China's economy has entered the new normal, which is not only reflected in the transformation of economic growth from high speed to medium speed, but also in the optimization and upgrading of economic structure and the change of economic growth driving factors. In this process, government investment plays an important role in driving and guiding. The government investment regulations, which promulgated in 2019, emphasize we should further improve the efficiency of government investment and regulate government investment behaviors. Qiu, et al.^[1] think fixed asset investment is still the main factor to promote economic growth at present, but its marginal return is decreasing and suggest we should maintain a certain proportion of fixed asset investment rate to promote the high-speed growth of GDP. Xinjiang is the core province of the Belt and Road, and it also plays an important role in developing foreign trade and driving the economic growth in the western region. Investment is the main driving factor of Xinjiang's economic growth, in which government investment accounts for about one third. Fixed asset investment in Xinjiang increased year by year, from 97.34 billion yuan in 2003 to 1208.91 billion yuan in 2017, and the growth rate reached 12.42 times (as shown in Figure 1). In the meantime, government investment also increased year by year, from 33.81 billion yuan in 2003 to 360.16 billion yuan in 2017.

However, the national investment effect coefficient¹ shows a clear down trend, from 28.44% in 2008 to 12.58% in 2016. Xinjiang's investment effect coefficient is lower than the national investment effect coefficient in most years (as shown in Figure 2). This shows that the GDP pulled by unit fixed asset investment in the whole country is decreasing year by year, and the investment benefit in Xinjiang is lower than the national average level. Therefore, it is of great practical significance to study the dominants of the government investment effect and put forward policy suggestions to improve the effectiveness and accuracy of government investment.

¹Investment effect coefficient is equal to the fixed asset investment divided by the GDP.

Many domestic scholars have made in-depth analysis and exploration on how to improve investment efficiency and optimize investment structure. Evans and Karras^[2] found that education investment in public investment has a significant positive effect on efficiency improvement, but public investment in other projects has no obvious effect, or even shows a negative impact. Zhu, et al.^[3] divided the factors which affect the investment effect of urban infrastructure into investment volume, subsystem investment effect and investment structure, and they found investment structure played an increasingly important role in investment effect of urban infrastructure by SDA analysis. Qin, et al.^[4] studied the effect of government investment from the perspective of industrial structure and residents' consumption. According to Luo, et al.^[5], unreasonable investment structure seriously hinder the sustainable, stable and healthy development of local economy, and optimizing investment structure should be emphasized in making investment decision. Ma and Li^[6] indicated that adjusting investment structure, which can improve investment efficiency, will release potential supply capacity and promote economic growth. Su, et al.^[7] showed that under the condition of maintaining equal investment, adjusting industrial structure and increasing investment in the tertiary industry has a significant positive impact on economy. Du^[8] found that more attention should be paid to the transmission mechanism of government investment to industrial structure adjustment and the degree of influence on industrial structure, by combing the relevant research of government investment. The research group of macroeconomic research center of Chinese Academy of Financial Sciences^[9] analyzed the macro effect of government investment, and they found investment structure should be continuously optimized under the given scale of government investment. Xu^[10] pointed out the impact of investment in different industries is different, and it was more practical to evaluate the efficiency of government investment through government investment structure. Zhou^[11] calculated, by compiling China's social accounting matrix in 2007 and 2012, unreasonable industrial investment structure led to the low efficiency of fixed asset investment in stimulating economic growth and employment. In addition, the effect of investment which is from national budget is better, while the effect of investment which is from other funds and domestic loans is terrible. Liu^[12] proposed that optimizing investment structure can increase effective investment and reduce ineffective investment. Jin^[13] believed that government was an indispensable condition and governance approach to achieve high-quality development, and the improvement of government investment effect would directly reflect the quality of economic development. Liu^[14] noted that future investment will optimize the input structure of elements and optimize the industrial structure to play a key role in optimizing the supply structure on the same side. Cui^[15] through analyzing the relationship between private investment, industrial structure and economic growth, put forward that the government should speed up the implementation of policies and measures to promote the development of private investment, steadily promote the optimization and upgrading of industrial structure, and cultivate a new motive force for economic growth. Xu^[16] proposed that the current level of supply structure in China is at the bottom of the global ranking, and it is necessary to continue to optimize the investment structure and make up for the existing shortcomings. Guo, et al.^[17] proposed to enter the stage of high-quality development, and the investment structure of infrastructure should be adjusted to tilt to the fields of new infrastructure and livelihood infrastructure in order to promote the upgrading of industrial structure. Wang, et al.^[18] analyzied the general change trend of Chinese government investment and the preference of all kinds of government investment for industries. Yin, et al.^[19] demonstrated that the government investment efficiency in Xinjiang, Gansu, Qinghai and other places is low, because the overall economic development level of these areas is not high, the vast administrative areas, scattered industries and population layout make the public infrastructure provided by the government not fully utilized. Lee, et al.^[20] studied Korea's research and development (R&D) investment performance, and decomposed R&D investment efficiency into pure R&D investment technical efficiency and scale efficiency.

From the existing research, scholars have done a lot of research on effect of investment, optimization of investment structure and so on, but there are few literatures to analyze the determinants of government investment effect. Therefore, this paper uses structural decomposition analysis method to decompose the change of government investment effect into the change of economic structure, technology and investment structure. And we make an empirical study on the effect of government investment in Xinjiang from 2007 to 2015. The results show that the government investment effect in Xinjiang shows a slight decline trend, but the effect of government investment in Xinjiang is relatively better than that in the whole society. During the period, the change of economic structure and investment structure have the negative impact on government investment effect, while the change of technology has the positive impact on government investment effect. In addition, these impacts have strong sectoral heterogeneity. The effect of government investment in the production and supply of electricity, gas and water has a positive effect and a large positive spillover effect. The effect of government investment in transportation, storage and post, water conservancy, environment and public facilities management, agriculture, forestry, animal husbandry and fishery products and services have declined, but the positive spillover effect of government investment is large. Part two is model construction. Part three is data source and data processing, the focus is to determine the caliber of government investment and prepare non-competitive input-output table of Xinjiang. Part four is empirical analysis. In the end, based on the results of the study, some suggestions are put forward to improve the effect of government investment.

This paper uses the method of structural decomposition analysis (SDA) to explore the influencing factors of government investment effect, so it is necessary to establish an investment effect model based on SDA. Investment effect is the main index to evaluate the economic benefits of macro investment. It refers to the GDP increased by unit fixed asset investment in a certain period. The GDP calculated by income method is equal to the value added in the input-output table. Therefore, the investment effect coefficient can also be expressed as the value added driven by unit investment.

The classical input-output model is: $X=(I-A{)}^{-1}F$, where $X$ is the total output vector; $A=(a_{ij}{)}_{n\times n}$ is the direct consumption coefficient matrix, and $a_{ij}$ is the direct consumption coefficient, also called technical coefficient. It means the direct consumption of sector $i$, when sector $j$ products unit production. And it reflects the technical and economic relationship between sector $j$ and sector $i$ at a certain technical level. Note $\tilde{B}=(I-A{)}^{-1}$, where $\tilde{B}$ is called Leontief inverse matrix, also called complete consumption coefficient matrix, which comprehensively reveals the complicated economic relations among various industrial sectors of the national economy. $F$ represents the final demand of each sector. This formula represents the output driven by final demand. Then the value added driven by final demand is: $V=A_{V}X=A_V(I-A{)}^{-1}F$, where $A_V$ is the coefficient of direct value added. As the final demand includes investment vector, the value added driven by investment can be calculated, and then divided by the total investment is the investment effect coefficient.

The calculation formula of total investment effect is

where $A^D$ is the direct consumption coefficient matrix of the non-competitive input-output table, $I_c$ is the column vector of investment structure.

The calculation formula for the investment effect of sub sectors is

where $\widehat{A_V}$ is the diagonal matrix with $A_V$ as the diagonal elements.

SDA has developed into a mainstream economic analysis tool in the field of input-output, which is widely used in economic growth, technological progress, industrial research, trade, price, resource and environmental protection. Its basic idea is to measure the contribution of each independent variable change to the dependent variable change by decomposing the change of a dependent variable in the economic system into the sum of the independent variable changes. Input-output technology can analyze the complete correlation between sectors, thus we can calculate the direct contribution and the indirect contribution (Chen and Yang^[21]). The results of SDA decomposition are not unique, and some studies show that when the dependent variable is decomposed into n factors, there are $n!$ decomposition methods. But the average value of $n!$ possible decomposition results is very close to the bipolar decomposition results (Dietzenbacher and Los^{[22, 23]}; De Boer^[24]). Therefore, this paper uses the bipolar decomposition method to decompose the above investment effect model.

Note the base period is $0$ and the reporting period is $1$. $△EIC$, $△\widehat{A_V}$, $△B$, $△I_c$ respectively represent the changes of the investment effect coefficient vector, direct value-added coefficient matrix, complete demand coefficient matrix and investment structure vector from the base period to the reporting period. Then, formula (2) can be decomposed into:

where $C(△\widehat{A_V})$ is the contribution of the change of direct value-added coefficient to the change of investment effect. It represents the direct value added driven by unit output, which reflects the change of economic structure to a certain extent. Thus we call it the change in economic structure; $C(△B)$ represents the contribution of the change of direct consumption matrix to the change of investment effect. The direct consumption coefficient matrix is also called the technical coefficient matrix, which reflects the technical and economic relations among various industrial sectors at a certain technical level, so it is called the technical change; $C(△I_c)$ is the contribution of the change of investment structure to the change of investment effect.

This paper explores the determinants of Xinjiang government investment effect changes in 2007–2012 and 2012–2015. Thus we need non-competitive input-output table of Xinjiang in 2007, 2012 and 2015 and the structure of government investment of Xinjiang in corresponding years. Because of no ready-made data available, we make the following data processing:

In the Xinjiang statistical yearbook, there are only 19 sectors² in total investment and total amount of fixed assets in whole society. According to the regulations on government investment issued in 2019, the government investment funds should be invested in social public welfare services, public infrastructure, agriculture and rural areas, ecological environment protection, major scientific and technological progress, social management, national security, etc. Therefore, we assume the government investment is mainly in agriculture, forestry, animal husbandry and fishery, power, gas and water production and supply industry, construction industry, transportation, storage and postal industry, scientific research and technical service and geological survey industry, water conservancy environment and public facility management industry, resident service and other services industry, education industry, health and social security and social welfare industry, culture, sports and entertainment industry, public management and social organization industry. Under the assumption that the proportion of government investment is the same as that of fixed asset investment in the whole society, we can calculate the proportion structure of government investment in 19 sectors.

²The 19 sectors include: Agriculture, forestry, animal husbandry and fishery, mining, manufacturing, production and supply of electricity, gas and water, construction, transportation, warehousing and postal services, information transmission, computer services and software, wholesale and retail, accommodation and catering, finance, real estate, leasing and business services, scientific research technology and geological exploration, water conservancy environment and public facilities management, resident services and other services, education, health and social security and social welfare, culture, sports and entertainment, public management and social organization.

The key point of compiling the non-competitive input-output table is to divide the intermediate use part $x_{ij}$ in the competitive input-output table of Xinjiang into three parts, one part is the intra provincial intermediate input $x_{ij}^D$, the other part is the import intermediate input $x_{ij}^{IM}$, and the last part is the inter provincial transfer input $x_{ij}^{PIM}$. Corresponding final intra provincial use $Y_i$ is divided into the volume of intra provincial products using $Y_i$, note $Y_i^D$, the volume of imported products using $Y_i$, note $Y_i^{IM}$, the volume of inter provincial transfer in products using $Y_i$, note $Y_i^{PIM}$. As shown in Table 1.

In this paper, the proportion assumption method is used, calculated:

Among them, ${\alpha }_i^{IM}=\frac{I{M}_i}{X_i-E{X}_i-PE{X}_i+I{M}_i+PI{M}_i}(i=1,2,\cdots ,n)$ is the proportion of each sector imports in the total demand, ${\alpha }_i^{PIM}=\frac{PI{M}_i}{X_i-E{X}_i-PE{X}_i+I{M}_i+PI{M}_i}(i=1,2,\cdots ,n)$ is the proportion of inter provincial transfer of each sector in the total sector demand.

At first, we obtain the non-competition input-output table in 2007 by means of proportion assumption method, and then it is combined into 19 sectors. In the compilation of Xinjiang's 2012 non-competitive input-output table, due to the fact that the total inflow of sector S19, namely communication equipment, computer and other electronic equipment manufacturing industry is greater than the provincial demand (total inflow / provincial demand = 1.0023), there is a negative value of the provincial intermediate input. In order to solve this problem, we adjust the inter provincial transfer out of the sector S19, so that the total inflow equals to the intra provincial demand. Then we combine the 139 sectors non-competitive input-output table in 2012 to 19 sectors. In the preparation of Xinjiang's 2015 non-competitive input-output table, the total transfer out of the oil and gas production product sector is far greater than the sum of output and total transfer in, that is, the calculated demand in the province is negative. There are also some sectors where the total inflow is greater than the provincial demand, resulting in negative value of the provincial intermediate input in the preparation process. To solve the above problems, we assume that the transfer in proportion of these sectors is the same as that of 2012, and adopt the transfer in proportion of 2012 to apportion it, and finally obtain the non-competitive input-output table of Xinjiang in 2015.

According to Table 2, the effect of government investment decreased in 2007–2015 due to the negative impact of economic structure change and investment structure change, while the technical change has a strong role in promoting the effect of government investment. Among them, from 2007 to 2012, the effect of government investment decreased by 1.76%, from 2012 to 2015, the effect of government investment decreased by 3.85%. The change of economic structure is the main reason to pull down the effect of government investment, while the technology change is the main reason to improve the effect of government investment. This result is consistent with Fan, et al.^[25], and they show that the adaptability level of the fixed asset investment structure and industrial structure in the western region is generally not high.

Tables 3 and 4 respectively show the influence of various factors on the effect of government investment in different sectors in 2007–2012 and 2012–2015. From 2007 to 2012, the effect of government investment in four sectors has increased, such as production and supply of power, construction industry, education, public management, social security and social organizations. The main factor that promote the growth of the investment effect of the production and supply of power and construction industry is the change of investment structure. The main factor that promote the growth of the investment effect of education and public management, social security and social organizations is the change of economic structure.

The investment effect in seven sectors has declined, and the sectors with a large decline are agriculture, forestry, animal husbandry and fishery products and services, transportation, storage and postal services, water conservancy and environmental protection and public facilities management. The main reasons for the decline of investment effect in these industries are the change of economic structure and investment structure.

According to Table 4, from the perspective of the contribution of various factors, technological change has the greatest impact on the production and supply of electricity, gas and water, health and social work. Under the positive impact of technological change, the investment effect of these two sectors has increased; the change of economic structure has an impact on transportation, warehousing and postal administration, scientific research and technical services, water conservancy environment and public facilities management, residential service repair and its other services, culture and sports, entertainment and other five sectors contributed the most, and all were negative. It shows that although the investment in this sector is increased, due to the unreasonable industrial structure, it can not match the corresponding investment efficiently, so the investment effect is difficult to improve; the change of investment structure has the greatest impact on the three sectors of agriculture, forestry, animal husbandry and fishery products and services, construction industry, education, etc., which shows that the increase of investment in this sector should also pay attention to improving quality and efficiency, and play a key role in investment.

From the perspective of specific department, the agricultural, forestry, animal husbandry and fishery products and services sectors are the most negatively affected by the change of investment structure. Their contribution has increased from $-$7.42% in 2007–2012 to $-$3.84% in 2012–2015, and the investment effect has increased from $-$7.1% to $-$4.01%, indicating that the investment structure needs to be further optimized to promote the increase of investment effect. From 2007 to 2015, the production and supply sectors of electricity, gas and water were positively affected by changes in economic structure, technology and investment structure. Among them, the investment structure change in 2007–2012 contributed the most to the investment effect; the technology change in 2012–2015 contributed the most, followed by the economic structure change and investment structure change, and the investment effect decreased from 15.98% to 11.46%. It shows that the department should pay attention to technological progress and improve the investment effect through technological improvement. Transportation, storage and postal sectors, the two stages of economic structure changes have the greatest impact on the investment effect, with the contribution of $-$7.96% and $-$7.63% respectively, and the investment effect has declined from $-$6.73% to $-$7.43%. Analysis of the reasons may be that Xinjiang's economic development started late, and the investment in infrastructure is not profit-making. At the same time, Xinjiang has a vast area and weak transportation infrastructure, which has the characteristics of large investment, long payback period and low economic benefits. The results show that the unreasonable economic structure is the main reason for the decline of investment effect in this sector. At the same time, from the perspective of the overall effect of government investment, to remove the negative effect of the investment effect of this sector, the effect of government investment is on the rise, so it can be concluded that the investment effect of transportation storage and postal sector deserves attention.

According to the direction of government investment, each department can be divided into government investment department and government investment indirect pulling department. Government investment departments mainly refer to the departments invested by the government, such as agricultural, forestry, animal husbandry and fishery products and services, production and supply of electric power, gas and water, construction industry, transportation, storage and post, scientific research and technical services, water conservancy, environment and public facilities management, residential services, repair and other services, health and social work, culture, sports and entertainment, public management, social security and social organization. Government investment indirect pulling sectors refer to sectors without government investment or with a small proportion of government investment, mainly including mining, manufacturing, wholesale and retail, accommodation and catering, information transmission, software and information technology services, finance, real estate, leasing and business services.

On the whole, the spillover effect of various government investment departments is increasing year by year. In 2007, 2012 and 2015, the total spillover effect of government investment was 3.88 billion yuan, 19.07 billion yuan and 41.26 billion yuan respectively, accounting for 22.6%, 31.5% and 34.2% of the total pull effect of government investment. From the perspective of sectors, the production and supply industries of electric power, gas and water not only have good investment effect, but also have large spillover effect; the investment effect of transportation, storage and post, water conservancy, environment and public facilities management, agriculture, forestry, animal husbandry and fishery products and services has declined, but the spillover effect is large. It shows that Xinjiang's water conservancy, transportation, rural, ecological and other infrastructure are still relatively weak, so it is necessary to further increase investment and consolidate the development foundation to promote sustainable and healthy economic development (see Table 5).

Based on the above results, we can obtain the following conclusions. From 2007 to 2015, economic structure change contributed the most to government investment effect change, followed by technology change and investment structure change. Their contributions respectively are $-$15.56%, 13.71% and $-$3.75%. And the impacts of these factors on the investment effect of different sectors are heterogeneous. In addition, the positive spillover effects of government investment are increasing year by year.

The internal logic of the new normal of economic development is to speed up the transformation of economic development mode, realize the transformation of economic growth power, and maintain medium and high-speed growth on the basis of improving the development balance, inclusiveness and sustainability^[26]. Based on the above research and analysis, this paper puts forward the following suggestions:

First, we will continue to promote the construction of key areas and weak links in infrastructure. We will increase investment in transportation, warehousing and postal services, water conservancy, environment and public facilities management, power, gas and water production and supply, guide more private capital to participate in infrastructure construction, and gradually narrow the gap between Xinjiang and the mainland in infrastructure construction. Second, we should strengthen the adjustment of economic structure, rationally arrange the industrial structure, moderately increase the proportion of investment in the primary industry, effectively improve rural production and living conditions, and promote the coordinated development of urban and rural areas. To increase the matching degree of investment structure and industrial structure, so that the infrastructure provided by the government can be fully utilized, so as to improve the investment efficiency. Third, We will increase investment in such industries as scientific research and technical services, environmental and public facilities management, residential services, repair and other services. In the future, the development of high-end service industry can not only promote economic growth, but also improve service efficiency and promote the development of agriculture and manufacturing industry^[27]. Xinjiang should attract more mainland enterprises, especially those assisting Xinjiang, to participate in the development of service industry and enhance the new driving force of Xinjiang's economic development. Fourth, we will create a good investment environment. The main reasons for the low efficiency of investment in the western region are the late start of economic development, the low level of productivity, and the ineffective operation and income of the invested funds^[28]. If we don't strengthen the cultivation of soft market environment in the western region, the government's investment benefit will be greatly reduced^[29]. Most of the public sector projects invested by the government have strong positive externalities. Through strengthening the management of government investment projects, we will achieve the leading role of government investment. Fifth, we will seize the opportunity of opening to the west, accelerate the construction of the core area of the Silk Road Economic Belt in Xinjiang, and improve the level of opening up and export-oriented economic development.