THE MULTIVARIATE REGRESSION MODEL OF THE PRICES OF CHINA S URBAN COMMERCIAL RESIDENCE

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1 THE MULTIVARIATE REGRESSION MODEL OF THE PRICES OF CHINA S URBAN COMMERCIAL RESIDENCE Ming Xuan YU, Dan GAO, Han Jue WANG Business school, RENMIN university of China Abstract: There are various factors affecting the prices of urban commercial residence. In this paper, five socioeconomic indicators, that is, gross regional product, per capital gross regional product, per capita disposable income of urban households, Engle coefficient of urban households and the total floor space of residence buildings(year-end), are selected out and the method of SPSS backward regression analysis is applied, to establish multivariate regression models for the prices of urban commercial residence in Beijing, Shanghai and Chongqing. The analysis of characteristics of price models for residence in various regions will provide reference to analyzers of the real estate market as well as the macro control department of the government. Keywords: Prices of residence; GRP; Engel s coefficient; per capita disposable income; regression analysis 1 Introduction In recent years, the real estate industry in China has undergone a rapid development and the prices of urban residence have been rising steadily. From January to February in 2006, the average price of pre-sale commercial housing dealings in Beijing reached 6776 Yuan/square meter with a rise of 997 Yuan/square meter compared with the corresponding period of the former year and the markup was up to And the average dealing price of the residence in stock reached 4187 Yuan/square meter with a growth rate of 8.1%. The price of residence not only becomes a hot issue highly focused on by common people, but also becomes a socioeconomic issue to which the government attaches much importance. Therefore, it is urgent and necessary to conduct empirical researches on the prices of urban commercial residence and to probe into the interrelation between residence houses and social economy. Among various factors affecting the prices of commercial residence, development level of urban macro economy, people s living standards and stock level in residence market take on comparatively notable effect. The multivariate regression models established on the basis of the fact mentioned above can reflect the harmony between the prices of urban residence and economic development level from a side face. It will do benefit for the deepening of the real estate market analysis and it will also provide reference to the macro control department of the government. 2 Summarization of correlation studies both in the country and abroad 2.1 Correlation studies in foreign countries The correlation between the prices of residence and urban economic indicators has once aroused many foreign scholars interests and multivariate regression analysis is the basic method in common use. Clapp and Giaccotto 1994 selected monthly price data of residence dealings within the period from October,1981 to September, 1988 in three American cities and towns. They took price indices of residence dealings as dependent variable and took certain indicators of economic changes as independent variables. Their conclusion after regression analysis was: economic changes had preferable ability to explain and forecast the changes in prices of residence in various cities. Quigley 1999 selected data within the period from 1986 to 1994 in 41 American city areas and took the average price of residence as the explained variable and took employment, income, housing vacancy rate, total population, quantity of households, quantity of residence under construction, and quantity of residence permitted to be constructed as explanatory variables.

2 His conclusion after regression analysis was: correlation indicators of Economic Fundamentals could explain the price tendency of residence in various cities, and the explanatory power of each explanatory variable on the prices of residences in various cities varied according to different stages of urban economic development. Mini Seko 2003 conducted analysis of average sale price data of private residence and basic economic indicators such as inhabitants annual incomes and gross population within the period from1998 to 2001 in 46 Japanese counties. In his opinion, the prices of residence are of comparatively strong correlation to Economic Fundamentals, thus Economic Fundamentals could be taken use of to forecast the prices of residence. The studies mentioned above have two points in common: firstly, regression method has been used to elicit the price models for residence, during which process real prices or price indices of residence are taken as dependent variables and urban economic indicators are taken as independent variables; secondly, there exists certain correlativity between the prices of residence and urban economic indicators, so the correlation indicators can be used to explain and forecast the price fluctuation of residence. 2.2 Correlation studies in China The real estate of residence in China didn t start its general adoption of the market principle until the middle of 1990s, accordingly Chinese scholars began their studies on correlations between the prices of residence and economic indicators at a comparatively late time. Restricted by the development stage of real estate and statistic data, primary studies mainly focused on determining the nature of the correlation between the prices of residence and economic indicators. Meanwhile, division of real estate prices from the prices of residence has not been made yet. Up till to 1998 the nation confirmed to take the residence industry as a new aspect of economic growth and supported the development of the residence industry and pushed forward merchandizing and socialization of residence houses, so the degree of general adoption of the market principle in residence houses industry became higher and higher. Under such circumstance, the statistics of correlation data about real estate of residence have been gradually enriched, which made it possible for Chinese scholars to conduct quantitative analysis of the residence prices and economic indicators. Liu Liming 2002) deems that, as an environmental factor, the changes in economic development will lead to changes in supply and demand relations in the real estate market and it will become the most decisive factor in the form of real estate prices as time goes by. Li Li and Li Yonghui 2002 think there is important correlativity between the prices of real estate and national policies, inhabitants income levels and the prosperity of economic development and they point out that the analysis of these factors is of great significance in grasping precisely the price tendency of real estate. Domestic quantitative studies of real estate market and economic indicators mainly focused on aspects such as contributions that real estate has done to GDP Yang Baocheng, Dong Wei, and Wang Daijing, 2005,relation between real estate and economic growth or economic circle Wang Yang 2005,real estate investment level and macro economy Wang Songtao, Liu Hongyu 2006 and so on while quantitative studies of the relation between the prices of residence and economic indicators are rare. Shen Yue and Liu Hongyu 2002 selected the real estate prices in China and a series of urban economic indicators such as price indices weighing the consumption level of Chinese inhabitants, economic indicators weighing urban inhabitants income and expenditure, and GDP weighing the macro economic development. After studies of their correlativity, their conclusion was: there existed important action and reaction between the prices of real estate and macro economy, and the prices of real estate are based on the platform of macro economic development level. Xu Chunqin 2005 used multivariate linear regression and reached his conclusion that there existed highly correlativity between the average price of residence and per capita disposable income of urban households and completed floor area of commercial residence. At present, domestic quantitative studies of the correlation between the prices of residence and economic Economic Fundamentals: a collective name of economic situation, the status of economic development, the change of economic prosperity and regional economic intercourse.

3 indicators just begin. Both methods and angles of studies await to be further improved and perfected. 3 Train of research thought The residence market is of regional characteristics. The main economic variables affecting the prices of residence and their manners and degrees of affecting differ from region to region, and the correlativity between residence prices and socioeconomic factors will differ too. Based on what mentioned above, the paper plans to conduct individual empirical research on the correlation between the prices of residence and socioeconomic factors in Beijing, Shanghai and Chongqing During this process, statistic analysis technology in SPSS multivariate regression is adopted to investigate and probe into the main socioeconomic factors and degrees of their correlation to the prices of residence in those three cities with different economic development levels and different regional characteristics, and finally, corresponding multivariate regression models for the prices of residence will be worked out. The average sale price of commercial residence Yuan/square meter (variable code P) is chosen as the explained variable of the regression model, that is, the dependent variable. The socioeconomic factors affecting the prices of residence can be divided into three aspects: urban macro economy development level, people s living standards and stock in residence market, the detailed content of which are showed in table 1. The correlation data of the six variables mentioned above in the period from 1995 to 2004 in Beijing, Shanghai and Chongqing was collected and then logarithmically transformed. The next step is to adopt Backward method of SPSS software to conduct analysis, that is, according to the correlativity between independent variables and dependent variables and collinearity among independent variables, the independent variables not meeting the requirements are stepwise excluded and multivariate regression equations with various independent variables are established. Finally, the most reasonable price model for urban residence will be decided on the basis of different test critical values of F. Table1 Factors Affecting the Prices of Urban Commercial Residence Category Factors Independent Variables Variable code Urban Macro Economy gross regional product a hundred million yuan G Development Level per capital gross regional product yuan PG People s Living Per capita disposable income of urban households yuan I Standards Engle coefficient of urban households E Stock in Residence Market the total floor space of residence buildings(year-end) a hundred million square meter 4 Multiple regression model for the prices of residence in Shanghai, Beijing and Chongqing 4.1 Price model of commercial residence during the period form 1995 to 2004 in Shanghai Model R R Square Adjusted R Square Table 2 Std. Error of the Estimate Model Summary Change Statistics R Square Change F Change Df1 df2 Sig. F Change S Durbin- Watson 1.986(a) (b)

4 a Predictors: (Constant), S,E,PG,I,G b Predictors: (Constant), S,E,PG,G c Dependent Variable: P The paper uses Backward method to carry through stepwise regression analysis of the average sale prices of commercial residence in Shanghai within the period from 1995 to 2004 and five socioeconomic indicators. The elicited abstract of the models, variance analysis and correlative coefficients can be seen in table 2, table 3 and table 4 respectively. Table 3 ANOVA Model Sum of Squares Df Mean Square F Sig. 1 Regression Residual Total Regression Residual Total a Predictors: (Constant), S,E,PG,I,G b Predictors: (Constant), S,E,PG,G c Dependent Variable: P Table 4 Coefficients Model Unstandardized Coefficients B Std. Error Beta Standardized Coefficients 1 (Constant) G PG I E S (Constant) a G PG E S Dependent Variable: P Through judgment and interpretation of tables from 2 to 4, it is distinct to make out that the variable per capita disposable income is excluded from model 2 its values of R R 2 F and t-test value are all superior to those of model 1. The t-test value of constant term and four independent variables in model 2 show: the regression coefficient of the constant term, independent variable GRP and Engle coefficient of urban households are notable with the confidence level under 5 ; the regression coefficient of per capita GRP and the total floor space of residential building in the city are notable with the confidence level under 10. After an overall adjustment, R 2 equals to which shows 94.3 of the fluctuation of the interpreted variable and dependent variables are explained by this model. The regression equation on the basis of model 2 is as follows: ! 2.072! 2.862! P = e G PG E S T Sig.

5 This model demonstrates the prices of commercial residence in Shanghai are most affected by gross regional product; meanwhile, the prices are of relatively great relation to per capital gross regional product, Engle coefficient of urban households and per capita disposable income of urban households. 4.2 Price model of commercial residence houses during the period form 1998 to 2004 in Beijing city The same method is applied to conduct backward regression analysis of the average sale prices of commercial residence in Beijing within the period from 1998 to 2004 and five socioeconomic indicators. Table 5 lists the correlative coefficients of regression and results of correlation test. Table 5 Coefficients a Model Unstandardized Coefficients B Std. Error Beta Standardized Coefficients 1 (Constant) G PG I E S (Constant) PG I E S (Constant) I E S (Constant) I E Dependent Variable: P Through the analysis of table 5, the following conclusion can be reached: among four models established by regression, the values of R R 2 F in the last three models can pass the test and F-test value will become larger and larger as certain collinear independent variables and certain independent variables of weak correlation are excluded gradually. Although the three models can all pass the F test, model 2 is of comparatively weak ability to pass the t-test; one of the independent variables in model 3 and its constant term has not passed the t-test, but the value of adjusted R 2 is the highest among all the models only two of the independent variables in model 4 enter into the regression model and its constant term has not passed the t-test either, and the value of R 2 is less than that in model 3. With a comprehensive consideration of R R 2 F and t-test and in virtue of the fact that model 3 can accept more independent variables to enter the model if possible, model 3 is chosen as the final regression model. The regression equation is as follows: t Sig.

6 ! ! P = e I E S The model demonstrates the prices of commercial residence houses in Beijing are mainly affected by three variables, that is, per capita disposable income of urban households, Engle coefficient of urban households and the total floor space of residence of the city at the end of the year, among which the coefficient of the total floor space of residence of the city at the end of the year is not notable with the confidence level under 10 and the ability of explanation is relatively weak. 4.3 Price model of commercial residence houses during the period form 1997 to 2004 in Chongqing Model Table 6 Coefficients Unstandardized Coefficients B Std. Error Beta Standardized Coefficients 1 (Constant) G PG I E S (Constant) G PG I E (Constant) G PG I (Constant) a G I Dependent Variable: P The same method is applied to conduct backward regression analysis of the average sale prices of commercial residence in Chongqing and five socioeconomic indicators within the period from 1997 to Table 6 lists the correlative coefficients of regression and results of correlation test. Through the analysis of table 6, the following conclusion can be reached: the values of R R 2 F in four models established by regression can all pass the test and F-test value will become larger and larger as certain collinear independent variables and certain independent variables of weak correlation are excluded gradually. Table 6 shows: the coefficients of independent variables in model 1 and model 2 can not pass t-test; when compared with model 4, although model 3 has three independent variables entering into the regression model, coefficients of two independent variables in model 3 can not pass the t test, while the constant term and two independent variables in model 4 can pass the notability test of 5 and with a better ability of explanation. t Sig.

7 After a comprehensive consideration, model 4 is chosen as the final regression model. The regression equation is as follows: ! P = e G I The model shows that the prices of residence houses in Chongqing are mainly affected by GRP and per capita disposable income of urban households. 5 Conclusion Through regression analysis and model construction of the prices of commercial residence and socioeconomic factors in Shanghai, Beijing and Chongqing, the following conclusions can be reached: (1) The real estate market is of regional characteristic. Factors such as developmental level of macro economy, income level of inhabitant and stock level in the real estate market will all affect the prices of residence, but because of difference in regional economic development phases and difference in regional characteristics, factors affecting the prices of residence in different regions differ in quantity, manner as well as degree. Therefore, it is necessary to carry through individual analysis in combination with specific characteristics of different regions when researches on the change tendency of the prices of residence take place. (2) The development of real estate market in China is imperfect and the changes in house prices can not finely reflect the changes in economic indicators. General adoption of the market principle in China s commercial residence houses market took place in a comparatively late time. In 1998, the policy of terminating physical housing allocation system became effective, but in fact, from 1998 to 1999, physical housing allocation as a whole did not come to a full stop. Meanwhile, the land management under the planned economy system also restrained the process of general adoption of the market principle in China s commercial residence market. Along with the reform of residence distribution system deepened and the establishment of public bidding system in land market, the degree of general adoption of the market principle in China s residence industry is prompted rapidly. In this market which is at its elementary stage, the rise and drop of house prices can not commendably explained by economic indicators. (3) The real estate market in China is immature and the prices are not totally fixed by market laws. The commercial residence market counts for much about the national economy and the people s livelihood yet at present, the development of the market is immature, so it is necessary for government to regulate by means of macroscopic readjustment and control. Thus, the market is not totally depends on the self-regulation function of market mechanism and the price changes are not always aroused by market laws. (4) Due to the short-time development of the real estate industry in China, the data statistics of real estate just begins and the statistic methods are imperfect. For example the spatial distribution of trade sampling site of commercial residence varies greatly from year to year, as a result, there exists variance in price data in different time and the comparability is weak. Therefore, it is of much difficulty to establish effective price model of residence. The paper offers a way of establishing price models for urban residence, and practical models needs to be further perfected during the process of continual amplification of the data. References Clapp J M, Giaccotto C. The influence of economic variables on local house price dynamics. Journal of Urban Economics, 1994(1) Duochang Chen, Dongliang Mao. The Theoretical Standard of the Stable Long-term Rise in House Price. Finance and Trade Research 2005(3) Honghua Wu. An Analysis of Factors Affecting the Prices of Real Estate. Journal of Wenzhou University 2001(7) Li Li,Yonghui Li. A View of the Affecting Factors and Change Trend of the Prices of Real Estate. Dong Yue Trbune 2002(6) Peter Fortura, Joseph Kushner. Canadian Inter-City House Price Differentials. AREUEA Journal, 1986(4) Qingchun Xu.The Multivariate Linear Regression Model of the Average Price of Commodity Apartment. China

8 Price,2005(9) Quigley J M. Real estate prices and economic cycles. International Real Estate Review, 1999(1) SekoM. Housing prices and economic cycles. Paper presented in the Housing Market and the Macro Economy: the nexus conference, Hong Kong, China, 2003 Yue Shen Hongyu Liu. A Study on Relation between the Prices of Real Estate and Macro-economy Indicators. Price: Theory & Practice