Enhr Conference 2011 5-8 July, Toulouse Ineres raes, house prices and he purchasing power for housing 1 Frank Vasmans Cenre for Economic Sudies, Universiy of Leuven (K.U.Leuven) e-mail: Frank.Vasmans@econ.kuleuven.ac.be Erik Buys Cenre for Economic Sudies, Universiy of Leuven (K.U.Leuven) e-mail: Erik.Buys@econ.kuleuven.ac.be Absrac Real income and he real ineres rae have been widely considered as wo imporan deerminans of house prices. We find ha he purchasing power for housing, which is based on he ne presen value of fuure income flows, is a more powerful concep. I is inuiive and realisic in naure for firs ime buyers who need subsanial morgage-financing. Based on aggregaed yearly ime series daa for Belgium from 1973 o 2009, we find ha nominal house prices are coinegraed wih he purchasing power for housing. We also find evidence for full capializaion effecs of fiscal advanages. Economerical resuls for he income-elasiciy are in line wih he heoreical supposiion of our model, namely 1. The raio price-o-purchasing power for housing is more sable han he price-o-income raio, while he ineres rae elasiciy as derived from he imposed funcional form of purchasing power for housing is higher han generally found in lieraure. Keywords: house prices, ineres rae elasiciy, coinegraion, purchasing power for housing, income, ne presen value, repaymens, borrowing consrain, long run relaionship, capializaion, price-o income, morgage-financed. Inroducion Exising research has no provided adequae explanaions for he price dynamics of he housing marke (Leung, 2004). OECD (2005) comes o a similar conclusion in is review of recen empirical sudies on house price deerminans. House prices do no appear o be linked o income by a sable long-run relaionship and he semi elasiciy of ineres raes ranges beween 0 and -9.4. Moreover here are imporan mehodological issues. Mos sudies use error correcion models (ECM) alhough Gallin (2006) has demonsraed ha house prices and income in he US are no coinegraed. More in general he concludes ha aggregaed daa are likely o be spurious due o small sample 1 Thanks go o he Flemish Policy Research Cenre for Spaial Planning and Housing, o he paricipans of he EMF-ENHR Seminar on Housing and Morgage Markes, Brussels, 30-31 March 2011 for heir useful commens and o Roel Helgers.
Mixié : an urban and housing issue? 2 esing. This is a serious problem as ECM only models he shor erm dynamics righ if he long-run equilibria are esimaed correcly. In oher cases esing for coinegraion is done bu for a specific funcional form and a specific daase. This implies ha rejecing he coinegraion hypohesis is only valid for he funcional form applied and he specific daase. The user cos approach for insance indicaes ha here is some heoreical evidence for coinegraion beween house prices and income. See e.g. Meen (2002) who found ADF coinegraion saisics close o heir criical values for boh US and UK daa. Bu ECM s based on user cos approaches also have heir weaknesses. They usually ignore financial marke mechanisms. Moreover, housing affordabiliy may be closely relaed o financial marke mechanisms and governmen regulaion. In many counries, he sae has developed new approaches o risk managemen ha can widen access o owner occupaion (Scanlon, 2004). So far, housing affordabiliy is mainly analyzed in one-direcion: he house price is given, while endogeneiy is o be expeced: households are borrowing consrain and his consrain may impac he house price. McQuinn and O'Reilly (2008) ry o solve some of hese problems by modeling he demand-side deerminans of house prices in Ireland as a funcion of he average amoun borrowed by households given curren disposable income and ineres raes. In his way McQuinn and O'Reilly hope o capure ha mos house purchases are morgage-financed and ha he amoun len by morgage providers is ulimaely a funcion of income and ineres raes. The same funcional form is used by Bourassa (1996) o ge a hold on affordabiliy. We ake a similar saring poin. Firs we give a deailed heoreical framework for he concep of he purchasing power for housing and poin o some differences wih oher house price models. In a las sep we apply his approach o explain he Belgian house prices. Theoreical framework The concep purchasing power for housing The main idea is ha he concep of curren income should be adjused because households don pay for heir house a once bu wih fuure cash flows, namely morgage repaymens. The level of hese repaymens is relaed o curren income. Morgage providers ranslae hese fuure repaymens ino a loan via he ne presen value mehod, where he morgage ineres rae comes ino play. Thus insead of using income and ineres rae as wo disinc variables, we inroduce he concep of purchasing power for housing, which we define as he ne presen value of a proporion of fuure income sreams (morgage repaymens) in a given ime period (morgage erm). The demand curve for housing can hen be defined as he willingness o pay a cerain amoun of monhly income for a cerain period. As households compee for house-holding, a vicious upward spiral of house prices can maerialize wihou much raionale abou fuure house price appreciaion. I suffices ha a buying a house in general is seen as a good invesmen. However, households are bounded by budge and borrowing consrain, imposing a limi on house price appreciaion. This model assumpion differs from he user cos approach (e.g. Poerba 1984) ha reflecs raional asse pricing fundamenals. One of he key elemens in he user cos formula is he expecaions on fuure price or ren appreciaion. The lack of good esimaes for hese variables is a major drawback. We firs decompose he house price ino five financial componens, which is in line wih he model a morgage provider would use o calculae a loan wih fixed annuiies and fixed ineres rae for a household. Le α denoe he repaymen raio, he fixed proporion of nominal ne income (Y) a household allocaes iniially on average o yearly morgage repaymens. Given income (Y), morgage ineres rae (i) and
3 Workshop 01: Housing Finance and Regulaion duraion of he loan (n), we can calculae he average loan ha an average household would borrow o buy a house by calculaing he ne presen value of fuure repaymens: L αy n 1 = (1) = 1 1 ( + i) This loan is relaed o he house price P, as i can be expressed as L + D, where D is he deposi or down paymen. We model his down paymen o be proporional o Y, and use he parameer β as he down paymen raio. This yields L = (1-β)*P. We also incorporae he ne effec of he ax relief (nr). This ne effec is reaed as exra funds for repaymens. The price of a house a ime can hen be expressed as follows: P ( i ) n 1 1 αy + nr + 1 β i (2) Which is an exac relaionship. So he impac of he diversiy of all house price deerminans should always be refleced in hese five financial facors. Unforunaely, ime series daa of hese variables are hard o obain. Esimaing he purchasing power for housing is in fac he same process as calculaing housing affordabiliy by means of borrowing consrains (Bourassa, 1996). Affordabiliy analyses he impac of house prices on household expendiures, where he purchasing power for housing akes reasonable esimaes for α, β and n o deermine long-run house price equilibria. These are wo sides of he same coin bu wih a differen causal direcion. Gan and Hill (2009) draw a disincion beween he conceps of purchase affordabiliy - wheher a household is able o borrow enough funds o purchase a house - and repaymen affordabiliy - he burden imposed on a household of repaying he morgage. Purchase affordabiliy is linked wih β and n, while repaymen affordabiliy is linked wih α. Higher α, β and n decrease affordabiliy, and migh be invoked by house price increases due o shorage, demographic pressure, and so on. However, for he variables income and ineres rae, i is plausible o assume ha he causal direcion is mainly one way: changes in income and ineres rae resul in changing house prices, while he reverse effec is raher unlikely. So if we observe ha α, β and n are more or less consan over ime, here would even be no need for an economeric model since he relaionship in he equaion is exac, and no parameers need o be esimaed. The ime series purchasing power for housing is calculaed wih he relaionship above, for plausible and fixed α, β and n and wih acual daa for Y and i. In he second sep we analyze wheher he purchasing power for housing is coinegraed wih acual house prices. The purchasing power for housing, which is denoed by X can hus be wrien as: X ( i ) n αy 1 1 + nr + 1 (3) β i Purchasing power for housing is hus a nonlinear funcion of income and he ineres rae. The ne ax relief is kep consan (see infra). The effec of each variable is no easy o inerpre: no only has income a direc influence on he house price, bu α, β and n can also be influenced by income and he ineres rae and so indirecly have an exra effec on house prices. These variables are correlaed, namely α( P, Y, β, i, n,...), β ( P, Y, α, i, n,...) and n( P, Y, α, i, β,...), where income and he ineres rae are assumed o be exogenous.
Mixié : an urban and housing issue? 4 The effec of income and he ineres rae on he purchasing power for housing hus covers only par of he effec of hese variables on he house price. Based on his formula, we will analyse he following funcional form : P = β X +... (4) We could also use a decomposiion of Y by aking he log (formula 5), which would lead o a funcional form ha is more similar o he user cos approach and oher models ha can be found in lieraure (formula s 6-7). ( ( i n ) ) Log(P ) log (α Y + nr) - log(1-β ) - log(i ) + log 1 1+ (5) ( ) 1 ( ) 2 ( ) ( ) ( ) Log P = β Log Y + β Log i +... (6) Log P = β Log Y + β i +... (7) 1 2 If we compare formula 5 wih formula s 6 & 7 we noe ha he ineres rae is no a linear funcion of P, since he las erm is a combinaion of ineres rae and duraion. Moreover, our model would sugges o model a log-log specificaion using he nominal ineres rae. In his paper we are no aemping o bridge he link beween differen modeling approaches. So we focus on formula (4), where we expec he parameer esimae o be around 1 in case n, β and α do no differ oo much hroughou ime. Therefore, we firs give an overview of how hese financial variables are relaed wih house prices and illusrae he imporance of each variable by a sensiiviy analysis where he impac of a change of each variable on house prices is calculaed, keeping he ohers consan. Ineres rae and semi ineres rae elasiciy of purchasing power for housing In our model we ake he nominal fixed ineres rae as reference ineres rae 2. We don include inflaion as a variable, because all he daa are in nominal erms. As boh Kearl (1978, 1979) and Schwab (1982) sugges, inflaion, by raising nominal ineres raes, may have an effec on housing demand hrough he 'fron-loading' of morgage ineres paymens in real erms, which is called he il effec. Real repaymens are iled owards he earlier periods. Meen (1989) herefore included a measure of expeced inflaion separaely. Moreover, he real morgage ineres rae can only be approximaed since he nominal ineres rae is given, bu fuure inflaion should be esimaed 3. Empirical resuls of Berkovec and Fulleron (1989) also give evidence ha he lower income classes are inhibied o buy a house due o he repaymens consrains as a resul of high inflaion, while Brunnermeier and Jullieard (2006) find opposie resuls. We use he nominal morgage rae because i is inheren on our model assumpion, where borrowing consrains are he cenral heme, and no invesor s raional expecaions. Since he ineres rae is par of he purchasing power for housing concep, we firs derive he semi ineres elasiciy for he purchasing power for housing. Since X, he purchasing power for housing, is a funcion of i, and assuming ha he oher variables (α,β,n,y) are independen of i, he derivaive of X wih respec o i can be calculaed as follows: -n n 1 X [1-(1+i) ] (1 + i) αy = - + n* i i² i 1 β (8) Hence, he semi ineres rae elasiciy is equal o: 2 In case of variable ineres raes, he purchasing power of housing concep is more difficul o apply because i is no clear how households incorporae he risk of variable ineres rae ino heir decision process. I may be ineresing for furher research. 3 The expeced inflaion is less volaile han curren inflaion so he choice wheher or no o incorporae inflaion ino he model is less imporan han one would expec a firs sigh.
5 Workshop 01: Housing Finance and Regulaion X - + n* (1 ) i + i X = n i ( 1 (1 + i) ) -n [1-(1+i) ] n 1 (9) The semi ineres rae elasiciy is a funcion of he ineres rae iself, and he morgage erm. As illusraed by figure 1, he purchasing power is highly dependen on he curren level of he ineres rae and he morgage erm as he semi ineres rae elasiciy is no a consan. In he user cos approach and mos economeric models, he ineres rae is no modeled as being dependen on n, as McQuinn (2008) already noiced. While his difference would no lead o serious differences in case i would be high, i migh yield o differen resuls when i is low as figure 1 illusraes. Clearly he choice of model, borrowing consrain versus raional expecaions, is crucial and he specific choice will depend on specific regional marke mechanisms 4. Recen ineres raes are hisorically low, and as figure 1 illusraes, heavily influence he purchasing power for housing. A one percenage poin decrease of he ineres rae increases purchasing power for housing wih 10% wih i = 4% and n = 25. Figure 1. Semi ineres rae elasiciy for he purchasing power for housing 0% 0% 2% 4% 6% 8% 10% 12% 14% -5% duraion semi ineres rae elasiciy -10% -15% -20% -25% -30% -35% -40% ineres rae low average high infinie Down paymen and morgage duraion: he rade-off beween boh Gan and Hill (2009) sugges ha deregulaion of he morgage marke has aced o increase average morgage lenghs while reducing average down paymen raio s. So, a household wih a given iniial level of wealh and expeced fuure income sream can buy a more expensive house han before, i.e. purchase affordabiliy has improved. Clearly, here is an ineracion beween boh facors: a smaller β can be offse by a larger n. I is however no clear how purchase affordabiliy should be inerpreed. In case here is a higher down paymen requiremen, a household should save par of is income firs, bu 4 Even in case he user cos approach is more appropriae, i may be ineresing o invesigae if modeling o infiniy is appropriae in case of low ineres raes.
Mixié : an urban and housing issue? 6 his disadvanage may be more han offse by a shorer morgage lengh. So, i may be more relevan o look a β and n as a whole o deermine he invesmen horizon, he full lengh a household has o finance a home. So he ime horizon of invesmen is acually larger han he morgage lengh (see figure 2). Figure 2. The ime horizon of invesmen Yearly invesmen Invesmen Savings Saving period Morgage repaymens Acual purchase Morgage lengh ime Repaymen raio and morgage duraion: no rade-off beween boh? We assume α o be relaively consan over ime, alhough changes in oher housing expenses heaing, axes, imposed qualiy condiions of housing may have an impac. If α would be oo high, repaymen affordabiliy would be low (Gan and Hill, 2009). Noe ha α is calculaed as he raio of he firs repaymen o curren income. Since we work wih fixed annuiies, he repaymen affordabiliy is mainly an issue a he sar of repaymens, which is no necessarily he case for variable ineres rae morgages. Borrowing for a longer period is no only suiable for relaxing he pressure on high down paymens, spreading he morgage burden can also lead o a lower repaymen raio. This rade-off seems also o be pleasan for young households. However, we argue ha here is a risk for fallacies of composiion (Caballero, 1992). Somehing ha is opimal for person A individually and opimal for person B individually is no necessarily opimal for persons A + B ogeher. If many individuals change heir idea abou an opimal morgage lengh, his could cause a longer morgage lengh wihou a lower repaymen raio. So, if he average household gradually decides o borrow for a longer period, his change of Zeigeis or social epidemic (Shiller, 2007) will be capialized in higher house prices. Iniially repaymens raio s could be lower wih longer morgage duraions, bu due o house -hold compeiion, low repaymen raio s only happened o be for a shor ime period. I illusraes ha he causal relaionship beween higher house prices and longer morgage lengh migh be bidirecional and ha financial mechanisms ha ease he access o capial, are capialized in house prices. Higher house prices can lead o longer morgage duraions, bu longer morgage duraions can also lead o higher house prices. This simulaneiy is difficul o prove economerically, bu here are reasons o believe ha in Belgium morgage lengh resuled in higher house prices since 2005, because a new fiscal policy was inroduced for home-buyers, resuling in longer fiscal opimal morgage lenghs. This effec is sronger in case of low ineres raes which lead o higher ne presen values for values in he far fuure. The marginal uiliy for an addiional year of morgage duraion is higher and can serve as an acceleraor for his effec o ake place. In addiion, hisorical appreciaion raes were high, inciing household propensiy o consume housing, because of he higher expecaions of fuure house price growh as described by Shiller (2007).
7 Workshop 01: Housing Finance and Regulaion In he sense ha morgage duraion can have an impac on house prices, we can even speak of a semimorgage duraion elasiciy, which can easily be derived from formula (3). Figure 3 illusraes his semi-morgage duraion elasiciy for differen n and i. In case he ineres is zero, house prices increase by he inverse of he duraion. -n ( ln ( 1+i )*( 1+i) ) X X = n ( 1 (1 + i) n ) (10) Figure 3. semi-morage duraion elasiciy for he purchasing power for housing semi morgage duraion elasiciy 6% 5% 4% 3% 2% 1% 0% 0% 2% 4% 6% 8% 10% 12% ineres rae 20 years 25 years 33 years Table 1 summarizes he effec of a change in one variable on he house price, all oher variables kep equal. I is ineresing o noe ha he down paymen raio seems o have lile impac on house prices. We capure he impac of ineres and income in he concep of purchasing power for housing. We don capure he effec of longer morgage duraions as perceived in mos counries since 2000. However, we give evidence ha low ineres raes are o a cerain degree a necessary condiion for long morgage duraions, alhough we don sae ha he low ineres raes caused he longer duraions. Fiscal policy can also be an incenive, as are oher facors like demographic pressure or a supply shorage. Table 1. The effec of a change in one variable on he house price, all oher variables kep equal Iniial sae Change Impac on house price Ineres rae 5% - 1% (pp) + 9% Down paymen raio 80% - 1% (pp) + 1,2 % Repaymen raio 25% + 1% (pp) + 4% Income + 1% + 1% Duraion 20 y. + 1 y. + 3 % Tax relief In he concep of purchasing power for housing we rea ax relief as a kind of income measure. So we assume full capializaion: morgage ineres ax relief makes housing no more affordable o new
Mixié : an urban and housing issue? 8 buyers. In lieraure one can find mixed evidence 5 for his hypohesis (e.g. Berger e al., 2000; Brounen and Neueboom, 2008; Saarima, 2010; Bourassa and Grigsby, 2000). Demographic facors and housing supply As saed by he lieraure, demographic facors and housing supply are imporan facors. However, alhough ofen found o be significan in he shor-run, long-run effecs are less clear. In our model we herefore focus firs on ineres raes and income. The effec of demographic pressure can be emporarily in naure, since i may be offse by exra housing supply in he long run. Price elasiciies of supply and demand can vary over ime and are heavily inerwined. One could argue ha he equilibrium beween demand and supply for demographics is based on quaniies, which implies ha he long-run equilibrium is a horizonal line. On he conrary income and he ineres rae have a permanen price effec which is no offse in he fuure by oher facors. Changes in prices can emporarily resul in differen demand and supply quaniies, bu in he long run, one could expec he equilibrium line o be verical. The underlying assumpion is ha equilibria in he long run will be se wheher or no via governmen inervenion according o he fac ha here is no shorage, nor excess sock, and housing affordabiliy is guaraneed for mos households. The former resuls in he horizonal equilibrium line on he lef in figure 4, he laer in he verical equilibrium line on he righ. However, his doesn mean ha land availabiliy is no an issue. On he conrary, scarciy of land is a condiion for his heoreical framework o hold, oherwise house prices would be more in line wih building coss, and no wih affordabiliy. House -holding compeiion is also only a valuable saring poin if here is no demographic shrinkage, jus like long morgage erms are only emping when ineres raes are low. Clearly, his heoreical framework focuses on price drivers like income and ineres rae, bu some condiional facors of supply and demand should be presen in i o make sense. Figure 4. Long run equilibria price price Demografics and housing supply quaniy Income and ineres rae quaniy Long run equilibrium 5 a lack of saisical significance migh no be aken as evidence ha full capializaion should be rejeced since i may be due o a misspecified model, especially he specificaion of he ime-lag (he rae of adjusmen) seems o be sensiive o deermine he rae of capializaion.
9 Workshop 01: Housing Finance and Regulaion Empirical Resuls Empirical specificaion In his paper we check wheher here is a long-run relaionship beween he house price and he purchasing power for housing. Raher han including he (nominal) ineres rae and (nominal) income separaely in a linear regression model, we include he purchasing power for housing. We check wheher house prices and purchasing power for housing are coinegraed. If so, we addiionally esimae an ECM. Coinegraion is esed for using he Engle-Granger approach and implies he exisence of a long-run relaionship beween he wo ime series. The model we esimae in he regression analysis is a fairly simple linear regression model, namely he following equaion: Y = βx + u Variables Y and X are in levels. Y denoes he price of housing, X is a marix or vecor of explanaory variables, β is a vecor of parameers ha we esimae and u is a vecor of residuals. We perform regressions wih differen alernaives for boh Y and X, and check wheher here are β s, for which he residuals (denoed by ε ) are saionary (inegraed of order zero). To check for saionariy we perform ADF-ess. We use adjused criical values since he residuals are esimaes and are likely o be less volaile han he rue error erms generaing he daa. We esimae hree differen models. The firs or base model uses purchasing power as a sole explanaory variable. Theoreically, if he house price is only a funcion of purchasing power for housing, we should find ha he base model performs relaively well. The second model also includes he growh rae of he populaion beween 25 and 35 years. These demographic evoluions migh have an imporan effec on he price of housing due o an increase or decrease in he demand. Finally, he hird model conains boh purchasing power and a consan. Including a consan migh improve he fi of our model and provides a good robusness check for our model assumpions. Afer having esimaed he model using he daa in levels, we esimae he corresponding error correcion models (ECM) which show he shor run dynamics of house prices. Noe ha esimaing an ECM is only valid when here is a coinegraion vecor, i.e. wo or more variables are coinegraed and are subjec o a long-run relaionship. From he ECM we can derive he speed of adjusmen owards he long-run equilibrium. More formally: Y = β X + γ ECT + ε (12) 1 Where: ECT = + µ (13) 1 1 In his equaion γ represens he speed of adjusmen, and is he firs-difference operaor, where ECT -1 can be inerpreed as he deviaion from he long-run equilibrium. γ should be smaller han 0, implying ha here is convergence owards he long-run equilibrium. No consan is included in his framework, since we implicily assume ha here is no deerminisic increase/decrease in he price of housing. Case sudy: he Belgian housing marke In order o es he model we use he Belgian case. Regional characerisics heavily influence he housing markes mechanisms and herefore we shorly describe he Belgian housing marke. Homeownership is he enure choice of he large majoriy of households (75%). There are more firs-ime buyers relaive o second ime buyers due o high ransacion coss which amoun o 20% of he house (11)
Mixié : an urban and housing issue? 10 price. Approximaely 85% of he purchases is morgage-financed (Heylen, 2007). A fixed, long erm ineres rae is almos sandard, wih excepion of he years 2005 and 2010, when variable ineres raes were more common. The governmen imposed caps on he yearly adjusmen of variable ineres raes o proec cusomers, which possibly invoked morgage providers o se higher margins on he variable ineres rae, making hem less aracive for cusomers. Homeownership is fiscally favorable, which implies ha households have an incenive o buy a house relaive o rening one in he privae marke. The share of social housing is negligible. Belgium is densely populaed and land is relaively scarce. Building plos are mosly owned by privae individuals, who consider i as a good invesmen. We hus assume ha he supply of housing is raher inelasic due o land consrains, and hence, he link beween house prices and consrucion coss is minimal 6. Since 2005 he morgage ax relief 7 is replaced in Belgium by a morgage repaymen ax relief for firs homes only. This is generally a ax relief wih a fixed amoun, around 2770 / year per person 8, while he previous ax relief was around 2500 / year per household (e.g. Valenduc, 2008). For he majoriy of households, he ax relief hus more han doubled. This ax relief should be muliplied by he marginal ax rae of abou 50% o ge he ne effec of he ax relief. Alhough here is mixed evidence abou capializaion, i seems plausible o assume ha a ax relief will be more easily capialized if he ax relief is comprehensive and easy o calculae, which is he case for Belgium. Because of hese fiscal incenives he expeced cos of owning a house is less han he cos of rening, and hus housing enure is no neural. Households have a serious incenive o buy a house as reurns for homeowners ouperform hese for landlords due o fiscal and governmen policy. Households can be considered as he driving force for house prices, since hey consiue he vas majoriy of buyers. We use annual aggregaed daa for Belgium for he period 1973-2008. Since he purchasing power for housing focuses on morgage-based financing and affordabiliy, annual median sales prices for normal houses are aken as a reference. 9 We assume ha his is he main caegory of houses sold. Furhermore we perform some robusness checks by performing similar regressions for boh Q75 and he mean. The median house price is in line wih hose of aparmens, bu far lower han he prices for villa s. Ideally we would have income saemens of young 2-person households (age 30-35), bu since hese are no available for his period we compose a number of new ime series based on differen evoluions of income. For annual changes we ake he indices of nominal GDP, nominal GDP/capia, and nominal GDP/(capia > 20 years) wih reference year 2005. As a reference for 2005 we ake he median of he nominal afer-ax income for a 2-persons household of age 30-35. Annual income is afer-ax income for he year 2005 muliplied wih he index of he corresponding year. The ineres rae ha is used o compue he purchasing power for housing is he nominal long erm morgage ineres rae. Furhermore we make differen scenarios on how people use he ax relief ( woonbonus ). We develop hree differen scenarios. Firs, people do no consider he ax relief as an addiional means of income. Second, people consider he ax relief as an addiional income, bu incorporae i only rigidly. Third, people incorporae he ax relief fully from 2005 on. The las scenario implies ha his addiional income is fully capialized in he house price. We assume ha people are willing o inves a fixed fracion of heir disposable income (30%) for housing and furhermore assume ha he down paymen raio is consan over ime (20%). Since no daa is available on hese wo variables, we fix hese by assumpion. A las imporan disincion is on he duraion of morgages. Up o 2005 we assume ha he morgage duraion is fixed a 20 years. This is a reasonable assumpion. In 2005, however, a ax relief is inroduced. Due o fiscal opimizaion we again differeniae hree differen scenarios. In a 6 See Meen (2002) for a discussion. 7 The earlier morgage ax relief was a combinaion of a fiscal advanage on boh ineres and capial repaymens. 8 The ax relief is indexed each year. For 2005 i was 2490 per person, while in 2010 i was 2770. Afer 10 years, his amoun decreases wih approximaely 600. For households wih more han 3 children a he sar of he morgage here is an addiional 70 euro. 9 Adminisraive sales daa are spli ino 3 caegories: aparmens, normal houses and villa s.
11 Workshop 01: Housing Finance and Regulaion firs scenario he morgage duraion is unadjused and remains fixed a 20 years from 2005 onward. In he second scenario he morgage duraion is adjused o 22 years. The hird scenario considers he possibiliy ha morgage duraion shifs o 25 years. Again, due o lack of daa availabiliy, we consider differen scenarios as robusness checks. Resuls Table 2 presens a summary of he possible coinegraion relaionships we find in he daa. I indicaes a coinegraion relaionship a he 10% level. As menioned before adjused criical values are used. The able presens only he resuls of he base model. Table 2. Coinegraion relaionships base-model Tax relief No incorporaed Rigid adjusmen Fully incorporaed Duraion (from 2005 on) 20 22 25 20 22 25 20 22 25 Price Q50 GDP x x (Y) GDP/capia x x x GDP/(capia>20) x x x Q75 GDP GDP/capia GDP/(capia>20) x x Mean GDP GDP/capia x GDP/(capia>20) x The able indicaes ha here is poenial evidence for a coinegraion relaionship beween purchasing power and he house price. The mean house price is clearly coinegraed wih purchasing power when we assume ha households fully incorporae he ax relief ino heir budge. This implies ha he ax relief is fully capialized in he price of housing. Despie ha we esimaed a raher simple model - he model conains only one explanaory variable - we find a number of coinegraion relaionships indicaing he presence of a long-run equilibrium. Table 3. Coinegraion relaionships (model wih demographics included) Tax relief No incorporaed Rigid adjusmen Fully incorporaed Duraion (from 2005 on) 20 22 25 20 22 25 20 22 25 Price (Y ) Q50 GDP x x x GDP/capia x x GDP/(capia>20) x x x Q75 Mean GDP GDP/capia GDP/(capia>20) GDP GDP/capia GDP/(capia>20) Including demographics does no significanly aler he resuls as obained by he base model. Again, a number of coinegraion resuls are idenified. x x x
Mixié : an urban and housing issue? 12 Table 4. Coinegraion relaionships (model wih consan) Tax relief No incorporaed Rigid adjusmen Fully incorporaed Duraion (from 2005 on) 20 22 25 20 22 25 20 22 25 Price Q50 GDP x x (Y ) GDP/capia x x GDP/(capia>20) x x Q75 GDP x x x GDP/capia x x x GDP/(capia>20) x x x Mean GDP x GDP/capia x GDP/(capia>20) x Finally, including a consan in he model shows an increase in he number of coinegraion relaionships. Furhermore, observe he rade-off beween incorporaion of he ax relief and morgage duraion. Individuals have an incenive o increase morgage duraion whenever house prices increase. The ax relief is also likely o be incorporaed ino he house price. However, we are no able o idenify beween hese wo effecs. This does however no invalidae our previous conclusions. Table 5 presens some summary saisics concerning he parameer esimaes for which a coinegraion relaionship is found. Table 5: Average value β regression model (when coinegraed) Model Base model Base + Demographics Base + consan Price Q50 0.92595619 0.92602974 0.85361611 Q75 1.2547974 1.2846864 1.1166972 Mean 0.96373931 0.96786714 0.87596142 Alhough his able does no provide all informaion i gives some imporan insighs. Observe, for example, ha he coefficien esimae is dependen upon he price. Obviously, he coefficien esimae for Q75 is higher han he equivalen esimae for Q50. Furhermore we noice ha he esimaes for he mean are close o one, which is wha we would expec if he mean house price is fully deermined by he purchasing power of housing. The esimaed coefficiens sugges ha here is a one-o-one connecion beween he house price and purchasing power. McQuinn and O Reilly (2007) examined in heir model of cross-counry house prices a similar approach, bu wih he variables in logs. This is mainly due he fac ha heir saring poin differs. They assumed ha he shor-run price of housing depends on he amoun ha can be borrowed, while we assume o be i on he long run. Neverheless, hey also found coinegraion relaionships beween house prices and he amoun borrowed by households. However, heir parameer esimaes - on average a coefficien of 0,6 for 16 OECD counries for he period 1980:Q1 o 2005:Q4- are harder o inerpre in he log-specificaion (P = e α X β). Their migh be an idenificaion problem beween he α s and heir β s. In a period of high house price increase one should expec ha he β would be a leas 1. Based on previous ables we choose o presen he esimaion resuls for he median price and he model wih boh purchasing power and a consan. The regression resuls are in able 6.
13 Workshop 01: Housing Finance and Regulaion Table 6: Regression resuls base model + consan (Q50) Q50 Coef. Robus P> Diagnosic ess Sd. Err. Rigid GDP PP 0.85043 0.01830 46.47 0.000 R 2 = 0.981 adjusmen Consan 6857.89 1342.885 5.11 0.000 RMSE = 5309 of ax relief, GDP/ PP 0.86472 0.02073 41.71 0.000 R 2 = 0.979 morgage capia duraion 25 Consan 4985.52 1452.473 3.43 0.002 RMSE = 5607 years from GDP/ PP 0.87591 0.02103 41.63 0.000 R 2 = 0.979 2005 on capia > 20 Consan 3472.59 1480.622 2.35 0.025 RMSE = 5671 years Fully incorporae GDP PP Consan 0.86303 6333.83 0.03054 1648.589 28.26 3.84 0.000 0.001 R 2 RMSE = 0.976 = 5994 ax relief, GDP/ PP 0.87625 0.03369 26.00 0.000 R 2 = 0.973 morgage capia Consan 4502.75 1805.051 2.49 0.018 RMSE = 6390 duraion 22 years from 2005 on GDP/ capia > 20 years PP 0.88780 0.03423 25.94 0.000 R 2 = 0.972 Consan 2958.56 1857.329 1.59 0.120 RMSE = 6444 Table 6 displays he regression resuls for 6 differen specificaions, he variables of which are all coinegraed. Observe he small sandard errors due o he superconsisency of parameer esimaes when he variables are coinegraed. The coefficiens for purchasing power (denoed by PP) show ha here is almos a one-o-one relaionship beween purchasing power and he median price of housing. Figure 5: Acual values vs. fied values (Levels) 0 50000 100000 150000 1970 1980 1990 2000 2010 year Fied values Q50 Q50woonhuizen house prices
Mixié : an urban and housing issue? 14 The figure 5 displays he acual values versus he fied values of he model in levels. A coinegraion relaionship is presen using his specificaion. The model does reasonably well explaining he general evoluion. Now ha we have shown he long-run equilibrium relaionship beween purchasing power and he price of housing we can also esimae shor-run dynamics by inroducing an appropriae ECM. The error correcion model exends a regular model in firs-differences by including he lagged (1 period) residuals of he model in levels. Noe ha hese residuals are o be inerpreed as deviaions from he long-run equilibrium. The coefficien for he error correcing erm (ECT) displays he speed of convergence owards he long-run equilibrium. Since he firs hree specificaions perform reasonably well (based on he RMSE-saisics), we show he resuls of he ECM s for hese specificaions. Table 7 displays he resuls of he hree ECM s. Table 7: Error Correcion Models Q50 Coef. Robus P> Diagnosic ess Sd. Err. GDP PP 0.6394626 0.07755 8.25 0.000 R 2 = 0.7028 ECT -1-0.26969 0.13515-2.00 0.054 RMSE = 3476.2 GDP/capia PP 0.6343608 0.08270 7.67 0.000 R 2 = 0.6734 ECT -1-0.25270 0.13737-1.84 0.075 RMSE = 3644.1 GDP/capia > PP 0.6330462 0.08399 7.54 0.000 R 2 = 0.6675 20 years ECT -1-0.25351 0.1372-1.85 0.074 RMSE = 3676.8 The ECM s clearly show he shor-run dynamics beween Q50 and PP, where PP denoes purchasing power. Observe ha he median price of housing increases wih approximaely 0.63 euro if purchasing power increases by 1 euro. Furhermore observe ha he error correcion erm is negaive and significan (a he 10% level). I hus seems appropriae o sae ha here convergence owards he long-run equilibrium is presen. Whenever here is a deviaion from he long-run equilibrium, a correcion akes place. Noe however, ha he RMSE s as repored are raher high implying an imperfec fi of he model. This migh be due o misspecificaion of shor-run dynamics in our model. Conclusions The approach of he purchasing power for housing is somewha unconvenional. Variables in nominal erms, levels wihou log-specificaion, and a specific modeling of he ineres rae in funcion of he morgage duraion are no sandard conceps in house price lieraure. However, he purchasing power for housing faciliaes he inerpreaion of he impac of differen financial variables ino which he house price can be decomposed and gives good empirical resuls for Belgium. I ranslaes a microeconomic finance mechanism o he macro-economic house price explanaion. The semi ineres rae elasiciy is higher han generally found in lieraure, which no even capures he effec ha he ineres rae is also a faciliaor for longer morgage duraions. However, longer morgage duraions iself canno be capured by he purchasing power for housing concep. In he case of Belgium, we inroduced an innovaion, where morgage duraion could increase because of fiscal opimizaion of he ax relief. This ax relief (2005) is easily incorporaed ino he model and he model showed evidence ha i is fully capialized ino he house prices. This is in line wih he fac ha he Belgian house price index performed he highes climb beween 2005:Q1 and 2008:Q4 among 20 counries on he basis of OECD daa. Increased governmen suppor in he form of higher ax reliefs affecs house prices, jus as income and ineres raes do, which is quie inuiive.
15 Workshop 01: Housing Finance and Regulaion McQuinn and O Reilly (2007) also found ha house prices are coinegraed wih he amoun borrowed for 16 counries. However, he link beween he parameer esimaes and longer morgage duraions, as observed in many counries, as well as new financial producs and policy inervenions is no easy o inerpre in heir modeling approach. The main focus of his paper is an enlargemen of he price-o-income raio. This raio could raise over ime, bu a more han equivalen ineres rae decrease could lead o lower repaymens a he same ime. Hence, i is more suiable o compare house prices wih he purchasing power for housing, which is acually an affordabiliy measure. If his raio mouns up, i means ha house prices increase more han wha households could afford on he basis of income and ineres evoluion, resuling in a longer invesmen horizon (higher down paymens or longer morgage duraion), or a higher repaymen raio. ECM s are suiable o correc for his in he shor run. However, his paper provides heoreical background o model he raio beween house price and purchasing power for housing direcly since here is evidence ha boh series are coinegraed. Variable ineres raes are no addressed in his paper bu ineresing for fuure research. Is he consumer surplus represened by he difference in wha households would acually pay in he shorerm in erms of ineress on variable ineres raes and wha hey would pay in erms of ineress on fixed ineres raes, also capialized in house prices? In his case, he affordabiliy risk is shifed o laer periods. References Berger T., Englund P., Hendersho P. & Turner B. (2000) The capializaion of ineres subsidies: evidence from Sweden. Journal of Money, Credi and Banking 32 (2) pp. 199-217. Berkovec, James & Fulleron, Don, 1989. "The General Equilibrium Effecs of Inflaion on Housing Consumpion and Invesmen," American Economic Review, American Economic Associaion, vol. 79(2), pages 277-82, May. Bourassa S.C. & Grigsby W.G. (2000) Income ax concessions for owner-occupied housing. Housing Policy Debae 11 pp. 521 546. Brounen D. & Neueboom P. (2008) De effeciviei van hypoheekreneafrek. Economisch Saisische Berichen 4529 120-121. Brunnermeier, M. K. and Julliard, C.,2006. Money Illusion and Housing Frenzies.NBER Working Paper No. 12810, Caballero, R. (1992) A fallacy of composiion, American Economic Review, v. 82, p.1279-1292. De Vries, P. & P.J. Boelhouwer (2009) Equilibrium beween Ineres Paymens and Income in he Housing Marke, Journal of Housing and he Buil Environmen, pp.19-29 Gallin, 2006 J. Gallin, The long-run relaionship beween house prices and income: evidence from local housing markes, Real Esae Economics 34 (3) (2006), pp. 417 438 Gan, Q. & Hill R.J., Measuring housing affordabiliy: Looking beyond he median, Journal of Housing Economics, Volume 18, Issue 2, June 2009, Pages 115-125. Gyourko, Joseph, Chrisopher Mayer and Todd Sinai. 2006. Supersar Ciies, NBER working paper. Heylen, K., Le Roy, M., Vanden Broucke, S., Vandekerckhove, B.& Winers, S. (2007), Wonen in Vlaanderen. De resulaen van de Woonsurvey 2005 en de Uiwendige Woningschouwing 2005, Deparemen Ruimelijke Ordening, Woonbeleid en Onroerend Erfgoed
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