CC BY
15
Вестник СибГАУ. Том 17, № 3
UDC 339.13.017
Sibirskii Gosudarstvennyi Aerokosmicheskii Universitet imeni Akademika M. F. Reshetneva. Vestnik Vol. 17, No. 3, P. 830-835
SIMULATION OF THE COST OF RESIDENTIAL PROPERTY IN KRASNOYARSK FOR 2013-2014
L. M. Savchenko, I. L. Savostyanova, S. I. Senashov*, A. G. Yuzaeva
Reshetnev Siberian State Aerospace University 31, Krasnoyarskiy Rabochiy Av., Krasnoyarsk, 660037, Russian Federation *E-mail: sen@mail.sibsau.ru
Data on the cost of secondary residential real estate in the city of Krasnoyarsk for the years 2013 and 2014 was collected and analysed. The number of objects in 2013-4031 items, in 2014-1037 items. Each flat is characterised by 13 parameters: number of rooms, layout, residential district, floor, total number offloors in the building, material of the walls, telephone, total useful floor area, living space, kitchen area, WC-and-bathroom unit, kitchen stove, availability of a balcony or stanza. On the basis of ordinary least squares (OLS) an adequate linear model of the cost of a flat for the years 2013 and 2014 was created. Their own significant factors were found for the models of each year. Also separate models for flats in Oktyabrsk and Sverdlovsk districts of the city of Krasnoyarsk for the year 2014 were created. It was examined how the influence of general factors on price formation changed. The number of rooms factor started to have a smaller effect on the price of residential real estate. The negative coefficient on this parameter increased by 1.5 times. Layout also started to have a smaller effect on the price. The negative coefficient increased by 2 times. Residential district: the negative coefficient on this parameter has become smaller which indicates that the location of the flat in the city has started to have a larger effect on the price. Total useful floor area: the effect of this factor did not change. Living space: a change in this factor's coefficient turned out to be the most prominent because it increased by almost 5 times. From the analysis of models of the price offlats in Oktyabrks district one of important factors is availability of a balcony or stanza. For flats in Sverdlovsk district important factors are material of the walls of the building and availability of a telephone. These facts can be explained by the specific characteristics of these districts. When analysing residuals of the obtained linear models heteroscedasticity of the residuals can be seen; it was shown by Goldfeld-Kvant, White and Glazer tests. With the help of generalised least squares (GLS) on the basis of the linear model new models with homoscedastic residuals were created. The created models adequately describe experimental data.
Keywords: cost of secondary residential property, OLS, GLS, multivariable linear regression model, heteroscedas-ticity, homoscedasticity.
Вестник СибГАУ Том 17, № 3. С. 830-835
МОДЕЛИРОВАНИЕ СТОИМОСТИ ЖИЛЬЯ В Г. КРАСНОЯРСКЕ ЗА 2013 И 2014 ГОДЫ
Л. М. Савченко, И. Л. Савостьянова, С. И. Сенашов*, А. Г. Юзаева
Сибирский государственный аэрокосмический университет имени академика М. Ф. Решетнева Российская Федерация, 660037, г. Красноярск, просп. им. газ. «Красноярский рабочий», 31
*E-mail: sen@mail.sibsau.ru
Собраны и проанализированы данные по стоимости вторичной жилой недвижимости в г. Красноярске за 2013 и 2014 гг. Количество объектов в 2013 г. - 4031 единица, в 2014 г. - 1037 единиц. Каждая квартира характеризуется 13 параметрами: количество комнат, планировка, микрорайон, этаж, всего этажей в доме, материал стен, телефон, общая площадь, жилая площадь, площадь кухни, санузел, кухонная плита, наличие балкона или лоджии. На основе метода наименьших квадратов (МНК) построена адекватная линейная модель стоимости квартиры для 2013 и 2014 гг. Для моделей каждого года выявлены свои значимые факторы. Также построены отдельные модели для квартир Октябрьского и Свердловского районов г. Красноярска за 2014 г. Рассмотрено, как изменилось влияние общих факторов на ценообразование. Фактор «количество комнат» стал оказывать меньшее влияние на цену жилья: отрицательный коэффициент, стоящий при этом параметре, возрос в 1,5 раза. Такой фактор, как планировка, также стал оказывать меньшее влияние на цену: его отрицательный коэффициент возрос в 2 раза. Фактор «микрорайон»: отрицательный коэффициент при данном факторе уменьшился, что говорит о том, что местоположение квартиры в городе стало оказывать большее влияние на цену. Фактор «общая площадь»: влияние этого фактора не изменилось. Фактор «жилая площадь»:
изменение коэффициента данного фактора оказалось наиболее заметным, так как он увеличился почти в 5 раз. Из анализа моделей стоимости квартир для Октябрьского района выявлено, что одним из важных факторов является наличие балкона или лоджии. Для квартир Свердловского района важными факторами являются материал стен дома и наличие телефона. Данные факты объясняются спецификой этих районов. При анализе остатков полученных линейных моделей наблюдается гетероскедастичность остатков, она выявлена тестами Голдфелда-Кванта, Уайта и Глейзера. С помощью обобщенного метода наименьших квадратов (ОМНК), на основе линейной модели построены новые модели с гомоскедастичными остатками. Построенные модели адекватно описывают опытные данные.
Ключевые слова: стоимость жилья, МНК, ОМНК, линейная регрессионная многофакторная модель, гете-роскедастичность, гомоскедастичность.
Introduction. Real estate is an important link in the market system of the country. Real estate objects are not just goods providing personal needs of the people but at the same time they are assets that bring income. Residential real estate like all real estate objects in the country has cadastral valuation of the cost which often does not coincide with the market price of the flat. Therefore the problem of developing such models of the flat cost that are adequate for the real existing secondary residential market situation is currently important.
Problem statement. Earlier the cost of secondary residential property for the period 1998-2012 in the city of Krasnoyarsk was studied in the works [1-9].
The task of this investigation is to build and analyse linear models of the cost of secondary residential real estate for the years 2013 and 2014.
First step is to analyse the market and collect data. If we look at the quantity demanded then it did not change as regards distribution of preferences between one-room and two-room flats. Around 60 % of deals in the secondary market cover one-room flat segment, two-room flats are less demanded and three-room and four-room flats are least demanded.
In connection with the unstable situation in the currency market in the year 2014 flats up to RUR 1.5 m sold best of all. While in the year 2013 this amount was RUR 3.0 m.
During these two years the trend in construction of new small-size residential property did not change and was quite high. Construction was mainly carried out in suburban districts or by way of infill construction inside the city.
Cost distribution of a square meter in secondary residential property depending on the district was stable. The most expensive flats were located in the districts Centre, Academgorodok, Vzlyotka, Kopylova, Svobodniy. In its turn the most inexpensive residential property of a typical layout could be obtained in the districts Cheryomushki, Energetiki.
From year to year the price of a square metre steadily increases.
According to the Krasnoyarsk Region Rosreestr (Federal Service for State Registration, Cadastre and Cartography) monthly report for the year 2014 the number of deals in the secondary market was increasing as compared with the previous year. Because of the unstable situation in the currency market people were withdrawing money from their bank accounts and investing it in real estate. Mainly flats up to RUR 1.5 m were being purchased.
In most cases one-room flats were specially demanded, less frequently two-room and three-room flats.
Small-size residential property located mainly on the edge of the city was sufficiently demanded.
Having collected enough information a data base will be formed [10; 11]. At this stage spelling mistakes occurred during data collection will be eliminated; all symbolic names will be replaced with the corresponding numeric equivalents that were established by real-life means during enquiries and previous investigations. This will result in a prepared data base which we can apply mathe-matics-and statistic analysis methods to.
Solution of the problem. For a start it will be required to make a decision on the type of the model that will be used for forecasting of the cost of residential property in the city of Krasnoyarsk. There are three model types: additive, multiplicative, and aggregate. In this investigation we used additive model presented by the linear regression formula because it is simple and reliable, imposes less strict requirements to the amount of initial information, and it is adapted to taking account of possible dependences between the parameters in a better way. Regression analysis was conducted on the basis of OLS with the use of which sum of squared deviations of the values of the variable under study from the ones predicted by the model will be minimised [12; 13].
Data base for the year 2013 counts 4031 flats, in 2014 -1037 flats. Each flat is characterised by 13 parameters: number of rooms, layout, residential district, floor, total number of floors in the building, material of the walls, telephone, total useful floor area, living space, kitchen area, WC-and-bathroom unit, kitchen stove, and availability of a balcony or stanza.
Prices for the real estate objects and their characteristics are taken from [10; 11].
We suggest the cost of residential property is described by the following linear multivariable regression equation:
Zl = a0 + ax X1 +... + a13 X{3, (1)
where Z i - cost of i flat; ai - coefficients determined by OLS; Xj -j factor of i flat.
Coefficients of equation (1) were found with the use of Ordinary Least Squares (1).
Models describing the cost of flats in the city of Krasnoyarsk for the years 2013 and 2014 were obtained.
Model for 2013 is written as:
Z1 = 985.67- 308.15X1 - 47.3X2 - 55.7X3 -
(122.9) (34.23) (13.9) (5.98)
-198.52X4 + 65.6X5 + 4.62X6 + 81.7 X7, (2)
(33.21) (1.58) (1.45) (41.37)
BecmHUK Cu6rAY. TOM 17, № 3
XI - number of rooms in i flat; X2 - layout of i Hat; X3 -district where i flat is located; X4 - material of the building's walls in i flat; X5 - total useful floor area of i flat; X'6 - living space of i flat; X7 - WC-and-bathroom unit in i flat.
Qualitative factor X2, layout of the flat, is substituted with the values: individual layout (this is a layout of the flat in the building built as per individual design; usually there are no two absolutely similar flats; it is characterised with large floor area, its kitchen is 10-15 sq. m., a high ceiling, large corridor, one or several stanzas) - 1, New layout (construction started in the 1980s, the buildings are made of bricks and panel, mainly nine-, twelve-storey buildings; such flats are characterised with their kitchen at least 9 sq. m., separate room, WC and bathroom are separated, a stanza) - 2, Leningradka (construction of such buildings started in the 1970s, material of such buildings is panel or block; stanza in such flats is located at the end of the building, and the rooms are arranged on one and the same side along a long and wide corridor) - 3, Stalinka (flats in three-five-storey buildings construction of which started from the 1950s, main characteristics of such flats are a high ceiling and large living space, the rooms are separated, WC and bathroom are separated) - 4, Improved layout (construction of such buildings started in the 1970s, the buildings are brick and panel five-storey buildings, later nine-storey buildings appeared) - 5, Khruschyovka (construction of such buildings started in the 1960s, they are made of panel and bricks with thin walls, the flats themselves have a low ceiling, small-size kitchen (not more than 6 sq. m.), communicating rooms, combination bathroom, narrow corridor) - 6, Studio (a type of residential property which has the form of either a small-size one-room flat or a room with a built-in kitchen and a WC-and-bathroom unit) - 7, Section (living space where there are 6 rooms, one kitchen, a shower and a toilet in one section) - 8, Communal flat (in the communal flat live several families or individuals; they occupy one or several rooms, they share the same shower, toilet and kitchen, and also corridor and entry way) - 9, Hostel (this is separate rooms arranged along the corridor; WC-and-bathroom units, showers and kitchen are common and also located in the corridor) - 10.
As X3, district, the following values are used: Aca-
demgorodok - 1; Centre, Severniy, Kopylova, Zheleznodorozhnikov, Zelyonaya Roscha, Solnechniy, Railroad station - 2; Vzlyotka, Innokentyevskiy, Region's hospital - 3; Studencheskiy gorodok, Predmostnaya square, Yubileynaya, Vetluzhanka, Botanicheskiy - 4; Kosmos, Ketskhoveli, Krasnoarmeysakya, BSMP, GorDK, DOK - 5; Svobodniy, S/z Oktyabrskiy - 6; Pok-rovka, Zaton, Circus - 7; Kalinina, Severo-Zapadniy, Pashenniy, Yemelyanovskiy, Meat factroy, Kozulskiy - 8; Trade Centre, Rodina, TYUZ, Sputnik, Ocean, Badzhey - 9; Yenisey cinema, Yenisey station, Divnogorsk, Udachniy -10; Pervomayskiy, Zlobino - 11; KrasTEC, Uyarskiy -12; Vodnikov - 13; Cheryomushki, Energetiki, Shinniki, Beryozovskiy, Sosnovoborsk - 14.
As X4, material of the building's walls, the following values are used: slag block - 0, solid mass - 1, brick - 2, panel - 3, wood - 4.
As X7, type of WC-and-bathroom unit, the following values are used: combined - 1, separated - 2, two units - 3.
Taking into account the above mentioned values the built model of the cost of a flat for the year 2014 is written as:
Z1 = 631.457- 520.085X1 - 91.522X2 - 44.533X3 +
(194.427) (79.22) (30.944) (12.153)
+ 65.815 X 5 + 22.833 X6 + 35.464 X8
(3.873) (4.769) (16.353)
(3)
X{ - number of rooms in the flat; X2 - layout of the flat; X3 - district where the flat is located; X'5 - total useful floor area of the flat; X6i - living space of the flat; X8i - floor on which the flat is located.
The symbol entry's values of the factor X2, layout of
the flat, correspond to the values of the factor X2i of the model (2) for 2013.
The symbol entry's values of the factor X3i , district,
correspond to the values of the factor X3 of the model (2) for 2013.
Its standard error is shown under each coefficient.
The factors: number of rooms in the flat, layout of the flat, district, total useful floor area, living space of the flat influence the cost of the flat both in the model for 2013 and in the model for 2014. Apart from the above mentioned factors the following influences cost formation in 2013: material of the building's walls and availability of a WC-and-bathroom unit; and in 2014 - floor on which the flat is located.
Let us study how the influence of the general factors on cost formation changed. The number of rooms: this factor started to have smaller effect on the cost of residential property. This can be seen from the fact that the negative coefficient at this parameter increased by 1.5 times. Layout: this factor acts similar to the previous one - the negative coefficient increased by 2 times. District: the negative coefficient at this factor decreased which shows that the location of the flat in the city started to have bigger effect on the price. Total useful floor area: the influence of this factor did not change. Living space: the change of this factor's coefficient turned to be the most prominent because it increased by almost 5 times.
When studying the models for heteroskedasticity a Goldfeld-Kvandt test was conducted. The criteria imply calculation of the ratio of the residuals' sum of squares in the regressions for the first n and the last n SS
observations: F =—- = 4 42, where SS, and SS2 -
paCH SS 1
sums of deviation squares in the first and the last regressions correspondingly. FTa6jI = 1,19 . It can be seen from the calculations that FpacH is bigger than FTa&J, therefore heteroskedasticity is observed. Also Glazer and White test were carried out with the use of which it was
confirmed that the residuals e = Y' - Z' for the models (2) and (3), with a probability of 95 % are heteroscedastic. Therefore there are external unknown factors influencing the models (2) and (3). In order to get rid of their influence it will be required to build homoscedastic models.
For a start we will introduce new variables equal to:
N' =
Z'
Ml =
1
m'
1 J y[(ë)
(4)
-10.59 M 3
(2.55)
- 3.9 M4 - 51.69M5 +
(0.61) (10.86)
+ 0.29M6 +18.61 M7 + 2.13M8 -
(0.02) (13.4) (0.74)
- 0.01 M9 + 0.48M10.
(0.02) (0.1)
And model for the year 2014 is written as:
n' = - 332.6258 +100.552M1 + 7.577 M2 +
(5)
(10.28)
(3.04)
(1.25)
+ 2.373 M3 +1.921 M4 + 1.299 M5 + 4.99M6 + (6)
(0.44) (0.63) (0.52) (0.15)
+ 1.685 M 7 + 1.592 M 8 + 9.485 M 9.
(0.17)
(0.52)
(3.2)
where Z' - cost of i flat; X1 - layout of i flat; X2 -
floor of i flat; X'3 - total floor area of i flat; X4 -availability of a balcony or stanza in i flat.
Then with the use of GLS a new model with homoscedastic residuals was built:
N' = 42.09 (1.11)
4827.028М1 -187.322М2.
(546.86) (68.03)
(8)
With the OLS we got models with unbiassed estimators. In order to get estimators with smaller sampling variances we will use GLS. We will build new models with homoscedastic residuals.
Model for the year 2013 is written as:
N' = -3.23+ 2705.39Ml + 23.19M2 -
(10.15) (572.17) (9.28)
The tests conducted showed that the models (5) and (6) allow us to calculate the cost of flats in the city of Krasnoyarsk for the years 2013 and 2014 with a reasonable accuracy.
Also we can study individually some of the districts in Krasnoyarsk. To calculate the cost of flats multivariable linear regression models are used (1). We will start with the studying of the model of the cost of a flat in Oktyabrsk district for 2014.
General characteristics of the district. Oktyabrskiy district is one of the oldest districts of the city; in June 2013 it was 75. By the act of All-Russian Central Executive Committee Presidium dd. June 25, 1938 Kaganovichskiy district was established in Krasnoyarsk which was re-named Oktyabrskiy in 1957. In November 1979 Oktyabrskiy district was divided into two -Zheleznodorozhniy district came out of it. Since then Oktyabrskiy district is a relatively new fast-developing district with all infrastructure characteristic of the new modern urban territory. For a short period of time a recent suburban part of the city has turned into the modern districts and buildings making a large district of the city. As for architecture and town-building Oktyabrskiy district has its own specific features. This particular feature is that the district's bigger part neighbours on the urban green belt [14].
With the use of OLS the following model was built: Zl = 517.4-125.8X1 + 53.1 X2 + 51.8X3 +143.6X4, (7)
(145.81) (29.45) (16.14) (1.79) (25.25)
Let us compare the factors of the two models: the model of the cost of flats in Krasnoyarsk for 2014 (3) and the model of the cost of flats in Oktyabrskiy district for 2014 (7). In both models there are such factors as: layout of the flat, total useful floor area of the flat, floor. For Oktyabrskiy district there is one more important factor which is availability of a balcony or stanza.
The next model to be studied will be a model of the cost of a flat in Sverdlovsk district for 2014.
Now there are 24 objects being built in the territory of Sverdlovsk district, most of them are in the residential district Pashenniy. There a few large residential communities are being intensively built - residential areas Beliye Rosy, Utiniy Plyos, residential complexes "Yenisey", "Panorama", "Premyera". One more centre of the district is residential area Yuzhniy Bereg where Small building clusters keep growing. Development of a district next to the fourth bridge that was named Tikhiye Zori has started.
Nevertheless we cannot say that Sverdlovsk district is a sample of a complex approach to the recultivation and territory development: in its time the former plant's lands were sold by portions and now they belong to different owners. Absence of free land does not allow to create a full-featured social infrastructure of the district [15].
With the use of OLS the following model was built:
Zl = 172.158 - 97.55X{ + 106.96X2 -- 73.37 X3 + 20.16X 4 + 42.29X5,
(9)
where Z' - cost of i flat; X\ - layout of i flat; X2 -district of i flat; X3 - floor of i flat; X4 - material of the walls of i flat; X5 - availability of a telephone in i flat.
Comparison of significant factors of the model of the cost of flats in Krasnoyarsk for the year 2014 (3) and cost of flats in Sverdlovsk district for the year 2014 (9) showed presence of such factors as: layout of the flat, floor, and district. Also for Sverdlovsk district the important factors are material of the building's walls and availability of a telephone in the flat.
Then with the use of GLS a new model with homoscedastic residuals was built:
N = 105.6 + 0.76M 1 + 0.75M 2.
(10)
Conclusion. On the basis of ordinary least squares (OLS) an adequate linear model of the cost of a flat for the years 2013 and 2014 was created. Their own significant factors were found for the models of each year. Also separate models for flats in Oktyabrsk and Sverdlovsk districts of the city of Krasnoyarsk for the year 2014 were created. It was examined how the influence of general factors on price formation changed.
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Вестник СибГАУ. Том 17, № 3
The number of rooms factor started to have a smaller effect on the price of residential real estate. The negative coefficient on this parameter increased by 1.5 times. Layout also started to have a smaller effect on the price. The negative coefficient increased by 2 times. Residential district: the negative coefficient on this parameter has become smaller which indicates that the location of the flat in the city has started to have a larger effect on the price. Total useful floor area: the effect of this factor did not change. Living space: a change in this factor's coefficient turned out to be the most prominent because it increased by almost 5 times. From the analysis of models of the price of flats in Oktyabrks district one of important factors is availability of a balcony or stanza. For flats in Sverdlovsk district important factors are material of the walls of the building and availability of a telephone. These facts can be explained by the specific characteristics of these districts.
References
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Библиографические ссылки
1. Сенашов С. И., Юферова Н. Ю., Сурнина Е. В. Информационная система оценки стоимости квартир на вторичном рынке жилья как инструмент управления инвестициями // Вестник СибГАУ. 2009. № 4(25), ч. 1. С. 219-223.
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