L2D 008097-Urban Sprawl, Lan Values and the Density of Development

8/3/2019 L2D 008097-Urban Sprawl, Lan Values and the Density of Development

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U r b a n S p r a w l , L a n d V a l u e s a n d t h eD e n s i t y o f Development

JohnR.Ottensmann

The character of the residential de-velopment occurring at the periphery ofa metropolitan area has extensive anddiverse economic and social implications.The kinds and prices of housing pro-duced, the population groups served, andthe cost and problems of providingpublic services are all determined by theworkings of the development process.An understanding of this process re-quires an examination of the relation-ships between land prices and the loca-tion and intensity of development.Urban sprawl-the scattering of newdevelopment on isolated tracts, sepa-rated from other areasby vacant land-isfrequently cited as one negative conse-quence of the development process. Theseparation of residential areas by vacantland leads to increased costs in providingutilities and other public services. Resi-dents are forced to travel farther to en-gage in most activities, using moreenergy resources and producing more airpollution. The scattered subdivisionsbring the negative impacts of urbaniza-tion to far largerareas of formerly agri-cultural or wilderness land. And finally,although this effect is impossible toquantify, many have strenuously ob-jected to sprawl on aesthetic grounds,arguingagainst the formless characteroftypical urbandevelopment.Urban sprawl is not without its de-fenders. Lessinger [1962] argued thatthe scatter of new development might

prevent the development of large,homo-geneous residential areas that would besocially segregated and ultimately be-come large, homogeneous slums. Boyce[1963] suggested that sprawl retains anelement of flexibility for future urbandevelopment appropriate under condi-tions of uncertainty and imperfectknowledge. The reservation of land forlater development in more intensive uses,either residential or commercial, couldproduce an urban pattern that may bemore efficient in the long run, based onrecent theoretical work by Ohls andPines [1975].A basic discussion of the nature ofsprawl has been provided by HarveyandClark [1965]. Clawson [1962] and Sar-gent [1976] have suggested the im-portance of landowner speculation in theprocess. Bahl [1968] considered the roleof the property tax, while Archer[1973] attributed sprawl to the failureof the residents of the new areas to beconfronted by the full costs of develop-ment.Land values play a critical role in theallocation of land, thereby shaping the

The author is Assistant Professor, PrograminSocial Ecology, Universityof California,Irvine. Hewishes to thank Professors J. Bonham, F. StuartChapin Jr., A. Allan Schmid and an anonymousreferee or theircommentsandsuggestions.'For a summary of the costs of sprawl, seeClawson[1971, pp. 140, 152-59, 320]. The mostcomprehensiveeview s the reportby the RealEstateResearchCorporation1974].

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pattern of development. Maisel [1963],Neutze [1970] and Muth [1971] haveprovided theoretical statements aboutthe determination of land values that areparticularly applicable to the issues ofconcern here. Empirical studies of dif-ferences in land values between urbanareas include those of Maisel [1964],Mittelbach and Cunningham [1964],Schmid [1968] and Witte [1975].2The density at which land is de-veloped for residential purposes is thefinal important characteristic of develop-ment at the urban periphery. Harrisonand Kain [1974] have examined thedensities of fringe development overtime and the cumulation of this incre-mental development to form the urbanpattern. Two studies, by Neutze [1968]and Schafer [1964], have focused on thedevelopment of apartments at the urbanfringe.3This paper addresses this triad ofcharacteristics of peripheral urban resi-dential development: urban sprawl, landvalues and density of development. First,an account of the development process isgiven. Hypotheses are developed in-volving the variations of these threefactors across urban areas. Finally, thepredicted relationships between the rateof urban growth, land values and densityof development are tested using datafrom the past two decades for metropoli-tan areasin the United States.

THENATUREOFPERIPHERALGROWTHThe desire for accessibility to theurban center might be expected to resultin continuous development extendingout from that center, since people seekmore accessible locations and are willingto pay more for them (see, for example,

Alonso [1964] ). This must be the case,however, only in static situations or iflandownersare shortsighted and considerjust the returns from development in thecurrent p.eriod.More reasonably, ownerscompare the returns from immediate de-velopment with their expectations ofthe returns from development in thefuture, deducting the costs of holdingthe land and discounting the returnsto their present values.4 As a result,some owners may withhold their landand forgo current development whiledevelopment occurs on less accessibleland farther from the center. For ex-ample, current demand might supportonly the development of single-familyhousing beyond a certain distance.Future urban growth, however, couldgenerate a demand for multifamilyhousing yielding far higher returns,causing the most accessible land to bewithheld duringthe currentperiod.5An explanation of urban sprawl re-quires more than expectations of futuregrowth. Given the conventional assump-tions, similarly situated landownersshould face a common future and shouldreach the same decisions with respect todevelopment. But landowners varywidely with respect to their situations,knowledge and attitudes, which affectsboth future expectations and real and

2Many more studies have dealt with intraurbanvariations in land values. A good introduction to thiswork is Mills [1969]. For more recent references, seeWitte [1975].3As was the case with land values, many studieshave dealt with intraurban variations in populationdensity. See, for example, Muth [1969] and Mills[1972].4Bahl [1968] has specified the conditions underwhich a landowner should either withhold his land,develop it or sell it.SOhls and Pines [1975] have demonstrated thatsuch skipping of close-in land in favor of higher-den-sity development at a later time may prove to be moreefficient for the society in the long run.

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perceived holding costs. Some importantdifferences include landowner incomes,income tax positions, alternative invest-ment opportunities, the possible use ofthe land in agricultural production andeligibility for preferential property taxtreatment.6 These differences willproduce variations in landowner deci-sions to develop or withhold their land,resulting in the fine-grained pattern ofurban sprawl that is observed as develop-ment occurs at the periphery of urbanareas.7Differences in the levels of future ex-pectations may be important in account-ing for variations in the patterns ofresidential growth between cities. Hypo-theses are derived involving the relation-ships between expectations, urbansprawl, land values and densities of cur-rent development. Consider two identi-cal urban areaswith the same patterns ofdemand for residential development inthe current time period. Considering

only this current demand, landowners incomparable locations would obtainsimilar returns from current develop-ment in the two cities. The cities differonly in the levels of expectations of thelandowners: In one city, only slowgrowth and low levels of future residen-tial demand are anticipated after thiscurrent time period, while rapid growthand high demand are expected in theother. Thus, landowners in the first citywill tend to have lower expected presentvalues of returns from future develop-ment than their more optimistic counter-parts in the second city. There will, ofcourse, still be variations in landownerexpectations within each of the cities.When the landowners compare theirinitial expectations regarding returnsfrom current development (the same inboth cities) with the anticipated returnsfrom future development, the patterns

of decisions will vary between cities.Given the lower levels of expected futurereturns, current development will bemore attractive to a higher proportion oflandowners in the first city. The higherfuture demand in the second city will bemore appealing, causing more of theseowners to withhold their land in favor offuture development. (This decrease inthe supply of land for current develop-ment will produce an increase in landprices and returns from current develop-ment, enticing some of the reluctantowners back into the development oftheir land before an equilibrium isreached.) This forms the basis for thefirst hypothesis: The quantity of landwithheld from current development-theamount of urban sprawl-should vary di-rectly with the levels of expectation con-cerning future residential demand. Putanother way, landowners in rapidlygrowing cities will reserve more land forfuture development. The more growththey expect, the greater their tendencywill be to sit tight and wait for higherreturns to their land.The withholding of land decreases thesupply available for current developmentat any distance from the center. This willforce the price for land up (also causingsome additional land to be released for

6Clawson [1962] and Kaiser et al. [1968] providegood accounts of the factors which influence land-owner behavior.7The argument assumed the existence of largenumbers of landowners at any given location in orderto discuss the proportions with higher or lower ex-pectations who would or would not withhold theirland. Withsmallnumbers of landowners at any location,the argument can still be used if their expectations areassumed to be subject to a probability distributioncomparable to the distribution of expectations amongthe larger number of landowners. Then the large land-owners' decisions concerning future expectations andthe withholding of land would be probabilisticallydetermined, still producing random variation andsprawl.

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current development). Thus the secondhypothesis: Land values should varydirectly with the levels of expectationconcerning future residential demand. Inthose cities that are growing morerapidly, higher future expectations willforce current land values up.A higher price for land will cause de-velopers to use less land in the produc-tion of housing, substituting other inputsfor land. The third hypothesis is, then, asfollows: Density of residential develop-ment on land that is developed (and notwithheld) should vary directly with landvalues and with levels of expectationconcerning future residential demand.Ironically, the faster growing cities,while having more sprawl, will actuallybe denser in those areasthat are actuallydeveloped.The traditional assumption of employ-ment being concentrated in a singlecenter has become less tenable with thedecentralization of commercial and in-dustrial activity in most large urbanareas. The development of multiple cen-ters of employment near the edge of thefully developed portion of the citywould not alter the desire of new resi-dents to locate close to their places ofwork. However, the generally shortercommuting distances would lessen theresistance to locating at even greaterdis-tances from the center, increasing de-mand farther out and further en-couraging dispersed development. Inaddition, the emergence of the peri-pheral centers might increase the poten-tial for future higher-density develop-ment in their vicinities, creatinga greaterincentive to withhold land. Thus, de-centralization of employment would beexpected to lead to even more urbansprawl.In summary, when expectations aboutfuture development potential are high,

more land will be withheld from de-velopment, land values will be higher,and the densities in developed areas willbe higher. More will be done on lessland, at higher prices, as the owners waitfor still higher expected returns fromfuture development.

TESTINGHEHYPOTHESESThe second and third predictions out-lined above, involving variations in landprices and density of development acrossurban areas, have been tested empiri-cally. The procedures followed and thevariables used in these tests are describedin this section. The first of the hypo-theses involved the withholding of landfrom development to produce urbansprawl; unfortunately no data could befound that were appropriate to examinethe prediction in this case.A model incorporating the two hy-

potheses in the form of linearregressionsis tested using data from StandardMet-ropolitan Statistical Areas (SMSAs) inthe United States. For the first set ofregressions,measures of land value serveas the dependent variable. Expectationsof future development measuredby ratesof population growth are expected to bepositively related to land values. Twoadditional independent variablesare alsoincluded in these regressions-populationand income. Larger cities have greateraggregate demand for residential space,and higher incomes allow individuals tooffer more for such space. Thus, bothvariableswould be expected to be signifi-cant factors affecting land values andshould be positively related to these val-ues. For the second set of regressions,the density of current development isthe dependent variable. Land values andpopulation growth should both, as hy-

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Ottensmann:UrbanSprawlpothesized, be positively related to thedensity of development. Populationshould also be positively related, sincethe greater demand for space in largecities forces more intensive use. The roleof income is less clear in this case: High-er incomes could increase land valuesand hence densities, but could also en-able households to purchasemore space.A variety of land price data for metro-politan areas in the United States hasbeen assembled by Schmid [1968]. TheNational Association of Home Builders(NAHB) has gathered information fromits members regarding the averagepriceof raw suburbanland purchasedby themfor their own use in residential develop-ment in a large number of urban areasfor 1960 and 1964. These data on landvalues per acre should be indicative ofthe overall level of prices for land fornew residential development in eachSMSA, even though they cover only theactivities of the NAHB members. Like allattempts to collect land value informa-tion, these NAHB data are undoubtedlyaffected by significant inaccuracies andproblems in coverage.Thus, it was felt tobe appropriate to consider alternativesources of information. Data on theprices of lots sold for new residentialdevelopment are an alternative. Such in-formation is somewhat easier to comeby, but suffers two shortcomings: lotsizes vary and other development costsaffect the final price of a lot. Therefore,lot prices can be only imperfect mea-sures of the variation in land valuesacross urban areas. NAHB data on lotprices in 1960 and 1964 (covering theprices of developed lots for single-familyhome building reported by NAHB mem-bers in surveys) and Federal Housing Ad-ministration (FHA) data on lot prices in1950 and 1964 (covering the prices fordeveloped lots for single-family homes

with FHA-insured mortgages in eachSMSA) are included in the tests of themodels. These data also cover only aportion of the land market, but providealternative tests and extend the temporalrangeof the tests.8Following the example of Harrisonand Kain [1974], the percentage of newhousing units constructed during a de-cade as single-familydwellings is taken asthe surrogate measure for density of de-velopment. Of course, percent single-family development is inversely relatedto the density of development, so thedirection of the hypothesized relation-ships must be reversed. While variationsdo occur in the densities at which bothsingle-family and multifamily develop-ment take place, the choice betweenthese types undoubtedly accounts formost of the variation in developmentdensities across SMSAs. The data avail-able refer to the SMSAs as a whole andare therefore affected by central city re-development. However, data for theSMSA fringes would have missed signifi-cant peripheral development occurringwithin central cities.9As mentioned earlier, rates of popula-tion growth are taken as measures oflandowner expectations regardingfuturedevelopment. The current rate of growthin the metropolitan area was consideredto be the major factor which landownerscould observe and, hence, the major fac-tor affecting expectations. Landownersin a rapidly growing city will be more

8 All of the land price variables were obtained fromthe appendix tables in Schmid's study [1968, pp.60-93]. He obtained the information from a varietyof FHA and NAHB documents for which he providescitations. No corrections were made for inflation; thisshould be considered when interpreting the results.9The percentages of new construction in single-family units in each SMSA were obtained from theU.S. Bureau of the Census [1963, Table 6; 1973a,Table A-6].

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likely to anticipate rapid growth in thefuture. Such a measuremay not be ideal,but it is difficult to imagine that expec-tations will not be related at all to expe-rience.Finally, the last two independent vari-ables are the SMSA populations andmedian family incomes at or prior to thetime of development being considered.Thus, 1950 values are used with 1950land prices and percent single-family de-velopment during the 1950-1960 de-cade, and 1960 values are used with 1960and 1964 land prices and 1960-1970development. The SMSA boundaries ineffect at each census were employed, asit was felt that these areas and figureswere most relevant for landowner deci-sions at those times.10Due to differences in the data sources,various data were available for differentnumbers and sets of SMSAs. Dependingupon the variablesemployed, regressionscould include anywhere from just over

fifty to nearly two hundred SMSAs. Afull set of data was availablefor fifty-oneSMSAs. Comparisons were made of theresults of regressionsrun with both thislimited sample and with all of the casesavailable for the particularvariables. Dif-ferences were relatively minor and didnot affect the substantive interpretationsof the results. Therefore, for simplicityand comparability, all of the results re-ported here refer to the same sample offifty-one SMSAs. lDifferent functional forms were usedin regressions for some of the variables.For example, a logarithmic transforma-tion of the population variable wastested in all of the regressions.None ofthe tests was conclusive. Examinationsof residuals favored neither form. All ofthe variables in the regressions reportedhere are in arithmetic form.The final issue involved the selection

of the appropriatetime period of popu-lation growth to use in representing thelevel of landowner expectations. The ini-tial supposition was that the level of ametropolitan area's population growthjust prior to or during the period ofdevelopment considered would most di-rectly influence landowner expectations.However, should landowners exhibitrather more prescience than is expected,the rate of population growth in a futureperiod would be a more appropriatemeasure of those expectations. Testswith alternative population growth mea-sures failed to support a claim for anyspecial powers of prediction by land-' SMSA population changes, populations, andmedian family incomes were obtained from the U.S.Bureau of the Census [1953, Table 2; 1962, Table 3;1973b, Table 3].Schmid [1968, p. 51] conducted a multiple regres-sion analysis using the same 1960 NAHB price data(with a larger number of cases). Schmid's dependentvariable was percent appreciation of the land pricesover farm land values. This is highly correlated withthe land prices themselves, since farm land prices aremuch smaller and vary less. (However, any error in thefarm land price data is magnified by this procedure,producing large variations in the percent appreciationvariable.) The larger set of independent variables usedby Schmid varied from the current independent vari-ables in several ways. First, Schmid used data for boththe cities and the urbanized areas, while the presenttests use data for the SMSAs. The latter units are more

commonly used and make possible the measurementof population change within fixed boundaries. Thechanges in urbanized area boundaries from census tocensus, combined with changes in the procedures usedfor their delineation from 1950 to 1960 (see Clawson[1971, pp. 23-25]), complicate their use. Second,Schmid uses multiple measures of population and landarea for urban size and its change. Land area is mean-ingless for SMSAs, and single measures reduce prob-lems of multicollinearity. Finally, Schmid includesmeasures of population density, fringe population andcommutation to the central city. These also dependupon the locations of urbanized areas of central cityboundaries, and they were not felt to be important tothe formulation of the problem given here." The sample of 51 SMSAs had a mean populationin 1960 of 1,188,000 and a mean rate of populationchange from 1960 to 1970 of 19.3 percent, while thelarger sample of 169 SMSAs had a mean population of540,000 and a mean rate of change of 16.4 percent.

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Ottensmann:UrbanSprawlowners. The rate of population changefrom 1940 to 1950 was the better pre-dictor of 1950 land values, while the1950 to 1960 change best accounted forvariation in the 1960 and 1964 land val-ues. Densities of development, measuredby the percent single-family units con-structed in the 1950-1960 and 1960-1970 decades, were predicted best byregressions including rates of populationchange during those same decades. Theseare the population change measures usedin the tests reported here.The hypotheses yielded two equationsfor the prediction of land price and den-sity of development. Land price is seenas a function of expectations (measuredby population changes) and other vari-ables (population and income); densityof development is seen as a function ofland prices, expectations and the othervariables. As they are stated, the equa-tions constitute a recursivesystem. Landprices are determined by demand, bothpresent and future, and in turn deter-mine densities of development. The re-cursive nature of the system is reflectedin the temporal sequence involved in thevariables selected: 1950 lot prices areused to predict densities of developmentfrom 1950 to 1960, and 1960 lot andland prices are used to predict densitiesfrom 1960 to 1970. The ten-year timeperiods of the census data on densities ofdevelopment undoubtedly extend be-yond the effects of the land prices at thebeginning of each decade. Therefore, theavailableland and lot price data for 1964are also used, even though this tempo-rally follows the 1960 to 1964 develop-ment.The possibility exists that densities ofdevelopment could affect land prices aswell, creating a situation involving simul-taneous causation. In such a case, ordi-nary least-squares procedures for esti-

mating the parameterswould be inappro-priate. Alternative models were consid-ered, with the density of developmentvariable (from either decade) included asa predictor of land prices. Two-stageleast-squares procedures were used toestimate the parameters, with popula-tion, income and the population changevariables considered as exogenous. Ineach case, the parameter values asso-ciated with the original three predictorsof land prices were hardly changed fromthose obtained with the recursivemodel,while the parameterassociated with den-sity of development was insignificant.For this reason, only the results from therecursivemodel, obtained using ordinaryleast-squares regression, are reportedhere.12

EMPIRICAL ESULTSThe first set of regressions involvedtests of the hypothesis that land valueswould be directly affected by levels ofexpectation and hence populationchange. In addition, population and in-come levels were also expected to havedirect effects on land prices. The resultsof six regressionswith alternativedepen-dent variables as measures of land valueare shown in Table 1. (All regressionsinvolve fifty-one SMSAs. A significancelevel of 0.05 is used throughout this re-

search.)These simple three-variableregressionmodels account quite well for the varia-tion in land values. In five of the sixcases, the coefficients of determination(R2) were significant and ranged from0.41 to 0.55. Only with FHA lot prices12The results of the various alternative tests re-ferred to in this section can be provided by the authorto those who are interested.

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TABLE 1LAND VALUE REGRESSIONS(Standard Errors in Parentheses)

Dependent Variable Independent Variables Constant R2Population Change Population Median Income(Percent) (Thousands) (Dollars)

NAHB Land 25.49* 0.67 0.21 -152 0.47*Price, 1960 (7.70) (0.15) (0.27)NAHB Land 47.71* 1.32* 0.43 -1426 0.55*Price, 1964 (12.81) (0.24) (0.45)NAHB Lot 4.60 0.27* 0.37* 609 0.41*Price, 1960 (4.45) (0.084) (0.15)

NAHB Lot 10.03 0.52* 0.86* -1535 0.53*Price, 1964 (7.26) (0.14) (0.25)FHA Lot 9.16* 0.19* 0.37* 122 0.42*Price, 1964 (3.79) (0.072) (0.13)FHA Lot 1.23 0.085* -0.025 972 0.11Price, 1950 (1.57) (0.038) (0.093)*Significantly ifferent rom zeroat the 0.05 level.

in 1950 did the model fail to account forvery much of the variation. Land valueswere positively related to populationchange, population and income, as waspredicted. The only discrepancy was avery insignificant negative coefficient forincome, again for 1950. Quite a few ofthe regression coefficients were signifi-cantly different from zero. Overall, theresults lend considerable support to thehypotheses suggested earlier.The best results came in the predic-tion of NAHB land prices in 1960 and1964. These variables were the mostsatisfactory measure of land values. Co-efficients of determination of 0.47 and0.55 mean that about half of the varia-tion in these land prices across metro-politan areas was accounted for. The re-gression coefficients varied between thetwo regressions for 1960 and 1964 butgive an idea of the strength of the rela-tionships. A one percent increase in therate of population growth produced atwenty-five to fifty dollar per acre in-

crease in land prices across the fifty-onemetropolitan areas. Each additionalthousand in the population was asso-ciated with something on the order of adollar increment in land values. A one-dollar increase in median incomes pro-duced a twenty- to forty-cent increase inland values. The coefficients for incomewere not significant and were subject toconsiderably more error.13Roughly comparable relationshipsheld with the four lot price variables.The coefficients tended to be muchsmaller for population change and popu-lation. Since the dependent variable wasprice per lot, not price per acre, and lots

'3Schmid [1968, p. 51] found populationto besignificantlyrelated to the percentappreciation nlandprices seenote 10). Percentpopulationchange nthe centralcity was also significant,but change n theurbanizedarea was not. This may haveresulted romthe problems nvolved n the use of urbanized reas omeasurepopulationchange,notedearlier. naddition,Schmid's esultswere affectedby multicollinearity.

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TABLE 2DENSITY OF DEVELOPMENT REGRESSIONS(Standard Errors in Parentheses)

Regression Independent Variables Constant R2Population MedianLand Value Change Population Income(Thousands) (Percent) (Millions) (Thousands)

%Single-Family Development,1960-70, with:NAHB Land Price, 1960 -1.45* -0.22* -1.58 -3.55* 95.6 0.59*(0.64) (0.080) (0.81) (1.27)NAHB Land Price, 1964 -0.51 -0.24* -1.88* -3.60* 94.7 0.56*(0.39) (0.085) (0.89) (1.32)NAHB Lot Price, 1960 -2.01 -0.27* -2.05* -2.97 96.2 0.57*(1.19) (0.079) (0.77) (1.37)NAHB Lot Price, 1964 -1.21 -0.25* -1.93* -2.73 93.2 0.57*(0.73) (0.080) (0.81) (1.43)FHA Lot Price, 1964 -3.66* 0.26* -1.94* -2.39 96.2 0.61*(1.26) (0.075) (0.70) (1.31)%Single-Family Development,1950-60, with:FHA Lot Price, 1950 -8.68* -0.043 -0.39 -4.05 109.9 0.28*(3.23) (0.037) (0.88) (2.05)

*Significantly ifferent rom zeroat the 0.05 level.

tend to be smaller than an acre, thelesser values of the regression coeffi-cients were understandable. Incometended to have a greater impact on lotprices. Higher median incomes may haveled to greater lot sizes in some metro-politan areas, accounting for higher lotprices and a stronger relationship.The second set of regressions testedthe hypothesis that the density of resi-dential development would vary directlywith land value, population change andpopulation (Table 2). Since the percent-age of new housing units constructedduringa decade as single-familydwellingsis being used as the surrogatefor density,the expected direction of all relationshipsis negative. Six estimates are reported.Attempts were made to predict percentsingle-family development during the1960-1970 decade using each of the

1960 and 1964 land price and lot pricevariables. The 1950 FHA lot price vari-able was used, with the 1950-1960 de-velopment as the dependent variable.The regression model was very effec-tive in accounting for variations in thepercentage of single-family developmentacross the metropolitan areas in the sam-ple. The coefficient of determinationwas significant in all of the five predic-tions of development density during theperiod from 1960 to 1970. The modelwas slightly less successful for the pre-ceding decade. Land values, populationchange, population and income are allinversely related to the percentage ofsingle-family development in each of theequations. The first three relationshipswere predicted, while the effect of in-come had been uncertain.Increases in land values caused de-

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dines in the development of single-fam-ily housing. During the 1960-1970 dec-ade, a one-thousand-dollar rise in landvalues produced a one-half to three andone-half percent decline in the percent-age of development in single-familyunits. Two of the five regression coeffi-cients were significantly different fromzero. (The wide variationin the five testswas not unexpected given the great dif-ferences in the five measures of landvalues, including prices both per acre andper lot.) The rate of population changehad a significant (five out of five) impacton the density of new development; aone percent increase in the growth rateproduced about a quarter of a percentdecrease in the level of single-familydevelopment. Likewise, a million in pop-ulation was associated with a two per-cent decline in the dependent variable.Finally, median income had a sometimessignificant negative effect, with a thou-sand dollars in income associated withabout a three percent lower level of sin-gle-family housing. This suggests, per-haps, that the effect of income in raisingland values (measured imperfectly here)may be more important than any in-crease in the demand for space by thehigher-incomehouseholds.The one model for the prediction ofthe percentage of development in single-family units from 1950 to 1960 yieldsgenerally comparable results. The effectof FHA lot prices in 1950 was dramatic(and significant), with a one-thousand-dollar increase in lot prices associatedwith nearly a nine percent decline in thelevel of single-family development. Popu-lation change and population have some-what smaller effects, while the effect ofincome is slightly greater. None of thesecoefficients was significant, however.The results of these empirical testsconfirm the original hypotheses: The

rate of population change positively af-fects the levels of land values, whilethese two variables in turn clearly andpositively affect the densities of residen-tial development, as measured by thepercentage of development in single-family units. The models account forapproximately half of the variation inthe dependent variablesin all but a fewof the tests.

CONCLUSIONThe success of the land value model

helped confirm the theoretical accountof the role and importance of landownerexpectations in the residential develop-ment process. Other alternative explana-tions of the levels of land values havebeen provided, however; the derived de-mand model developed and tested byWitte [1975] is one of the best exam-ples. She has achieved higher coefficientsof determination but only at the expenseof considering a greater number of inde-pendent variables. The simple, straight-forward model tested here, with butthree independent variables, must beconsidered as a valid alternative.The success in predicting density ofdevelopment provides far more encour-agement for the theoretical account ofthe residential development process pre-sented above. Both land values and land-owner expectations clearly influence thepercentage of development in single-fam-ily units, as predicted. Neutze [1968, pp.93-102] examined the influences ofland prices, city size and growth onapartment development, but his resultswere not conclusive. The Harrison andKain predictions of density [1974, pp.66-67] used city size as a surrogate forland rents. Their examination of densi-

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ties over an extended period made theuse of land rents impossible in their re-search. The present model effectivelypredicts the density of new residentialdevelopment, relating it to both land val-ues and landowner expectations withinthe context of a theoretical account ofthe peripheralgrowth process.The first hypothesis-that levels oflandowner expectations directly affectthe quantity of land withheld and henceurban sprawl-was not tested. The con-ceptual problems involved in the mea-surement of sprawl are very great, andappropriate data are not available incomparable forms across metropolitanareas.The description of the nature of pe-ripheralurban development given in thispaper highlights the role of landownerexpectations concerning future growthin shaping the pattern of future develop-ment. Relatively little is known aboutthe way in which these expectations de-velop or the correspondence betweenthese expectations and reality. Schmid[1968] has pointed out that landownerexpectations might well diverge from arealistic appraisalof future urbangrowthpossibilities, and further observed that"there is no a priori reason to expectthat a bad guess about the future willnot continue for a number of years, withresulting higher monopoly-like prices tomany consumers" [1968, p. 42]. Such abad guess would also be reflected in theentire pattern of urban development,with more land being withheld-andmore sprawl-than would actually bewarranted. Especially at the presenttime, when many urban areas seem to bepassing from periods of rapid expansioninto an era of much slower growth, pos-sible lags in landowner expectationscould present a serious problem. Thispaper has provided a point of departure

for the investigation of such problems byproviding an explanation of the natureof the development process incorporat-ing the important elements of landownerexpectations, urban sprawl, land valuesand the density of development.

ReferencesAlonso, William. 1964. Location and Land Use.Cambridge, Mass.: Harvard University Press.Archer, R. W. 1973. "Land Speculation and

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L2D 008097-Urban Sprawl, Lan Values and the Density of Development

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