Exploring the spatial distribution of house prices in Shanghai using urban models

The factors influencing housing unit prices for different areas within the city are more complex, with location in relation to the city center or regional center, number of jobs, accessibility and surrounding services being factors that are often taken into account. In addition, studies have shown that factors such as, , and , have an impact on housing demand and house prices. The diversity of influencing factors and the complexity of the mode of action need to be considered in predictive modeling of house prices, along with the assessment of the demand characteristics of buyers and the modeling of the spatial distribution of house prices.

The overall distribution of house prices in Shanghai shows Xuhui, Huangpu and Pudong as the core single center. There are some sudden changes in some areas(Fig 1).

Regression model

Since house prices are the result of multiple factors, a statistical approach can be considered to establish a multiple regression model for forecasting. Firstly, based on the available data, correlation analysis and principal component analysis are conducted on many potential factors affecting house prices such as distance from city center, distance from public transportation, population density, jobs, and average new knowledge, and the obtained correlation factors are subjected to multiple regression analysis to establish a linear or nonlinear fitting model for house prices.

The regression fitting model is based on the trend evolution of past data and can predict house prices based on multiple variables. The drawback is that it weakens the spatial properties of house prices and the complex relationship of multiple factors.

Central place model and land use model

The linear model is further combined with the geospatial model to estimate the characteristics of the distance to the city center based on the surrounding land use type and accessibility. A large number of models on the degree of urban land development and utilization patterns. Based on the correlation between the spatial layout and land use house prices of land use types and house prices, some predictions can be made for the distribution of house prices in space.

Central place model and land use model take into account the spatial elements and the influence on the overall house price, but it is essentially a static and linear model, which lacks consideration for the correlation and transformation between variables. In the process of home purchase, different demands can be substituted for each other, so the diversity and variability of supply and demand need further consideration.

Multi-agent model(CA) based on the relationship between supply and demand

The multi-agent model reveals the law of action by simulating the process of macroscopic changes due to changes in microscopic rules of action. Meanwhile CA is a dynamic and non-linear model, which has better explanation ability for diversified factors and complex action processes.

To explore the spatial distribution of house prices in Shanghai, the CA model is established. Based on the market economic principles such as supply and demand, the multi-factor model is established by considering the balance of supply characteristics, purchasing demand and purchasing ability.

Supply: Housing in any region has its basic attributes. The geographic location of the house, its relationship with the city center/sub-center, road traffic and public transportation conditions, surrounding land use and other elements of itself are considered as supply characteristics. Price attributes are changing values and will be adjusted in real time according to the supply and demand situation. For the determination of the boundary conditions of the price, the house is initially priced as the average price in the adjacent area at a certain distance.

Demand: Buyers have demand attributes. There is a certain demand for the length of commuting distance, the number of jobs and services in the area where the house is located, the surrounding land use and environment, etc., and there is a certain correlation and substitutability between various demands. Utility functions for different factors need to be established to assess the overall demand. For unpredictable demand, random numbers are used to differentiate in the parameter setting.

There are three stages within one interaction: supply and demand assessment, selection and adjustment.

The selection of houses is performed first in the purchase, and when the house supply attributes satisfy the demand attributes of the agents, the demand for the house will begenerated, and the number of times the house agents select is used as their demand value. Eventually all agents will select the house closest to the demand for purchase. Since the house price is constantly fluctuating and changing, the effect of supply and demand on the unit price of the house needs to be considered. In each interaction, when the number of demand generated by agents is greater than the number of housing supply in the area, the resulting oversupply is the most significant cause of the increase in the unit price of a house. On this basis the price will be adjusted upwards and the adjustment value will be a function of the demand. Similarly, when the demand is less than the supply, the house will be adjusted downward in price. If an agent never purchases a home, his or her corresponding demand will decrease.

New agents and houses will be created continuously in each cycle. The uncertainty of supply and demand is the specific reason for price fluctuations. The final model will not have a stationary price distribution when equilibrium is reached, but will fluctuate within a relatively small range of near-steady-state conditions. Therefore, it is possible to dynamically consider the outcome of the distribution of house prices.

The model has some limitations. First, the variety of factors considered is limited, and because the types of factors are determined artificially during the construction of the model, less consideration is given to the diversity and variability of agents’ own demand situations, the characteristics of housing and regional culture and history, and many other factors and correlations between variables, which reduces the realism of the model. Second, the city is considered as an independent entity, and the influence of the surrounding cities is not considered. In Shanghai, due to the faster intercity transportation and relatively low housing prices, the neighboring cities have competitive advantages for the distribution of housing prices within the city of Shanghai will have some influence.