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

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

Subjects / Keywords:
Homeowner's insurance -- United States   ( lcsh )
Mortgage guarantee insurance -- United States   ( lcsh )
Economics thesis Ph. D
Dissertations, Academic -- Economics -- UF
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bibliography   ( marcgt )
non-fiction   ( marcgt )

Notes

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

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University of Florida
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oclc - 03122543
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Full Text












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-


. -- --1-- T


p
- A- A-


.. -. A-l 2 -- ^ /-


.I


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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


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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


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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-


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rhP VA


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nrnor-rn


ic 1 occ


rhbn 1 nn


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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,


un-













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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 -


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ircalE


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