2.1 Selection of indicators for protecting innovative achievements

Drawing on the method of Zheng et al. (2017), the law enforcement effect was included in the comprehensive evaluation of the level of innovation achievement protection, in order to better reflect the actual effect of innovation achievement protection. The specific calculation process of the comprehensive indicator for innovation achievement protection is as follows:

where IPR_it represents the level of innovation achievement protection in a certain province, and L_it and E_it represent the legislative and law enforcement levels of innovation achievement protection in the t-th year of province i, respectively. The calculation of L_it is represented by the G-P index, and the strength of E_it is determined by the weighted average of four secondary indicators: the degree of social legalization, the government's law enforcement attitude, the allocation of relevant service institutions, and the awareness of protecting social innovation achievements (where the weights of the four secondary indicators are consistent). Among them, the score for the degree of social legalization in a province was calculated based on the proportion of lawyers in that province. Specifically, when the proportion of lawyers to the total population in the t-th year of a province exceeds 0.05%, the value is 1. If it is less than 0.05%, the actual value is divided by 0.05%. The government's enforcement attitude indicator was measured by the completion rate of patent infringement cases in the t-th year of the province. The indicators for the allocation of relevant service institutions were represented by the ratio of law firms in the province that can handle innovation dispute resolutions. The indicator of social innovation achievement protection awareness was measured by the number of patent applications per 10000 people. Specifically, when the number of patent applications per 10000 people in a certain province is not less than 10 in the t-th year, this indicator is recorded as 1. Otherwise, the actual number of patent applications per 10000 people is expressed as one-tenth of the actual value. The larger the comprehensive indicator value for innovation achievement protection, the higher the comprehensive level of legislation and law enforcement for innovation achievement protection in the province.

2.2 Index of the internal structural upgrading level in the productive service industry

According to the Statistical Classification of Productive Service Industries (2019) and the classification standards of service industries in the China Third Industry Statistical Yearbook, the provincial-level productive service industries were divided into six categories: transportation, warehousing and postal, wholesale and retail, information transmission and software and information technology services, leasing and business services, scientific research and technology services, water conservancy and environmental and public facility management.

The setting of the evaluation index system for the internal structural upgrading of the productive service industry drew on the ideas of Cheng et al. (2011), and an index system was constructed from four aspects: promoting economic development and improving people's livelihoods, technological innovation, industrial upgrading, and energy conservation and emission reduction capabilities. It was calculated using principal component analysis (see Table 1 for details). To address the issue of dimensional differences in the raw data for each indicator variable in Table 1, the variables were standardized using the following formula:

In formula (2), is the mean of variable; and is the standard deviation of variable.

Table 1

Index system for upgrading the internal structure of the productive service industry

To accurately calculate the matrix eigenvalues, variance contribution rates, and cumulative contribution rates of the standardized data for each variable, principal component analysis was performed on the processed data using the “Statistical Product and Service Solutions” software (SPSS 17.0). According to Kaiser's principle proposed in 1960, the number of principal components only retains the top m factors with a cumulative contribution rate greater than 90%. Therefore, the eigenvalues of the first m factors are greater than 1, so they basically represent the key information of the original indicator. The scoring formula for each principal component is:

In formula (3), Y_m is the score of the m-th principal component; U_mi is the load value of the m-th principal component; and X_i is the standardized data for each indicator calculated based on formula (2).

Then, the variance contribution rate of each principal component was used to calculate the comprehensive score of the system, and the comprehensive evaluation index for the upgrading of the internal structure of the productive service industry was obtained.

In formula (4), W_m is the variance contribution rate of the m-th principal component (m=1, 2, ^..., n), and I_iand Y_mi represent the comprehensive evaluation index of each indicator in the i-th year (i=1, 2, ^..., n) and the m-th principal component score in the i-th year, respectively.

For the convenience of empirical testing in the subsequent analysis, the 3σ principle in statistics was adopted, and the coordinate translation formula =L+Y_t was used to eliminate the influences of negative values in the principal component analysis results. The comprehensive index value of the internal structural upgrading of the productive service industry was obtained. The larger the value, the more reasonable and effective the internal structure of the productive service industry. The internal structural upgrading of the productive service industry will greatly improve the utilization of production factors. On the contrary, if the calculated internal structure upgrading index of the productive service industry is low, this indicates that the target structure has not been achieved within the productive service industry, and the overall technical level is not high.

3.1 Spatial autocorrelation test

First, the Moran index and its scatter plot were used to determine the spatial agglomeration degree of innovation achievement protection and internal structural upgrading of the productive service industry. The results in Fig. 1^① show that the Moran value of the innovation achievement protection variable passed the 5% significance level test, and it demonstrates a positive correlation phenomenon. Meanwhile, the Moran values of the internal structural upgrading of the productive service industry in each year show that except for 2010, the Moran values in other periods are also positive. Through the 10% significance level test, there was a positive correlation overall, indicating that their spatial distribution is not random, but there is a clear clustering phenomenon.

The Moran index scatter plot (Fig. 1) has four patterns, namely areas of high-high clustering (first quadrant), low-high clustering (second quadrant), low-low clustering (third quadrant), and high-low clustering (fourth quadrant). For example, the high-high clustering area of the innovation achievement protection variable represents an area with a high innovation achievement protection level surrounded by other provinces with similarly high clustering levels; while the high-low clustering areas are those with high levels of innovation achievement protection that are surrounded by other provinces with low clustering levels. The Moran scatter plot of variables related to the protection of innovative achievements and internal structural upgrading of the productive services shows that most regions are located in high-high and low-low clustering areas. This indicates that most regions with high levels of both are spatially concentrated, while regions with low levels of both are surrounded by other provinces with low levels.

Fig. 1

Moran scatter charts of innovation achievement protection (IAP) and internal structural upgrading of the productive services industry (I)

Note: The horizontal axis of each Moran scatter plot represents the standardized test variable, while the vertical axis represents its spatial lag term.

3.2 LISA cluster diagram of the local indicators of spatial correlations

To further analyze the spatial concentrations of variables related to innovation achievement protection and internal structural upgrading of the productive service industry, the mean comprehensive index of innovation achievement protection and the mean internal structural upgrading of the productive service industry in each province from 2000 to 2022 were used as samples, and the local indicator of spatial connectivity (LISA) was used for measurement. Figure 2 shows that the clustering degree of the innovation achievement protection level in various regions of China in 2000 was not high. Except for Guangdong and Henan provinces, which are located in high-value areas (with high-high (HH) agglomeration), most other regions were in the medium-low (with low-high (LH) or high-low (HL) agglomeration) and low value areas (with low-low (LL) agglomeration). Therefore, overall, the distribution of the innovation achievement protection level in various regions of China in 2000 is not clear. By 2022, the clustering phenomenon of innovation achievement protection levels in various regions had become more obvious, with seven provinces located in areas with high innovation achievement protection intensity, namely Hebei Province, Shandong Province, Henan Province, Anhui Province, Sichuan Province, Guangdong Province, and Hunan Province. There are six provinces located at the second level, namely Jiangsu Province, Shanghai City, Hubei Province, Shaanxi Province, Jiangxi Province, Guangxi Zhuang Autonomous Region, and Guizhou Province; and seven provinces located at the third level, namely Liaoning Province, Zhejiang Province, Fujian Province, Yunnan Province, Gansu Province, Chongqing City, and Shanxi Province. The remaining provinces are located at the fourth level, mainly in areas where the protection of actual innovation achievements is relatively weak. Overall, the spatial clustering characteristics of the innovation achievement protection level in 2022 are clearer. Most of the eastern and central provinces are in the high and middle areas (with high-high or high-low agglomeration) of innovation achievement protection, while the western and northeastern regions are in the middle and low areas (with low-high or low-low agglomeration) of innovation achievement protection.

Fig. 2

LISA cluster diagrams of the innovation achievement protection (IAP) variables in 2000 and 2022

Compared to the model of the innovation achievement protection level variables, the evolutionary path of the spatial distribution of internal structural upgrading variables in the productive service industry from 2000 to 2022 was relatively similar. According to the cluster diagram (Fig. 3) of the average level of internal structural upgrading in the productive service industry, although Guangdong Province, Shandong Province, and Henan Province were located in high-value areas (with high-high agglomeration) in 2000, most of the other regions were in medium or low value areas (with low-high, high-low or low-low agglomeration). Overall, the comprehensive level of the internal structural upgrading index in the productive service industry in various regions of the country was not high, indicating a relatively high proportion of traditional productive service industries, while the development of high-level productive service industries was insufficient. By 2022, the overall level of the comprehensive index for the internal structural upgrading of the productive service industries in the eastern, central, northeastern, and western provinces had significantly improved. The number of provinces in high-value areas (with high-high agglomeration) increased to eight, including Hebei Province, Shandong Province, Henan Province, Jiangsu Province, Guangdong Province, Guangxi Zhuang Autonomous Region, Hunan Province, and Sichuan Province. The number of provinces in the second tier increased to six, including Zhejiang Province, Jiangxi Province, Hubei Province, Anhui Province, Guizhou Province, and Yunnan Province. The internal structure of the productive service industry was relatively reasonable in 2022, and the proportion of high-quality productive service industry was relatively high. The provinces at the third level include Fujian Province, Shaanxi Province, Shanxi Province, and Chongqing City, which had more vitality in the development of high-level productive service industries. Other provinces were at the fourth level, and their development of productive services was relatively lagging, while traditional productive services still accounted for a high proportion. Overall, from 2000 to 2022, the number of first and second level regions for the upgrading index of the internal structure of the productive service industry had significantly increased, and the agglomeration area grew. Under the radiation of the development of the productive service industry in the first level region, the internal structures of the productive service industries in its neighboring areas were continuously upgraded, showing a development trend of point by line and line by line promotion.

Fig. 3

LISA cluster diagrams of the internal structural upgrading level (I) of the productive service industries in various provinces of China in 2000 and 2022

From the perspective of the spatial distribution of the protection of innovative achievements and the internal structural upgrading of productive service industries, there is a clear similarity and synchronicity in their clustering trends. Therefore, it was necessary to construct spatial econometric models to test the spatial relationships between the two variables.

4.1 Model settings

The theoretical mechanism of innovation achievement protection for upgrading the internal structure of the productive service industry is mainly reflected in three mechanisms. 1) Mechanism of action: Innovation achievement protection stimulates technological innovation and the differentiated business operations of productive service industry enterprises, gradually converging them into winners of the monopolistic advantage competition. Protecting and cultivating advanced elements through innovative achievements enhances the ability to formulate a standard system with intellectual property as the core, controls industrial development, leads foreign trade, governs the international production value chain, and enhances the ability to distribute benefits. 2) Formation mechanism: National capacity, industrial foundation, and practical needs are prerequisites for the protection of innovative achievements in productive service industries. The protection of innovative achievements will further deepen the formation of advanced elements, major country effects, and monopoly advantages in the productive service industry. It will also play a core incentive role in promoting independent innovation to become a strategic industry development in the productive service industry, and in integrating it with the manufacturing industry. 3) Implementation mechanism: Implementation must include the simultaneous advancement of endogenous technological progress and government-led protection of exogenous technological innovation, the integration of technological innovation protection and high-end achievements in productive service industries into manufacturing and transformation into new competitive advantages, and the positive feedback between the protection of advantageous technologies of multinational corporations and moderate reverse outsourcing.

To further examine the impact of innovation achievement protection on the internal structural upgrading of productive service industries, following the approach of Tang et al. (2018), the innovation achievement protection variable was included in the model of the factors influencing service industry structural upgrading. At the same time, considering the unbiased regression results and the availability of sample data, the influencing factors identified in the existing literature were added to the model. Specifically, we divided the influencing factors into three levels: supply, demand, and interaction (Tang et al., 2018). The supply level mainly covers innovation achievement protection, human capital, and infrastructure. The demand level mainly covers per capita income and population density. The interaction level mainly refers to the level of manufacturing development. Therefore, the following basic model was constructed:

In formula (5), I represents the index of internal structural upgrading in the productive service industry, IAP represents the variable of innovation achievement protection, HC, Infr, PC, PD, and MD represent variables of human capital, infrastructure, per capita income, population density, and manufacturing development level, respectively, ξ_it represents random perturbation terms, β₁, β₂, β₃, Φ₁, Φ₂, and Ω₁ represent the coefficients of each variable, and β₀ is a constant term.

According to spatial data analysis, there is a significant spatial correlation between the protection of urban innovation achievements and the internal structural upgrading of the productive service industry. Therefore, spatial correlation needs to be included in the model. Due to significant differences in the spatial correlation impact modes of observed values, the spatial econometric models can be further subdivided into spatial lag models (SLM) and spatial error models (SEM). The Spatial Lag Model (SLM) is:

In formula (6), I represents the index of internal structural upgrading in the productive service industry, the definitions of HC, Infr, PC, PD, and MD are the same as in formula (5), w_it is a random error term that follows a standard normal distribution, ρ represents the spatial lag coefficient that reflects the effect of internal structural upgrading observations of productive service industries in other regions on this region; W_ij represents the spatial weight matrix, β₁, β₂, β₃, Φ₁, Φ₂, and Ω₁ represent the coefficients of each variable, and β₀ is a constant term.

The calculation of W_ij draws inspiration from the concept of the gravity model, which combines the characteristics of economic correlation and geographical correlation (Hou et al., 2014). The specific formula is as follows:

In formula (7), Q represents the product of the average per capita GDP of two provinces during the sample period, and d_ijrepresents the distance between the centers of the two provinces^②.

The expression of the spatial error model is:

In formula (8), , and µ_it is a random error term that follows a standard normal distribution.

Table 2

Descriptions of the main variables

The spatial error coefficient (λ) reflects the spatial role of innovation achievement protection in neighboring regions in the internal structural upgrading of the productive service industries.

4.2 Variable and data descriptions

Due to the serious lack of data in Qinghai, Ningxia and Xizang, the sample data covers the panel data of 28 provinces, cities and autonomous regions in China from 2000 to 2022. The data mainly came from the Statistical Yearbook, China Urban Construction Statistical Yearbook, China Land and Resources Statistical Yearbook, and China Urban and Rural Construction Statistical Yearbook of various provinces from 2001 to 2023. The upgrading of internal structure and protection of innovative achievements in the productive service industry were measured by the indicators mentioned in Part 2 above. To address the issue of dimensional differentiation among the control variables, each variable was subjected to per capita percentage processing. Among other control variables, the human capital variable was represented by the proportion of graduates from ordinary high schools and universities to the total local population, infrastructure was measured by the per capita road paving area, and per capita income was replaced by the local average wage level. Population density was measured by the number of people per square meter of the jurisdictional area, and the level of manufacturing development was measured by the per capita added value of manufacturing. The descriptions of all the variables are shown in Table 2.

5.1 Overall sample estimation results

First, we determined whether there is spatial autocorrelation in the variables and influencing factors of the internal structural upgrading in China's productive service industry. To ensure the accuracy and stability of the regression results, Moran, Walds, Lratios, Lmsar, Lmerr and other methods were used for testing. Considering that these five indicators are mainly used for cross-sectional data testing, Deng's (2016) method was used to replace the spatial weight matrix W used in cross-sectional data with a block diagonal matrix, and the formula for calculating the block diagonal matrix is:

In formula (9), C is the block diagonal matrix, and I_T is the T-dimensional unit time matrix. The test results in Table 3 show that all five methods passed the 1% significance level test, indicating a spatial correlation between the internal structural upgrading of China's productive service industry and various influencing variables. The Hausman test results supported the null hypothesis, so the spatial fixed effects model is more appropriate. In addition, the LR test results indicated that there is a regional effect in the internal structural upgrading of the productive service industries in various regions of China, but no time effect, indicating that considering spatial interaction factors will significantly improve the robustness of the model regression results. Therefore, the optimization of the internal structure of the productive service industry in a certain region of China is influenced by the differences in the degrees of optimization in other regions during the same period. Thus, the internal structural upgrading of the productive service industries in adjacent provinces is mainly manifested as mutual impact, while the upgrading in the region for non-adjacent provinces is mainly manifested as error impact.

Table 3

Spatial Error Model (SEM) estimation results of the impact of innovation achievement protection on the internal structure upgrading of urban productive service industry

The spatial error coefficients (λ) in Model 1 of Table 3 are significantly positive, indicating a significant spatial dependence in the internal structural upgrading of productive service industries in various provinces of China. The internal structures of productive service industries in adjacent provinces are relatively better, and the internal structure of productive service industries in the local area will also be regionally optimized. In Model 1, the variable of innovation achievement protection is significantly positive and below the significance level of 1%, which means that increasing the degree of innovation achievement protection has a significantly positive promoting effect on the internal structure upgrading of China's provincial productive service industry. One possible reason is that, on one hand, improving the level of protection for innovative achievements stimulates technological innovation and differential business operations of productive service industry enterprises, gradually converging high-tech productive service industry enterprises into winners of the monopolistic advantage competition. On the other hand, improving the level of protection for innovative achievements is conducive to the accumulation of advanced factors in productive service industry enterprises, enhancing their ability to formulate intellectual property rights as the core standard system, and controlling industrial development to lead foreign trade and increase the proportion of high-level productive service industries.

5.2 Segmented estimation results

The regression results of models 2–5 in Table 3 indicate that there are significant differences in the regression coefficients for the protection of urban innovation achievements on the internal structural upgrading of productive service industries in the four major regions of China, namely the eastern, central, northeastern, and western regions. Overall, the regression coefficients for the protection level of innovation achievements in these four major provinces are all positive, but only those in the eastern and central regions are significant at the 5% level. Among them, for every 1% increase in the protection level of innovation achievements in the eastern region, the comprehensive index of structural optimization in the productive service industry increases by 0.408 units, and for every 1% increase in the protection level of innovation achievements in the central region, the index increases by 0.289 units, which may be due to the higher level of agglomeration of high-tech manufacturing enterprises in the eastern and central provinces compared to the western and northeastern provinces. High-end productive service industry enterprises that rely on the development of high-tech manufacturing industries need more protection of their innovative achievements as external institutional support, and promoting the technological innovation and internal structural upgrading of productive service industry enterprises relies more on improving contractual relationships to strengthen the protection of innovative achievements. Improving the level of innovation achievement protection that is suitable for the local high-level productive service industry and relying on the incentive effect generated by the innovation achievement protection system will be more conducive to the accumulation of advanced factors and promoting the internal structural upgrading of the local productive service industry. The regression coefficient of the protection level of innovation achievements in the eastern provinces is significantly higher than those of the other three sectors. This may be because the productive service industry is mainly concentrated in larger central urban clusters, and the eastern provinces have a significantly larger scales and numbers of urban clusters than other regions. There are also more high-tech manufacturing clusters in the eastern region, which is conducive to leveraging the effects of high-end productive service industries.

Among the other control variables, the human capital variable has a significant promoting effect on the overall optimization of the internal structure of the productive service industry, with the strongest promoting effect in the eastern region. This indicates that improving the human capital level has led to the aggregation of factors in productive service industry enterprises and the improvement of their technological level. The advantage of the human capital level in the eastern region is more obvious, so the promoting effect is greater. The improvement of infrastructure has a significant impact on the internal structural optimization of the productive service industry in the western and northeastern regions of China, while the driving effects in the other two regions are not significant, indicating that the improvement of infrastructure is crucial for the development of the productive service industry in underdeveloped provinces. The positive effect of per capita income on the internal structural optimization of the productive service industry shows a decreasing trend from east to west. Compared with the other three provinces, the per capita income of eastern provinces is generally higher. A high income will promote the extension of local consumption towards the high-end, thereby driving the development of high-level manufacturing and productive service industries. There are significant differences in the impacts of population density variables on the optimization of the internal structure of productive services. An increase in the population density promotes the internal structural optimization of productive services, and this promoting effect is more pronounced in the eastern and central regions, indicating that population agglomeration is conducive to the specialization and high-end development of productive services. The development level of the manufacturing industry has significant positive impacts on the internal structural upgrading of the productive service industry in the eastern and central provinces, but its impacts in the northeastern and western provinces are not significant, possibly because the development level of the manufacturing industries in the eastern and central regions are relatively high. As an intermediate input in the manufacturing industry, the high-end productive service industry is usually concentrated around high-tech manufacturing, and through coordinated development with the manufacturing industry, it can bring greater added value and profits. However, the industrial development in the three northeastern provinces and western regions is slow, and the level of agglomeration of high-end manufacturing industry is relatively low, so the driving effect on the development of the high-end productive service industry is relatively small.

5.3 Robustness testing

To reduce interference from endogeneity in the empirical research process, robustness tests were conducted from the aspects of exogenous changes in the agglomeration of productive service industries, selection of indicators for major variables, and measurement errors.

5.3.1 Reverse causality and outliers of changes in the protection level of innovative achievements

Changes in the protection level of innovation achievements in a province may be affected by the reverse effect of the internal structural upgrading of the productive service industry. For example, provinces with a more reasonable internal structure of the productive service industry may have a higher level of protection for innovation achievements. Therefore, drawing on the method of Xi et al. (2017), this study examined the reverse effect of upgrading the internal structure of the productive service industry on the protection of innovative achievements. The results in column (1) of Table 4 show that the impact of internal structural upgrading of the productive service industry on the level of protection of innovative achievements in the previous year is not significant. At the same time, to minimize the impact of sample outliers on the level of internal structural upgrading in the productive service industry, the top three and bottom three samples were removed. The results are shown in column (2) of Table 4. In addition, to eliminate any interference from the higher policy authority of municipalities directly under the central government and autonomous regions compared to other provinces, the samples from Beijing, Shanghai, Chongqing, and Tianjin (Inner Mongolia Autonomous Region, Guangxi Zhuang Autonomous Region, and Xinjiang Uygur Autonomous Region) were removed. The regression results are shown in column (3) of Table 4. Columns (2) and (3) clearly show that the regression coefficients did not change significantly, indicating that the more extreme values of internal structural upgrading in the provincial productive service industry and the interference due to factors from municipalities directly under the central government on the regression results are not significant.

Table 4

Robustness test of the empirical results