THE HEDONIC PRICING METHOD

Transcription

1 THE HEDONIC PRICING METHOD 1

2 General Background In the real world we are often confronted wth goods and servces wth a sngle prce for the whole bundle the good or servce (e.g. house) We are nterested n the prce of a characterstcs of the good. For example, the prce of a house depends on many factors ncludng envronmental characterstcs of the locaton Ths s the focus of the hedonc prce theory. Other hedonc prce s concerned wth labour markets, tmber markets, chld care servces, agrcultural products, fshery products, health servces and other commodtes In the case of housng market, by observng the prces of many houses wth dfferent characterstcs, we can nfer the mplct value that s beng placed on one characterstc, for example, ar qualty or tree cover or landscape beauty or neghbourhood, etc In the case of labour market, by observng wages assocated wth many dfferent occupatons we can nfer the value of small changes n rsk or any other factor Appled to prces of farmland as early as 1922 The formal model was developed by Rosen (1974)

3 Hstorcal Background 1926 Waugh studes the varaton of prces of vegetables 1938 Court looks at the car market n Detrot 1967 frst applcaton to the housng market: Rdker and Hennng Study the effects of ar polluton on prces of housng 1974 Rosen descrbes the frst formal model of the hedonc prcng method Other applcatons: Agrcultural goods Job market Chld care servce Cars Forestry Health Statstcal lfe Amentes and landscapes 3

4 Applcatons of Hedonc Prce Methods Hedonc Prce Method Housng prces Wage-amenty studes Wage studes/value of heath rsks Use nformaton on housng market to value people wllngness to pay for envronmental amentes Use nformaton on both housng market and wages to value people wllngness to pay for envronmental amentes Use nformaton on rsk premum to value people wllngness to pay to avod hazard. Ths nformaton s then used to value a statstcal lfe. 4

5 Introducton Hedonc prce method derve from consumer theory n whch utlty s related to the attrbutes of a good. It s one of the revealed preference technques used n valung nonmarket goods and servces No questonnare requred to conduct the study or survey n HPM Data are gathered from the market,.e. transacton of house sales. Thus, there s no need to a hypothetcal market. For example, some of the questons related to decson of buyng a house: The type of the house The locaton of our house Why we choose ths locaton Whch factors that push to choose one locaton rather than another The characterstcs of the area, etc 5

6 The choce of localzaton It can be seen that, the choce of housng s a composte good. For example, we decde the locaton based on dstance from work, avalablty of publc servces, dstance to central busness dstrct, dstance from schools, avalablty of green areas, avalablty of sport facltes, characterstcs of housng (# of bedrooms, # of bathrooms, flat, detached, etc.), neghbourhood characterstcs, etc. We assume that buyers choose houses that maxmze ther utlty However, the constrants n the maxmzaton problem s that the consumers have lmted by ncome, the prce of the houses and also the level of taxes that to be pad to the government Therefore, the housng market gve us some nformaton on buyers preferences for housng and for ther localzaton 6

7 Basc Idea of Hedonc Prcng Method The hedonc prcng method that apples to a house purchase s composed by a set of characterstcs. Consder the characterstcs of a house: Number of floors, presence of a garden, GCH, number of bedrooms, number of bathrooms, square footage of the house, type of house, age, materals, etc. And also: Dstance from publc transport, dstance from the cty centre, dstance from man roads, dstance from shops, dstance from sport facltes, crme rate, average ncome of nhabtants, presence of a unversty, etc. The composte good has a prce, but there s no explct prce for each characterstc that compose the good. 7

8 The hedonc prcng method apples ths concept to the envronmental characterstcs of resdental propertes The prce dfference between houses that have dfferent levels of envronmental qualty, keepng constant all other characterstcs, reflects the WTP for the dfferent level of envronmental qualty Thus, we can assess the value of an envronmental qualty, accordng to market prces of resdental propertes The varaton n envronmental qualty affects the prce of housng 8

9 Factors affectng house purchase In hedonc prcng method, t s hypotheszed that each house represents a unque combnaton of characterstcs The prce a potental buyer s wllng to pay (WTP) depends upon: 1. Physcal characterstcs: number of rooms, bathrooms, central heatng, age and condton of structure, etc. 2. Accessblty characterstcs: access to major centres of employment, shops, etc. 3. Publc sector characterstcs: accessblty to schools, post offce, etc., local tax rates, etc. 4. Neghbourhood and envronmental characterstcs: aspect, vew, tree cover, road traffc, water frontage, etc. 5. Alternatve use characterstcs: land wth plannng permsson for a hgher value use, etc.

10 Theoretcal Framework Consder an homogenous area that can be consdered a sngle market from the pont of vew of, say, houses For smplfcaton, each house s charactersed by a sngle characterstc, z, say, ar polluton We are nterested n the relaton between prce and ar qualty, p = p(z) The prce functon s an equlbrum concept (partal equlbrum) resultng from nteracton of supply and demand We assume that the market s perfect Producers and consumers cannot control the market prce Both producers and consumers take p(z) as gven

11 The consumer The consumer buys one house as well as other goods x The consumer s problem s maxmze utlty : U s utlty, y s ncome max U ( x, z ) s.t. x p( z ) y What s the amount of x for partcular values of z to acheve a certan level of utlty: U ˆ U ( x, z ) The budget for buyng the house, guaranteeng a certan level of utlty s y x Alternatvely, we can defne the consumer s problem as U ( y, z ) Uˆ ( y, z, Uˆ ) Ths s known as the bd functon t tells you the maxmum amount a consumer s wllng to pay as a functon of ncome and ar polluton xz,

12 Consumer choce Hedonc prce functon and two bd functons for two dfferent levels of utlty $ p(z) Q(y,z,U 0 ) Q(y,z,U 1 ) Utlty ncreases Ar qualty z

13 The producer The costs c of producng one house depend on nput prces r and the characterstcs z: c(r,z) The producer maxmses profts c( r, z ) Alternatvely the prce to obtan a certan level of proft gven a level of z s c( r, z ) ( r, z, ˆ ) Ths s known as the offer functon t tells you the mnmum amount a producer s wllng to accept as a functon of costs and ar polluton

14 Producer choce Hedonc prce functon and two offer functons for two dfferent levels of proft $ Profts ncrease F(r,z, p 2 ) F(r,z, p 1 ) p(z) Ar qualty z

15 Market equlbrum In the equlbrum, the margnal bd, the margnal offer, and the house prce are dentcal all partes n the market value the house the same, at the margn $ F 3 p(z) Q 3 F 2 Q 2 F 1 Q 1 Ar qualty z

16 Wllngness to pay $/unt MWTP 2 (z) MWTP 1 (z) Margnal mplct prce functon and margnal WTP for one more unt of z for consumers 1 and 2 p (z) Ar qualty z

17 Step-by-step procedures for calculatng of the consumer surplus wth hedonc prcng method 1. Defne value to be estmated Margnal wllngness to pay as revealed by margnal mplct prces 2. Collecton of data on prces and houses features Varous methods exst to collect these data. For complex studes ths data must be complemented wth nformaton on the soco-economc characterstcs of the households nvestgated Sales prce: preferred measure of value, may need to consder selecton bas Tax assessment or homeowner survey of value: measurement error may be a sgnfcant concern Rental or lease prces: approprate for some applcatons, tmng ssues can be of concern, care should be taken when nterpretng the mplct prces 3. Choose functonal form for the hedonc prce functon Lnear usually not approprate. Non-lnear functons mply non-constant margnal prces Sem-log functonal form often used, care must be taken when nterpretng the coeffcent estmates for the dummy varables Researcher judgment must be appled, and expectatons about relatonshps between certan characterstcs and sales prce wll gude choce of functonal form 4. Estmaton of the house prce functon Ths relates the prce of houses to the characterstcs explanng the house

18 Step-by-step procedures for calculatng of the consumer surplus wth hedonc prcng method 5. Calculaton of the mplct margnal prce of the envronmental good for each observaton Ths s the frst dervatve of the house prce functon wth respect to envronmental attrbute 6. Estmaton of the mplct nverse demand functon of the envronmental attrbute The prce pad s explaned by the quantty/qualty of the envronmental attrbute but also by the soco-economc characterstcs of the households 7. Calculaton of the consumer surplus Integraton of the mplct demand curve between the former level of envronmental qualty/quantty and the new one For localzed changes n amentes, the change n sales prce resultng from the change n the amenty s the measure of net-benefts f there are no transactons costs assocated wth movng between propertes. If there are transactons costs, the change n the prce net of transacton costs measures net benefts (or s an upper bound on net benefts) For non-localzed changes n amentes, a second-stage demand analyss s most approprate for computng a bound on net-benefts

19 Rosen s model Consumers (buyers) have a utlty functon: U(s,n,c) s = house characterstcs n = characterstcs of the area where the house s located c = other consumpton goods Budget constrant: m = c + p(s,n) m = ncome p(s,n) expendture for a house p(s,n) s assumed to change n a non lnear relatonshp wth the characterstcs of houses. That s, the cost of houses change n an unknown relatonshp wth number of rooms, etc. c s the expendture for all other goods 19

20 The maxmzaton of the utlty functon subject to the budget constrant, gves the usual frst order condtons. That s, the margnal rate of substtuton between each characterstc n and the consumpton of other goods s equal to the prce (coeffcent) of n and the prce of c. The prce of c s our numerare and we put t equal to 1. The prce of n descrbes the prce of a margnal change n n. The frst order condtons are: U U n c ( s, n, c) ( s, n, c) p n ( s, n) (U n s the partal dervatve of U wth respect to n) p n p( s, n) n Frst order condtons smply say that the consumer (buyer) s wllng to pay p n for a margnal change of n 20

21 Utlty maxmzaton and budget constrant Ths looks lke a normal example from your mcroeconomc class. We only add a non lnear constrant for a gven value of s, s*: c U n pn ( s*, n) U c U(s*,n,c) m=c+p(s*,n) n 21

22 The hedonc prce functon The functon that descrbes how housng prce changes when housng characterstcs change: p(s,n) s the hedonc prce functon The dervatve of the functon wth respect to one of the characterstcs n s the mplct prce of n. If we knew the hedonc prce functon and the mplct prce of n, we could estmate buyers WTP for n, gven that ths s equal to the margnal rate of substtuton between n and the other goods (numerare) 22

23 Indfference curves The budget constrant says that what we don t spend for other goods s spent for housng: p(s,n): c = m p(s,n) The utlty functon can be wrtten n ths way: U(s,n,c)=U(s,n,m p(s,n)) Therefore we can descrbe the utlty functon of consumers (buyers) wth ndfference curves (for gven values of m and s): Each ndfference curve gves for a constant level of utlty the expendture on housng and n for a gven level of ncome and s. p(s*.n) U n 23

24 Heterogeneous consumers People wth dfferent ncomes have dfferent ndfference curves, even f they have the same preferences (U has the same functonal form for all respondents) People wth dfferent preferences have dfferent ndfference curves In a world of heterogeneous consumers (buyers) that have dfferent levels of ncome, we have a contnuum of ndfference curves: p(s*.n) n 24

25 Hedonc equlbrum Suppose that consumers (buyers) consder exogenous the hedonc prce functon Consumers (buyers) maxmze utlty subject to the budget constrant and to the hedonc prce functon: p(s*.n) Hedonc prce functon n 25

26 Hedonc equlbrum consderng the supply The hedonc prce functon comes from the equlbrum of demand and supply of housng. Both are consdered exogenous. Sellers have soproft curves (π) p(s*.n) Sellers π b π a U k Buyers U n 26

27 Margnal Wllngness To Pay The man characterstc of the model s that buyers and sellers are effcently matched along the hedonc prce functon At any pont along the hedonc prce functon, buyers margnal wllngness to pay (and sellers wllngness to accept) for a change n n s gven by the dervatve of the hedonc prce functon wth respect to n. Ths mplct prce changes wth n f the hedonc prce functon s non lnear. The model can be generalzed to the case where we consder several characterstcs of resdental propertes and of the area where houses are located: p(x 1,x 2, x k ) 27

28 The Basc Hedonc Prcng Method A dfferentated or heterogeneous commodty s one n whch the characterstc of the good are fundamental to ts value All goods are heterogeneous top a certan extent but heterogenety s partcularly apparent n the housng market The hedonc functon s a mathematcal form that lnks the characterstcs, defned as X t the prce of the house, P. Thus we can present the hedonc functon: P=H(X) 28

29 Lnear functon The easest way of hedonc functon s a lnear functon: p x x... x 1 Where x 1 through x k are the attrbute levels for k selected attrbutes,, k through k are coeffcents. Suppose that x 1 s land area. The equaton tells us that f x 1 goes up by one square metre, the prce of the house rses by 1 dollars. It means that: P x1 1 1.e. the change n P s due to a change n x s constant and equal to 1, holdng all other ndependent varables constant. The queston s how to determne the hedonc prces for a partcular housng market In emprcal work, multple regresson analyss s used 2 2 If we were to value the envronmental asset or resource, one of the ndependent varables should nclude envronmental characterstc, 29 such ar qualty, percentage of tree cover, percentage of vew, etc k k

30 Model estmate Now we need to specfy a functonal form for p. Some possble functonal forms are gven n the next slde A common functonal form s the sem-log: ln p 1x1 2x2... x The coeffcents of the regresson functon gve the mplct prce, n natural logarthm terms, of the characterstcs of the house The mplct prce can be estmated for specfc value of the characterstcs of houses (for example, the average value) For the sem-log functon, the mplct prce of x 1 s gven by: p x 1 p 1 β 1 gves the percentage change n the prce of housng gven a percentage change n x 1 We usually estmate the mplct prce at the average value of housng k k 30

31 Functonal Forms for the Hedonc Prce Functon 31 Name Equaton Implct Prce Lnear Sem-log Double-log Quadratc Quadratc Box- Cox a P z P z ln z P ln ln N N j j j N z z z P N j j j N z z z P 1, ) ( ) ( 1 ) ( ) ( 2 1 z P P z P. z P z P. j j j z z z P ) 2 1 ( P z z z z P j j j j a The transformaton functon s P()=(P -1)/ for 0, and P()=ln(P) for =0. The same transformaton apples to lambda. The margnal effect s computed for 0. The margnal effect when =0 and =0 s the same for the double log. The quadratc Box-Cox s equvalent to the lnear Box-Cox, another common functonal form when j =0 for all and j. The margnal prce of the lnear Box-Cox s smply z -1 P 1-

32 Some lmtatons and assumptons Perfect nformaton: Buyers observe the characterstcs of houses and are able to perfectly descrbe the hedonc prce functon Buyers can purchase whatever combnaton of characterstcs they desre. They can always fnd the combnaton of bedrooms, bathrooms, locaton of the house that they want Implct prces allow us only to assess margnal varatons n the characterstcs of houses (but f we consder that all buyers are dentcal then we can consder non margnal changes as well too strong assumpton!) Example: f the average house has 3 bedrooms and costs X, I cannot say that buyers are wllng to pay Y for a house that has 7 bedrooms. We can t say that an ncrease of 4 bedrooms s a margnal change The estmate of non-margnal varatons requres the estmate of ndvdual demand parameters, whch s very dffcult 32

33 Econometrc problems Multcollnearty f a house has several bedrooms, t wll lkely have several bathrooms, etc. dstances: don t use too many dstances n your functon Heteroskedastcty Spatal autocorrelaton The value of one house wll be nfluenced by the value of surroundng houses Market extenson: homogeneous markets => bas If I only use the data of sold propertes and do not consder the characterstcs of unsold propertes, my coeffcent can be based (sample selecton bas) Soluton: 2 steps estmate 1) Probt model for the probablty of a sale wth both sold and unsold propertes 2) regresson model wth only sold propertes + Inverse Mlls Rato calculated n 1. Check f the coeffcent of the nverse mlls rato s sgnfcantly dfferent from zero. If t s not, then delete t from the regresson 33

34 Welfare Measurement wth Hedonc Prce Functon Econometrc model shows the mplct prce of amenty I s equal to the consumer s margnal WTP for the amenty Implct prces are most commonly reported result from hedonc studes If we were the value of consumers mght place on a change n an envronmental amenty, need to fnd the relatonshp between mplct prces and WTP for the change. Ths depends on the stuaton. Two changes: Change n localzed amenty (e.g. hghway nose, hazardous waste, ncnerator, local parks). Affects a small number of propertes equlbrum hedonc prce functon for the entre market s unaffected Change n non-localzed amenty (e.g. ar qualty). Amenty change affects a large number of houses shft n supply wll occur, thus we would expect a change n market equlbrum hedonc prce functon 34

35 Welfare Measurement wth Hedonc Prce Functon Change n localzed amenty Frst: Effect of renters, no transacton costs Decrease n amenty renter s no longer at the optmal soluton, face the same hedonc prce schedule as before the change at ther home If no transacton cost no change n welfare for the renter Owners: Realze a captal loss on the property because the decrease n amenty assocated wth the property WTP an amount of money up to the value loss of the property top avod amenty change the mplct prce Total WTP: sum of the mplct prces across property owners that receve a change n the amenty 35

36 Example: A hedonc Prce Model wth Housng Attrbutes (Haab and McConnel, 2002, p. 264) The envronmental dsamenty s ntrogen readng n well water The houses are part of the suburban housng market of Baltmore, Maryland When a house wth well water s sold, the water must be tested -> test of ntrate levels n the water Ntrates stem from excess agrcultural nutrents and undesrable for medcal reasons Standard for ntrates 10 ppm Levels hgher than that must be treated Illustraton s to emphasze the mportance of housng attrbutes Dependent varable: Sales prce s actual sellng prce Independent varables: house attrbutes, neghborhood attrbutes, scores of thrd grade students 36

37 Hedonc Prce Functon Varables Varable Descrpton Mean (n=1853) PRICE Sales prce TIMETREND Monthly tme trend, runnng from 1 to 84 over months of sales NUMBED Number of bedrooms 3.59 FULLBATH Number of full baths 1.98 LIVAREA Square feet of lvng area LOTSIZE Lot sze n acres DIST Dstance to Baltmore 4.04 SCORE Neghborhood elementary school test score 0.18 NITRATES Ntrates n well n ppm 4.05 HALFBATH House on publc sewer 0.25 POOLIN Number of half baths 0.66 HEATPUMP Inground pool 0.06 PUBSEW Heatpump 0.49 CARROL House n Carrol County 0.35 HOWARD House n Howard Country 0.13 BALTO House n Baltmore Country

38 Welfare measurement: Example (Haab and McConnel, 2002, p. 264) Lnear Model Sem-log Model Characterstc Estmate S.E Estmate S.E. TIMETREND b NUMBED 15206a a FULLBATH 22772a a LIVAREA 129.4a a LOTSIZE a a DIST a a SCORE a a NITRATES a HALFBATH 16805a a POOLIN a a HEATPUMP 35270a a 0.01 PUBSEW CARROL 11752a a HOWARD 59708a a 0.17 BALTO 22798a a Constant a a 0.87 Log-lkelhood ln(L R /L U ) Adjusted R a sgnfcant at the 5% level; b sgnfcant at the 10% level

39 Interpretaton from the regresson results Lnear Model: Margnal value of an extra bedroom s about $15,000 (coeffcent of NUMBED). The value of addtonal full bath s about $22,000 (coeffcent of FULLBATH) Sem-log functon Provdes approxmate percent changes n housng prces from a change n the attrbute level An extra bedroom would mply an ncrement n prce of about $16,500 for a house worth $200,000 (0.082*200,000=16,400) 39

40 Valung Changes n Envronmental Dsamenty Consder envronmental dsamenty ntrates n the well water. Increase n ntrates from 10 p to 15 ppm. Lnear model: h( z) WTP zc 5*1151 $5755 z c 95% confdence nterval: 57555*19.6*384 = $1992 to $9518 Sem-log model (when prce s valued at $200,000) h( z) * p * 20,000 $720 z c WTP 5*720 $3600 CI 20000*( *0.0017)*5 $268 to $

41 Further readngs: Haab, T. C., & McConnell, K. E. (2002). Valung envronmental and natural resources: the econometrcs of non-market valuaton. Cheltenham: Edward Elgar Publshng. ISBN: Taylor, L.O. (2003). The hedonc prce. In P.A. Champ, K.J. Boyle & T.C. Brown, (Eds.), A prmer on nonmarket valuaton (Vol. 3) (pp ). Dordrecht, The Netherlands: Kluwer Academc Publshers. ISBN