Impact of collaborative innovation on green total factor productivity in Yangtze River Economic Belt: Analysis based on endogenous spatial-temporal weight matrix

6 Technological innovation can promote high-quality economic growth. This paper discusses the promotion of green 7 total factor productivity from the perspective of collaborative innovation in the Yangtze River Economic Belt. 8 Firstly, the evaluation index system of collaborative innovation level is constructed from two aspects of 9 collaborative innovation elements and collaborative innovation environment. Then the entropy method is used to 10 measure its development level. The results show that the collaborative innovation level of provinces in the Yangtze 11 River Economic Belt presents an increasing trend year by year. Meanwhile, there are regional differences, which is 12 characterized by 'high in the middle reaches, middle in the downstream and low in the upstream' Secondly, the 13 SDM model based on endogenous spatio-temporal weight matrix is constructed to analyze the influencing factors 14 of green total factor productivity. The results show that collaborative innovation in the Yangtze River Economic 15 Belt has significant negative impact on green total factor productivity in terms of spatial interaction and fiscal 16 expenditure also has a negative impact. The spatial interaction between environmental protection and opening up 17 has a significant positive impact on green total factor productivity. However, the spatial interaction between 18 industrial structure and human capital on green total factor productivity is not obvious. Finally, this paper puts 19 forward some policy suggestions to improve green total factor productivity. 20


Highlights： 23
·Construct a mathematical model of collaborative innovation and green total factor productivity.

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The belt area is about 2.052 300 square kilometers, accounting for 21.4% of the country and its population 50 and GDP are more than 40 % of the country. It is rich in science and education resources. For example, the number 51 of ordinary colleges and universities accounts for 43% of the country, R&D expenditure accounts for 46.7% of the 52 country and effective invention patents account for more than 40% of the country. Otherwise, there are 2 53 comprehensive national science centers, 9 national independent innovation demonstration zones, 90 national high-54 tech zones, 161 national key laboratories and 667 enterprise technology centers along the Yangtze River.

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Therefore, relying on the advantages of regional talent and intelligence intensive, accelerating the cross-regional 56 collaborative innovation of the Yangtze River Economic Belt, strengthening environmental protection and 57 planning green development are the keys to the sustainable development of the Yangtze River Economic Belt.

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However, according to the data released by 《Driving Force Index of Science and Technology Innovation in 59 Yangtze River Economic Belt (2020)》, the average input index of scientific and technological innovation in the 60 Yangtze River Economic Belt is 0.12 and the average driving force index of scientific and technological innovation is 0.14, which both are at a low level. So, in the context of green development concept, what is the 62 development of collaborative innovation in the Yangtze River Economic Belt? Does it really promote regional 63 green total factor productivity? On the basis of considering the spatial spillover effect of collaborative innovation, 64 this paper discusses the relationship between collaborative innovation and green total factor productivity in the 65 Yangtze River Economic Belt. The conclusion will provide scientific reference for the Yangtze River Economic

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Belt to promote green total factor productivity through collaborative innovation.

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Collaborative innovation can integrate innovation elements and make innovation resources accessible within 81 the region, thereby enhancing the level of total factor productivity and promoting regional economic growth (Hu et  86 spatial lag model research shows that collaborative innovation in Yangtze River Delta urban agglomeration has 87 significant spatial spillover effect, which can promote regional economic growth through direct effect, indirect 88 effect and total effect. Hao and Yin (2019) established GMM and spatial panel Durbin model to study China's 89 science and technology collaborative innovation and economic growth from the perspective of temporal and spatial differences. It is found that the investment in science and technology collaborative innovation has a positive 91 impact on economic growth in the current period and local. By also using the spatial panel econometric model, Lv 92 et al. (2017). found that the spatial linkage of innovation resource synergy has a significant promoting effect on 93 regional economic growth. On the other hand, some scholars explored their relationship from other perspectives.

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For instance, Zhou and Li (2017) expounded the dynamic co-evolution of institutional innovation and 95 technological innovation to promote economic growth through a government-enterprise game model. Liu et al.

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(2017) believes that intra-regional synergy and inter-regional synergy of regional innovation networks are 97 significantly positively correlated with industrial economic growth. From the micro level, Ren and Gan (2016) 98 believe that the collaborative innovation system formed by business model innovation will promote the quality of

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(2019) believe that there is no significant impact between technological innovation and the green total factor 119 productivity of industrial water resources. Wang et al. (2020) believed that there is regional heterogeneity in the relationship between technological innovation and green total factor productivity. The improvement of 121 technological innovation in the western region of China helps to improve the green total factor productivity, while 122 the eastern and central regions of China have the opposite conclusion. In addition, technological innovation has a 123 significant positive impact on the local green total factor productivity and has a significant negative impact on the 124 green total factor productivity in the surrounding areas.

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In summary, although the conclusions of the impact of collaborative innovation on economic growth in the 126 above studies are not the same, they all verify the existence of the impact of collaborative innovation on total 127 factor productivity. And then the impact is uncertain. At the same time, most of the previous studies only examined 128 the relationship between collaborative innovation and economic growth without taking into account the ecological 129 and environmental effects of economic growth. That is to say, there was no further in-depth analysis of the impact 130 of collaborative innovation on green economic growth and little literature specifically conducts similar studies on 131 the Yangtze River Economic Belt. The main contributions of this paper are as follows: firstly, a mathematical 132 model is established to analyze the impact mechanism of regional collaborative innovation on green total factor 133 productivity. Secondly, this paper constructs an index system to measure regional collaborative innovation, 134 specifically analyzing the level of collaborative innovation in the Yangtze River Economic Belt and further 135 exploring its spatial dynamic evolution characteristics. Thirdly, the spatial economic matrix is established to 136 explore the impact of collaborative innovation on green total factor productivity in the Yangtze River Economic

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Belt from the perspective of spatial spillover effect. Therefore, this study has important guiding significance for 138 accelerating the high-quality development of China's green economy. Based on the production function, this paper constructs a spatial expansion model of collaborative innovation 142 and analyzes how collaborative innovation affects regional green total factor productivity growth through 143 provincial spatial spillover mechanism. Total factor productivity refers to the ratio of the total output of a system to 144 the input of various production factors. Green total factor productivity is the efficiency of resource development 145 and utilization based on total factor productivity, which takes energy consumption and environmental costs into Among them, , is the corresponding green total factor productivity of provinces i in years t; , is the 149 corresponding total output; , is the corresponding labor input, , is the corresponding capital input; and are 150 the share of labor and capital in the input respectively.

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In a fully competitive market, it is believed that the total output is realized by the combination of labor force Under the condition of equal proportion of input production factors, according to the production technology 158 conditions, the capital stock of the province can be expressed as : The total output of province i can ultimately be expressed as : 160 , = ( , , ) , Then the corresponding Eq. (1) can be transformed into : This formula shows that green total factor productivity can be decomposed into two parts, including 162 technological innovation of other production factor combinations represented by , and diversification of other

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Since technological innovation results need to be transformed into production technology to improve the 171 actual production efficiency. However, the transformation ability of innovation achievements will be affected by Taking logarithms on both sides of Eq. (11), we can get : The Eq. (14) shows that the average technical level of each region has a positive effect on green total factor 186 productivity. The level of local collaborative innovation has a positive effect on the local green total factor 187 productivity. While the level of collaborative innovation in surrounding regions has negative effect on the local 188 green total factor productivity. When the technical level of the region is higher than that of the surrounding area, 189 the level of local collaborative innovation has a greater positive effect on local green total factor productivity.

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When the technical level of the region is lower than that of the surrounding area, the level of collaborative 191 innovation in the surrounding area has a greater negative effect on local green total factor productivity. In comparison, when 0 < < 1, the regional collaborative innovation has a positive effect on the regional green total 193 factor productivity and the effect is larger. When > 1, due to spatial interaction, local collaborative innovation 194 has a negative effect on green total factor productivity in the surrounding areas and the effect is larger. Overall, 195 when the regional technology gap is small, collaborative innovation has a positive impact on local green total 196 factor productivity. When the regional technology gap is too large, collaborative innovation has a negative impact 197 on green total factor productivity in surrounding areas.  innovation environment synergy. The specific indicator system is shown in Table 1.

Calculation method of collaborative innovation 237
The measured methods of collaborative innovation include factor analysis, principal component analysis and

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Entropy method is an effective method for multi-index comprehensive evaluation of regional development. In this 246 paper, the weight of each index in each province of the Yangtze River Economic Belt is calculated and then the 247 comprehensive index of collaborative innovation is obtained by multiplying each index and its weight. The 248 process is as follows :

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(1) Dimensionless treatment of indicators. The indicators selected in this paper are positive indicators, so 250 dimensionless processing formula : (2) Coordinate translation and normalization of dimensionless data. Where A is the translation distance, the 252 value is selected as 1.

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(3) Calculation of index information entropy and difference coefficient. K = 1/lnn, n is the number of    (1) Explained variable: green total factor productivity. Green total factor productivity is an input-output 302 efficiency that considers energy and resource consumption. It is an important guarantee for transforming mode of 303 economic development and achieving sustainable economic growth.

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There are many methods to measure green total factor productivity. The traditional DEA model was proposed

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In this paper, the input indicators used to calculate green total factor productivity are labor, energy and 316 capital. On labor input, referring to the study of most scholars in total factor productivity research, this paper select 317 the provinces over the years of employment as a substitute indicator. With regard to energy input, taking into 318 account the regional differences in energy consumption types, the total regional energy consumption equivalent to 319 standard coal is selected as a substitute indicator. Regarding the capital stock index, we choose the total amount of 320 fixed capital formation to measure and use the perpetual inventory method for conversion. The investment price

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The expected output indicators in output are replaced by regional GDP and are reduced to constant price 324 levels based on 2000. In terms of undesirable output, using Chen Shiyi's (Chen 2009) method to calculate the total 325 CO 2 emissions of each province or city as the undesirable output index of the region. The specific indicators are 326 shown in Table 2.  school students * 6 + the proportion of junior high school students * 9 + the proportion of high school students * 338 12 + the proportion of college students and above * 16. The industrial structure of this paper selects the tertiary 339 industry output value and GDP ratio to measure. Fiscal expenditure is characterized by the ratio of regional fiscal 340 expenditure to regional GDP. The degree of opening to the outside world is measured by the ratio of regional 341 import and export volume to regional GDP; meanwhile, the RMB is converted according to the exchange rate of 342 the year. Before the model regression, the data are dimensionless to eliminate the impact of dimension.

Model construction 345
In order to reveal the influence mechanism of spatial factors on green total factor productivity, this paper uses 346 spatial econometric model analysis. This model is mainly divided into spatial lag model and spatial error model.  Table 3.   Tables 4 and Table 5.    Table 6. From the regression results, without considering the spatial interaction effect, it is 400 found that the regression coefficients of environmental protection, human capital and industrial structure are all 401 positive and pass the test at the significance level of 1 %, indicating that the three have a positive role in promoting 402 the green total factor productivity of the Yangtze River Economic Belt. However, collaborative innovation, fiscal 403 expenditure and opening up did not pass the significant test, indicating that the impact of the three on green total 404 factor productivity is uncertain.

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In the case of introducing space-time interaction effect, the regression coefficient of collaborative innovation 406 is negative and the test is passed at 1% significance level, indicating that the level of collaborative innovation in 407 the surrounding areas has a significant negative effect on the green total factor productivity of the region.  Note : * 、 * * 、 * * * are significant at the level of 10 % 、 5 % 、 1 % respectively.  Table 7.

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The results of Table 7 show that the direct effect of collaborative innovation is not significant but the indirect 440 effect is very significant and the coefficient is large, which has a significant inhibitory effect on the green total

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The direct effect of environmental protection and human capital is very significant, which can greatly 451 promote the growth of local green total factor productivity. However, its indirect effect is not significant,

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indicating that its spatial spillover effect is insufficient. Under the impact of this indirect effect, the total effect is 453 differentiated. That is to say, environmental protection has significantly promoted the growth of regional green 454 total factor productivity, while human capital has little effect on the growth of regional green total factor 455 productivity. In general, the growth of human capital will promote the growth of total factor productivity (Benhabib and Spiegel 1994). And if human capital is mismatched or under-matched, it will also lead to the 457 reduction of green total factor productivity (Lai and Ji 2015).

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The direct effect of industrial structure upgrading is very significant, which greatly promotes the growth of 459 green total factor productivity in the region. However, its indirect effect shows that it has a significant inhibitory 460 effect on the green total factor productivity in the surrounding areas. The reason is that the rational allocation of

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The direct effect of fiscal expenditure index is not significant, while its indirect effect is very significant. The

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results show that the growth of green total factor productivity in the surrounding areas is greatly inhibited and its 467 total effect also reflects a significant inhibitory effect, which is consistent with the regression results in the SDM 468 model. This may be due to the negative impact of fiscal policies aimed at promoting economic growth on the 469 environment, resulting in no significant contribution to productivity growth (Zhu and Li 2019). This shows that the 470 implementation of the current 'green finance' strategy needs to adopt diversified means other than green special 471 funds and green government procurement to promote the sustainable growth of green economy.

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The direct effect of openness index is not significant, while its indirect effect is very significant. The results

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show that it greatly promotes the growth of green total factor productivity in surrounding areas and its total effect 474 also reflects a significant promotion effect, which is consistent with the regression results of spatial effect in the  Note: The number in brackets is the t-statistics of the coefficient, and *, * *, * * * represent the significance at the levels of 10 %, 5 % and 1 %, respectively.

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It can be seen from Table 8 that  In this paper, the mathematical model is used to analyze the way that collaborative innovation affects regional 504 green total factor productivity. Meanwhile, the evaluation index system of regional collaborative innovation level 505 is constructed. The entropy method is used to calculate the collaborative innovation level of the Yangtze River

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Economic Belt and its evolution is analyzed. On this basis, the spatial Durbin model based on endogenous spatial-507 temporal weight matrix of economic matrix is used to explore the specific relationship between collaborative 508 innovation and green total factor productivity in the Yangtze River Economic Belt.

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And then the following conclusions are obtained: firstly, the level of collaborative innovation in each 510 province of the Yangtze River Economic Belt shows an upward trend year by year, which is characterized by 'high 511 in the middle reaches, middle in the downstream and low in the upstream'. The level of collaborative innovation in 512 the Yangtze River Economic Belt has a positive spatial correlation and σ convergence. Secondly, collaborative 513 innovation in the Yangtze River Economic Belt has a significant negative impact on green total factor productivity 514 in terms of spatial interaction. And its impact on local green total factor productivity is not significant. Oppositely, 515 the inhibitory effect on green total factor productivity in surrounding areas is very strong. Thirdly, environmental 516 protection and opening up in the Yangtze River Economic Belt have significant positive impact on green total 517 factor productivity in terms of spatial interaction. However, the former mainly affects local green total factor 518 productivity, while the latter mainly affects green total factor productivity in surrounding areas. Fiscal expenditure 519 has significant negative spatial effect on green total factor productivity, mainly inhibiting the growth of green total factor productivity in surrounding areas. The spatial interaction between industrial structure and human capital on 521 green total factor productivity is not obvious.

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Secondly, it is necessary to further strengthen environmental protection. Give full play to the spatial spillover 537 effect of environmental protection, strengthen the coordination of regional environmental policies and accelerate 538 the rational use of ecological environmental protection big data in environmental quality improvement and 539 regional cooperation will improve the efficiency of green economy. By optimizing the industrial structure and 540 layout, improve the energy consumption structure and actively develop energy saving and environmental 541 protection technology will contribute to promoting the development of green economy. Through diversified 542 industrial development, expanding the industrial chain and increasing the radiation effect of environmental 543 protection industry for economic development will contribute to promoting the development of green economy.

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Thirdly, it is necessary to accelerate the transition to green finance. Further optimize the fiscal expenditure of 545 local governments, increase the 'green expenditure' in fiscal expenditure and guide the flow of funds to green 546 industries will promote the transformation of economy to green. Continue to adhere to opening up. Pay special 547 attention to the development of foreign trade green industry and increase the export of green goods. Pay attention to the quality of foreign investment and give full play to its spatial spillover effect will help to promote the 549 balanced development of regional green economy.    Square concerning the legal status of any country, territory, city or area o bbnhjr of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.  Endogenous time-space weight matrix based on per capita income matrix

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