The Spatial Spillover Effect of Input and Output of Scientific Progress on Regional Economic Growth: The Case of Guangdong Province

This paper makes an empirical analysis of the spatial spillover effect of regional economic growth by using Moran’s I and Spatial Durbin Model to study the input and output of technological progress, with the panel data of 21 prefecture-level cities in Guangdong Province from 2008 to 2017. The empirical results show that the spatial autocorrelation exists in the economic development of Guangdong Province, and both the input and output of scientific research innovation have a significant positive effect on the regional economic growth. Under the spatial contiguity weights matrix, the output of scientific research and innovation has a more obvious spillover effect on the economic growth of neighboring cities than the input of scientific research and innovation.

the stage of high-quality development. Among them, scientific and technological innovation is the internal driving force for the further growth of regional economy. At present, many scholars have realized the positive effect of technological innovation on regional economy, and can quantify the technological innovation capacity between different regions. However, the existing literature mostly takes the input of scientific and technological innovation and economic growth rate as the research focus, ignoring the competition of scientific and technological innovation between neighboring regions will increase the investment of funds. The space spillover effect makes it easy to underestimate the impact of technological innovation on the quality of regional economic development. Therefore, this paper takes 21 cities in Guangdong Province as an example, uses the panel data from 2008 to 2017, and adopts the Spatial Durbin Model to study the spatial spillover effect of input and output of scientific and technological innovation on regional economic growth.
In fact, domestic and foreign scholars have done a lot of research on regional economic growth with regard to technological progress, which has laid a solid foundation for the following empirical analysis. New economic geography puts forward the spatial dimension on the basis of classical economics, and analyzes economic growth from the perspective of space. Lucas [1] proposed the concept of spatial spillover effect. Krugman [2] combined the assumptions of imperfect competition and increasing returns to scale, which brought the study of regional economics into a new dimension. Englmann [3] and Kubo [4] also pointed out that the spillover effects of regional economic growth include global spatial spillover effect and local spatial spillover effect, respectively. Viladecansmarsal [5] used the model of spatial econometric to study the spatial spillover effect between Spanish cities, and found that the increase in the population size and employment level of neighboring cities would strengthen the economic agglomeration of the place. Avijit and Niranjan [6] based on data from 1981-2007 in northeastern India, tested the local NDP with significant spillover effects, and the growth in most regions was higher than the regional average. Marco [7] considered that the core cities in the urban agglomeration have a spatial spillover effect on peripheral cities, and used panel data from 30 provinces in China to examine the effect of labor on economic growth in different regions of China, and concluded that the spillover effect of human capital leads to the agglomeration effect of economic growth.
In the study of the impact of scientific research innovation on regional economic growth, Benjamin and Marcos [8] considered that there is a competitive effect between the investment of R & D expenditures between countries, and policy incentives can promote the active interflow of private scientific research enterprises between countries. Qin [9] et al. based on Chinese provinces and concluded that the efficiency of inter-provincial innovation output has a strong spatial dependence and exhibits a two-way spillover effect. Kristy [10] [11] et al. used Iran as an example to analyze the inefficient technological innovation ability which has a negative effect on economic growth. Zhou [12] et al.
studied the impact of technological growth on government expenditure and found that the more investment in science and technology research, the higher the economic growth, the lower the macro-control effect of government expenditure. Zhang [13] found that spillovers caused by foreign direct investment had a positive and statistically significant impact on the productivity of Chinese innovation activities. Chen [14] et al. divided China into eight regions and discussed the issues of GDP, R & D expenditures and patents. Xiong [15] et al. concluded that the level of society played a coordinated role in the simultaneous development of technological innovation output and economic development.
In summary, technological progress is a new endogenous driving force for regional economic development. Studying the spatial spillover effect of technological progress in Guangdong Province is of great significance to the economic development and transformation of Guangdong Province. This paper will conduct research based on the following three aspects: first, study the spatial autocorrelation of the economy in Guangdong province. Second, choose the input and output of scientific research and innovation as explanatory variables, and at the same time select relevant control variables to construct a spatial econometric model. Third, empirical analysis based on the above spatial econometric model, to explore the specific effect of technological progress input and output on economic growth.

The Moran's I
The spatial autocorrelation test is used to determine whether there is a spatial spillover effect between cities. The Moran's I is the most common method. The  S is the sample variance, x is the sample mean, ij w is the spatial weight matrix element that describes the spatial relationship between area i and area j, and n is the number of spatial units in the area. The value of the global Moran's I is between (−1, 1), less than 0 means that the whole area is negatively spatially correlated, more than 0 means that the area is positively spatially correlated, and equal to 0 means that there is no spatial correlation. The larger the absolute value, when i I is more than 0, the spatial correlation of area i may be high-high or low-low association type. The high-high type is the area i whose attribute value is higher than the mean is the neighboring area whose attribute value is higher than the mean. The low-low type is that the area i whose attribute value is lower than the average is surrounded by the adjacent area whose attribute value is lower than the average. When i I is less than 0, the spatial correlation of area i may be high-low or low-high association type. The high-low type is the area i with the attribute value higher than the mean is the neighboring area with the attribute value lower than the mean. The low-high type is that the area i whose attribute value is lower than the average is surrounded by the adjacent area whose attribute value is higher than the average. When i I is close to 0, it means that there is no spatial association between this area and the adjacent area.

Setting of Spatial Weight Matrix
Because technological innovation requires excellent infrastructure and strong economic capital, the cooperation and competition between technological innovation in cities with similar economic strength will be stronger. It means the corresponding spillover effect will be more obvious. Taking into account the geographical environment and the actual situation of Guangdong Province, this paper uses traditional spatial contiguity matrix and economic distance weight matrix for testing. Spatial contiguity matrix means that the contiguity weight between two cities is 1, otherwise it is 0. The formula of the economic distance weight matrix is as follows: when i j = , the spatial weight is 0, and Y refers to the Real GDP per capita of the city during the sample period.

Spatial Durbin Model
The empirical part of this paper uses panel data and Spatial Autoregressive Model. The Spatial Autoregressive Model is mainly divided into Spatial Lag Model, Spatial Error Model and Spatial Durbin Model. Among them, the first two are special forms of the Spatial Durbin Model, so this article uses the Spatial Durbin Model, the general form is as follows: where ρ is the spatial autocorrelation coefficient, w is the spatial weight matrix, β and θ are the coefficients of the spatial lag term of the explanatory variable and the spatial lag term of the explanatory variable, and ε is the random error term.

Panel Data Sources
This

Global Moran's I Test
After constructing the two spatial weight matrices, the global Moran's I test was conducted on the Real GDP per capita of 21 prefecture-level cities in Guangdong Province from 2008 to 2017. The results are shown in Table 1. The results show that both spatial matrices indicate that there is a positive spatial correlation between the regional economic development capabilities of 21 prefecture-level cities in Guangdong Province. Among them, the spatial contiguity matrix has a larger Moran's I at a significance level of 0.01, which can explain the spatial spillover effect of the region. Therefore, later research uses spatial contiguity matrix for empirical analysis.

Local Moran's I Test
After the global Moran's I test, in order to deepen the spatial correlation of the regional economic development level between cities in Guangdong Province, based on the data of 2008 and 2017, the spatial contiguity matrix was used to calculate the local Moran's I. The results are shown in Table 2. Figure 1 is divided into type. It is a strong proof that the regional economic development level in Guangdong Province has a significant spatial correlation.

Spatial Durbin Model
This model is based on the Spatial Durbin Model and the Cobb-Douglas production function, and the variables are logarithmically processed and set as follows: where ρ is the spatial autocorrelation coefficient, W is the spatial weight matrix, β and θ are the coefficients of the spatial lag term of the explanatory variable and the spatial lag term of the explanatory variable, and ε is the random error term.

Test Spatial Econometric Model
In order to further ensure the rationality of the spatial econometric model, this  Table 3.
It can be seen that the LM test can pass at the significance level of 0.05. The three tests for spatial error reject the null hypothesis of no spatial autocorrelation, and the LM statistic in the spatial lag also rejects the null hypothesis. These results indicate that the spatial econometric model would be useful.  Table 3. It can be seen that the revised two Hausman statistic p is less than 0.01, which can reject the original hypothesis of random effects. Therefore, this article uses the fixed effect model.

Estimation Results of Spatial Durbin Model
The fixed effect model is divided into three types: spatial fixed-effect model, time effect model and double fixed-effect model. This paper fits the three fixed-effect models separately, and the results are shown in Table 4. It can be seen from the results that in any effect model, the explanatory variables InPat and InRD have a

Effect Decomposition of Spatial Durbin Model
Because of the regression analysis of the spatial econometric model with the spa- variables on the overall economic growth of the region, so the partial differential method is used to decompose the total spatial effect. The decomposition results are shown in Table 5.   level is negative. It shows that there is a surplus of labor, which indicates that the excessively rapid urbanization process has promoted the siphon effect on the surrounding labor in the developed regions, but excessive labor cannot be well configured. On the contrary, it hinders the development of regional economy.
The indirect effects of fixed asset investment and industrial structure also indicate that economic transformation and the development of high-tech industries are beneficial to neighboring cities and regions as a whole. sion of labor in each city, and establish a multi-industry and cross-regional multi-investment system for R & D. Finally, the government should establish an institution for innovation and development, whose main function is to evaluate the innovation capacity of each city, and to regulate and control different resources in cities with different innovation capabilities, so as to achieve a reasonable distribution of regional innovation production factors. In this way, inter-city coordination is strengthened during the formulation and implementation of various urban economic policies to effectively avoid the adverse effects of the vicious competition of scientific research and innovation on the overall regional economy.

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