House Price Index (HPI)

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1 House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales mehodology proposed by Case and Shiller (1989). In he repeaed sales mehodology an individual house price is characerized as a sochasic process in which he average variaion is measured by a marke price index, while he dispersion and volailiy respec o he marke average are modeled as a process wih log-normal disribuion (Calhoun, 1996). The esimaion of he index requires o idenify houses ha have been sold a leas wice during he period of analysis. The variables used for idenificaion of he properies are he address and he real esae regiser number. Then, informaion of he firs and second ransacions is merged o compue price variaions. Commercial appraisal value is used since he exac house price is no available, his value is used for morgage acquisiions. This indicaor allows o analyze facors affecing he equilibrium price of asses such as: supply shocks and he exisence of speculaive bubbles. Following his indicaor helps o assess he housing marke evoluion and relaed secors. Coverage: Iniially he index included informaion of morgages in he hree major ciies: Bogoá (including Soacha), Medellín (including Bello, Envigado and Iagüí) and Cali. In May 2014, informaion from more ciies was considered and ime series were updaed including informaion from Barranquilla, Bucaramanga, Cucua, Manizales, Neiva and Villavicencio. Periodiciy and publicaion The base period is 1990=100 and he series are deflaed using he aggregae CPI of he ciies involved in he index. Boh, nominal and real indexes are published. Annual indexes:

2 Toal housing price index corresponds o he aggregae of house price evoluion for he following ciies: Bogoá (including Soacha), Medellin (including Bello, Envigado and Iagüi), Cali, Barranquilla, Bucaramanga, Cucua, Manizales, Neiva and Villavicencio. Indexes by ciies: - HPI Bogoá (including Soacha). - HPI Medellín (including Envigado, Bello and Iagüi). - HPI Cali. - HPI oher ciies, includes informaion from: Barranquilla, Bucaramanga, Cucua, Manizales, Neiva and Villavicencio. Indexes by appraisal values: - HPI LIH: Low income housing. - HPI ELIH: Excluding low income housing. Annual indexes series are published four monhs afer he end of he year. Quarerly index: In quarerly basis only he oal aggregae index is produced. Toal housing price index corresponds o he aggregae of house price evoluion for he following ciies: Bogoá (including Soacha), Medellin (including Bello, Envigado and Iagüi), Cali, Barranquilla, Bucaramanga, Cucua, Manizales, Neiva and Villavicencio. Quarerly index is published four monhs afer he end of he quarer. Time series are revised each period because as new informaion is included, he esimaes may change. Source of informaion: The informaion come from disbursemens made for housing purchases offered by he main financial insiuions ha offer morgages in he counry: 1. Av. Villas 2. Bancolombia (includes Conavi)

3 3. BBVA (includes Granahorrar) 4. BCSC (includes Colmena) 5. Colparia 6. Davivienda (includes Bancafé) Mehodology The mehodology of his indicaor corresponds o weighed repeaed sales proposed by Case and Shiller (1989), in which he index is build from a hree-sage economeric esimaion, selecing he dwelling sold a leas wice during he period of analysis and ha has no have significan changes in heir physical srucure during ha period. The price dynamic for an individual is characerized as a sochasic process represened house,pi by: ln( P i ) H i N i (1) Where, β corresponds o he marke price index, is a Gaussian random walk, which describe how he change in he price of an individual house deviaes from he marke index variaion. And are errors normally disribued ha represen he idiosyncraic differences a ime. Equaion (1) implies ha he oal percenage change in price of house i ransacing in ime periods s and is given by: (2) (3) The following assumpions are esablished for he perurbaion erms: H H 0 H H (4) (5) (6)

4 Equaion (6) shows ha he dispersion of he lengh of holding period in he selling price of second hand houses is no relaed wih he dispersion generaed by he marke price a he ime of sale. From his specificaion and assumpions, he consrucion of he index is divided in he following sages: Firs sage: iniial β esimaes and esimaion of he errors. In he sample of repea sales, he change in price of house i, in equaion (2) can be expressed as follows: (7) Where is a dummy variable which equals 1 if he price of house i is observed for he second ime a ime, -1 if he price of he house i was observed for he firs ime a ime, and zero oherwise. Subsiuing (1) in (7) yields, (8) The parameer is esimaed by Ordinary Leas Squares (OLS). When A or B in equaion (4) are saisically differen from zero, he variance of changes wih he disance beween repeaed sales, he more disan he ransacions are, he greaer price variaion is assumed. Therefore, o obain more efficien esimaes of he mehod of Generalized Leas Squares (GLS) is used. Second sage: Esimaion of he variance of he random walk As quoed by Calhoun (1996) he prediced price of house i purchased in period s and sold in period is given by: (9)

5 The above equaion indicaes ha he esimaed price in period is equal o he iniial purchase price plus he expeced marke appreciaion beween he wo periods. The quadraic error forecas would be given by: (10) Calculaing he expeced value and using he assumpions in equaions (4), (5) and (6) he following equaion is obained: (11) The above equaion ses he second sage of he procedure. Through his equaion we can obain no only consisen esimaions, bu also evidence abou volailiy and dispersion of individual house prices around he marke index. The square roo of he esimaed values by equaion (11) is used as weighs in he final sage: Generalized Leas Squares (GLS). Third sage: The final esimaion of β, considers he following ransformaion of he series, which suppose no o affec he consisency of he parameers neiher he performance of he index. (12) Finally, he index is calculaed from he obained parameers by GLS: I 100 e ~ (13) Unlike convenional indexes, his mehodology produces a sandard error associaed o each esimaion, which is given by: σˆ Ι Ι σˆ βˆ (14) One issue of he geomeric index is ha i may underesimae he percenage change in he average value of a sample of houses, comprising individual houses of differen price values (high medium and low housing prices). Goezman (1992)

6 proposed he following correcion o he geomeric index, o solve he bias ha can generae he previous index. I 100 (15) Where is an esimae of he variance in house price growh raes associaed wih he diffusion of house prices afer periods. Daabase depuraion The repeaed sales daabase excludes dwellings wih inconsisen informaion such as incomplee idenificaion of he house (address or real sae idenificaion), or excessive changes in he appraisal value beween wo sales. Alhough he hisorical informaion is he same for he annual and quarer indexes, he calculaion is independen for each periodiciy. For he annual index only hose sales of he same dwelling ha occur in differen years are considered, while for he quarer index dwellings sold in he same year bu in differen quarers are included in he index. I. e. repeaed sales of a paricular house in he same period are excluded. Advanages The repeaed sales mehodology highlighs because of is economeric simpliciy and direc use from daa of he variables subjec of measuremen. Besides, i approximaes o a consan qualiy price index, since i requires ha he propery has been raded a leas wice during he period of analysis wihou having significan changes. Oher advanages are he use of informaion of values on he same unis a wo poins in ime, as well as he possibiliy of is reproducibiliy, ha is, ha differen analyss can obain he same esimaes if hey use he same informaion. Addiionally, he esimaion of average price of individual houses under

7 his mehod presens smaller sandard error compared o hedonic prices and firs ransacion (Case, Pollakowski and Wacher, 1991). Disadvanages I only uses a porion of he informaion available on sales ransacions (hose ha have been sold more han once during he period of analysis) wihou consider informaion of second hand houses ha only have had one owner. On he oher hand, several sudies have shown ha he age of he house is a source of bias, which unforunaely are no conrolled by he mehodology, affecing he assumpion of consan characerisics. Also, he mehodology does no consider he influences ha cerain waned characerisics of he house may have over ime on prices, as he change in he preference for having wo or more garages, or bahrooms, being near workplace, parks and oher feaures ha affec rends of he marke and consequenly he final price. Finally, because i is an economeric esimaion, he ime series can change as new informaion is available. Time series can be consuled on he websie of he Cenral Bank: hp://www.banrep.gov.co/es/series-esadisicas/see_precios_ipvu.hm

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