Optmal Densty for Muncpal Revenues Soj Adelaja and olcy nsttute 305 Manly Mles Buldng 1405 south arrson Road East ansng M 4883 USA. e-mal: adelaja@msu.edu Tel: 517-43-8800 10 Fax: 517-43-8769 Malka Chaudhur Mchgan State Unversty Department of Agrcultural Economcs 1 Cook all East ansng M 4884 e-mal: mukher1@msu.edu hone #: 765-53-869 Fax: 517-43-1800 Selected paper prepared for presentaton at the Amercan Agrcultural Economcs Assocaton Annual Meetngs ortland OR July 9-August 1 007 Soj Adelaja s the John A. annah Dstngushed rofessor n and olcy and Drector of the and olcy nsttute () at Mchgan State Unversty (MSU). Malka Chaudhur s a graduate student n the Department of Agrcultural Economcs at MSU and former Graduate Assstant at. The data support of Mchgan Realtors s greatly apprecated. Copyrght 007 by Soj Adelaja and Malka Chaudhur. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means provded that ths copyrght notce appears on all such copes. 1
Optmal Densty for Muncpal Revenues Abstract Dstrbuton of lot szes and mprovements affect property values hence zonng affects property tax revenues. f targeted zonng densty dverges from optmal muncpal revenue can be ncreased through zonng changes. Ths paper derves optmal lot sze that maxmzes muncpal tax revenues. edonc analyses of a Mchgan communty suggest that optmal lot sze s lower than current zonng on exstng propertes. The possblty that muncpal revenue can be enhanced through greater zonng densty hnts of a cost assocated wth exclusonary zonng. ocal governments should therefore serously consder the fscal mplcatons of ther zonng decsons as they pursue growth control. Optmal Densty for Muncpal Revenues
. NTRODUCTON n the Unted States property taxes are the prmary mechansm through whch local communtes rase revenues to support the provson of servces to ther resdents (Campbell 1951). ocal unts of government are constraned largely by the revenue generatng capacty of ther communty s exstng real estate endowment n decdng the level of servces to delver (Florestano 1981). Zonng s mportant because t affects the nature volume and tax-rateablty of future real property all of whch ultmately affect future muncpal revenue. The lnks between zonng and other land use regulatons development of varous land use classes future sze and value dstrbuton of varous land use classes and future muncpal tax revenues are becomng more obvous to communtes. Commercal ndustral and agrcultural land uses are usually vewed as good tax ratables - ther revenues exceed ther dependences on servces (Amercan Farmland Trust 004). owever whether or not a resdental property s a good tax ratable s a functon of ts attrbutes (nature and value) of mprovement and of lot sze. Both of these are a functon of zonng. Regulaton of the resdental property type s of utmost mportance as t has perhaps the most potental mpact on muncpal land use patterns growth sprawl and servce consumpton. A homestead s a bundle of attrbutes. ence property attrbutes are expected to be correlated wth lot sze preferences. A relatonshp should therefore exst between lot sze dstrbuton and aggregate property valuaton n a communty. Certan lot szes and ther assocated property attrbutes should be of greater demand than others due to consumer preferences affordablty demographcs and past land use regulatons (Spangenberg and McCormck). One should therefore expect a lot sze range to exst that yelds maxmum per home or per acre muncpal revenues for a communty. 3
artcularly mportant to communtes s the ablty to fnance muncpal nfrastructure that contrbute to the qualty of lfe (QO). Well-planned communtes that accommodate market forces whle balancng compellng government nterests regardng densty are better able to support nfrastructure such as parks forests farmland and wetlands as well as hgh qualty publc nfrastructure and protectve servces (ulten and eterson 1984) that enhance QO. An economc analyss performed for the East Bay Regonal ark Dstrct n Calforna concluded that parks open space trals assocated recreatonal and educatonal opportuntes envronmental and cultural preservaton alternatve transt modes and sprawl-lmtng characterstcs all contrbute postvely to qualty of lfe helped to boost the economy and provde extensve economc benefts for all area resdents (ES 000). Such balance s the foundaton of the Smart Growth Movement. 1 The fnancal stablty of a communty s an mportant element of sustanable growth and development and of QO. As the prncpal control mechansm for growth n most communtes zonng can also be mplemented wth a goal of fnancal stablty and QO n mnd. To the extent to whch a communty s not bult out but understands the relatonshp between lot sze and muncpal revenues t can target that Optmal ot Sze (OS) through zonng to maxmze muncpal tax revenue. Therefore a more systematc approach to zonng may be mplemented to help to maxmze revenue through a better dstrbuton of densty. A number of studes have examned the non-prce or non-value effects of zonng restrctons both from a theoretcal and emprcal perspectve (Mlls 1989; Foley 004; Gottleb and Adelaja 005a). For example Mlls examnes the effects of zonng on resource allocaton and ts net socal benefts. Foley examnes the mpact of zonng on the rate of land consumpton and concludes that large lot zonng results n decreased consumpton of land up to a pont where 4
successve decreases n densty results n greater land consumpton. More recently Gottleb and Adelaja (005a) examned the poltcal and economc dynamcs that lead to zonng change. The nature and drecton of the effects of zonng on land values are ambguous. For example on one hand one expects the wthholdng of land from development (restrctng supply through zonng or other means) to ncrease the equlbrum prce of land and housng. On the other hand however lmtng densty s expected to make raw land less valuable as an nput nto new housng producton. These effects run counter to each other makng the total mpact of densty restrctons on land prces relatvely dffcult to ascertan (Qugley and Rosenthal 005). One plausble perspectve s that the ultmate effect depends on supply characterstcs n the partcular land market the nature of consumer demand and assocated elastctes. A number of studes have looked at the mpact of zonng on property value. The analyss of the effect of urban zonng on the prce of sngle-famly resdental property n North Carolna confrm prmarly that large lot zonng especally n resdental areas sgnfcantly reduces the prce of sngle-famly resdental property makng housng more affordable (Jud 1980). Colton and Sheehan on the other hand concluded that zonng adversely affects housng affordablty. Contradctng the fndngs the research work by Gottleb and Adelaja (005b) found that down zonng of agrcultural land results n enhanced values for resdental propertes n the same communtes. Econometrc evdence for fscal zonng based on sample set drawn from ortland Washngton DC Seattle and Ramapo conclude that the changes n or varatons among suburban zonng restrctons are drectly reflected through the property value of the homesteads. On one hand adopton of more restrctve zonng reduces the value of underdeveloped suburban land subject to the restrctons and on the other hand ncreases the value of already-developed homes (Fschel 199). Despte the obvous muncpal revenue connecton no study has drectly 5
examned the mpacts of zonng on muncpal tax revenues or developed a framework for dentfyng optmal revenue mplcatons of densty. Ths paper ams to fll the gap n the lterature on the effects of zonng on muncpal revenues through lot values and mprovement values. t develops a conceptual model for evaluatng optmal muncpal revenues and utlzes a hedonc prcng framework to nvestgate the relatonshp between lot sze and muncpal revenues. The assocated emprcal hedonc property valuaton models were specfed to nclude power terms on lot sze so as to allow the estmaton of an optmal lot sze. Multple lstng data from Merdan Townshp n Mchgan s used n the hedonc analyss. Merdan Townshp s a metropoltan town strategcally located n the ntersecton of two major hghways. t s also geographcally close to ansng a major urban center and the captal of the state.. REENUE MCATONS OF ROERTY OT SZE Conventonal urban locaton theory by Alonso (1964) posts that lot sze s nversely related to populaton densty and monotoncally ncreases wth ncreased dstance from the central busness dstrct (CBD). Ths mples that n a perfect land market at any gven dstance from the CBD a mxture of dfferent lot szes would not be expected. n realty however dstance from the CBD and populaton densty s not the only determnants of lot sze. Dfferences n consumer preferences constrants on land local regulatons ncome and affordablty result n observed dfferences n lot sze even at a gven locaton. and assembly and subdvson are costly and sometmes even prohbtve hnderng Alonso-type parcel sze arbtrage and leadng to varatons n per acre prce of land n a gven communty (Tabuch 1996). Moreover observed lot sze dfferences may be a result of hstory and a consequence of a 6
cumulatve development processes under vsonary or shortsghted decson makng by developers and landowners (arrson and Kan 1974). ocaltes mpose restrctons on new development by regulatng lot sze through down zonng or thorough other ndrect means such as purchase of development rghts (DR) on agrcultural or open land transfer of development rghts (TDR) nfrastructure concurrency requrements (CR) development mpact fees clusterng requrements urban growth boundares (UGBs) etc (CMA 00). owever zonng s the focus of the paper. By mpactng on lot sze zonng should affect the number of parcels that could be developed the product mx housng choces the demand mx n the communty per acre lot value mprovement sze and attrbute the value of housng and ultmately muncpal tax revenues (see Fgure 1 for an llustraton of the zonng revenue pathway). The ultmate drecton of the effects of zonng on revenues s not clear. On one hand large lot zonng should reduce the number of buld-able lots n a communty and per acres. Ths can affect tax revenue postvely or adversely dependng on the elastcty of demand for housng. The muncpal revenue mpact s the product of two opposte effects: the mpacts on (1) property value per acre and () the number of buldable lot per acre. ence the net mpact entals two countervalng effects. The ultmate effect clearly depends on the relatve value of the elastcty of prce (per acre) and the elastcty of number of houses (per acre) wth respect to lot sze ( and ). Snce mprovements are related to parcel sze and value the ultmate effect should also depend on the elastcty of mprovement sze and attrbutes and the elastcty of mprovement value wth respect to lot sze ( and ). A revew of some of the prevous studes related to zonng s approprate at ths pont. n order to understand the pressure on local offcals we start wth studes that look at the motve 7
for zonng. Economc self-nterest seems to be a motve for zonng. Accordng to Qugley and Rosenthal (005) local homeowners seek to maxmze home values and mnmze tax burdens by controllng the poltcs underlyng land use enactments. and use restrctons whether voluntary market drven or regulatory tend to promote amentes that make communtes more attractve whch can n turn lead to hgher housng prces and reduces housng avalablty. The effects on total property valuaton s not clear n the lterature. Through down zonng the local unts of government tend to favor hgher mnmum lot szes to lmt growth. By elmnatng and restrctng hgh-rse apartments and allowng only lowrse apartments or sngle-famly homes or prohbtng ndustral uses and allowng retal uses only exclusonary zonng also tend to ncrease prce and decrease avalablty. 3 Gottleb and Adelaja (005b) renforce the noton that economc self-nterest and growth are central motves affectng zonng choces. They estmated that downzonng of agrcultural land has a sgnfcant postve mpact on the prce of the typcal homeowner s property n the same communty. Another Gottleb and Adelaja (005a) study concludes that the lkelhood of down zonng ncreases wth the ncrease n the amount of open space that remans to be protected decreasng n farm populaton declnng populaton growth and land values n the communty and the presence of alternatve growth management tools. omeowners seem to be usng ther poltcal clout to nfluence the lot sze mx n ther communty to acheve ther property value and other goals. Fgure () shows the medum and average lot szes of new sngle-famly houses sold n the US from 199 and 005 by regon. Fgure (3) presents nformaton on housng floor area by regon. The lot szes generally fell between 199 and 005 n all regons except the north-east regon and outsde Metropoltan Statstcal Area (MSA). Conversely medan and average square 8
footage of housng ncreased wthn the perod 1978 to 005 n the US wth the north-east regon lyng above the mean and areas outsde of Metropoltan Statstcal Area (MSA) lyng below the mean. The relatve growth of lvable space vs-à-vs lot sze suggests that the bult nfrastructure s more elastc wth respect to ncome and other drvers. Dfferental mpacts of specfc drvers on lot sze and square footage can be estmated through hedonc prcng models of housng (Glaeser and Gyourko 00). Conceptual Model A homestead () has two major attrbutes: (1) land (the sze of whch s measured by lotsze) and () mprovements (typcally measured n terms of attrbutes such as square footage). Obvously the value of land s drectly related to lot sze whle the value of mprovements s drectly related to the ntensty of mprovement attrbutes. Denote the value of a homestead (land and mprovements) as follows: n 1 = =. [1] = 1 s the value of the entre homestead. s the value of mprovements. s the value of land. s the per acre value of land (or prce). The vector s a vector of per unt prces or values of the th mprovements and s the degree of magntude or scope of the th mprovement type. Note that n equaton (1) n s the number of attrbutes assocated wth a homestead n-1 of whch are non lot-sze related. The attrbutes of mprovements can nclude home square footage number of bedrooms number of non-bedrooms or number of garages. The attrbutes of land nclude such thngs as wdth (frontage) depth and shape. Other homestead attrbutes not ted to mprovements or land ncludes such thngs as densty of housng and school qualty n the area. 9
nformaton on how the relatve values of land and mprovements vary wth lot sze s mportant n understandng property valuatons partcularly when there s a need to determne optmal lot sze for muncpal fnance consderatons. n the rest of ths secton the relatonshp between lot-sze and other components of housng are conceptualzed. The relatve shares of mprovements and land n the total valuaton of a property can be derved as follows. Assumng that each homestead can be quantfed n terms of value dfferentatng each sde of equaton (1) wth respect to one obtans: ( = = 1 1 n ). [] Equaton () can further be expressed n terms of elastctes: ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( ). 1 =1 = n [3] Snce and the followng can be derved from equaton (3) = = = 1 1 n ( ) ( ) ( ) ( ) ( ) ( ) = = 1 1 n [4] Where ( ) = ( ) = ( ) = = ( ) and (. = ) Substtutng these elastctes nto equaton (4) yelds: ( ) ( ) ( ) ( ) ( ) = = 1 1 n. [5] n equaton (5) and S = S = are shares of total value attrbutable to land and each mprovement. Equaton (5) suggests that the elastcty of homestead value wth respect to homestead demand s postve and depends on the elastctes gven above all of whch are 10
postve. Now consder a gven lot sze. s of course the varable that s regulated va zonng. Further defne = where s the elastcty of homestead demand wth respect to lot sze choce. The elastcty of homestead value wth respect to lot sze choce () s: ( ) S ( = S ) n 1 = 1 [6] or n 1 ( ) ( S ( = 1 )) = S [7] where =. Ths elastcty whch s the prce elastcty of land wth respect to the avalablty of land of a gven lot-sze measures the prce responsveness to the avalablty of land across a range of avalable lot szes. Wth a decrease n the supply of buld-able land resultng from a decrease n the avalablty of land n a gven lot sze the prce of land wll ncrease resultng n negatve value of the elastcty. Smlarly = whch measures the responsveness of total buld-able land to avalablty of land n a gven lot sze category. t measures the mpact of lot sze restrctons on developed land n the communty. = whch s the prce elastcty of th mprovement wth respect to lot sze measures the responsveness of the prce of mprovements to lot sze. Fnally = whch measures the responsveness of homestead mprovements to lot sze restrctons. Accordng to equaton (7) the mpact of lot sze avalablty on property value s a functon of the relatve value of the lot sze versus mprovement plus elastctes depctng the effect of lot sze on prce land consumpton mprovement attrbute values and mprovement attrbute demand. To understand these relatons t s mportant to know how these elastctes vary wth lot sze. We examne these elastctes below. 11
therto these elastctes have been treated as fxed. n realty they are context senstve and vary by locaton. To evaluate how some of these elastctes mght vary consder the land dmenson. The value of a lot s obvously correlated wth the lot sze tself. There s evdence to suggest that prce per unt of land on resdental propertes s nversely related to the sze of the parcel (Tabuch 1996). Due to economes of scale n nfrastructure and land constructon the unt land prce may decrease as the sze of the lot ncreases. The value of a lot should also be nversely related to ts dstance from the Central Busness Dstrct (CBD). Ths s consstent wth Mlls-Muth model of urban spatal structure whch suggests that land tends to be more avalable and low valued at greater dstances from the urban core. Moreover hgher-wage workers tend to lve farther from the CBD than do low-wage workers (Fernandez and Su 004). Ths concept s n lne wth the theory of bd-rent curve. 4 On the other hand the value of mprovements (homestead less the lot sze) should be drectly related to lot sze at least over a range of lot szes. As ncome rses both lot sze and mprovement demand should ncrease (Euler s Theorem) but probably not proportonately. The demand for mprovements should grow at a greater proporton than the demand for lot sze due to the fact that the former s more of a necessty than the other. The Engle curve for mprovements s expected to become flat earler than the Engle curve for lot sze. Whle both components are normal goods lot sze s more nearly a luxury good. Mtgatng factors whch affect ncome elastcty nclude affordablty. Fewer people can afford large homes. Both lot sze and mprovements dstrbutons must relate to ncome dstrbuton. t s demonstrated above that the prce elastcty of land wth respect to lot-sze elastcty of land wth respect to lot-sze prce elastcty of mprovements wth respect to 1
lot sze elastcty of mprovements wth respect to lot sze affect the total housng value and therefore muncpal revenue. To explore the relatonshp between optmal property tax revenue and lot sze consumer preferences and demographcs become relevant. To llustrate ths pont consder the followng equaton where aggregate housng demand s expressed as: * ( Y T E M ) = [8] * where s the prce of the housng s the vector of the prces of complements and substtutes for housng Y s the ncome T s a vector of taste and preference varables (such as townshp publc open space educatonal qualty and access to hghways) E s proxy for expectatons about (such thngs as prces apprecaton future of neghborhood and relocaton) and M s the vector of mscellaneous factors (such as household characterstcs famly sze etc). The demand for housng attrbutes s derved demand for housng. Thus the derved demand for lot sze () and housng attrbutes () (components of the housng bundle) can be expressed as: * ( Y T E M ) * ( Y T E M ) = and [9] =. [10] s the prce of lot-sze * * s the vector of prces of complements and substtutes for lot- sze s the prce of mprovements and s the vector of prces of complements and substtutes for mprovements. Consder the total land consumed by lot sze category n a communty. ot prce per acre can be denoted as ( Y ) and the total land beng consumed n a lot sze categorzed as ( ) where s the lot sze of the category. ence a varaton of the component of Equaton (1) can be expressed as follows: 13
( Y )( ( ) = ). [11] Assume for smplcty sake that ( ) follows a normal dstrbuton wth mean μ and varance σ. ence ( ( σ ) ( ) 1 σ π exp ( μ ) ~. [1] Smlarly the value of the mprovements s the product of the prce for each mprovements ( Y ) and the total magntude of mprovements ( )..e. = ( Y )( ( )). [13] ( ) where s the level of mprovements. We also assume that ( ) follows a normal dstrbuton wth mean μ and varance ( ) 1 σ π exp ( μ ) σ ( ( σ ) ~. ence. [14] The total value of the homestead can be expressed as: ( Y )( ( )) ( Y )( ( ) = ). [15] To fnd the value of lot sze that maxmzes the total value of the homestead dfferentate equaton (15) wth respect to ( )( ) ( Y )( ) ( )( ) ( Y )( ). = [16] At optmum valuaton of the value functon = 0 defnes the frst order condton for optmzaton. Therefore ( )( ) ( Y )( ) ( )( ) ( Y )( ) = 0. T [17] Manpulatng equaton () n order to express t n terms of elastcty one obtans ( )( )( ) ( Y )( )( ) ( )( )( ) ( Y )( )( ) = 0. [18] whch mples that 14
( ) ( ) ( ) ( ) ( )( ) ( )( ). 0 = = [19] ence ( ) ( ) =. [0] where s the relatve value of mprovements to lot sze. Further manpulaton yelds ( ) ( ) = [1] Smlarly ( ) ( ) = [] To derve the expresson for one can dfferentate equaton (1) wth respect to as follows: ( ) ( ) ( ) ( ) ( ) ( ) exp 1 σ μ σ μ π σ =. [3] Therefore ( ) ( ) ( ) σ μ = [4] whch mples that ( ) σ μ = [5] Smlarly consderng equaton (14) n order to derve the expresson for ( ) ( ) ( ) ( ) ( ) ( ). exp 1 σ μ σ μ π σ = [6] Therefore ( ) σ μ =. [7] Fnally substtutng values from equaton (4) and (7) nto equaton (0) one obtans ( ) ( ) ( ) ( ) ( ) σ μ σ μ =. [8] 15
The expresson for s central to property value determnaton and therefore tax revenues and can be derved n terms of the above referenced elastctes. t shows that at the optmal level the relatve value of mprovement and lot also depends on the elastctes above. The extent to whch a lot sze restrcton mpacts revenues depends on the rato of whch tself s determned by the prce elastcty of land wth respect to lot-sze elastcty of land wth respect to lot-sze prce elastcty of mprovements wth respect to lot sze elastcty of mprovements wth respect to lot sze. ence property valuaton and hence muncpal tax revenues are functons of the elastctes mentoned above along wth lot sze restrctons whch n turn may vary by jursdcton due to dfferences n ncome demographcs taste and preferences property mx housng stock as determned by the supply and demand of housng. The objectve of ths study s to understand the relatonshp between lot sze and optmal valuaton of land wth mplcatons for optmal muncpal revenue. The basc hypothess s that due to the dfference n the communty structure optmalty n sale value and hence taxable value are determned by elastctes.. EMRCA MODE SECFCATON To operatonalze the conceptual model above the proposed emprcal framework s to estmate the relatonshp between property value and ts determnants wth a specal focus on lot sze. We propose the hedonc prcng model as the basc emprcal framework for determnng the effect of lot sze on the taxable value of a homestead. n the case of lot sze our target varable a unque functonal specfcaton wll be used that allows the dentfcaton of an optma or several optma. Snce the ntroducton of the hedonc prcng model by Grlches (1971) an extensve lterature has developed on the applcaton of the model to value locaton structural and 16
envronmental amentes assocated wth resdental property. The hedonc procedure s frequently used to quantfy the effect of varous housng and neghborhood characterstcs on house prces. Emprcally the technque uses regresson analyss to varatons n market values to the property s characterstcs (lot sze age of the house number of bedrooms number of bathroom etc) (Goodman and Thbodeau 1995). 5 Based on prevous studes by Goodman and Thbodeau 1995 specfc attrbutes ncluded n our emprcal analyss nclude: (1) ot characterstcs ( Z ) such as lot sze frontage depth etc; () structural characterstcs( such as number of bedrooms number of half-bath and full bath number of garages basement number of stores etc; (3) neghborhood varables Z such as percentage of nonresdental areas percentage of undeveloped land employment densty etc; (4) proxmty varables Z such as proxmty of fre staton polce staton schools parks lbrares recreatonal facltes and hghways etc. ence the general specfcaton for the hedonc house prce equaton s: ( ( ) f ( Z Z Z Z ) j Sj Nj j ) Z S ) = [9] ( ) where s the value of the homestead and Z s the neghborhood characterstc Nj ( N ) Z Sj s the structural characterstc of the house etc. A consumer wth a vector of soco-economc characterstcs ω derve utlty from the varous characterstcs of the house Z Z Z Z and from the numerare non-housng good τ. The utlty functon of the buyer s specfed as follows: ( Z Z Z Z τ ϖ ) U = U. [30] j Sj Nj j The homebuyer s problem s to maxmze U (.) subject to: ( Z Z Z Z ) Y = τ [31] j Sj Nj j j Sj Nj j 17
where Y denotes level of ncome and τ represents non-housng expendture and ths would be a standard consumer optmzaton problem except that the budget constrant may be non-lnear. n a hedonc prces model there are two equatons to be estmated. The hedonc prce functon and the ndvdual s margnal wllngness to pay functon are respectvely ( ) f ( Z Z Z Z ) = and [3] j j j Sj Nj ( Z Z Z Z ) j sj Nj j j b = b [33] n equaton (33) b j th s the margnal wllngness to pay for the attrbute of the j th household. * Z sj s the vector of other structural characterstcs and z sj s the partcular structural (S) characterstc for whch we want to derve the margnal wllngness to pay functon. Equaton (3) can be estmated assumng a basc lnear functonal relatonshp. t can however be estmated through a non-lnear functon. For llustratve purposes smple plots of the taxable value of a house aganst the lot sze are presented n Fgure (4) for Merdan Townshp our case study. These ndcate some correlaton between taxable value and lot sze. These llustratons hnt at the endogenety of taxable value of a homestead vs-à-vs lot sze. A hedonc prcng analyss wll systematcally dentfy the functonal relatonshp between the varables and level of sgnfcance. A generalzed Box-Cox transformaton (Greene 1997) s used to dentfy the approprate functonal form n order to determne the range of lot szes that maxmzes the tax revenue. The flexble form approach ads n the estmaton of the amenty values wth no pror restrctons on the hedonc relatonshps and allows for the lkelhood rato tests of more tradtonal functonal forms (Mlon Gressel and Mulkey 1984). Rosen s (1974) poneerng work motvated semlog log-log as well as alternatve specfcatons usng the Box-Cox. The Box-Cox transformaton s gven by: 18
λ ( 1) λ f λ 0 and [34] λ = = ln λ f λ = 0 [35] where λ s the Box-Cox parameter. The Box-Cox transformaton below can be appled to a regressor a combnaton of regressors andor to the dependent varable n a regresson. The objectve of dong so s usually to make the resduals of the regresson more homoskedastc and closer to a normal dstrbuton (Greene 1997). The vrtue of the Box-Cox form s that t requres no pror restrctons on the attrbute relatonshps. For example f λ = λ 1 the specfcaton s lnear; f λ = λ 0 t s a double 1 = 1 = log and f λ = ; λ 1 t s sem log. Other combnatons yeld quadratc and exponental 1 0 = forms. Nested hypotheses testng wth the unrestrcted Box-Cox form and the tradtonal functonal forms can be conducted usng a lkelhood rato test statstc (Mlon Gressel and Mulkey 1984). By estmatng equaton (34) under the varous lnear hypotheses restrcted maxmum lkelhood values can be calculated. Under the null hypothess mnus two tmes the log of the rato of the restrcted to the unrestrcted lkelhood value s dstrbuted asymptotcally as chsquared wth two degrees of freedom (snce we have parametrc restrctons).. DATA Multple lstng data from Mchgan Realtors s utlzed n ths study. Merdan Townshp n the ngham County Mchgan s a fast growng metropoltan area. For the year 005 the resdental parcel count for the townshp was 1308 commercal parcel count was 663 ndustral parcel count was 47 and agrcultural parcel count was 5. The total assessed value of resdental property was $17486150 whch s approxmately 7.6% of the total real value of propertes n the county (Mchgan State Tax Commsson 005). Data on all real estate 19
transactons from October 04 through March 05 for whch actual sales had occurred were used n the analyss. roperty tax was not used as the dependent Mchgan law provdes a cap on property tax ncreases as long as property ownershp remans the same. ence the sales of property trggers an adjustment of taxable value and therefore tax lablty. The sluggshness of assessed value and the fact that t does not reflect market value s the prmary reason for usng sales prce data. The data conssted of 137 observatons (homesteads). Table (1) provdes a detaled dscusson on the nature of the varables n the estmated model. The dependent varable s SAERCE. The ndependent varables nclude the total square footage of the house above the ground (SQFTABOE) the total lot sze of the house (TOTOTSZE) the age calculated as the dfference between the year the house was bult and the sale date (AGE) the dummy varable ndcatng whether the house has a basement or not (DBSMT) the varable ndcatng the number of car places or garages (NOGARAGE) the dummy varable representng whether the garage s attached to the house (DATTACGAR) the dummy varable ndcatng whether the house has a sewage faclty (DSEWER) the total number of bedrooms (BDRMS) the total number of non-bedrooms or rooms other than bedrooms (NON_BDRMS) the number of full bath (FUBAT) the number of half bath (AFBAT) the number of stores of the house (DTYE) and the number of days the house has been n the market (DOM). n the followng secton the results of the Box-Cox transformaton and the hedonc prcng models estmated through usng the method of ordnary least square (OS) are presented.. RESUTS The lnear Box-Cox hedonc result s reported n Table (). The Box-Cox transformaton tests the null hypothess whether the data fts a lnear demand functon as opposed to a non-lnear 0
demand functon. The Box-Cox transformaton parameters θ and λ measure the degree by whch the dependent and the ndependent varables have been transformed. sgnfes the value of the lkelhood rato test (RT) statstc and χ denotes the ch-square value. The RT s a statstcal test of the goodness-of-ft between two models. A relatvely more complex model s compared to a smpler model to see f t fts a partcular dataset sgnfcantly better. The RT begns wth a comparson of the lkelhood scores of the two models: R = *(ln1-ln); Ths RT statstc approxmately follows a ch-square dstrbuton. To determne f the dfference n lkelhood scores among the lnear and non-lnear models s statstcally sgnfcant we next must consder the degrees of freedom. n the RT degrees of freedom s equal to the number of addtonal parameters n the more complex model. Usng ths nformaton we can then determne the crtcal value of the test statstc from standard statstcal tables (Greene 1997). Accordng to the values of the lkelhood rato test statstcs the thrd model and the forth models.e. the nverse and the lnear functonal forms are strongly rejected due to hgh values of ch-square n both the data sets whereas the second model.e. the log-log model s not rejected. Ths suggests that the log-log model s a better ft. Wth the demand functonal form dentfed a regresson analyss was performed usng Ordnary east Square (OS) method wth sales prce as the dependent varable and the other varables n Table (3) as ndependent varables. Box-Cox transformatons along wth the ncluson of squared and cube terms of lot sze have been used to be able to capture the possble curvature n the estmated relatonshps for dstance-related varables. Table (3) summarzes the regresson result for the log-log model and specfes the level of sgnfcance for each of the ndependent varables. Snce n ths model the explanatory nondummy attrbutes are transformed to logarthms the coeffcents of these varables can be 1
nterpreted as the respectve elastctes. Snce log transformaton s only applcable when all the observatons n the data set are postve the dummy varables were not transformed. The model specfcatons allow the examnaton of the effects n valuaton of lot sze usng lot sze squared lot sze and cubed lot sze. The 3 rd order of the lot sze varable allows one to observe the peak level of lot sze from a revenue perspectve. The varables TOTOTSZESQ and TOTOTSZECUBE are sgnfcant at 1% level of sgnfcance. The varables FUBAT DAGE10TO0 and TOTOTSZE are sgnfcant at 5% level of sgnfcance. The varables SQFTABOE DAGE0TO30 DAGEGREATER30 DBSMT DATTACGAR and NOGARAGE are sgnfcant at 10% level of sgnfcance. The varables BDRMS AFBAT and DOM are not statstcally sgnfcant at the 10% level of sgnfcance. Consderng that the data s cross sectonal n nature R-Square of 89% for Merdan Townshp s surprsngly hgh. The coeffcents are generally consstent wth expectatons except for DATTACGAR whch s negatve mplyng that a house wth attached garage s 55% less valuable than a house wth no attached garage. The effects of the lot sze varables were of great nterest. For example a postve relatonshp between square footage above and sale prce was estmated. ence mprovement nfluences prce and therefore tax revenue. Ths s consstent wth the study of Bn and olasky 003. The varable SQFTABOE s postve and statstcally sgnfcant suggestng a square footage prce elastcty of 0.44. Ths nflexble prce response s consstent wth prevous studes (Mahan olasky and Adams 000). The elastcty of prce wth respect to bedrooms s 0.07 also suggestng an nflexble prce response. Smlarly the elastcty of prce wth respect to full bath s 0.14. ouses that are 10 to 0 years old are 19% more valuable than the numerare group.e. age lyng wthn 0 to 10. Ths may reflect the effects of communty attrbutes: mature
communtes wth well-establshed neghborhood lkely to be more valuable than upstart communtes. owever as expected houses wthn the age of 0 to 30 are 36% less valuable than the numerare age group. ouses over the age of 30 years are even less valuable. Ths reflects the mpact of housng vntage (age) on property value. The coeffcent of NOGARAGE s 0.993703 and t s statstcally sgnfcant. Ths mples that for each addtonal garage the value of the house ncreases by 30%. mpact of ot Sze on Revenue To determne the lot sze that maxmzes property value ceters parbus set NSAERC E TOTOTSZE = 0. Therefore (.08) TOTOTSZE 3( 0.010) (.0457) TOTOTSZE ( 0.0306) TOTOTSZE ). NSAERCE TOTOTSZE = (.0150 TOTOTSZE = (.0150 [36] Settng equaton (41) equal to zero yelds (.0457 ( (.0457-4(.015)( 0.0306 ))( 0.0306) ) TOTOTSZE = sqrt ; [37] whch can be expressed as TOTOTSZE = (.0457.00158)0.0613; [38] The equaton (38) above suggests that there are two optma for Merdan Townshp 0.49 acres and 1.00 acres. Ths s consstent wth the two roots expected from a quadratc functon. ). CONCUSONS Ths paper conceptualzes the relatonshp between lot sze and muncpal tax revenues by examnng the lot sze that maxmzes property values. Double optmum wth respect to the mpact of lot sze on property values was dentfed wth the two peaks beng at 0.49 acres and 1.00 acres. The 0.49 acre peak s the hgher peak. The fact that the average zonng densty on all property n Merdan townshp s currently 0.8 acres suggests that greater densty than the current standard would yeld greater muncpal property tax revenue than the current densty. The fact that peak property values and therefore muncpal revenues vary along the range of lot szes 3
suggests that communtes should be mndful about the relatve poston of ther townshp optma n makng zonng decsons. n almost all debates about zonng ths ssue hardly ever comes up. Ths fndng s novel and s an mportant addton to the lterature. A more comprehensve study wll consder the cost sde of the muncpal fnance. Whle revenue can be easly attrbutable to property obtanng cost data s dffcult snce cost analyss would requre clear understandng of the allocaton of muncpal taxes to alter servces. That nformaton s not always avalable. The authors of these studes are currently workng on the decomposton of school cost. Ths would rely on accessor data augmented by data from the correspondng school dstrct on the number of kds orgnatng from each home. The ssue of optmal zonng for school fnancal optmzaton s clearly an ssue of sgnfcant nterest and the ongong analyss would shade some lght on ths ssue. REFERENCES Alonso Wllam. 1964. ocaton and and Use Cambrdge: arvard Unversty ress. Amercan Farmland Trust 004 "Cost of Communty Servce Studes." Farmland nformaton Center Fact Sheet. Bn Okmyung and olasky Stephen. 00. alung Coastal Wetlands: A edonc roperty rce Approach. Workng aper. Campbell Coln D. 1951. Are roperty Tax Rates ncreasng? The Journal of oltcal Economy ol. 59 No. 5. (Oct.): pp. 434-44. 4
Colton Roger D. and Sheehan Mchael. 001. nclusonary Zonng for Belmont: The ublc Need and the rvate Exacton Aprl. url; http:www.fsconlne.comworkhebelmontnexus-study.pdf Crecne John Davs Otto A. and Jackson John E. 1967. Urban roperty Markets: Some Emprcal Results and Ther mplcatons for Muncpal Zonng Journal of aw and Economcs ol. 10. (Oct.): pp. 79-99. Economc and lannng Systems. 000. Regonal Economc Analyss (Trends Year 000 and Beyond). Berkley CA East Bay Regonal ark Dstrct. Fernandez Roberto M. and Su Celna Space n the Study of abor Markets Annual Revew of Socology olume:30 (August 004) pp. 545-569. Fschel Wllam A. 199. roperty Taxaton and the Tebout Model: Evdence for the Beneft ew from Zonng and otng Journal of Economc terature ol. 30 No. 1 (Mar.): pp. 171-177. Florestano atrca S. 1981. Revenue-Rasng mtatons on ocal Government: A Focus on Alternatve Responses ublc Admnstraton Revew ol. 41 Specal ssue: The mpact of Resource Scarcty on Urban ublc Fnance. (Jan.): pp. 1-131. Foley Bran. 004. The Effects of Resdental Mnmum ot Sze Zonng on and Development: The Case of Oakland Mchgan unpublshed M.S. Thess Department of Agrcultural Economcs Mchgan State Unversty. Glaeser Edward. and Gyourko Joseph. 00. The mpact of Zonng on ousng Affordablty arvard nsttute of Economc Research Dscusson aper Number 1948 (March): arvard Unversty Cambrdge Massachusetts. 5
Goodman Allen C. and Thbodeau Thomas. 1995. Age-Related eteroskedastcty n edonc ouse rce Equatons Journal of ousng Research olume 6 ssue 1. Gottlebaul D. and Adelaja Adesoj O. 004. The oltcal Economy of Downzonng Selected aper prepared for presentaton at the Amercan Agrcultural Economcs Assocaton Annual Meetng Denver Colorado August 1-4. Gottlebaul D. and Adelaja Adesoj O. 005. Down-Zonng and ts mpact on roperty alues revsed and resubmtted for the Amercan Journal of Agrcultural Economcs and resubmtted on August 3. Green W..1997. Econometrc Analyss. Saddle Rver NJ rentce all. Grlches Z. rce ndexes and Qualty Change arvard Unversty ress Mass (1971). arrson Davd Jr. and Kan John F. 1974. Cumulatve Urban Growth and Urban Densty Functons Journal of Urban Economcs 1 pp. 61-98. ulten Charles R. and eterson George E. 1984. The ublc Captal Stock: Needs Trends and erformance Amercan Economc Revew ol. 74 No. apers and roceedngs of the Nnety-Sxth Annual Meetng of the Amercan Economc Assocaton. (May): pp.166-173. CMA S. G. N. 00. Gettng to Smart Growth 100 olces for mplementaton. Washngton D.C. nternatonal CtyCounty Management Assocaton: 104. Jud G. Donald. 1980. The Effects of Zonng on Sngle-Famly Resdental roperty alues: Charlotte North Carolna and Economcs ol. 56 No. (May). Mahan Brent. olasky Stephen and Adams Rchard M. 000. alung Urban Wetlands: A roperty rce Approach and Economcs ol. 76 No. 1. (Feb.): pp. 100-113. 6
Mchgan State Tax Commsson (005). 005. Ad alorem roperty Tax evy Report ansng State of Mchgan. Mlls Davd E. 1989. s Zonng a Negatve-Sum Game? and Economcs ol. 65 No. 1. (Feb.): pp. 1-1. Mlon J. Gressel J. and Mulkey D. 1984. edonc Amenty aluaton and Functonal Form Specfcaton and Economcs 60 pp. 378-387. Qugley John M. and Rosenthal arry A. 005. The Effects of and Use Regulaton on the rce of ousng:what Do We Know? What Can We earn? A Journal of olcy Development and Research olume 8 Number 1. Rosen Sherwn. 1974. edonc rces and mplct Markets: roduct Dfferentaton n ure Competton Journal of oltcal Economy olume: 8 ssue: 1 (Jan.-Feb.) ages: 34-55. San Dego County Assocaton of Realtors (003). 006. "oston Statement: Up-ZonngDown- Zonng.". Spangenberg John and McCormck Mchael ousng n the Communty: Choce Avalablty and Affordablty url:http:www.warealtor.comgovernmentqolpolces qolhousnggoals.pdf. Tabuch Takatosh. 1996. Quantty rema n Real roperty Markets and Economcs ol 7 No.. (May): pp. 06-17. 7
Endnotes 1 Smart Growth Amerca url: http:www.smartgrowthamerca.org Zonng can beneft some ndvduals and mpose cost on others. The extent to whch zonng mparts a net socal loss depends on how skllfully t s appled (Crecne Davs and Jackson 1967). 3 t has been argued that snce t s one of the most popular tools for lmtng development and curbng suburban sprawl the government should farly remburse the landowner for any negatve valuaton that may occur to hs property (San Dego Assocaton Of Realtors 003). 4 Bd-Rent s equvalent to the maxmum land rent a potental user would be wllng to pay for a gven ste locaton The Bd-Rent Curve shows how the ndvdual s bd-rent changes as a functon of the dstance from some crtcal central pont (C). Central pont s the pont at whch transport costs are mnmzed and bd-rent maxmzed for the gven use. Each potental use has ts own bd-rent curve and also central pont (Chapter 4: nsde the Cty : Some Basc Urban Economcs UR: web.mt.edu11.431jwwwfall910431_gmch04.ppt vewed on 061306). arger bundles wll be found n general at a greater dstance from the center of the communty where prces should be much hgher. n other words lot szes wll be hgher at great dstances from the center where property values are hgher. Ths suggests that an nverse relaton between lot sze and value of vacant land. 5 edonc method have been used extensvely n studyng housng by regressng the prce of a property on ts nternal characterstcs such as sze appearance features and condtons as well as the external neghborhood characterstcs such as the accessblty to schools and shoppng level of water and ar polluton value of other homes etc. 8
Table 1: arables Used n the edonc rcng Analyss of Merdan Townshp M.* Dependent arable Symbol Descrpton Nature of arable arable Sale rce SAERCE Sale prce of the house Contnuous ndependent arables ot characterstcs (Z ) Square footage SQFTABOE above Total square footage of the house above the ground Total lot sze TOTOTSZE Total lot sze of the house Structural Characterstcs (Z S ) Age AGE Dfference between year the house was bult and sale date. resence of basement DBSMT Whether or not the house has a basement. Contnuous Contnuous Dummy varable wth the followng classes: 0 to10 years 10 to 0 years 0 to 30 years and greater than 30 years. Dummy varable wth the followng classes: 1 f house has basement 0 otherwse. No. of garages NOGARAGE No.of garages. Dscrete 1 or or 3 etc resence of DATTACGAR Whether or not garage garage s attached to the house. Sewage faclty DSEWER Whether or not house has a prvate sewage faclty. Dummy varable wth the followng classes: 1 f the house has an attached garage 0 otherwse. Dummy varable wth the followng classes: 1 f the house has the house has sewage faclty 0 otherwse. Bedrooms BDRMS Total number of Dscrete 1 or or 3 etc bedrooms Non-bedrooms NONBDRMS Total number of nonbedrooms Dscrete 1 or or 3 etc Full bath FUBAT No.of full baths Dscrete 1 or or 3 etc alf bath AFBAT No.of half baths Dscrete 1 or or 3 etc Type Stores DTYE No. of stores Dummy varable wth the followng classes: 1 f house s a Ranch 0 otherwse. Days on Market DOM No. of days house was n the market Dscrete 1 or or 3 etc * The data came from multple lstngs nformaton from Merdan Townshp Mchgan. Due to the slow market only 137 observatons of actually sold property were avalable. 9
Table : near Box-Cox edonc Results Model 1 Model Model 3 Model 4 near Box-Cox og-og nverse near Merdan Townshp θ -.03405 0.00-1.00 1.00 λ -.03405 0.00-1.00 1.00-1450.6565-1451.5871-1474.847-1490.79 χ _ 1.86 48.38 80.15 30
Table 3: Effects of arcel Attrbutes on roperty alues n Merdan Townshp arable Name % mpact on Sold rce (og dependent arable) constant 8.63311*** nsqftaboe 0.437197*** lnbdrms 0.077039 lnfubat 0.1490905** DAGE10TO0 0.1890373** DAGE0TO30-0.3683*** DAGEGREATER30-0.35373*** DBSMT 0.900491*** DATTACGAR -.554949*** NOGARAGE 0.993703*** AFBAT 0.015856 DOM - 0.0000596 TOTOTSZE 0.0149934** TOTOTSZESQ -.08491* TOTOTSZECUBE 0.0101* R-square 0.8945 * ** and *** represent sgnfcance at the 1 5 and 10% levels respectvely. 31
Fgure 1: Conceptualzed Effects of Zonng on Muncpal Revenue Number of arcels Tax Rate er acre ot value ( ) Total ot alue: = * Zonng ot Sze () mprovement Sze and Attrbutes ( ) mprovement Attrbute alues ( ) Total mprovement alue: = * Muncpal roperty Tax Revenue 3
Fgure : Medan and Average Square Footage of ots Under New Sngle-Famly ouses n the US 199-005 Average Square Feet ot Sze Unted States 50000 nsde MSAs Regon 40000 30000 0000 10000 0 0000 199 1993 1994 1995 1996 1997 1998 1999 Years Medan Square Feet ot Sze 000 001 00 003 004 005 Outsde MSAs North-east Mdw est South West Unted States nsde MSAs Regon 15000 10000 5000 0 199 1993 1994 1995 1996 1997 1998 1999 Years 000 001 00 003 004 005 Outsde MSAs North-east Mdw est South West Source: Medan and Average Square Feet by ocaton Characterstcs of New ousng US Census Bureau http:www.census.govconstc5annmalotszesold.pdf 33
Fgure 3: Medan and Average Floor Area n New Sngle-Famly ouse USA 1978 to 005 500 Medan Square Feet of Floor Area Unted States nsde MSAs Regon 1500 500-500 500 1978 1980 198 1984 1986 1988 1990 199 Years 1994 1996 1998 000 00 004 Average Square Feet of Floor Area Outsde MSAs Northeast Mdw est South West Unted States nsde MSAs 1500 Outsde MSAs Regon 500-500 1978 1980 198 1984 1986 1988 1990 199 Years 1994 1996 1998 000 00 004 Northeast Mdw est South West Source: Medan and Average Square Feet by ocaton Characterstcs of New ousng US Census Bureau http:www.census.govconstc5annmalotszesold.pdf 34
Fgure 4: Taxable alue and ot-sze for Recently Sold ouses n Merdan Townshp M (Oct 004-March 005) by ot Sze and Range of ot Sze. Taxable alue er Acre ($) 800000 700000 600000 500000 400000 300000 00000 00000 100000 100000 0 0 0.1 0.1 0.9166 0.9166 0.387511 0.387511 0.536731 0.536731 0.75481 0.75481 0.977961 0.977961 0.3099174 0.3099174 0.336915 0.336915 ot sze (Acres) ot sze (Acres) 0.339 0.339 0.344356 0.344356 0.3696051 0.3696051 0.390663 0.390663 0.418738 0.418738 0.468099 0.468099 0.4993113 0.4993113 0.550964 0.550964 0.736915 0.736915 11 1.504809 1.504809 Taxable value value 350000 300000 350000 50000 300000 00000 50000 00000 150000 150000 100000 100000 50000 0 Taxable alue per acre by range 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.9 1 1.5179 Range of ot Sze Taxable alue Taxable alue 35