortgage in¬
surance industry; and (3) the introduction of subsidized single-family
housing and mortgage insurance programs within the FHA system. The
creation and growth of these three basic alternative sources of default
For a review and evaluation of the current state of knowledge
concerning the price elasticity of housing supply see Sneed (1974).
As might be expected, no estimates of this elasticity are equal to
zero. At the same time, however, none of the models utilized in ob¬
taining these estimates is completely satisfactory (Sneed, 1974).

19
insurance coverage have greatly affected the post-war evolution of the
mortgage insurance market. Consequently, they have influenced the ex¬
perience of the Section 203 program over this period. We now discuss
each of these later entrants.
With the intention of aiding the post-war adjustment of returning
veterans to civilian life through the provision of housing credit as¬
sistance, the Congress, in 1944, enacted the Servicemen's Readjustment
Act. This act authorized the Veterans Administration to guarantee
lenders against default loss on home mortgages made to eligible
veterans. These guarantees serve essentially the same purpose as the
FHA insurance coverage—they reduce the default risk on the mortgage
and, thereby, encourage lenders to increase the supply of mortgage
funds. There are, however, several features that distinguish the VA
home loan guarantee from FHA mortgage insurance. First, the VA guar¬
antee is only available to eligible veterans, where eligibility is
defined by legislative decree. The requirements imposed for such eli¬
gibility have been altered several times over the years in order to
admit veterans of later conflicts and to prolong the period during
which the individual veteran remains eligible to exercise his option to
purchase a home under the program. The number of individuals having
the option to insure thier loans under the VA guarantee program has,
therefore, fluctuated over time with variations in the number of per¬
sons leaving the armed services and with variations in the eligibility
requirements of the program. Second, the coverage provided to the
mortgagee under the VA guarantee program is less than 100 percent. It,
therefore, provides default loss protection on a coinsurance basis,
with the lender remaining exposed to some degree of risk. The coverage

20
provided for in the act, however, stipulates that the Veterans Adminis¬
tration absorb the lesser of 50 percent (later raised to 60 percent) of
the outstanding balance on the loan or $2,000 (raised to $4,000 the
following year and increased several times hence) before the lender
begins to experience a loss. Thus, by providing coverage on the top
portion of the loan (as opposed to a deductible or a percentage loss
sharing), the VA guarantee does provide complete insurance coverage
unless the property securing the loan experiences a very severe depre¬
ciation in value. Consequently, the coverage provided exposes the
lender to very little actual risk.^ Third, the Veterans Administra¬
tion collects no insurance premium for the guarantee service (although
for a three year period in the late 1960's a single origination fee of
one-half of one percent of the loan was levied). Therefore, the VA
form of default insurance is subsidized, being provided at zero cost to
the eligible mortgagor. Fourth, the financing terms available on the
VA-guaranteed loan are generally more liberal than those on FHA-insured
mortgages. Loan-to-value ratios are quite high, often approaching 100
percent (indeed, in some instances they have exceeded 100 percent of
the actual value of the property and have allowed the mortgagor to
borrow most of the real estate closing costs, sometimes placing as
little as $200 equity in the loan). Also, there is no ceiling placed
on the size of the mortgage eligible for the guarantee (although the
limitation placed on the size of the potential insurance claim
Coverage of the top X percent of the mortgage loan may be vir¬
tually equivalent to complete (100 percent) coverage if the lender's
subjective probability distribution over percentage default losses on
the loan places a near-zero probability on the event that default loss
will exceed X percent. In such a situation, the additional coverage
provided on FHA-insured loans may be of little value.

21
discourages lenders from originating extremely large mortgages under
this program). Like FHA, the VA guarantee program stipulates the maxi¬
mum rate of interest that may be charged on the mortgages that they
insure, and these rates are altered from time to time to reflect market
conditions (although, at times, these rates have departed considerably
from those charged on uninsured mortgages).^
The second source of competitive pressure exerted on the FHA
í
Section 203 program has been the re-emergence of the private mortgage
insurance industry. The first firm to enter this industry since the
collapse in the early 1930's was the Mortgage Guaranty Insurance
Corporation which began operations in 1957 in the state of Wisconsin.
Since that time, the volume of insurance written by the private mort¬
gage insurance industry has increased dramatically as new firms have
entered, insurance reserves have accumulated, and as state laws forbid¬
ding the operation of private mortgage insurance companies have been
relaxed to allow these firms to expand their market (the final state
relaxing prohibitions against the activities of these firms was New
York in 1973). The number of single-family units insured by the mem¬
bers of this industry moved from 12,484 in 1960 to 64,850 in 1965,
157,760 in 1971, and 505,180 in 1973. ^ A few declines have occurred
in the volume of insurance written by these firms over this period, but
such declines have generally coincided with declines in overall housing
and mortgage lending activity. Presently, the number of companies in
^Further information concerning the VA system of home loan guar¬
antees may be found in Foard and Frantz (1973, pp. V, 47-74).
12
Data provided to the author by Mortgage Insurance Companies of
America, Washington, D. C., the trade association for the firms in this
industry.

22
this industry is approximately 10, having declined somewhat in the last
two years through merger activity that occurred in the early 1970 's
(Little, 1975, p. 121). The percent of the private market accounted
for by the Mortgage Guaranty Insurance Corporation (the largest firm in
the industry) has been steadily eroded over the years. It stood at 100
percent from 1957 until 1961; then, in the latter year, it declined to
93.76 percent. By 1965 it had fallen to 75.97 percent, and by 1970 it
was down to 65.18 percent (Little, 1975, p. 122). This trend has con¬
tinued into the 1970's with the 1972 market share falling to 60.00 per¬
cent and declining further in 1973 and 1974.
Although there have been no comprehensive studies carried out to
determine the existing entry conditions in the private mortgage insur¬
ance industry, a recent examination that was designed to determine the
adequacy of the contingency reserves of the major firms in this indus¬
try concluded that entry barriers were low (Little, 1975). This infer¬
ence was made primarily from an examination of state regulations
regarding paid in capital and contingency reserve requirements; and,
therefore, the conclusion relates only to absolute barriers to entry
(Bain, 1956). Given the recent growth experience in the number of
firms in this industry, however, one must suspect that this conclusion
is accurate of overall barriers to entry also (such as economies of
scale, etc.). The industry may thus be described as a relatively young
one that has been characterized by rather steady growth in both the
size of the market and the competitive structure exhibited.
The typical default insurance contract marketed in this industry
provides coverage of the top 20 percent of the outstanding balance on
the loan and stipulates a premium rate of one-fourth of one percent of

23
this outstanding balance. Thus, both the coverage provided and the
price charged on these contracts are lower than those under the Section
203 program; and, like the FHA program, neither the coverage nor the
13
price has varied measurably over time. Again, it is not clear how
much risk the lender is exposed to under such a plan. For some loans,
coverage of the top 20 percent may be considered as virtually equiva¬
lent to complete coverage (see footnote 10 above). Finally, the insur¬
ance contracts written by the firms in this industry place no ceilings
on the size of the mortgage nor on the interest rate that may be applied
to the loan.
The third and final major entrant into the default insurance market
was the single-family subsidized housing and mortgage insurance pro¬
grams that were incorporated in the FHA system by the National Housing
Act of 1968. The largest of these has been the Section 235 program
which combined direct housing subsidies with default insurance in order
to increase homeownership among lower income households. Although this
program was suspended in January, 1973, the volume of activity carried
out under the subsidy programs during the brief period in which Section
235 was active is far from insignificant—the largest insurance volume
occurred in the first quarter of 1972 when 33,240 new and 5,354 exist¬
ing single-family units were insured. Eligibility for participation in
these subsidy programs has been limited by household income with the
ceilings varying by family size. Like the insurance written under Sec¬
tion 203, the coverage provided under this program has been 100 percent,
13
Several different payment schemes have been offered by these
firms (without varying the basic rate) and, recently, a policy covering
the top 25 percent of the mortgage balance has been introduced. For a
detailed description of these aspects of the private mortgage insurance
industry see Kohlhoss (1972) and Little (1975).

24
and ceilings have been placed on the mortgage size and allowable rate
of interest. No premiums have been collected for the insurance service
provided, however, and mortgagors received direct subsidization of
mortgage payments under the program (Foard and Frantz, 1973, p. II, 4).
Thus, the monopoly situation initially enjoyed by FHA's Section
203 program has gradually disappeared. New firms and additional fed¬
eral government programs have entered the default insurance market over
time, and the competitive pressures exerted on this program have in¬
creased accordingly. The degree of substitutability between the cover¬
age offered under the Section 203 program and these alternative sources
of default insurance is not, however, immediately apparent. On an
a prvLonÁ. basis, all that can be said is that some degree of substitu¬
tion should exist between these various suppliers of default insurance
coverage. Both the VA guarantee and the subsidy programs of FHA carry
explicit eligibility requirements that reduce the direct substitution
between these programs and Section 203 insurance coverage. To the
extent that these programs provide insurance to individuals that would
not have entered the housing and mortgage markets (and, hence, the mort¬
gage insurance market), substitutability with Section 203 will be
lowered (though probably not eliminated). In such a case, direct com¬
petition in the default insurance market is not generated, but increases
in the volume of activity carried out under these programs may still
reduce the demand for Section 203 coverage by the price effects gener¬
ated in the housing and mortgage markets. That is, the increased demand
exerted in these markets through increases in activity in the VA and
subsidy programs should put upward pressure on mortgage interest i .
and the price of housing services which, in turn, should reduce the

25
demand for Section 203 coverage. To the extent that these programs
provide insurance coverage to individuals that would have otherwise
purchased homes under the Section 203 program, however, substituta¬
bility will be increased since direct competition in the default insur¬
ance market will also be exerted (particularly since both of these
programs provide coverage at subsidized rates). Finally, the degree of
substitutability between Section 203 coverage and the insurance pro¬
vided by the private firms in the market is also uncertain because of
the market difference in the level of coverage offered (100 percent and
20 percent, respectively).
It is theoretically possible that the lower level of coverage pro¬
vided by the private mortgage insurance firms generated an overall
increase in the size of the default insurance market that has been
approximately equal to the volume of insurance written by these firms;
i.e., it is possible that the bulk of their business has been derived
from previously uninsured loans. As was mentioned previously, however,
it is also possible that the lower coverage provided by these firms is
regarded by lenders as being only marginally more risky than the full
coverage provided by FHA. If this has been the case, then competition
between the private firms and Section 203 has been direct and the sub¬
stitutability between these sources of default coverage has been large.
Thus, the degree of substitutability cannot be inferred from theoreti¬
cal considerations alone.
The Volume of Insurance under Section 203
The early history of the FHA Section 203 insurance program indi¬
cates that it was quite successful insofar as achieving a large volume

26
of activity and maintaining actuarial soundness. FHA-insured housing
starts as a percent of total private housing starts moved from 6 per¬
cent in 1935 to 16 percent in 1936, 18 percent in 1937, and 30 percent
in 1938 (Haar, 1960, p. 33). Volume of activity in terms of the number
of mortgages on new units insured under the Section 203 program along
with the total housing starts for the entire country (both insured and
non-insured) in five year intervals for the 1935-1969 period is given
in Table 2.1. From June, 1937, through November, 1957, $17,003 billion
in home mortgage insurance on new units and $13,527 billion on existing
units had been written under the Section 203 program. This volume of
insured mortgages financed a total of 2,600,345 new and 1,980,783 exist¬
ing housing units (Haar, 1960, p. 28).
Table 2.1. Privately Owned Housing Units Started under the
FHA Section 203(b) Mortgage Insurance Program
Compared with Total Housing Starts in the U.S.;
1935-69
Years
Total U.S.
Section 203(b)
Section 203(b) as percent
of total
1935-39
1,710,000
353,798
20.69
1940-44
1,772,700
388,731
21.93
1945-49
5,379,000
406,715
7.56
1950-54
7,708,000
1,094,970
14.21
1955-59
6,935,600
1,156,289
16.67
1960-64
7,160,000
894,535
12.49
1965-69
6,903,700
688,893
9.98
Source:
Table 157 of the
7 972 HUV StaUitical
VnaAbook,
U.S. Department of Housing and Urban Development,
U.S. Government Printing Office, Washington, D. C.

27
The actuarial soundness of this early business is evidenced in the
fact that the initial funds borrowed from the U.S. Treasury in order to
implement the FHA insurance system were repaid within a few years of
operation. As of 1972, FHA's insurance reserves were over $1.6 billion
and the outstanding insurance in force on Section 203 loans amounted to
almost $103.2 billion (Examination o/J Financial Statements Pertaining
to Insurance Operations, Federal Housing Administration, 1972). In
spite of the continual liberalization of the financing terms on the
mortgages insured, the Section 203 program has routinely and consis¬
tently met all insurance claims made against it, and by the middle of
1971, it had accumulated $76 million in excess reserves beyond those
required by actuarial computations (which, themselves, are estimated
conservatively using the period of the 1930's as the base from which
projected insurance claims are computed).
With regard to the more recent activities of FHA (over the decade
of the 1960's and the early 1970's) no significant change is apparent
if one examines only the total single-family activity (including Sec¬
tion 203 and the subsidy programs). Of the total mortgaged housing
starts, FHA single-family programs insured 13.6 percent in 1966 and
over 25 percent in 1971 with these starts representing approximately
129,000 units in 1966 and more than 300,000 in 1971 (Burgess, 1973,
p. 1). If attention is focused, however, on the unsubsidized Section
203 program with which we are concerned in this study, a different
picture emerges. Insurance activity under this program has declined
considerably over the decade of the 1960's, and this decline has accel¬
erated in the early 1970's. The volume of insurance written under this
program in terms of the number of housing units insured per quarter is

28
given in Figures 2.2 and 2.3 for new and existing units separately for
14
the 1960:1 through 1974:2 period.
From these graphs, the decline in Section 203 insurance volume has
obviously been more pronounced and continuous for policies written to
cover mortgages on new units. Also, the decline appears to have begun
earlier for this category of insurance. A plausible explanation for
this observation lies in the private mortgage insurance firms' tendency
to concentrate their activity on the insurance of mortgages written on
new housing units (Semer and Zimmerman, 1975, p. 155). Such a tendency
makes sense if default risk is generally lower on such properties since
both the coverage provided and premium charged by these firms are below
those of the Section 203 program.^ For the present, however, this
explanation of the observed difference in declines for Section 203 in¬
surance written on new and existing units must remain at the specula¬
tive stage. The extant data on the insurance volume of the private
firms in the industry do not separate activity by the type of property
securing the mortgage. This shortcoming is typical of the overall hous¬
ing and mortgage market data which, to a large extent, are generally
• * 16
unsatisfactory.
In addition to the declining volume of insurance being written
under the Section 203 program, significant increases have been
^Calculated from monthly data in FHA MonthZiJ Rzpotá ofa OpeACltlOHA--
Home Mortgage Pnogham, RR:301 (Homes).
"^Greater attention will be devoted to this issue in Chapter IV of
this study.
■^The literature relating to these markets is replete with refer¬
ences to the low quality and general unavailability of crucial data.
Indeed, a complete time series on private mortgage insurance volume
spanning a period since re-emergence of the industry did not exist prior
to the one that I gathered for use in this study.

CD O M f- p CD O íw ^ O ÍJ O
Dwelling Units (000)
Figure 2.2.
Number of New Single-Family Dwelling Units Insured under the Section
203 Mortgage Insurance Program; 1960:1-1974:2
ISJ

Dwelling Units (000)
Year and
Quarter
Figure 2.3. Number of Existing Single-Family Dwelling Units Insured Under the FHA
Section 203 Mortgage Insurance Program; 1960:1-1974:2 ^
o

31
experienced in the average insurance loss per claim since 1971. If the
current trend continues, the actuarial soundness of the program may
become jeopardized at the current premium level. The present soundness
of the insurance fund supporting this program may be largely attributa¬
ble to past successes of the Section 203 program and interest earnings
on past reserves ("Actuarial Briefing Paper," 1974).
Since FHA's Section 203 program was intended to function on an
actuarially sound basis and since the program must cover certain non¬
variable costs (such as the maintenance of numerous insuring offices
throughout the country) in order to continue its operations, it seems
necessary that a certain volume of insurance activity be maintained if
the program is to function on the basis envisioned by its enabling
legislation. Therefore, the absolute number of mortgages insured under
the Section 203 program is a crucial factor in the determination of
FHA's future role in the unsubsidized single-family default insurance
market, and it will be this measure of FHA activity to which our atten¬
tion will be directed throughout this study.
Since this number is influenced not only by the competitive pres¬
sures exerted by new and growing entrants in the default insurance
market, but also by the overall size of that total market (which, in
turn, is influenced by the number of houses sold and mortgages origi¬
nated), it is also of interest to trace the Section 203 market share
over time. This is given in Figure 2.4 where market share is defined
as Section 203 insurance volume divided by the sum of Section 203
insurance, VA insurance, private mortgage insurance, and FHA subsidized
insurance volumes.

Percent of Market
Year and
Quarter
Figure 2.4. Share of the Default Insurance Market Accounted for by the FHA
Section 203 Mortgage Insurance Program; 1960:1-1974:2
co
NJ

33
Clearly, the observed decline in the volume of activity under
FHA's Section 203 program has not been generated solely or predomi¬
nantly by decreases in the overall demand for mortgage insurance—
particularly in recent years. Instead, the decline appears to have
resulted, at least partially, from a loss of insurance volume to the
competitive suppliers of default coverage. In order to be certain that
this has been the case, however, we must investigate other factors that
may have been significant contributors to this decline. And to do this,
we must develop a more complete theory of the mechanisms involved in
determining Section 203 activity over time. Before attempting to de¬
velop such a theory, however, it will be useful to present a brief
review of some recent literature that will be employed in the construc¬
tion of this theory.

CHAPTER III
LITERATURE REVIEW
The Scarcity of Relevant Literature
There have been no rigorous studies undertaken to acertain the
factors that have led to the observed decline in the volume of single¬
family unsubsidized insurance written by FHA. Naturally, over the last
several years, various papers have emerged that have examined the de¬
cline in activity in a more or less logical fashion, usually focusing
the reader's attention on one or, possibly, two factors that are char¬
acterized as "the" cause of shrinking volume.^ These studies, however,
typically fail to describe the causal mechanisms through which the
hypothesized effect operates (i.e., the theoretical foundation for the
conclusions that are reached is either implicit in the argument, or
more often, totally absent). Also, the statistical techniques employed
in these studies (in the rare instances in which empirical evidence is
presented) generally fail to allow for more than one explanatory
variable. Typically, a simple two-way table or graph is employed that
reveals the time path of the volume of FHA activity and the time path
of the hypothesized causal factor (Bazan, 1974, p. 9). Conclusions are
then drawn from the contemporaneous movements of these two paths.
^Examples of such studies include S. Baskin (1971), H. B. Bazan
(1974), Booz-Allen and Hamilton Management Consultants (1973), C. L.
Burgess (1973), A. Diamond (1973), J. B. Hedlund (1973), Mortgage
Bankers Association of America (1971), R. L. Reppe (1973), J. L. Short
it CLÍ. (1972), and B. Whitten (1973).
34

35
There is a danger of attributing cause to a suprious relationship with
such techniques; and, even if the qualitative nature of the conclusion
reached is correct, the policy maker is denied the parameter estimate
that is crucial in the design of effective action. The causal factors
collectively suggested in these papers, however, were not ignored in
the analysis conducted in this study since, for the most part, they do
receive theoretical support when closely examined.
In order to provide a background of the little economic literature
that exists that is relevant to default insurance, the studies of
George von Furstenberg and Henry Aaron will be described and critically
2
evaluated in this chapter. These studies are later employed as a
starting point from which we derive a theory of the demand for mortgage
insurance. This theory then provides a framework for the specification
of an econometric model of the mortgage insurance sector from which
inferences may be drawn concerning the causal factors that underlie the
observed decline in FHA activity. Thus, while the analyses carried out
by these two authors are not specifically concerned with the fall in
FHA volume, they do provide a basis from which our study may proceed.
The works of Aaron and von Furstenberg received a cursory review
in a recent paper by Greenston eX at. (1974) that was published by the
Urban Institute. While criticisms revealed in this paper are fundamen¬
tally sound, there exist several inaccuracies and exclusions that tend
to detract from the discussion somewhat. These will be briefly men¬
tioned in this chapter, but a great deal of attention will not be
2
These works include Aaron (1972), von Furstenberg (1969), von
Furstenberg and Green (1974), von Furstenberg (1970a) and von
Furstenberg (1970b).

36
devoted to them. Also, the brevity of the review provided in the Urban
Institute paper leaves some confusion with regard to the methodologies
employed in these studies which this chapter will attempt to clarify.
Inasmuch as the basic conclusions reached in their review are correct,
however, the findings in this chapter will not differ in any major
respects. We turn now to the studies to be reviewed.
Studies of Default Behavior by von Furstenberg
George von Furstenberg has published a number of articles con¬
cerned with explaining and predicting default probabilities and ex¬
pected default losses on home mortgages (see footnote 2). The model
developed in each of these articles is empirical in nature with very
little theoretical analysis of the default phenomenon. The units of
observation employed in the statistical analyses are cohorts of FHA
insured single-family mortgages. While there are some differences in
the vector of exogenous variables incorporated in the estimating equa¬
tions utilized in these studies (which may be attributable to the lack
of a well developed theory), they are quite similar in the basic method
employed and the important conclusions reached. Therefore, only the
first of these studies will be reviewed in detail.
This paper, which appeared in the JOuAtUlt 0$ F-¿nCMCZ, represents
one of the first empirical examinations of the causal factors determin¬
ing default risk on home mortgages that utilized multiple regression
techniques. The purpose of the study was to develop estimating equa¬
tions that could be employed to predict average default probabilities
for groups of FHA insured loans in order to measure the intra-program
transfers that arise under Section 203. As pointed out by

37
von Furstenberg, such transfers take place within the FHA insurance
program because non-homogeneous risk classes are pooled within the
Mutual Mortgage Insurance Fund of FHA and a single price is charged to
all purchasers of the insurance coverage backed by this fund (i.e., the
transfers arise as a result of a departure from an actuarially fair
pricing scheme)."^
Since the mortgages being examined are completely insured and
since the insurance premiums do not reflect the relative default risks,
the common technique of inferring the degree of risk on a financial
asset from the relative interest rate paid cannot be employed. Instead,
it is necessary to predict the expected default probability for a
cohort of FHA insured loans (measured by the percentage of loans in the
cohort that entered default status in a given year) from the basic
financing characteristics of the loans in the cohort, especially with
regard to the average loan-to-value ratio and term to maturity of these
loans. While the actual mechanisms through which these characteristics
influence default behavior are not made clear in the article, it is
suggested that their effect on borrower equity is the connecting link.
The cohorts utilized in this study are defined by each combination
of term to maturity, loan-to-value ratio, and classification of insured
loans on the basis of the type of property securing the loans (new or
existing). Then, through the use of the equations that are developed
to predict the default probabilities of the individual cohorts, the
author is able to make inferences concerning the risks on these loans
3
The important effects of this pricing system are dealt with in
Chapter V of this study.

38
without reliance upon any financial market mechanisms (as might be re¬
flected in interest rates or insurance premiums in the absence of FHA).
The discussion carried out by von Furstenberg in the following
section of his paper seems to implicitly contain a loose-knit theory of
default behavior on home mortgages. There is an obvious recognition of
the importance of borrower equity in determining default probability
and the role of financing variables in influencing borrower equity over
time. But, a unified theory is never made explicit in this paper, nor
does it appear in any of the others. One is tempted to conclude that
von Furstenberg viewed the theoretical issues behind the discussion as
being too obvious to warrant a rigorous, detailed examination. But,
when one considers the myriad of factors (financial, economic, and
demographic) that could, theoretically, affect default probability (all
acting and interacting to determine both the equity position of the
borrower and his individual reaction to that equity position) and the
logical channels through which these factors might operate, the absence
of a more explicit theoretical treatment must be viewed with concern.
It is this absence of a rigorous theoretical construct that detracts
from the work done by von Furstenberg. And, as mentioned above, the
apparent inconsistencies in the specifications of the estimating equa¬
tions utilized in later studies probably arise as a result of this
absence.
Since defaults on a group of mortgages originated at a given mo¬
ment in time do not occur immediately but are spread over time, von
Furstenberg attempts to fit this time path of defaulting loans employ¬
ing the loan-to-value ratio on the given cohort as a variable that
shifts the entire path up or down without altering the actual shape of

39
the time distribution of defaults. He then fits his estimating equa¬
tion separately for twenty, twenty-five, and thirty year mortgages
further separated by new or existing properties securing the loan.
Such unpooled estimation is appropriate under the hypothesis that the
structural coefficients of the relationship other than the constant
term differ by term to maturity and property type. In this situation,
a single regression using the pooled sample that attempts to incorpo¬
rate these effects through the addition of simple dummy variables that
allow only for intercept shifts will be clearly misspecified. By fit¬
ting separate equations, the hypothesis above may be tested, and the
pooling decision made in accordance with the results. For this reason,
the approach adopted by von Furstenberg in fitting the relationship
initially using the unpooled samples seems reasonable. This yields a
total of six regression equations.
A ptLÍOtví information concerning the shape of the time path for de¬
faulting mortgages is employed to determine the functional form of the
estimating equations. This shape is generally characterized by Figure
3.1. Defaults as a percentage of all loans originated in a given year
tend to rise for the first three or four years and then fall fairly
rapidly and approach the zero axis by the end of the eleventh or
twelfth year. While the level of this curve fluctuates with the risk-
related characteristics of the loan, this functional form is consis¬
tently found in actuarial studies of home mortgages and appears to be
quite stable over time and over mortgage characteristics (D. L.
Armstrong, 1973).
Von Furstenberg hypothesizes that, for a given term to maturity
and a given type of property securing the loans (new or existing), a

40
Percentage
Defaulting
Years Since Loan
Origination
Figure 3.1. Time Path of Defaults on Home Mortgages
higher loan-to-value ratio for the cohort of mortgages will shift this
curve upward leaving its functional form unchanged. Then, the skewed
age distribution is represented by the natural exponential function
(D/E)t = aQ ta2 ea3t
where (D/E)^ is the percent of loans endorsed in a given base year that
enter default status at t years after endorsement; and a^, a9, and a^
are constants.
The variable that is used to capture the effect of the loan-to-
value ratio is given by f 10 (1 - L/V)] where L/V is the loan-to-value
ratio on the mortgage contract. It, therefore, measures ten times the
percentage down payment on the loan. An explanation of why this parti¬
cular transformation is employed is not given. Incorporating this as a
shift variable in the above expression (affecting the position, but not
the shape of the time path of default percentages), von Furstenberg
writes

41
2
(1) (D/E)t = aQ [10 (1 - L/V0]al t&2 ea3C
from which he writes his estimating equation as
(2) In (D/E) = In aQ + a In [ 10 (1 - L/V) ] la^tlt + a^2 + u
Notice that, in this derivation, the disturbance term, u, is not
included in: the equation until after the logarithmic transformation
has been carried out to characterize the relationship in a form that is
linear in the parameters. The stochastic element mystically appears in
an additive fashion. This econometric shell game is technically unap¬
pealing, but is often used. Obviously, the assumption that is implicit
in this transformation is that equation (1) is actually given by
(la) (D/E)t = aQ [10 (1 - L/V) ]ai ta2 e33^ eU
where the stochastic part of the relationship (i.e., the distribution
of (D/E) for given values of L/V and t) is assumed (implicitly) to be
log-normally distributed. Also, no evidence is given to demonstrate
that the disturbance term in equation (2) is in accordance with the as¬
sumptions of the classical linear model that would assure the alleged
properties of unbiasedness and efficiency from the ordinary least
squares estimation technique that is employed.
Another technical shortcoming is found later in the paper when
von Furstenberg pools new and existing units and incorporates a dummy
variable to capture the effect of a different type of property securing
the loan. Prior to this pooling, no formal test of a significant dif¬
ference between the vector of coefficients estimated in the separate
unpooled regressions is carried out (i.e., a Chow test). An initial
examination of these coefficients (given in Table 1) indicates a rather

42
marked difference which implies that the effect cannot be characterized
by a simple shift parameter that enters additively. If the slope coef¬
ficients themselves differ between the two groups, merely allowing an
intercept shift will not correct properly for the effect. Consequently,
such pooling may not be warranted. None of these econometric questions
is mentioned in the Urban Institute review of von Furstenberg's analy¬
sis, but the basic lack of an explicit theoretical framework is duly
noted.
The estimates obtained in the unpooled regressions are given in
Table 1 from the original paper (von Furstenberg, 1969, p. 467). Given
the apparent differences in the structural coefficients in these un¬
pooled regressions, they are (in my own view) the preferred estimates.
They are reported here only to indicate the qualitative impact of the
loan-to-value ratio and term to maturity on default probabilities.
From these equations, von Furstenberg predicts default probabili¬
ties on cohorts of FHA-insured mortgages. Then, an attempt is made to
transform these predicted probabilities into expected default losses
by utilization of a weighting factor that is based upon the assumption
that the insurer's loss, given the occurrence of default, will decline
with the age of the mortgage.
In all, we stipulate that the insurer's loss per foreclosure
declines with the age of the mortgage in default, but less
than in proportion to the reduction in principle outstanding
(von Furstenberg, 1969, p. 470).
This hypothesized relationship between default loss given foreclosure
and time since origination is primarily founded upon conjecture, and
it is not subjected to any empirical verification. A more rigorous
approach would have strengthened the analysis considerably (perhaps

Table 3.1. Regressions of Default Rates on the Age (t) and Loan-Value (L/V) of Mortgages Grouped by Terms
(A) "New" Home Mortgages
Term in Years:
20
25
30
Variable Name
Regr.
Coeff.

t-Value
Regr.
Coeff.

t-Value
Regr.
Coeff.
{Sa>
t-Value
Intercept
-7.2553
-7.4260
-5.6395
1 (1 - L/V)
-1.8613
(.2871)
-6.48
-1.6373
(.1639)
- 9.99
-1.6464
(.0896)
-18.37
2 t
.4094
(.4302)
.95
1.4544
(.1975)
7.36
1.0398
(.1102)
â–  9.44
V2
- .0290
(.0180)
-1.61
- .0247
(.0105)
- 2.36
- .0395
(.0059)
- 6.70
r^ (unadjusted)
.1722
.3691
.5535
r
.4150
.6075
.7440
F-Value
15.19
65.71
142.62
D. of Freedom*
219
337
345
(B) "Existing" Home Mortgages
Intercept
1 (1 - L/V)
-5.9936
- .9877
(.1293)
-7.64
-5.3754
-1.3148
(.0460)
-28.60
-5.2139
-1.1212
(.1050)
-10.68
2 t
.9550
(.1611)
5.93
.5085
(.0565)
9.00
.5852
(.1291)
4.53
3 t2
- .0485
(.0086)
-5.64
- .0275
(.0030)
- 9.10
- .0517
(.0069)
- 7.48
rA (unadjusted
r
F-Value
D. of Freedom*
.2157
.4644
31.89
348
.7252
.8516
303.54
345
.3415
.5844
59.66
345
The maximum number of observations in each run is 352 (32 annual default cells times 11 L/V's), but
cohorts containing less than 40 mortgage endorsements were excluded.

44
employing individual mortgages as the units of observation and applying
a Tobit analysis to predict both the probability of default and ex¬
pected loss given default).
Incorporating the weighting factor that is postulated on the basis
of this assumption, von Furstenberg reaches the following conclusions
that are in basic agreement with the theoretical model developed in the
following chapter of this study:
1. Expected default loss is directly related to the loan-to-
value ratio on the mortgage contract; and
2. Expected default loss is also directly related to the
term to maturity on the mortgage contract
These qualitative results are strengthened in the following chapter
by addressing the default probability—expected loss issue from a purely
theoretical point of view. They are then incorporated with a theoreti¬
cal analysis of the loan contracting process that is developed as an
extension of the descriptive treatment provided by Aaron in his analysis
of the effect of default insurance on this process. Together, these
will provide the basic variables for a demand for FHA insurance equation
that can be more fully specified by the addition of product differentiat¬
ing factors and that can be imbedded in a set of behavioral equations
depicting the market for default insurance on home mortgages. We now
turn to a review of Aaron's work.
Aaron's Analysis of the Contracting Process
on Mortgage Loans
Henry Aaron's analysis of the effect of FHA insurance on the con¬
tracting process that takes place in the mortgage market between the

45
borrower and the lender is contained in his book, SkzlXeA and Sub^-id-iW-
Who 8ene¡$¿tó {¡aom FtdeAal Housing, Fotidu (1972). The book itself
deals with all of the major housing-related programs and policies car¬
ried out by the federal government (including incentives provided for
homeownership through the income tax system). These are described in
adequate detail to provide the reader with an understanding of the im¬
portant functions of each, and estimates of the benefits derived by
income class are attempted in order to identify the direction of the
major redistributive effects. The default insurance and loan guaranty
operations of FHA and VA are discussed in Chapter V.
The first part of the chapter briefly describes FHA's Section 203
program and the system of VA loan guarantees, providing some historical
perspective for them. The second section (which is the one of primary
interest here) develops an analytical model of the tradeoffs that exist
and the negotiations that occur between the mortgagee and the mortgagor
in arriving at a mutually agreeable contract and the influence that the
provision of default insurance will exert on the outcome. The last
section of the chapter provides estimates of the benefits derived by
mortgagors from the provision of such insurance for various income
classes separately for FHA and VA borrowers (this section drawing
heavily from the empirical work of von Furstenberg discussed above).
The review here will focus on the borrower-lender model developed in
the second section.
The model portrayed in this section is graphical and descriptive
in nature with very little explanation provided for the relationships
hypothesized to exist. The analysis is weak in several respects and
these weaknesses result in a rather blatant misinterpretation in the

46
conclusion of the chapter. Nonetheless, the description provided of
the contracting process provides an intuitively appealing framework
from which a more rigorous treatment can be developed. It is cast
within the framework of a two party bargaining model with loan contract
terms (specifically, the downpayment and the interest rate) being the
subjects of negotiation. Insurance coverage is entered exogenously.
The model used is described by the following graph, adapted from
Figure 5-1 of Aaron's (1972, p. 83) book.
Ratio of Equity
to Value
Interest
Rate
Figure 3.2. Lender and Borrower Tradeoffs Between Interest
Rates and Downpayments
In this graph, (E/V) is the ratio of borrower equity to property value,
i is the contract interest rate, and L? are lender indifference
curves, and 1^ and are borrower indifference curves. The lender is
described as deriving increased utility from higher interest rates (as
higher rates increase profits) and from increased borrower equity (as

47
increased equity decreases expected default loss). The borrower is
described as deriving increased utility from a reduction in either of
these terms as such a reduction decreases the required downpayment and
the price of the borrowed funds. Although Aaron describes the indiffer¬
ence curves in this graph as representing the utility functions of the
borrower and the lender, it is clear that they must, instead, be inter¬
preted in terms of indirect utility functions since neither actual
profits (for the lender) nor real goods (for the borrower) are captured
in the graph. Ideally, one would describe a utility of profits function
for the lender and a utility of real goods (including future goods)
function for the borrower, derive indirect utilities as functions of
loan contract terms, and incorporate these into the bargaining model
with which Aaron begins. Also, the convexity of the lender and the con¬
cavity of the borrower indifference curves in Figure 3.2 are not for¬
mally defended in Aaron's analysis, but instead, they are merely drawn
as exhibiting these properties.
Default insurance is introduced by arguing that
Lenders are willing to accept more liberal terms when loss
protection is available than when it is not because it enables
them to avoid the risk of large loss from unusually frequent
or costly foreclosures. Furthermore, loss protection insu¬
lates lenders from losses due to such unpredictable events as
increased unemployment, declines in property values, or slow¬
downs in economic growth (Aaron, 1972, p. 82).
This argument is translated in terms of Figure 3.2 by asserting that
curve indicates the most liberal combinations of interest rates and
downpayment requirements at which lenders will make loans if no loss
protection is available, and that curve indicates the most liberal
combinations that lenders will accept if they are protected from de¬
fault loss. Although Aaron does not make it explicit in his analysis,

48
the implication is that the level of utility along is equal to the
level of utility along L? so that insurance protection is depicted in
his model as a shift in the lender's indirect utility surface. With
regard to the borrower's indirect utility function, however, no shift
occurs so that the level of utility along I? exceeds the level of
utility along 1^ in the graph. Thus, the equilibrium outcome of the
negotiation process between the borrower and the lender shifts from
point A to point B with the provision of default insurance with a re¬
sultant increase in borrower utility and constant lender utility.
While it is not made clear in Aaron's analysis, the two points of equi¬
librium in the graph must be viewed as two of an infinite number of
such points lying along the contract curve of the negotiating parties.
Supposedly, some force is exerted from outside the negotiation process
to determine which of these equilibrium solutions results—such as the
tightness of the mortgage market existing at the time of negotiation.
Insurance coverage also enters from outside since it is not pictured in
the graph, and it too influences the equilibrium outcome.
Another point that should be mentioned that is ignored by Aaron is
that the result pictured in the graph (a decrease in downpayment and an
increase in interest rate) is solely a result of the actual utility
functions underlying the indifference maps drawn. Given different
lender and/or borrower preferences, the post-insurance equilibrium solu¬
tion could easily result in the opposite movement (an increase in down-
payment and a decrease in interest rate), or it could result in a
reduction in both terms of the loan. The important point revealed in
the graph is that, by providing the lender with default insurance, the
borrower should be able to negotiate more favorable terms—a lower

49
downpayment for a given rate of interest or a lower interest rate for
a given downpayment or some combination of these, depending upon the
actual preference maps involved.
Overall, there are two fundamental weaknesses inherent in Aaron's
analysis. First, the conclusions derived flow from the actual indif¬
ference curves drawn and basic underlying assumptions remain hidden in
these curves (such as risk aversion utility functions for lenders).
Second, the graphical approach forbids the direct incorporation of in¬
surance coverage into the bargaining process and, therefore, leads to
the complete exclusion of both the insurance premium and the lender's
risk premium (both of which are crucial in the decision of whether to
insure the loan). Since the insurance premium (which is just as much
a cost to the borrower as higher interest rates or larger downpayments)
is not incorporated in the graph, it would appear that all borrowers
could increase their utility by providing the lender default insurance
on the loan, and we would be led to expect all loans to be insured.
Also, exclusion of the lender's risk premium results in a mistaken
measurement of the benefits of the FHA insurance program--benefits are
calculated as the difference between the expected default loss on the
loan and the insurance premium paid with no consideration of lender
risk premiums. Thus, many purchasers of FHA insurance are seen as de¬
riving negative net benefits from participation in the program. Since
insurance coverage is not forced upon anyone, one must ask why a
rational consumer would willingly pay for a good that yielded benefits
valued less than the price charged. Aaron's rationalization of this
result is unconvincing.

50
Higher income households or those with low loans in relation
to value received default protection worth less than the
premium charged for it. It would appear that lending insti¬
tutions could profitably offer such borrowers conventional
loans with an interest charge greater than the current con¬
ventional rate but less than the FHA premium. Their failure
to do so may reflect a judgment that in the absence of price
inflation and attendant rises in property values, FHA home
mortgage insurance would be severely underfinanced, perhaps
by considerably more than 20 percent, so that virtually
everyone would realize a net benefit under FHA mortgage
insurance (Aaron, 1972, p. 89).
Such a global view on the part of lenders is questionable. Had
Aaron incorporated the lender's risk premium into the analysis, such
contortions would have been unnecessary. In fact, what Aaron interprets
as borrowers' net benefits represents only the income redistribution
taking place within the FHA program because of the non-actuarially-fair
pricing scheme employed in supplying insurance coverage. With all pur¬
chasers of insurance coverage being charged the same premium, it is
obvious that some will pay more than and some less than the expected
default loss on their individual loans if the program is to break even.
Such departures from the actuarially, fair rate structure, however, do
not fully represent borrower benefits; and such an interpretation must,
by necessity, understate the real benefits derived from the insurance
purchased. While Aaron does recognize the redistribution that occurs
and the reason for its occurrence, he mistakenly identified this redis¬
tribution as the net benefits derived from the program because risk
premiums are ignored.
The following chapter will adopt Aaron's basic approach by viewing
the mortgage contracting process as a basic choice problem in which
there exists tradeoffs among loan contract terms, interest rates, and
insurance coverage. It will, however, extend the analysis by including

51
the term to maturity on the loan in the contract terms, explicitly con¬
sidering the lender's risk premium, and deriving the conditions under
which insurance will be desirable from the borrower's point of view.

CHAPTER IV
A THEORETICAL MODEL OF DEFAULT RISK
AND DEFAULT INSURANCE
Introduction and Overview of the
Theoretical Model
The theoretical model developed in this chapter analyzes the de¬
fault insurance market from both the demand side and the supply side in
order to reach an understanding of the basic mechanisms involved in the
determination of the quantities of insurance written. It is intended
to explain both the overall market volume of insurance written and the
individual volumes that are written by the various supply-side partici¬
pants in that market. The model that is derived will be seen to differ
from the standard microeconomic competitive market analysis in three
important respects. First, the model incorporates uncertainty concern¬
ing mortgagor default behavior. Such uncertainty is, of course, the
basic source of default insurance demand, and it is accounted for in
the model by use of the state-preference approach to decision making
under uncertainty. Second, the model explicitly introduces constraints
of an institutional nature on the supply side of the market. These
constraints have been particularly influential in the market for de¬
fault insurance because of the importance of federal involvement and
the intensity of state regulatory actions in this market. And third,
the model recognizes the essential non-homogeneity of the insurance
products supplied in this market. Such non-homogeneity results in a
52

53
segmented market structure that requires individual supply-side par¬
ticipants' behavior to be further constrained by the actions of other
participants in the market (some of which exhibit behavior that is not
motivated by profit considerations).
The model assumes that the default insurance market represents one
sector of a larger three sector system consisting of the housing market,
the mortgage market, and the default insurance markets. Together, these
three sectors determine the quantity of houses sold, the quantity of
mortgage funds loaned, and the quantity of insurance contracts written.
It is further assumed that the housing and mortgage markets are deter¬
mined simultaneously and that the default insurance market is determined
recursively from the outcome of the equilibrating process occurring in
the other two markets. One might imagine that the demand for and supply
of housing services influences the demand for mortgage funds and that
the demand for and supply of mortgage funds simultaneously influences
the demand for housing services. Then, we assume that the demand for
default insurance is determined from the demand for and supply of mort¬
gage funds but that the outcome achieved in the default insurance
market does not exert any simultaneous feedback effects on the housing
and mortgage markets. This basic assumption concerning the structure
of the larger three sector system is necessary if we are to examine the
default insurance market in isolation without more detailed explicit
modeling of the other two sectors.
The model also assumes that the home mortgage default insurance
market is itself determined by the actions of three sets of participants
the mortgagor, the mortgagee, and the supplier of default insurance
coverage. The first two sets of these participants interact in what is

54
viewed as a competitive mortgage market under conditions of default
loss uncertainty to determine the market demand for mortgage default
insurance. Thus, the model explicitly recognizes the derived nature of
the demand for default insurance coverage where the primary source of
this demand is found in the demand for and supply of mortgage funds.
The relevant behavior of these two participants is explored in the two
sections of this chapter that follow this introductory section.
The final set of default insurance market participants (the sup¬
pliers of default coverage) is composed of four major actors: the FHA
Section 203 program, the private mortgage insurance industry, the
Veterans Administration home loan guarantee program, and the FHA subsi¬
dized housing and mortgage insurance programs. Of these four actors,
the last three are assumed to be subject to supply constraints of an
institutional nature which result in their services being rationed on
the basis of non-price characteristics. For the VA and FHA subsidy
programs, the characteristics that are used to ration the services pro¬
vided are the prior military service and the family income of the in¬
surance applicants of the two programs, respectively. For the private
mortgage insurance industry, the objective of maximizing profits sub¬
ject to the constraints faced in this market (regarding both the
quantity that may legally be written given the state laws forbidding
entry and the regulations concerning maximum contingent liabilities
that may be assumed and the price that may practically be charged
given the presence of a supply schedule for Section 203 coverage that
is infinitely price elastic) dictates that the service be rationed ac¬
cording to the default risk exhibited on the individual contracts.
This mode of behavior on the part of the private mortgage insurance

55
industry implies cream-skimming from the previous customers of the
Section 203 program.
Finally, the coverage supplied by the various actors in the market
is considered to be non-homogeneous but substitutable. This implies
a segmented market structure and results in the overall mortgage de¬
fault insurance market being determined from the operations of four
inter-related submarkets (one for each supplier of coverage). And,
since neither cream-skimming nor rationing may occur in a competitive
market in long run equilibrium, the model must be interpreted as short
run in nature. We now derive a theoretical construct that will allow
us to incorporate these complexities in our analysis of the home mort¬
gage default insurance market.
Default Probability and Expected Default Loss
on Individual Mortgage Loans
Since the fundamental purpose of mortgage insurance is to reduce
the lender's exposure to default risk on insured loans, a theoretical
analysis of default behavior provides a logical first step in the
development of a comprehensive theory of default insurance. At this
preliminary stage of the analysis, we are not concerned with the default
insurance market itself, but rather, with the mode of behavior that
gives rise to the phenomenon of mortgagor default. An understanding of
such behavior will prove useful in later stages of the analysis when
the demand side of the default insurance market is approached. The
factors that are important in the determination of default risk on in¬
dividual mortgage loans will influence the demand for insurance coverage
on these loans and, as a result, will affect the overall market for
default insurance.

56
As pointed out in the preceding chapter, the existing body of
economic literature contains very little explicit theoretical analysis
of mortgage default risk, although a considerable amount of empirical
research has been conducted in this area."*" Therefore, in the develop¬
ment of a theory of default insurance, it will be useful to first
examine the mortgage default phenomenon from the perspective of economic
theory. This section attempts to analyze default behavior from such a
perspective. The basic purpose is to present the phenomenon of default
on home mortgages as the logical outcome of a rational decision process
that is influenced by certain observable factors.
The model of individual default behavior developed in this section
utilizes the following notation:
= the individual's net assets other than the mortgaged
property in period t;
I = the individual's income net of consumption expendi¬
tures in period t;
V = the market value of the mortgaged property in period
t, seen as a random variable with density function
f (V );
t v t ’
r = the contractual interest rate on the mortgage obliga¬
tion, constant over all t;
. M
t
L/V
D
= the mortgage balance outstanding in period t;
= loan-to-value ratio on the mortgage at origination;
= 1 - L/V = downpayment on the mortgage at origination
expressed as a percent of the price of the house;
Empirical studies that deal primarily with the estimation of de¬
fault probability equations include: Baza and Kirzner (1975); Herzog
and Earley (1970); Knight (1969); von Furstenberg (1969, 1970a, 1970b,
1970c, 1971, and 1974); and Williams it af.(1973). None of these
studies, it should be noted, attempts to carry the empirical analysis
to relationships explaining expected default losses which, from both' the
lender's and the insurer's point of view, are more relevant than simple
probabilities of default.

57
T = contract life of the mortgage obligation from
origination to maturity; and
g = probability of default on the mortgage obligation
in period t.
Adopting this notation and ignoring, for the moment, any legal
considerations raised by default, we may write the individual's wealth
in period t (which we denote by W ) as
\ X + I + V - (1 + r) M , with no default
Wt - ) ‘ '
+ I , with default.
If V were non-stochastic, it is obvious from this expression that
the individual attempting to maximize wealth in period t would default
on the loan if his equity in the mortgaged property became negative,
where equity in period t (which we denote by E ) is given by
(1) E = V - (1 + r) M .
t t t
This result, however, must be amended in light of the effect that
defaulting on the mortgage will have on the individual's future ability
to borrow funds. Credit ratings are based (at least, to some extent)
upon past behavior in paying debts. This means that the individual
will have to weigh the gain in utility from increased wealth brought
about by defaulting in a negative equity situation against the loss in
utility brought about by a decrease in future access to capital markets
that is generated by such behavior. Consideration of this factor means
that (1 + r) will have to exceed V by a sufficient amount to com¬
pensate the individual for this decline in his ability to borrow funds
before default will occur. This amount will vary over individuals, and
for a given individual, it may vary over time. We may, however, assume

58
it to be constant for a given individual at a given moment in time. So
doing, we denote this value by C^, which represents the value of the in¬
dividual's credit rating to him at period t. Certain demographic char¬
acteristics found entering the various regression equations of default
probability studies may be seen to function through this factor, i.e.,
individuals with particular characteristics (race, age, income, etc.)
may value credit ratings higher or lower than others in a systematic
fashion.
With V still assumed to be known with certainity, the equity/
default probability relationship can be described as
E + C > 0 implies g^ = 0
E + C <0 implies g =1.
t t K 6t
Here, we have the case where a slight decline in below (1 + r)
does not result in default on the loan because the small gain in the
mortgagor's wealth position does not warrant the damage that will be
done to his credit rating by defaulting on the loan. The individual
may be perfectly willing to suffer negative equities if he places suf¬
ficient value on his future access to capital markets. Consideration
of the myriad factors that may, theoretically, influence C is beyond
the scope of this analysis, but it seems clear that such factors may
2
be very important in determining individual default behavior.
Transactions costs involved in selling a house would have the
opposite effect of Ct and could make default the optimal choice even in
a positive equity situation if sufficiently large. Assume that the in¬
dividual must relocate and is forced to terminate the mortgage obliga¬
tion in order to be able to afford housing in the new location. His
choice, then, is whether to sell the house and successfully retire the
loan or simply default on the mortgage. Denoting transactions costs in¬
volved in selling by Z^, default will be optimal if Vt + Ct < (1 + r) Mt
+ Z^• Therefore, even if Vt > (1 + r) Mt, default may still be optimal

59
V , however, is not known with certainty. The value of the mort¬
gaged property is subject to fluctuation as a result of changes in vari¬
ous factors beyond the control of either the mortgagee or the mortgagor.
For example, the construction of a new highway through the neighborhood
containing the mortgaged property may be announced; an adjoining neigh¬
borhood may be re-zoned; or the local or national economy may experience
an economic downturn. All of these occurrences will affect the market
demand for the property securing the loan and, therefore, influence the
value of that property. In order to capture the effect of these various
factors in the model, we assume V to be a random variable with a proba¬
bility density given by f^CV ). Since it appears likely that the proba¬
bility distribution of the value of the mortgaged property will vary
over time, we allow for the possibility that the density functions,
f (V ) will differ for different time periods. In particular, changes
over time in the conditions of the neighborhood, the property, or the
local housing market will affect the functional form of ft(V ).
k
We now define V as the value of the mortgaged property in period
t at which E plus C becomes zero, i.e.,
t t
(2) V* = (1 + r) M - C .
t t t
Then, the individual's expected wealth in period t (denoted by E [W ])
can be written as
if Zt > Ct by a sufficiently large amount. This factor, however, is
likely to be fairly constant over individuals and over time.
Consequently, we do not incorporate it explicitly in the theoretical
model, although such incorporation could be easily adopted if the model
were being developed for more specific purposes than those here.

60
(3) E [ Wt ]
*
V
t
oo
+
*
V
t
[ X + I + V - (1 + r) M ] f (V ) dv
1 t t t t t t t
where the first integral on the right-hand side represents the indi¬
vidual's wealth position if the value of the mortgaged property becomes
sufficiently low to make default the optimal (expected wealth maxi¬
mizing) policy and the second integral represents the individual's
wealth position if the value of the property remains sufficiently high
to warrant continuation of the mortgage payments. If one felt it
desirable to assume that property values remain non-negative, the lower
limit of integration for the first integral on the right-hand side of
equation (3) could be replaced with the value zero. Such an assumption,
however, is not required for our purposes so we maintain the more gen¬
eral expression above.
Maximization of this expected wealth requires that the individual
•k
default on the loan as soon as V declines to V . Given our definition
t t
k
of V in equation (2) above, we know that the probability of default in
period t is given by
(4) gt = Pr [ Vt < (1 + r) Mt - Ct ] .
Then, by definition of a cumulated distribution function we know that
(5) gt
(1 + r) M
f (V ) dV
t t t
— OO

61
This expression reveals the channel through which neighborhood and
property characteristic variables found in many of the default proba-
3
bility studies may be seen to function. By affecting the time path of
property values (hence, f^iV^)), these factors influence default proba¬
bilities both in the present period and in future periods. Housing
market disruptions created by local or national recessions can also be
seen to function through this channel. For example, the distributions
f _^(V ^), i = 1, . . . , n, may all be shifted to the left (i.e., the
expectation of future property values may be reduced) by an exogenous
occurrence such as the decay of the neighborhood in which the mortgaged
property is located, thus increasing the probability of default in the
present and all future periods.
For a given distribution of values for the mortgaged property at
time t (i.e., given f^V^)), equation (5) implies that
(6)
(7)
and
(8)
3M
3C
0 ,
0 ,
0 .
Given that default probability bears such a close relationship to
the density function of property values, the phenomenon of redlining
may be explained as a divergence between lenders' subjective notions
concerning ft(Vt) in future periods and the housing market's capitaliza¬
tion of these future values into the selling price of the property. To
the extent that expected future declines in the price of a house are
not capitalized into the selling price, lenders will be unwilling to
make loans on the house.

62
Intuitively, for a given probability distribution of property values,
the greater the outstanding mortgage balance, M^, the greater will be
•k
the probability that V^_ will decline to and, as a result, the
greater will be the probability that the mortgagor will default on the
loan, g^. The inequality in expression (7) merely illustrates the ob¬
vious point that the greater the value that the mortgagor places on his
credit rating, C , the lower will be the probability of default, g^.
And, the result given in (8) indicates that default probability will be
directly related to the contract interest rate, r. This last finding
stems from the reduction in owner equity at any given moment in time
that results from higher interest rates. For the moment, we focus our
attention on the relationship in expression (6).
Given the interest rate and the price of the mortgaged property
(denote this price by P, where P = V at t = 0), the important elements
in determining the time path of the outstanding mortgage balance are
the percentage downpayment, D, and the contract life of the mortgage, T.
If we ignore interest charges and assume a constant, even reduction of
the principal on the loan, the outstanding balance in period t may be
4
written as
(9) M = P (1 - D) - t [ P (1 - D)/T ] , t = 0, . . . , T.
The first term on the right-hand side is the original mortgage amount,
and the second term is the cumulative amount of the loan that has been
4
Today, most mortgage loans exhibit constant, level payments,
which this formulation does not. The formulation for the outstanding
balance ón such loans, however, is much more complex and utilizing it
does not alter the qualitative results; therefore, the simplier ap¬
proach is adopted.

63
paid by the borrower at time t. Obviously, M > 0 for all t except the
last (when t = T) in which case M = 0 and the mortgage is retired.
From this expression we see that
(10)
3M
_ J
9D
â– P + t - < 0
= 0
and
(11)
> 0
for t = 0, . . . , T - 1
for t = T,
for D < 1
= 0
for D = 1.
These results indicate the qualitative relationship between the out¬
standing mortgage balance in period t and the percentage downpayment
(in expression 10) and term to maturity (in expression 11). For a
given purchase price, this outstanding balance will be lower the larger
the downpayment and the shorter the term to maturity.
9M
9M
Ignoring the special but uninteresting cases where - = 0,
o D o 1
we may combine the above results via the chain rule and expression (6)
to obtain the results that
(12)
and
(13)
9g 9g 9M
6t _ 6t t
9D 9M 3D
t
9g 9M
—I _L > o
9M 3T
t
These results stem from the effects of initial downpayment and term to
maturity on the outstanding mortgage balance and through this, borrower
equity. For a given loan at a given moment in time, M will be larger

64
(and, for a given V , will be smaller) the smaller is D and the
larger is T.
The inequalities given in expressions (12) and (13) above describe
the qualitative relationship between default probability and loan con¬
tract terms. Since the mortgagee's actual default loss (or the insur¬
ance claim on 100 percent insured loans) in the event that default
occurs is (ignoring foreclosure and transactions costs) equal to the
negative equity position of the mortgaged property, expected default
losses will also be influenced by contract terms. If we let E [ L ]
denote the expectation of default loss on the given loan in the given
period and adopt the simplifying assumption that property values fluc¬
tuate in a continuous fashion"* so that the mortgagor will default when
k
the value of the mortgaged property equals V exactly, we have
E [ L. ]
— CO
[ V - (1 + r) M ] f (V ) dv
L t v ' t 1 t t t
= - V
t
-CO
f (V ) dv + (1 + r) M
tv t t t
f (V ) dV
tv t t
— 00
[ -(1 + r) M + C + (1 + r) M ] g
t t t J Bt
Ct *t*
This assumption represents an obvious departure from descriptive
reality. It is necessary, however, if we are to derive a precise ex¬
pression for expected default loss under the assumption that mortgagors
enter default at precisely the optimal point. To the extent that non¬
continuities forbid such behavior (through, for example, discrete jumps
in the value of a given piece of property), our derived expression will
understate these losses. The qualitative relationships that this assump¬
tion allows us to derive, however, will remain valid.

65
Obviously, under the assumptions that the mortgagor attempts to maxi¬
mize expected wealth after taking the value of his credit rating into
account and that property values vary continuously, default will occur
as soon as negative equity in the property (given by the difference
between and (1 + r) M^) is equal to in absolute value. Then, the
actual loss to the lender in the event of default will always be equal
to C^, and expected loss is the actual loss times the probability of
default occuring.
Thus, the expected default loss to the mortgagee depends upon the
probability of default loss and the degree of negative equity that the
mortgagor is willing to absorb to protect his credit rating. Recall,
however, that this latter variable also influences g^ because it is
"k
included in our definition of (expression (2) above). Also, recall
that it bears a negative relation to g^_ (expression (7) above), so that
its net effect on E [ ] becomes ambiguous. Intuitively, the greater
the value that an individual places on his credit rating the lower will
be the probability that default will occur but, in the event that it
does occur, the larger the actual loss is likely to be. Such a result
emphasizes the inherent weakness of limiting the analysis of default
risk to the explanation of default probabilities.^3
With regard to the terms on the mortgage contract, however, it is
clear from the above expression that
Obviously, a similar result would have applied to had this
factor been incorporated in the model. Here, transactions costs would
tend to increase the probability of default but would (assuming that
these costs are lower for lenders than for individuals because of
possible scale economies, greater bargaining strength with brokers,
etc.) tend to reduce actual losses in the event that default occurs.

66
3E [ Lt ]
(14)
1 t
< o ,
3D
(15)
3E [Lt ]
> 0 ,
3T
and
(16)
3 E [ L t ]
> 0
3r
for a given f^(V^). That is, expected default loss is inversely re¬
lated to the percentage downpayment (or directly related to the loan-
to-value ratio), directly related to the term to maturity, and directly
related to the contract rate of interest on the mortgage obligation.
These are the basic qualitative relationships that will be employed in
the following section of this chapter in examining the individual's
decision of whether to borrow on an insured or an uninsured basis given
the market rate available on the two types of loan. These results
receive strong empirical support from the default studies of von
Furstenburg and others. Therefore, no attempt is made to replicate
these results in this study, and the reader is referred to the regres¬
sion results presented in Chapter III above.
The Demand for Default Insurance Coverage
Recognizing the influence that financing terms have on default
risk, we now consider the impact that such risk exerts on the indi¬
vidual lender's supply of mortgage funds and, through this, the market
price (or rate of interest) on such funds. By focusing attention on
the mortgage lender, we will be able to shed some light on the basic
source from which the demand for mortgage default insurance is derived

67
(this source being the lender's aversion to default risk), and we will
then be in a position to draw inferences concerning the important fac¬
tors that are likely to determine this demand.
In so doing, it will be expedient to adopt several simplifying
assumptions that constitute rather drastic departures from real world
situations. An extended discussion of the methodological role of as¬
sumptions in the derivation of theoretical models is, obviously, beyond
the scope of this study. Instead, we can merely express the opinion
that the violence that is done to descriptive accuracy through the use
of these assumptions does not jeopardize the usefulness of the conclu¬
sions that they enable us to obtain. Some of the basic assumptions
that are employed in this section include:
1. Mortgage markets are workably competitive in the sense
that individual lenders take prices (or interest rates)
as given.
2. Mortgage lenders are viewed as suppliers of mortgage
funds only.
3. Individual mortgage loans are viewed as marginal units
to the lender (although, in reality, they differ in
size).^
These three assumptions represent only the most basic and most obvious
departures from reality that are embodied in the model below. Other
somewhat less brazen assumptions will be adopted as the analysis
proceeds.
The first conceptual difficulty that must be confronted in our
analysis of lender behavior is that even within the confines of as¬
sumption 2 above, we must recognize the essential heterogeneity of
^On the application of marginal analysis to non-continuous prob¬
lems, see Friedman (1953, p. 15).

68
individual mortgage loans. Since the financing terms on individual
mortgage loans vary considerably across such loans, and since these
terms have been shown to influence default risk, our analysis should
allow us to separate mortgages of distinct term-related risk levels.
Because of this risk heterogeneity, there will not exist a single mar¬
ket price for mortgage funds; but instead, there will exist a market
price vector for loans with different financing terms at any given
moment in time. In this way, we can allow the market price of an in¬
dividual loan to reflect the inherent default risk on that loan. To
accomodate this essential feature in the model below, we apply the con¬
cept of commodity hierarchies (Sweeney, 1974) to the mortgage market.
Specifically, we interpret default risk as a quality variable and assume
k classes of loans that are distinguishable and mutually exclusive re¬
garding the default quality (risk) exhibited. These classes are con¬
sidered to be defined by the contract terms of the loans within the
class; i.e., all 30 year, 90 percent loans are assumed to exhibit
essentially identical default risk and are, therefore, classed together
at one quality level. We also assume that individual lenders originate
a large number of loans in each quality class so that the marginal
analysis may be applied to individual classes of loans. Then, ranking
these loan classes in ascending order of default risk (or alternatively,
in descending order of loan quality) we may write the market vectors of
loan prices (r) and quantities (M) as
and

69
where, through the operation of the market, we will see that the prices
that are established will increase with the default risk exhibited,
i.e.,
r. < r. for 1 < i < j < k .
i J - “
Also, by assumption, each class quantity, 1R , is formed by summation of
n^ loans, each of which is reasonably equivalent with regard to the
default risk exhibited, so that
n.
1
M. = £ M. . ,
J
i=l
Ji
and the total quantity of loans originated by the given lender in the
given period will be
i n-
k J
M
£ M.
j=l i=l
Ji
Then, the total revenue obtained by the lender will be
R = r H =
£ r. M.
j=l J J
and, obviously, with positive prices and r given to the firm,
dR
dM
= r > 0 .
Finally, in order to simplify the analysis, we assume that the time

70
period referred to in this section is defined by the maximum maturity
of the loans originated so that the r vector will represent the percent¬
age interest charges over the life of the various loan classes.
Given this conceptual framework, we turn to our analysis of lender
behavior. In so doing, we adopt the following additional notation and
assumptions.
E L. is the total default loss to the lender in the given
j=l J
period on all loans originated in that period. Assuming
that total default loss increases with the quantity of
loans originated and recalling the influence of loan con¬
tract terms on default risk, we may write the total default
loss for each class, L., as a function of the quantity of
^ l
loans originated in that class, the financing terms that
serve to define the class, and a random variable, Zy So
doing, we have L. = L. (M., (L/V)., T., Z.), where (L/V).
J J J 111 1
is the loan-to-value ratio and T. is the term to maturity
J
8L.
that together define class j loans. Obviously, > 0,
j
and from the conclusions reached in the preceding section,
3L, 9L.
f 0.
3(L/V) .
J
o -n
> 0 and -r^r- > 0. Also, we assume that â–  â– 
3T.
9M
£ C. is the total cost of supplying mortgage funds that
j=l J
are unrelated to default risk. It includes administrative
costs and the opportunity costs of the funds made available.
It is seen as an increasing function of the quantity of
loans originated, both in total and within loan classes, so
T
that CT = CT (M^) and C. = C. (M.) where
J J J dM1
> 0 and

71
dC.
3
dM.
3
> 0.
of risk,
Also, assuming that
we will have
these costs
dC.
1
dM. ‘
3
are
independent
Utilizing this notation, we may describe the profit function of
the mortgage lending institution (assuming for the moment that none of
the loans originated carry default insurance coverage) as
T
TT
T
where it is the total profit for the given period which is given by the
sum of the individual profits on each loan class,
T y
TT = E IT . .
Then, we may write total profits as
k
E
3=1
IT .
3
k
E
3=1
r. M.
3 3
k
E L. (M., Z.)
3=1 3 3 3
k
E
3=1
(M ) .
Due to the presence of the random variable, Z, in this equation, the
lender's profits will be stochastic.
Assume that the lender possesses a utility of profits function
that satisfies the von Neumann-Morgenstern axioms (see Horowitz, 1970,
T
pp. 342-351). Let this function be given by U = U (it ), and let the
function be defined over profits from individual loan classes,
U_. = Uj (ir.). Then, adopting the objective of expected utility maximi¬
zation, we may write the lender's objective function as
(18)
E [ U (ttT) ] =
k
E [ U ( E r . M.
3 = 1 3 3
k
E L. (M., Z.)
j=l 3 3 3
k
-EC. (M.)) ] .
3 = 1 3 3

72
Differentiating this expression partially with respect to each of the
lender's control variables (the lh's),
3E [ U (tt )]
3M.
1
= E [
3U
9tt ,
3L.
(rj 9M
1
dC.
1
dM.
J
) ]
an dc- aiT 3L.
E t cf^) (r - ^)] - Etcf;) (3^)].
13 J 3
3 = 1. • • • , k
where
3U
air.
is the lender's marginal utility of profit from class j
loans. Setting each of these k expressions equal to zero and simplify¬
ing, we obtain the first-order conditions necessary for the maximization
g
of the expected utility of profits,
(19)
dC.
1
dM.
3
+ E [
3L.
3
3M.
3
cov [
au
a tt .
] +
3L.
1
3M.
1
E [
3U
3tt .
3 = 1.
or
8
Setting this expression equal to zero, we obtain
dC. _ 3L.
313
E [ ( ) (r . - ,
oTT . i dM.
J J
1 ) ] - E [ (|^-) (^)
3tt .
3
3M.
3
= 0
dC
3L.
(rj dM.
w r—] - E [ (|^-) (^-)] = 0.
) E f
3
3 7T .
3
3tt .
3
3M.
3
Then, since the expected value of a product of two random variables is
equal to the product of their expected values plus the covariance be¬
tween these random variables,
dC
(r. -
3 dM.
3
3U
i) E[H
3L.
3tt .
3
3L.
-E ‘It:1 ei m1’ ■cov !!r ■ 3M.
3 3 3 3
= 0.
Dividing by E[-—] and moving all negative terms to the right-hand side
oTT .
yields expression (19),

73
Assuming that the second-order conditions are met (i.e., that the
lender is indeed maximizing the expected utility of profits), these
expressions give the total interest charges that the borrower of class
j loans will have to pay in order for the lender to be willing to
originate the marginal loan in that class. The expressions implicitly
define the lender's supply schedule of mortgage funds for each of the
k loan classes.
dC. 3L.
We know (by assumption) that -7-7- > 0 and E [ —~ ] >0. The third
dM. dM.
J 1
term on the right-hand side of the expressions given in (19) above are
the covariances between the marginal utility of profits and the mar¬
ginal default loss divided by the expectation of the marginal utility
of profits. The denominators of these terms are assumed to be always
positive (i.e., U is assumed to increase monotonically) so the signs
depend upon the signs of the covariance terms in the numerators. If
the lender is risk averse, U (tt .) will be concave as in Figure 4.1.
Figure 4.1 Utility of Profits Function for a Risk Averse
Lender

74
Then, under the assumption that lenders are risk averse, the covariance
terms in the expression given in (19) will be positive. This is be¬
cause the marginal utility of profit will, under this assumption, vary
inversely with the level of profit which will itself vary inversely
with marginal default loss. That is, as marginal default loss rises
profits will, pcUU-buó, fall and the marginal utility of profits
will rise. Therefore, under the assumption that mortgage lenders are
risk averse, the final term on the right-hand side of the expression
given in (19) above is positive and is added to the other two (positive)
9
terms on that side. These terms may be interpreted as the risk pre¬
miums (Pratt, 1964) required by mortgage lenders to originate loans in
each of the k classes. Denoting these risk premiums by P^ , equation
(19) becomes
(20)
dC. 3L.
+ v
1 J
3 =1, •••, k
9L.
Recall that we are intrepreting E as the lender's expecta-
i
tion of default loss on the individual mortgage loan being considered
dC.
for origination and â–  as the costs of making funds available for this
dM.
3
loan. Therefore, equation (20) states that the total interest charge
on the individual loan in each quality class must equal the marginal
Note that the assumption that U (irj) is concave is crucial to
this result. If lenders were risk neutral, U (tt^) would be linear and
cov [
0,
so that the third term in expression (19) would disappear. Also, if
lenders were risk lovers, U (tj) would be convex, and by an argument
similar to the one above,
cov [
3L.
3M.
1
< 0.

75
non-default costs of providing the funds plus the expectation of de¬
fault loss on the loan plus some positive risk premium that depends
upon these default losses and the lender's degree of risk aversion. In
the absence of default insurance if the borrower is unwilling to pay
this amount, then the loan (with the given terms for class j loans)
will not be originated.
Now, we relax the assumption that default insurance is not availa¬
ble and replace it with the assumption that such insurance is available,
where this insurance provides the lender with b (100) percent coverage
against default loss (0 _< b _< 1). The price per percentage unit of
coverage is assumed to be p so that the cost of providing a b (100)
percent level of coverage is pb (100). Since such coverage directly
reduces the default risk faced by the lender, provision of a b (100)
percent level of coverage by the borrower will reduce the interest
charges on a loan of the j1”*1 class to
dC. 3L.
(21) r - —■ + (1 - b) E [ ] + (1 - b) P ,
j j
j = 1, ..., k
And including the insurance cost of providing this level of coverage,
we obtain the total price for insured mortgage funds of the j^ class
as
T, dC. 3L.
(22) rj = jm1 + (1 - b) E [-^ ] + (1 - b) P. + pb (100) ,
^ j j J
j = 1, .... k
The decision faced by the potential borrower of a class j loan,
X'
then, is whether to insure the loan and pay r. or borrow the funds

76
without insurance coverage and pay r^ . Obviously, it will be to the
borrower's advantage to provide default coverage on the loan if"^
(23)
I'
r. < r.
J 3
3 = 1,
k
Substituting equations (20) and (22) into the inequality in (23) gives
us the result that the loan will be insured whenever the following
condition is met
3L.
(24) p (100) < E [^ ] + P. , 3 = 1, • • • , k
3 2
Obviously, if all insurance coverage were priced at the actuarially
3L.
fair rate with no loading factor (i.e., p (100) = E [ —-p- ] ), then all
oM.
3
loans originated with risk averse lenders (P > 0) would be insured.
As discussed in Chapter II, however, all four sources of default
insurance coverage (Section 203, VA, private firms, and FHA subsidy
programs) provide a fixed coverage at a fixed price so that actuarial
fairness is not attained under any of the available plans. In such a
situation, p and b are given and the probability that condition (24)
3L.
will be met will depend upon the size of E [ ] and Pj. Since, from
3 3Lj
the preceding section of this chapter, we know that E [— ] is an
oM.
3
increasing function of the loan-to-value ratio and term to maturity on
the marginal loan being negotiated, then for a given P , it is the
level of these terms that will determine whether the loan will be in¬
sured or not. Higher loan-to-value ratios and longer terms to maturity
increase the probability that for any given insurance plan, condition
Notice that, under our assumption that mortgage markets are com¬
petitive, it makes no difference in the outcome which party pays the
insurance premium (borrower or lender).

77
(24) will be met. Also, it is obvious from this condition that the
probability that the loan will be insured will decrease with increases
in the price per unit of insurance coverage.
3L.
Finally, if we allow p to vary, hold E [ ] and P. fixed, and
j J
sum the individual demands for coverage, we obtain the market demand
for default insurance. Given the conclusions reached in the previous
paragraph, we may expect this market demand to be a decreasing function
3L.
of p. Also, if we allow for variations in E [-rrp- ] through like varia-
oM.
J
tions in the loan-to-value ratio and term to maturity, then we may
expect these factors to induce shifts in the market demand for default
insurance coverage with increases in these terms leading to outward
shifts in this demand. We turn now to the supply side of the default
insurance market.
The Supply of Default Insurance Coverage
Default insurance on home mortgages, like most service goods,
differs from the standard manufactured good in that the product itself
(the insurance contract) is not "produced" until a mutually agreeable
price has been settled upon by the purchaser and the supplier of the
insurance coverage. Consequently, inventories of insurance contracts
cannot exist, and the quantity of insurance produced and consumed must
be equal in every period of time. An excess demand in the 2.X. ante.
sense, however, may exist at the quoted premium rate; and, when this
occurs, the service can be expected to be rationed on the basis of the
perceived degree of underwriting risk exhibited by individual insurance
applications (if, of course, the supplier of insurance coverage is
profit-motivated). Thus, the underwriting procedure employed in the

78
provision of insurance coverage may be used as a rationing device, and
the extent to which it is being used as such may be inferred from the
number of insurance applications that are denied coverage. The amount
of rationing that must take place through the underwriting process,
however, can be seen to depend upon the pricing structure adopted by
the insurance firm in marketing its product.
If this pricing structure consists of multiple premium rates, then
the underwriting process may be used to classify individual applicants
into the various risk categories for which these premiums are intended.
This combination of pricing and underwriting is employed in the pro¬
vision of many types of insurance (health, auto, life, etc.). With
such a multiple rate premium structure, the underwriting process trans¬
lates applicants' risks into premium rates and only serves as a ration¬
ing device for those exhibiting risks that cannot be covered by the
highest premium rate class. Such risks are then denied coverage at
existing rates and are, thereby, frustrated in their attempt to obtain
insurance by non-price rationing of the service.
It is theoretically possible to eliminate rationing through the
underwriting process by allowing the number of risk classes enumerated
to approach the number of insurance applications. In this situation,
the risk that is determined through underwriting is translated into a
price for coverage for every applicant. The individual applicant is
then free to decide whether the coverage is worth the price and he is
not denied coverage outright. With such a pricing structure, the in¬
surance service would be provided at exactly actuarially fair rates
(defined above). Such precise pricing, however, would be very unlikely
to occur in practice because the costs involved in attempting to predict

79
expected claims in the underwriting process soon outweighs the benefits
of greater enumeration of risk classes. At some number of classes
(that is usually considerably lower than the number of applicants) it
becomes cheaper to ration the service on non-price grounds than it
would be to create more classes and prices. Therefore, information
costs generally limit the degree of risk-rating that is feasible in
practice.
At the opposite extreme, there may exist only one price and one
category (those deemed eligible for insurance) offered by the supplier
of insurance coverage. As mentioned in the preceding section and in
Chapter II, it is this latter extreme that describes the supply mecha¬
nism employed by all four participants in the default insurance market.
Under each of the insurance plans available, a single price is quoted
and individual applicants are either qualified or disqualified on the
basis of certain criteria. Therefore, under none of the plans is the
individual loan's expected default loss translated directly into a
price for insurance coverage. With only one category of eligible
applicants, additional insurance coverage may not be called forth under
any of the four plans by ineligible applicants who are willing to pay
higher premium rates. Therefore, the quantity of insurance supplied
under any of these plans does not rise with the premium rate, and each
plan's supply schedule will be infinitely price elastic at the quoted
rate.
Such pricing behavior would not be observed in a competitive
market composed entirely of profit motivated suppliers of insurance
coverage. It is, however, observed in the default insurance market and
may be explained in the following manner. First, none of the three

80
federal government suppliers of coverage in this market attempt to
maximize profits. The VA and the FHA subsidy programs have, as their
explicit objective, the subsidization of the financing costs of parti¬
cular groups of mortgagors (veterans and low-income families). The
Section 203 program is constrained by its enabling legislation to
charge a single price for all coverage provided (Chapter II above),
and it is intended only to attain actuarial soundness (which, combined
with the single rate premium structure, implies average cost pricing
behavior). Then, the private firms in the market, which must be as¬
sumed to be profit motivated, are constrained in their pricing and
supply behavior by the activities of these federal government programs.
Specifically, they must price their service within the interval between
the premium rates quoted on these programs (0.5 percent per annum of
the outstanding mortgage balance for the Section 203 program and zero
for the VA and FHA subsidy programs). Any price equal to or below the
lower bound of this interval would, obviously, require that negative
profits be earned (i.e., the insurance service would require
subsidization). And, any price that is above the upper bound would
result in a zero (or near-zero) volume of insurance written since mort¬
gagors would generally be able to obtain the coverage that the lender
requires for a loan of given terms at a lower price from the Section
203 program. Within this interval, one might expect that competition
among the private firms themselves would, in the long run, force some
differentiation of risk classes. As noted above, however, the actual
number of classes that may be distinguished is limited by the ability
of these firms to separate individual risks on an (LX ante, basis, i.e.,
by the ability to accurately predict expected default losses on

81
individual mortgages. Within the relevant price interval, such separa¬
tion of risks may be extremely difficult. Also, the private mortgage
insurance industry is still in the early stages of development, and
competitive pressures within the industry have only recently begun to
materialize. It should be noted, however, that some initial signs of
risk rating within the 0 to 0.5 premium rate interval have emerged
within the last few years (Little, 1975). But, given the very recent
nature of this development, we may safely ignore price variations within
the private mortgage insurance industry in our analysis. In the long
run, this single-rate assumption for the private firms in the market
may become invalid as the industry grows, as intraindustry competition
increases, and as predictive capabilities are improved through accumu¬
lated actuarial experience. In this regard, the short run character of
the model becomes apparent.
Given the prices at which coverage is provided under the four de¬
fault insurance plans, the market supply curves for the individual
participants will appear as in Figure 4.2.
Price (%)
Supply (Section 203)
Supply (Private)
Supply (VA and subsidy)
0 Quantity ($)
Figure 4.2. Supply Curves of Individual Default Insurance
Market Participants
0.50
0.25

82
The price of coverage under the different insurance plans is given
on the ordinate: one-half percent per annum of the unpaid balance for
the Section 203 program; one-quarter percent for the private firms; and
zero for the VA and subsidy programs of FHA. The quantity is given on
the abscissa: the number of dollars insured against default.
Obviously, if the four types of coverage were homogeneous and the above
supply schedules operative, the VA and FHA subsidy programs would usurp
the entire default insurance market. The fact that this event has not
been forthcoming may be explained by observing that these two programs
are operated under rather severe supply constraints. The VA program is
constrained by the number of eligible veterans that choose to purchase
a house in the given period, and the FHA subsidy programs are con¬
strained by the number of low-income families choosing to purchase a
house in the given period and (probably more severely) by the funding
level authorized for the programs. Given these supply constraints, the
VA and FHA subsidy programs insurance services must be rationed accord¬
ing to the prior military service and the family income of individual
applicants. Consequently, a condition of excess demand should exist
for these forms of insurance coverage in all periods.
Also, if we are dealing with the market for default insurance
coverage for the nation as a whole, we might also expect the supply of
private mortgage insurance to be subject to a constraint. This expecta¬
tion stems from two basic considerations. First, over the period with
which we are concerned, there have been constraints of an institutional
nature placed upon the quantity of insurance that these firms are al¬
lowed to write. These constraints include state prohibitions against
the marketing of private mortgage insurance which have been effective

83
until 1973 when the last state forbidding such insurance (New York)
relaxed its prohibition against these firms; and state regulations that
limit the growth of the contingent liabilities of these firms by stipu¬
lation of a maximum ratio between liabilities and reserves,^ And
second, given the rather narrow interval within which these firms are
forced to price their insurance services (discussed above), they will
be unable to write coverage profitably on the higher risk loans. They
will, therefore, ration their services on the basis of the underwriting
risk exhibited by individual loans, and we may expect a situation of
12
excess demand to exist for the coverage that they provide.
Additionally,, we must recognize that the services provided under
the various insurance plans that are available is not homogeneous.
Basic differences in coverage, financing terms, mortgage limits, etc.,
that were detailed in Chapter II serve to differentiate the four kinds
of insurance. It, therefore, becomes necessary to view the default in¬
surance market as consisting of four sub-markets of substitute insur¬
ance products, where three of these sub-markets are characterized by
conditions of excess demand.
Then, ignoring the subsidy programs and VA for graphical conveni¬
ence (their treatment would parallel that of the private firms below),
In the long run, such constraints may be expected to disappear
as the private firms in the industry lobby to have state prohibitions
relaxed and as contingency reserves accumulate. But, over the period
of the 1960's and early 1970's, these supply constraints do appear to
have been effective.
12
Mathematically, one could write the profit function of a mort¬
gage insurance firm as the difference between premium income and ex¬
pected claims. Then, the problem of the private mortgage insurance
firm would be maximize the value of this function subject to both price
and quantity inequality constraints.

84
we can depict the market for default insurance as two inter-related
markets as in Figure 4.3. Then, assuming that the supply constraints
in the non-Section 203 markets are effective, the demand for Section
203 insurance (which in the absence of supply constraints under this
program will determine the quantity of Section 203 insurance written)
will be influenced by the quantity of default insurance written by the
alternative suppliers of default coverage. In Figure 4.3, the excess
P P
demand existing in the private market (Q^ - Q ) with the given supply
constraint will, to some extent, be channelled into the market for
Section 203 coverage, thereby raising the level of demand in that
market. If the two forms of insurance were perfect substitutes (i.e.,
if the coverage provided were homogeneous) then the demand for Section
203 insurance would be given by the horizontal distance AB in the graph.
They are not, however, perfect substitutes for reasons mentioned
above; and, as a result, we are unable to deduce the quantitative rela¬
tionship between the excess demand for private insurance and the level
of demand for Section 203. But, as is obvious from Figure 4.3, an in¬
creased supply of the rationed (constrained) insurance will result in
a decrease in the excess demand in that market (holding the level of
demand constant) and, mLitcubU, mcutandti, a decrease in the demand for
Section 203 coverage. Thus, a partial relaxation of the supply con-
P' p p'
straint to Q reduces excess demand in the private market to Q - Q
o U S
and the demand for Section 203 insurance at the existing price falls to
Indeed, it has been shown that the effect of a change in the
rationed quantity of any good on the demand for an unrationed related
good will be proportional to the substitution effect of a change in the

Private Market
Section 203 Market
Price (%)
Figure 4.3. The Relationship Between Private Market Supply Constraints and Section 203 Demand in the
Default Insurance Market

86
price of the unrationed good on the demand for the rationed good in a
free market (Tobin and Houthakker, 1951; Houthakker, 1961, pp. 714-715).
This means that if the two goods are substitutes, then an increase in
the quantity of the rationed good will reduce the demand for the un¬
rationed good, as is pictured in Figure 4.3.
Obviously, since the price of insurance coverage under each of the
four sources of supply has remained constant throughout time in both
absolute and relative terms, it will be impossible to directly measure
the own price elasticity of demand or the cross price elasticities of
demand for the different types of coverage. Any empirical analysis of
the default insurance market will, of course, implicitly contain the
effect of own prices, but such effect will, due to the complete lack of
variation, be imbedded in the constant term of the regression equations.
Also, because of the effect stated above, the cross price elasticities
of demand will be imbedded in the coefficients of the rationed
quantities. It is of interest to note, however, the effect that changes
in the number of related rationed goods will exert on the own-price sub¬
stitution effect of the unrationed good. Samuelson (1947) has shown
that the own-price substitution effect for the unrationed good will be
larger in absolute value as the number of rationed goods is reduced.
This result is referred to as the principle of Le Chatelier because of
its analagous relationship with the theorem employed in thermodynamics
(Samuelson, 1947, p. 38, footnote 13). As Samuelson points out, this
principle provides an exact basis for the classic distinction elaborated
by Marshall between the long run and the short run (Houthakker, 1961,
p. 715; Samuelson, 1947, pp. 36-46). Since excess demand must equal
zero in the long run, no rationing occurs and own-price substitution

87
effects will be larger. Thus, at a given level of consumption, price
elasticities of demand will be larger in absolute value in the long run
than they are in the short run. With regard to the Section 203 program,
this result implies that as rationing in the default insurance market
is eliminated over time (through, for example, relaxation of legal con¬
straints on the private firms in the market) the demand for insurance
coverage under this program can be expected to become more price
sensitive.
We now summarize the important findings contained in this chapter
and relate them to the decline in insurance activity under the Section
203 program.
Summary: Basic Theory of Decline
The model that has been developed in the preceding sections con¬
tains several theoretical implications that provide a basic framework
for analyzing the operation of the default insurance market over the
post-war period and particularly for examining the causal forces behind
the decline in insurance activity under FHA's Section 203 program.
This framework will be adopted in the following chapters as the basis
for an empirical model designed to yield inferences about the causes of
this decline. The model will, of course, serve to both test the theo¬
retical framework and provide empirical evidence of the quantitative
impact of the various factors implied by the theory.
The first major implication emanating from the above theory is that
total default insurance market activity is primarily determined by the
level of demand for such insurance. This result stems from the single
price supply mechanism employed by all participants in the market which

88
leads to individual program supply curves that are infinitely price
elastic up to the point at which supply constraints become effective.
Some influence on total insurance market volume may, of course be
exerted by fluctuations in the level of these constraints; but to the
extent that Section 203 coverage serves as a substitute for the cover¬
age provided by other (supply constrained) participants in the market,
such fluctuations will only affect the distribution of insurance market
activity among these participants and will not affect the total volume
of insurance written. To the extent, however, that Section 203 does
not serve as a workable substitute for the other forms of coverage
offered in the market, variations in the level of the supply constraints
imposed on these other participants will influence the observed quantity
of total insurance written. But, since these constraints are not
altered in response to market conditions but, instead, fluctuate with
legal and other institutional changes (such as the number of veterans
leaving the armed services), they may be considered as exogenous.
Therefore, the estimation of an empirical behavioral relationship with
total insurance volume as the dependent variable will not encounter the
usual simultaneous equation problems confronted in most market analyses,
and such a relationship may be interpreted as a demand equation with
(as mentioned above) the price term implicit in the constant.
Also, the above theory implies that total default insurance market
demand will be an increasing function of the overall level of activity
in the mortgage market since the demand for default coverage is derived
from the demand for and supply of mortgage funds under conditions of
default uncertainity. Obviously, if more mortgages are originated,
then, caíeAxA pcUvibtxA, more insurance will be demanded at the existing

89
premium rate since market demand is given by a simple summation across
individuals who find it optimal to insure their loans (where the essen¬
tially binary decision to insure is governed by whether or not condition
(24) is met for each loan). Also, the level of the financing terms that
are available on insured mortgages will exert an influence on this total
demand. For a given volume of mortgage originations, a larger propor¬
tion will be insured (i.e., condition (24) will be met for more of the
given total) the higher is the loan-to-value ratio and term to maturity
on the loans deemed eligible for insurance. Consequently, total market
demand will be an increasing function of overall mortgage market
activity and the level of financing terms available on insured loans.
More important for our basic purposes in this study, however, are
the implications of the theoretical model for the Section 203 insurance
program. First, the theory implies that the volume of insurance writ¬
ten under this program is completely demand-dependent. Any observed
variations in activity under the program must be generated through
shifts in the demand schedule for Section 203 coverage. Therefore, we
must look to factors that create such demand shifts in order to explain
the movements in Section 203 insurance volume over time (i.e., to ex¬
plain the decline). Since such an explanation is the primary purpose
of this study, most of the remaining efforts will be directed at
investigating these factors.
The theory developed above contains several important implications
concerning the factors that are likely to have led to these demand
shifts. Three basic sets of factors are implied. Given some degree of
substitutability between Section 203 insurance coverage and the cover¬
age provided by alternative suppliers, the demand for the former will

90
be an increasing function of the excess demand for the latter. This,
in turn, implies two sets of factors that can be expected to influence
the level of demand for Section 203 coverage. First, the overall level
of housing and mortgage market activity will directly influence the
level of demand under this program since increases in the total demand
for default insurance will be fed (either directly or indirectly) into
this demand schedule. Increases in total demand will raise the demand
for all forms of coverage; and, with supply constraints on the VA,
private, and subsidy programs, the Section 203 demand will, a. {¡omtLohÁ.,
increase. And second, inverse demand shifts for Section 203 coverage
may be expected to occur with fluctuations in the level of the supply
constraints imposed on these alternative programs. As these 'con¬
straints are relaxed, the volume of insurance written by these suppliers
of default coverage will increase, the excess demand existing in their
related markets will be reduced, and the demand for Section 203 will
decline. And third, the demand for Section 203 coverage will depend
upon the level of financing terms available on mortgages insured under
this program relative to the terms available on insured loans elsewhere
in the market. Since the coverage provided and price charged for
Section 203 insurance are above those of alternative suppliers of de¬
fault coverage, the risks insured should be expected to be higher under
this program. Assume an individual loan exists that is not eligible
for insurance under the VA or subsidy programs. Assume further that
condition (24) is met for both Section 203 and private coverage. Then,
since the net savings on the loan that is obtained by providing default
coverage is equal to the amount by which the right-hand side of (24)
exceeds the left-hand side, the individual will select the type of

91
coverage that is desired on the basis of a comparison between the level
of risk that is acceptable to the two insurers in relation to the
prices charged for coverage. Given these prices, he will select the
type of coverage that yields the largest difference between price and
risk (where risk is defined here as the sum of expected default loss
and risk premium on the loan). And, the likelihood that this differ¬
ence will be greater for Section 203 coverage is increased as the risks
acceptable for insurance under this program are increased relative to
the risks under the alternative source of coverage. Therefore, the
more liberal Section 203 terms become (i.e., the higher the loan-to-
value ratio and term to maturity) relative to the rest of the market,
the greater will be the demand for insurance coverage under this
program.
Adopting this theoretical framework, we are now in a position to
begin specification of an empirical model of the default insurance
market that may provide useful insights concerning the post-war opera¬
tion of this market and the decline of FHA's basic single-family unsub¬
sidized program. Given the nature of this market (with three of the
four participants' insurance volumes being determined primarily by
variations in the level of their respective supply constraints), the
availability and quality of the relevant data (alluded to in Chapter II),
and the current level of federal interest in FHA, particular attention
will be devoted to that portion of the model that relates to Section
203 insurance volume.

CHAPTER V
THE EMPIRICAL MODEL: SPECIFICATION
Introduction and Overview of the Empirical Model
The empirical model that is developed in the remaining chapters of
this study utilizes the theoretical framework of the preceding chapter
to specify a set of structural equations that, together, determine the
total default insurance market activity and allocate this total to the
various participants in that market. The model contains six behavioral
equations and one identity. Because of the nature of the theoretical
model, however, these equations are, for the most part, non-simultaneous.
This results from the assumption that the supply constraints determining
non-Section 203 insurance volumes are effective over the entire sample
period. This assumption constitutes a fundamental maintained hypothesis
throughout the analysis; and as a result, simultaneity between the in¬
surance volumes of the various participants in the market is not incor¬
porated in the model.
Separate equations are specified for the following dependent
variables: total market volume; VA volume; private volume; Section 203
volume on new units; Section 203 volume on existing units; and Section
203 processing time. This final equation is specified to explicitly
account for simultaneity between Section 203 volume and processing time
and also to investigate certain hypotheses concerning the factors that
determine this processing time. The first three of these equations
92

93
contain no right-hand endogenous variables while the last three do con¬
tain such variables. The addition of a simple identity to account for
the volume of insurance activity under the FHA subsidy programs, then,
serves to complete the model's description of the default insurance
market for single-family mortgages. Consequently, this entire market
and all four sub-markets are accounted for by the model and, as a re¬
sult, individual program market shares are implicitly explained.
The basic results that may be expected to flow from this model
fall logically into two broad categories. First, conclusions should
emanate concerning the overall functioning of the default insurance
market, including those factors that operate to determine the total
activity in this market and those factors that allocate this total
among the various sub-markets that are present. And second, a defini¬
tive explanation of the Section 203 decline should be forthcoming from
this model, thereby facilitating (but by no means assuring) rational
policy reactions on the part of federal decision-makers concerned with
this program. We now specify the equations that constitute the empiri¬
cal model and relate them to the theoretical model that has been
developed.
Equation 1: Total Market Volume
The first equation in the model determines total default insurance
market activity (i.e., the sum of the insurance volumes written by VA,
private firms, Section 203, and FHA subsidy programs). This equation
provides the principal connecting link from the housing market and
mortgage market sectors to the default insurance market sector that is
described by the model. Also, the view that the demand for default

94
coverage is, in general, derived (recursively) from the demand for
mortgage funds is made explicit in this equation, and we are able to
allow activities in the housing and mortgage markets to exert a direct
influence on the default insurance market.
From the theory developed in Chapter IV, the total market volume
is determined by the level of demand for default insurance (which,
itself, depends upon the number of mortgages originated and the financ¬
ing terms applied to these originations) and the level of the supply
constraints imposed on the non-Section 203 participants in the market.
Therefore, we first specify the total volume of mortgage insurance
written as an increasing function of mortgage originations. Since the
insurance contract cannot be written unless the loan to be insured is
originated, we specify the relationship between originations and insur¬
ance with no constant term. Thus, the hypothesis is that some portion
of originations are insured in the given period, i.e., that
(la) TOT = F1 1 (ORIG)
where we expect the coefficient F^ ^ to be greater than zero and where
the variables in this equation are defined as:
TOT = the total number of single-family units insured.
it is defined in our model as the sum of the single¬
family insurance volumes of FHA (Section 203 plus
subsidy program volumes), VA, and the private firms
in the market; and
ORIG = total single-family mortgage originations, both
insured and uninsured, in millions of 1971 dollars.
It is assumed that these are given exogenously to
the mortgage default insurance market by the out¬
come of a simultaneous process operating in the
housing and mortgage markets.
Now, from the theoretical model, we hypothesize that the propor¬
tion of total mortgage originations that are insured, F , is an

95
increasing stochastic function of the loan-to-value ratio and term to
maturity on all insured mortgages, and the exogenous factors that deter¬
mine the level of the supply constraints imposed on the VA, subsidy
programs, and private insurance volumes. For the loan-to-value ratio
and term to maturity series, we would ideally employ weighted averages
of the terms offered on all insured mortgages; but, since no data exist
on the terms offered on privately insured loans, we adopt the simple
averages for those insured under Section 203. Since, in general, the
terms offered under the VA and FHA subsidy programs are more liberal
(i.e., higher loan-to-value ratios and term to maturities) and the
terms offered on privately insured mortgages are less liberal than
those under the Section 203 program, these series should approximate
the terms available on all insured loans fairly well. The exogenous
variable used to determine the level of the supply constraint for VA
guaranteed loans is the number of veterans eligible for such loans.
For the subsidy program supply constraint, we adopt a simple binary
variable that is equal to one over the 1968-1971 period during which
the greatest funding for these programs was authorized. And finally,
in order to determine the level of the supply constraint imposed on the
private firms in the market, an index that measures the degree of
availability of private mortgage insurance in the national market was
constructed. It is defined as
50
PMIA = E d. w.
. , li
where

96
and
d.
i
before private insurance became available in
state i
after private insurance became available in
state i
w. = a weighting factor equal to the number of single¬
family housing units in state i divided by the
total number of single-family housing units in
the U.S. in 1970.
Thus, this availability index varies from zero (before 1957 when pri¬
vate mortgage insurance was completely unavailable) to one (after the
third quarter of 1973 when private mortgage insurance became available
. 1
in all states).
Thus, we specify the following relationship:
(lb)
Fl.l
—
b1 Q + b1 L (LFHA) + b1 2 (TFHA) + bx 3 (VET)
+ b1 4 (SD) + b1 5 (PMIA) + el
where
the variables in the equation are defined as:
LFHA
=
average loan-to-value ratio on Section 203 in¬
sured loans;
TFHA
=
average term to maturity on Section 203 insured
loans:
VET
=
number of veterans eligible for VA loan
guarantees;
SD
=
a dummy variable that is equal to one over the
1968-1971 period and is equal to zero otherwise
PM IA
=
private mortgage insurance availability index
(defined above); and
61
=
a random variable.
This index was suggested by Fred Eggers of the U.S. Department of
Housing and Urban Development.

97
Substituting (lb) into (la) and dividing by ORIG yields our estimating
equation as:
(lc) TOT/ORIG = b o + b (LFHA) + b± 2 (TFHA) + b ' (VET)
+ b . (SD) + b, c (PMIA) + e
1.4 1.5 1
which may be fit using single equation estimation techniques,
c The hypotheses that are implied by the theoretical model are that
b q, . . . , b^ j. will all be positive. The logical basis from which
these hypotheses stem is that increases in mortgage originations will
generally result in increases in the demand for mortgage insurance
which, in turn, results in increases in the volume of insurance written
(b^ o > 0). The proportion of the additional originations that are
insured, F^ increases with more liberal terms on insured loans
(b^ ^ > 0 and b^ ^ > 0) and with increases in the level of supply con¬
straints imposed on non-Section 203 participants in the default insur¬
ance market (b^ > 0, b^ ^ > 0, and b^ > 0). Finally, F^ is a
random coefficient that varies over the sample and, as a result, was
not tested statistically. It should, however, remain positive over all
observations (i.e., an increase in originations should never decrease
the demand for insurance).
Equation 2: VA Insurance Volume
The number of mortgage guarantees issued by the Veterans Adminis¬
tration in any given period does not adjust to the market demand for
the service provided at the price charged (as noted above, this price
is essentially zero). Instead, the supply of these guarantees is
constrained by the number of veterans that are eligible by law for

98
such guarantees. Therefore, the number of eligible veterans consti¬
tutes the supply constraint that is effective in the VA sub-market, and
the volume of guarantee activity in this sub-market will be determined
solely by movements in this constraint. Thus, we specify the following
equation for VA volume:
(2) VA = b2>Q + b2 1 (VET) + e2
where
VA = the number of single-family mortgage guarantees
issued by the Veterans Administration in the
given period, and
e2 = a random variable.
VET was previously defined, and b2 and b^ ^ are the parameters to be
estimated.
The only hypothesis regarding this equation is that b2 will be
greater than zero, i.e., that increases in the number of veterans
eligible for VA guarantees will result in increases in the number of
guarantees issued. Since VET is determined by influences that are
exogenous to the model, the variations in this supply constraint are
exogenous and a single equation (non-simultaneous) estimation technique
is appropriate.
Equation3: Private Mortgage Insurance Volume
Like the VA sub-market, the private default insurance sub-market
is assumed to be characterized by a condition of excess demand at the
price quoted. Supply constraints have forbidden these firms from meet¬
ing the entire demand at this price and, as a result, variations in the
observed quantity of insurance written by the private firms has been

99
completely dependent upon their capacity to increase insurance volume
in the national market. As mentioned in Chapter II, such capacity has
been constrained over our sample period by two major factors. First,
legal prohibitions in the various states have constrained the capacity
of these firms to expand output. Until 1957, this constraint was con¬
stant at a zero level of output because private mortgage insurance was
forbidden in all states. Since that time, these prohibitions have been
gradually relaxed with the last state (New York) allowing these firms
to enter in 1973. And second, the capacity of the private mortgage in¬
surance industry to expand output has been constrained by their ability
to accumulate the contingency reserves required to write additional
policies (the requirement in most states is a 25 to 1 ratio between in¬
surance liability and reserves). Together, these two factors have op¬
erated to determine the private firms' capacity to write new policies
and meet the excess demand for the coverage that they provide.
In attempting to specify a behavioral equation to determine the
insurance volume written by the private firms in this sub-market, then,
we have only to determine the movements of the supply constraint faced
by these firms over time. To do this, we employ the private mortgage
insurance availability index, PMIA, described above. We do not,
however, have data on the contingency reserves of the private firms in
the market. Since these reserves are generally accumulated over time
as the firm or firms carry out business in a given state, we hypothesize
that the response of private mortgage insurance volume to an increase in
the availability index is characterized by a distributed lag structure.
Specifically, we postulate that the effect of legal availability on in¬
surance volume will build up over a number of quarters as private firms

100
complete the necessary applications to carry out business, set up in¬
suring offices within the state, and begin to accumulate contingency
reserves. Then, the effect of an increase in the availability index
should decline beyond a certain number of quarters as a sufficient
number of firms enter and a sufficient volume of insurance becomes
feasible to reduce the excess demand in the particular state. In no
quarter, however, should an increase in availability lead to a decline
in private insurance volume, so the coefficients of the distributed lag
structure should remain positive.
These considerations led to the adoption of a second degree poly¬
nomial distributed lag structure of the Almon variety. Some experi¬
mentation with the length of time over which the lagged effect takes
place led to the use of a twelve quarter response period. No con¬
straints were imposed on the first or last period coefficients.
Therefore, the specification adopted for the private mortgage insurance
equation is given by:
(3) PMI = b3fl+b31 (PMIA) + b3 2 (PMIA1) + ...
+ b3 (PMIA11) + e3
where we require that
(3a) b3 i = a + 6 (i) + 6 (i)^ for i = 1, ..., 12
and where
PMI = the number of single-family units insured by the
private mortgage insurance industry in the given
period;
PMIAi = the private mortgage insuarnce availability
index (defined previously) lagged i periods; and
a random variable.

101
The parameters . .. , ^ are t'ie coef ficients to be estimated
with b^ b^ 22 S:'-ven from estimation of a, B, and 6 from (3a)
above.
The hypotheses that stem from the discussion above are that
b^ • • • > b^ 22 be positive and that b^ ^ and b^ ^ will be
smaller in size than the coefficients that lie between them in the lag
structure, i.e., that
0 ' b3.1 •= b3.j * b3.12 ’ 0 for j - 2, .... 11
Finally, since the private mortgage insurance supply constraint is ex¬
ogenous to the model, no simultaneity problems arise in this equation.
Equation 4: Section 203
Insurance Volume on New Units
The empirical model employed in this study specifies separate
equations for Section 203 insurance volumes on new and existing units.
This separation of insurance volume by property type was specified for
two reasons. First, the observed decline in insurance activity has
been somewhat different for the two categories of property securing the
mortgage, with the decline beginning earlier and progressing more con¬
tinuously for insurance written on new units (see Chapter II). And
second, the marginal impact of variations in the explanatory variables
employed may differ depending upon the type of unit insured (perhaps
because of differences in sellers—builders versus owner occupants).
Therefore, the coefficients in these two equations may differ substan¬
tially, and separate estimation may be appropriate. As will become
evident later in the study, such separation does appear to have been
warranted.

102
As noted above, the theoretical model of the preceding chapter im¬
plies that Section 203 insurance volume is demand-dependent. Thus, the
Section 203 equations constitute demand equations where, due to the com¬
plete lack of variation in premium rates, the price terms are implicit
in the constant intercepts of the relationships specified. Other fac¬
tors that may be expected to affect the level of demand for Section 203
coverage that are implied by the theoretical model can be logically
grouped into three categories: the level of supply constraints imposed
on alternative suppliers of default insurance; the relative terms
available on Section 203 insured mortgages; and other product differ¬
entiating factors that may serve to shift the demand for coverage under
the Section 203 program. This section explores each of these categories
in some detail in order to arrive at the specification that will be
used in the estimation.
Supply Constraints on Alternative Sources of Default Coverage
The theory of Chapter IV implied that the demand for Section 203
insurance coverage would be inversely related to the actual level of
the supply constraints imposed on the VA, subsidy program, and private
insurance volumes because of the substitutability between the services
provided under these programs and that provided by Section 203. Given
our maintained hypothesis that the supply of insurance by these alter¬
native sources is constrained by exogenous (non-price) factors and that
these supply constraints have remained effective throughout the sample
period, the level of these constraints will be equal to the actual
volume of insurance written by these non-Section 203 participants in
their various sub-markets. Therefore, volumes observed under these

103
alternative insurance programs should bear an inverse relationship with
Section 203 demand, and each of these volumes should be included in the
Section 203 demand equations.
In addition to the simple substitutability issue between alterna¬
tive suppliers of default coverage, a particularly important question
arises regarding the insurance volume of the private firms in the market.
As was pointed out previously, the supply mechanism employed by Section
203 consists of the classification of mortgage insurance applicants into
a single eligible category to which a single price of insurance coverage
is quoted. There are fundamental, long-term problems created by such a
supply mechanism that will, over time, lead to a decrease in the volume
of business and an increase in the average claims rate experienced on
remaining business insured under Section 203. These effects arise from
the incentives created by this supply mechanism and the operation of an
2
increasingly competitive private market. They can be forestalled for
a period of time by product differentiation on the part of Section 203,
but (in the absence of legal prohibitions on entry into the industry)
they cannot be avoided indefinitely. The related phenomena of cream-
skimming and adverse selection give rise to these effects and could
possibly account for a large part of the problems presently being ex¬
perienced by FHA in the single-family unsubsidized market. The mecha¬
nism whereby Section 203's price structure gives rise to these phenomena
is the subject of this sub-section.
Since the payment of insurance claims on foreclosed properties is
one of the primary costs of carrying out a default insurance program,
2
This statement and the remainder of this sub-section draw heavily
from Mark Pauly (1970).

104
the probability of default and expected default loss on properties in¬
sured must affect the expected costs of providing insurance coverage.
Furthermore, since the probability of default and expected default loss
differ on individual mortgage contracts (varying with the financing
terms of the loan) the expected costs of providing a given level of
coverage must vary from one contract to another. Therefore, if the in¬
surance program is to be actuarially sound (as the FRA unsubsidized
program was intended to be) and a single price is to be charged on all
insurance written, then the price charged must be equal to the average
cost of providing coverage on all contracts written. This, in turn,
means that, paAÁbiii, mortgagors purchasing Section 203 insur¬
ance will be charged a premium rate that is higher (lower) than the
expected costs of providing the insurance service to them as the proba¬
bility of their defaulting and expected default loss is lower (higher)
than the average for all Section 203 insured loans. In other words,
the better (or preferred) risks within the FHA unsubsidized program
must pay insurance premiums that exceed the marginal costs of providing
coverage to them; and, conversely, the worse risks within this program
pay premiums that are less than marginal costs. In effect, the higher-
than-cost premiums of the preferred risks serve to offset the lower-
than cost premiums of the worse risks; therefore, an internal

105
cross-subsidization of insurance premiums takes place within the
3 4
Section 203 program.
This means of pricing the insurance service constitutes a form
of price discrimination.'’ The relative price of the insurance service is
distorted from that which would exist under pure competition and, as
a result, the distribution of the service among consumers will be
similarly distorted. A smaller than optimal volume of coverage will
be purchased by the better risks and a larger than optimal volume of
coverage will be purchased by the worse risks than that which would be
desirable from a welfare economics point of view (Pauly, 1970).
From the point of view of Section 203, such price discrimination
will, in the long run, lead to a loss of business and an increasing
average default rate on remaining business. Since many of FHA's
Notice that the direction of the subsidization that occurs needs
bear no particular relation to mortgagor income since a monotonic rela¬
tionship between income and default probability does not appear to
exist although the trend will be in favor of a progressive redistribu¬
tion (Aaron, 1972; von Furstenberg, 1970). Also, the size of the
subsidy is not subject to direct control by those designing or imple¬
menting the program, but rather, it depends upon the actual risks on
the insured loans. For these reasons, internal cross-subsidization
within an insurance program represents a highly inefficient means to
carry out the subsidy function (Pauly, 1970).
4
It should also be noted that the payment method employed by FHA
in collecting insurance premiums compounds this subsidization process.
By collecting premiums in monthly installments, defaulting mortgagors
are allowed to "default" on insurance premiums also. Therefore, those
mortgagors who do not default (who, by definition, are generally those
with a lower probability of default) must pay part of the premiums of
those mortgagors who do default in order for the insurance fund to be
actuarially sound. Payment of insurance premiums prior to the coverage
period is necessary to correct this form of cross-subsidization.
"*Price discrimination is defined as either the charging of differ¬
ent prices to different consumers for goods that cost the same amount
to produce or the charging of the same price to different consumers for
goods that cost different amounts to produce. The latter definition
describes the pricing policy of Section 203.

106
customers are forced to pay insurance premiums that exceed the costs
of providing the service to them, new firms will be attracted into the
mortgage insurance industry (as has been happening since the Mortgage
Grarantee Insurance Corporation entered in 1957) because it is prof¬
itable for them to offer these preferred risks a lower premium rate
per unit of insurance coverage. It is, obviously, preferable from the
point of view of these better risks to opt for this private insurance
unless the Section 203 coverage is differentiated sufficiently to
render private coverage an unacceptable substitute since the total cost
of securing the mortgage (interest charges plus insurance premium) is
lower with such insurance. The private coverage may not, itself, be
priced at the actuarially fair rates; but, for the preferred risk cus¬
tomers, the lower level of premiums offered represents a closer approxi¬
mation to such rates than that available under Section 203. Over time,
the competitive process should force rates in the private market toward
the actuarially fair levels.
This process of bidding away the preferred risk customers is known
as cream-skimming^ and should be expected to occur and continue as long
as two conditions co-exist: (1) some purchasers of default insurance
are paying more than the actuarially fair price for the insurance cov¬
erage; and (2) there is some operational mechanism by which these pre¬
ferred risks may be distinguished. In the mortgage insurance industry,
^Some very recent evidence of such an occurrence is found in Little
(1975). The private firms in the industry have begun to distinguish
multiple risk categories to which the price of coverage varies with risk.
^Purely on grounds of economic efficiency, the process of cream-
skimming is desirable since the very existence of the "cream" is an in¬
dication that a non-optimal pricing policy is being followed (Alfred E.
Kahn, 1971).

107
this process should not be expected to occur overnight; but rather, it
should proceed over time in an iterative fashion with the very best
(and most easily distinguished) risks being bid away first (perhaps
contracts on new units) and increasingly worse risks being bid away
later (perhaps contracts on existing units) as actuarial experience is
accumulated.
Also, the process of cream-skimming is limited by the capacity of
the private mortgage insurance industry to increase the volume of in¬
surance written, i.e., by the level of the supply constraints faced by
the private firms in the industry. As legal prohibitions have been
dropped and as reserves have grown, the volume of insurance written by
these firms has increased and the cream-skimming process has accelerated
apace. Thus, Section 203 should be expected to lose customers over
time as the private mortgage insurance industry grows and as competi¬
tion from and within this industry allows the better risks to obtain
their coverage at a lower price in the private market; and, the coeffi¬
cient for private firms' volume in the Section 203 demand equation may
be interpreted in terms of this process.
With regard to the effect of this process on the average default
rate (and thereby, the actuarial soundness of the single price being
charged) of Section 203 insurance loans, the outcome is obvious. The
private mortgage insurance industry will be unwilling to insure the
higher risk categories unless the actuarially fair price (or above) can
be charged for the provision of such insurance. But, since these cus¬
tomers are presently receiving their insurance at subsidized rates
(with the subsidy coming from the lower risk customers), it will be
impossible to bid them away by offering insurance at actuarially

108
fair rates. Therefore, the poor risk customers will remain within
the Section 203 insurance program and the average quality of the mort¬
gages within this program will decline as cream-skimming progresses.
This is the adverse selection that necessarily results from the proc¬
ess; and, eventually, it should necessitate an upward revision of the
price charged for Section 203 insurance if the single-price supply
g
mechanism is retained and insurance reserves are to remain positive.
Consequently, declining volume with rising claims rates can be seen to
be a direct result of FHA's failure to offer actuarially fair insurance
rates to individual customers.
This result, that appears to be inevitable in the long run, can be
temporarily forstalled by product differentiation efforts on the part
of Section 203. As we pointed out previously, the demand for Section
203 default insurance is affected by the relative terms available on
the loans insured under this program. These and other characteristics
serve to distinguish this insurance from private insurance and, hence,
can be manipulated in such a way as to counteract the effects of cream-
skimming on the part of the private firms by reducing substitutability
between the services provided. Such manipulations, however, can be ex¬
pected to be followed by similar adjustments in the characteristics of
loans insured in the private sector as firms in this sector seek to
Notice, however, that this new, higher premium rate will still
represent an average of the costs of providing coverage to remaining
Section 203 customers. Therefore, those who had previously paid pre¬
miums that were marginally below the actuarially fair rate may now be
forced to pay premiums that are above this rate; and consequently, it
now becomes profitable for the private firms to bid these customers
away. Ultimately, if Section 203 were to maintain its single price
supply mechanism and charge a premium rate sufficient to maintain
actuarial soundness, its business would be reduced to the very worse
risk customers at the margin between insurable and uninsurable risk.

109
attract the preferred risks from Section 203. Therefore, these adjust¬
ments cannot be effective in the long run. As long as the single price
supply mechanism is adhered to and as long as the price charged is suf¬
ficient to cover the costs incurred (i.e., no overall subsidization of
total insurance premiums occurs) such measures will have only temporary
effects—Section 203 will continue to lose business and experience in¬
creasing claims.
This hypothesis that cream-skimming has taken place in the default
insurance market and that such cream-skimming has been an important
contributing factor in the decline of the Section 203 program cannot be
tested directly without detailed data on the risk-related characteris¬
tics of privately and Section 203 insured loans. Such data is unavaila¬
ble at this time, so a direct test of this hypothesis cannot be carried
out. Two indirect tests, however, will be conducted that will help to
verify the legitimacy of this theoretical result. First, the inclusion
of private insurance volume in the Section 203 demand equations should
give an indication of the substitutability of this type of coverage for
that offered by the FHA program. A negative sign will, of course, indi¬
cate that substitution has occurred and, as a result, indirectly confirm
the cream-skimming hypothesis. And second, an additional test of this
hypothesis will be carried out by including private mortgage insurance
volume as an explanatory variable in a regression equation with the
Section 203 default rate as the dependent variable. Here, a positive
sign will provide additional confirmation (though still indirect) of
the cream-skimming hypothesis.

110
Relative Terms Available on Section 203 Insured Loans
From the theory presented in Chapter IV above, we may expect the
contract terms on Section 203 insured mortgages (these terms being the
loan-to-value ratio, term to maturity, and rate of interest) relative
to the terms on non-Section 203 insured loans to have an influence on
the volume of insurance written under Section 203. The rationale for
this expectation is that these terms influence the default risk on the
loan and, for a given price of insurance coverage, it is this risk that
determines the value of the insurance to the borrower (i.e., the size
of the interest savings cum insurance premium to be gained by insuring
the loan). The greater the risk an insurer is prepared to accept for a
given price, the greater is the savings to the borrower from purchasing
the insurance. Therefore, we may expect an alteration of any of the
contract terms on Section 203 insured loans relative to other loans
available in the market to influence the volume of Section 203 activity
as such alterations affect the relative attractiveness of these loans
from the borrower's point of view. Specifically, as the term to
maturity and loan to value ratio on Section 203 insured loans are in¬
creased relative to the term to maturity and loan-to-value ratio on non-
Section 203 loans, the demand for Section 203 insurance should increase.
Therefore, the empirical model will incorporate the difference between
the average Section 203 and conventional terms to maturity and loan-to-
value ratios for mortgages originated in the given quarter in the two
Section 203 demand equations. By the theory of Chapter IV, the a pfuiohA.
expectation regarding the signs of the coefficients of these variables
is that they will be positive.

Ill
With regard to the interest rate differential between conventional
and Section 203 insured loans, competition in the mortgage market (to
the extent that workable competition exists) should maintain a differ¬
ence approximately equal to the market's valuation of the differences
in risk on the two types of loan. This difference, then, can be thought
of as an interest rate risk premium (Pratt, 1964), and its size and
sign will depend upon this relative risk—which, in turn, will depend
upon the risk-related contract terms. If these terms were identical on
conventional and Section 203 insured loans, then the risk premium
should remain positive and fairly constant over time if both rates are
determined competitively (i.e., the Section 203 rate should be below
the conventional rate). This is because, C.&íe/L¿4 paAÁbuA, the lender's
risk exposure is always greater on conventional loans since they are
either uninsured or coinsured as opposed to the 100 percent coverage
offered under Section 203. The interest rate charged on FHA-insured
loans is, however, constrained by the regulated interest rate ceiling;
and, at times, the differential between the conventional and the FHA
interest rates may come to exceed the equilibrium risk-related
differential. The market's reaction to this situation is the payment
of points by the borrower to the lender of FHA-insured loans (Hood and
Kushner, 1971) to compensate for the unwarranted (by risk differences)
differential. Such points represent the payment to the lender for fore¬
gone interest earnings created by originating Section 203 insured loan.
If the point system works perfectly, the effective interest rate dif¬
ferential would be brought back into equilibrium and the departure of
the regulated rate from the market difference would not influence the
volume of FHA activity at all. Due primarily to legal and institutional

112
constraints, however, the point system may not function perfectly, and
the conventional-FHA differential may exceed the equilibrium value.
Since the FHA interest rate is not constrained in the downward direc¬
tion, the differential should never depart from the market-determined
equilibrium in the negative direction (i.e., the interest rate differ¬
ential should never fall below that dictated by the market's valuation
of the risk difference between the two types of loans). If we denote
the equilibrium risk-related differential by p, then
i - i > D
CON FHA - F
where i„^XT is the interest rate on conventional loans and i_„. is the
CON FHA
Section 203 effective interest rate (i.e., including points). Note
that p, itself, need not remain constant over time; but, instead, it
will vary as the risk-related terms on Section 203 insured loans change
in relation to conventional loans.
As long as the equality in the above relation holds, the differen¬
tial will not influence the demand for Section 203 insurance (although
the actual level of interest rates will, of course, affect the overall
quantity of mortgage funds demanded). But, when the inequality holds
due to imperfections in the point system, lenders will become unwilling
to originate FHA-insured loans, and the volume of insurance written
under the Section 203 program will fall. This means that we should ex¬
pect to obtain a negative sign when the differential between the con¬
ventional and the FHA effective interest rates is incorporated as an
explanatory variable in the Section 203 demand equations. This, along
with the preceeding expectations concerning the signs of the coefficients

113
on the other loan contract term differentials will be tested in the
empirical model of this study.
Other Factors that Serve to Differentiate the Section 203 Insurance
Service
In completing our specification of the Section 203 demand equa¬
tions, we add other factors that may serve to differentiate the Section
203 service in the default insurance market. For the most part, these
factors represent program requirements that are specific to Section 203
coverage and are expected to have reduced the demand for this form of
insurance. This sub-section describes these additional influences and
the variables that will be used to represent them and makes explicit
the hypothesized direction of impact on the demand for Section 203
insurance.
FHA mortgage limit
The nominal price of housing has, in general, tended to rise over
time. Mortgages eligible for Section 203 insurance are, however, con¬
strained by a legislated ceiling on the dollar amount insurable under
this program. This ceiling is adjusted from time to time by Congress
to reflect increases in housing prices. But, such increases are rela¬
tively infrequent (only five increases occurred from the second quarter
of 1952 to the second quarter of 1974). Therefore, the Section 203
insurance program constantly runs the risk that the proportion of all
mortgages falling above this ceiling will be increased through a gen¬
eral rise in housing prices that is unmatched by an increase in the
legislated ceiling. As this occurs, the demand for Section 203 insur¬
ance should, ce/tíe2t¿ó paSLÍbuA, decline.

114
In order to measure the effect of this factor, a variable will be
constructed that measures the difference between the Section 203 mort¬
gage limit and the average price of homes sold in the given quarter
(either new or existing depending upon which equation it enters). The
assumption here is that the distribution of housing prices about the
average remains reasonably constant over time (although the distribu¬
tion itself may move to the right as inflation increases all prices) so
that the simple difference between the Section 203 limit and this aver¬
age will reflect changes in the proportion of home sales falling within
the Section 203 limit. By the argument presented above, we should ex¬
pect a positive sign for the coefficient of this variable in the Section
203 demand equations.
FHA processing time
Once the mortgage origination process has begun and the insurance
decision is made, an application must be filed for approval by the
insurance supplier. In the private market, such approval is generally
completed within a day. Approval from FHA, however, may take longer
than this since additional red tape and requirements are placed on
these loans and, consequently, result in a slower processing of
applications. Such delays in issuing commitments to provide insurance
constitute a disincentive to purchase Section 203 insurance to both the
borrower and the lender; and, therefore, any increase in such delays
should result in a decrease in the volume of insurance written under
Section 203 (i.e., a leftward shift in the demand curve for Section 203
insurance).

115
In order to account for this influence in the regression equations,
we will include the percent of applications received by FHA that are
processed (i.e., on which a commitment is issued or rejected) within
three days. By the argument presented above, our hypothesis is that a
positive sign will result on the coefficient of this variable in the
Section 203 demand equations.
There are two basic problems introduced by using this measure as
an explanatory variable in the regression equation. The first—which
we can correct for—is the simultaneity between volume of activity and
processing time. As processing time rises, Section 203 loses business
and volume declines; but, with fewer applications to process, the time
required for processing should fall. Therefore, this variable is not
truly exogenous in the model. Such simultaneity will be corrected for
by utilizing a simultaneous estimation technique (two-stage least
squares will be employed). The second problem--which cannot be cor¬
rected for—is the imperfection with which this variable measures the
desired effect. In measuring the percent of cases processed within
three days, all applications that are incorrectly filled out are
excluded. In other words, processing time begins with the receipt of a
perfectly filled out application, but demand may respond to the diffi¬
culty in filling out such an application. This introduces the errors-
in-variables estimation problem and could result in a biased estimate
of the coefficient of processing time. Consequently, some qualifica¬
tions concerning this coefficient may be in order.

116
HUD reorganization
The reorganization of the Department of Housing and Urban Develop¬
ment in November, 1969, and the splitting of FHA's various functions
related to the provision of insurance (underwriting, property disposi¬
tion, legal services, etc.) could, quite possibly, have contributed to
the decline in Section 203 insurance volume (Bazan, 1974). However,
given the supply mechanism employed by FHA, this effect must (as
previously pointed out) have operated through a shift in the demand
schedule for Section 203 insurance. Given the timing of both the re¬
organization and the downward turn in Section 203 activity, one could
easily commit the fallacy of pOAt hoc CAgo ptioptCA hoc. That is, we
must take care not to attribute cause merely on the basis of temporal
ordering. We should, instead, inquire as to the mechanism through
which the reorganization could conceivably have influenced the demand
for Section 203 insurance.
This mechanism is primarily found in the length of time required
by FHA insuring offices to process applications which, in turn, influ¬
ences the demand for Section 203 insurance. If, as a direct result of
the reorganization, inefficiencies were generated within FHA that
caused increasing delays in processing applications, then we should (as
discussed earlier) expect an ensuing decline in the demand for Section
9
203 insurance. This effect is, consequently, already captured in our
9
Obviously, such inefficiencies may generate increases in the
costs of providing insurance (such as the efficiency with which acquired
properties are disposed of); but these should not, by themselves, affect
the demand for Section 203 insurance. They will, instead, affect the
actuarial soundness of the insurance fund and the overall adequacy of
the prescribed premium rate.

117
processing time variable discussed previously and will not require an
additional explanatory variable in the equations determining the volume
of Section 203 insurance activity. The empirical test of the reorgani¬
zation argument will come more directly through our specification and
estimation of the equation determining FHA processing time which is dis¬
cussed more fully later. In that equation, a binary variable will be
included to represent the reorganization. This variable will be de¬
fined to be zero prior to the reorganization and one after. So defined,
we should observe a negative sign for the coefficient of this variable
as reorganization contributes to processing delays which, in turn,
leads to a lower percent of applications processed within three days.
This will constitute our test of the reorganization hypothesis."*^
Secondary market activity in FHA insured loans
FHA-insured mortgages, along with conventional mortgages, are
bought and sold by investors and originators in the secondary mortgage
market. An increase in the demand for FHA-insured loans in this market
should increase both the yield and the liquidity of such mortgages.
This, in turn, should increase the relative attractiveness of FHA insur¬
ance to the mortgagee; and, consequently, it will result in an increase
in the demand for Section 203 insurance.
A caveat is in order concerning the ability of an empirical model
to test directly the entire reorganization argument. Horace Bazan, in
his study of FHA (1974), hypothesizes that if it had not been for the
reorganization, FHA administrators would have been better equipped to
respond to other exogenous causes of declining volume; and, FHA would,
therefore, never have been allowed to experience a decline of the magni¬
tude witnessed in recent years. Obviously, this "ability to respond"
argument constitutes an essentially untestable hypothesis and will,
therefore, not be dealt with in the present study. It may, however, be
entirely correct.

118
Demand for FHA-insured mortgages in the secondary market arises
primarily from the purchase of such loans by the Federal National
Mortgage Association (FNMA), the Government National Mortgage Associa¬
tion (GNMA), and the Federal Home Loan Mortgage Corporation (FHLMC).
Data on the net purchases of FHA-insured loans by these three entities
will be summed and included as a single explanatory variable in the
regression equations explaining the volume of FHA activity. This is,
of course, equivalent to assuming the marginal effect of a secondary
market purchase to be the same regardless of the institution purchasing
(usually for resale) the loan. The hypothesized sign of the coefficient
of this variable is, of course, positive with more secondary market
purchases of FHA loans leading to a larger volume of Section 203 insured
loans being originated.
FHA processing requirements
The imposition of additional eligibility requirements over time on
subdivisions seeking FHA approval creates increasing burdens on builders
seeking to make homes available with FHA insured financing. The most
important requirements in this regard have been the: (1) A-95 Review
Requirement that requires builders to obtain approval from local plan¬
ning agencies for proposed projects; (2) Environmental Clearance that
requires builders to prepare and submit environmental impact statements
of varying complexity for projects of varying size; and (3) Affirmative
Marketing requirements that require the builder to submit detailed
plans for advertising of proposed projects in order to attract minority
buyers. These, of course, have their effect only on the insurance of
new homes and should not influence the insurance of existing units.

119
In the insurance of the former, however, the effect of these require¬
ments should be to reduce the relative attractiveness of Section 203
insurance compared to other insurance plans available since similar re¬
quirements are not imposed on these other plans.
These requirements have been imposed over time in a discrete,
discontinous fashion and will, therefore, be somewhat difficult to
account for in an empirical analysis with time series data. Binary
variables (which are defined to be equal to one after the imposition of
each additional requirement and zero before) may be used in attempting
to capture the effect of these requirements; but, since the require¬
ments themselves were all introduced within a three-year period from
1969 to 1972, such variables would be extremely collinear and would
make estimation of their separate influences quite difficult. Therefore,
a single binary variable was employed that was set equal to one after
the first quarter of 1972 and zero before that time. Obviously, inter¬
pretation of the coefficient of this variable will be somewhat ambiguous.
It will essentially pick up the influence of all three processing re¬
quirements plus any other institutional changes that occurred around
that period. Therefore, the marginal influence of each one of these
factors was not estimated, but their total combined effect was, hope¬
fully, captured in this single variable. Since all of these factors
should lead to a decrease in the demand for Section 203 insured loans,
the sign of the coefficient should be negative in the FHA equation for
new units.

120
Housing starts as a proxy for overall housing and mortgage market
activity
Finally, the demand for Section 203 insurance will be influenced
by the overall level of activity in the housing and mortgage markets.
This is due to the derived nature of the demand for mortgage insurance
and the demand for mortgage funds. Both of these demands have as their
ultimate source the demand for housing services. Consequently, we in¬
clude single-family housing starts as a proxy variable for this overall
level of activity in the Section 203 demand equations. The a pfvioKÁ.
expectation was, of course, that the coefficient of this variable would
be positive with a greater level of activity increasing the demand for
Section 203 insurance.
Consideration of all of the factors listed above leads to the fol¬
lowing specification of the Section 203 demand equation for new units:
(4) FHAN = b + b (PROC) + b. _ (PMI) + b. „ (VAN)
4.0 4.1 4.2 4.3
+ b. . (SUBN) + b, c (TRM) + b, , (LTV)
4.4 4.5 4.6
+ b4>7 (I) + b4>g (SEC) + b4>9 (LIMN) + b4>1Q (D)
+ b4>11 (STS) + e4
Variables entering this equation that have not been defined previously
are:
FHAN = the number of new single-family units insured by
FHA under the Section 203 program;
PROC = the percent of FHA single-family applications on
which a commitment to insure or denial was issued
within three days of receipt of the application,
averaged over all insuring offices;
VAN = the number of new single-family units guaranteed
by the Veterans Administration;

121
SUBN = the number of new single-family units insured by
FHA under its subsidy programs (primarily
Section 235);
TRM = the difference between the average term to
maturity on Section 203 insured loans and conven¬
tionally financed loans;
LTV = the difference between the average loan-to-value
ratio on Section 203 insured loans and conven¬
tionally financed loans;
I = the difference between the average interest rate
on conventionally financed loans and the average
effective interest rate on FHA insured loans;
SEC = net secondary market purchase (gross purchases
minus gross sales) of FHA insured mortgages by
FNMA, GNMA, and FHLMC in constant dollars;
LIMN = the difference between the mortgage limit on
Section 203 insured loans and the average price
of new homes sold;
D
STS
e
4
= a binary variable that is set equal to zero prior
to the second quarter of 1972 and is equal to one
thereafter intended to pick up the gross effects
of FHA processing requirements;
= single-family, non-farm housing starts. It is
employed throughout as a proxy variable for the
overall level of housing market activity; and
= random variable
PMI was defined in equation (3) above, and b. ..., b. ,, are the
4.0 4.11
parameters to be estimated.
With regard to the hypotheses that have been developed concerning
the signs of these parameters, the a pAX.O-'rt expectation is that b^ ^,
b4.5’ b4.6’ b4.8’ b4.9’ and b4.ll wil1 be Positive and b4.2> b4.3’
b^ b^ ^, and b^ ^ will be negative. Section 203 volume on new
units should increase with increases in the percent of cases processed
within three days (b^ ^ > 0), with increases in the relative liberal¬
ness of Section 203 loans (b, r > 0 and b. , > 0), with increases in
4.5 4.6

122
secondary market purchases of FHA insured loans (b >0), with higher
mortgage limits relative to housing prices (b^ g > 0), and with in¬
creases in overall housing activity (b^ ^ > 0). Volume should de¬
crease with increases in the volume of insurance written by alternative
suppliers of default coverage (b^ ^ < 0» b^ ^ < 0> and b^ ^ < 0), with
increases in the conventional minus FHA interest rates (b^ y < 0), and
with the addition of extra processing requirements (b^ < 0). No
hypothesis exists concerning the sign of b;
Given our interpretation of the factors determining PMI, VAN, and
SUBN (i.e., that a situation of excess demand characterizes the markets
for these types of coverage), the only right-hand endogenous variable
in this equation is PROC. Because of the simultaneity between this
variable and FHAN, however, it was necessary to adopt a simultaneous
equation estimation technique in fitting the relationship. Two-stage
least squares was used.
Equation 5: Section 203
Insurance Volume on Existing Units
The demand equation for Section 203 insurance on existing proper¬
ties follows closely the demand for insurance on new units specified
above. Therefore, the extended discussion of each variable with its
rationale for inclusion in the equation will not be repeated here. The
same basic arguments apply to the equation for existing units without
modification. Essentially there are two minor differences. First, the
processing requirements variable, D, does not enter this equation be¬
cause these requirements are imposed only on new units (subdivisions
particularly). And second, the variables employed refer only to

123
existing units where it was possible to make the distinction between
property types. Thus, the demand for Section 203 insurance on existing
units is specified as:
(5) FHAE = b5 Q + b5 (PROC) + b5 2 (PMI) + b5 (VAE)
+ bc . (SUBE) + b . (TRM) + bc , (LTV) + bc , (I)
5.4 5.5 5.0 5./
+ b5 g (SEC) + b5 9 (LIME) + b51Q (STS) + e5
Variables entering this equation that have not been defined previously
(i.e., those for which disaggregation by property type was feasible)
are:
FHAE
VAE
SUBE
LIME
e5
All other variables were defined above, and b^ ..., b^ ^ are the
parameters to be estimated.
Our hypotheses concerning the signs of these parameters are that
b5 1’ b5 5’ b5 6’ b5 8’ b5 9’ and b5 10 wil1 be Positive and b5 2’
b^ 3, b^ and b^ ^ will be negative. Verbalization of these hypothe¬
ses follows that given for the Section 203 equation for new units and
= the number of existing single-family units insured
by FHA under the Section 203 program;
= the number of existing single-family units guar¬
anteed by the Veterans Administration;
= the number of existing single-family units insured
by FHA under its subsidy programs (primarily
Section 235);
= the difference between the mortgage limit on
Section 203 insured loans and the average price of
existing homes sold; and
= a random variable.
is, therefore, not repeated.

124
Equation 6: Processing Time of FHA Applications
This equation, the final behavioral equation of the model, deter¬
mines the processing time on FHA applications (as measured by the per¬
cent of cases on which processing is completed within three days of
receipt of the insurance application). Its specification is included
in the model for two reasons. First, the hypothesis was expressed in a
preceding section that the 1969 reorganization of the Department of
Housing and Urban Development served to increase processing time which,
in turn, served to reduce the demand for Section 203 insurance and,
thereby, contributed to the decline in activity under this program. It
is necessary, in order to test the first part of this hypothesis, that
a behavioral equation be estimated with processing time as the dependent
variable. Second, as was pointed out above, one would expect that
Section 203 volume and processing time are determined simultaneously.
Therefore, processing time should be made endogenous to the model so
that the estimation procedure can allow for this simultaneity. While
such estimation may, of course, be carried out without actually specify¬
ing the functional form of the processing time relationship, it does
require that all exogenous variables entering this relationship be in¬
cluded in the reduced form equations. Consequently, little additional
effort is required to fit the structural equation; and, by so doing, we
can subject the hypothesis above to empirical verification.
The average amount of time required to process FHA single-family
applications (the time lapse between receipt of application and issu¬
ance of commitment to insure or denial) is postulated as being func¬
tionally related to three variables. First, we hypothesize that

125
processing time will increase as the number of loans insured increases;
and, since insurance volume is, in turn, hypothesized to be influenced
by processing time, the two are determined simultaneously. Second,
processing time should decrease as staffing is increased in terms of
the number of man-years per application available in FHA for single¬
family processing. And third, processing time is hypothesized to have
increased as a result of the 1969 reorganization. Together, these con¬
siderations lead us to the following specification of the FHA process¬
ing time equation:
(6) PROC = b, _ + b, , (FHAT) + b, _ (LOAD) + b. _ (REOR)
b.U b.l b.Z b. 3
+ 6 6
The variables in this equation are defined as:
FHAT = the total number of single-family units (both
subsidized and unsubsidized) insured by FHA in
the given period;
LOAD = the number of man-years expended in initial
processing of FHA single-family applications
divided by the total number of single-family
applications received (i.e., man-years per
application);
REOR = a binary variable that is set equal to zero
prior to the first quarter of 1970 and is equal
to one thereafter. It is intended to pick up
the influence of the 1969 reorganization on the
speed with which applications are processed;
and
= a random variable.
PROC was defined previously, and b , ..., b are the parameters to
6.0 6.3
be estimated.
With regard to the anticipated signs of the parameters, it must be
remembered that our measure of processing time, PROC, moves inversely

126
with the actual amount of time required to process applications.
Consequently, the hypotheses developed above, if they are to be sup¬
ported by the evidence, should result in b^ ^ and b^ ^ being negative
and b, „ positive. The percent of cases processed within three days
should decrease with increasing volume and the reorganization and in¬
crease with staffing available per application. No CL pKÁ.OKÁ. expecta¬
tion existed concerning b . And, since FHAT and PROC are determined
6. U
simultaneously, two-stage least squares were employed to estimate the
11
parameters.
Equation 7: FHA Subsidy Programs Identity
The following equation is true by definition and, therefore,
constitutes an identity:
(7) SUB = TOT - FHAN - FHAE - VA - PMI
All variables in this identity have been previously defined and there
are no hypotheses embodied in it. Also, since there are no unknown
parameters and no stochastic elements involved, estimation need not be
carried out. The equation is merely written to complete our descrip¬
tion of the default insurance market.
Actually, only part of that FHAT variable is endogenous in this
equation—the Section 203 portion of total volume. Subsidy program
volume should be relatively insensitive to processing time variations.
As a result, the two-stage procedure was employed by subtracting actual
Section 203 volume from total FHA volume and adding predicted Section
203 volume back to the total, where predicted volume was generated from
the reduced form equations for Section 203. Then, application of ordi¬
nary least squares to the equation with this predicted FHAT variable
would be analogous to two-stage least squares estimation. It should be
noted, however, that the estimates of the standard errors of the coef¬
ficients of this equation would not be exactly the same as those pro¬
duced by direct estimation by two-stage least squares since the predicted
values of FHAT would be used in calculating them.

127
Summary
The set of equations that constitutes the complete empirical model
for this study is given by:
(1) TOT/ORIG = b o + bp (LFHA) + b (TFHA) + b 3 (VET)
+ b , (SD) + b, c (PMIA) + e,
1.4 1.5 1
(2) VA = b2_Q + b21 (VET) + e2
(3) PMI = b3 o + b3 (PMIA) + b3 2 (PMIA1) + b3 (PMIA2)
+ b0 . (PMIA3) + b. . (PMIA4) + b., , (PMIA5)
+ b3 (PMIA6) + b3 (PMIA7) + b3 (PMIA8)
+ b3 1Q (PMIA9) + b3 (PMIA10) + b (PMIA11)
(4) FHAN = b + b (PROC) + b, 0 (PMI) + b. _ (VAN)
4.U 4.1 4.2 4.3
+ b, , (SUBN) + b, r (TRM) + b, , (LTV) + b, ^ (I)
4.4 4.5 4.6 4.7
+ b4 g (SEC) + b4 g (LIMN) + b4 1Q (D)
+ b4>n (STS) + e4
(5) FHAE = b5 Q + b5 1 (PROC) + b5 (PMI) + b5 (VAE)
+ b_ (SUBE) + b. , (TRM) + b_ , (LTV) + b_ _ (I)
5.4 5.5 5.6 5.7
+ b5 g (SEC) + b5 9 (LIME) + b5 1Q (STS) + e5
(6) PROC = b, n + b, . (FHAT) + b£ „ (LOAD) + b, „ (REOR)
6.U b.i 6.2 6.3
+ 6 6

128
(7)
SUB
—
TOT - FHAN
- FHAE - VA
- PMI
And the
hypothesized signs of
the coefficients
to be es
timated for
each
equation
are:
(1)
bl.i
>
0
j
= 0, 5;
(2)
b2.1
>
0;
(3)
b3.j
>
0
j
= 1, 12
(4)
b4.1
>
°; b4_2 <
0; b4.3 <
0;
b4.4 <
05 b4.5 "
0;
b4.6
>
V
x
o
o
cr
oo
V
0;
b4.9 >
°; b4.10 <
0;
b4.11
>
0;
(5)
b5.1
>
0; b5.2 <
0; b5.3 <
0;
b5.4 <
0; b5.5 >
0;
b5.6
>
0; b5.7 "
05 b5.8 >
0;
b5.9 >
0; b5.10 >
0;
(6)
b6.1
<
0; b6.2 >
°; b6.3 <
0 .
The following chapter presents the results obtained from the esti¬
mation of this model and interprets these results,

CHAPTER VI
THE EMPIRICAL MODEL:
ESTIMATION AND INTERPRETATION
Data Employed, Estimation Techniques, and Qualifications
The data that have been collected to carry out the estimation of
this empirical model are national quarterly observations over the
period from the fourth quarter of 1952 through the second quarter of
1974, yielding a total of 87 observations. Documentation of these data
is given in Appendix 2 at the end of the study. The three major
sources of these data are the QiuaAtCA.liJ National. Housing Maakd-t Vata
Sank assembled by Eugene Brady for the Federal Home Loan Bank Board
(1971), the Vata Rcaouacca lnc.oapoA.atid National Vata Bank, and the
Federal Housing Administration's Statistics Division.
A problem was encountered regarding the series used to measure FHA
single-family processing time, PROC.. This series is only available
from the third quarter of 1965. Restricting our sample to the period
over which this series is available would result in a loss of 51 obser¬
vations on all other variables in the model and, thereby, the neglect
of a considerable amount of information. Such a loss would reduce the
overall efficiency of the estimation procedure and increase the proba¬
bility of a Type II error. In order to avoid this loss and to be able
to employ the larger sample in fitting the two Section 203 demand equa¬
tions, it was necessary to estimate the processing time reduced form
equation first using the smaller sample (36 observations) and predict
129

130
the values for this variable backward over the period for which actual
observations were unavailable. Then, the complete series (predicted
before the third quarter of 1965 and actual thereafter) was employed in
estimating the two Section 203 equations, thereby making it feasible to
utilize the additional information contained in the larger sample.'*'
Such a practice obviously introduced the errors-in-variables problem
which can lead to biased estimates of the structural coefficients. The
tradeoff faced in this situation, then, may be described as one of in¬
creasing estimation efficiency at the expense of possible biasedness.
Given the large number of variables included in the Section 203 equa¬
tions and the extent to which the sample size would have to be reduced
in order to avoid this source of bias, the decision was made to opt for
the increased efficiency of the larger sample. The problem was, of
course, constrained to equations 4, 5, and 6 of the model.
The estimation techniques that were applied to the various equa¬
tions in the model differed according to the particular problems that
were encountered. Equations 1 and 2 contain no endogenous variables
on the right-hand side and are not specified with a distributed lag
structure. Therefore, these equations were initially estimated using
ordinary least squares. The Durbin-Watson statistic for the second
equation, however, indicated the presence of positive first-order
serial correlation which, if uncorrected, would result in inefficient
estimates. Therefore, a generalized least squares estimation procedure
’'‘The predicted values for PROC remain well within the range of
observed values for this variable. Also, as a check, the smaller
sample was employed in fitting the Section 203 equations, and no seri¬
ous divergencies emerged. Consequently, the results obtained by employ¬
ing the larger sample are presented in this study.

131
was adopted for this equation. Since the first-order coefficient of
2
autocorrelation was unknown, it had to be estimated. Consequently,
the resulting estimates of the structural coefficients of this equation
constitute feasible Aitken's estimates. Therefore, they will exhibit
the asymptotic property of consistency. The Durbin-Watson statistic
for the first equation, however, fell within the indeterminant range.
Therefore, the ordinary least squares estimates of the coefficients of
this equation were retained. As a result, these estimates should ex¬
hibit the small sample properties of efficiency and unbiasedness.
Equation 3 also contains no right-hand endogenous variables, but
it is specified with a polynomial distribution lag structure of the
Almon variety in which we have constrained the polynomial to be of the
second degree (allowing for one turning point only in the structure of
the lagged effects). Here too, the Durbin-Watson statistic from the
initial estimation results indicated the presence of positive first-
order serial correlation. Therefore, the Cochrane-Orcutt procedure was
also applied to the distributed lag equation so that feasible Aitken's
estimates were obtained for the coefficients of this equation also. As
a result, these estimates will also exhibit the asymptotic property of
consistency. Also, since private mortgage insurance volume (and private
mortgage insurance availability) remained at zero until 1957, the first
seventeen observations of our sample were dropped for the estimation of
this equation. With both the left-hand and right-hand variables iden¬
tically equal to zero over this part of the sample, the inclusion of
2
The Cochrane-Orcutt iterative technique was employed to arrive at
an estimate of this coefficient (see Johnston, 1972, p. 262).

132
these observations in the estimation would distort the estimates of the
slope coefficients.
Finally, equations 4, 5, and 6 contain right-hand endogenous
variables so that a simultaneous equation estimation technique becomes
appropriate. Investigation of the rank and order conditions for iden-
tifiability of these three equations was carried out under the main¬
tained assumption that the coefficients of the system hypothesized to
be different from zero are, indeed, significantly different from zero
and that those hypothesized to be equal to zero are not significantly
different from zero. This is the test of the necessary and sufficient
conditions for identification under the assumption of zero coefficients
outlined by Kmenta (1971, pp. 544-545). The results indicated that all
three equations are over-identified. Therefore, the two-stage least
3
squares estimation procedure was adopted for these equations. As a
result, these estimates will also exhibit the asymptotic property of
consistency. Therefore, with the exception of equation 1, none of the
estimated coefficients will exhibit the small sample properties of un¬
biasedness or efficiency. Consequently, any statistical test that one
might wish to carry out on the structural coefficients of equations 2
through 6 must be interpreted as being asymptotic in nature.
Prior to presenting the estimation results, a word of caution must
be expressed. The coefficients given below must be interpreted as
rough approximations at best. They should not be accepted as precise
measures of constant, exact relationships. The degree of accuracy
3
See footnote 11 of the preceding chapter for an explanation of
the technique employed to arrive at two-stage least squares estimates
for equation 6.

133
exhibited by these estimates depends upon a myriad of factors, some of
which we can know very little about. Most obviously, the precision of
the estimated coefficients in describing the actual relationships in¬
volved is dependent upon the overall accuracy of the data that comprise
the sample. Concern has already been expressed about the adequacy of
one of the series employed (the processing time variable). Others,
however, are subject to similar qualifications, particularly the mort¬
gage origination series, interest rate series, and private mortgage in¬
surance volume series. Also, some of the factors that have possibly
affected the variables that are endogenous to the model were qualita¬
tive in nature and, as a result, could only be incorporated through the
use of binary (intercept shift) variables. Such variables are rather
crude, and particularly in a time series model, they are liable to pick
up the effects of any excluded influences that occur contemporaneously.
And finally, as mentioned in Chapter II, the overall quality of extant
housing and mortgage market data is notoriously poor, particularly in
the earlier periods such as the 1950's. The net result of these con¬
siderations is to increase the errors-in-variables estimation problem
which, in turn, increases the likely bias of the estimated coefficients.
Further qualification is required when one admits possible non-
linearities in the relationships hypothesized to exist and the likeli¬
hood that the structural coefficients have not remained constant over
the entire sample period. And finally, it is quite likely that the use
of national data has resulted in the well-known aggregation bias
problem. This last source of bias will exist in the estimates obtained
unless the extremely unlikely condition is met that the structural co¬
efficients and functional form of the relationships hypothesized to

exist are precisely the same for all micro-areas of the country over
which our data are aggregated (Green, 1964, pp. 99-106).
Hopefully, these rather severe qualifications do not destroy the
usefulness of the estimation results but, rather, guard one against
their unwarranted misuse. The value of the empirical exercise lies in
the additional information that it may shed on the basic issues that
the model is designed to address. Fundamentally, such information lies
in the confirmation or contradiction of the theoretical conclusions
that have been reached regarding these issues, i.e., in providing an
inductive test of the deductive process that generated these conclusions
(Tintner, 1968, p. 56). The interpretation provided in the following
section will follow this basic view of the role of empirical research
in economics.
Estimation Results and Interpretation
The estimated relationships that result from the application of
the procedures described above are now presented. The notation employed
is the following: n is the number of observations utilized in the esti¬
mation; S. E. is the estimated standard error of the regression; F is
the F-statistic for the equation calculated from the transformed varia¬
bles employed to correct for the serial correlation in equations 2 and
3 with the degrees of freedom in parentheses (not given for equations 4,
2
5, and 6); R is the coefficient of determination (uncorrected for
degrees of freedom) calculated from the transformed variables in equa¬
tions 2 and 3 (not presented for equations 4, 5, and 6 because it is
not directly relevant to two-stage least squares estimation results);
p is the estimated first-order autocorrelation coefficient (for equations

135
2 and 3); and the estimated standard errors (asymptotic for equations 2
through 6) of the respective structural coefficients are given in paren-
4
theses under each coefficient. The following relationships result
from this estimation:
(1) TOT/ORIG = 71.0853 - 0.7884 (LFHA) + 0.0471 (TFHA)
(25.1110) (0.3165) (0.8208)
+ 0.0004 (VET) + 4.7954 (SD) + 11.0117 (PMIA)
(0.0001) (1.0396) (3.7341)
n = 87
S. E. = 2.8432
F (5, 81) = 34.2045
R2 = 0.6786
(3) VA
n
S. E.
F (1, 84)
R2
P
27988.7185 + 2.6023 (VET)
(29738.1900) (1.8886)
86
14208.1
357.8726
0.8099
0.8809
Significance levels are given in Appendix 1 of this study. They
are not presented in the text because of the questionable practice of
carrying out multiple tests on a single sample. Readers wishing to
know the significance level of a particular coefficient, therefore, are
referred to the appendix.

136
(3)
S. E.
F (12, 44)
R2
PMI = -420558.6297 - 29050 (PMIA) + 9610 (PMIA1)
(69220) (47450)
+ 40740 (PMIA2) + 64360 (PMIA3) + 80450 (PMIA4)
(37390) (37780) (41730)
+ 89020 (PMIA5) + 90070 (PMIA6) + 83600 (PMIA7)
(44090) (42930) (38070)
+ 69610 (PMIA8) + 48090 (PMIA9) + 19060 (PMIA10)
(31270) (29070) (40900)
- 17500 (PMIA11)
(65470)
n = 57
12843.4
31.6237
0.8961
P = 0.8905
(4)
FHAN = 198.5872 - 465.4113 (PROC) - 0.0706 (PMI)
(34587.5573) (266.7015) (0.0562)
- 0.0722 (VAN) - 0.5349 (SUBN) + 1484.8154 (TRM)
(0.0275) (0.2065) (764.5105)
+ 1754.6223 (LTV) - 2399.7518 (I) + 2.3357 (SEC)
(323.3988) (2159.7312) (1.4153)
+ 0.2595 (LIMN) - 2834.9750 (D) + 13684.5238 (STS)
(0.2759) (5337.9418) (4007.2573)
n =
S. E.
87
4041

137
(5)
FHAE = 31375.1970 + 53.0163 (PROC) - 0.5118 (PMI)
(57068.1026) (419.4966) (0.0979)
- 0.3298 (VAE) - 1.0623 (SUBE) + 1489.7717 (TRM)
(0.1471) (1.1344) (2569.2259)
- 3176.6337 (LTV) - 20884.4941 (I) + 5.5557 (SEC)
(1076.8106) (6335.9194) (4.3450)
+ 4.2575 (LIME) + 53062.7643 (STS)
(0.9766) (12702.3642)
n = 87
S. E. = 14029
(6)
PROC = 125.7520 - 0.0002 (FHAT)
- 556.1184 (LOAD)
(13.5603) (0.0001)
(463.8870)
- 19.9460 (REOR)
(3.6809)
n = 36
;. E. = 9.72
Given the size of this empirical model, it will be convenient to
discuss these estimation results on an individual equation basis.
Particular attention will be devoted to the results obtained for the
two Section 203 equations.
Equation 1: Total Insurance Volume
The results for this equation provide rather strong support for
the hypothesis that supply constraint shifts in the VA, private, and
subsidy markets are directly related to the volume of total mortgage
insurance written out of a given volume of originations. All of the
coefficients for the variables used to reflect these supply constraints

138
shifts are of the hypothesized sign and their standard errors are rela¬
tively small. Also, the variable coefficient relating originations to
insurance was calculated from the estimated coefficients via expression
(lb) in Chapter V, and it was found to remain positive over all obser¬
vations as hypothesized. Its average value over the sample period is
12.38. Therefore, it does appear that the size of the overall market
for default insurance is directly related to the level of activity
being carried out in the mortgage market. This result is, of course,
not surprising given the derived nature of the demand for mortgage
insurance.
The results relating to the effect of financing term variations on
the proportion of mortgage originations insured, however, are not very
encouraging. The sign of the coefficient for loan-to-value ratio
variations is the opposite of that hypothesized, and the standard error
of the coefficient for term to maturity variations is relatively large.
These discouraging results for the financing terms hypothesis could, of
course, stem from several different kinds of estimation problems.
First, a degree of collinearity exists between LFHA and TFHA with the
simple correlation coefficient between these variables standing at
0.9347. Second, the degree of variation experienced by these two
variables has not been extremely large over the sample period. The
range of variation for LFHA was 83.7 to 95.3 over the observed values,
and the range for TFHA was 21.7 to 31.7. And third, it is possible
that the FHA terms do not accurately reflect the movement over time in
the overall financing terms available on insured mortgages. To the ex¬
tent that these unavoidable estimation problems have not determined the
empirical results, however, we are forced to conclude that financing

139
term variations have been relatively unimportant in determining the
proportion of mortgage originations that are insured over time. This,
of course, does not deny the possibility that such terms have exerted
an important influence on the allocation of total insurance volume
among the various participants, especially between Section 203 and the
private firms in the market, through their effect on product differen¬
tiation and substitutability.
Equation 2: VA Insurance Volume
The empirical results obtained from the estimation of this highly
(perhaps overly) simplified specification provides weak support for the
hypothesis that the supply constraint in the VA market is determined by
the number of veterans that are eligible for the VA guarantee. The
sign of the VET coefficient is as hypothesized and the (asymptotic)
standard error of the coefficient is relatively small. While they do
not provide a direct test of our maintained hypothesis that the VA
market is characterized by a condition of excess demand throughout the
sample period, these results do tend to increase one's confidence in
the use of this hypothesis in the theoretical construct.
Equation 3: Private Insurance Volume
The results obtained from the second degree polynomial distributed
lag structure imposed on this equation are encouraging. The coeffi¬
cients of the lag structure increase for the six quarters following the
relaxation of legal prohibitions against the selling of private insur¬
ance and then decline. With the exception of the coefficients for the
unlagged effect and the eleventh quarter lagged effect, all estimates

140
are of the hypothesized sign. Also, the (asymptotic) standard errors
are, in general, relatively small, particularly for the mid-range
lagged effects. Therefore, the hypothesis that private mortgage insur¬
ance volume is determined by a combination of legal availability and
(unobserved) contingency reserve accumulation received moderately strong
support from this equation.
Here also, the maintained hypothesis of an effective supply con¬
straint receives indirect support. And, since the private mortgage
insurance availability index, PMIA, achieved its upper bound (equal to
one) in the third quarter of 1973 and since the accumulation of con¬
tingency reserves sufficient to meet the market demand in a given state
appears to be complete by the end of the third year following entry
into the state, we may expect the supply constraint relating to the
private national market to become ineffective by 1977. By the princi¬
ple of Le Chatelier (Chapter IV and Samuelson, 1947, p. 38), this
reduction in the number of rationed substitutes should result in an
increase in the own price substitution effect of the demand for Section
203 coverage. Given the relative price of this coverage, the elimina¬
tion of the private mortgage insurance supply constraint will also
imply that Section 203 will continue to write default insurance only to
the extent that its product is differentiated (by differences in cover¬
age level, terms, etc.) from the coverage provided by the private firms
in the market.
Equation 4: Section 203 Insurance Volume on New Units
This equation and the one to follow serve (along with the theo¬
retical considerations that have led to them) as the primary source of

1 Al
the conclusions reached in this study regarding the causal factors in¬
volved in the decline of insurance activity under the Section 203
program. Therefore, the detail that is devoted to the interpretation
of these two equations will be greater than that afforded to other equa¬
tions in the model. Since these Section 203 equations are quite similar
in specification, we will discuss the new units equation in detail and
then dwell on the existing units equation only to the extent warranted
by differences in the empirical results obtained.
The first coefficient in this equation for which we have developed
a hypothesis is the coefficient attached to the processing time variable,
PROC. The resulting sign is in direct conflict with our hypothesis.
The negative sign estimated by the equation implies that, holding every¬
thing else constant, Section 203 volume declines as the percent of cases
processed within three days increases, i.e., faster processing leads to
a loss of insurance volume. Also, the (asymptotic) standard error of
this coefficient is relatively small. This result casts further doubt
on the adequacy of the data series used to measure processing time
fluctuations. But, to the extent that it can be believed, it also casts
considerable doubt on the hypothesis that increases in FHA processing
time contributed to the decline in activity.
All other signs in this equation are as hypothesized, and the over¬
all accuracy of the parameter estimates (i.e., the relative size of the
standard errors of the estimates) is encouraging. All three of the
alternative suppliers of default insurance appear to have substituted
for Section 203 coverage. This is inferred from the negative signs for
PMI, VAN, and SUBN and the relatively small (asymptotic) standard errors
of the coefficients of these three variables. From the relative sizes

142
of these coefficients, the private insurance and VA guarantees appear
to have had approximately the same marginal effect on Section 203
volume written on new units (reducing this volume one unit for every
thirteen units insured by them), and the subsidy programs appear to
have exerted a larger marginal effect (reducing 203 volume on new units
one unit for every two units insured). This, of course, does not imply
that the subsidy programs contributed more to the actual decline since
the total volume of activity under these programs was relatively small
and confined to the post-1968 period with large declines in insurance
activity under these subsidy programs occurring in 1973 and 1974. It
does appear, however, that these programs were influential in reducing
Section 203 volume during the period in which they were active.
The fact that the PMI coefficient is negative and estimated with a
relatively small (asymptotic) standard error lends indirect support to
the cream-skimming hypothesis. While a direct test of this hypothesis
would require knowledge of the risk-related characteristics of the in¬
dividual loans insured by the private firms in the industry, it is
clear from the equation that the insurance volumes attained by these
firms did come, at least partially, at the expense of the Section 203
program. An additional (though still indirect) test of the cream-
skimming hypothesis will be provided at the end of this chapter.
The two relative financing term variables, TRM and LTV, both re¬
sult in positive coefficients as was hypothesized, and the (asymptotic)
standard errors estimated for these coefficients are relatively small.
Thus, the empirical evidence from this equation supports the hypothesis
that relative financing terms are an important determinant of the
allocation of total default insurance market demand among the various

143
participants. It also supports the hypothesis that long run declines
in the relative financing terms advantage of Section 203 insured mort¬
gages have contributed to the declining insurance volume under that
program. This appears to be particularly true of the declining differ¬
ence between Section 203 and conventional loan-to-value ratios since
the coefficient for this variable is larger and since the decline in
the value of this variable has been larger also. The average loan-to-
value ratio advantage of Section 203 insured loans declined 43 percent
over the sample period, from a difference of 25.9 percentage points in
1952 to a 14.7 percentage point difference in 1974. Given the esti¬
mated coefficient, this decline in LTV implies an overall loss of
19,652 new units per quarter under Section 203. And, the difference
between Section 203 and insured conventional loan financing terms (for
which data are not available) are bound to have declined even more. As
will be seen later, however, these results appear to be specific to the
insurance of new units only. But, with respect to these units, the
erosion of relatively more liberal financing terms under Section 203
does appear to have contributed to the declining volume of insurance
activity.
The variable measuring the effective interest rate difference
between conventional and Section 203 insured loans attains the hypothe¬
sized sign, but the estimated standard error is relatively large cast¬
ing some doubt on the strength of the relationship between I and
Section, 203 insurance volume on new units. Thus, the empirical evidence
fails to provide strong support for the hypothesis that a failure to
adjust the fixed rate allowed on Section 203 loans has been an important
cause of the declining volume of activity under this program. From this

144
result, we are inclined to conclude that the discount point system has
served adequately to correct for non-market interest rate differences
for the insurance of new units.^
Secondary market net purchases of FHA-insured loans carries a
positive coefficient that is estimated with a relatively small standard
error. Thus, the equation lends support to the hypothesis that pur¬
chases of FHA-insured mortgages by FNMA, GNMA, and FHLMC increase the
demand for Section 203 coverage. Given the commitment process employed
by these institutions in purchasing loans, this finding comes as little
surprise (see Bartke, 1971). While these secondary market participants
do not originate loans, the announcement that loans of a certain va¬
riety will be purchased encourages originators that sell to these in¬
stitutions (particularly mortgage bankers) to initiate loans of the
given type requested. Thus, the commitment process directly encourages
the origination of particular kinds of loans, and the purchase of FHA-
insured loans by secondary market institutions is almost equivalent to
a direct demand for Section 203 coverage. Therefore, we conclude that
secondary market activities have tended to support Section 203 volume
over the sample period. In the absence of such activity, the decline
in this volume would have been even more severe than that experienced.
Recent institutional changes that allow for secondary market pur¬
chases of privately insured mortgages by FNMA and FHLMC (in 1971) and
GNMA (in 1973) should contribute to future declines in Section 203
volume as FHA's historical dominance in the secondary market is reduced.
~*This finding is in basic agreement with that of Lawrence Smith
(1970). Note, however, that our conclusion here applied only to the
effect of I on the insurance of new units. As will be seen in our
discussion of equation 5 below, a stronger impact is found for the in¬
surance of existing units.

145
It should be noted, however, that the higher percentage coverage pro¬
vided under Section 203 may be of a much greater value to the secondary
market investor. Often, such an investor is unfamiliar with both the
property securing the mortgage and the mortgagor who is actually borrow¬
ing the funds. In many instances, he is located in a different region
of the country. Because of these features of secondary market invest¬
ment, the ultimate lender will be unable to assess the default risk on
the mortgage instrument and, as a result, the extra coverage afforded
on Section 203 loans may be relatively more important. An inquiry into
the value of 100 percent coverage to secondary market investors would
appear to be appropriate as the only source of such coverage continues
to decline in the primary market. The policy implications of such an
inquiry could be very important for national housing objectives.
The coefficient for the variable measuring the difference between
the FHA mortgage limit and the average price of new homes sold has the
hypothesized sign, but the standard error of the estimate is relatively
large. The hypothesis that adjustment lags in the mortgage limit have
contributed to the Section 203 decline in insurance written for new
units does not, therefore, receive strong support from the empirical
evidence. It should be pointed out, however, that a rather strong as¬
sumption is required in applying this measure to the hypothesis that
was developed. That is, we were forced to assume that the distribution
of housing prices remained constant except for an overall shift to the
right so that the difference measured by LIMN would reflect the propor¬
tion of houses sold that were above the mortgage limit. It was not
possible to obtain data on the actual proportion of homes sold that
were priced above the limit over the whole sample period. Therefore, the

146
lack of stronger support for this new hypothesis may stem from the in¬
adequacy with which the desired variable has been measured.
A similar conclusion applies to the binary variable intended to
capture the effect of processing requirements (A95 Review, Environ¬
mental Clearance, and Affirmative Marketing). It, too, results in a
coefficient of the hypothesized sign, but its standard error is also
relatively large. Therefore, subject to the qualifications that were
made explicit in Chapter V concerning the use of binary variables with
time series data, we are forced to conclude that the addition of these
requirements in the late 1960's and early 1970's resulted in an ambigu¬
ous (perhaps zero) effect on Section 203 volume.
Finally, the hypothesis that Section 203 volume is directly influ¬
enced by the overall level of activity in the housing market (from
which the demands for mortgage funds and default insurance are derived)
is supported by the positive sign of the coefficient on housing starts,
STS. Given the relatively small (asymptotic) standard error with which
this coefficient is estimated, we can be fairly confident of this
result. It should be recalled, however, that this variable should not
be interpreted as the direct causal force at work since it is employed
as a proxy variable only. But, the results in this and the following
equation tend to indicate that the variable serves well in this role.
Equation 5: Section 203 Insurance Volume on Existing Units
The empirical evidence revealed in this equation is, for the most
part, quite similar to that detailed in equation 4 above. Where the
results are in basic agreement, one may hold the conclusions drawn with
somewhat increased confidence. In such cases, the interpretation of

147
the findings will not be repeated here. Instead, since the estimated
equations do diverge in some respects, this section will only point out
the areas of possible conflict in results and attempt to reconcile such
conflicts.
First, the processing time variable in the equation for existing
units results in a coefficient of the hypothesized sign. The positive
coefficient estimated here would imply that Section 203 demand responds
positively to increases in the percent of cases processed within three
days and, therefore, appears to contradict the conclusion drawn from
equation 4 that increases in processing time did not contribute to the
decline. The standard error of this estimated coefficient, however, is
quite large and, as a result, no real conflict in results appears.
Therefore, our conclusion concerning processing time is further sup¬
ported by the results of this equation even though a positive sign is
attained. None of the empirical evidence presented supports the hy¬
pothesis that processing delays were an important cause of decline.
Second, while the coefficient for the insurance volume of FHA's
subsidized insurance programs maintains the hypothesized sign, the
relative size of the estimated (asymptotic) standard error is disap¬
pointingly large. This result, however, is probably attributable to
the