Valung Beach Qualty wth Hedonc Property Models Crag E. Landry* Department of Economcs Center for Natural Hazards Research East Carolna Unversty, Greenvlle, NC 27858 landryc@ecu.edu; 252-328-6383 and Paul Hndsley Department of Envronmental Studes Eckerd College, St. Petersburg, FL 33711 hndslpr@eckerd.edu; 727-864-7722 *Author for correspondence; Crag Landry s Assocate Professor, Department of Economcs and Assstant Drector, Center for Natural Hazards Research, East Carolna Unversty; Paul Hndsley s Assstant Professor, Department of Envronmental Studes, Eckerd College; we thank Fan-Chn Kung, Okmyung Bn and an anonymous revewer for helpful comments. 0
Valung Beach Qualty wth Hedonc Property Models Abstract Ths paper explores the nfluence of beach qualty on coastal property values. We hypothesze that beach and dune wdth provde local publc goods n the form of recreaton potental and storm/eroson protecton, but servces are lmted by dstance from the shorelne. Our fndngs support ths hypothess, as extendng the nfluence of beach qualty beyond 300 meters from the shore generally results n statstcally nsgnfcant parameter estmates. For houses wthn ths proxmty bound, beach and dune wdth ncreases property value. We argue that nterpretaton of MWTP for beach qualty depends upon ndvdual understandng of coastal processes and expectatons of management nterventon. Key words: beach, dune, qualty, wdth, coastal, eroson, hedonc, property value 1
Valung Beach Qualty wth Hedonc Property Models Introducton Coastal shorelnes are hghly dynamc envronments; nteractons of coastal landforms, ocean, and atmosphere determne the physcal characterstcs of shorelnes, leadng to a dynamc equlbrum where rates of change are the result of a combnaton of physcal forcng processes, spatal characterstcs, underlyng geology, vegetatve communtes, and physcal characterstcs of human development. Because the eastern coast of the U.S. les on a passve geologc margn, much of the coast s characterzed by a wde and gently slopng contnental shelf and coastal plan. At the ntersecton of land and ocean exsts an extensve barrer sland system whch spans more than two-thrds of the Southeast Atlantc shore (Morton and Mller 2005). These barrer slands are essentally well developed sand bars, formed as a consequence of wave energy dsspatng on land and depostng sedments on the shore. These systems are n constant flux from both regular processes, such as long shore currents, waves and tdes, as well as less frequent, hghenergy events lke hurrcanes and nor easters. Sea level change also plays an mportant role n barrer sland evoluton. The natural appeal of coastal envronments has led to extensve development of many coastal areas, ncludng barrer slands. Accordng to the Pew Oceans Commsson (2003), between 1998 and 2015 the coastal populaton of the U.S. wll ncrease by almost 20 percent from 139 mllon to 165 mllon. Hazards assocated wth natural coastal processes pose a rsk to the ncreasng numbers of people and growng amounts of captal and nfrastructure. Unremttng waves and sporadc storms drve sedment flux along the coast. The overwhelmng majorty of shorelne n the eastern U.S. (80 to 90 percent), 2
however, has exhbted net eroson n recent decades (Galgano and Douglas 2000). Clmate change threatens to ncrease the ntensty of storms and rase sea level 18 to 59 centmeters over the next century (IPCC 2007), whch would hasten shorelne change and exacerbate coastal eroson. Clmatc change affects coastal property and nfrastructure through both chronc shorelne eroson as well as dscrete devastaton due to storms. Beaches and dunes buffer development from coastal eroson. Whle beaches can be decmated by storms, they typcally exhbt sgnfcant recovery n ntervenng perods. Wth sea level rse, chronc eroson could be an ncreasng threat to beaches, dunes, and hnterland. In decades to come, few landforms wll see changes as dstnct as barrer slands, and development on barrer slands wll be heavly nfluenced by ths evoluton. Analyss of exstng development suggests that 25 percent of homes wthn 500 feet of the U.S. coast could be lost to eroson n the next 60 years, at a potental cost of $530 mllon dollars each year (Henz Center 2000). In lght of these hazards, owners and prospectve owners of coastal property must decde f the rsks are relevant to them and f so, what actons should be taken to mtgate these rsks. These decsons are drven by numerous factors ncludng ther envronmental knowledge, expectatons of change n envronmental and market condtons, rsk preferences, and wealth. Prospectve buyers can choose to locate further from the ocean as a form of self-protecton, but ths can lmt recreaton potental and vsual amenty. For those desrng proxmty to the ocean, buyers can search for propertes that exhbt favorable envronmental rsk factors, such as hgher elevaton above sea level and wde beaches and dunes. The sandy beach also provdes for recreaton and lesure potental, whle dunes may enhance or detract from recreaton and 3
lesure dependng upon how people perceve them. If market partcpants vew these envronmental factors as nfluencng coastal rsk and recreaton potental, market prces should reflect mplct values for both protectve and recreatonal aspects. In ths study, we focus on the relatonshp between resdental property values and measures of beach qualty specfcally hgh- and low-tde beach wdth and dune wdth. Local beaches affect the aesthetcs of the coastal landscape and provde space for recreaton and lesure actvtes. Local beach wdth also reflects the amount of eroson rsk a property faces and affects flood/storm surge rsk. Wder beaches provde an mportant buffer for absorbng waves and storm surge durng hgh ntensty storm events. Dunes also functon as storm buffers. Narrow beaches and dunes often reflect hgh eroson rates, and thus potental for loss of beachfront or near ocean land and structures due to eroson. We use hedonc property prce models to nvestgate coastal property owners wllngness to pay (WTP) for envronmental amentes that also reduce rsk. The nterpretaton of the relatonshp between housng prces and beach qualty s made substantally more dffcult by varablty n homeowners ) knowledge of natural coastal evolutonary processes, ) perceptons of the effectveness of beaches as storm and eroson buffers, ) subjectve evaluatons of nearby beaches for aesthetcs, recreaton, and lesure, and v) expectatons of future coastal management actons. Informaton on hstorcal rates of coastal eroson s generally avalable, but often not wdely dssemnated. Coastal management actons can nclude constructon of shorelne armor to protect property (often at the expense of beach qualty) and artfcal replenshment of beach and dune sand to bolster the beach. All of these factors wll nfluence subjectve value for beaches and expectatons of future envronmental 4
condtons when prospectve buyers are bddng on coastal propertes. The dynamcs of coastal processes can make collecton of approprate data dffcult because beach and dune wdth fluctuate over tme; areas can wtness perods of eroson and accreton, and perodc beach replenshment can ntroduce dscrete shfts n resource qualty. We attempt to address homeowners perceptons of beach qualty, understandng of fundamental beach dynamcs, and expectatons of communty-level nterventon n coastal evolutonary processes n our theoretcal model and nterpretaton of emprcal results. We fnd that beach and dune qualty do nfluence nearby property values n accord wth theory of beaches as local publc goods. That s, for coastal propertes located close to the shorelne, beaches at that shorelne have an effect on market value. But, as we consder homes located further from the shore, the relatonshp between beach qualty and sales prce becomes nsgnfcant. Our data suggest that values for propertes wthn 300 meters are nfluenced by local beach qualty, whle those at greater dstances are not (wth the only excepton beng an unexpected negatve sgn on low-tde beach wdth for proxmty measures of 500 and 600 meters). Margnal Wllngness-to-pay (MWTP) for houses n close proxmty to the beach ranges from $421 to $487 for an addtonal meter of hgh-tde beach, or $272 to $465 for an addtonal meter of low-tde beach. MWTP for ncreases n dune wdth range from $212 to $383 per meter. These welfare measures presumably reflect perceved storm and flood protecton as well as recreaton opportunty and amenty value that coastal households ascrbe to nearby beaches and dunes. Gven the beach and dune system s nherent volatlty and local government s predlecton wth attempts at 5
shorelne stablzaton (e.g. seawalls and beach replenshment), nterpretaton of margnal mplct prces depends upon property owner s expectatons of resource change over tme. If property owners expect beaches and dunes to be mantaned ether naturally or through management, margnal mplct prces can be nterpreted n the conventonal manner. If, on the other hand, property owners expect beaches and dunes to degrade over tme, MWTP from the hedonc model s an upper bound on true wllngness to pay. Coastal Resource Qualty and Property Values Prevous Lterature Numerous studes have estmated household values for spatally varable envronmental amentes n coastal housng markets. Proxmty to water (Shabman and Bertelson 1979; Mlon, Gressel, and Mulkey 1984; Edwards and Gable 1991; Pompe and Rnehart 1995a,b, 1990; Earnhart 2001; Parsons and Powell 2001; Landry, Keeler, and Kresel 2003; Bn, Kruse, and Landry 2008; Pompe 2008), water vew (Kulshreshtha and Glles 1993; Lansford and Jones 1995; Benson et al. 1998; Pompe and Rnehart 1999; Bn et al. 2008), and water qualty (Leggett and Bockstael 2000) have all been shown to nfluence coastal property values, and estmates of MWTP for these amentes have been produced usng property sales data. Others have used hedonc property models to estmate ncremental opton prce assocated wth coastal flood hazard (Hallstrom and Smth 2005; Bn, Kruse, and Landry 2008; Bn et al. 2008), eroson hazard (Kresel, Randall, and Lchtkoppler 1993; Landry, Keeler, and Kresel 2003; Pompe 2008), or wnd hazard (Smmons, Kruse, and Smth 2002). 6
Lkely due to the dffcultes n gatherng adequate data and nterpretng results, less attenton has been pad to beach qualty. Pompe and Rnehart (1995a) examne coastal South Carolna property sales between 1983 and 1991, ncludng beach wdth from 1989 as a covarate. They clam that beach wdth remaned farly constant durng the study perod. Ther results suggest a postve relatonshp between property value and beach wdth. 1 Smlarly, Landry, Keeler, and Kresel (2003) analyze coastal property sales n Georga between 1990 and 1997, ncludng beach wdth measured n 1997 as a covarate n ther hedonc regresson model. They, too, fnd a postve relatonshp, but note the potental for ms-measurement of the beach wdth effect gven the lmted nformaton on beach qualty and longer perod of sales data. Pompe and Rnehart (1999) make use of tme-seres beach qualty data, gathered by a state agency, whch should provde better accuracy for analyss of property values over a specfed tme perod. Employng a smlar specfcaton to ther prevous analyss (1995a), they examne the mpact of hgh-tde beach wdth, low-tde beach wdth, and average beach wdth at the nearby shore, as well as beach wdth at a popular recreaton ste. They fnd a postve and statstcally sgnfcant relatonshp for beach wdth at nearby beaches, regardless of the specfcaton, but nsgnfcant results for the popular recreaton beach. These results suggest that nearby, or local, beaches are of greater mport to property owners, lkely reflectng recreaton value n addton to eroson and flood protecton. The dearth of valuaton estmates for beach qualty s unfortunate, as these measures can play an mportant role n beneft-cost analyss (BCA) of beach management strateges. Early attempts at BCA (Bell 1986; Slberman and Klock 1988; Pompe and 7
Rnehart 1995b; Kresel, Keeler, and Landry 2004; Kresel, Landry, and Keeler 2005) faled to take account of coastal dynamcs. Ths s problematc, as beneft estmates that do not take beach evoluton nto account wll be based. Landry (2008) and Smth, et al. (2009) employ dynamc optmzaton methods that explctly ncorporate coastal geomorphology nto the resource management problem. To be appled, however, the models requre accurate estmates of benefts and costs of beach wdth. As recognzed by Pompe and Rnehart (1999) and Landry, Keeler, and Kresel (2003), the nterpretaton of hedonc prce parameters that reflect coastal resource qualty depends upon market partcpants knowledge of coastal processes and expectatons of future coastal management actons. Home buyers who vew beaches as statc resources and those who expect management agences to mantan beaches to a certan standard may have a dfferent perspectve on beach qualty than those expectng that beach wdth may fluctuate n the future. We note that knowledge and expectatons of fluctuatons n resource qualty are not unque to coastal envronments, as polluton levels, urban publc goods, and crme (all of whch have been shown to nfluence property values) can also change over tme. Fluctuatng resources n the coastal zone, however, are perhaps a more salent case, as objectve assessment suggests that n most nstances beach and dune wdth are expected to change over tme. Asde from knowledge and expectatons, mplct values for the qualty of nearby beaches and dunes wll reflect perceptons of ther effectveness as storm and eroson buffers as well as ther perceved aesthetc value and ther support of recreaton and lesure actvtes. 2 Theory 8
The theory of hedonc prces orgnates wth Rosen (1974), but s based on the ntutve noton that the compettve market prce of a dfferentated commodty reflects the mplct value of attrbutes of the commodty. We focus here on the consumer sde of the housng market. A home buyer s Hcksan rent functon (θ) for a property wth a vector of attrbutes a = (a 1,, a n ) s mplctly defned as: U(y - θ, a, λ) = u, where U s a strctly concave utlty functon wth the usual propertes, y s normalzed (by prce of numerare good x) annual household ncome, and λ s vector of varables representng demographc factors, knowledge of coastal processes, and expectatons of coastal management practces. Ths structure gves rse to a famly of ndfference curves θ(a, y, u, λ) n attrbute/rent space that defne household annual WTP for a (Palmqust 2004). The Hcksan bd functon s then: T t θ ( a, y, u, λ) B( a, y, u, λ) = (1 + r) θ ( a, y, u, λ), (1) T r t= 0 where r s the dscount rate, and the asymptotc result holds by the rules governng sum of an nfnte geometrc seres. In a perfectly compettve envronment, all consumers take the hedonc prce schedule, P(a), as gven. Maxmzng utlty subject to a contnuous housng prce schedule mples equalty of the gradent of the ndvdual s bd functon and the gradent of the hedonc prce schedule n equlbrum (see equaton (2) and pont A n top panel of fgure 1); ths s the geness of the hedonc prce functon when housng supply s taken as fxed (a common assumpton n the short run and for stuatons where exstng housng stock domnates the market (Palmqust 2004)). Conventonal applcatons of the hedonc prce method take the vector of housng attrbutes as constant over tme. A notable excepton s housng age (Clapp and Gaccotto 1998), whch evolves along a smple and known trajectory, but can exhbt 9
dscontnutes n mplct prces due to countervalng forces (obsolescence versus vntage effects). For those ndvduals that vew barrer slands as statc envronments, equaton (1) may be a reasonable representaton of preferences for beach and dune qualty. Lkewse, for ndvduals that expect beaches and dunes wll be mantaned at a constant level by some external authorty over the relevant perod they occupy a unt of housng, equaton (1) could be accurate. In ths case, the gradent of an estmated hedonc prce equaton can provde an estmate of margnal wllngness to pay for attrbute a : P( a) B( a, y, u, λ) 1 θ ( a, y, u, λ) =. (2) a a T r a Ths s depcted as pont A n fgure 1. [Fgure 1 about here.] For those that expect beaches and dunes to fluctuate, however, equaton (1) s ~ 0 0 T ncorrect. Defne an expected tme path for attrbute as a ( a, λ ) = [ a,..., a ], where the superscrpt ndexes tme. Ths expected tme path s based on current condtons, and reflects ndvdual-level characterstcs λ, such as knowledge of coastal processes and t 0 expectatons of management nterventons. It s reasonable to assume a a > 0 t, because hgher ntal quantty of attrbute should be assocated wth greater expectatons of / 0 a, t a condtonal on knowledge and expectatons and all else beng equal. Let expected resource qualty be represented as the arthmetc mean of the elements of 10
the attrbute tme path, α = t T a t. Ths expectaton wll vary across j bdders, but we suppress the j subscrpt for smplcty. Under these condtons the Hcksan bd functon s: T t= 0 t t 0 ( 1+ r) θ ( a, a ( a, λ), y, u, λ), (3) - where a - s a vector of attrbutes other than and a ( a 0, λ) represents the expected condtons for attrbute n perod t. Ths expresson does not smplfy asymptotcally as n (1), because the scale factor of the nfnte sum (θ( )) s not constant. All else beng equal, we would expect an ndvdual that expects a to decay (grow) to bd less (more) than and ndvdual that expects a to reman constant. The bd, however, wll also be nfluenced by ndvdual specfc varables λ, such as ncome, rsk tolerance, educaton, t knowledge, and expectatons. 3 In a compettve equlbrum, utlty maxmzaton stll mples equalty of the gradent of the ndvdual s bd functon and the gradent of the hedonc prce schedule. Wth respect to the dynamc characterstcs assocated wth housng, ths equalty holds at the current attrbute level, a 0, on the hedonc prce schedule, because all buyers are bddng on the same observed attrbute. Indvdual preferences, however, reflect expectatons of resource qualty over tme, and we can thnk of margnal wllngness to pay of the bd functon beng evaluated at α. More generally, the margnal bd reflects the expected present value of the sequence of margnal rents: P( a) a 0 = T t= 0 (1 + r) t θ ( a - t,a ( a, λ), y, u, λ) a. (4) a a 0 t t 0 11
In essence, the home buyer s not payng for current attrbute level n perpetuty, but the expected sequence of future attrbute levels. The current value margnal rent or wllngness to pay, θ a a a t t 0 / /, s nonnegatve; snce the rent functon s strctly concave n utlty-bearng attrbutes of a (Palmqust 2004), the margnal wllngness to pay s dmnshng n t a, as shown n the bottom panel of fgure 1. Thus, the nterpretaton of margnal wllngness to pay depends ~ 0 0 T upon ndvdual expectatons regardng attrbute a, a ( a, λ ) = [ a,..., a ]. Let c expectatons of the current qualty n perpetuty be gven by α - standard nterpretaton c of hedonc prce parameters mples that MWTP s evaluated at α (pont A n fgure 1). Ignorng the dscount factor for the moment, for ndvduals that expect a to decay d c (expected value denoted α < α ) the margnal rent n (4) s ncreasng wth dmnshng resource qualty over tme, all else beng equal. For those that expect resource qualty to g c mprove (expected value denoted α > α ), on the other hand, the margnal rent n (4) s decreasng over tme wth mprovng resource qualty. In ether case, the dscount factor s dmnshng exponentally over tme, whch should ensure that the overall ndex n (4) s decreasng over tme. The mplcatons are that present dscounted value of margnal rent, or margnal bd, n (4) reflects the value of expected future attrbute levels. In ths case, the gradent of the hedonc prce functon, P a a, wll provde only a bound on the true margnal 0 ( ) / value. If the housng attrbute (beach or dune qualty n our case) s decayng over tme, the gradent of the hedonc prce functon wll be an upper bound to the true margnal d c value because the expected characterstc level, α, s less than the constant level, α. 12
Ths case s depcted as pont B n fgure 1. The bas n margnal wllngness to pay s labeled n the bottom panel b, as Bas d. Under the assumpton that the attrbute s growng, the gradent of the hedonc prce functon wll be a lower bound on the true g value because the expected characterstc level, α, s greater than the constant level, c α. Ths case s depcted as pont C n fgure 1, and bas n estmaton of MWTP s labeled n panel b as Bas g. Thus, the nterpretaton of hedonc prces for beach and dune wdth depends upon ndvdual knowledge and expectatons of trends n qualty of the beach and dune system. We note that bas s not completely analogous to the classc errors-n-varables problem (see, e.g., Wooldrdge (2002), pg. 74), as one mght presume. We assume that current beach and dune qualty, a 0, are completely observable. We do not, however, observe people s expectatons of a, for whch we assume α s a suffcent statstc. If expectatons were observable, we could nclude ther average n the hedonc prce regresson equaton. In dong so, we would obtan unbased estmates of margnal wllngness to pay, as both margnal value and quantty of the attrbute would be expressed n comparable unts - present-value for margnal WTP and expected value for attrbute level. 4 Wthout nformaton on ndvdual expectatons, we can only focus on the relatonshp between sales prce and observed qualty levels. In some sense ths s reasonable, as bddng among potental home buyers reflects competton over the array of exstng condtons across property locatons. The parameters of the estmated equaton should be useful for predctng sales prces, condtonal on the dstrbuton of expectatons n the bdder populaton. The problem perssts, however, n attemptng to 13
nterpret margnal mplct prces for beach and dune qualty as a pont on an ndvdual MWTP functon. As bds reflect expectatons of resource change and management nterventons, the present value of MWTP wll reflect some expected level of resource qualty, whch can dffer from the current observed level n some cases. Ths mples that MWTP s potentally beng evaluated a dfferent level of resource qualty than currently observed, as ndcated at ponts B and C n the bottom panel of fgure 1. We also note that ths complcaton s n addton to other dffcultes assocated wth dentfyng ndvdual preferences n the second stage of hedonc estmaton (Palmqust 2004). Study Area and Data Tybee Island, the northernmost barrer sland on the Georga coast, s located roughly 19 mles east of Savannah, Georga. The sland has a relatvely small year-round populaton of 3,392 people (2000 estmate). Tybee Island became a tourst destnaton n the late 1800 s, leadng to resdental and commercal development on the sland. The Island now offers the regon, whch ncludes Savannah and Atlanta, a popular beach resort destnaton. Tybee Island has experenced numerous shorelne engneerng modfcatons over the past hundred years. Hstorcally, Tybee Island has eroded on ts northeastern porton and accreted on ts southeastern porton (Oertel, Fowler, and Pope 1985). Much of the hstorcal eroson can be attrbuted to harbor dredgng on the Savannah Rver (Grffn and Henry 1984). Eroson on the sland has been addressed usng numerous stablzaton projects, ncludng sea walls, grons, and rprap. Also, between 1976 and 2000, there were fve major beach replenshment projects. 14
Our dataset ncludes 372 real estate transactons for sngle-famly resdences that occurred between January 1990 and December 1999. All property sales records wth complete nformaton on arms length transactons were gathered from the county tax assessor database. Descrptve statstcs for the dataset are presented n table 1. The average real home sales prce s $151,906 (1999$). The data also nclude numerous structural attrbutes such as heated square footage (mean = 1703), lot square footage (mean = 8345), number of bedrooms (mean = 2.8) and bathrooms (mean = 2.1), presence of garage (mean = 0.18), presence of ar condtonng (mean =0.86), and the age of the home at the tme of sale (mean = 30 years). Spatal characterstcs nclude oceanfront homes (mean = 0.06), nlet front homes (mean = 0.03), homes borderng marsh (mean = 0.04), and dstance from the nearest beach (mean = 332 meters). [table 1 about here] The orgnal beach qualty measurements used n ths analyss reflect condtons exstng n sprng of 1997. Thrty-two transects were measured usng an electronc range fnder, and an addtonal eght transects were nterpolated to provde regular and complete coverage of Tybee s beach. Gven the length of Tybee Island, we collected measurements, on average, n 140 meter ntervals. Thus, beach qualty measures for 1997 reflect condtons at a maxmum of approxmately 70 meters from the nearest beach for all Tybee Island propertes. For each transect, hgh- and low-tde beach and dune wdths were recorded. For the 1997 measurements, the mean hgh-tde beach wdth s 26.4 meters, and the mean low-tde beach wdth s 75.9 meters. The average dune feld wdth s 67.6 meters. 15
In order to control for temporal varablty n beach qualty, we combne four sources of nformaton: the observed beach wdth calculatons from 1997, U.S. Geologcal Survey (USGS) shorelne transects depctng the eroson rate between 1970 and 1999, hstorc beach replenshment data for Tybee Island, and anecdotal evdence from local government documents. We utlze these sources of nformaton to estmate shorelne change durng our study perod (1990 1999). USGS contans archval data on shorelne eroson rates, n meters per year, between 1970 and 1999 usng 95 transects that cover Tybee Island from the Northern Gron to the Southern tp of the sland (Mller et al. 2005). These data cover most of the shorelne, except for the narrow beaches on the north sde of Tybee along the Savannah Rver. Whle these data reflect the rate of shorelne change over ths perod, they also ncorporate fluctuatons n shorelne poston resultng from beach replenshment projects. As these projects bolster shorelne poston, mpled eroson rates wll be naccurate estmates of the natural eroson rate. To correct for ths, we recalculate the annual eroson rate for each transect takng nto account changes n shorelne poston resultng from beach replenshment. Our adjustments are accomplshed usng secondary data for beach replenshment projects on Tybee Island (U.S. Army Corps of Engneers 1994; Appled Technology and Management, Inc., 2002). These data allow us to control for large dscrete changes n beach wdth due to sand replenshment actvtes. Between 1970 and 1999, Tybee Island wtnessed sx beach replenshment operatons for a total of nne projects on dfferent reaches. Of these nne projects, one utlzed poor fll materal and dd not produce an apprecable effect on beach qualty, so we omtted t from our calculatons. For each 16
project, we had nformaton on the volume of sand (n cubc yards), the berm elevaton, the depth of closure, and the project s shorelne length. We were able to estmate the change n beach wdth resultng from replenshment usng the followng formula: W = V ( B + DC ) (5) where W s beach wdth, V s sand volume, B s the berm elevaton, and D C s the depth of closure (USACE 2008). Table 2 gves the change n beach wdth for each project. Estmated ncremental wdth, W n equaton (5), s used to adjust USGS shorelne poston measures n order to produce an adjusted shorelne eroson rate. For those reaches of shorelne that have receved replenshment sand, the adjusted eroson rate s greater than the mpled rate, and should more accurately reflect the hstorcal rate of shorelne change. [table 2 about here] Annual beach wdth for each transect and year from 1990 to 1999 are estmated usng the adjusted annual eroson rate, the change n wdth resultng from a gven beach replenshment project (f applcable), and the 1997 beach wdth measurements. For reaches that were replenshed n 1995, we subtracted the total amount of the change n beach wdth due to replenshment for years 1990 1994. For reaches that were replenshed n 1999, we added the total amount of change n beach wdth for 1999. To verfy our beach wdth estmates, we referred to anecdotal nformaton and shorelne maps from the Tybee Island Beach Management Plan (Elfner 2005) and the Savannah Harbor Beach Eroson Study (Appled Technology and Management 2002). The orgnal 17
USGS data suggest that 67.5% of the shorelne s erodng, whle the remanng 32.5% was accretng between 1970 and 1999. The average adjusted hgh-tde (low-tde) beach wdth was 26.5 (76.1) meters. The maxmum adjusted eroson rate was 3.35 meters/year and the maxmum adjusted accreton rate was 5.95 meters per year. As ndcated n table 1, the average adjusted eroson rate s 1.03 meters/year, and the average adjusted accreton rate s 0.56 meters/year. Methods For our purposes, we consder local beach condtons as those at the shorelne that s the shortest Eucldean dstance from a gven parcel. For most parcels, these beaches are located along the ocean, but for a few parcels on Tybee Island s extreme north sde, these beaches are on the Savannah Rver. We assume that qualty of the nearest beach s a local publc good, but that ths relatonshp s lmted by dstance from the shorelne. For those houses n close proxmty to the shore, the nearest beach can provde protecton from storm surge and eroson, n addton to provdng for convenent recreaton and lesure opportuntes. For houses located a sgnfcant dstance from the shore, however, beach condtons at any partcular pont are arguably less mportant. For these households, storm surge and eroson are much less of a concern. Moreover, for households located away from the beach, sgnfcant dstance must be traveled n order to engage n beach recreaton, such that many wll bke or drve, and thus ther recreaton ste choces are lmted less by what s nearby and more by what s accessble (va road networks and access ponts, and gven parkng avalablty). To model beaches as local publc goods, we ncorporate dstance from the shorelne nto our hedonc prce models 18
by nteractng a proxmty dummy varable wth beach qualty. As we are uncertan a pror what dstance represents and approprate cut-off for beaches as local publc goods, we estmate a seres of models wth the cutoff varyng from 100 meters to 600 meters n one-hundred meter ncrements. Our beach qualty measures of nterest hgh- and low-tde beach wdth and dune wdth exhbt sgnfcant correlaton, as could be expected. Hgh-tde beach wdth, lowtde beach wdth, and dune wdth are postvely correlated, wth par-wse correlaton coeffcents sgnfcantly dfferent from zero (rangng between 0.629 0.819). As such, f we nclude all beach qualty measures n a sngle model, standard errors wll be large due to multcollnearty. In what follows, we estmate separate models for hgh- and lowtde beach wdth and dune wdth. The problem of spatal dependence has garnered ncreasng nterest n the hedonc valuaton lterature (Dubn 1988; Km, Phpps, and Anseln 2003; Bn, Kruse, and Landry 2008; Bn et al. 2008), and can be thought of as a clusterng of property values based on locaton or common proxmty. Sales prces can cluster n space due to common, unobserved locaton factors (such as school qualty, local crme rate, local government servces, and other ntangble neghborhood characterstcs) or because surroundng parcels have smlar structural characterstcs (such as archtectural desgn, dwellng and lot sze, and unobserved housng characterstcs) that reflect style or common practce at the tme of neghborhood development/housng constructon. Our regresson model takes the form: P = P(a, ε, Ψ), (6) 19
where a s a vector of structural and envronmental housng attrbutes, ε s a random error term, and Ψ s a spatal weghts matrx that explctly defnes the spatal structure of sales prce dependence. We use a contguty matrx that dentfes propertes wthn 400 meters as neghbors ; ψ j = 1 when and j are located wthn 400 meters of one another, and ψ j = 0 otherwse. Theory dctates that the structure of Ψ be treated as exogenous to the model (Anseln and Bera 1998), and prmary results of the paper are not senstve to the choce of dstance. Prelmnary regresson model dagnostcs ndcated the presence of spatal dependence n sales prces, 5 so we focus attenton upon the spatal lag model: ln P = ρ ΨP + βa + ε, (7) where ρ s the spatal autoregressve parameter, ΨP s the vector of spatally lagged dependent varables for weghts matrx Ψ, β s a vector of unknown parameters to be estmated, and ε s a vector of ndependent and dentcally dstrbuted random error terms (Anseln and Bera 1998). The presence of the spatally lagged dependent varable nduces correlaton wth the error term, whch renders ordnary least squares based and nconsstent. Margnal effects n a spatal lag hedonc model reflect nduced values on neghborng parcels stemmng from the spatal autocorrelaton structure. For contnuous varables, the margnal effect s gven by β P. For bnary varables, the margnal 1 ρ effect s P { exp( β ) 1} 1 ρ (Halvorsen and Palmqust 1980). Results 20
We explore the nfluence of coastal resource qualty on housng prces wth three types of specfcatons. The frst two nclude hgh-tde and low-tde beach wdth, respectvely, and the thrd ncludes dune wdth. For each specfcaton, we explore an array of effects varyng by dstance from the shorelne for the nfluence of beach qualty on local property values. Our dstance cutoffs range from 100 meters to 600 meters from the shore (n 100 meter ncrements). Across most specfcatons, estmated parameters for cutoff dstances greater than 300 meters were statstcally nsgnfcant. 6 Thus, we present results for beach and dune qualty nteracted wth dummy varables representng parcels 100 meters, 200 meters, and 300 meters from the shorelne. For our dataset, the proportons of propertes that fall wthn these cutoff dstances are 21%, 39%, and 50%, respectvely. [table 3 about here] Results for hgh-tde beach wdth are presented n table 3. All structural and locaton characterstcs (such as ocean frontage, nlet frontage, and marsh frontage) have the expected sgn. Most of the estmated parameters are statstcally sgnfcant for 1% chance of Type I error, except for lot square footage, presence of garage, marsh frontage, and hgh-tde beach wdth. Beach wdth, however, s statstcally sgnfcant at the 5% level. The parameter on hgh-tde beach wdth s postve, ndcatng that the natural log of property value s ncreasng n beach wdth. The spatal lag parameter s sgnfcantly dfferent from zero, and the lkelhood rato test rejects restrctng ths parameter to zero. The coeffcent on nlet frontage ndcates that ths locaton s more hghly valued than ocean frontage, but both are valued above nland propertes. The log-lkelhood value s 21
the largest for the 200 meter cutoff model, suggestng that ths specfcaton could provde a better ft to the data. 7 [table 4 about here] Results for low-tde beach wdth models, presented n table 4, are smlar to hghtde model, n terms of parameter sgns and patterns of statstcal sgnfcance. The exceptons are that dstance from the shorelne s sgnfcant at the 5% level n the 200 and 300 meter models, whle low-tde beach wdth s statstcally sgnfcant at the 1% level n all models. Thus, property values appear to be ncreasng n low-tde beach wdth, and the results are stronger than the case of hgh-tde beach wdth. As noted n footnote 5, however, for models that consder 500 and 600 meters proxmty to the shorelne as an approprate specfcaton for local beach qualty, we obtan negatve and statstcally sgnfcant parameters on low-tde beach wdth. We are uncertan what could be drvng these unexpected results. The log-lkelhood value for these seres of models s also largest for the 200 meter cutoff specfcaton. [table 5 about here] Table 5 presents parameters for the dune wdth model. Agan, the pattern of parameter sgns and statstcal sgnfcance s smlar to the beach wdth models. The parameter estmate for dune wdth s postve and statstcally sgnfcant at the 1% level n each model, suggestng that property values n close proxmty to the beach (100 300 meters from the shorelne) are ncreasng n the wdth of the dune feld at the nearest 22
beach. Agan, of the three models estmated, the log-lkelhood value s the largest for the 200 meter cutoff model. Estmates of margnal wllngness-to-pay (MWTP) for beach and dune wdth are presented n table 6. Standard errors are calculated usng the delta method. MWTP for hgh-tde beach wdth s $71 per meter (95% confdence nterval (CI): $1 - $114) for the 100M model, $168 per meter (95% CI: $32 - $302) for the 200M model, and $196 per meter (95% CI: $22 - $369) for the 300M model. The standard errors for hgh-tde beach wdth are somewhat larger than other models, gvng rse to rather wde confdence ntervals. These are average welfare measures for all coastal propertes. MWTP estmates for hgh-tde beach wdth condtonal on proxmty to the shore (.e. beng located wthn the cut-off dstance) are $447 per meter for the 100M model, $487 per meter for the 200M model, and $421 per meter for the 300M model. [table 6 about here] MWTP estmates for low-tde beach wdth are $74 per meter (95% CI: $34 - $114) for the 100M model, $154 per meter (95% CI: $82 - $226) for the 200M model, and $126 per meter (95% CI: $34 - $218) for the 300M model. These are roughly smlar to hgh-tde estmates, wth slghtly lower pont estmates for 200M and 300M models. The confdence ntervals are tghter, reflectng hgher p-values for beach wdth parameters n the low-tde models. MWTP estmates for low-tde beach wdth condtonal on proxmty to the shore are $465 per meter for the 100M model, $447 per meter for the 200M model, and $272 per meter for the 300M model. 23
Welfare estmates for dune wdth are the most precse. MWTP for dune wdth s $52 per meter (95% CI: $18 - $85) for the 100M model, $132 per meter (95% CI: $73 - $191) for the 200M model, and $98 per meter (95% CI: $27 - $170) for the 300M model. MWTP for dune wdth condtonal on proxmty to the shore are $325 per meter for the 100M model, $383 per meter for the 200M model, and $212 per meter for the 300M model. Other welfare measures of nterest from the hedonc property models nclude ocean frontage (WTP rangng from $39,000 to $75,000 across all models), nlet frontage (WTP rangng from $121,000 to $128,000 across all models), and dstance from the shorelne (MWTP rangng from -$41 to -$84 per meter across all models) Dscusson Usng spatal lag hedonc prce regresson models, we fnd evdence that coastal resource qualty affects market values of nearby propertes. Our results suggest that hgh- and low-tde beach wdth and wdth of the dune feld have a sgnfcant postve effect on property values wthn 300 meters of the shorelne. We do, however, fnd contradctory results for low-tde beach wdth at dstances of 500 and 600 meters from the shore. For hgh-tde beach wdth and dune wdth, estmated values for models of proxmty greater than 300 meters are statstcally nsgnfcant. Overall, we nterpret ths pattern of results as supportng our specfcaton of coastal beach qualty as a local publc good, nfluencng the value of property n close proxmty to the shore. Across all specfcatons, 200 meter proxmty to the shore as a measure of local beach qualty provded the best ft to the data (based on log-lkelhood values). Whle we attempted other specfcatons for the dstance-beach qualty relatonshp (such as, Pompe and 24
Rnehart s (1995a,b; 1999) approach of ncluded beach wdth and an nteracton term for beach wdth and dstance from the shore), our results dd not support these models, as beach qualty varables were statstcally nsgnfcant. More research s necessary to explore the proxmty-beach qualty relatonshp, and to further nvestgate the contradctory results we fnd for low-tde beach wdth. Theory suggests that the nterpretaton of MWTP estmates depends upon ndvdual property owners perceptons of the durablty of coastal resource qualty and expectatons of future beach management actvtes. For property owners that are gnorant of coastal dynamcs, beaches may be vewed as a statc resource that can provde storm protecton and recreaton opportunty n perpetuty. In ths case, hedonc parameter estmates for beach qualty can be nterpreted as parameters for conventonal structural attrbutes, lke square footage, number of bedrooms, etc. Lkewse, for those that expect beach qualty to fluctuate but beleve that coastal management practces (e.g. beach replenshment) can mantan the beach over some relevant tme perod, parameters can be smlarly nterpreted. Under these crcumstances, coastal property owners are wllng to pay, on average, $71 to $196 for an addtonal meter of hgh-tde beach wdth, wth estmates dfferng based upon the defnton of local beach wdth (.e. proxmty measure employed). For those propertes located n close proxmty, average MWTP ranges from $421 to $487 for an addtonal meter of beach wdth at hgh tde. These MWTP measures are estmated at current average hgh-tde beach wdth of 26.5 meters. Estmates of average MWTP for ncreases n low-tde beach wdth range from $74 to $154, evaluated at the current average low-tde beach wdth of 76 meters. For those propertes located n close proxmty, average MWTP ranges from $272 to $465 for 25
an addtonal meter of beach wdth at low tde. For beaches, these welfare measures reflect perceved storm and flood protecton benefts, as well as recreatonal and lesure value of local beaches. Average MWTP for ncreases n dune wdth ranges from $52 to $132 per meter, evaluated at current average of 68 meters. For propertes n close proxmty to the shorelne, average MWTP ranges from $212 to $383 for an addtonal meter of dune wdth. These welfare measures reflect perceved storm and flood protecton afforded by sand dunes and any amenty value that coastal households ascrbe to the dunes. All prevous papers that have employed hedonc property models to value beach qualty (Pompe and Rnehart 1995a, b; Pompe and Rnehart 1999; Landry, Keeler, and Kresel 2003) have nterpreted parameters n a straghtforward and conventonal manner. We argue that the nterpretaton of margnal mplct prces depends upon ndvdual perceptons of beach qualty. Current expertse on barrer sland systems dentfes beach condtons as hghly varable over tme, respondng to waves, currents, storms, and changes n sedment supply. As such, an nformed buyer would expect changng beach condtons over the tme that they occupy a coastal property. We show that for those who expect beach and dune condtons to degrade over tme, margnal mplct prce estmates provde an upper bound on true wllngness to pay. We obtan ths result because margnal prces are derved from the gradent of the hedonc prce functon, evaluated at the current level of resource condtons, but ndvdual bd functons wll reflect the present dscounted margnal value for expected level of condtons over tme. Thus, the bd functon s evaluated at a lower expected level of resource qualty than the hedonc prce functon (as shown n the lower panel of fgure 1, pont B). Snce the margnal bd 26
s decreasng n beach wdth, the hedonc gradent wll provde an upper bound on true wllngness-to-pay (wth bas ndcated n the lower panel of fgure 1 as Bas d ). The opposte result obtans for those that expect resource qualty to mprove over tme, and the margnal mplct prce estmated from the hedonc prce functon wll be a lower bound on true wllngness-to-pay (as shown n the lower panel of fgure 1, pont C, wth bas Bas g ). Unfortunately, lttle nformaton s avalable that mght elucdate ndvdual coastal homeowners perceptons of the durablty of coastal beach resources or ther knowledge of coastal processes. Ths remans an mportant area for future research. Conclusons Coastal areas have been wtness to expandng development the last several decades, and these areas face consderable rsk due to myrad forces that shape and contnually reshape the coastal landscape. Ths s especally true for barrer slands. Chronc shorelne eroson and storm rsk pose serous threats to prvate property nvestments and publc nfrastructure on barrer slands. Optons for ndemnfcaton of these hazards are somewhat lmted, as nsurance s restrcted n terms of coverage, hazards, and avalablty. Elements of the natural terran and constructon qualty, however, can also affect rsk. For example, ground elevaton above sea level, dstance from the shorelne, and elevaton of housng structure can help to allevate flood rsk. For eroson rsk, on the other hand, optons for self-protecton are somewhat more lmted. For those that want to lve n close proxmty to the shore, selectng a locaton wth a low hstorcal eroson rate, a wde beach, and robust dune feld are optons for protectng property nvestments for eroson. 27
In ths paper, we use hedonc property models to estmate economc value of beach qualty beach and dune wdth. Such estmates are nsghtful n ganng an understandng of property owners preferences for envronmental qualty, and are nformatve for polcy analyss of coastal eroson management optons (Landry 2008; Smth, et al. 2009). We fnd that beach and dune qualty do nfluence property values, but that ths relatonshp s lmted by proxmty to the shorelne. Ths fndng provdes support for our contenton that beach qualty s most lkely to be a local publc good, because nearby beaches afford protecton and provde recreaton potental to houses n close proxmty. For houses located further away from the shorelne, storm, flood, and eroson rsk are lkely to be consderably lower, and beach recreaton choces are lkely to be nfluenced by road networks, access ponts, and avalable parkng. These factors suggest that beach qualty at the nearest shore would be less mportant for houses located further away, and our data support ths noton. Methods for augmentng property data wth nformaton on accessblty n order to learn somethng about the value of beach recreaton for homes located further from the shore s a topc for future research. As coastal sedments are gven to seasonal and chronc fluctuaton due to the varous forces that shape the shorelne, beach qualty s somewhat unque as a housng attrbute. Unlke structural characterstcs, beach qualty s expected to undergo exogenous change n the future. Whle change could also be expected for neghborhood and envronmental attrbutes of resdental property, beach qualty seems to be a more salent dynamc characterstc because expert assessment predcts that t s expected to change over tme. Buldng upon ths dea, we ncorporate dynamc housng characterstcs nto the conventonal hedonc property prce framework. Theory ndcates 28
that f property owners expect beaches and dunes to be mantaned as statc attrbutes, ether as a result of natural forces or through management nterventons, margnal mplct prces can be nterpreted n the conventonal manner. If, on the other hand, property owners expect beaches and dunes to change over tme, MWTP derved from the hedonc prce functon provdes only a bound on true wllngness to pay. In the case of expected future eroson, MWTP for beach and dune wdth provde an upper bound on economc value because ndvdual bds reflect a lower expected attrbute level n perpetuty than s currently avalable. Margnal wllngness to pay estmated from the hedonc prce functon s beng evaluated at the lower expected attrbute level, whch mples the margnal value assocated wth the current, observed qualty level s less, by strct concavty of the bd functon (as shown n fgure 1, pont B). We note that economc value for other attrbutes of coastal housng markets, such as dstance from the shore and ocean front status, could also suffer from a smlar type of bas. Lastly, the nfluence of perceptons, belefs, and expectatons on economc value of beaches can potentally complcate polcy analyss because mplct values derved from market prces may reflect expectatons of certan polces beng mplemented over others (e.g. beach replenshment over shorelne retreat). In such cases, these values may not be relevant for analyzng other management approaches. 29
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