THE PRICE AND QUANTITY OF RESIDENTIAL LAND IN THE UNITED STATES (SHORTER PAPER)

Transcription

1 THE PRICE AND QUANTITY OF RESIDENTIAL LAND IN THE UNITED STATES (SHORTER PAPER) Sepember 28 h 2004 We esimae he marke value of he housing sock in he Unied Saes o be $24.2 rillion in he second quarer of This figure is more han wice annual US GDP and 1.7 imes he combined capializaions of he NYSE, Nasdaq and Ame x exchanges a he end of Because housing accouns for such a large fracion of naional wealh, changes o he price of houses may have imporan macroeconomic effecs. 1 Ineres in he macroeconomic effecs of house price flucuaions has been heighened by he curren boom in he housing marke: he house price index for he aggregae Unied Saes rose by 48 percen in real erms beween 1996 and he second quarer of In his paper we argue ha one way o progress owards a beer undersanding of house price dynamics is o spli house prices ino wo facors. The firs facor, srucures, can be priced explicily for a paricular house as he replacemen c os, afer accouning for depreciaion, of he physical building. The second facor, which we call land, is he facor ha makes a house worh more han he cos of puing up a new srucure of similar size and qualiy on a vacan plo. Thus land is he marke value associaed wih a home s locaion, and he size and araciveness of he plo. We show ha he growh rae of he aggregae price of housing is a weighed average of he growh rae of he price of srucures and he price of land, where he ime-varying weighs are given by he relaive shares of land and srucures in he oal marke value of he housing sock. This relaionship allows us o consruc price and quaniy series for land given publicly-available (bu appropriaely adaped) series for house and srucure prices, and for he marke values of housing and exising srucures. Our series are he 1 A large empirical lieraure invesigaes wealh effecs from house price changes on aggregae consumpion and saving (see, for example, Case, Quigley and Shiller, 2001). Changes in he price of housing also have implicaions for risk-sharing and asse pricing (see, for example, Lusig and van Nieuwerburgh 2004 and Piazzesi, Schneider and Tuzel 2003), as well as disribuional effecs in heerogeneous-agen economies (Bajari, Benkard and Krainer, 2004).

2 firs consan-qualiy price and quaniy indexes for he aggregae sock of residenial land in he Unied Saes. Noe ha we do no direcly measure he price of land, bu raher infer i from daa on house prices and srucures coss. Wih he excepion of land sales a he undeveloped fringes of mero areas - where land is relaively cheap - here are very few direc observaions of land prices from vacan lo sales, because mos desirable residenial locaions have already been buil on. Our indirec approach allows us o circumven his poenially inracable measuremen problem. Decomposing he price of a house ino he price of a srucure and he price of land is a useful exercise, since very differen forces are likely o drive prices of he wo componens. The cos of puing up new srucures is driven largely by he produciviy of he consrucion indusry relaive o oher secors of he economy, and o he cos of some basic maerials. 2 Thus one should no expec changes in demand-side facors such as demographics or ineres raes o have much impac on he relaive price of srucures, jus as one would no expec such facors o impac he price of cars or any oher produced goods. By conras, land is largely non-reproducible, and herefore he price of land is primarily driven by changes in he demand for housing. 3 The disincion beween srucures and land may herefore shed new ligh on empirical work ha aemps o uncover he driving forces behind house price dynamics. For example, Case and Shiller (2004) poin ou ha income growh raes and ineres rae changes, wo of he mos commonly-cied fundamenals driving house prices, show lile cross-regional variaion, while here are dramaic regional differences in price dynamics. 4 One imporan lesson from our decomposiion is ha one should expec house 2 See Davis and Heahcoe (2004a) for an analysis of he shares of residenial srucures accouned for by value-added from he consrucion, manufacuring, and services indusries. 3 We define residenial land as land wih a residenial srucure on is surface. We esimae ha he sock of residenial land has grown quie slowly over he pas hiry years, leading us o believe ha high-qualiy residenial land is inelasically produced. 4 A well known example of a failure o predic house prices on he basis of fundamenals is Mankiw and Weil (1988), who argued ha he baby bus of he 1970s would lead o declines in house prices in he 1990s.

3 price dynamics o look quie differen in regions where land s share of house value is high (such as San Francisco and Boson) compared o regions where i is relaively small. In paricular, changes in demographics or ineres raes migh have large effecs on house prices in regions where land s share is high, whereas prices should be largely pinned down by consrucion coss where land is cheap. Thus regions ha share similar fundamenals migh experience noiceably differen house price dynamics. Our disincion beween srucures and land is analogous o he angible versus nonangible capial disincion in sock marke valuaion. A second analogy is he decomposiion of he Consumer Price Index ino a core componen, and a second componen capuring energy (and possibly food) prices. Jus as changes in ineres raes likely are correlaed wih energy and non-energy prices differenly, we will show ha ineres raes are quie differenly correlaed wih land and srucures prices. Findings: Beween 1970 and 2004, we esimae ha land accouns, on average, for 47 percen of he value of he housing sock. Land s share in he value of he enire housing sock is large despie he fac ha he cos of raw land ypically accouns for a small fracion (around 11 percen) of he marke value of new homes. We conclude ha a large fracion of he marke value of exising homes reflecs he value of aracive locaions. A business cycle frequencies we find ha he price of land is 1.6 imes as volaile as GDP and almos wice as volaile as he price of srucures. Given ha land accouns for around half he oal value of housing sock, we conclude ha flucuaions in house prices are primarily aribuable o flucuaions in he price of land. The correlaion beween he price of residenial land and srucures prices is low, as is he correlaion beween residenial land prices and farm land prices. Our decomposiion has some esable implicaions for house prices a he regional level. Firs, we verify ha over he curren land price boom, house price gains have ypically been larges in regions where house prices (and hus land s share) were relaively high a he sar of he boom. Second, regions where prices are higher (indicaing higher land

4 values) end o be he same regions where prices are more volaile, consisen wih our claim ha land prices are more volaile han srucures prices. Third, here is a long-run correlaion beween iniial price levels and subsequen price growh, consisen wih he finding ha he rend growh rae for land prices exceeds ha for srucures. Finally, we look for facors ha migh be able o accoun for land price dynamics by running some simple regressions. We regress house prices, srucures prices and land prices on income and ineres raes. Ineresingly we find ha while he coefficien on ineres raes in he land price regression is negaive, as one migh expec, he coefficien on he same variable in he srucures regression is posiive. Thus he overall correlaion of ineres rae changes wih aggregae house prices is small. 5 ACCOUNTING AND MEASUREMENT h We sar by defining he marke value of a home in period, ph, as he sum of he replacemen cos of he srucure afer accouning for depreciaion, ps, and he marke s value of he land and associaed ameniies, pl: l h s l (1) ph ps pl In he above equaion, h p, s p, and = +. l p are he qualiy-adjused prices per uni of he home, physical srucure, and land and ameniies (hereafer called land ) andh, s and l are he qualiy-adjused quaniies. Our key assumpion is ha if he replacemen cos of srucures and he nominal value of land are revalued beween periods and +1, hen he house iself is appropriaely revalued, implying (2) p p p p p p h s l + 1 h + 1 s + 1 l ph = ps + pl. h s l 5 These simple regressions indicae ha slower fuure house price growh is likely because shor-erm ineres raes are likely o rise.

5 Rearranging erms, equaion (2) may be rewrien as h s s l l p 1 p 1 ps p pl (3). h = s + h l h p p ph p ph Equaion (3) implies ha he growh rae of he price of a house beween periods and +1 is a simple weighed average of he growh rae of he replacemen cos of he srucure and he growh rae of he value of he land. Based on equaion (3), if we were o observe ime series for he growh rae of home prices, he growh rae of srucures coss, he replacemen cos of srucures and he marke value of he housing sock, hen we could infer a ime series of growh raes of land prices. In principle, hese daa are publicly available. Freddie Mac publishes he Convenional Morgage Home Price Index (CMHPI), a quarerly price index for homes ha sars in 1970:Q1 for he aggregae Unied Saes. Since his series is based on repea sales, in principle i capures he growh rae of home prices holding qualiy consan. The Bureau of Economic Analysis (BEA) publishes a quarerly price index for residenial srucures ha measures he growh rae of srucures coss; he BEA also publishes esimaes of he aggregae replacemen cos of residenial srucures. Finally, Census daa can be used o esimae he marke value of all homes in he Unied Saes. We modify and adjus hese daa in order o produce a coninuous quarerly price and quaniy series for residenial land ha is free of concepual and saisical measuremen errors. We now highligh our mos imporan modificaions. All prices, excep where noed, have been deflaed by he NIPA price index for core consumpion. 6 House Prices: We suspec ha he CMHPI is measured wih error, and ha measuremen error is responsible for growh-rae spikes ha are especially prevalen from (see he solid line in Figure 1). To see how measuremen error in he CMHPI would impac our esimaed volailiy of land prices, consider he following model for measuremen 6 All of our price indexes are end-of-quarer measures wih base year We conver he NIPA core consumpion price index (a middle -of-quarer measure) o an end-of-quarer measure by using he geomeric mean of he published NIPA daa for he curren and subsequen quarer. For more deails, see he Appendix of Davis and Heahcoe (2004b).

6 error. Suppose ha he naural log of he (inflaion-adjused) CMHPI is measured wih error ha is disribued independenly and idenically over ime, ha is * (4) ( ) ( ) log p = log p + e, h h h where h * h p + 1 is he rue level of he real CMHPI and 1 e + is measuremen error. Leing g h + 1 h* denoe he observed growh rae of house prices, andg + he rue bu unobserved growh rae, equaion (4) implies * (5) g = g + e h h h Now le he observed growh raes of srucures coss and he inferred growh rae of land s l prices beween and +1 be denoed g + 1 and g + 1 respecively. Suppose (for simpliciy) s ha g + 1 is no measured wih error. Equaions (3) and (5) can be combined o express g + as he rue bu unobserved growh rae of land prices plus a erm ha depends on he l 1 error in he observed growh rae of he CMHPI, 1 (6) g ph g ps g ph e h s h l h* s h. + 1 = l + 1 h l + 1 pl ph pl Noice ha as long as he expeced value of e h + 1 is zero, he inferred growh rae of land prices is unbiased. In he analysis secion, we show ha land s share of marke value l h ( pl / ph) hisorically ranges beween 0.40 and 0.55, implying he uncondiional sandard deviaion of measuremen error in land prices is somewhere 1.75 and 2.5 imes he sandard deviaion of he measuremen error in he observed growh rae of house prices ( e h + 1 ). To obain an accurae esimae of he volailiy of house prices and, by equaion (6), of land prices, we use he Kalman Filer o uncover a series for house prices ha is free of measuremen error. In paricular, we assume he growh rae of he rue bu unobserved real CMHPI is a random walk, h* h* (7) g = g + u,

7 where he growh rae shocks, u + 1, are independenly and idenically disribued over ime, wih [ ] 0 Eue s = for all and s. We allow he variance of 1 e + o change in 1975, since he growh raes of he real CMHPI appear much less volaile afer his dae. 7 Alhough he saisical model described by equaions (4) and (7) is relaively simple, i fis he daa well. 8 The esimaed sandard deviaion of u + 1 is 0.4 percen, he sandard deviaion of e + 1 in he daa is 1.5 percen, and he sandard deviaion of e + 1 in h* he pos-1975 daa is 0.4 percen. The esimaes for he sequence g +, along wih growhraes of he raw inflaion-adjused CMHPI daa, are ploed in Figure 1 as he dashed line. The correced growh esimaes are less volaile han he raw CMHPI, especially in he early par of he sample. 9 Given our specificaion of he measuremen error process, i is h* no surprising ha he inferred rue log level of he real CMHPI, log ( p + 1 ) repored series exremely closely. 1, racks he Replacemen Cos of Srucures: We make wo adjusmens o he BEA s published series for he replacemen cos of residenial srucures. Firs, we use quarerly Naional Income and Produc Accouns (NIPA) daa on gross invesmen in residenial srucures, along wih a quarerly esimae of depreciaion, in a perpeual invenory accouning sysem ha convers he published annual replacemen cos series o a quarerly series. Second, he BEA reas expendiures on commissions from exising home sales as if i is residenial invesmen when calculaing an esimae of he replacemen cos of srucures. We believe his is a concepual error and subrac our esimae of he accumulaed value of commissions on exising home sales from he BEA s published esimae of he 7 Documens on he Freddie Mac web sie sugges ha he CMHPI is consruced wih significanly less daa han he pos-1975 series. 8 In paricular, simulaions show ha he model closely reproduces firs-order auocorrelaions of observed growh raes. 9 We use he filering procedure in he EViews package o produce he smoohed esimaes of h* g + 1. Davis and Heahcoe (2004b) use a 3-quarer cenered moving average of observed growh raes o correc for h* measuremen error in he CMHPI. The pos-1975 esimaes of g + from he Kalman filer procedure are very similar o he 3-quarer cenered moving average. 1

8 replacemen cos of all residenial srucures. 10 This correcion reduces he BEA s published esimae of he replacemen cos of srucures by approximaely 8 percen. Marke Value of Homes: We creae an esimae of he marke value of all homes (owned, rened, and vacan) from 1970:Q1 o 2004:Q2 using he following perpeual invenory sysem: 11 h h p 1 h h (9) p h + = ph h + p h p In his sysem, he marke value of housing a +1 (he lef-hand side) is se equal o he revalued marke value of housing a (firs erm, righ-hand side) plus any ne-new addiions o he sock of housing (second erm, righ-hand side). To generae a ime series for he marke value of all residenial housing unis, we benchmark equaion (9) o an esimae of he marke value of he housing sock ha is derived from micro daa from he 2000 Decennial Census of Housing, and use he (correced) CMHPI o revalue he sock beween any wo periods. We calculae ne new addiions o he sock of housing as he sum of ne new addiions o he replacemen cos of srucures and ne new addiions o he sock of residenial land, i.e. 12 (10) p h 1 h. 1 = p s l 1 s 1 + p 1 l s To calculae ne new addiions o srucures, p+ 1 s+ 1, we subrac esimaes of expendiures on commissions and depreciaion from NIPA gross invesmen in srucures. l Our esimae of ne new addiions o residenial land, p+ 1 l+ 1, is based on assumpions 10 Our reasoning is he following: if a house ransacs hree imes in one year, he cos of rebuilding he srucure should no auomaically increase by 18 percen. We derive an esimae of he sock of commissions implici in he BEA s published esimae of he replacemen cos of srucures using a perpeual invenory sysem. See he Appendix of Davis and Heahcoe (2004b) for deails. 11 The Flow of Funds Accouns, published by he Federal Reserve Board, has an esimae of he marke value of owner-occupied housing. We do no use his esimae because i does no include he value of renal homes or vacan homes. Also, we have uncovered measuremen problems wih he published Flow of Funds esimaes - specifically, he growh rae of capial gains implied by he published series end o be unusually large or small when daa sources used o benchmark he esimaes change. One such example is he period, when he benchmark daa source changed from he Annual Housing Survey o he American Housing Survey. As a consequence of hese findings, he Flow of Funds esimaes are currenly under review by saff members of he Federal Reserve Board. 12 Noe ha equaions (1) and (10) joinly imply equaion (3), he equaion from which our land price series is derived.

9 he Census Bureau uses o infer he value of srucures pu in place from sales prices of newly-buil homes. 13 Thus our series for ne new addiions o he sock of housing is consisen wih he way he Census Bureau measures consrucion value pu in place. We compare he prediced marke value of all housing unis for 1980 and 1990, calculaed via equaions (9) and (10) and benchmarked exclusively o he 2000 Census, o he aggregae marke value of housing unis when calculaed using micro daa from he 1980 and 1990 Decennial Census of Housing. In 1990, we under-predic he marke value relaive o he Decennial Census by 4% and in 1980 we over-predic by 4%. We view a 4% discrepancy over a weny year period as broadly vindicaing our mehodology. ANALYSIS In Figure 2 we plo price indexes for residenial land, exising homes, and he replacemen cos of srucures. 14 In real erms, land prices have increased by a facor of 2.7 since 1970, while home and srucures prices have increased by 88 percen and 38 percen respecively. In addiion o having differen rend growh raes, land and srucures prices also exhibi differen paerns wihin he sample. For example, beween 1970 and 1982, he real price of land declined, whereas real replacemen coss rose by 26 percen. By conras, from 1982 hrough he end of 1995, land prices rose by 40 percen (mosly beween 1982 and 1989), while srucures prices fell. Beween 1996 and he second quarer of 2004, real house prices increased 48 percen. Over he same period, replacemen coss rose by only 21 percen. Thus rising land prices accoun for mos of his house-price boom; he cumulaive appreciaion in he real price of land implied by our mehodology is 84 percen. 13 The Census assumes ha raw land accouns for approximaely 11 percen of he sales price of new homes buil for sale. 14 Noe ha he numbers repored in his secion are differen from hose of Davis and Heahcoe (2004b). Davis and Heahcoe (2004b) repor figures appropriae for he value of residenial land under 1-4 uni srucures, whereas we repor saisics relevan for he value of residenial land under all srucures, including srucures in 1-4 uni buildings and 5+ buildings.

10 Averaging over our sample period, residenial land accouns for 47 percen of he value of he housing sock and 88 percen of GDP. There are no clear long-erm rends in he marke value of he sock of land relaive o eiher of hese variables. Since he mid 1990s, however, he value of land has been rising quickly, such ha by he second quarer of 2004 residenial land accouned for 53 percen of he value of he housing sock, and 114 percen of GDP, a record for our sample. The consan-qualiy sock of residenial land and associaed ameniies in residenial use has grown a an annualized rae of beween 0.3 and 0.6 percen since he firs quarer of The average annual growh rae is jus over 0.4 percen. 15 The fac ha he real quaniy of residenial land has risen so smoohly over ime means ha flucuaions in he value of he sock of land are almos enirely aribuable o flucuaions in land prices. Noe ha while land accouns for approximaely 50 percen of he value of he enire housing sock, he cos of purchasing raw land for newly-buil houses is only around 11 percen of wha hese houses sell for. The implicaion is ha a large fracion of he marke value of land under exising houses reflecs he value placed by home-buyers on hese older homes locaions, and ha he locaions of newly-buil houses, on average, are considered much less desirable. Table 1 documens some saisical properies of our price index for residenial land a business-cycle frequencies. Firs, noe ha land prices are volaile: he real price series for land is 1.6 imes as volaile as GDP, 1.5 imes as volaile as he price series for exising homes, and 1.8 imes as volaile as he series for srucures prices. This las finding, coupled wih he fac ha land accouns for around half he oal value of housing sock, suggess ha flucuaions in house prices are primarily aribuable o flucuaions in land prices raher han flucuaions in srucures prices. 16 Indeed, he conemporaneous correlaion beween land and home prices is 0.92, while he correlaion beween land and srucures prices is only Ineresingly, residenial invesmen leads he price of residenial land. This suggess ha changes in he demand for housing, which should 15 For comparison, he real sock of residenial srucures has been growing a an average rae of 2.7 percen while he US populaion has been growing a 1.4 percen per year. 16 This mirrors he consensus ha mos flucuaions in he value of corporae capial are driven by flucuaions in he value of inangible raher han angible capial.

11 show up immediaely in land prices, are no he primary facor driving changes in residenial invesmen. Figure 3 compares our land-price series o he price-per-acre of farm land for he aggregae Unied Saes. 17 This is he only oher published aggregae price series for land in he Unied Saes of which we are aware. Figure 3 indicaes ha farm land prices and our measure of he price of residenial land have lile in common. One migh expec o see a connecion beween farm prices and residenial land prices, especially a he urbanrural fringe where agriculure and residenial developmen are compeing for land. Recall, however, ha flucuaions in aggregae land value primarily reflec changes o he value of land under exising homes, boh because he quaniy of new developmen is small relaive o he exising house sock, and because land accouns for a smaller fracion of he price of new homes. We conclude ha farm land and residenial land are essenially differen goods, whose prices are deermined by differen facors. 18 REGIONAL IMPLICATIONS Our analysis has some ineresing esable predicions for prices a he regional level. We do no have esimaes for land s share by region, bu i is reasonable o assume ha crossregional differences in consrucion coss are small relaive o differences in land prices, and herefore ha differences in house prices are primarily aribuable o differences in he fracion of a ypical home s marke value aribuable o he value of he associaed land. 19 Three implicaions follow. 17 The annual farm price-per-acre series is available from he Unied Saes Deparmen of Agriculure web sie, hp:// We linearly inerpolae he annual daa o generae a quarerly price-per-acre series. 18 There is some evidence o sugges ha demand for housing is an imporan deerminan of farm land prices. In paricular, farm land prices end o be highes in regions where fuure non-agriculural developmen is mos likely. According o he USDA web sie, in January 2002, he average price per acre of farmland in he US was $1,210. The average for he Norheas region was $2,810, and he average for New Jersey (he pricies sae) was $8, See Gyourko and Saiz (2004) for evidence on regional variaion in consrucion coss.

12 Firs, regions in which house prices (and hus land s share) are higher should exhibi more dramaic house price appreciaion in periods when land prices are rising faser han consrucion coss. In paricular, regions in which prices were already highes a he sar of he mos recen boom should have also experienced he fases subsequen price growh. Second, regions wih more expensive housing (and higher land shares) should exhibi greaer house price volailiy, since land prices are more volaile han srucures prices. Third, over he pas 25 years or so, price growh in regions wih high iniial prices should exceed growh in regions wih low iniial prices, since he rend growh of land prices has exceeded ha of srucures prices, especially since he early 1980s. Table 2 repors MSA ( Meropolian Saisical Area ) level daa ha we use o formally es he firs wo of hese predicions. In he firs column, we lis he esimaed average price of a single-family owner-occupied deached house for various MSAs in 1998, sored from mos expensive o leas expensive. The average house prices for hese mero areas were calculaed using micro daa from he 1996 and 1998 Meropolian American Housing Surveys (AHS-M). 20 The second column of Table 2 liss he cumulaive nominal percenage growh o house prices from 1998:Q2 o 2004:Q2 as measured by he MSAspecific CMHPI. 21 The final column of Table 3 liss he sandard deviaion of quarerly growh in he MSA-specific CMHPI from 1992:Q2 o 2004:Q2. 22 Casual inspecion suggess ha he MSAs wih he highes home values experienced boh he fases house price appreciaion and highes price volailiy, consisen wih our esimaes of he relaive appreciaion and volailiies of land prices and srucures coss. The op-five MSAs in his able, ranked by average house value in 1998, experienced 20 The ciies lised in his able are he comp lee se of MSAs sampled in he AHS-M in eiher 1996 or For he 1998 sample, he lised average house prices are calculaed direcly from he AHS-M micro daa. For ciies in he 1996 sample, we calculae a 1998 esimae by muliplying our esimaed average value from he 1996 AHS-M micro daa by growh in he ciy-specific CMHPI from 1996 o In boh years, he AHS-M op codes he op 3 percen of repored house values in each ciy; we correc for he op code by muliplying each op coded value by 1.5. Our work wih he 2000 Decennial Census of Housing and proprieary 2001 Survey of Consumer Finances daa leads us o believe ha his is an accurae adjusmen. 21 We believe ha he MSA definiions used in he CMHPI are he same as hose in he AHS-M. 22 We chose 1998 as a saring poin for looking a growh since i is he approximae saring poin of he mos recen boom and i corresponds o an AHS-M inerview year. Sandard deviaions are calculaed going back o 1992 so ha rankings of house values in 1998 represen somehing like he average for he period.

13 average cumulaive growh in nominal house prices over he pas 6 years of 94 percen and a sandard deviaion of growh in he pas 12 years of 1.9 percen while he boom five MSAs experienced average nominal growh in house prices of 33 percen and average sandard deviaion of 0.7 percen. Formal esing of he Spearman rankcorrelaion coefficiens allows us o rejec he hypoheses ha he rank of he MSA-level average house price in 1998 is (i) uncorrelaed wih he rank of he subsequen growh in home prices and (ii) uncorrelaed wih he rank of he sandard deviaion of growh in home prices. Finally, o invesigae he long-run correlaion beween iniial price levels and growh, we seleced he MSAs for which house price daa is available in eiher he 1979 or he 1980 Meropolian Annual Housing Surveys (he predecessor o he American Housing Survey) and correlae average house prices in he second quarer of 1980 wih cumulaive house price growh beween 1980:2 and 2004:2. 23 The associaed Spearman rankcorrelaion coefficien is 0.52, posiive and saisically significan, as expeced. REGRESSION ANALYSIS I is a commonly held belief among real esae professionals and some business economiss ha house prices are sysemaically posiively correlaed wih income and negaively correlaed wih ineres raes. 24 To explore he relaionship beween prices and fundamenals, we regress log real house prices, srucures prices, and land prices on log real aggregae personal disposable income, he log nominal 3-monh annualized T-Bill rae, and he log of he inflaion rae (o capure he effec of changes in real ineres raes). The coefficien esimaes, adjused sandard errors, and uni roo ess on residuals are repored in Table Noe his is no he same se of ciies repored in he daa in Table 2. A able summarizing he daa is available on reques. 24 See, for example, Duca (2004). 25 See foonoes o Table 3 for more deails on he repored coefficiens, sandard errors, and uni roo ess. Qualiaively, our resuls appear o be robus o many differen variable choices and funcional form specificaions.

14 Consider firs he land price regression in he hird row of he able. We find ha real land prices are (i) negaively correlaed wih ineres raes, (ii) srongly increasing in real income, and (iii) co-inegraed wih income and ineres raes. These findings are consisen boh wih convenional wisdom in he real esae profession, and wih our argumen in he inroducion ha land prices should be primarily deermined by demandside facors. By conras, he srucures price regression indicaes lile evidence of a sysemaic relaionship beween srucures prices and hese oher variables: coefficiens are insignifican or marginally significan, and uni roo ess sugges a spurious regression. This is consisen wih our prior ha real srucures prices should be largely driven by supply-side facors, such as produciviy in he consrucion secor relaive o he res of he economy. Focusing on he firs row of Table 3, he house price regression, i appears ha house prices are uncorrelaed wih nominal ineres raes. Recall ha house prices are a weighed average of land prices and srucures coss. Thus he near-zero coefficien esimae on ineres raes in he house price regression is a mix of he insignifican posiive esimae from he srucures price regression (row 2) and he significan negaive esimae from he land price regression (row 3). The apparen absence of a co-inegraing relaionship beween house prices, income and ineres raes is a furher consequence of his off-seing ineres rae effec, coupled wih he lack of a clear relaionship beween srucures prices and fundamenals. 26 CONCLUSIONS We now discuss some poenial fuure applicaions for he land price series we develop, and some broader implicaions of he properies of land prices we have discussed in his paper. Our finding ha land prices are co-inegraed wih income and ineres raes suggess ha our land price series will prove useful for undersanding he naure of he curren boom in house prices (Terrones and Orok 2004 and McCarhy and Peach 2004) 26 Using panel daa, Gallin (2003) also finds ha i is difficul o rejec he hypohesis of no co-inegraion beween house prices and income.

15 as well as for forecasing fuure house prices. 27 The implicaions for regional house price dynamics of our srucures versus land decomposiion also meris furher exploraion. To his end, Davis and Palumbo (2004) are currenly adaping he mehodology developed in his paper in order o produce MSA-level series for land prices. The finding ha he value of residenial land exceeds GDP has implicaions for he calibraion of macroeconomic models, and in paricular he appropriae arge capial o oupu raio. Finally, our empirical evidence suggess ha house prices in regions where land s share is high should be more sensiive o ineres raes, wih implicaions for moneary policy. REFERENCES Bajari, P., Benkard, C. and J. Krainer, 2004, House Prices and Consumer Welfare, Sanford GSB Working Paper no Case, K. and R. Shiller, 2004, Is There a Bubble in he Housing Marke? An Analysis, Brookings Papers on Economic Aciviy (1), Case, K., Shiller, R. and J. Quigley, 2001, Comparing Wealh Effecs: The Sock Marke Versus he Housing Marke, Naional Bureau of Economic Research Working Paper no. W8606. Davis, M. and J. Heahcoe, 2004, Housing and he Business Cycle, Federal Reserve Board Finance and Economics Discussion Series Working Paper no Also forhcoming in he Inernaional Economic Review. Davis, M. and J. Heahcoe, 2004, The Price and Quaniy of Residenial Land in he Unied Saes, Federal Reserve Board Finance and Economics Discussion Series Working Paper no Davis, M. and M. Palumbo, 2004, The Price and Quaniy of Land in Major Unied Saes Ciies, Mimeo. Duca, J., 2004, How Vulnerable Are Housing Prices?, Souhwes Economy (2), Gallin, J., 2003, The Long-Run Relaionship beween House Prices and Income: Evidence from Local Housing Markes, Federal Reserve Board Finance and Economics Discussion Series Working Paper no Gyourko, J. and A. Saiz, 2004, The Supply Side of Urban Revival, Mimeo. 27 See Davis and Heahcoe (2004b) for a simple forecasing exercise.

16 Hamilon, J., 1994, Time Series Analysis, Princeon: Princeon Universiy Press. Lusig, H. and S. Van Nieuwerburgh, 2004, Housing Collaeral and Consumpion Insurance Across US Regions, Mimeo. Mankiw, N. and D. Weil, 1989, The Baby Boom, The Baby Bus, and he Housing Marke, Regional Science and Urban Economics (19), McCarhy, J. and R. Peach, 2004, Are Home Prices he Nex Bubble?, forhcoming in he Federal Reserve Bank of New York Economic Policy Review. Piazzesi, M., Schneider, M. and S. Tuzel, 2004, Housing, Consumpion, and Asse Pricing, Mimeo. Terrones, M. and C. Orok, 2004, The Global House Price Boom, Chaper 2 of he Sepember World Economic Oulook published by he Inernaional Moneary Fund, 1-19.

17 TABLE 1: BUSINESS-CYCLE PROPERTIES OF LAND PRICES, 1970:1-2004:2* l l c p Corr(X -s, p / p ) SD% rel. o X -s = -4 -s = +4 l p GDP RESI h p s p l * p = he price index for consan-qualiy residenial land divided by he NIPA consumpion price index excluding food and energy; GDP = real chain-weighed GDP ($2000); RESI = real chain-weighed residenial invesmen in srucures ($1996); p = he correced Freddie Mac s CMHPI divided by he NIPA consumpion price index excluding food and energy; and p = he price index for he replacemen cos of srucures divided by he NIPA consumpion price index excluding food and energy. All variables are measured quarerly; he price variables are measured a he end of he quarer; he NIPA consumpion price index excluding food and energy is convered from an average hroughou he quarer (as published) o an end-of-quarer basis by aking he geomeric mean of he repored price index for he curren and fuure quarer. All daa are available for public download a hp://morris.marginalq.com. GDP and RESI are aken direcly from he NIPA; he CMHPI has been correced for measuremen error; and he price index for he replacemen cos of srucures is aken from he NIPA and adjused as in Davis and Heahcoe (2004b). All variables have been logged and HP-filered wih parameer?=1600. h

18 TABLE 2: HOUSE PRICE LEVELS, GROWTH RATES, AND VOLATILITY BY CITY AHS-M Esimaed Average Nominal Growh in CMHPI, SD, Quarerly Nominal Growh MSA Survey Year House Value, 1998:Q2-2004:Q2 1992:Q2-2004:Q2 1998* San Francisco, CA 1998 $456, % 2.02% San Jose, CA 1998 $416, % 2.46% Oakland, CA 1998 $285, % 2.07% Boson, MA 1998 $236, % 1.35% Washingon, DC 1998 $223, % 1.55% Seale, WA 1996 $221, % 0.82% Balimore, MD 1998 $175, % 1.40% Sacrameno, CA 1996 $173, % 2.22% Providence, RI 1998 $145, % 1.91% Sal Lake Ciy, UT 1998 $168, % 1.36% Harford, CT 1996 $163, % 1.55% Minneapolis, MN 1998 $146, % 0.96% Alana, GA 1996 $144, % 0.64% Norfolk, VA 1998 $131, % 1.16% Cincinnai, OH 1998 $134, % 0.38% Cleveland, OH 1996 $133, % 0.57% Birmingham, AL 1998 $121, % 0.71% Rocheser, NY 1998 $111, % 0.84% Tampa Bay, FL 1998 $111, % 1.22% Indianapolis, IN 1996 $110, % 0.46% S. Louis, MO 1996 $109, % 0.64% Houson, TX 1998 $106, % 0.92% Memphis, TN 1996 $105, % 0.79% Oklahoma Ciy, OK 1996 $80, % 0.72% Avg. House Value and Nominal Growh, Spearman Rank Correlaion Coefficien Avg. House Value and Sd. Dev. of Growh, Spearman Rank Correlaion Coefficien * Average value for single -family deached homes in he MSA as defined by he AHS-M. For AHS Survey Year 1998, he value is calculaed direcly from AHS-M micro daa. For AHS Survey Year 1996, he 1996 average value is calculaed from he AHS-M micro daa and his average is scaled by growh in he MSA CMHPI from 1996:Q2 o 1998:Q2.

19 TABLE 3: REGRESSIONS OF HOUSE, STRUCTURES, AND LAND PRICES ON FUNDAMENTALS Coefficiens and T-Saisics* Uni Roo Tess** Log real disposable income Log nominal 3-monh T- Bill*** Log nominal inflaion rae*** Augmened Dickey- Fuller Phillips- Perron (1) Log real house prices (2.34) (-0.47) (0.83) Do No Rejec Do No Rejec (2) Log real srucures prices (2.03) (0.66) (1.46) Rejec a 5% Rejec a 10% (3) Log real land prices (4.98) (-2.24) (1.33) Rejec a 1% Rejec a 1% * Coefficiens are esimaed using Sock-Wason procedure wih wo leads and wo lags of he growh raes of all variables, quarerly daa, sample period 1970:Q4 o 2003:Q3. T-Saisics (in parenheses) are calc ulaed according o Hamilon (1994), p ** Uni-roo ess on residuals assuming no consan and no ime rend. The es saisic repors wheher he null hypohesis of no uni roo can be rejeced. When we include a consan, he assumpion of a uni-roo in he land price regression error can be rejeced a 10% for he Augmened Dickey-Fuller and 5% for he Phillips-Perron (he resuls for he oher regressions change slighly as well). *** The 3-monh T-Bill and inflaion raes are he average annualized rae during he quarer.

20 FIGURE 1: ANNUALIZED GROWTH RATES OF INFLATION-ADJUSTED CMHPI Growh Raes Repored Correced

21 FIGURE 2: LAND, HOUSE, AND STRUCTURES PRICES 2.8 Price Indexes (Relaive o Consumpion) 2.4 Index (1970:1 = 1) Residenial Land Homes Replacemen Cos

22 FIGURE 3: RESIDENTIAL LAND PRICES AND FARM LAND PRICES 2.8 Price Indexes (Relaive o Consumpion) 2.4 Index (1970:1 = 1) Residenial Land Farm Land