A Spatial Bayesian Hedonic Pricing Model of Farmland Values

Transcription

1 1 A Spatal Bayesan Hedonc Prcng Model of Farmland Values Cotteleer G. 1, Stobbe T. 2 and Van Kooten G.C. 1,2 1 Agrcultural Economcs and Rural Polcy,, Wagenngen Unversty, Wagenngen, The Netherlands 2 Department of Economcs, Unversty of Vctora, Vctora, B.C., Canada Abstract In 1973, Brtsh Columba created the Agrcultural Land Reserve (ALR) to protect farmland from development. Ths study nvestgates whether the ALR has been effectve near the cty of Vctora. Therefore, we employ a GIS-based hedonc prcng model and quantfy ALR specfc measures. Bayesan Model Averagng n combnaton wth Markov Chan Monte Carlo Model Composton are used to address specfcaton uncertanty. Results show that zonng schemes are partly credble. Zoned farmland sells for lower prces than other farmland. However, farmland located closer to the cty of Vctora s prced hgher and hobby farmers pay hgher prces than conventonal farmers. Keywords Farmland prces, Bayesan Model Averagng, Hedonc prcng. I. INTRODUCTION As ctes grow and spread nto the countrysde, agrcultural land s often the frst vctm of urban development. Despte programs and laws to protect agrculture, farmland prces n the rural-urban nterface have ncreased sgnfcantly, often beyond the reach of farmers wshng to enter the sector or expand ther operatons. Because land prces are drven by the development and not agrcultural potental of land, farmng near urban areas becomes more dffcult both fnancally and logstcally. In the current study, we examne the effect of urban encroachment on farmng near Vctora, the captal of Brtsh Columba, Canada s westernmost provnce. BC s agrcultural land s lmted, wth the most productve land located near the most-rapdly growng urban centers Vancouver, Vctora and Kelowna n the Okanagan Valley n the Interor. To protect the 1.1% of the Provnce consdered prme farmland from development, the government created the Agrcultural Land Reserve (ALR) n The ALR s a zonng ordnance that prevents agrcultural land from beng subdvded or used for non-agrcultural purposes wthout permsson from the Agrcultural Land Commsson (ALC). The ALR permts only one dwellng per parcel, whch s ntended to serve as a farmer s resdence. Speculaton by developers and purchases of farmland for resdental purposes (rural estates) are the man factors that drve up agrcultural land prces near urban centers. We seek to determne emprcally whether speculaton n antcpaton of changng land desgnaton s happenng on ALR land. We employ a GIS-based hedonc prcng model to quantfy ALR specfc measures and nvestgate characterstcs that contrbute to farmland prces near the urban frnge. We also employ spatal econometrc technques that take nto account spatal dependences that are not ncorporated as covarates n the hedonc prcng model. The problem wth spatal econometrc technques s that they requre a pror specfcaton of a weghtng matrx of spatal relatons between observatons, although choce of a specfc relatonshp s arbtrary (Anseln, 1988). Another problem s that there s lttle n the way of theory to gude the choce of the covarates to be ncluded n the hedonc prcng model. Ths means that there s both parameter uncertanty and uncertanty n the choce of the spatal weghtng matrx. Our objectve s, therefore, to nvestgate whether the ALR has been effectve n preservng farmland near Vctora, but n a way that resolves uncertanty n the applcaton of the spatal hedonc prcng model. To address the latter ssue, we apply Bayesan Model Averagng n combnaton wth Markov Chan Monte Carlo Model Composton (MC 3 ) to deal wth model uncertanty. The beneft of Bayesan Model Averagng s that t does not assume there s only one correct model specfcaton; rather, fnal parameter estmates are weghted averages based on a whole range of possble model specfcatons, ncludng dfferent explanatory varables and dfferent specfcatons of the weghtng matrx. Furthermore, the MC 3

2 2 framework makes sure that model specfcatons wth hgh posteror probabltes are taken nto account n the weghted averages. Although the MC 3 framework has been extended to spatal econometrc models by LeSage and Parent (2007), and LeSage and Fscher (2007), the current research explctly ncorporates the selecton of dfferent specfcatons of the weghtng matrx (based on nearest neghbors, dstances and spatotemporal patterns) n both MC 3 procedures for the spatal lag and error dependence models. To our knowledge, ths extenson of the MC 3 procedure consttutes an addtonal contrbuton of our research. II. A BAYESIAN APPROACH TO HEDONIC PRICING MODEL SPECIFICATION To nvestgate the mpact of BC s Agrcultural Land Reserve (ALR) and such thngs as land fragmentaton on farmland prces, we specfy a hedonc prcng model (see (Rosen, 1974). Gven the spatal nature of the data, t s mportant to ncorporate spatal dependence n the model. Spatal dependence can be ncorporated as spatal lag or spatal error dependence. A general formulaton that ncludes both s (Anseln, 1988): P = αι+ ρw1p + Xβ + u, wth u = λw2u + ε and ε ~ N(0, σ2i), [1] where P s a vector of property prces, X s a matrx of property characterstcs, β s a vector of assocated coeffcents to be estmated, α s a constant to be estmated and ι an assocated vector of ones, ε s a vector of error terms; W 1 and W 2 are spatal weghtng matrces. The spatal weghts are specfed a pror between all pars of observatons. In our model, where each observaton corresponds to a farmland sales transacton, each element w j weghts the degree of spatal dependence accordng to the proxmty or dstance between parcel and any other parcel j; ρ s the coeffcent of the spatal lag dependence structure; and λ s the coeffcent n a spatal autoregressve structure for the error term. When λ=0 and ρ 0, (1) represents the Spatal Autoregressve (SAR) model. If ρ=0 and λ 0, we have the Spatal Error Model (SEM). Lackng gudance regardng the choce of a weghtng matrx, we specfy a varety of dfferent types: Several varatons employ bnary weghts, two are based on dstances, and two are based on spatotemporal patterns. In the case of bnary weghts, an element n the weghtng matrx equals one f two observatons are consdered to be neghbors and zero f not. Because there s uncertanty about whch weghtng matrx and set of explanatory varables to use n our hedonc prcng model, we employ Bayesan technques that allow us to specfy posteror model probabltes for each specfc model we wsh to consder. These model probabltes tell us how lkely t s that a gven model s the correct one. Rather than basng parameter estmates only on the model wth the hghest posteror probablty, we use Bayesan Model Averagng and weght the estmates of the whole range of potental models wth the posteror model probabltes, whch are gven by (Koop, 2003): p ( M y) = M [2] m= 1 p( y M ) p( M ) p( y M m ) p( M where p(y M ) s the margnal lkelhood that model M s the correct one and p(m ) are the pror model probabltes. If, a pror, the researcher consders each model to be equally lkely, all pror model probabltes are equal to 1/M, where M s the total number of models to be consdered. In ths case the posteror model probabltes are determned only by the margnal lkelhoods. The margnal lkelhood for model s (Koop, 2003): p( y M ) = p( y θ, M ) p( θ M ) dθ, [3] where p(y θ,m ) s the lkelhood and p(θ M ) s the pror for the parameter vector θ. In our case, θ ncludes ether [α, β, σ 2, λ] or [α, β, σ 2, ρ], dependng on whether one consders the spatal error or lag model. The specfcatons of the margnal lkelhoods for the spatal lag and error dependence models are provded n LeSage and Parent (2007). To derve the posteror model probabltes, we need to consder each possble model specfcaton. Wth k m )

3 3 potental explanatory varables and δ potental specfcatons of the weghtng matrx, there are 2 k δ models to consder, whch s practcally nfeasble. (For example, wth k=21 and δ=6, there are 12,582,912 models to consder.) Therefore, we use Markov Chan Monte Carlo Model Composton (Madgan, et al., 1995). The stochastc process generated by MC 3 explores regons of the model space wth hgh posteror model probabltes. The number of teratons n the MC 3 procedure s pre-specfed. At the start of the Markov chan, a regresson model s chosen at random. Suppose the current model s M. The model that s proposed n the next step of the chan has ether one varable more than the current model ( brth step ), one varable less than M ( death step ), or one varable of M replaced by a varable not currently n the model ( move step ). The proposed model M j s then compared to the current model M and the probablty of acceptance s gven by: p(accept new model) = p( M mn 1, p( M j y) y) A random draw usng the probablty from [4] of acceptng the new model and not acceptng t determnes whether the new model ndeed replaces the old, whether M j replaces M. Ths procedure for proposng new models s extended by LeSage and Fscher (2007) to nclude uncertanty wth respect to the choce of the spatal weghtng matrx n the MC 3 procedure. However, only dfferent numbers and types of nearest neghbor based weghtng matrces are ncluded n ther procedure. As ndcated above, we specfy sx dfferent weghtng matrces (two bnary, two dstance based, and two spatotemporal). We extend ther selecton procedure by employng the MC 3 procedure that consders sx dfferent weghtng matrces. We begn the MC 3 procedure by consderng a regresson model wth a randomly selected weghtng matrx and randomly selected varables. Next we use 100,000 teratons to determne posteror model probabltes for each of the models vsted durng one of the 100,000 teratons. Each teraton nvolves the followng steps: [4] Current model: M Step 1: Toss a far de wth two sdes 1s, two sdes 2s and two sdes 3s Outcome Decson 1. Exclude varable from model at random 2. Add at random a new explanatory varable not currently n model 3. Drop current explanatory varable at random from model; replace wth randomly chosen explanatory varable not now n model Choose new model M j over M wth probablty gven by (4). Step 2: Toss a con Outcome Decson Heads Retan current weghtng matrx (retan model M j or M ) Tals Choose new weghtng matrx at random from those not currently n model (Choose new model M j+ over M j or M wth probablty gven by (4). Model for next teraton: M m = one of (M j+, M j, M ) s chosen wth some probablty. Based on the MC 3 procedure, for each varable we can calculate the probabltes that ths varable should be ncluded n the model. Incluson probabltes for varables are calculated as the number of tmes a varable s ncluded n a model that was accepted dvded by the total number of teratons (draws). Ths dffers from the ncluson probabltes n LeSage and Parent (2007). They base the ncluson probabltes on the number of tmes a varable s ncluded n each unque proposed model. We argue that our measure better reflects the ncluson probabltes for two reasons: Although they mght be unque, proposed models can be rejected and, therefore, they do not always have hgh posteror model probabltes. Further, we rather base our estmate on the total number of draws, nstead of the number of unque proposed models.

4 4 III. DATA AND VARIABLES Our study area s the Saanch Pennsula of southern Vancouver Island, a rch agrcultural area just north of Vctora. We use 533 observatons of farmland parcels that were sold n the perod 1974 (the year followng creaton of the ALR) to The data nclude all sngle cash transactons but exclude sales that ncorporated more than one parcel. A dummy varable ( vacant land ) s used to dstngush between propertes that do or do not have substantal structures, such as farmhouses, barns, poultry and mlkng facltes, etc. Only parcels were selected that could be lnked to all ffteen datasets we used, so that for each observaton all explanatory varables were avalable. Fnally, f propertes were sold more than once, we ncluded only the most recent transacton n our analyss, because the structure of our weghtng matrces cannot handle multple sales of the same property. The dfferent data sets come from the B.C. Mnstry of Agrculture and Lands, the B.C. Assessment Authorty, other government agences, and prvate sources. The GIS-based hedonc prcng model uses the per hectare market value of land as the dependent varable; the covarates nclude sze of the farmland parcel, type of farm, topographcal features of the land, a fragmentaton ndex, dstance to Vctora, an ALR dummy varable and the number of hectares excluded from the ALR each year. IV. EMPIRICAL RESULTS AND DISCUSSION The Bayesan model averaged estmates are not based on all unque models vsted n each of the 100,000 teratons. Means and t-statstcs for the coeffcents are only calculated for the 1000 models wth the hghest margnal lkelhoods n the spatal lag specfcatons and the 200 best models n the spatal error specfcatons. The reason that less models are used for the spatal error specfcatons s that t s smply too tme consumng to calculate the means and dsperson measures for more than 200 models the combnaton of 200 models and 5000 draws per model took about 60 hours. For the spatal lag specfcatons, the combnaton of 1000 models and 10,000 draws per model takes about 10 hours. For the spatal lag specfcatons, 100,000 draws n the MC3 procedure produces 18,164 unque models. For the spatal error specfcatons we fnd 8,535 unque models n 100,000 draws. Both the Bayes factor and the sgnfcance of the coeffcent for spatal dependence ndcate that SEM specfcatons are preferred over SAR specfcatons. The Bayes factor s often used to compare two model specfcatons assumng that pror model probabltes are the same. Therefore, we only present the results for the SEM specfcaton. Based on the MC3 procedure, we can conclude that the spatal error structure s best descrbed by the dstance-based weghtng matrces. The specfcatons of the fve models wth the hghest posteror model probabltes resultng from the MC3 procedures are provded n Table 2. In ths table, ones ndcate the ncluson of a certan varable or weghtng matrx and zeros ndcate excluson. Posteror model probabltes for the fve best models and probabltes for the ncluson of each of the varables and spatal weghtng matrces are also presented n Table 1. The Bayesan model averaged means and t-statstcs for β, σ2 and λ are provded n Table 2. For both the spatal lag and error specfcatons, the models that ncluded only the varables lot sze, GDP and vacant land are preferred over larger models that nclude more varables. In general, smaller models wth fewer covarates have hgher posteror model probabltes than larger models wth more covarates. Ths s smlar to our fndngs (see Table 1). Ths partly explans why the estmated means for the coeffcents are only sgnfcant for the varables lot sze, vacant land (=0 f a sgnfcant structure exsts on the property) and GDP. In case a varable s not ncluded n a model, mplctly the estmated mean of the coeffcent and t-statstc for that covarate wll be set to zero. However, we found that coeffcents of varables wth low probabltes of beng ncluded can be hghly sgnfcant n some of the model specfcatons.

5 5 Table 1: Spatal error MC3 model selecton nformaton (100,000 draws and 8535 unque models) Varables M1 M2 M3 M4 M5 Varable probabltes ALR ALR boundary Dstance to ALR boundary (km) ALR excluded ha Fragmentaton ndex Gran Vegetable Tree frut Small frut Cows Poultry Vacant land Log of dstance (km) to Vctora Cty Hall Log of dstance (km) to Vctora arport Log of nearest dstance (km) to Patrca Bay hghway GDP Interest rates Maxmum elevaton n meters Average dfference elevaton level ( m/ha) Log of lot sze (ha) Hobby farm W 5 nearest neghbors W Delaunay W dstances W squared dstances W dstances temporal W squared dstances temporal Model probabltes We conclude that farmland parcel szes are mportant n explanng prces per ha. The log of parcel sze s hghly sgnfcant (p<0.01) and has a negatve effect on the log of prces per ha. Ths s contrary to the expectaton that farmers seek to acqure large propertes to realze economes of scale because larger parcels have hgher productvty levels than small ones (Cavalhes and Wavresky, 2003). There are several explanatons for ths result. Frst, average parcel sze s only 3.76 ha, so the lkelhood that economes of scale are an ssue s small. Another reason for ths unexpected result s that, when agrcultural land s purchased for development purposes n expectaton that t wll be excluded from the ALR n the future, ts value s sometmes negatvely related to the sze of the parcel. The reason s that the costs of subdvdng land ncrease relatve to benefts as the sze of the parcel ncreases (Colwell and Munneke, 1999). Fnally, snce ALR land cannot be subdvded wthout gong through the Agrcultural Land Commsson, the negatve coeffcent on parcel sze suggests that much of the land n the Saanch Pennsula s bought for the purpose of rural estates and hobby farms. In Brtsh Columba, property taxes that are some 70% lower apply to land classfed as farm status than to equvalent land that s not n ths category. The revenue threshold for attanng farm class status s qute low: The property must generate an annual gross ncome of $2500 or more at least once every two years f the farm s between 0.8 and 4.0 ha n sze. For propertes less than 0.8 ha, the gross ncome threshold s $10,000, whle t s $2,500 plus 5 per cent of the property s assessed value f the farm exceed 4 ha. As most buyers would not be farmers, an ncrease n property sze much beyond the 0.8 ha threshold, and especally beyond 4 ha, would be vewed negatvely.

6 6 Table 2: Spatal error Bayesan model averagng estmates (5000 draws, 500 burn-n draws, based on top 200 models) Varables Averaged coeffcents Averaged t-statstcs ALR ALR boundary Dstance to ALR boundary (km) ALR excluded ha Fragmentaton ndex Gran Vegetable Tree frut Small frut Cows Poultry Vacant land Log of dstance (km) to Vctora Cty Hall Log of dstance (km) to Vctora arport Log of nearest dstance (km) to Patrca Bay hghway GDP Interest rates Maxmum elevaton (m) Average dfference elevaton level ( m/ha) Log of lot sze (ha) Hobby farm λ R-squared Adjusted R-squared We hypotheszed that land wthn the ALR would be valued hgher than land outsde the ALR f farmland preservaton s expected to be permanent. We test ths hypothess wth the ALR-dummy and conclude that land located wthn the ALR sells at a lower prce than that outsde the ALR, but ths result s not sgnfcant. Ths suggests that speculaton s takng place on at least some ALR land. However, t could also be that, snce farmland outsde and n the ALR s ncreasngly used for large rural estates, there s lttle dfference between prces as the effect of ALR zonng has been negated to a large extent. Regardng the credblty of the ALR, we also tested whether ncreased exclusons of land from the ALR resulted n greater speculaton. As expected, the estmated coeffcent on ths varable s postve, suggestng that, as more land s excluded from the ALR, land values are hgher, whch s suggestve of speculaton. However, ths effect s agan not statstcally sgnfcant when averaged over all models. We also test the hypothess that, f zonng wthn the ALR s credble, ALR land close to the edges of the ALR wll sell for less than ALR land n the ALR nteror, due to negatve urban spllovers. All the ndcators we use to test ths hypothess (dummy for parcels at the ALR boundary, dstance to the ALR boundary and the fragmentaton ndex) pont n the same drecton. All estmates coeffcents support the hypothess that the ALR boundary s credble, none of the results can be consdered statstcally sgnfcant. The varablty wth respect to these varables agan ndcates that the ALR boundary s only credble for a small subset of land n the ALR. Macro-economc varables are mportant n the model because the data span a perod of more than 30 years. Prces are expected to rse and fall jontly wth macro-economc changes. For example, we fnd that farmland prces rse sgnfcantly (p<0.01) wth ncreasng GDP. As the country s GDP ncreases, people are wealther and able to spend some of ther addtonal ncome on land purchases, ncreasng the demand for land and thus ts prce. Furthermore, as nterest (and mortgage) rates ncrease, borrowng s less affordable and the demand for property declnes (and property prces fall), but not sgnfcantly.

7 7 Not surprsngly, vacant land s sgnfcantly (p<0.05) less valuable than land that has no structures on t. Whle ths result s partly accounted for by the fact that productve farm enterprses would requre some structures, t s prmarly drven by the exstence of a resdence on the property. A resdence substantally ncreases the value of the land, but not by as much as mght be expected. That s, farmland wthout a resdence remans much more valuable than ts use n agrculture would suggest. V. CONCLUSIONS In ths study, we were partcularly nterested n determnng whether B.C. s Agrcultural Land Reserve was perceved to be an effectve nstrument for preservng farmland. We used spatal hedonc prcng models to nvestgate ths queston. We also wshed to resolve the uncertanty of the choce of explanatory varables and the spatal weghtng matrx n our model. Therefore, we used Markov Chan Monte Carlo Model Composton n combnaton wth Bayesan model averagng to resolve ths model uncertanty. Although basc model uncertanty could be resolved usng these methods, we found they had some drawbacks as well. Frst, these methods are tme consumng, although greater computng power partly addresses ths ssue. Further, these methods seem to results n lower bounds on the estmated means and t- statstcs of the coeffcents of nterest. However, wth more specfc pror nformaton ths ssue mght also be partly resolved. Usng these technques, we could nonetheless draw conclusons about whch varables have hgh and low ncluson probabltes. Lot sze, GDP and vacant land were very mportant n explanng farmland prces. Furthermore, we learned that our data are better descrbed by a spatal error process than a spatal lag process, and that the nverse squared dstance weghtng matrx best descrbes ths spatal error process. Wth respect to the credblty of the ALR, we conclude that speculaton s lkely an mportant phenomenon, affectng at least part of the ALR, even though the estmated sgns all support the hypothess that the ALR s credble. For example, ALR land s sold for less than land outsde the ALR, land at the ALR boundary sells for less, and farmland that s more fragmented and farther away from the heart of the ALR sells for less. However, these fndngs are not very robust, as none of these estmates are statstcally sgnfcant and the ncluson probabltes for these varables are all very low. Therefore, we can conclude that the ALR s only partly credble, wth speculaton takng place at least on some parcels. Furthermore, smaller parcels are sold for hgher prces per ha than larger parcels, ndcatng that economes of scale n agrculture do not appear to play a role. An alternatve explanaton s that the hgher prces per ha sgnfy that farmland s most lkely bought for resdental purposes by those cravng a rural lfestyle n close proxmty to a large urban area. To some extent, t s possble that the requrements for obtanng farm class status and thereby lower property taxes may, counter-ntutvely, be workng aganst agrcultural preservaton n BC. As smaller farmland parcels are clearly preferred by buyers, the low threshold for achevng farm tax status makes t cheaper to own a large rural estate rather than an urban resdental lot. A landowner does not need to be a professonal or effcent farmer, but can smply be a hobby farmer. By rasng the threshold or mplementng other hurdles to achevng farm status, the government could reduce the desrablty of lvng on large rural estates, but perhaps to the detrment of serous agrcultural producers. Overall, t appears that hgh prces for small farm propertes and nexperenced farmer-buyers bode ll for sustanng vable commercal agrculture on the urban frnge. It may also hnder preservaton of open space n the longer run f such open space s beng protected under the guse of preservng farmland for agrcultural purposes only. REFERENCES 1. Anseln, L. "Lagrange Multpler Test Dagnostcs for Spatal Dependence and Spatal Heterogenety." Geographcal Analyss 20, no. 1(1988): Anseln, L. Spatal Econometrcs: Methods and Models. Dordrecht: Kluwer Academc Publshers, 1988.

8 8 3. Cavalhes, J., and P. Wavresky. "Urban nfluences on perurban farmland prces." European Revew of Agrcultural Economcs 30, no. 3(2003): Colwell, P. F., and H. J. Munneke. "Land prces and land assembly n the CBD." Journal of Real Estate Fnance and Economcs 18, no. 2(1999): Koop, G. Bayesan Econometrcs. Frst ed. Chchester: John Wley & Sons, Ltd, LeSage, J., and M. M. Fscher (2007) Spatal Growth Regressons: Model Specfcaton, Estmaton and Interpretaton. Ftzwllam College, Cambrdge. 7. LeSage, J., and O. Parent. "Bayesan Model Averagng for Spatal Econometrc Models." Geographcal Analyss 39(2007): Madgan, D., J. York, and D. Allard. "Bayesan Graphcal Models for Dscrete Data." Internatonal Statstcal Revew 63, no. 2(1995): Rosen, S. "Hedonc Prces and Implct Markets: Product Dfferentaton n Pure Competton." Journal of Poltcal Economy 82, no. 1(1974): Use macro [author address] to enter the address of the correspondng author: Author: Geerte Cotteleer Insttute: Wagenngen Unversty Street: Hollandseweg 1 Cty: Wagenngen Country: The Netherlands Emal: geerte.cotteleer@wur.nl