Institutions, Credit rationing and housing development

Transcription

1 Insiuions, Cedi aioning and housing developmen Fenanda Bollo and Fenando Gacia São Paulo School of Economics, Geulio Vagas Foundaion, Bazil Absac One of he basic pinciples ha allow a smooh opeaion of he makes is he equilibium beween supply and demand. Accoding o his pinciple, when demand exceeds supply, he pice mechanism will y o bing he sysem back ino equilibium. When his hinking is applied o he housing make, i leads o he conclusion ha any inequaliy in housing supply o demand is ansioy. Noneheless, he fac ha a consideable shae of he populaion live in pecaious homes fo geneaions seems o speak agains he viues of make mechanisms in he esoluion of housing disequilibia. Sigliz and Weiss (1981) ague ha in he face of asymmeic infomaion, unde some condiions he equilibium of he cedi make can be maked by aioning. Asymmeic infomaion woking hough he effecs of advese selecion and of incenive has impacs on he eun funcion of bank loans, which leads o inees aes used in housing loans o be diffeen fom hose ha balance supply and demand fo cedi, causing cedi aioning. Lieaue of he New Insiuional Economics (NIE) in un poins ou he fac ha insiuions can educe he degee of unceainy by lessening he effecs of asymmeic infomaion. Regading he housing make, he degee of popey ighs, as well as he mogage insiuion which acs as a conac enfocemen ool, povide he cedi make wih infomaion on he qualiy of he boowe and hus boaden he social scope of his make. The pupose of his aicle is o undesand how he equilibium in he housing make is influenced by cedi aioning and o wha exend insiuional developmen affecs his scaciy and he inees aes of housing loans. The model developed in his aicle, which combines he adiion of dynamic models of housing invesmen wih he pemises of he New Insiuional Economics and he consideaions of Sigliz and Weiss (1981) and (1992) on aioning in he cedi make, allows us o idenify he ole of insiuions on housing developmen. Key-wods: Popey ighs, Mogage foeclosue coss, Asymmeic infomaion, Raioned cedi make, Housing developmen JEL Code: R21, R31, G21, D23

2 1. Inoducion One of he basic pinciples ha allow a smooh opeaion of makes is he equilibium beween supply and demand. Accoding o his pinciple, when demand exceeds supply, he pice mechanism bings he sysem back ino equilibium, educing demand o inceasing supply unil a balance is eached whee no shoage of goods is found. The lack and suplus of goods in make ae, wihin his conex, ansioy siuaions ha empoally bind wo sable equilibiums. When his hinking is applied o he housing make, i leads o he conclusion ha any inequaliy in housing supply o demand is also ansioy. A possible excess of demand caused, say, by a demogaphic boom o by a lage migaion flow would aise housing pices in a given egion, i.e., leading o highe ens. These highe pices would in un igge new invesmen, consideing ha a a given inees ae, he yield of eal esae invesmen would be moe aacive han ha of ohe invesmen alenaives. In he case of a family ening a home, highe en in compaison o he inees ae would signal ha his would be a good ime o seek a mogage. In he case of a family wih savings, his highe en would ell hem ha his would be he igh momen o use hei asses invesed in ohe ways o buy a home. In eihe case, a shoage of homes in he make would lead, hough highe pices, o geae eal esae invesmen, wih a simulaneous gowh of boh demand and supply of cedi in financial make. The pice mechanism in housing makes was fis fomalized in Muh (196), lae impoved on by Muh and Goodman (1989), summaizing he housing-make analysis in he paial equilibium adiion. By admiing he exisence of an homogeneous housing sock, he capaciy o geneae housing sevices became an inceasing funcion of he capial sock. Following his adiion, he financial make supplies all he necessay capial fo invesmen in he housing make, a fac which endes any disequilibia ansioy. The same agumen of invesmen behavio was esablished in a dynamic conex by Tobin (1969). Consideing he case of housing make, Tobin s q can be defined as he aio beween housing make pice and he cos of eplacing a housing capial uni. This elaive pice would signal he eal esae make, which pice would also eflec he ne eun of housing invesmens. In his ap- 1

3 poach, eal esae appeciaion is given by he diffeence in cuen pice and expeced value of housing capial, less is depeciaion, plus he en owned. The equilibium condiion in he financial make, which pesupposes he exisence of abiage, imposes he equaliy beween he eun on invesmen and he make inees ae. Any excess demand fo housing sevices would appeciae eal sae make pice elaively o he cos of eplacing a housing capial uni, leaving Tobin s q highe han 1, which induces invesmens. A he long em, housing capial accumulaion would incease he supply of housing sevices cleaing his make. The excess demand lass only fo he ime necessay fo he planning and building of new homes. 1 One aspec in common in all hese appoaches is he pefec cedi make pemise, which povides all he necessay capial o cay ou he desied eal esae invesmens. Noneheless, if he capial make does no supply he necessay capial fo caying ou he desied eal esae invesmens, he ise in en pices caused by an excess demand will no necessaily subside. Consequenly, hee will be ohe facos affecing he equilibium in he eal esae make. In paicula, if he housing cedi make is aioned, fo any eason whasoeve, he adjusmen dynamics can be diffeen fom ha analyzed by he appoaches above descibed. In addiion, he fac ha a consideable shae of he populaion, paiculaly in less-developed naions, has lived in pecaious homes fo geneaions appaenly speaks agains he viues of make mechanisms in he esoluion of housing disequilibia. We use he wod appaenly, because in mos of hese naions, i mus be said, boh he eal sae make as well as he cedi make ae no necessaily of he so ha ensues sable dynamic equilibiums wihou aioning. The line of hinking descibed above assumes a seies of condiions o achieve his, which ae no necessaily fulfilled in developed counies and mainly in developing naions: (i) popey ighs mus be secued; (ii) legal safeguads mus ensue he binding of conacs; (iii) boh he en and he inees ae mus be feely se by he paies; and (iv) hee mus be only one financial make, which efficienly allocaes savings. 1 Following he adiion of aional expecaions, Sheffin (1983) sums up he pevious agumens and fomalizes a dynamic model of housing, in which appeciaion of housing pices, inflaion, and axes dive housing invesmens. 2

4 Obviously, if one o moe of hese condiions is no fully saisfied, he make mechanisms will lose hei equilibium-seeking chaaceisics and he elaive scaciy will no be addessed auomaically along ime. This happens because in a make in which hese condiions ae no pesen, he eun on invesmens will be suounded by unceainy and eal esae cedi could be aioned. Sigliz and Weiss (1981) ague ha in he pesence of asymmeic infomaion, he equilibium of he cedi make can be aioned, in he sense ha, among appaenly idenical cedi applicans, some ae able o secue cedi and ohes no, o hee ae some paicula goups of individuals in sociey ha ae edlined fom he cedi make. This happens because when banks povide cedi, hey y o maximize hei eun by focusing on he following wo aspecs: he cos of loanable funds, and he isk involved in he pojec undeaken. Accoding his auhos, because he impefec make infomaion, he ems of cedi conacs he need fo collaeal and he inees ae se by he bank as well as he amoun of he loan can indeed affec he qualiy of he goup of boowes in wo ways: (i) he advese selecion effec of boowes 2 ; and (ii) he incenive effec 3. This aicle analyzes he eal esae make, emphasizing he ole of cedi in long-em adjusmen. I goes on o evaluae how asymmeic infomaion and he absence of liquidiy mechanisms, he esul of he lack of he fou condiions descibed above can end up aioning eal esae cedi. Finally, i suggess a aioned-cedi model fo housing make, in which he sho-em inees ae, cedi availabiliy and insiuional developmen play a fundamenal ole in he equilibium of he housing make. 2 By dissuading safe invesos, i.e., hose who inves in less isky pojecs, fom seeking loans in banks, he conac can change he disibuion of he goup of boowes. Consideing ha he bank s expeced eun depends on he pobabiliy of hose loans being epaid, boowes who ae awae of he scan pobabiliy of paying back hei loans and ae willing o pay highe inees aes will auomaically be consideed low-qualiy boowes. Likewise, inasmuch as highe guaanee demands educe he aveage degee of isk-avesion of he goup of boowes, he banks eun is also educed. 3 The incenive effec eflecs changes in he behavio of invesos, who pefe highe-isk pojecs. Adjusmens in he pime inees ae (which is also a pa of he loan s cos) and in he ems of he conacs {C, } affec he behavio of he boowe: wih a highe pime inees ae, we see a educion in he expeced eun fo he inveso of he pojec o be financed, which leads such inveso o seek highe-isk pojecs. These ae pojecs wih slim chances of success, bu if successful can bing subsanial euns. 3

5 2. Raioning in cedi make: he geneal agumen Following Sigliz and Weiss (1981), in a make wih impefec infomaion, banks do no know how o sceen he individual boowe, because hey ae no able o diecly conol he acions of all boowes 4. Thus, loan conacs ae dafed so as o induce boowes o ake acions ha ae of inees o he bank and o lue high-qualiy boowes, wih low-isk pojecs. One of he mechanisms ha help so ou good and bad boowes is he loan s inees ae. Fo a given inees ae, he expeced pofis of he fim incease wih he isk of he pojec. To see if he inees ae acs as a poecion mechanism fo banks, he following is se by he auhos: fo a given loan inees ae ( ˆ ), hee is a ciical value of isky pojec θˆ fo which he agen boows fom he bank, if and only if θ > ˆ θ. Supposing ha all loans have he same amoun, he ne eun fo he boowe is descibed by equaion (1). In his equaion, he inveso s expeced eun is he highe of he following values: (i) he level of wealh (W), plus he eun of he pojec (R), less he amoun of he loan, ineess included (B +.B); o (ii) he level of wealh, less he amoun of he collaeals equied by he cedi conac (C). The fis value holds if pojec is successful, ohewise holds he second value. Theefoe, he value of θ fo which he agen s expeced eun is zeo mus saisfy he following condiion: (1) (, θ) max[ W + R ( + 1) B; W C] df( R, θ), whee i is he pime inees ae, W is he iniial level of wealh, C denoes he pesen value of collaeal C. Theefoe, W W (1 + i) and C C (1 + i). Analyzing he cedi supply side, he banks expeced eun on a loan, because of he advese selecion effec, is a deceasing funcion of he isk degee of he loan and is given by expession (2). Accoding o his equaion, he boowe mus pay o he bank he oal amoun of he deb o he mos he can pay if he pojec failues, (R + C). 4 In his pape, we conside only loans supplied by he fomal cedi make. An exension of his agumen o an economy wih infomal cedi make, in which social noms ae he ue mechanism of conac enfocemen, could be seen in Ghosh, Mookhejee and Ray (2). 4

6 (2) ρ ( R, ) min( R + C; B(1 + )) The advese selecion agumen, in which highe inees aes can lead o falling bank euns, comes fom he fac ha on aveage he qualiy of he boowes deeioaes; i.e., he highe he inees aes, he geae he value of θ. This esul is obained when equaion (1) is diffeeniaed: θˆ d B df( R, θˆ) (1+ ) B C > d / θˆ The second way in which he inees ae affecs he banks expeced eun on ganed loans is he change in boowe behavio: as climbing inees aes aise he aaciveness of high-isk pojecs, he banks eun is diminished. Theefoe, wih an incease of, he expeced eun of a pojec wih a high chance of liquidaion falls less han he expeced eun of a pojec wih a smalle chance of liquidaion. If a isk-neual inveso feels indiffeenly befoe wo pojecs, a ise in he inees ae will lead he agen o choose he pojec wih a smalle chance of liquidaing he loan. Fom his agumen follows he main poposiion abou he elaion beween loan inees ae and he expeced eun of banks. Accoding o his poposiion, ρ() will no be a monoonic funcion of, which implies ha hee will be a ρ, associaed o, ha maximizes expeced euns of banks. Since is supposed ha loans supply is an inceasing monoonic funcion of he expeced eun of banks, hee will be a level L of loans supply ha maximizes banks pofis. Figue 1 illusaes how he cedi make woks when he inees ae is used as a shield agains he incenive effec and he advese selecion effec ha can educe he banks expeced eun. In figue 1, he hid quadan shows he banks cedi supply in elaion o he expeced eun: he highe he loan s expeced eun, he geae he cedi offeed. Howeve, as shown in he second quadan, he banks expeced eun inceases a deceasing aes in elaion o he inees ae. Theefoe, hee is an opimal ae of inees, ha maximizes he banks expeced eun, above which his eun sas o decease. A equilibium inees ae, which maximizes he banks expeced eun, hey supply L. Any loan inees ae incease above would also educe loan supply. 5

7 L L D Z L L S L S L m ρ ρ Figue 1: Equilibium in he aioned cedi make Consideing ha loan demand is a deceasing funcion of loan inees ae, which is also illusaed in he fis quadan of figue 1, fo some supply of loanable funds, hee is any excess demand fo cedi, illusaed by he diffeence Z, beween L D and L S, which pevail a inees ae. I can be seen ha in a scenaio of excess demand fo loans, hee ae boowes willing o pay inees ae m >, which is he inees ae a which demand maches supply. Bu consideing ha banks seek o maximize hei pofis, hey will no lend o individuals who ae willing o pay a ae above. Evenually, as agued by Sigliz and Weiss (1981), he incease in loanable funds would shif upwad he loan supply cuve, educing he excess demand fo funds, bu wihou any change on loan inees ae. Only if he demand fo funds is fully saisfied, i.e., when hee is no cedi aioning, inceases in loanable funds will pomoe a decease on inees aes. As a consequence, he cedi make does no have compeiive foces ha lead, in any siuaion, he supply of funds o mach is demand, and cedi is heefoe aioned. 6

8 Howeve, accoding o Sigliz and Weiss (1981), he inees ae is no he only conac faco ha maes. The amoun of he loan and is collaeals also affec he boowes behavio. If banks demand highe guaanees, his can lead o boowes willing o bea smalle isks, in less isky pojecs. On he ohe hand, demand fo highe collaeal can lead o a educion in he banks eun: if hee is oal avesion o deceasing isk, and if all individuals (wih idenical uiliy funcions) face he same invesmen oppouniies, wealhie individuals will be moe willing o offe moe collaeal, which illusaes hei disposiion o embak on iskie pojecs han ae less wealhy individuals. The effec of his advese selecion can dominae he posiive effecs of collaeal equiemen. As a consequence, hee is also a limi afe which i is no longe lucaive fo banks o aise he equiemen fo guaanees in he pesence of excess demand fo cedi, jus as i happens wih he loan s inees ae. Thus, he aioning of he cedi make akes place if he following hee condiions ae me: (i) hee is impefec infomaion; (ii) he effecs of advese selecion and incenive ae consideable; and (iii) he banks expeced eun unde he Walasian equilibium mus be lowe han in any ohe conac wih cedi aioning. In Sigliz and Weiss (1992) his analysis is expanded fo he case in which boh poblems incenive and advese selecion ae pesen. In his model, he banks use he equied guaanees and he inees aes as insumens o sceen and encouage boowes. One of findings of his wok is ha he whole class of loan applicans can be aioned and ha his aioning mus ake place wih evey conac. 3. The aioned cedi make fo eal esae pojecs Based on he Sigliz and Weiss (1981) and (1992) aioning model, i is possible o descibe a make fo lending o eal esae pojecs, wih mino changes. Le s iniially conside ha infomaion is impefec, ha is, banks do no know how o sceen he individual boowe cedi isk. Theefoe, he loan inees ae and he mogage equiemens end up being he mechanisms ha educe he effecs of advese selecion and incenive. Equaion (3) expesses he opimal loan inees ae, which is se up in ode o maximize bank s expeced euns. In he same way, we can define he amoun of cedi supplied by banks, 7

9 L, as a monoonic funcion of and of he amoun of loanable funds in eal esae make (S). (3) max ( ρ( R, )) ρ (4) L l, S), l > and l > ( S Noe ha he banks pofis ae defined as he diffeence beween and loan coss, which ae deemined by he economy s pime inees ae, he oppouniy coss, and he coss elaive o safeguading he popey ighs, incued, say, in evaluaing he value of he eal esae popey and in foeclosing mogages. In his sense, we say ha opeaional coss associaed wih he degee of insiuional developmen ae included in banks spead. 5 The cedi demand fo eal esae pojecs saisfies hee basic pemises: (i) i is segmened ino fou diffeen levels of wealh 6 Wc, Wb, Wba e Wa, such as Wc < Wb < Wba < Wa; (ii) wealh is compised eal asses, which can be used as collaeals C, being ha Cc < Cb < Cba < Ca, and of human capial income, fom likely inheiance and eiemen, H; and (iii) hee is a minimum iniial wealh level (Wi > C) o allow family i o be included in he goup demanding housing cedi, which will have is pojecs eviewed by he banks. Figue (2) illusaes agen s behavio in his make. Each individual has a safe invesmen alenaive wih eun ρ, wih expeced uiliy Ui(Wi, ). Families belonging o he c goup ae no pa of he cedi demand because hey do no possess he minimum wealh equiemen (Wc < C). Fo hese families, boh he expeced uiliy of invesing in a safe invesmen as well as ha of a self-financed housing invesmen ae geae han he expeced uiliy of aking ou a loan o undeake 7 a eal esae pojec. Families wih wealh beween Wb and Wa demand cedi, because he expeced uiliy fo aking ou a loan a he bank is geae han he isk-fee invesmen. Howeve, a subse of families, hose which have wealh locaed in he Wba ineval, will sill undeake a pojec, even if hey do no qualify fo a loan, because he expeced uiliy fom hese loans is above ha of ohe invesmen alenaives. Lasly, he goup Wa epesens he se of 5 By consucion, hese coss ae a nonmonoonic funcion of insiuional developmen. 6 Accoding o Sigliz (1981) i is supposed ha all boowes ae isk-avese wih he same uiliy funcion U(W), U >, U < and ha individuals diffe only when i comes o wealh. 7 Housing invesmen wih self-financing, fo low-income families, can be seen as self-building. 8

10 families wih he geaes wealh. The families in his goup do no need cedi and embak on isky invesmens in eal esae using only hei own asses. EXPECTED UTILITY BORROWING SELF-FINANCED RISKY INVESTMENT SAFE INVESTMENT ALL SELF- FINANCE SELF-FINANCED RISKY INVESTMENT W c W b W ba W a Wˆb ALL APPLY FOR LOANS Figue 2: The segmened housing cedi make W To bee undesand wha deemines he goup of families ha demand eal esae cedi and he easons fo which, and ha of families demanding bu no eceiving cedi undeake a eal esae pojec, i is necessay o analyze he expeced-uiliy funcion ha maximizes he eun of he pojec fo a given level of iniial wealh. Following Sigliz and Weiss (1981), families ha secue cedi and cay ou a eal esae pojec obain an expeced uiliy, given by he following expession: (5) max { (( 1) ) ( ) (( 1) )(1 ( ))} ˆ R U W ρ + R p R + U W ρ p R V ( W ), in which p(r) is he pobabiliy of a pojec being successful. The value ha maximizes he expeced uiliy of he inveso is he maximum eun beween a safe invesmen and a self-financed pojec V W ) max{ U( W ρ), Vˆ ( )]. I can be seen ha: ( W 9

11 du( Wρ) U ρ dw dvˆ ( W ) and [ U 1 p + U 2(1 p)] ρ. dw I can hus be esablished ha isk avesion is absoluely deceasing; he geae he family s iniial level of wealh, he lesse he expeced uiliy of he safe invesmen in elaion o he invesmen in a isky pojec wih self-financing, since: du( W dw ρ) dv W ) < ˆ ( dw Theefoe, hee is a ciical value of wealh Wb, such as, if he wealh is geae han his value, families no able o secue cedi sill embak on he eal esae pojec hese ae families in he ineval Wba. Fo families wih absolue and deceasing isk avesion and wealh below his ciical value, he expeced uiliy is give by equaion (6): (6) maxu( W ρ (1 + ˆ) + R) p + U(( W C) ρ )(1 p) V ( ). { B W R In his case, individuals ake ou loans if, and only if, V B W ) V ( ). Bu. ( W since dv B / dw ( U 1 p + U2(1 p)) ρ, only when Wi > C, i is pofiable o ake ou a loan. I is assumed ha hee is wealh diffeen fom zeo, called Wb, such as Vb(Wb) U(ρ,Wb) which is ue fo some values of ρ. Using he same agumen above, i becomes clea ha in Wb he ac of aking ou a loan ensues medium uiliy ha peseves he spead of eminal wealh in compaison wih no aking ou he loan and no embaking on he pojec. Theefoe, if dv B / dw > dw, dv( W ) / fo Wb < W < Wˆ b, all individuals qualify o ake ou a loan. Consideing ha W Wˆ < b, if hee is a loan, he wealhies individual will be he one benefied 8. I is ime now o analyze he effecs of changes in exogenous vaiables on he housing cedi make. Paicula aenion is given o he effecs on equilibium in egads o: (a) insiuional changes ha lead o a educion in he mogage ansacion coss; (b) changes in moneay policy ha imply in vaying he 8 This esicion is weake han he imposiion of a scale of pojecs ha exceeds he wealh of any individual. 1

12 cos of oppouniy of loans o of loanable funds; (c) policies fo he ganing of subsidies; and (d) policies ha secue popey ighs. (a) The effecs of a educion in he mogage ansacion coss The cos of foeclosing mogages is one of he componens of he banks oal loan cos ha is inimaely associaed o he legal sucue and o law enfocemen. In supposing a educion is such coss bough, say, by he ceaion of a eal esae fiduciay owneship ile he banks oal loan cos is hus educed and, when passed on o he loan s inees ae, changes he equilibium of he aioned cedi make. The effec of he educion in he cos of foeclosing eal guaanees on he demand and offe of cedi is shown in figue (3). EXPECTED UTILITY L L D BORROWING SELF-FINANCED RISKY INVESTMENT L S SAFE INVESTMENT L S SELF-FINANCED RISKY INVESTMENT ALL SELF- FINANCE W c W b W ab W a Wˆb ALL APPLY FOR LOANS W (a) (b) Figue 3: The educion in he cos of foeclosing mogages ρ The educion in he loan s inees ae gives he inveso s expeced-uiliy funcion in elaion o his iniial wealh (W) a seepe slope. This means ha equaliy beween he expeced eun of he safe invesmen and ha of boowing asses and embaking on he eal esae pojec becomes ue fo a lowe level of iniial wealh. This means ha he numbe of families ha seek cedi ises, fo a given wealh disibuion. The esul on he cedi supply of loanable funds is shown in figue (3.b). In he gaph s second quadan, we see he cuve ha elaes he loan s inees ae and he banks expeced eun shif downwads and 11

13 lefwads. This is aibuable o he educion in he incenive and advese selecion effecs, which igge an expansion of he banks expeced eun a he same ae of he loan s inees ae. In he hid quadan, which epesens he elaion beween he offe of funds and he banks eun, we see a ise in he supply of housing cedi, up o he poin whee he new aioned-equilibium inees ae is eached he one ha maximizes ρ. Lasly, in he fis quadan, which epesens he elaion beween he loan s inees ae and he supply and demand of funds, we can see he ise in demand on he cuve L D, epesening an incease in he numbe of families demanding mogage cedi, and he upwad and lefwad shif of supply cuve. A his new equilibium, hee is an offe L geae han he pevious one, all ohe consan paamees emaining consan. The new esuling equilibium also povides fo cedi aioning; howeve, i can be geae o lesse han he pevious one, depending on he slope of he wo cuves. (b) The effecs of moneay policy: highe liquidiy Analyzing he demand fo loanable funds, a cu in he inees aes educes he cos of oppouniy of a isk-less invesmen govenmen bonds, fo example ha offe euns a ae, and inceases availabiliy of funds fo housing loans. This change educes he slope of he expeced-uiliy cuve of he iskless invesmen in figue (4.a), and causes he supply cuve of he fis quadan of figue (4.b) o shif upwads and lefwads. On he ohe hand, hee is a dop in loan coss and a consequen ise in euns of boowing and embaking on a housing pojec, which shifs he loan s expeced-uiliy cuve upwads and lefwads. I can be seen ha wih diminishing inees aes, i is expeced ha he supply of loanable funds ises and eaches ha lowe-income shae of he populaion. Hee we have he pemise ha hee ae auomaic mechanisms fo channeling liquidiy fom he financial make o he housing-cedi make. Should no such mechanism exis, an effec on he cedi supply lesse han ha of equilibium wih an auomaic expansion of he cedi supply can be expeced. Cedi eaching he lowe-income segmens of he populaion can be explained by he incenive effec: he moe divesified he cedi, he less is he isk of he pool of boowes. 12

14 EXPECTED UTILITY BORROWING L L D SELF-FINANCED RISKY INVESTMENT SAFE INVESTMENT L S L S SELF-FINANCED RISKY INVESTMENT ALL SELF- FINANCE W c W b W ab W a Wˆb ALL APPLY FOR LOANS W (a) (b) Figue 4: Highe liquidiy in he cedi make (c) The effecs of a social policy of subsidies As seen above, in ode fo a family o join he housing-cedi make, i is necessay fo his family o have a minimum iniial wealh. Moeove, he highe he aio beween oal iniial wealh and he collaeal, he lesse he isk on he banks expeced eun, somehing which should diminish he possibiliy of cedi aioning. Noneheless, housing policies ha aise he lowe-income families iniial wealh level only expand aioning, if such policies ae no followed by a consisen cedi expansion. The lump-sum ansfe of wealh fom he iche o he pooe layes of sociey does no change he cuves in figue (5.a). Howeve, i does change wealh disibuion in sociey, aising he pecenage of families wih wealh in he ineval beween Wb and Wa. This effec is shown as he upwad shif of he cedidemand cuve in figue (5.b), which if no followed by a cedi expansion will lead o geae aioning. ρ 13

15 EXPECTED UTILITY L L D BORROWING L D SELF-FINANCED RISKY INVESTMENT SAFE INVESTMENT L S L S SELF-FINANCED RISKY ALL SELF- INVESTMENT FINANCE W c W b W ab W a ALL APPLY FOR LOANS (a) W ρ (b) Figue 5: The policy of subsidies (d) The effecs of secuing popey ighs To shed some ligh on he impoance of secue popey ighs, and is elaion wih he developmen of a cedi make, i migh be wohwhile o quoe De Soo (2). The auho agues ha hee ae families in poo counies ha hold subsanial asses, bu he lack of due popey ighs pevens hese asses fom being used as collaeal fo cedi puposes, hus limiing he poenial use of his popey. In conas, he cies he case of ich counies, whee popey ighs ae well defined and he full poenial of asses is exploied. This means ha wihin an envionmen whee popey ighs ae safeguaded, hee would be oom fo a seconday make fo mogage secuiies. Raising he level of wealh of hese families sokes he cedi make, which in un leads o housing developmen. Figue (6) shows he effecs of secuing popey ighs in he housing-cedi make. Consideing ha popey ighs aise he wealh of he families, he cuve of he families wealh is shifed ighwads, inceasing he numbe of families demanding housing cedi. Howeve, in ode o have a posiive effec of hese policies on he cedi make, and consequen impovemen of he housing developmen, i is no enough o secue popey ighs. If he cedi offe emains unchanged, he esul will be a highe excess demand fo cedi. 14

16 EXPECTED UTILITY BORROWING L LD L D SELF-FINANCED RISKY INVESTMENT SAFE INVESTMENT L S L S SELF-FINANCED RISKY INVESTMENT ALL SELF- FINANCE W c W b W ab W a ALL APPLY FOR LOANS W (a) (b) Figue 6: Popey ighs To peven he new demand fom deeioaing he aioning siuaion, hese new policies mus come hand in hand wih insiuional changes ha ensue safeguading measues fo mogage foeclosue. The easoning of he effecs of hese measues on he educion of bank coss, developed in case (a), would hen also apply, leading o geae cedi supply, as shown in figue (6.b). ρ 4. Saionay equilibium in he eal esae make wih aioning in he cedi make As analyzed in he pevious secions, aioned equilibium in he cedi make esponds o changes in wealh disibuion, in he economy s inees aes, and in he coss of foeclosing a mogage. Wealh disibuion and mogage foeclosue coss in un espond o insiuional changes. We mus now evaluae hese effecs on he dynamic equilibium of he housing make. This is done in his secion, incopoaing he mechanisms ha goven he cedi make in a housing invesmen model based on Tobin s appoach. To focus he analysis only on he effecs on he equilibium of a aioned cedi make, he basic sucue of he housing invesmen models is peseved as much as possible. I is assumed ha a any momen of ime, he economy has N families ha gow a a consan ae n. I is also consideed ha he demand of he epesenaive family fo enal popey (k d ) depends diecly on his family s wealh (w) and invesely on he value of he en (R), as shown in equaion (7). In he sho em, 15

17 he supply of eal esae popey is fixed expession (8) which implies ha he en ae is deemined only by demand condiions, as saed in equaion (9). d (7) k f ( w ) β. R, f > and β > w s (8) k k k (9) R f ( w ) k β Following Tobin (1969), q is defined as he aio beween make pice ( p ) and he eplacemen cos of one uni of housing capial ( c ) equaion (5.4). When q > 1, he make pice of one housing uni is geae han he cos of building an idenical housing uni. In his case, i is said ha hee is incenive o inves, moe specifically in ou case, in he building of new housing unis. If q < 1, convesely, i is cheape o buy a eady home han o build one; in his case he families ae no encouaged o inves in he building of homes. (1) p q c If we suppose ha he consucion cos is consan, q becomes he elaive eal esae popey s make value, and i will vay accoding o p flucuaions, which is deemined by eun, less depeciaion, povided by enal income. Fo he enal seco, he eun fom one peiod o he nex will be he aio beween he oal amoun available o he owne in he following peiod and he value of he popey in he iniial peiod. The oal amoun available o he owne in he subsequen peiod will be he following: he new make value of he popey, plus en income, less depeciaion of he pevious sock. Fo coninuous ime, equaion (11) defines he invesmen s ae of eun: q + R δq (11) Reun & q Because capial make is no pefec i can be affeced by asymmeic infomaion ha leads o cedi aioning families ae no able o fully abiage beween gains in he en make and hose fom he financial asses make. In fac, if he en income, ne of depeciaion, is above he inees ae, families will 16

18 have incenives o seek bank loans and inves in housing. Howeve, in a make of aioned cedi, no all families ha have he necessay condiions o apply fo cedi acually secue a loan. Fo his eason, euns do no convege: he eun of housing invesmen, due o cedi aioning, is geae han he inees ae of housing loans. Defining he inees ae p as he one which would pevail wee he cedi make pefec, he ae of eun can be expessed as follows. q + R δq (12) Reun & p q (13) p λ, λ 1 Noe ha, as illusaed in figue (7), p is he make inees ae ha would pevail if expeced eun of loans ρ wee a monoonic funcion of, i.e., if boh advese selecion and incenive effecs would no pevail. In such a case he supply cedi cuve would also be monoonic. If he cedi demand is fully saisfied, hen λ is null, implying ha p. L L D L S p Figue 7: Inees ae in boh aioned and non aioned cedi makes Fom his expession we deive he dynamic equaion of q expession (14). I should be noed ha he inees ae of housing loans, as fomulaed in 17

19 secion 3, is a funcion of he make inees ae, of mogage foeclosue coss, and of he ohe adminisaive coss, and is defined by he pocess in which banks maximize he eun of hei loans. Noe ha we assume a deceasing elaion beween he degee of insiuional developmen, given by law enfocemen and popey ighs, and he mogage foeclosue coss. In his sense, less insiuionally developed economies will show geae loan aes in housing cedi make. p f ( w ) k (14) q& (. q R ( λ. q β (15) k & i ( n k The accumulaion of he housing capial pe family is given by expession (15). Wha in essence changes is he invesmen funcion of he families. Hee i is defined wih he aggegaion of invesmen pefomed by hee wealh layes of sociey: a, b and c, such ha Wc < Wb < Wa. We assume ha all layes gow a a consan ae n. As aleady agued in secion 3, hee is a W, which is he minimum ciical wealh level ha a family mus have o belong o he aioned-cedi make, such ha Wc < W < Wb. The invesmen of families ha belong o he a and c layes ae self-financed, as descibed in secion 3, and i depends only on he eal esae make value, because hey ae supposed o be based on idenical and homoheic pefeence sucues. Equaion (16) expesses his elaion, whee π q 1 is he excess of eal esae make pice ove uni consucion coss, and σ >, showing ha a geae eal esae make value will simulae invesmens. (16) i c i a σ. π Fo he b laye of wealh, he invesmen funcion is defined by he sum of he financed invesmen, which is deemined in he equilibium of he cedi make L, wih self-invesmen pefomed by hose families ha seek cedi bu do no eceive i. Please noe ha L is he financed value of he popey, which can be expessed by he poduc of he numbe of conacs wih he pice of financed eal esae. On behalf of simpliciy, i is assumed ha he self-invesmen shae of his laye of wealh is idenical o he invesmen funcion of he ohe wealh layes. Expession (17) shows his elaion. 18

20 (17) i b l + σ.( π ) Loans pe family ( l ) in he aioned-cedi make ae given by equaion (18), which esablishes he basic elaion discussed in he las secion among he amoun of loans, inees ae, mogage foeclosue coss and loanable funds. (18) l g(, s ) In his equaion, a educion on he pime inees ae has posiive impacs on he cedi supply pe family, so ha g <. On he ohe hand, an expansion on loanable funds pe family ( s ) has a posiive effec on cedi supply, so ha, g s >. Thus, he invesmen pe family is defined by expession (19). Subsiuing his las expession in (2) we aive a he equaion of capial accumulaion. (19) i g(, s ) + σ.( q 1) (2) k & g(, s ) + σ.( q 1) ( n. k Equaions (14) and (2) fom a sysem of diffeenial equaions wih saddle sabiliy, as showed in he Mahemaical Appendix. Based on hese equaions, in he appendix we also deive he cuves of saionay dynamics of q and of k, as well as he seady sae equilibium. This sysem is showed in figue 8. q k& q q& k k Figue 8: Seady sae equilibium in housing make 19

21 Finally, i is wohwhile o poin ou he effecs of insiuional changes on he equilibium of he housing make, which compee wih changes in wealh disibuion and moneay policy. These effecs can be evaluaed by he model s compaaive saics, which is calculaed fom he applicaion of he implici funcion heoem in he sysem fomed by equaions (A.1) and (A.12), if all ohe paamees emain consan. ( λ 1 β dq λq fw d + β dw + ds n dk g g σ ( s Poposiions 1, 2 and 3 below bing he eacion of changes in he inees ae, in he economy s aveage wealh, and in he availabiliy of loanable funds in he equilibium of he housing make. Poposiion 1: A ise in pime inees aes depesses he pice of eal esae, bu his i can have eihe posiive o negaive impacs on he seady-sae sock of housing capial pe family. This conclusion emeges diecly fom he deivaes of q and k in elaion o. The fis deivae, dq β.( g.( λ λqσ <, d σ + β( n ( λ is negaive, since he numeao is negaive, unlike he denominao, which is posiive. Bu he second deivae could have eihe posiive o negaive signal, since g is a negaive paamee: dk ( g + λqβ( n ). d σ + β ( n ( λ Poposiion 2: The expansion of wealh aises make pices of eal esae and leads o a geae sock of capial. This esul comes fom he deivaes of q and k in elaion o w, due o he posiive effec of wealh on demand fo housing sevices: dq β. f w.( n dk β. f w. σ > and >. dw σ + β( n ( λ dw σ + β( n ( λ 2

22 Poposiion 3: An incease in loanable funds bings a seady-sae equilibium wih geae level of welfae, in which he housing capial pe family is highe, and he pice of eal esae is lowe. This agumen is implied diecly by he fac ha an expansion on loanable funds has a posiive impac on cedi supply pe family, as discussed in secion 3. dq ds g S σ + β( n ( λ dk g S. β.( λ < and >. ds σ + β( n ( λ Theefoe, he moneay policy ha leads o a low pime inees ae, alhough leaves eal esae invesmens moe aacive, does no necessaily leads o an incease in he sock of housing capial, since aioning on eal esae cedi make can inhibi housing invesmens. In is un, housing policies ha dive moe funds o cedi make, as a consequence of developing an envionmen whee popey ighs ae safeguaded, i.e. impoving he seconday make fo mogage secuiies, have unambiguous welfae effecs, since hey leads o low eal esae popey pices and high housing capial pe family. 5. Concluding emaks The model developed in his aicle, which combines he adiion of dynamic models of housing invesmen wih he pemises of he New Insiuional Economics and he consideaions of Sigliz and Weiss (1981) and (1992) on aioning in he cedi make, allows us o idenify he ole of insiuions on housing developmen. Economies ha bee ensue popey ighs, wih he effecs his has on wealh disibuion in sociey, each highe levels of housing developmen. This degee of popey ighs is inimaely associaed o he ganing of popey iles. In socieies in which land is no popely held, his aibuion is smalle, which in un educes he demand fo cedi and he ole his make can play in housing developmen. On he ohe hand, insiuions ha ensue due fulfillmen of conacs, such as legislaion ha allows auomaic mogage foeclosue, o a seconday make fo mogages, educe he ansacion coss and consequenly he inees ae of eal esae loans. This has a negaive effec on cedi aioning, which al- 21

23 lows banks o finance moe families, wih he consequen impac on housing developmen. The agumen fomalized in his pape cooboaes he agumens of Bazel (1997) and De Soo (2), among ohes, on he ole of insiuions and of popey ighs in economic developmen. Fuue eseach in his field should heefoe seek o empiically idenify if cedi is aioned and if popey ighs affec he equilibium pice of housing loans. In his aea, i is wohwhile o compae counies wih developed cedi makes and insiuions wih ohes in which neihe insiuions no he financial make ae developed. Refeences Bazel, Y. (1997): Economic Analysis of Popey Righs, Cambidge Univesiy Pess. De Soo, H. (2): The mysey of capial: why capialism iumphs in he Wes and fails eveywhee else. Basic Books. Ghosh, P., Mookhejee, D. and Ray, D. (2): Cedi Raioning in Developing Counies: An Oveview of he Theoy. In Mookhejee, D and Ray, D., A Reade in Developmen Economics, London: Blackwell (2). Muh, R.C. (196): The Demand fo Non-Faming Housing. In Habege, A.C.: The Demand fo Duable Goods. Chicago. The Univesiy of Chicago Pess, 196. Muh, R.C. e Goodman, A.C. (1989): The Economics of Housing Makes. Hawood Academic Publishes. Sheffin, S. (1983): Raional Expecaions. Cambidge Univesiy Pess. Sigliz J. E; Weiss A. (1981): Cedi Raioning in Makes wih Impefec Infomaion. The Ameican Economic Review, Vol. 71, No. 3, pp

24 Sigliz J. E; Weiss A. (1992): Asymmeic infomaion in cedi makes and is implicaion fo macoeconomics. Oxfod Economic Papes, New seies Vol. 44, No. 4, pp Tobin, J. (1969): Geneal Equilibium Appoach o Moneay Theoy. Jounal of Money, Cedi and Banking, vol 1, Mahemaical Appendix q & k & ( λ g(. q, s) + σ.( q f ( w ) k β 1) ( n. k J q& q k& q q& k k& k ( λ σ 1 β ( n J ( n ( λ. 1 σ. < β (A.1) f ( w ) k q & q β ( λ, dq 1 <.( ) dk β λ + δ q& (A.2) g(, s ) + σ.( q 1) k& k, ( n dq dk k& ( n σ > (A.3) q f ( w ).( n + g(, s ) + σ.( q β.( λ.( n 1), (A.4) k ( g(, s ) + σ.( q 1)). β.( λ β.( λ.( n 23