Research on the investment Efficiency of Real Estate in Shanxi Province Based on DEA

: The investment efficiency of real estate can, to some extent, reflect the development of a province's real estate industry. A good efficiency can also be conducive to economic growth and social stability. This paper uses DEA model to measure the real estate investment efficiency of 11 prefecture-level cities in Shanxi Province from 2017 to 2021, which helps to understand the current state of investment efficiency in Shanxi Province. The results found that the mean value of TE in Shanxi Province is 0.8136, the mean value of PTE is 0.9145, and the mean value of SE is 0.9369, indicating that Shanxi is inefficient and there is still room for improvement.


INTRODUCTION
The real estate industry is one of the basic industries of our national economy and influences economic development to a large extent [1]. Therefore, it is imperative to improve the investment efficiency of the real estate industry as the main goal [2].
Foreign literature on this aspect of real estate investment is less researched. Jreisat A (2017) used DEA model to dissect the investment efficiency of real estate enterprises and found that enterprises are prone to produce benefits when their inputs and outputs are proportional [3]. Chen et al. (2020) used the DEA-Malmquist method to analyze the combined various factors of production units in the real estate industry productivity [4].
In recent years, there has been more literature on the efficiency of real estate investment in China. Menghui Peng (2019) studied the development of real estate investment efficiency in China using the BCC model and the CCR model [5]. Liu and Fang (2019) studied the innovative technology and investment scale of real estate firms using DEA model and concluded that technology affects investment efficiency [6]. Chunjing Xia (2020) studied the efficiency of real estate innovation using DEA model and found the causes of inefficiency in it [7].
In summary, there is a large literature on the efficiency of real estate investment using DEA models, but it lacks systematicity [2]. Therefore, in this paper, a more systematic study on the investment efficiency of prefecture-level cities in Shanxi Province is conducted using DEA model

CHOICE OF EVALUATION MODEL
The Data Envelopment Analysis (DEA) model is a mathematical planning method, in which the sampling principles and selected sampling data are determined first, then the sampling data are analyzed and studied according to the principles, and the efficiency value of each decision unit is derived. Then the direction of improvement and the degree of sample data to be improved in the observation period are pointed out according to the efficiency value.
Linear programming model: If u*, v* is the optimal solution of (3), then zu*, zv* is also the optimal solution. Let The optimal solution θ* denotes the efficiency value of this DMU, and θ* takes the value (0,1]. If θ*=1, the DMU is in a technically efficient state on the production frontier; if θ*<1, the DMU is in a technically inefficient state [2]. The smaller the value of θ*, the lower the efficiency. (2) Output perspective:

ANALYSIS OF REAL ESTATE INVESTMENT EFFICIENCY IN SHANXI PROVINCE
This paper summarizes the input-output indicators chosen by some scholars in recent years to study the efficiency of real estate investment, as shown in figure 1[1].

Figure 1 Summary table of input and output indicators in the relevant literature
Combining the selection of indicators by scholars in the figure, the following evaluation indicator system is selected in this paper--Input indicators: the amount of investment completed in the current year, the number of real estate employees, and the area of housing construction. Output indicators: the area of completed houses, sales of commercial properties [6].
(1)Comprehensive Technical Efficiency (TE) = pure technical efficiency × scale efficiency [1]. Looking at Table 1, the average value of TE of real estate industry in Shanxi Province during 2017-2021 was 0.8136, and the overall DEA was inefficient. Taiyuan and Datong had TE value of 1 in four out of five years, with an integrated investment efficiency average of 0.9949 and 0.9432 respectively, ranking first and third in the province. TE values in the range of 0.8-0.9 were Jincheng, Shuozhou and Yuncheng; TE in Shuozhou had a significant downward trend. The cities with TE values below 0.8 include Yangquan, Jinzhong, Xinzhou, Linfen and Lvliang.
Among them, TE in Linfen gradually rose and started to reach effective investment in 2019; Xinzhou and Lvliang fluctuated but maintained an upward trend in a longer period of time; Yangquan and Jinzhong fluctuated significantly and remained in an unstable state.
(2)Pure Technical Efficiency (PTE) measures the degree of use of technology, reflecting its own management level and the technological innovation capacity of the company [1]. Looking at Table 2, the average value of PTE of investment in real estate industry in Shanxi during 2017-2021 was 0.9145, with an overall state. Taiyuan, Datong, Yangquan, and Shuozhou had a PTE value of 1 every year during 2017-2021, indicating that the real estate industry in these cities had a high PTE and the level of technological innovation was always in the leading position in Shanxi. The prefecture-level cities with the average value of PTE in the range of 0.9-1 include Changzhi, Jincheng, Yuncheng and Xinzhou, among which Changzhi had a pure technical efficiency value of 1 for four years in five years, with an average value of 0.9864. Jincheng and Xinzhou had fluctuations in PTE value of the real estate industry, but it started to gradually rise and reach a effective state again in 2019. Only Jinzhong, Linfen and Lvliang had average PTE values below 0.9, indicating that the level of technological innovation and management in these cities was low, and the management level and technological innovation should be increased in order to improve PTE and thus achieve effective investment.
(3)Scale Efficiency (SE) assesses whether the unit can be in the optimal scale state, reflecting the gap between the actual scale and the theoretical optimal scale [1]. Looking at Table 3, the average value of SE of real estate investment in Shanxi in 2017-2021 was 0.9369, which did not reach the optimal scale state, indicating that the SE of real estate investment is currently a key factor limiting the improvement of the overall efficiency of real estate investment. Only Taiyuan and Datong have had a SE value of 1 in four out of five years, indicating that these two cities have the best scale of real estate investment in the province. Jincheng, Changzhi, Xinzhou and Linfen have reached 1 in three out of five years, and the SE of real estate investment in these places had all fluctuated and then gradually returned to scale efficiency, which was appropriate to continue to maintain. The average value of SE is lower than 0.9 in Yangquan, Shuozhou and Lvliang.