Research on the Influencing Factors of Producer Services Agglomeration—Based on the Yangtze River Delta Urban Group

Based on the panel data of 16 cities between 2003 and 2018 in China City Statistical Yearbook, this paper analyses the current situation and the influencing factors of Producer Services Agglomeration in the Yangtze River Delta. The research adopts spatial econometric methods with spatial weight matrix. The empirical result shows that the agglomeration trend of producer services in Yangtze River Delta is obvious, and the spatial agglomeration pattern is gradually formed. Opening degree and human capital have positive impacts on producer services agglomeration. The agglomeration is negative. And city scale has no effect on the agglomeration. At last, the paper puts forward some suggestions to improve the level of producer services agglomeration in the Yangtze River Delta.


Introduction
As the high-end industry types in the value chain, producer services are of great importance to promote China's economic quality development. In the development process, producer services have the characters of industrial agglomeration. As the representative of industrial agglomeration, gathering centers like Singapore Science Park, Shanghai World Financial Center, Hangzhou and Ningbo International Shipping Service Center develop rapidly in recent years. Conceptually, the agglomeration of productive services refers to the fact that producer services companies are linked together and concentrated in specific geographical areas because of their commonality and complementarity. The performance is manifested in two aspects. At the industry level, the producer service industry is unevenly distributed across the country. At the regional level, the producer service industry is concentrated in specific regions. Domestic and overseas scholars have found that the external effects [1] and the scale effect have brought a positive impact on the regional development pattern and economic growth. Mukesh et al. suggested that productive service industry agglomeration would promote regional economic development by improving the investment environment and strengthening technical exchanges [2]. Chen Jianjun considered that producer services agglomeration make economic factors flowing freely and spontaneously, improve space contact pattern between areas, bring scale economy and knowledge spillovers to the regions [3]. Zeng Yi found that the producer service industry can improve the quality of regional economic growth significantly [4]. Since producer services agglomeration has played a very important role in China's sustainable economic development, this paper creates the influencing factors model of producer services agglomeration, trying to analyze how various factors influence productive service industry and whether there is a difference in the role and the effects between different factors. About the influencing factors model of producer services agglomeration, domestic scholar Chen Jianjun constructed an analysis framework for the agglomeration factors of productive service industries earlier, and analyzed agglomeration factors from four aspects: knowledge intensity, city size, information technology and the system [5]. Wu Fu, Cao Lu start the research from the relationship between the two global and domestic value chains, analyzed agglomeration factors from four aspects: the degree of concentration in manufacturing, dependence on external demand, the level of information and the city grade [6]. Chen Hongxia analyzed from three aspects: traditional location factors, policy factors and agglomeration factors [7]. With reference to the above analysis framework, this paper attempts to select human capital, city size, manufacturing level, and degree of openness as explanatory variables from the four aspects of factors: cities, space and systems, as to study the state and influencing factors of productive service industry agglomeration and figure out how to promote the level of regional agglomeration. Due to the differences in the level of producer services in various regions [8] and the development of the productive service industry in the Yangtze River Delta is better [9] [10], this paper selects the Yangtze River Delta city as the research object to analyzes the state and influencing factors of the agglomeration of the producer service industry.

The Theoretical Assumptions
From neoclassical economists Alfred Marshall proposed the external economic theory; scholars began to focus on aspects of industrial agglomeration, pointed out that enterprises gather together due to the pursuit of external scale effect.
The external economic theory explains the increasing income of agglomeration from the three aspects of sharing labor market, intermediate product input and tion costs into the analytical framework, re-study location selection and inter-regional trade issues, and believe that all economic behaviors are spatially non-uniformly distributed, and explain why economic behaviors are concentrated in some areas and the reasons for the differentiation in the regional space.
Neoclassical economists have summarized the reasons for agglomeration into three categories: market demand, external economy (including labor market sharing, specialized input and the flow of knowledge) and contingency factors. Based on the above review, this paper created the "elements-space-city-institutional" framework to study the reasons of productive service industry agglomeration.

The Angle of Production Factors
The productive service industry, as a high-knowledge industry, has human capital as its main input and higher requirements for the quality of labor factors. The increase and free flow of high-level personnel can promote innovation ability of enterprises, which makes enterprises have access to collective learning and tacit knowledge in the industry. Due to the special attributes of the producer service industry, it is very likely that the new enterprise will be separated from the original enterprise. The professional talents will leave the original enterprise and set up a new enterprise, thus promoting the production service industry to gather in the region. Therefore, this paper proposes hypothesis 1: the improvement of human capital level plays a positive role in the agglomeration of urban productive service industry.

The Angle of Space
The producer service industry was originally located between the secondary industry and the tertiary industry. With the refinement of the division of labor, it gradually became independent from the manufacturing industry. The consumption target of the producer service industry is not the ordinary consumer but the producer of the manufacturing industry. It is attached to the secondary industry and is the supporting service industry of the secondary industry. Therefore, the development of the productive service industry cannot be separated from the manufacturing industry development. According to the definition of the producer service industry, the level of manufacturing development is a factor that affects the producer service industry agglomeration. Therefore, this paper proposes hypothesis 2: the improvement of manufacturing level is conducive to the agglomeration of productive services.

The Angle of City
The producer service industry is the product of the improvement of the social trial services related to agglomeration, which will help the producer service industry to reduce production costs and obtain agglomeration benefits and comparative advantages. The agglomeration of productive services brings diversity of services to the region, attracts consumers and producers from other regions, and further promotes the snowballing agglomeration of the producer service industry. Therefore, this paper proposes hypothesis 3: The increase in city scale has a positive impact on the agglomeration of productive services.

The Angle of Institution
The level of agglomeration in the producer service industry is often closely re-  Table 1, there are differences in producer services agglomeration level between cities, and in general the overall agglomeration trend is evident. Represented by three cities of Shanghai, Nanjing and Hangzhou, each city has formed a scale gathering to a certain extent, and the spatial agglomeration pattern of the productive service industry in the Yangtze River Delta is taking shape. According to the average of the regional entropy of each city, the 16 central cities in the Yangtze River Delta can be divided into four grades. The location entropy values of the six major producers in Shanghai are all greater than 1, and the average location entropy is 1.7609, in the interval of [1.50 -2.0], far greater than the average of 0.7784 in all cities. The degree of agglomeration of Shanghai production service industry is highest among the 16 cities; therefore Shanghai is the central city in the central-peripheral model. According to the numerical values from large to small, the location entropy of Nanjing is 1.4436, Hangzhou is 1.3831, Zhoushan is 1.2420, Zhenjiang is 0.8268, Ningbo is 0.7978, the location entropy of five cities is all in the range of [0.70 -1.50], showing that the agglomeration level of five cities is great in the rank, the average values of the location entropy of the six sub-sectors of the five cities are higher than the average level of the city, so this article will rank Nanjing, Hangzhou, Zhoushan, Zhenjiang, Ningbo as the second level. The third level includes six cities, which   Table 2.

Spatial Correlation Analysis
This paper first constructs a spatial weight matrix based on geographic distance,  The ratio of the number of university students in higher education institutions in cities and the number of students in 16 cities in the Yangtze River Delta.

Independent variable
City size (CS) The ratio of population of each city in the Yangtze River Delta and the total number of urban population.

Independent variable
Manufacturing level (I) The ratio of industrial production value of each city to the total industrial production value of 16 cities in the Yangtze River Delta.

Independent variable Degree of openness (O)
The ratio of the actual amount of foreign investment in each city to the amount of foreign investment in 16 cities. and then judges whether there is correlation between city groups through Moran index. The Moran index is an important indicator for measuring spatial autocorrelation and can be divided into global and local Moran indexes. This paper choose global Moran index to measure spatial correlation, the specific expression is shown in Equation (2), in which x refers to the representatives of regional observations, ij w is spatial weight matrix representing close relationship between regions [11]. Moran index is between [ ] 1,1 − , a value less than 0 represents a negative correlation, indicating the presence of significant gaps between adjacent cities' development level; value greater than 0 represents a positive correlation, indicating significant agglomeration of regional economic activity; value 0 represents not relevant, the economic activities in the region are randomly distributed.

Econometric Model
Based on the latitude and longitude coordinates of 16 cities in the Yangtze River Delta, this paper constructs a binary 16 × 16 spatial matrix by using Geoda soft-  and consider the space factor in the econometric model is required.
Because the data of the Yangtze River Delta has spatial correlation and does not satisfy the assumption that the ordinary least squares data are independent of each other, this paper selects the spatial constant coefficient regression model considering the spatial correlation, which includes the following two models: 1) Spatial Lag Model to measure variables in the region is whether there is room for spillover effects that affect the variables will affect other regions. The model expression is shown in Equation (5), where Y is the dependent variable, W is the spatial weight matrix, X is the explanatory variable, and β is the parameter vector, µ is the random error vector.
2) Spatial Error Model to measure the impact of error shocks of dependent variables in other regions on the local region. The model expression is shown in Equations (6) and (7), where ε is the random error vector, λ is the spatial error coefficient and W is the spatial weight matrix.
According to the general discriminant criterion proposed by Anselin and Florax in 1995: In the spatial correlation test, it is generally more appropriate to determine the select of the spatial lag model and the spatial error model by comparing the Lagrangian statistic LMERR and LMLAG. If the LMLAG statistic is more significant than the LMERR statistic, the spatial lag model is more appropriate. On the contrary, it shows that the spatial error model is more suitable. If both LM tests are significant, then the robust LM statistic is compared and the model with more robust statistic is selected. The LM test results (see Table 3) Based on the theoretical framework of "element-space-city-institution" pro-  (8), where W is a spatial weight matrix, which β is a parameter vector and µ is a random error vector.
Next, a Holsman test of the spatial econometric model is adopted to further determine whether a random effect or a fixed effect analysis should be used. The results of the Holsman test show that the statistical probability value of the spatial lag model is 0.3297, which is greater than the significance level, which indicating that the random hypothesis model should be adopted [12]. Based on the above Lagrangian multiplier statistic test results, this paper uses the spatial lag model, random effect to analyze.

Empirical Results
This paper uses Matlab software to analyze the influencing factors of the agglomeration of the production service industry in the Yangtze River Delta. The specific results are shown in Table 4. The empirical results show that degree of openness and human capital level is positive to the agglomeration of production service, which verify hypothesis 2.1 and 2.4. The impact of changes in the size of the city to productive service industry is not obvious, upgrading of the manufacturing level is not conducive to productive services agglomeration. The empirical results reject the hypotheses 2.2 and 2.3, which will be further analyzed below. As the degree of openness to the outside world can accelerate the flow of  Note: "***", "**", "*" indicate it is significant at 1%, 5%, and 10% levels The coefficient before the city scale did not pass the significance test, indicating that the impact of city size on the agglomeration of the producer service industry is not obvious. This may be caused by the fact that when the size of the city is too large, the company tends to spread the layout in various places to cut down the costs of factors such as transportation, which is not conducive to the agglomeration of the productive service industry. The expansion of city scale will also be accompanied by the emergence of non-economic factors such as rising living costs, traffic congestion and environmental pollution, which will make the producer service industry change to non-aggregation. This shows that the city size and the agglomeration economy are not necessarily linear. The city size is not the better the bigger it is. The coefficient value before the manufacturing level is negative and passed the significance test, indicating that the improvement of the manufacturing level is not conducive to productive services agglomeration, rejected the hypothesis 5. The possible reason is that the economic

Conclusions
The article found the agglomeration of producer service in Yangtze River Delta was evident and the pattern of spatial concentration is forming gradually. The vor of deepening regional production, increasing productivity, promoting the overall development of economic. This paper puts forward some suggestions to accelerate the agglomeration of service industry.

Recommendations
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The Deficiencies and Prospects
Producer services agglomeration research is an emerging research direction in the field of industrial agglomeration research and is in the initial stage of research. The research in this paper only analyzes the status quo, characteristics and influencing factors of producer service industry agglomeration in the Yangtze River Delta. Although some research conclusions have been drawn, due to the limited academic knowledge of author, this research still has some shortcomings. First, in the analysis of the factors affecting the agglomeration of productive service industry, although this paper proposes four influencing factors using the "element-space-city-institution" framework, this paper does not use mathematical model to deduct and analyze this. In future research, we can consider putting various influencing factors into the mathematical model for analysis, and then using numerical simulation to obtain more general conclusions. Secondly, this paper takes the Yangtze River Delta region as an example to study the influencing factors of the agglomeration of productive service industries. It has not been studied and analyzed with national data. Since the producer service industry itself is a relatively large departmental category, which has a wide distribution range. In the subsequent research, we can study from other regions or the whole country to get more general conclusions. These are the deficiencies of this research, and also some prospects of future research.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this paper.