UFDC Home  Search all Groups  UF Institutional Repository  UF Institutional Repository  UF Theses & Dissertations   Help 
Material Information
Subjects
Notes
Record Information

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 threeyear 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to Professor Jerry Milliman for extensive comments am grateful for his assistance in obtaining a lar number of recent unpublished studies relevant my topic.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 inn 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 WorkR 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 tj3 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 . . CrossSectional . . . 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 firstorder 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 CobbDouglas 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 firstorder 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 largescale 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. tn 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 largescale 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 fouryear 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 ab/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 eab/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. eab/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 largescale 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 outofpocket 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 largescale 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 ysiso fvariance 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 incomehigh housing areas among low incomelow 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:tateoftheart 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 WisconsinMilwaukee 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 WisconsinMilwaukee. The universal innercity problem of pollution is also present in Milwaukee as evidenced by particulate isopleths presented in Figure 2. About threefourths 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 q Glen daf \ I1 ' A :' ^ t 785 r" 9 Si Ts' S. .. .. .. .... s 7 5 j. J 7n Green id + Hales Cudahy Corners Gr jndl +, ... I+T . + i +c" ,1o Franklin Oak CSreeko ! J ^ er^7"1^ j ^ t.say ^i^..1.^^,^^, ^^^*/j1^^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 oldworld 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 unitland area ratios in the county, while the inner city represents the highest housing unitland 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 sevencounty 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 timelocation 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 . 1122) ex $ a = U(H, subject to the budget constraint = PG + 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 secondorder 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 locationspecific 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 utilityprice 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 twodimen 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 firstorder 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 firstorder equations which are amenable to parameter estimation. A CobbDouglas specification satisfies both of these requirements. This function is specified = alln(H) + (lal)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 CobbDouglas 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. CobbDouglas 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 CobbDouglas 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 firstorder 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(yT( 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 outof opportunity cost components. It is assumed that the outof 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 CobbDouglas 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, 281283). ***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 industryoccupa 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 occupationindustry categories are likely to be *A logical or past income. first As w nn *1 .in 4n choice ith most an instrument cross '., ibr, 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 incomeage relationship even ,500 household to overwhelm incomeage 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 ageincome 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 ageincome 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 industryoccupation regression model is used calculate a predicted permanent income for each household observation used to estimate for each taste the housing tasteincome variable expenditure interaction the predicted term equation, is constructed permanent income. An instrument multiplying instrumental variables estimation procedure (Johnston, 1972, 278281) can now be used to derive consistent estimates taste variables. C CI~l I 1 cn n N< t 00 r4 L fI 0 a C) a 0 0X U < rt X C; 0 *14 0 k (U M 5t 0) Cflb rr 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 husbandwife 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 husbandwife 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 shortterm 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 heademployed 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 'Yrf '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 incomeagerace 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 crosssectional 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 expenditurepermanent 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 RENTERSHousing 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 OWNERSDwelling 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 tvalues 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 rentincome ratio displays a significant variation only because age. dwelling unit valueannual 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 valueincome ratio estimates displayed in Table TABLE RentIncome Ratio Household Type Additional ratio for: Basic rentincome Each 10 years Black ratio Head household Each child household .195 .0124 .202 .0128 .00640 .00698 .02340 .02658 Additional ratio for: Basic valueannual 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 valueincome ratios vary from 1.6 to 2.1 and average 1.8. The rentincome ratios derived present study are based on contract rent rather than gross rent used in the Ekanem study. Gross rentincome 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) + (1al)ln(y  (.58 + .41(y/160)) TIME  alln(p(X,  (lal)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. Longrun competitive equilibrium requires that the value output equals the sum of factor payments, that HE = H.P *S + PLL 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 newhouse 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 bidprice 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 = HSP(X, Y)L = PL( where P(X, = price of housing services as a function of location, consider the existence of locationspecific 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. owneroccupied 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 valuerent 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 owneroccupied 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 blackwhite 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 longrun 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 longrun 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 blackwhite 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 racehousing relationship treated in a rather restricted manner in this study. Another cause racerelated price differentials is the existence pure racial dis crimination. This occurs when whites rent to blacks only a markup 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 blackwhite 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. blackwhite 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 blackwhite 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 groundlevel 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 OilRand 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 twomile 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 owneroccupied 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 northsouth 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 firstorder 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 + a2YAVLS 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 locationrelated 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 yx , 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 .1676tt 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 blackdominated 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 onehalf 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 tvalue 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 homeowners. 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 ionaverage 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 tvalue system. of this one would coefficient expect, indicates this that coefficient it is signif icant at the 1 percent level. An indirect bilityrelated 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 MDRMSPAR70 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 MDRMSPAR70 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 baselocation land index measures been cost ignored. of purchasing the base3o 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 baselevel 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  .  1321381 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 accessibilityre lated price of land calculated in the last section, reveals a plateau comprised eleven contiguous census tracts. This three squaremile 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 il 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 lefthand side of (10), multiplying both sides of the denominator collecting terms on the lefthand 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, 130139) 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 (XXb) (YYb) (XYXbYb) (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 NorthwestSoutheast 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 crosshatched. 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 crosssectional view of the sur face. The crosssectional 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.r0e 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 priceaccessibility 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 crosssectional 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 Lshaped as a result of the expressway that passes through Milwaukee on the South and West sides. Highspeed 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 nelement 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 WorkResidence 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 workplaceresidence 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 timelocation 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 workresidence 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 