An econometric model of residential choice

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Title:
An econometric model of residential choice
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vi, 155 leaves : maps ; 28cm.
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Jackson, Jerry Ross, 1945-
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Subjects / Keywords:
Residential mobility -- Mathematical models   ( lcsh )
Housing -- Milwaukee   ( 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 131-135.
Statement of Responsibility:
by Jerry Ross Jackson.
General Note:
Typescript.
General Note:
Vita.

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University of Florida
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aleph - 000168843
oclc - 02890059
notis - AAT5243
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Full Text














AN ECONOMETRIC ;ItDEL OF RESIDENTIAL CHOICE




















By


JERRY


ROSS


JACKSON


A D ISSERTATION


FRpS' TrO* .
Il l, '^ i.> tn r- Ia) L u.


'THE 'NI V1RSI7Y 0
IN PARTIAL DUL51LI1:{NT OF T;if
DEGREE O0 DOCTOR OF


'l.ORJCA


CO;UCIL. OF


PHILO nphY
















ACKNOWLEDGMENTS


enjoyed


support


many


people


during


the completion


this


project.


Alan


Winger


provided


the initial


guidance


encourage-


ment


in pursuing


this


topic.


chairman


my committee,


Roger


Blair,


deserves


a special


thanks,


not only


for his


substantive


comments


for his unfailin


support


and friendship


over


the three-year


gestation


period


of this


dissertation.


am indebted


to Professor


Jerry


Milliman


for extensive


comments


am grateful


for his


assistance


in obtaining


a lar


number


of recent


unpublished


studies


relevant


my topic.


would


also


like


to thank


Professors


Robert


Emerson


Arnold


Heggestad


for reading


and comnientin


on my


dissertation


on rather


short


notice.


Their


co moments


increased


the readibility


a number


of sections


deal--


ing with


the statistical


estimation


of my model.


am also


indebted


a number


of people


at the Federal


Reserve


Ba nk


of Chicago.


of time,

valuable


computer

insight


Karl.


Scheld


support, a

on a number


was


more


than


nd encouragement.


of difficult


generous


John


problems.


in the provision


Sturrock

I will


provided


always


grateful


for his willingness


to discuss


the problem of


the week,


am grateful


to Pauline


Rudder


for providing


expert


typing


support


and to Roger


Thrysel ius


for his help


in preparing


the figures


charts


in thi s


nanuscrip t.

















fiTA LE


OF CONTENTS


ACKNOWLEDGMENTS

ABSTRACT

CHAPTER


INTRODUCE ION


OUTLINE OF


STUDY


A NEW


APPROACH


TO RESI D NTIAL MODELING


S 4


TEST SITE
A Profiles
The SEWRPC


1]E DATA
Milwaukee


Data


BASE


Base


AN EPPIRTCAL
A Modific
Consume
An Emnpiri


'tODEL
i-nn C


action of t

cal Model
( In;


SPATIrA


L CON
atial


lnsuri2


IUMER B
Theory


EHAV IOR


Behavior


SPATIAL, VA
Fu.ncti
Th[e Ihe


Est i
/+ o


PI AT I.ON


ma t
Rel


nal F

ion Rt
at i.v


IN THE


orm and


ross


PRICE


the


csul ts .
Price of


ii


OF 0i


Hiedonic
Equation

housing S


HOUSING
Enuati
4


SERVICES
on .


* . a .
* a . a .


crvices


COMMIf LTI. L,


The D
Eva lu


TIME ANI)
e Work-R


trtiv
atic


St io n
u Cr{it


of
i ri


SPATIAL ALL
ence Comm ute
an OQtimal L
a for Locati


0CATION
STimes
location
on Predi


PROCESS


tion .


A SIMULATION 0
Smti.lm tion


!.j(' L
ET..il


tIio I
3^I -''
'1E ^ -' *


S I'.,;S LENTI AL


the S

o' *O:


pati a


as tj-3


CHOICE
I Mode


CCUrilCV


SUMMARY


AND i', ',c~ i S


VII.


VI .I.


P T rTT.'r A lIfTV


<-


g


1


I









1972 Household History Survey


Price Statistics for


Census


Tracts in Milwaukee


Delineation of Census Tracts


of Accessibility


used for an Examination


Indexes


Delineation of
View of the


Census


Price Su


Tracts used for a
rface . .


Cross-Sectional
. . .


BIOGRAPHICAL SKETCH















Abstract


sser


taticn


resent


to the Graduate


Council


of the University


Florida


in Partial


Fulfillment


of the Requirements


the D


egree


doctor


Philosphy


AN ECONOMETRIC


MODI)EL


OF RESIDENTIAL


CHOICE


Jerry


Ross


Jackson


June,


1976


Chairman:


Major


Roger


Department:


Blair


Economics


In this

to construct


study,


the spatial


an econometric


model


theory


of urban


consumer


behavior


residential


choice


is utilized

e. This


model


differs


from existing


empirical


models


in that


the locational


behavior


of households


is based


on a theoretical


structure,


rather


than


ad hoc


assumptions.


Household


preferences


are represented


in the model


a utility


function

allows t


between


spatial


which


he mode


housing


theory


is amenable to

1 to explicitly


services,


consumer


parameter

represent


the price


behavior


estimation.


This


the tradeoffs


of housing


is extended


formulation


made


commuting


to incorporate


households


costs.


neigh-


borhood


effects


and multiple


workplace


locations.


Given


estimates


of housing


of the utility


services,


a moving


function


household's


parameters


referred


the relative


location








The housing


expenditure


function


derived


from


the first-order


con-


editions


of utility


maximization


is estimated


instrumental


variables


to provide


values


of the utility


function


parameters.


A hedonic

the relative p


price


rice


regression


of housing


equation


services


is estimated

residential


in order

location.


to derive

It is


assumed


that


accessibility


advantage


is fully


capitalized


in the price


land and


that


households


produce


housing


services


from land,


structure,


and neighborhood


characteristics


associated


with


the dwelling


unit.


follows


that


the price


of land


varies


residential


location and


prices


of the other


attributes


are


spatially


constant.


relative


price


housing


services


is determined


constructing


price


indexes


where


price


of the input


factor


land


varies


over


space.


The model


is estimated


and tested


using


data


for the city


of Mil-


waukee.


data


derived


housing

from th


expenditure


e Southeaster


equation is

n Wisconsin


estimated

Regional


using household

Planning Commission's


1972


Home


Interview,


Internal


Trip


Report


and Household History


Surveys.


The primary


data


source


for the estimation


of the hedonic


price


index


is the 1970


Census.


results


of this


study


show


that


a modified


version


of the


spa-


tial


theory


consumer


behavior


can


be successfully used


as the theoret-


ical


basis


an empirical model


of household


residential


choice.


A Cobb-Douglas


tion


utility


consumers


function


tastes


appears


for housing


to provide


and other


a good


goods.


representa-


hedonic


index estimation


results


indicate


that


the price


of housing


services
















CHAPTER


INTRODUCTION


OUTLINE


OF STUDY


In this


study,


the spatial


theory


consumer


behavior


utilized


to construct


an econometric model


of urban


residential


choice.


This model


differs


from existing


empirical


models


in that


the locational


behavior


of households


is based


on a theoretical


structure,


rather


than


ad hoc


assumptions.


Household


preferences


are represented


in the model


utility


function


which


is amenable


to parameter


estimation.


This


formulation


allows


the model


to explicitly


represent


the tradeoffs


made


households


between


housing


services,


the price


of housing


commuting


costs.


spatial


theory


consumer


behavior


extended


to incorporate


neighborhood


effects


multiple work-


place


locations.


Given


estimates


of the utility


function


parameters


and the


relative


price


of housing


services,


a moving


household


s preferred


location


is predicted


determining


the residential


location


that


provides


maximum


utility.


housing


services


and commuting


time


characterizing


that


location


represent


the optimal


values


of those


variables.










The housing


expenditure


function


derived


from


the first-order


conditions


of utility


maximization


is estimated


instrumental


variables


to provide


A bedonic


price


values


of the utility


regression


equation


function


is estimated


parameters.


in order


derive

tion.

ized i


the relative

It is assumed


n the price


price

that


of land


of housing


accessibility


and that


services


advantage


households


residential

is fully c


produce


loca-


apital-


housing


services


from land,


structure,


and neighborhood


characteristics


associated


land


butes


with


varies


the dwellin


residential


are spatially


unit.


location


constant.


It follows


and prices


relative


that


the price


of the. other


price


of housing


attri-


ser-


vices


is determined


constructing price


indexes


where


the price


of th


input


factor


land


varies


cver


space.


The model


is estimated


and tested


using


data


for the city


Milwaukee.

household


The

data


housing

derived


expenditure


from


equation


the Southeastern


is estimated

Wisconsin Re


using


gioaal


Planning


Commission'


(SEWRPC)


1972


Home


Interview,


Internal


Trip


Report


and Household


History


Surveys.


The primary


data


source


the estimation of

The remaining


the hedonic

chapters o


price


f this


index

study


is the 1970 Census.

are organized as fol-


lows.


Chapter


examines


two existing


approaches


to modeling


residential


choice.


deficiencies


in these


approaches


considered


examining


several


representative


models.


Chapter


ft r. ...4


are


r


4


I~









function


is posited


and the housing


expenditure


equation


is esti-


mated


to provide


utility


function


parameters.


Chapter


is devoted


to the estimation


an index


of the rel-


active


price


of housing


services.


The determinants


of housing


value


are examined


expenditure

indexes of


and a hedonic


is estimated.


the relative


Implic


price


regression

it prices


of housing


equation

are used


services.


for housing

to construct

Commuting


times


for each


census


tract


are


derived


in Chapter


The mechan-


ics of the actual


household


residential


prediction


res-


solution


tion and


of several


evaluation


operational


of the model


difficulties


are


also


surround in


discussed


predic-


in Chapter


The model


is tested


for predictive


performance


in Chapter


VII.


each moving


household,


the residential


location


that


provides maximum


utility


is considered


to be the moving


destina-


tion.

Chapter


In addition


the pri


to the utility

ce estimates o


function


f Chapter


parameter


estimates


the commuting


times


derived


in Chapter


information


on family


income,


work-


place


location,


and social


characteristics


for each moving


house-


hold


is used


to evaluate


the utility


function


at each


location.


The model


is evaluated


comparing


actual


moving destinations


with


predicted


destinations.


major


conclusions


and quantita-


tive


findings


of this


study


are summarized


in Chapter


VIII.

















CHAPTER


A NEW


APPROACH


TO RESIDENTIAL MODELING


For nearly


problem of


two decades


forecasting


economists


the locational


have


grappled


decisions


with


of urban


house-


holds.


The earliest


models


of locational


choice


were


generally


developed as

These models


subsectors

relied on


of large-scale


observed


urban


empirical


simulation


regularities


models.


pre-


diet


residential


location.


unsatisfactory


performance


these


tural


forecasting models


models where


led to the


behavioral


recent


relations


are


development


based


struc-


on economic


theory.


While


these


newer models


have


not been


fully


tested


appears


that


they


are


unable


to capture


many


of the


essential


elements


affecting


residential


location.


Diffi-


culties


arise


in using


the theory


consumer


behavior


to model


locational


choice


because


the theory


does


not explicitly


*It should


implies


a choice


noted
both


at this


ecation


point


that


residential


and housing


choice


ctice,


residential


locations


are


considered


to be characterized


an ex-


isting
choice


level


housing


and the choice


services.


residential


Consequently,


location


res


identical


, in practice,


are


equivalent


in meaning.


**For


see Brown


a description


(1972)


Lowry


thirteen
(1967).


of these


simulation models









incorporate


spatial


variation


in the price


of housing


services


and spatial


variation


in commuting


costs.


theory


consumer


behavior


been


modified


recently


to include


a spatial


dimension.


Although


recent


model


builders


have


noted


havior,


this


the spatial


theoretical


extension


of the theory


specification


been


consumer


considered


simplistic


sumption


to form


of a single


the basis


workplace


an empirical


model.


and the disregard


as-


of externali-


ties


are generally


cited


as the


two most


unsatisfactory


characteristics


of the spatial


theory


consumer


behavior.


purpose


of this


study


is to modify


the spatial


theory


consumer


ternalities


behavior


to incorporate


to use this


extended


multiple


theor


workplaces


as the basis


empirical


model


model


represents


of residential

an improvement


location.


over


existing


resulting

models fo


empirical


r several


reasons.


Spatial


variation


in the price


of housing


services


explicitly


represented.


Households


are


portrayed


as utilizing


housing


attributes


to produce


homogeneous


housing g


services;


this


approach


allows


one


to avoid


the arbitrary


establishment


numerous


housing


submarkets


based


on dwelling


unit


type


and neigh-


borhood


characteristics.


Most


important,


this


approach


provides


a model


which


explicitly


represents


the simultaneous


choice


housing,


location


and all other


goods.


t-n rrCiirlntini (1 nr


mnrisl.n


used


ex-


lnr'ainn


t-^Q onrnavnr hT


&1 fh ,i,,fyh









developed


in this


study


in historical


perspective


to estab-


lish


the need


a new


approach,


rest


of this


chapter


examines


the two major


existing


approaches


to modeling


residen-


tial


location.


Interest


in modeling


the location


decisions


of households


received


greatest


impetus


from


the large-scale


simulation


models


of the early


and mid


1960


These


models


typically


rely


on observed


empirical


regularities


to describe


household


loca-


tional


behavior.


Although


these


empirical


descriptions


occa-


sionally


reference


economic


factors


as justification


locational

generation


relationships, be

are characterized


havioral


equations


a reliance


of this model


on heuristic


mathe-


matical


relationships.


residential


location


submodels


of the Detroit


Regional


Transportation


Land


Study


(TALUS)


and the Bay


Area


Transportation


Study


(BATS)


can be considered


representative


the first


generation


approach.


The TALUS


study was


a four-year


project


begun


in the mid


1960'


to provide


estimates


of growth


the Detroit


area


to 1990.


The Detroit


model


allocates


house-


holds


over


1446


zones.


residential


subsector


forecasts


total


number


of nonmoving


households


life


cycle


for each


zone.


Mov-


households


are determined


comparing


forecast


totals


present


zone


population.








Spatial


allocation


of moving


households


depends


on initial


neighborhood


type


and life


cycle.


Eight


neighborhoods


are de-


fined


using


discriminant


and factor


analysis


on zone


characteris-


tics.


For each


of the


seven


life


cycles,


urobabilities


moving


from neighborhood


type


to neighborhood


type


are as-


signed.


An attractiveness


index


for each


zone


is then


used


allocate movers


to zones


within


each


neighborhood.


While


the TALUS


residential


submarket


represents


an innova-


tive

these


approach to forecasting

forecasts are derived


residential


a purely


location b

descriptive


behavior,

mechanism.


Little


consideration


of economic


factors


is evident


in this


model.


The Bay A

Land Use Model


trea


Transportation


(PLUM)


to allocate


Study


developed


households


a Projective


as part


a large-


scale


model.


basic


rational


behind


the PLUM allocation


that


household


location


can be described


the distribution


function


a-b/t


where


is the probability


an individual


living


less


than


from his


place


work.


probability


of locating


some


zone


of width


k is


Pt+k- t


ea-b/t


This


counties.


function


was


Predicted


estimated


total


separate


emp loymen t


for each


is distributed


of nine


to residential


zones


on the basis


of the estimated


distribution


function.


ea-b/t+k









locations;


however,


the allocation


rule


is still


little more


than


a descriptive mechanism.


None


of the other


structural


factors


affecting


While


these


household


first


location


generation


is explicitly


models


represented.


seem simplistic,


especially


in light


some


of the


more


recent


efforts


modeling


residential


location,


they


represent


a logical


first


step


in the development


of residential


models.


Since


economic


theory


in the early


not been


and mid


1960


brought


's. little


to bear


guidance


on urban


was


problems


available


structural


specification.


forecasting


approach


adopted


early model


builders


appears


to have


been


the best


avenue


avail-


able


at the time.


Only when


these models were


completed


the unsatisfactory nature


of the residential


location


submodels


and the urban


simulation models


in general


become


evident.


While numerous


large-scale


modeling


efforts


were


being


C0on-


pleted


in the mid


and late


1960


, a great


deal


of empirical


theoretical


analysis was


brought


to bear


on structural


aspects


of the urban


economy.


influences


of commuting


cost,


exter-


nalities,


race,


and accessibility


on the spatial


distribution


households


were


popular


topics.


Disappointment


over


the large-


scale


forecasting models


the burgeoning


interest


in the


structure


spatial


of the urban


sturcture


economy


to adopt


destined


a structural


future


studies


approach


of urban


less


ambitious


- -t









best


residential


examples


location


of the new


structural


are the National


Bureau


approach


of Economic


to modeling


Research


(NBER)


urban


simulation


model


(Ingram,


Kain,


and Ginn,


1972)


an econometric


model


of residential


location


developed


Granfield


(1975).


These


second


generation models


typically


approach


issues


from a microeconomic


viewpoint


and are much more


disaggregated


than


previous


models.


The NBER simulation model


represents


most


ambitious


of the


new models.


Although


this model


is concerned


with


aspects


urban


development,


heavy


emphasis


is placed


on the housing market.


Residential


location


is accomplished


in the demand allocation


sub-


model


where


households


are assigned


one of 44 residence


zones.


Households


are described


as belonging


to one of 72 household


types


depending


on family


size,


family


income,


education


of the household


head.


Demand


equations


are used


to predict


housing


type


income


groups


where


average


metropolitan


prices


for the different


housing


types


are the independent


variables.


Once


housing


type


is chosen,


location


is derived


allocating


households


to the residential


zone


which minimizes


both


opportun-


and out-of-pocket


travel


costs.


*Only


predict
studies


disaggregated


individual


which


models


household


examine


which


location


the spatial


can actually be
are considered.


influence


used


on residential


recent
location


develop models


(1975)


and Reachovsky


for predicting


(1974).


Urban


location,
Institute


see Straszheim


Leeuw,


1972)


has also


developed


a simulation model


of the urban


S S


sing market.











The NBER model also portrays vacancy generation,


supply and pricing in the housing market.


filtering,


This model undoubtedly


represents


the most complete model of


the urban housing market


and the first large-scale structural model of an urban area.

Although household behavioral relations are based on economic


theory,


the mechanism used to simulate locational choice is


rather unsatisfactory.


Intraurban variation in the price of hous-


ing is not allowed to directly affect the housing type or location


of moving households.


In addition,


the allocative scheme models


the choice


of housing and the choice of


location


as two separate


decisions.


This


recursive


process


is a poor representation of


the siuultaneous character of housing and locational choice.


A model of


residential location has recently been advanced


Michael Grdnfield


(1975).


This model


uses


a three equation


recursive


process


to allocate households to a dwelling unit type


and location and to determine housing expenditure.


are first portrayed


Households


as determining an annual housing budget as a


function


of current income,


neighborhood median


income and occu-


patron.


The housing budget


is then used along with race of house-


hold, neighborhood median income,


accessibility and commuting


travel


mode


to determine location


as a distance from the CBD.


Having


determined distance from the CBD and the housing


budget,


a third equation


is used to select housing type.


-Housing










Milwaukee.


Although


the s ipLJc it.


of this model is attractive,


anal ysis-o f-variance


tests


),;. simulated and actual observations


indicate that location


is not predicted with much success.


Like the NBER model,


this model


represents a simultaneous


choice as a recursive process aad fails


national influence of


to account for the lo-


intraurban variation in the price of


housing.


This approach does,


however,


appear to represent an


improvement over the NBER allocation scheme.


The generally


accepted price elasticity of housing demand of -1 is consistent


with a housing expenditure equation


(first step) which omits


the price of housing


services


as an independent variable.*


locational equation can be expected to perform satisfactorily

if housing and income can be described by smooth spatial distri-


butions.


That is,


this equation will not predict well when high


income-high housing areas


among low income-low housing


are dispersed in an irregular fashion


^- u.">


The attractiveness of this


model lies in the simplified approach to residential modeling.

The two second generation models surveyed above obviously

do not represent the ultimate *n empirical models of residential


location.


These recent :Iio :uling efforts,


however, make a signifi-


cant contribution to the s:tate-of-the-art by constructing models


based directly


on vtconomic .


theo cy.


'The models address in more













detail

istics


than previous efforts (iffereitic


in household character-


as they influence location and housing choices.


influences of


some


neighborhood effects such


as race and neighbor-


hood prestige


sre also incorporated.


The next step in the evolutionary process of empirical model

development must overcome two basic faults found in the second


generation models.


The first fault of existing models is the


inability to utilize spatial variation in the price of housing


services


in the allocation process.


The second fault is the


failure to capture the simultaneous nature of households'


of housing,


choice


location and all other goods.


It is demonstrated in Chapter


IV that a slightly modified


version of


the spatial


theory of consumer behavior can be used


as the theoretical basis for a model which


difficulties.


overcomes


Before developing the empirical model,


these two

it is neces-


sary


to consider two pragmatic aspects of locational modeling.



















TEST


CHAPTER
SITE AND


THE DATA


BASE


Milwaukee


was chosen


as the


test


site


for the empirical


model


veloped


in this


study.


Access


a rich


data


source


through


the South-


eastern


in this


Wisconsin


choice.


Regional


Milwaukee


Planning


is also


Commission


considered


was


a dominant


to be typical


factor


many


urban


areas.


The city


does


represent


an extreme


in terms


popu-


nation


or area


nor does


possess


special


characteristics


which


might


tend


to make


results


a study


based


on this


area


significantly


different


from


those


most


other


urban


centers.


many


points


in this


study,


specific


characteristics


of Milwau-


are referenced;


therefore,


IL is instructive


to present


a brief


profile


of the city


in the first


section


of this


chapter.


The second


section


discusses


the major


data


source


used


in this


study.


Accessi-


ability


a number


of extensive


SEWRPC


surveys


allows


a More


complete


test


of the empirical


model


than


would


be possible


using


only


pub-


listed


information.


A Profile of Milwaukee


Milwaukee,


ci tv


with


and is surrounded


a population


of 717,000,


the nineteenth


large


is the twelf

st Standard


largest


Metropo.i. tan


J _


I_ _


I


I


d


I








Milwaukee represents


.1 ature


indS'trZIal community.


Manufacturing


of nonelectrical machinery

in terms of employment, fo


is the most


important manufacturing activity


allowed by electrical machinery,


transportation


equipment,


food and kindred manufacturing and printing and publishing.


The labor force in the city


is over 290,000.


Ten percent of the resi-


dent work force in Milwaukee are employed at the CBD and 69 percent


are employed within the city.


Like other urban areas, Milwaukee has


undergone a substantial industrial and commercial decentralization in


the last fifty


years.


The spatial distribution of manufacturing em-


ployment in Figure 1 indicates the importance of a number of satellite


manufacturing centers.


The University of Wisconsin-Milwaukee and


Marquette University also represent significant employers in the city.


In 1970 these institutions employed over


3,000 individuals.


The impor-


tance of


these universities on the housing market is probably more


closely related to the


size.


of the student body.


In 1970,


29,000 stu-


dents attended both institutions with 18,000 of chat number enrolled at

the University of Wisconsin-Milwaukee.


The universal


inner-city


problem of pollution


is also present in


Milwaukee


as evidenced by particulate isopleths presented in Figure 2.


About three-fourths of


the land area in Milwaukee


centration of 75 micrograms per cubic


inec er


is subject to a con-


which is designated by the


U.S.


Environmental Protection Agency


as the maximum


average


annual


level


which


should be permitted in order


to protect human health


(South-


eastern Wisconsin


Regional Planning Commis.sion,


1974).


The Milwaukee



















Brown Bayside
Dser
Ariver HitI

*: I*S





aa
I -- 1IS









"..- Shorewood
1 1 1 r' tI

^- 9 i ndfle f

S'Wiscoh


: --- 'A'J" ,-"CBD


I 1,' 1 UnLive

West Allis





Greenfiek4
S-.----- *.-.- I i !1ll


Hales Cudahy
Corners Grendal



Sonlth


Franklin


ersity


is in- Milwaukee




ette
rsity


Milwauke,


Cak Creak



flit


,!!1


v


I


I


,9







16









70

+ tOWn .
S Der, r
R or w Hills
,. ..fx P oint




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r" 9 Si














Ts'





S. .. .--. .. .... -s 7 5
j. J- 7n


Green id +




Hales Cudahy
Corners Gr jnd-l
+, ... I+T -.- -+ i +c" ,1o








Franklin Oak CSreeko
! J ^ er^7"1^
j ^ t.sa-y ^i-^..1.^^,^^, ^^^*--/j-1-^^I

I fr^F^i^^^^~t8
I 1,m *M ii~ ^ ''niJ ^ 11^- ^ <-'l'^' ^^ .-
* *Ifj ~ t'- j~-_ ^ f ^ ^


















Brown tysidB
Dear
Rivar Hill
.-*- .Fox Point




"- y"= "^ \ Glendal, "" 'o

'^ Whitefish
.. J -- '*S

SShorewood











st Alis






-C'
St. Francis
Greer i p-'-- i


Hales 1 -85 Cudahy (
Corners Greendale


South
Milwaukee



Franklin Oak^ Creek
\









sisting


a bypass


which


nearly


encircles


the city


arteries


which


approach


the CBD from


west,


nor th


and south.


influence


of this


expressway


system


on commute


time


is examined


in Chapter


The influx of


blacks


I rom


the south


increased


the Milwaukee


black


population

ern cities

suburbs.


from

this

In the


in 1950


inrigratiou.


last


was


decade,


to 105,000 by

accompanied


the number


1970.


a white


of whites


As in other


flight


leaving


North--


to the


Milwaukee


nearly


twice


the number


of arriving


blacks.


It is evident


from


Figure


that


blacks


live


a highly


segregated


corridor


extending


a northwesterly


direction


away


from


the CBD.


The social


character


of Milwaukee


is heavily


influenced


ethnic


background.


The German


and Polish


communities


are


still


very


much


evident


in Milwaukee


today.


The conservative


character


of the


city


is usually


said


to result


from


the old-world


orientation


most


Mi iwaukeans.


Milwaukee


is characterized


somewhat


less


poverty


unemployment


than


mo s t


large


metropolises.


Crime


is also


less


a prob-


in Milwaukee


than


most


cities


of the


same


size.


There


is probably


more


diversity


of incomes


and housing


in Mil-


waukee


than


many


cities


because


of the city's


geographical


character.


Milwaukee


extends


over


eighteen


miles


from


southern


to northern


boundaries.


The northernmost


census


tracts;


represent


some


of the


low-


est housing


unit-land


area


ratios


in the


county,


while


the inner


city


represents


the highest


housing


unit-land


ratios.


Rent


and dwelling


unit


value


also


vr 1 v


considerab


across


census


tracts.


was


* L*-


I


*- 7


I


I ,
















Brown ~ Bayside
*
Deer I
iive r Hills .
Fox Point



] Glendale L '

.... ,Whitefish
2 .L.
Bly










._
+ if








,St. Fran ci s
Grenf iShoreweldod










i Hales r r----- J Cudahy
Cornerrs Greendale


South
Milwaukee


Franklin Oak Creek


- 10% b


lack


- 25% black

- 75% black


-- 100%


black








locational


decisions


of households


in Milwaukee


can


be followed


successful


applications


of the


same


model


to other urban


centers.


The SEWRPC Data Base


In 1972


the Regional


Inventory


of Travel


was


undertaken


SEWRPC


to provide


new


information


on travel


habits


and social


eco-


notmic


characteristics


Wisconsin


region.


of families


inventory


in the


seven-county


consists


survey


southeastern


The three


surveys


used


in this


study


were


obtained


personal


interview


from


percent


sample


of households.


first


survey


utilized


is the Home


Interview


Survey


where


formation


is collected


on the following


items:


family


composition,


race


of household


members,


dwelling


unit


type,


household


loca-


tion


work


status


and work


locat ion


of household


residents.


sur-


definition


responses


for this


survey


is given


in Appendix A.


The Internal


Trip


Report


provides


information


on work


trips


for each


household member


in the Home


Interview


Survey.


Trip


origin,


trip


desti-


nation,


trip


purpose,


starting


time,


arrival


time,


and mode


of travel


variables


of interest


in this


survey.


survey


definitions


the Internal


Trip


Report


are presented


in Appendix


The Household


History


Survey


presents


information


on ownership


status


value


or rent,


length


tenure


and family


income


for each


household


surveyed


in the Home


Interview


Survey.


survey


defini-


tional


information


is given


in Appendix


Variables


of interest


from


each


survey


are merged


household.


are


I









data file contains the following information on each household:


sam-


pie number,


race of head,


age of head,


occupation and industry of em-


ploymrent of head


, number of


children,


presence of


relatives in the


household,


home location,


work location,


commuting time to and from


work location, ownership status,


value


or rent,


family income, and


length of cime at present location.


This data source is unique in that


are available by household.


many variables of interest


All information necessary to estimate the


demand function parameters is present.


In addition,


reported commuting


times are used in Chapter VI


off matrix to be used


to derive a commute time-location trade-


to predict location.
















CHAPTER


AN EMPIRICAL HODEL


OF SPATIAL


CONSUMER


BEHAVIOR


spatial


theory


consumer


behavior


is usually


considered


simplistic


to have


any value


in describing


actual


locational


decisions


of households.


disregard


of externalities


and the assumption


single


workplace


are generally


cited


as the


two most


unsatisfactory


features


in the spatial


theory.


The objective


of the first


section


of this


chapter


to modify


the theory


to incorporate


these


factors


which


play


such


an integral


part


in the spatial


distribution


of residential


activity.


An empirical


model.


which


is consistent


with


the extended


spatial


theory


consumer


behavior


is specified


and estimated


in the second


section.


Modification of the Spatial Theory of Consumer


Behavior


The spatial


theory


consumer


behavior


been


unified


tended


most


recently


Richard Muth


(1969)


** According


to Muth


basic


model,


consumers


choose a


level


of housing


services


and goods


consumption


as well


as location


in order


to maximize


their


utility


function,


lizing,
see In


*For


general di


the spatial


gram,


Kain,


scuss


tneory
and Ginn


ion of


diffi


cifi


(197


, pp.


culties


cation


-20)


encounter


emnpiri


and Straszheim


red in
models
(1975,


uti-


. 11-22)


ex-


$ a









= U(H,


subject


to the budget


constraint


= P-G


+ p(k)


*H + T(k,


where


= consumption


of housing


services


= quantity


of the composite


commodity


consumed


household


= price


of the composite


commodity


= distance


to the central


business


district


(CBD)


p (k)


= price


uint


of housing


as a function


of distance


the CBD


T(k,


= cost


per trip


as a function


of location


and income


mutliplied


a given


number


of trips


to the CBD


= income


It is assumed


that


economic


activity


occurs


some


point


(CBD)


on a uniform


limitless


plane


with


the remaining


locations


avail-


able


for residential


purposes.


Households


make


a fixed


number


of trips


to the CBD


only


a cost


on distance


which

wage


is the

income.


same


in all directions


Income


is included


and depends


as a commuting


cost


determinant


to reflect


the opportunity


cost


of time


spent


com-


muting.


It is assumed


that


work


time


constant


so that


the time


spent


in leisure


and commuting


together


is also


constant.


The price


of the composite


good


and the


wage


rate


are assumed


to be spatially


constant.


Before


discussing


the implication


of this


theoretical


specifica-











including


"travel


time


costs


in trip


costs


and the money value of


travel


t inme


in the income


variable


in the consumer's


budget


constraint.


This


specification


is incorrect.


Mo vemen t


away


from


the CBD in-


creases


cost


of commuting;


however,


this


cost


is exactly


offset


an increase


in Muth's


income


measure.


This


specification


provides


a net result


not incorporating


the opportunity


cost


of travel


in the


consumer


allocation


problem.


difficulty


can be remedied


Becker's


(1965)


concept


of full


income.


Full


income


equals


wage


nonwage


income


as well


as the opportunity


cost


of all


leisure.


classical


This


model


concept


is the relevant


incorporates


leisure


income


as a good.


constraint


Hereafter


when


is used


to represent


full


income.


Muth'


specification


of the


consumer


problem assumes


that


consumer


rece


ives


no utility


or disutility


from


commuting.


Consumers


reveal


a locational


preference


as a result


of spatial


variation


in both


the price


of housing


services


and commuting


costs.


Other


things


equal,


more


accessible


locations


are preferred


to less


accessible


locations


because


more


income


net of transportation


expenditure


is available


to purchase G


and H.


Lagrangean


function


resulting


from


and (2)


necessary


conditions


for household


equilibrium are


derived


by taking


the partial


derivative


of L with


respect


to H


and X.


sum


L using


This


w





p









. OU
?H
- 4

3G
all

-


- xp(k)


(H3p(ki
3k


+ T(k))
-k


= PG


+ p(k)H


+ T(k,y)


the simultaneous


solution


of the first


second


equations


gives


BU
MI
H(k)
p(k)


The condition


of spatial


equilibrium


is derived


from


the partial


derivative


of the Lagrangean


with


respect


to k.


Setting


this


expres-


sion


equal


zero


gives


Hap(k)
ak


_ 3T(k,y)


This


equation


states


that


in equilibrium,


the savings


in housing


exDenditure


commuting


brought


cost.


about


Since


a short


the change


move


is exactly


in total


offset


commuting


cost


a change


with


re-


spect


an increase


in distance


to the CBD,


y)/3k,


is always


positive,


equation


declines with


distance


also

from


requires

the CBD.


a price


of housing


a stable


services


equilibrium


which


to ob-


tain,


the second-order


conditions


require


that


the price


of housing


decrease


a decreasing


rate


with


distance


from


the CBD


(see


Muth,


1969 ,


25).


Muth


uses


this


economic


theory


of spatial


consumer


behavior


along


with


a spatial


theory


of the firm


to develop


test


hypotheses


con-


*


r* C' 'C / 4% 1 1 1 ., nf aa4


PU
= BG
PG


- XP


aT(k,


rl nnl: y^- *~ <" T4^


^*t -P Ti < n f* n^


nnnC LI ^^^ -


/-^<4 ^ f^4 *


^h rt 4- *- n -<- /










Although Muth's


theoretical


formulation


been


used


in countless


theoretical


studies


of urban


structure,


no one has used


the model


as a


conceptual


basis


for building


a disaggregated


model


of residential


cation.


suit


neglect


of the heroic


of this


assumption


approach


a single


in empirical


workplace


studies


location


a re-


and the


fact


that


externalities


involved


in urban


housing


consumption


completely


ignored.


Externalities


that


affect


the urban


housing


market


include


pol-


lution,


neighborhood


status,


neighborhood


racial


composition


other


factors


except


structural


and accessibility


characteristics


which


influence


rent


a dwelling


unit.


housing


services


concept


provides


a vehicle


for specifying


the relationship


between


externalities and


household


behavior.


Muth


was


the first


recognize


that


dwelling units


can be


con-


centualized


as providing


occupants with


a homogeneous


good


called


housing


services.


According


to this


approach


dwelling


units


valued


only


for the housing


services


that


they


provide.


price


housing


services


refers


to the price


a flow


of services


from


dwelling


unit,


the price


of the


asset.


Housing


expenditure,


which


refers


to the total


expenditure


on housing,


equals


the price


times


the number


of units


of housing


services


consumed.


fnr Yamn nrn


Sln nw


(197'1


P11in -


and Sheshilnski


are


are


s^^


..


and Orn -









It is assumed


that


households


combine


dwelling


unit


attributes


in order


to produce


housing


services.


Although


Muth


never


detailed


the relation


between


attributes


and housing


services


output


this


pro-


cess


can be described


a household


production


function


of the follow-


form:


= H(L,


where


= housing


services


= vector

= vector


of land


attributes


of structural


attributes


Neighborhood


effects


can be incorporated


in the Muth


theoretical


framework


recognizing


them as


location-specific


unpriced


public


goods


which


influence


the household


production


process


a manner


analogous


to the influence


of public


goods


on the production


process


of firms.


This


relationship


can be represented


= H(L,


where


= vector


of neighborhood


effects


for beneficial


for detrimental


neighborhood


neighborhood


effects


effects


or amenities


or disamenities


*Becker


(1965)


and Muth


(1966)


are credited


with


originating


idea that


commoditi


purcha


consumers


are inputs


in the


pro-


auction


of goods


description


consumed


consumer


within


the household.


behavior which


For a brief


incorporates


analyti-
household










The household


production


function,


and the marginal


product


conditions


simply


formalize


the notion


that


the existence


a disamenity


(amenity


at some


location


is considered


tc decrease


(increase)


level


of housing


services


derived


from


dwelling


units


located


in that


neighborhood.


Treating neighborhood


effects


as inputs


in the housing


services


production


function allows


the extended


model


to retain


basic


specification


a price


of housing


services


which


varies


only


as a function


of accessibility.


While


model


the neglect


is generally


of neighborhood


considered


serious,


effects


in the original


assumption


Muth


of a monocentric


urban


economy


is wholly


unacceptable


to most


empirical


model


builders.


suburbanization


of manufacturing


and commercial


activity


a well-


known


phenomenon.


Although


it is conceivable


that


the CBD may


still


be the focus


an urban


economy,


it is unrealistic


to expect


distance


to the CBD


to be


a suitable


proxy


for accessibility when


considering


household


locational


decisions.


reason


for using


the monocentric


assumption


to facilitate


analytic


solution.


one is willing


to fore


some


analytical


con-


venience,


however,


severe


monocentrnc


restriction


can be dropped


with


no harm


fiction


to the implications


is achieved


replacing


of the theoretical

k (distance to th


model.


e CBD)


Thi

with


modi-


a car-


tesian


coordinate


notation


where


represents


a residential


loca-


tion


and (


represents


an employment


location.


_I_


~__~I__









The modified


model,


whi ch.


incorporates


both


neighborhood


effects


and the multimodal


nature


of the urban


economy


can now


be written


= U(H,


= H(L


, N)


*G + p(X,


Y)-HI


+ T(.)


where


= price of ho
residential


servi


locati


ces


where


as a function


X and Y


represent


cartesian


coordinates


= T((X,Y)


, cXw,
total


Y), y) =
commuting


cost


from


the residential


location


to the work


location,


first


order


conditions


of utility


maximization


for the modi-


field


model


are


same


with


respect


to the marginal


utility-price


conditions.


The condition


of spatial


equilibrium


is given


-Hap (X,Y)
ax

-H9p(X,Y)


=_ T(*)
ax

=_ T(-)
aY


These


equations


state


that


the chan


in housing


expenditure


duced


a short


move


in the direction


of either


axis


is offset


change


in commuting


expense.


These


conditions


are


simply


the two-dimen-


sional


equivalent


of the condition


of spatial


equilibrium in


the basic


Muth


model.


It is


apparent


that


the relatively minor modifications


required


to incorporate neighborhood


effects


and multiple


workplace


locations


have


not changed


the basic


theoretical


framework.


remainder of


T(-)


(,w,


Yw,)









An Empirical Hodel of Consumer Behavior


The empirical


model


of residential


location


developed


in this


study


is based


directly


on the modified


spatial


theory


consumer


havior


presented


in (8).


destination


location


of each


moving


house-


hold


is predicted


determining


the residential


location


that


provides


maximum satisfaction.


This


destination


can be determined


only when


the general


empirical


utility


and household


relations.


production


objective


of this


functions


section


are replaced


to specify


a utility


function


and to estimate


its parameters.


Since


it is


not possible


to estimate


utility


function


parameters


directly,


one must


posit


a specific


utility


function and


then


use the


first-order


conditions


of utility maxmization


to estimate


utility


func-


tion


utility


parameters.


function


This

which


approach re

corresponds


quires


a functional


to actual


behavior


form fo

as well


r the


as one


which


provides


first-order


equations


which


are amenable


to parameter


estimation.


A Cobb-Douglas


specification


satisfies


both


of these


requirements.


This


function


is specified


= alln(H)


+ (l--al)ln(G)


functional


of -1 and


form of


a net income


implies


elasticity


a price


of housing


elasticity


demand


of housing


of 1.


demand


Net income


refers


to income net


of transportation


costs.


gross


income


elas-


ticity


depends


on income


commutin g


time;


typical


values


for the


data


sample


used


in this


section


for estimation


yield a


corresponding









gross


income


elasticity


of between


.96 and


Considering


the nearly


identical


income


elasticity


elasticity


figures,


is ignored


the distinction


in the discussion


between


of prior


gross


elasticity


estimates.


elasticity


restrictions


implied


the Cobb-Douglas


utility


function


appear


to coincide with


actual


household


behavior.


study


of the


cross


sectional


demand


for housing


de Leeuw


(1971)


reviews


previous


estimates


of the income


elasticity


of the demand


for housing.


De Leeuw


finds


that


past


studies


indicate


an income


elasticity


for *


renters


of between


and 1.0.


Homeowner


elasticity


estimates


range


from


to 1.46.


De Leeuw presents


new


evidence


based


on census


Bureau


of Labor


Statistics


data


which


indicates


income


elasticities


slightly


below


1.0 for


renters


and about


1.1 for homeowners.


Although


hampered


estimation


the quality


of the price

of the housing


elasticity


price


of housing


information,


demand i

appears


that


a unitary


price


elasticity


of housing


demand


is also


consistent


*Maximizing


with


respect


to the budget


constraint


in (8)


gives


the demand


for housing


services


= aI(y


p(X,Y)


gross


income


elasticity


of housing


demand


is given


yH v
ay H


p(X,Y)


1 ST(')
- _T()) ___ y__
Sy al(y T(-)) 1 T( )
p(X,Y) Y


**It is


necessary


assume


that


the full


indifference


a1 .5


can


- T("


m -- Im m









with the empirical

a price elasticity


evidence.

of around


Muth'

-1.0.


Margret


time

Reid


series

(1962)


analysis


also


suggests


presents


an estimated

elasticity f


price


igure


elasticit

of around


of -1.0.


-1.4.


Lee'


De Leeuw'


(1968)


s (1971)


estimates


cross


yield


sectional


study


indicates


price


elasticity


ran


of from


to -1.5.


Cobb-Douglas


utility


specification


also


implies


a price


elasti-


city


-1 and


a net income


elasticity


of 1


for the composite


good


Considering


the Ccurnot


Engel


aggreg


action


restrictions


on a system


of demand


equations,


however,


the elasticity


estimates


obtained


from


housing


studies


are


close


enough


to the implied


elasticities


of the


Cobb-Douglas


utility


function


to justify


accepting


the utility


func-


tion


as consistent


with


empirical


evidence.


next


step


in deriving


an empirical


utility


function


to esti-


mate


parameter


expenditure


relation


This


from


is accomplished


the first-order


deriving


conditions


the housing


of utility maximi-


zation.


Given


a stochastic


disturbance


term


the resulting


equa-


tion


for housing


expenditure


HE = H*p(X,


It is evident


from


equation


that


represents


the proportion


of income


net of transportation


costs


devoted


to housing.


It is assumed


that


this


proportion


changes with


the life


cycle


of the household


with


other


demographic


factors


in the following manner:


=a


tJhPrs n.


min1 nir t c


I


life rcyle


and demograohic


characteristics


and the


(1960)


= al(y-T(









Incorporating


the differences


taste


represented


housing


expenditure


equation


we obtain


the following


econometric


model


t U


Where


= income


net of transportation


costs


and u is


a sto-


chastic


disturbance


term.


Several


issues


must


be considered


before


equation


(12)


can be esti-


mated.


First


must


be replaced


an estimated


cost


commuting.


Next


the problem of


measured


versus


permanent


income


must


be considered.


Finally,


the data


sample


used


for estimation must


be chosen


from


Southeastern


Wisconsin Regional


Plannin


Commission


data


file.


established


earlier


that


is composed


of both


out-of-


pocket


opportunity


cost


components.


It is assumed


that


the out-of-


pocket


cost


of commuting


is proportional


to the time


spent


commuting.


Meyer,


Kain,


and Wohl


(1965)


estimate


this


expense


at 2.9


cents


mile.


Assuming


an average


intrametropolitan


commuting


speed


of 20


miles


hour


converts


this


to 58


cents


hour.


Household


valuation


of time


spent


commuting


is family well


estab-


lished


empirically.


Kraft


and Kraft


(1974)


recently


reviewed


previous


estimates


of the value


of time


spent


in commuting.


five


previous


studies


surveyed


indicate


that


commuting


time


is valued


at from 40


to 42


percent


of the


wage


rate.


The Krafts'


own


results


indicate


value


of 41


percent.


It is assumed


here


that


household


heads


value


their


commuting


time


at 41


percent


of their


wage


rate.


Total


trans-


Itn a .-4 r 4 a nf ls ^


was


= ay


- T(


nnn <" mT rr


*~ J. *


m*Wl a^* V /^*


f\S-









where


TIME

y/160


= number

= monthly


of hours

earned


per month


income


spent


divided


commuting

160 hours


yield


an hourly wage


The income


variable


used


in the theoretical


model


in the


pirical


form


estimating


studies w

permanent


which


supports


income.


the housing


expenditure


the choice

consequence


equation


a Cobb-Douglas


of using measured


is to bias


functional


income


the coefficient


(and


components,


= 1,


toward


zero.


This


situation


is simply


a special


case


the econometric


problem which


arises


when


the explanatory variables


are subject


to measurement


error.


This


bias


can be quite


of housing


estimate


significant

es derived


as attested

in the 1950s.


to by the income

These estimates


elasticity

range


from about


zero


As established


above,


more


recent


studies


which


incorporate


permanent


income


indicate


an income


elasticity


about


1.0.


A downward


stitution


biased


of housing


estimate


for all other


implies

ods which


a marginal

is biased


rate o

in the


f sub-

same


direction;


this


bias


makes


households


appear more


willing


to trade


housing


for other


goods


in search


an optimal


location.


h
B/(l+c /
2.v


e0as
2')


ymptoti2


where


variance


bias


of the OLS estimate


variance


true


given


measurement


income


y plim
error


(6) =
in income


values.


**See Johnston


(1972,


281-283).


***For


a brief


review


of these


works


see Lee


(1964).


em-









This


result


can be demonstrated


considering


an estimate


which


contains


a downward


bias


of magnitude


v such


that


- V


where


equals


the estimated


value


of the


true


parameter


The estimated


utility


derived


at each


location


is given


= alln(H)


= alln(H)


- al)1n(G)

- al)ln(G)


- vln(H)


+ vln(G)


= U + vln(G/H)


(14)


Since


the predicted


destination


location


of each moving


household


is defined


as that


location


which


corresponds


a maximum


of the esti-


mated


utility


function,


implies


that


a downward


biased


estimate


results


an inferred


allocation


of households


to locations


charac-


terized by


a lower


level


of housing


services


that


would


be the


case


were a


consistent


estimate


One approach


to deriving


a consistent


estimate


to utilize


the instrumental


the selection


variables

a variable


estimation


technique.


or instrument


which


This


approach


is correlated


requires


with


true

error


variable

(the tr


(permanent


ansitory


income)


component


uncorrelated


of measured


with


income).


measurement

instrument


is then


used


along with measured


income


to derive


coefficient


estimates


which are


consistent.


Fortunately,


detailed


data


on occupation


industry


affiliation


of household


heads


collected


in the Home


Interview


Survey provide


= al








opportunity


to construct


an instrument


permanent


income.


It is


reasonable


assume


that


workers


in the


same


occupation


and industry


and of the


It follows


same


that


race


regressin


perceive


the reported


nearly


income


same


figures


permanent


on age


income.


race


of individual


workers


industry


and occupation


produces


a fitted


gression


line


that


maps


race


onto


permanent


income.


Those


ported


negative


income


observations


transitory


income


lying


below


component


regression


and those


above


line


reflect


indicate


pre-


sence


a positive


occupational


classifications


and 75 industry


categories


provide


a rather


total


detailed


of 1246


picture


observations


of each


respondent


on reported


income


s job


classification.


occupation,


industry,


race


were


compiled


for males


employed


in 23 of the industry-occupa-


tion


categories


industry


for Milwaukee


and occupation


county.


and reported


data


income


are


is regressed


stratified


on age


race.


The relevant


estimated


coefficients


are then


used


to derive


instrument


permanent


income


for each


household


in the housing


penditure


data


sample.


is recognized,


course,


that


the predicted


permanent


income


an imperfect


measure


of the


true


permanent


income.


Personal


charac-


teristics,


such


as native


intelligence


personality


and insufficient


disaggregation


of occupation-industry


categories


are


likely


to be


*A logical


or past


income.


first
As w


nn *1 .i-n 4-n


choice


ith most


an instrument


cross


'., i-br, C I"TJDD


sectional


some


surveys,


weighted
the only


average
income


re-


re-


component.


ex-


A. *q ~ Y~. -a .%- ,- --- -- S ---------------


nir ,i l 'lrn ,S


* -


,U A d dlml


-^










of the most


important


sources


of inaccuracy.


The instrumental


variables


approach,


however,


will


still


yield


consistent


coefficient


estimates


the expenditure

not correlated


variables


function


with


used


as long


the transitory


as the predicted


component


in the instrument


permanent


of reported


regression


models


income


income.


include


ported


income,


age,


race.


Race


is represented


in the regression


models


as a binary


variable,


which


assumes


the value


one


for blacks


zero


for whites.


is used


as it is reported


in the


survey.


ported


income


is indicated


in the data


file


as belonging


one of


income


classes.


The first


through


fifth


categories


have


a $2


,000


range


with


the first


category


beginning


zero.


The sixth


throu


h tenth


classes


are composed


the following


ranges


$12,000


- $14


,999,


$15,000


- $24


,999,


- $49


,999,


$50, 000


The first


and last


cate-


gories


are not indicated


of the observation


used


in this


esti-


nation.


It should


The midpoint


be noted


of each


that


range


is used


measurement


error


as the dependent


occurring with


variable.


the depen-


dent


variable


does


cause


coefficient


bias


as is the


case


measure-


ment


error


in the independent


variables.


The few observations


in the original


sample


of 1289)


reporting


income


problem.


in the $25,


Each


to 49,999


observation


annual


reporting


income


an income


range


in this


created


class


a particular


appears


an outlier.


This


situation


causes


the income-age


relationship


even


,500


household


to overwhelm


income-age


relationship


of all


- e>g


- C


1 C- -


* 2*L .


re-


one


- T


1


T-


1__


__


*











estimated


coefficiencs


for the 23 models


are


presented


in Table


kinds


of age-income


relationships


are evident


in Table


first


is characterized


a significant


coefficient


on the


variable.


This


result


is expected


when


an increase


in job


skills


or an institu-


tional


salary


schedule


causes


permanent


income


to increase


over


time.


second


age-income


relationship


is characterized


a coefficient


on age which


not statistically


different


from zero.


Occupations


characterized


a low


skill


level


are expected


to fall


in this


category.


It should be


noted


that


the coefficient


of determination


regression


characterized


an insignificant


coefficient


good


indication


of the ability


of the predicted


permanent


income


represent


true


permanent


income


since


this


statistic


provides


infor-


nation


only


on the variation


in income


explained


by variation


race.


instrumental


variables


approach


can now


be outlined


more


detail.


relevant


industry-occupation


regression


model


is used


calculate


a predicted


permanent


income


for each


household


observation


used


to estimate


for each


taste


the housing


taste-income


variable


expenditure


interaction


the predicted


term


equation,


is constructed


permanent


income.


An instrument

multiplying


instrumental


variables


estimation


procedure


(Johnston,


1972,


278-281)


can now


be used


to derive


consistent


estimates


taste


variables.


C


CI~l


I


1





































cn n


N<- t-


00 r4


L f-I


0- a
C) a 0
0X U <
-r-t X C;














0
*1-4


0 k
(U
M 5-t

0)
Cflb


r-r H


O CN


r)
3U


a 0

uS


4J4)s






























































































































































































































































































































































































































































m
a










Having


be focused


meters


derived


an instrument


on the selection


of the expenditure


a data


equation.


permanent


sample


was


income,


attention


estimating


decided


to include


para-

only


husband-wife


families


(with


or without


children)


in the estimation sub-


sample


in order


to decrease


the number


of required


life


cycle


demo-


graphic


variables


a manageable


size.


Since


husband-wife


families


account


for 91


percent


of all


persons


not


residing


group


quarters


and 83


percent


of all families


in Milwaukee,


this


subsample


can


still


be considered


representative


of the total


urban


population.


also


necessary


to omit


all families


with


unemployed


heads


since.


commuting


costs


and workplace


location


are unknown.


Families


with


employed


spouses


were


also


excluded


from


the sample


because


it is


not possible


to determine


permanency


of the secondary


income.


Mincer


(196


shown


that


many


spouses


take


jobs


on a short-term basis


offset


a decline


in measured


income


below permanent


income.


Addition-


ally


it is


not clear


households


value


spouse


commuting


time.


examination


of the employed


head-employed


spouse


family


type


a topic


which


requires


further


research.


Because


of the possibility


that


homeowners


possess


different


tastes


than renters, th

ership category.


renter


ie housing


households


expenditure


data


housing expenditure

as reported monthly


sample

variable

rent.


is stratified

e is directly a

As demonstrated


own-


available

in the


next


chapter,


it is reasonable


to expect


expenditure


for housing


ser-


C -, -.--


- -1


'Yr-f 'In<


Tn 44,4 e


was


r ~ ~~.n C3' 5 / *^fA


*










is used


as the dependent


variable.


actual


regression


coefficient


estimates


are related


the conversion


ratio


that


is used


to derive


housing


expenditure


from dwelling


unit


value.


For convenience


in in-


terpreting


the results


of the estimation,


dwelling unit


value


is used


to estimate


owner


equation.


selection


of the estimation


subsample


has greatly


reduced


required


number


taste


variables


which


must


be specified.


Taste


variables


used


include


of head


of household


(AGE),


number


of child-


ren (CHILD),


presence


a relative


in the household


(REL),


and a bi-


nary variable


indicating


race


of the head


(RACE).


regression


models


can now


be written


= ay


+ anAGE*y


+ a2CHILD'y


- + a3RELy


a4RACEy


where DV


represents


dwelling


unit value,


HE is housing


expenditure


rent


u are net full


income


a stochastic


term


as defined


previously.


An estimation


sample


of 93


renters


owners


is available


the SEWRPC


data


files


to estimate


the housing


expenditure


and dwelling


unit


value


equations.


each


household


in the estimation


samples,


the coefficients


reported


from


in Table


the relevant


are used


income-age-race


to construct


regression


an instrument


model


permanent


income.


The expenditure


equations


are estimated


using


both


OLS and instru-


-~~ -


* .


I


1


~


I


.










"family

a query


income"


on family


specifying


income


one of


probably


ten income


provides


classes.


an income


answer


figure


that


closer


to permanent


income


than


previous


month


s or previous


year


s in-


come


as is usually


reported


in cross-sectional


studies.


housing


expenditure


and dwelling


unit


value


regression


results


presented


in Table


show


that


use of


reported


income


does


appear


to bias


the estimates


of the housing


expenditure-permanent


income


ratio


downward.


small,


As suspected


apparently


however,


because


extent


of the method


of this


used


bias


to obtain


is comparative-


the income


data


in the SEWRPC


survey.


At the


mean


value


of the life


cycle


var ia-


bles,


renters


estimates


exhibit


a bias


of about


percent


while


owners


estimates


are


biased


downward


percent.


regression


the dependent


results


variable,


are quite


housing


good


expenditure,


considering


also


the fact


contains


that


measurement


error


as a result


of the


use of


seven


rent


value


classes


used


to collect


rents


this


differing


information.


as much


avera


as $31.67.


rental


In light


range


of this


incorporates


measurement


error,


the regression standard


error


of $36.03


represents


an exception-


ally


good


fit.


standard


error


for the


owners


equation


of $5,897


even


less


than


average


spread


of $


000 found


in the ownership


value


classes.


of the estimated


relationships


are characterized


a high


value


for the coefficient


of determination


(R2).


This


is partly


a re-










TABLE
OLS and Instrumental Variables
Expenditure and Dwellin


2
Estimation
Unit Value


RENTERS-Housing


of the Housing
Equations


Expenditure


Equations


AGE*Y


RACE*Y


CHILD*Y


REL*Y


.1316
11.17


.0008064
.61

.0008318
.58


-.0152
1.27

-.0173
1.40


-.004169
1.73

-.004542
1.83


-----


.930


.929


35.77


36.03


OWNERS-Dwelling


Unit


Value


Equations


.431
.10

.442
.84


-.004365
1.17

-.003722
.95


-.03224
.17

-.05011
.26


-.01377
.53

-.01408
.52


.4645
2.17

.4659
2.15


.942


.941


5860


5897


t-values are
SE = standard


presented
error of


below
the r


the coefficient


egres


estimates.


sion.










specification,


the relevant


measure


of variation


in the dependent


vari-


able


is variation


from


zero


instead


of the usual


measure


of variation


from


the sample


standard


error


mean


of the dependent


of the regression


variable.


provides


a more


In this


case,


meaningful


measure


of goodness


of fit.


coefficient


estimates


and their


standard


errors


indicate


that


the rent-income


ratio


displays


a significant


variation


only


because


age.


dwelling


unit


value-annual


income


ratio


also


displays


little


significant


variation


across


taste


variables


except


presence


of relatives


in the household.


Since


only


four


households


include


relatives,


this


coefficient


probably


cannot


be interpreted


being


representative


of all such


households.


race


variable was


included


to reflect


possible


differences


taste


of the nine


black


renter


and six black


owner


households


in the


data


samples.


insignificance


of these


coefficients


suggests


that


race


is not,


at least


in Milwaukee,


a factor


in determining


housing


expenditure.


regression


coefficients


presented


in Table


are somewhat


dif-


ficult


to interpret


because


the income


variable


represents


full


income


net of transportation


costs.


It is preferable


to convert


the coeffi-


clients


so that


they


relate


to the


more


usual


income measure.


con-


verted


coefficients


are presented


in Table


rent-


and value-income


ratio


estimates


displayed


in Table










TABLE


Rent-Income


Ratio


Household


Type


Additional


ratio


for:


Basic


rent-income


Each 10


years


Black


ratio


Head


household


Each


child


household


.195


-.0124


.202


-.0128


-.00640

-.00698


-.02340

-.02658


Additional


ratio


for:


Basic


value-annual


Each


years


Black


income


ratio


Head of


household


Each


child


household


Relative


2.199


-.067

-.057


2.216


-.0211

-.0216


-.0495

-.077


.714

.716










16 SMSAs


in the sample


.182.


Estimated


value-income


ratios


vary


from


1.6 to 2.1 and


average


1.8.


The rent-income


ratios


derived


present


study


are based


on contract


rent


rather


than


gross


rent


used


in the Ekanem


study.


Gross


rent-income


ratios


can be estimated


from

by 1


.


the ratios

231 where


derived


1.231


in this


represents


study


by multiplying


the ratio


gross


the original


rent


ratios


to contract


rent


for the city


of Milwaukee.


This


procedure


results


an approx-


imate


gross


ren t


income


ratio


for Milwaukee


.187.


average


value-


income


ratio


of 2.00


also


lies


well


within


the Ekanem


range.


satisfactory


estimation


of the utility


function


parameter


completes


the first


step


in constructing


an empirical


model


based


the theory


of residential


choice


as given


in (8).


remaining


steps


can be enumerated


examining


the actual


allocation


procedure


of house-


holds


used


in Chapter


VII.


Information


in the budget


constraint


can be incorporated


in the


utility


function


substitutin


for G


so that


= alln(HE)


+ (1-al)ln(y


- (.58


+ .41(y/160))


TIME


- alln(p(X,


- (l-al)ln(PG)


(16)


where


HE = Hp(X,


each


moving


household,


the utility


function


is evaluated


each


possible


destination.


That


location


which


represents


a maximum


of the utility


function


is considered


the destination


location.


94i


r


-









Since


the price


of all other


goods


(PG)


is the


same


for all loca-


tions


in the city,


the last


term of


can be ignored


in solving


the spatial


location


problem.


In order


to evaluate


(16)


additional


information


is needed.


level


of housing


expenditure


price


of housing


services


must


be determined


for each


possible


destination


location.


In addition


the commuting


time


for the household


head must


also


be known


for each


possible


residential


location.


next


chapter


is devoted


to the estimation


of the housing


ser-


vices


price


residential


zone.


Chapter


uses


the SEWRPC


internal


trip


survey


to compile


average


commuting


times


between


work


locations


and each


residential


zone.


level


of housing


expenditure


each


residential


zone


is taken


directly


from


census tract


data.
















CHAPTER


SPATIAL


VARIATION


IN THE


PRICE


OF HOUSING


SERVICES


price


must


be determined


presented

dwelling


of housing


in


in the last

units varies


services


order to

chapter.


at alternative


evaluate

Since t


location,


it is


the empiri


he attribut


not possible


residential

cal utility

e mix of di


locations

function


fferent


to derive


relative


price


of housing


services


a direct


comparison


rents


different


locations.


The hedonic


approach,


however,


can be used


con-


trol


for attribute


differences


in making


rent


comparisons.


The hedonic

hypothesis that


approach

the price


to constructing


a commodity


price


indexes


be decompos


is based

ed into


on the

the


prices


of the attributes


of that


commodity.


When


the price


a corn-


modity


is regressed


on its attributes,


the regression


coefficients


rep-


resent


the implicit


or hedonic


prices


of those


attributes.


In the


housing


market,


the price


at least


one


attribute


must


vary


loca-


tion


in order


give


rise


to spatial


variation


in the price


of the


commodity,


estimate


housing


services.


the attribute


prices


obj ective


for different


of this


chapter


residential


locations.


different


attribute


prices


are then


used


as price


vectors


in the


con-


struction


of conventional


price


indexes.


It has only


recently


been


recognized


that


market


structure


pro-










slon


curves


equation.


determine


Since


the functional


the price,


it follows


forms


that


of the demand


the functional


and supply


form of


hedonic


regression


equation


is related


to the determinants


of the supply


demand


curves.


purpose


of the first


portion


of this


chapter


to determine


what


structure


of the urban


housing market


implies


about


the func-


tional


form of


the hedonic


regression


equation


of housing


expenditure.


In the second


specified


and third


sections,


and estimated.


last


the hedonic


section


regression


of this


equation


chapter utilizes


estimated


attribute


prices


to determine


the relative


price


of housing


for each


residential


zone.


Functional


Form and


the Hedonic Equation


Ignore


for the moment


the spatial


nature


the housing market


the existence


of neighborhood


effects.


It is assumed


that


house-


holds


produce


housing


services


from


dwelling


unit


attributes


according


to the household


production


function


= f(S,


where


= housing


services


=- vector

= vector


of structural


of land


characteristics


characteristics


*The


only


study


in the


literature


which


explicitly uses


assumptions










Given


a competitive market


for housing


services


a competitive


input


market,


the suppliers


of dwelling


units


operate


under


same


production


technology


as households.


Firms


combine


structure


land


characteristics


in the production


of housing


services


in such


a way


as to maximize


profit,


given


the price


of housing


services


the price


that


firms


must


to obtain


structure


and land


attri-


butes.


Since


the producer


a price


taker


in both


input


and final


markets,


inefficiency


in production


results


in less


than


normal


profits.


Only


those


firms


wno


correctly


perceive


the household


produc-


tion


technology will


survive.


Long-run


competitive


equilibrium


requires


that


the value


output


equals


the sum of


factor


payments,


that


HE = H.P


*S + PL-L


where


HE = housing


expenditure


= price


of housing


services


= price


vector


of structural


characteristics***


*Replacing


more
does
does


the assumption


realistic assumption


not alter


practice


the results


price


of competitive


a monopsonistic


as long


discrimination


input
input


as monopsonist


among


housing


markets with


market


(i.e.,


for labor
organized


services


labor)


producers.


**This


ers typically


tory of
do not
produce


mechanism


select


at least
perceive
housing


apparent


new-house


partially


the household


services


in the market


nlans


completed


sell


dwelling


production


in an inefficient


new


new units


units.


function


houses.
from an


Those


correctly


manner must


reduc


Build-
inven-


builders


and thus
e their


profit


margin


to sell


the dwelling unit.









= price


vector


of land


characteristics


= housing


services


Equation


provides


a theoretical


rationale


for deriving


implicit


prices


in a competitive


market


regressing


product


expenditure


(i.e.,


price)


on attributes.


admit


a spatial


dimension


to the analysis


assume


that


there


a limited


supply


of land


at each


level


of accessibility.


Households


are willing


pay more


for housing


services


more


accessible


sites


because


of the lower


commuting


costs


associated


with


these


locations.


limited


quantity


of land


accessibility


level


prohibits


reduction


higher


of


price


this spatial

of housing s


price


services


differential

is received


through


more


entry.


Since


accessible


loca-


tions,


it is in the interest


of each


producer


to increase


his bid-price


for more


accessible


land


until


the point


is reached


where


the higher


price


paid


for land


exactly


offsets


the higher


price


received


out-


in the profit


function.


Competitive


bidding


insures


that


land


prices


in the housing market


just


exhaust


the price


advantage


of the


more


accessible


sites.


In light


of the influence


of the limited


quantity


of land


and the


spatial


dimension,


the hedonic


equation must


be modified


so that


HE = HS-P(X,


Y)-L


= PL(


where


P(X,


= price


of housing


services


as a function


of location,









consider


the existence


of location-specific


unpriced


public


goods


as inputs


in the production


of housing


services.


Choice


production


site


determines


the levels


of public


intermediate


goods


tering


in the production


process.


Since no


price


is paid


for these


inputs,

other f


their


actors


contribution

as a rent.


to housing

Competitive


expenditure


bidding


goes


one


producing


age


of the

nts for


that


land


associated


with


the neighborhood


effects


assures


that


price


of land


will


rise


(fall)


until


the production


advantage


(disad-


vantage)


of that


site


is exhausted.


Thus,


the total


factor


payment


to land


includes


a rent


which


equals


the contribution


of the public


good


to housing


expenditure,


P(X,


* H*N.
aN


The hedonic


equation must


written


HE = HS'P(X,


= PL(X,


*L +P


H.*N +
3N


implicit


both


price


on the marginal


one unit


product


of neighborhood


of the neighborhood


attribute


effect


depends


in the produc-


tion


of housing


services


and the price


of housing


services


at that


site.


Since


the marginal


product


of neighborhood


effects


tends


to increase


while


the price


of housing


services


decreases


with


declining


accessi-


ability,


it is


not possible


to determine


a priori


the spatial


character


of the implicit


price of neighborhood


effects.


Initially,


the hedonic


regression


model


is specified


assuming


that


these


two effects


cancel.


P(X,


Y)_H
aN


can noW


be replaced


with


a constant


hedonic


price,


This


assumption


is examined


later


in this


chapter.


en-










The hedonic


regression


equation


specified


in the


next


section


incor-


porates


land,


a number


neighborhood


of restrictions


and structural


imposed


More


characteristics


enter


specifically,


the regression


equation


as single


independent


variables;


the implicit


prices


of neigh-


borhood


and structural


attributes


are measured


the regression


coef-


ficients


on these


variables.


A technique


called


trend


surface


analysis


is used


to enable


the estimated


price


of land


to reflect


different


values


at each


location.


The Hedonic


Regression


Equation


estimation


of the hedonic


regression


equation,


it was


neces-


sary


to divide


the city


of Milwaukee


into


a number


of residential


zones


considered


services


homogeneous


available.


with


Because


respect


census


to price


tracts


and quantity


are


delineated


of housing


partly


the basis


of dwelling


unit


homogeneity


and because


the majority


data


available


cannot


be disaggregated


beyond


census


tract


level,


it was


decided


to make


residential


zone


census


tract


boundaries


coterminous.


census


tract


division


appears


to perform well


according


to the


criterion


of providing


small


intrazone


variation


relative


to interzone


variation


in the relevant


variables.


An analysis


of Detroit


census


tract


data


reveals


that


sum


of squared


differences


between


indi-


vidual

greater


observations


than


and the metropolitan


sum of squared


mean


differences


is from


between


to 16 times


the observations


. w----










and the


teristics


than


census tract

structure and


are


census


not,


tracts.


means

gross


in most

In thi


for number


rent.


cases, r

s study,


of bathrooms,


In addition,


relevant

data f


rooms


neighborho


areas


rom other


much s

sources


per unit,

od charac-


smaller

are ag-


gregated


to the


census


tract


level


or determined


for the midpoint


census


tract.


The description


of data


and variables


in the hedonic


regression


equation


which


follows


is most


conveniently


divided


into


a discussion


of the dependent


variable,


housing


expenditure,


and three


groups


independent


variables


including


structural,


neighborhood


and land


char-


acteristics.


Housing


Expenditure


Housing


expenditure


refers


to the


payment


for housing


services


unit


of time.


This


information


is provided


directly


for rental


units


as the


average


census


tract


gross


rent.


owner-occupied


dwelling


units


is necessary


to impute


rents


from


average


dwell-


unit


value.


A weighted


average


of the imputed


rent


and the


average


gross


rent


provides


a measure


average


monthly


housing


expenditure


for each


census


tract.


There


are


economic


reasons


for believing


that


multiplication


constant


conversion


ratio


an acceptable


manner


of imputing


rent


from market


value.


Since


many


households


are


free


to either


rent


own a home,


true


cost


of owning


a home


should


be approximately









equal


to rental


costs.


If these


costs


were


not the


same,


households


could


be expected


to shift


from one


ownership


category


to the other


until


demand


pressures


cause


the differential


to disappear.


a hous-


ing market


at equilibrium,


rent


must


provide


the landlord


with


a return


which


equals


countered


opportunity


in renting.


This


cost


of his investment


relationship


was


stated


plus


expenses


recently


en-


John


Shelton


(1968)


Annual


Rent


= PT +M


+ OB + OC


+ V + MC


where


= property


M = maintenance

OB = obsolesence


= opportunity


cost


of the landlord'


investment


= vacancy allowance

= management costs


Using


the 1970


property


tax rate


for Milwaukee


estimates


of the


various


costs


from Shelton


s article,


can be written


Rent


Rearranging


.0435MV


terms


.01MV


and dividing


+ .015MV


12 gives


.07MV


Monthly


+ .03Rent


Rent


+ .O5Rent


.012


* MV,


where MV


is the market


value.


Based


on the value-rent


relationship


reported


above,


the dependent


variable,


average


monthly


housing


expenditure,


AVRENT,


is defined


each


census


tract


as follows:


AVRENT4


.012"V .


--I-


+ GR,










= number


of owner-occupied


dwelling


units


census


tract


= number


of rental


dwelling


units


census


tract


Structural


Characteristics


Four


variables


are used


to capture


the variation


in housing


expen-


diture


caused


variations


in the structural


characteristics


of dwell-


units.


These


variables


are all


taken


from


the 1970


census


housing


and include:


MDRMS


- median


number


rooms


in the


census


tract


AVGAGE


- average


of the dwelling


units


PGTIBATH


- percent


of units


with


more


than


one bathroom


PBLT40


- percent


of dwelling


units


built


before


1940


MDRMS


and PGTIBATH measure


the size


of the dwelling


unit.


Both


variables


should


be positively


related


to housing


expenditure.


AVGAGE


reflects


the obsolescence


of the dwelling


unit


as a result


passage


of time.


PBLT40


was


included


to reflect


technical


change


sucn


as new heating and


cooling


systems


which


were


not available when


older


units


were


constructed.


signs


of coefficients


on AVGAGE


PBLT40


are expected


to be negative.


Neighborhood


Characteristics


Neighborhood


characteristics


encompass


those


attributes which


fluence


rent


dwelling


units


are not related


to accessibility


or the


structure.


first


neighborhood


characteristic


to be


con-










preference"


hypothesis


is used


to specify variables


reflecting


racial


preferences.


Assume


that


whites


V aversion


to living


among


blacks


greater


than


blacks


aversion


to living


among


other


blacks.


If this


were


case,


then


whites


would


be willing


a greater


premium


to live


among whites


than


would


blacks.


two groups


would


then


separate.

blacks fo


As long


,r a white


as whites are

neighborhood,


Swilling


segrega


pay

tion


a greater


will


premium


continue


than


to exist.


Given


white


tastes,


rent


for identical


dwelling


units


will


tend


to be lower


on the white


side


of the black-white


boundary


than


the white


interior,


some


blacks


perfer


integration


then


rents


the black


side


of the boundary will


greater


than


in the black


terior.


Bailey


(1959)


has shown


that


in long-run


equilibrium,


rent


the boundary will


be equalized


implying


that


housing


prices


in the black


interior will


be lower


than


in the white


interior.


"funneling"''


effect,


however


, may


prohibit


long-run


equilibrium


from being

migrants t


attained.


o the central


t is reasoned

city which o


that


occurred


the large


influx of


in the last


black


decade


an excess


demand


for black


housing.


A positive


black-white


price


dif-


ferential


continues


to exist


because


it is difficult


for blacks


to enter


at first


influence


house


ehold


appear


neighborhood
production


that
ects


function


this


on pre


approach


scuss


ion which


erences


incon


focuses


stent


where neighborhood


on the


with


effects


are inputs
sistency i


previous
MTT


the production


illusory.
sections


nsider


housing


services.


the utility


= U(H,G)


S,N,L)


I' I


This


and production


Since


I, t


apparent


incon-


functions


U 9H
H 3N









the surrounding white


housing


market.


If this


funneling


effect


important


in Milwaukee


then


black


submarke t


rents


would


be expected


greater


than white


submarke t


rents.


An examination


of Milwuakee


census


tract


data


for 1960


and 1970


suggests


however


that


the funneling


effect


is probably not


important.


The black


submarket


in Milwaukee


consists


a corridor


extending


from


center


of the city


a northwesterly


direction.


Less


resistance


to black


expansion


is likely


to be encountered


when


this


pattern


exists


(see


Haugen


and Heins,


1969).


In addition,


in the last


decade,


Milwau-


experienced


a white


exodus


totaling


70,200


individuals


while


black


influx numbered


only


42,630.


With


an increase


of 4,499


dwelling


units


over


same


period,


excess


demand


factor would


appear


to be important.


It should


be pointed


out that


the race-housing


relationship


treated


in a


rather


restricted manner


in this


study.


Another


cause


race-related


price


differentials


is the existence


pure


racial


dis-


crimination.


This


occurs


when whites


rent


to blacks


only


a mark-up


over


the price


charged


whites.


There


are


a number


of other


influences


which


are closely


related


race


are


actually


a result


of other


*For
(1969).


empirical
The idea t


verification


hat


black-white


this
rent


hypothesi


diff


see Haugen


erentials


arise


and Heins
because


of the large
attributable


immigration


to Becker


blacks


into


a contained black


submarket


(1957).


There


little


doubt


that


black


entry


to the white


submarket


restricted.
black-white


Couran t


rent


(1975)


differentials


for a theoreti


as a result


which


higher


edicts


discrimination-


iritir'0d


- r A i- i


1I"


fnr hin nrlc


S 1 T Ti


hCrr (1Q7Qc3


Fnr a ninA


ca*


nf A4; a -


L


,,,,,,1.










factors.


cost


of providing


housing


to blacks


greater


cause


a larger


family


size


causing


greater


depreciation


of the hous-


stock.


Greater


uncertainty


rent


payments


because


of low


fluc-


tuating


incomes


would


also


appear


as black-white


rent


differentials.


nature


of the


census


tract


data


prohibits


the investigation


these


factors.


The racial


variables


of this


study


are included


only


to reflect


household


valuation


of neighborhood


racial


composition.


The variables


corresponding


to the racial


model


outlined


above


BOUND


- white


boundary;


a binary


variable


assuming


a value


of 1


for those


census


tracts


where


the black


population


greater


than


less


than


percent.


BBOUND


- black


boundary,


a binary


variable


assuming


value


of 1


for those


census


tracts


which


are greater


than


33 and less


than


percent


black.


BINT


- black


interior;


a binary variable


assuming


the value


of 1


for those


census


tracts


which


are more


than


percent


black.


The expenditure


effect


of residing


a white


interior


census


tract


is included


in the intercept


term.


The coefficient


of WOUND


is expected


to be negative


indicating


the reluctance


of whites


live


among


blacks.


In light


of the


apparent


excess


supply


of housing


in the black


submarket,


it is expected


that


the coefficient


on BBOUND


I- --- -4 ~ ~ --


E-- r.~


4- 1, ,-nn r.rFC
*_~ ~ fl *


.. n C r LTniTTKTi'


'Pt1 r'=o--


are


,,11,,,


--- I -


L -









ficient


of BINT


is hypothesized


to be less


than


that


of BBOUND


reflect-


the black


taste


for integration.


A number


grouped


of the


under nuisance


remaining


neighborhood


and employment


center


characteristics

externalities.


can


These


include


PEXPWAY


- linear


distance


expressway


routes


in each


census


tract


divided


census


tract


land


area.


PRAIL


- linear


distance


of railroad


routes


in each


census


tract


divided


census


tract


land


areas


PAR70


- calculated


existing


ground-level


concentration


suspended


particulates


in 1970


measured


as the annual


geo-


metric


mean


in microgram


cubic


meter.


EMPD4


- measure


of manufacturing


employment


within a


mile


radius


of the midpoint


of the


census


tract.


PEXPWAY


and PRAIL


are calculated


by measuring


the linear


distance


or expressway

Oil-Rand McNal


and railroad

ly road map.


routes

Rail


in each


census


expressway


tract


using


influences


the Mobil


are


expected


to negatively


affect


housing


expenditure


primarily


because


of the


asso-


ciated


noise


pollution.


Concentration


of suspended


particulates


one


of the


most


notice-


able


forms


of air pollution.


These


particles


remain


suspended


in the


atmosphere


or slowly


settle


and consist


soot,


dust


ash.


Suspended


particles


soil


clothing,


buildings,


and automobiles









cause


irritation


eyes


and lungs.
C,-


The primary


sources


of suspended


particulates


are industrial


processes,


power


generation


space


heating


(see


Southeastern


Wisconsin


Regional


Plannin


g Commission,


1974).


A map


of particulate


isopleths


(lines


of equal


particulate


concentra-


tion)


in Milwaukee


was used


to assign


concentrations


of particulate


matter


to each


census


tract.


coefficient


of PAR70


is expected


to be negative.


EMPD4


is the total


manufacturing


employment


in plants


over


employees


located


within


a two-mile


radius


of the midpoint


of the


census


tract.


This


variable


is included


to represent


the disamenities


which


accompany


proximity


to employment


centers;


EMPD4


a measure


of accessibility.


Data


on individual


manufacturing


firm


size


rived


wuakee


from


the 1970


county.


Wisconsin


Street


address


Unemployment


compensation


is determined


files


locating


each


for Mil-


of the


firms


in the Wisconsin Manufacturers


Association


s Classified


Directory


of Wisconsin Manufacturers


(1970).


Each


address


is then


located


the Mobil


variable


road


to determine


is expected


to reflect


the appropriate


the negative


census


influence


tract.


of noise


This


pol-


lution


congestion.


last


neighborhood


variables


to be discussed


reflect


the social


character


of each


census


tract.


TRANG


is the number


of households


have


moved


to existing


homes


in the


census


tract


from


1965


to 1970


divided


the number


of existing


homes.


This


variable


measures


social


are









stability


of the neighborhood.


A neighborhood


characterized


a large


portion


of transients


is expected


to negatively


influence


rents.


PINMI1G


is the


percent


of the population


have


moved


into


census


tract


from


outside


the SMSA since


1965.


Foreign


values


customs


recent


migrants


are expected


to decrease


rent


that


native


resident


is willing


for a dwelling


unit


a census


tract


characterized


a high


portion


migrants.


Neighborhood


social


homogeneity


is measured


the variable


PPMEQ.


constructing


this


variable,


percent


of the labor


force


engaged


in professional


and managerial


occupations


is calculated


for each


census

tract

this


S


tract.


figure and

variable in


PPMEQ


is the squared


the Milwaukee


creases


average


difference


of 17.75


as the neighborhood


between


percent.


becomes


more


census


The value


homogeneous.


PRENT


is the


percent


census


tract


dwelling


units


which


rented.


It is commonly


believed


that


owner-occupied


dwelling


units


are better


maintained


than


equivalent


rental


units.


An explanation


this


phenomenon


is that


the opportunity


cost


of labor


in the maintenance


activity


of homeowners


is considerably


less


than


the market


determined


labor


cost


incurred


landlords


(see


Dildine


and Masey,


1974).


This


effect


influences


housing


services


output


altering


the quality


structural


characteristics


and through


the external


effect


of neigh-


borhood


dwelling


unit


appearance.


This


relationship


between


homeowner


status


maintenance


implies


a negative


coefficient


for PRENT.


are









Local


public


services


such


as school


quality,


fire


protection,


and police


protection


as well


as property


tax rates


are


included


in the hedonic


equation


because


the study


area


incorporates


only


municipality.


influence


of these


effects


is captured


in the in-


tercept


Land


term.


Characteristics


Land


characteristics


are measured


the single


variable,


average


census


tract


lot size,


AVLS.


It is recognized,


course,


that


indi-


vidual


lots


differ


in value


as a result


of features


such


as spe-


cial


topographical


escaping.


These


characteristics,


special


shape


characteristics


of lot,


and maturity


can be expected


of land-


to be much


less


important


when


data


are aggregated


census


tract


since


such


features


tend


to "average


out"


within


each


census


tract.


Residential


land


area


in each


census


tract


is derived


by measuring


total


land


area


from


the 1970


SMSA


census


tract


and subtracting


non-


residential


land


area


estimated


from


the Mobil


road


map.


AVLS


determined


dividing


residential


land


area


number


of housing


units.


A number


of the original


218 Milwaukee


census


tracts


to be


eliminated


from


the sample


because


of problems


encountered


construct-


ing AVLS.


The estimation


of residential


land


area


was


particularly


subject


error


in sparsely


populated


census


tracts


tracts


with


*It is


nated


against


assumed


that


different


in the provision


parts


of these


of Milwaukee


services


are


or in the


not discrimi-
assessment


property


taxes.


one









large


amount


of manufacturing


activity.


After


eliminating


those


cen-


sus tracts


for which


was


impossible


to estimate


residential


land


area


a total


of 147 observations


remained


in the sample.


As indicated


in equation


the portion


of housing


expenditure


explained


average


lot size


(AVLS)


is PL(X,


*AVLS.


In order


include


this


term


in the


regression


equation,


PL(X,


must


be specified


as some


the price


mathematical


of land


function.


to depend


L(X,


functionally


notation simply


on spatial


requires


location.


Spatial


location


is generally


represented


distance


to the


cen-


tral


business


district


(CBD),


or by


some


accessibility


index,


The rationale


cent


using


decentralization


distance


of economic


to the CBD is that


activity,


even


with


the CBD is still


re-


the primary


focus


of the urban


economy.


If distance


to CBD were


accepted


as the


proper


accessibility mea-


sure


such


that


PL(X,


where


is the distance


from


the CBD


census


tract


then


propriate


terms


in the regression


model


would


PL(X,


*AVLS


= aoAVLS


+ aid- AVLS


where


are


the coefficients


to be


estimated.


stance


to CBD reduces


location


a single


dimension.


Conse-


quently,
models c


this


urban


distance


land


specific


use.


cation
Mills


frequently used
2) for a rather


in theoretical


elaborate


rhon rcar4 r'nl


SrinnQnl


0Tht 1 01 r 'in nfl mn nl ra 1i r


--


m1i m


Y)i = ao


orPiir 1 nt r^ r^ r"


U~n ^ f A -*T f" ^I









accessibility


index


recognizes


the multimodal


nature


of the


modern


urban


economy.


index


is generally


computed


where


= accessibility


index value


census


tract


= employment


census


tract


= distance


from


census


tract


census


tract


= parameter


of the index


= number


census


tracts


There


are a prior


reasons


for suspecting


that


neither


of these


approaches


provides


an adequate


measure


of the accessibility


residential


location.


With


recent


increase


in manufacturing,


commercial,


and financial


subcenters,


it is


no longer


necessary


most


residents


to frequent


the central


business


district


except


perhaps


occasionally


for very


highly


specialized


products


or services.


Even


if land


values


do tend


to rise


with


proximity


to the CBD,


the regular


symmetric


price


surface


dictated


the usual


simple


function


of dis-


tance


to CBD would


seem


to be


an inadequate


functional


specification.


While


an accessibility


index


does


allow


one to incorporate


non-


symmetric


price


surfaces,


these


indexes


seem


to replace


one


form of


functional


rigidity with


another.


Figure


presents


several


accessi-


ability


indexes


census


tracts


along


a north-south


ray extending










through


center


of Milwaukee.


These


census


tracts


are delineated


on the map


in Appendix


Alternate


values


a are assumed


manufacturing


data


for all


census


tracts


in Milwaukee


county


used.


While


the accessibility


index


approach


provides


an intuitively


more


appealing


representation


of locational


advantage,


it is evident


from Figure


that


a rather


inflexible


relationship


is implied


between


the accessibility


location


and the spatial


distribution


employment.


A more


appealing


formulation


of PL(X,


would


allow


the data


determine


both


the peaks


of the price


surface


and the price


level at


location.


An approach


called


trend


surface


analysis


is often


used


geography


to accomplish


just


such


an objective.


To utilize


this


method


it is


necessary


to specify


the degree


a polynomial


equation


which


to be used


to represent


the price


surface.


For in-


stance,


if the


true


price


surface


can be represented


as a plane


then


the relevant


polynomial


is first-order


can be written


PL(X,


+ alX


+ a2Y


where

census


X and Y

tract.


are

The


cartesian


resulting


coordinates


independent


for the midpoint


variables


of each


in the hedonic


regression


equation


PL(X,


"AVLS


= a AVLS
0


+ alX AVLS


+ a2Y-AVLS


The de


gree


the preferred


polynomial


equation


can be determined


examining


the regression


residuals


for spatial


correlation.


If the


are


are


- ao












































Accessibility


Index


Values


/
I


.4
~ -


U-.-.


ensus


Tract


Scale

Mile


Census
Tract









sented


in the regression


equation


then


positive


residuals would


tend


to be grouped


together,


surrounded


by negative


residuals.


* The


predicted


location-related


price


of land


can also


be examined


to make


inferences


about


true


price


surface.


Since


the price


of land


pically


decreases


a decreasing


rate,


a price


surface


polynomial


too low


an order


is likely


to predict


a negative


price


for land


on the


outer


fringe


census


tracts.


polynomial


degree


to be used


a study


depends


on the number


extrema


in the


true


price


surface.


A quadratic


polynomial


allows


one extremum,


a cubic


allows


four


extrema


a quartic


allows


nine


extrema.


Information


and prior


from


information


the residual


on major


map,


employment


the predicted


centers


was


price


used


surface,


to select a


quartic


price


surface


in the preferred


regress


ion.


terms


of PL (X,Y)


are X,


, y2X,


, y3X,


y22
y-x


, y4


Each


of these


polynomial


terms


is multiplied


AVLS


to form independent


variables


for the regression


equation.


Before


turning


to the empirical


results,


a brief


review


of variable


definitions


is provided


by means


a tabular


listing


of variables


Table


*Spatial
correlation.


because


autocorrelation


Residuals


of specification


repr


esents


display


error


or b


an exte


scernible


because


nsion


spatial


regres


temporal
patterns


sion model


auto-
either


should


have


an autoregr


essive


structure.


The relation


between


spatially


auto-


correlated


residuals


ecifi


cation


error


used


here


to determine


proper


form of


the price


polynomial.







71

TABLE


Hedonic


Index


Variable


Definition


Dependent


Variable


Description


Source


AVRENT


Average


census


tract


rent


Independent


Variables


MDRMS


Median


rooms


AVGAGE


Average


housing


units


PGTIBATH


Percent


of units


with


more


than


one


bath


PBLT40


Percent


of units


built


before


1940


BOUND


Binary variable


esignating


percent


and < 33


percent


black


BBOUND


Binary


variable


designating


> 33


percent


percent


black


BINT


Binary
black


variable


designating


> 90


percent


PEXPWAY


Expressway


distance


divided


land


area


PRAIL


Rail


distance


divided


land


area


PAR70


Suspended


particulates


for midpoint


census


tract


EMPD4


Employment


within


a two mile


radius


TRANG


Percent


of population


moved


in last


five


years


PINMIG


Percent


population


moved


from


outside


SMSA


in last


five


years


PPMEQ


Neighborhood


homogeneity measure


PRENT


Percent


of housing


units


being


rented


AUT~~ A n.n --


1 S- a


AXTT o










AVLS*Y


Average


size


and location


interaction


term


AVLS*Y4


Average


lot size


and location


interaction


term


tUnless


noted


otherwise


variables


refer


census


tract


values.


SOURCES


IU.S.


Bureau


the Census,


Census


of Population


and Housing:


1970,


Census


Tract,


Final


Report


PHC(1)-131,


Milwaukee,


Wisconsin


SMSA.


2
Census


Tract


Map,


issued


with


source


Mobil


Travel


map,


Rand


McNally


and Company,


1974


edition.


4Prospectus


Southeastern


for a Regional


Wisconsin


Regional


SAir Quality Maintenance
i Planning Commission, 19


7


Planning Progr
4 (preliminary


version).


5Classified


Directory


of Wisconsin


Manufacturers,


1970,


Milwaukee,


Wisconsin Manufa


cturers


Association.


6Unemployment


March
State


1970,


Wisconsin


Compensation


Department


Employers by Location
of Industry, Labor a


and Type
nd Human


of Business,
Relations,


of Wisconsin.


am,









Estimation


Results


econometric


specification


of the hedonic


price


regression


equa-


tion


assumes


an additive


error


term.


The ordinary


least


squares


esti-


mation


results


are presented


in table


It is evident


that


planatory


explain


power


96.83


of the model


percent


very


of the variation


high.


independent


in AVRENT.


variables


standard


error


of the regression


percent


is only


of the mean Milwaukee


10.06 which


rent.


represents


Only


an error


of about


two of the coefficients


have


signs


which are


counter


to the hypothesized


signs.


The transiency


measure


(TRANG)


and the


measure


of immigration


(PINMIG)


have


unexpected


positive

(P1(X,Y))


coefficients.


Six of


are significant


at t


the fifteen

he 5 percent


price o

level;


if land

nine


variables

are significant


at the 10


percent


level.


purposes


of interpreting


the individual


coefficient


estimates,


the influence


of each


independent


variable


is discussed


in the


same


as it


was


presented


in the last


section.


Structural (


Characteristics


Although median


rooms


(MDRMS)


average


age (AVGAGE)


have


hypothesized


signs,


neither


is statistically


significant


at the 5


per-


cent


confidence


level.


Percentage


of dwelling


units


with more


than


bath


(PGTIBATH)


the expected


sign and


is highly


significant with


coefficient


over


five


times


greater


than


the standard


error.


Percent


of units


built


before


1940


(PBLT40)


also


the expected


sign


ex-


or-





74


TABLE


Hedonic Price


Regression


Equation


Standard


Standard


Variable


Coefficient


error


Variable


Coefficient


error


209.8


30.06tt


AVLS


5.302


1.526tt


MDRMS


AVGAGE


PGTIBATH

PBLT40

TWBOUND

BBOUND

BINT

PEXPWAY

PRAIL


PAR70


EMPD4


TRANG


PINMIG


PPMEQ


2.100


- .4376

1.020

- .3612

-14.99

-34.63

-21.71


-2643

-328


- 1.473


.0006703


25.97


1.375


.02823


3.173


.4634

.1882tt

.1676t-t

3.286tt

4.609tt

5.098tt

1355.t

908.2

2.131

.0002114tt


17.28

.2380tt


.01600t


AVLS*Y


AVLS*X

AVLS*YX

AVLS*Y2

AVLS*X2

AVLS*Y3

AVLS*Y2X

AVLS*YX2

AVLS*X3

AVLS*Y2x2

AVLS*Y3X


AVLS*X3Y

AVLS*Y4


AVLS*X4


.09419


-1.002

.1350

- .1884

- .4176

- .001574

.05428

.09359

.1138

.03102

.003971


.005757

.002629


.002085


.2247


.5193

.1201

.07306tt

.2025t

.005556

.02430

.05388

.06365

.009263tt

.004120


.01305

.001220t


.01662


PRENT


- 1.226


.1391tt


.9683


.9601


Standard error of the


regression


= 10.06


= variables which


are


significantly different from


zero


the .01 level and the .05 level, respectively.









are in this


category.


coefficient


of PBLT40


implies


that


a dwelling


unit


built


before


1940


rents


for $36.12


less


than


one built


after


1940.


implication


for PGTIBATH


is that


on average


dwelling units with


more


than


one bathroom


rent


an additional


$101.96.


This


coeffic-


ient


cannot


be interpreted


as the price


an additional


bathroom


since


dwelling


units


in this


category


are likely


to have


as many


four


or five


bathrooms.


The coefficient


is interpreted


to reflect


presence


of those


structural


attributes


in larger


dwelling


units which


are not measured


Neighborhood


MDRMS.


Attributes


As hypothesized


in the model


of racial


discrimination


average


rent


in the white


boundary


is less


than


in the white


interior.


The dif-


ference


ferential


is significant


of $14.99


at the 1


or about


percent


percent


level


of the


indicates


average


a rent


Milwaukee


dif-


rent.


The hypothesized


relationship


between


average


rent


in the black


boundary


and in the black


interior


does


appear


to hold.


gression

higher i


coefficients


n the black


indicate


interior


that


than


rents


in the black


are about


boundary.


percent


This


result


is consistent


with


a black


taste


for segregation.


This


differential


might


also


appear


if the black


interior


census


tracts


are


characterized


some


itly


desired


represented


neighborhood

in the model


or structural


This


attribute


is unlikely,


that


however


since


explic-

ghetto


housing


is typified


smaller


and older


dwelling


units


located


re-










As hypothesized,


the coefficients


of BINT


BOUND


indicate


that


rents


in black-dominated


areas


are substantially


less


than


white


neigh-


borhoods.


The coefficients


impl


rent


discounts


of about


percent


percent


for residents


in BBOUND


and BINT,


respectively.


These


results


substantiate


our speculation


that


white


outmigration


left


an excess


supply


of housing


available


in neighborhoods


open


to blacks.


The existence


an expressway


route


(PEXPWAY)


in the


census


tract


shows


the expected


negative


sign


and is significant


at the 1


percent


level.


Dwelling


units


located


in those


census


tracts


rent,


on average,


for about


$4.73


month


less.


presence


of rail


lines


in the


cen-


sus tract


(PRAIL)


has the expected


sign


the coefficient


is about


only


one-half


the size


of its standard


error.


PAR70


is included


as an independent


variable


to reflect


the in-


fluence


of air pollution.


coefficient


has the expected


sign;


quality


appears


to account


for a $7.36


monthly


rent


differential


between


center


of the city


and the


outer


census


tracts.


Unfortunately,


the coefficient


is rather


imprecise


with


a standard


error


nearly


twice


the size


of the coefficient.


This


lack


of precision


is probably


a re-


suit


of the generally


poor


nature


of air quality


data.


Manufacturing


proximity


has the expected


sign


is highly


signif-


icant.

studies


This

have


result


is of special


not typically


significance


recognized


this


since


hedonic


externality.


price

influence


on rent


an increase


- ~ n .


in neighborhood manufacturing


- .-1 ..


activity


- tr i t


one


,c,,^ J --** -fj *"_


r.


,,, -- *


,,, LL


ir.


-J


.4









Both


transiency


measure


(TRANG)


and the influence


of immigrants


PINMIG)


have


the wrong


sign.


Although


TRANG


is only


a little


larger


than


its standard


error,


PINMIG


is highly


significant


with


a t-value


of 5


was


hypothesized


earlier


that


PINMIG


represents


the dis-


utility


of native


Milwaukeeans


living


in close


proximity


to inmigants


possessing


appear


strange


to pick


customs.


the higher


PINMIG,


cost


and probably


of providing


TRANG,


rental


some


units


extent


to recent


migrants


who live


in the


same


area


with


others


of similar


backgrounds.


Unfortunately,


nature


of the data


does


not permit


this


analysiS


resolve


these


questions.


PPMEQ measures


the social


homogeneity


of the neighborhood.


coefficient


is of the expected


sign


is significant


at the .05 level.


An increase


in homogeneity


one standard


deviation


implies


a monthly


rent


increase


of $6.02.


PARENT


was


included


to reflect


the greater maintenance


activities


of home-owners.


As expected,


the coefficient


on this


variable


nega-


tive;


the standard


error


of the coefficient


indicates


significance


the .01 level.


Land


Characteristics


The coefficients


of primary


interest


are on the iocat ion-average


lot size


interaction


terms.


Of the fifteen


polynomial


coefficients,


are significantly


different


from


zero


at the 5


percent


confidence


level


and nine


are significant


at the 10


percent


level.


The only


inter-










cartesian

positive;


coordinate

the t-value


system.

of this


one would


coefficient


expect,

indicates


this

that


coefficient


it is signif-


icant


at the 1


percent


level.


An indirect

bility-related p


test


rice


of the ability


of land


of PL(x,y)


to evaluate


to measure


the function


the accessi-


for each


residential


zone


according


to the equation


PL(X,


= 5.3


.094Y


- 1.00X


+ .135YX


.188Y2


.418X2


.00157Y3


.054


.00263Y4


.0936YXt

.00209X4


+ .114X


+ .0310Y2X2


.00397Y3X


+ .00576X3Y


A contour map


of the calculated


price


conforms


to the expected


price


surface.


The calculated


price


is always


positive


and increases with


increasing


accessibility


to employment


opportunities.


Since


the land


price


surface


very


similar


to the housing


services


price


surface,


an examination


of these


features


is postponed


until


the discussion


the relative


price


of housing


services.


In deriving


the functional


form


for the hedonic


regression model,


initially


assumed


that


the spatial


variation


components


the implicit


price


of neighborhood


effects


cancelled


each


other.


This


assumption


permitted


for the original


unobservable,


price


a spatially


term,


it is difficult


constant


P(x,


to test


3H
Nthis
this


price,


Since


proposition.


to be substituted


and H
and


are


Indirect


evidence,

constant


however,

hedonic p


indicates


rice


that


it is reasonable


for neighborhood


effects.


to assume


Since


a spatially


the size


4 4 4 r


was


3Y2X


P(X,


I F-


1


A










neighborhood


effect,


an additional


term


comprised


of the interaction


between


the primary


size


variable,


MDRMS,


and each


neighborhood


effect


included


in alternative


regression models.


tendency


for either


the price


or the marginal


product


component


of P(x,


to dominate


should


be reflected


a significant


coefficient


on the interaction


term.


For all but


one alternative


run the interaction


term was


not sta-


tistically


different


from


zero.


In addition,


the inclusion


of the


interaction


term


left


the other


coefficients


nearly


unchanged.


including


the term MDRMS-PAR70


did alter


the coefficients


on MDRMS


and PAR70


and provided


a coefficient


on the interaction


term


tha t


statistically


significant.


This


alternative


specification


used,


however,


because


the interaction


term


in this


case


appears


flect


accessibility


to the CBD


not a spatial


variation


in the price


of neighborhood


effects.


This


result


not surprising


since


particu-


late


isopleths


appear


as nearly


concentric


rings which


radiate


from


center


of the city.


Two factors


support


this


observation.


First,


coefficients


on MDRMS-PAR70


and PAR70


indicate


that


a change


in the


level


of particulate


matter


has a positive


influence


on housing


expen-


diture


dwelling


for dwelling


units


units with


in the central


fewer


part


than


rooms.


of Milwaukee,


That


an increase


partic-


ulate


matter


increases


rents.


This


implication


counter


to the known


effect


of air pollution


and is consistent


with


a functional


specification


a.


was


run


was


was


re-


I*


II ~


_ _


* A


_









loWe:


-'rrCe


under


the interactioC


specification.


these


reasons,


the significant


coefficient


on the interaction


term was


considered


to indicate


a spatial


variation


in the price


of neighborhood


character-


istics.


failure


of these


alternative


neighborhood


price


specifi-


cations


suggest s


that


the spatial


constant


equation


adequate


representation


of the influence


of neighborhood


effects.


This


section


has examined


the empirical


estimates


of the implicit


prices


of three


input


groups


in the production


of housing


services.


In general,


both


the estimated


the magnitude


prices


and signs


conform


of the implicit


a prior

prices.


notions

The im


concerning


iplicit


price


of the input


land was


shown


to vary


location


as was


sug-


gested


the hedonic


equation


developed


using


prior


information


the structure


of the urban


housing market.


estimated


price


land


will


be used


in the


next


section


to compute


the relative


rent


dwelling


units


at different


locations


in the city.


The Relative


Price


of Housing


Services


estimated


implicit


prices


from


the hedonic


regression


equa-


tion


derived


in the last


section


can now be


used


to estimate


the rela-


tive


price


of housing


services


for each


residential


zone.


It has


been


established


that


the factor


prices


of neighborhood


and structural


char-


acteristics


can be considered


spatially


constant.


price


of land


varies


spatially


Both a


as a result


Laspeyres


of the demand


and Paasche


index


for more

the price


accessible

of housing


sites.

services









of purchasing


current


attribute


bundle


at the


current


location


relative


to the


cost


of purchasing


same


bundle


at the


base


location


That


p (X,


= PL(X,


*L + PN'N


PL(Xb


*N + P


This


index


represents


a downward


biased


estimate


of the relative


price


of housing


services


because


the substitution


of structural


attributes


for the expensive


The Laspeyres


base-location


land


index measures


been


cost


ignored.


of purchasing


the base-3o-


cation


attributes


at the


current


location


prices


relative


to the


base


location


ces.


That


Lt(X


SPL(


Y)"L


+ PN


PL(Xb


Similarly,


the Laspeyres


index


provides


an upward


biased


estimate


cause


the base-level


quantities


of the attributes


at the


present


site


represents


an inefficient


use


of the less


expensive


land.


*Instead


unit


housing


comparing


attributes


index captures


a base


cos


cost
and p
t of


renting


resent


a fixed


location,


purchasing


bundle


a "true


a reference


of
cost


dwell-
of


level


housing se
of housing


rvices


at the


services


base
hosen


sent


location.


as a reference


then


If the base


true


level


index is of


the Laspeyres


serves


type


as a ref


while
erence


if the
then


resent


true


location
index i


housing
s of the


services
Paasche


out-
type.


These


two indexes


independent


of the


are identical


refer


ence


(that


output


cost


housing


serve


of housing index
ices) if the hou


hold


production


function


homo


thetic.


In this


case


the Laspeyres


and Paasche


indexes


represent


outer


ounds


on the


true


price


index.


a descriptive


review


this lit


erature


see


John Muellbauer


(1974


1975)
.1- .------------ 1


See Wold


and Jureen
- .- -


132-1381


an analysis


-~ -


se-


*L + P


Yb)-


, b)


Yb) 'Lb





ut.


Before


calculating


it must


be decided


which


location


serve


as a base


location.


Examination


of the accessibility-re-


lated


price


of land


calculated


in the last


section,


reveals


a plateau


comprised


eleven


contiguous


census


tracts.


This


three-


square-mile


area


represents


most


accessible


location


in Milwaukee;


the eleven


tract


averages


of attributes


and land


prices


are used as


base


values.


Calculated


values


are


presented


in Appendix D.


factors


must


be considered


in evaluating


these


housing


services


price


indexes.


First


the statistical


degree


of confidence


which


can be


placed


in the variation


of the price


index must


be established.


Then


the correspondence


between


the estimated


price


surface


prior


infor-


mation


on the spatial


nature


of the price


of housing


services


must


evaluated.


The remainder


of this


section


examines


two issues.


A Statistical


Evaluation


of Spatial


Housing


Services


Price


Indexes


The price


of housing


services


is important


in determining


residen-


tial


location


only


if the price


varies


spatially.


It is appropriate,


then,


to examine


the statistical


significance


of the price


variation


displayed by


the estimated


price


indexes.


The significance


of the spatial


price


variation


can be determined


testing


the null


hypothesis


o i-l
1^


PiXi
ii.


, PL(X,


nDb,









depending


on whether


the Laspeyres


or Paasche


index


is being


tested,


= price


characteristics


at the base


location,


= price


of characteristics


at the


current


location;


against


the alternative


hypothesis


PiXi
1 1


b
P.X
lij


Rejection


the null


hypothesis


in favor


of the alternative


pothesis

different


indicates

from 1,


that

which


the estimated

is the base p


price


rice


index


of housi


is significantly

ng services.


The appropriate


test


statistic


can


be derived


examining


relation between


the price


index and


the hedonic


regression


equation.


definition

31


P.iXi
1 1


biC.
i i


pbi


biC_
1 -i


+ b 7AVLS
1/


+ b 17AVLS
17


C b.AVLS" (X,
i=18


Z b.AVLS' (X,
i=18


where


= implicit


prices


of neighborhood


structural


characteristics


to C16


= current


values


for neighborhood


structural


characteristics


AVLS


= average


lot size


to b16








b
(X,Y)i


= polynomial


sterns


of P


for the base


location.


Substituting


expression


in (1)


the left-hand


side


of (10),


multiplying


both


sides


of the denominator


collecting


terms


on the


left-hand


side


provides


a null


hypothesis


terms


of hedonic


prices


such


that


b


E bi
i=18


The null


and alternative


hypothesis


can now


be written


(12)


where


= [0


. 0


-Y)]
b


and B


= the full


vector


of implicit


prices.


It is


apparent


from


(12)


that


testing


the null


hypothesis


spatial


testing


variation


a linear


in the price


combination


of housing


of regression


services


is equivalent


coefficients.


appro-


private


test


statistic


(see


Theil,


1971,


130-139)


where


= full


vector


= ordinary


lea


of estimated

st squares r


implicit


prices


esidual


vector


= matrix


of independent


variables


= number


of observation


mi .1ns


number


of independent


- (X,


* (4


(X-Xb) (Y-Yb) (XY-XbYb)


(X'X)-1w)1/2










absolute


value


represents


a price


index


value


which


is statistically


different


from


1.0 at the 5


percent


level.


It is difficult


to assess


the significance


lar results


of the spatial


in Appendix


price


Table


variation


and Figure


examining


are


used


the tabu-


to summarize


this


variation.


In Table


the estimated


price


of housing


services


and the sig-


nificance


of the estimate


is provided


for those


census


tracts


falling


along


a ray extending


from


the northwest


to the southeast


corners


Milwaukee


county.


These


census


tracts


are delineated


on the map


Appendix


census


tracts


along


this


ray represent


a cross


sec-


tLon


of the price


surface


and incorporate


some


of the highest


lowest


price


areas


of the city.


Judging


from


the values


presented


Table


one can be quite


confident


in the belief


that


true


price


of housing


services


exhibits


considerable


spatial


variation.


inability


of the


test


to reject


the null


hypothesis


as the interior


census


tracts


are approached


is expected


since


those


tracts,


in fact,


do have


prices


that


are close


to 1.0.


Proceeding


in the northwesterly


direction


away


from


the base


cation,


a price


of less


than


.985


is significantly


different


from


1.0.


Prices


below


.969


are significant


when


moving


along


towards


test


the Laspeyres


statistic
and Paasche


developed
indexes.


in this


section


is the


same


for both


**Census


ficulty


tracts


in determining


were


not included


residential


land


in the sample


area.


because


It is obvious


of dif-


from


*The







86

TABLE 6


Price of


Census tract
-iIL II ,. ,


Housing


Laspeyres


Services

Index


along


a Northwest-Southeast Ray


Paasche Index


t value


.879


.704


.906


.859


2.94*


.927


.882


2.54*


.934


.920


2.47*


.944


.921


2.59*


.958


.934


2.47*


.971


.972


2.16*


.984


.985


1.66*


.997


.997


1.10


1.00


1.00


1.15


1.01


1.01


1.00


.989


1.01

1.00


1.00


.990


.985


.981


1.17


.970


.969


1.96*


.963


.957


2.37*


.954


.963


4.05*


.925


.960


4.05*


.916


.880


4.10*


.906


.884


4.16*
















Brown Bayside
Deer
iRiver Hills
.m iFox Point




Glendale ( /

Whitefish
n n 0 Bay


Shorewood




Wauwatosa







West Allis




... --*- -St Fra ncis
Greenfield



Hales ,, Y Cudahy
Corners Greendage


South
Milwauke


Franklin


Oak Creel


e
U


k









southeast.


These


results


imply


a rather


high


degree


precision


the estimated


price


index.


In Figure


census


tracts


that


are not significantly


different


from 1.0


at the 5


percent


level


are


cross-hatched.


Approximately


three-


fourths


of the land


area


of Milwaukee


contains


dwelling


units


that


sell


for prices


which


differ


significantly


from 1.0.


suggests


that


the highest


portion


of the price


surface


can


be represented


as a pla-


teu extending


east


to west


through


the middle


of the city.


Evaluation


of the Estimated


Price


Surface


estimated


price


surface


is represented


in Figure


by means


a contour map


in Figure


a cross-sectional


view


of the


sur-


face.


The cross-sectional


view


is taken


along


same


as was


used


to examine


the statistical


significance


of the price


index


in the last


section.


A simple


average


of the Laspeyres


and Paasche


price


indexes


is used


It


to represent th

is not possible


e price


surface


compare


this


in this


section.


information


on the spatial


variation i

information


n the pri

derived


of housing


from other


services


hedonic


reported


studies


in this


for a number


study with


reasons.


Most


hedonic


price


studies


have


not recognized


the spatial


variation


the price


of land.


In addition,


these


studies


typically


include


some


measure


of accessibility


as a separate


independent


variable.


The im-


plicit


prices


estimated


in these


studies


are


undoubtedly


biased


because


of misspecification.


attempt


to construct


indexes


from


the hedonic



















Brown Bayside
Dear
River Hills
Fox Point



i) ,
*


_.__ -.88 I Glendale "


S~w Whitefish
Bay

.8 -.98-.
e r!
) litiShorewoot:Md


Wauwatosa n ,.9 8-.9








West Allis
1.r0-e





r f i lr l
tVe t Al li


03I I:I I 10'

St, FranCIS
Greenf el d =' t15 (:


fHales Gr e en
Corners Greendala


Franklin


I r
i- Cudahy =




South
Milwaukee
/


Oak Creek


---q


I


Y


\



























Relative


price


Region of convexity


I
I
I
I
I
- -W


I
I
I
---Region


of convexity4


Census Census
Scale --


tract


LIract


mile
mile


1 1









icance


surface


of the price


suggest


index


ts that


and the irregular


simple


shape


accessibility


the land


measure


price


an inade-


quate


representation


of the land


price-accessibility


relationship.


predicted


housing


services


price


surface


can,


however,


be eval-


uated


in light


of prior


information


on the Milwaukee


transportation


network,


manufacturing


employment


locations


and theoretical


and empir-


ical


considerations


derived


from


the simple


theory


of spatial


consumer


behavior.


The cross-sectional


view


in Figure


highlights


some


general


characteristics


appears


of the price


as a plateau which


surface.


rapidly


high


drops


off and


priced

then


area in Milwaukee

resumes a more


gentle


slope.


simple


theory


consumer


behavior


requires


a price


surface


that


decreases


at a decreasing


rate;


that


the slopes


the price


function must


represent


convex


functions.


This


shape


quite


evident


in Figure


Muth


(1969)


derives


a number


of testable


relationships


in his


work


on the theories


spatial


producer


consumer


behavior.


suits


indicate


that


the price


of housing


declines


a rate


of about


percent


per mile.


The estimated


price


indexes


of this


study


show


a 1.9


percent


and a 1.8


percent


decline


per mile


calculated


as the


percent


change


from


the base


location


to the


outermost


census


tract


on each


of the


ray.


Examination


of the


contour


in Figure


highlights


the in-


nr mlho lit- c r *H nn


tuTnrlc -


re-


CI nlr


I 1-


n *vm 1 /,T^r\ In ^nTrt k


1 /-\/-> ^ ^ i t










price


surface


plateau


is located


a fairly


central


location


with


respect


to manufacturing


employment


location.


Prices


drop


all directions


increase


again


as one moves


a northeasterly


direction


approaching


the University


of Wisconsin.


The price


sur-


face


also


rises


again


in the southernmost


census


tracts


of Milwaukee


response


to the manufacturing


center


in Oak


Creek.


contour


lines


appear


to follow


a fairly


regular


concentric


pattern

however,


as predicted


the distortion


the simple


caused


spatial

uneven e


theory


employment


consumer behavior;

distribution and


expressway


system


is clearly


evident.


The heavy manufacturing


activity


in West


Milwaukee


pulls


contour


lines


in that


direction.


outermost


contour


line


is nearly


L-shaped


as a result


of the


expressway


that


passes


through Milwaukee


on the South


and West


sides.


High-speed


expressway


commuting makes


many


locations


along


the inter-


state


equally


desirable


from


an accessibility


view point.


outer


contour


line


dips


back


toward


center


of the city


following


terminal


stretch


expressway


in that


area.


The influence


of the CBD does


appear


to be


as strong


as many


have


suggested.


contour


line


reflecting


a price


of .95


.97,


how-


ever,


does


down


somewhat


encompass


locations


close


to the CBD.


Although


prior


knowledge


of the characteristics


of the actual


price


surface


is rather


limited,


it is readily


concluded


that


the predicted


price


surface


conforms


very


closely


to the expected


pattern.


The esti-


















CHAPTER


COMMUTING


TIME AND


SPATIAL


ALLOCATION PROCESS


purpose


of this


chapter


is to determine


the commuting


times


which


characterize


each


census


tract


and to resolve


a number


opera-


tional


questions


which


arise


in the actual


prediction


and evaluation


of the model.


Each


muting


census


times where


tract


is characterized


n represents


the number


an n-element vector


of employment


com-


locations.


For a household


employed


at the ith work


location,


the ith element


each


census


tract


vector


is used


as the commuting


time


in evaluating


the utility


function


at alternative


locations.


Internal


Trip


port


portion


of the 1972


SEWRPC


survey


is used


in the first


section


this


chapter


to compile


these


commute


time


vectors.


The second


section


presents


the allocation


mechanism


used


pre-


dict


residential


allocation


process


location.


Several


are resolved.


issues

e final


which


arise


section


in the actual


of this


chapter


proposes


a number


of criteria


use


in evaluating


the forecasting


accuracy


of the model


developed


in this


study.


Average


Work-Residence


Commute Times


The Internal


Trip


Report


establishes


workplace


residence


- -j-.2?


SC 1 .- .. .-


t _,


I _


m -


I


I


^ -_ J


L..


^ ^ 1 -


I.__










hold


member


for the day previous


to the


survey


date


are


recorded.


Infor-


nation


on travel


mode,


trip


origin


and destination


tracts,


purpose


the trip,


origin


time


and arrival


time


are included


for each


trip.


Observations


on workplace-residence


trips


are


used


to compile


aver-


commute


lowing modes


times.


were


To construct


used:


this


automobile,


variable,


railroad,


trips


bus,


made


taxi


the fol-


and motorcycle.


It is felt


that


average


travel


times


from a


work


location


to each


residential


zone


provide


a satisfactory


representation


of the commuting


time-location


options


faced


each moving


household


employed


at that


work


location.


Although


a majority


of the 252


sectors


in Milwaukee


County


identified


by means


of the Internal


Trip


Report


Survey


as representing


employment


locations,


it is not


possible


to derive


average


commute


times


for household


heads


employed


at most


of these


locations.


In nearly


cases,


so little


employment


is actually


located


in the


zone


that


an insufficient


number


of work-residence


trips


are recorded


in the 3


percent


SEWRPC


survey


sample.


It is apparent


bution

solely


from


of manufacturing


concentrated


Figure


employment


one


which

, that


presents

although


or two locations,


the spatial

employment


a distinct


modal


distri-

is not

pattern


is evident.


The approach


used


here


to construct


average


commute


times


for each


workplace


zone


was


to begin


with


the largest


workplace


mode


to construct


average


trip


data


this


successively


smaller modes


are