# The Effect of Innovation Investment on Environmental Total Factor Productivity

Authors: You-Qun Wu; Jie Li; Jin-Chao Ma
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Based on the panel data of 30 provinces (except Tibet) in China from 2012 to 2019, this paper uses the ML index method and spatial econometric model to evaluate the impact and spillover effect of innovation investment on environmental total factor productivity. The study found the following conclusions. (1) Environmental total factor productivity showed a fluctuating upward trend as a whole, and the driving force of environmental total factor productivity growth mainly came from technological progress. (2) There is global spatial correlation and positive spatial spillover effect in regional environmental total factor productivity. There is a certain spatial correlation in provincial environmental total factor productivity, and the improvement of environmental total factor productivity in this region will promote the improvement of environmental total factor productivity in surrounding areas. (3) Innovation investment, economic development, and foreign investment level play a significant role in promoting the improvement of environmental total factor productivity, and energy structure and human capital level have a negative impact on the improvement of environmental total factor productivity. (4) Innovation investment, economic development, human capital, and foreign investment have positive spillover effects on the improvement of environmental total factor productivity in the surrounding areas, while the energy structure shows negative spillover effects.


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## Body

## 1. Introduction

In recent years, a series of ecological and environmental problems such as environmental pollution, resource depletion, and climate change have become more and more intense all over the world. They will also become the bottleneck factors restricting China’s green development and the improvement of people’s livelihood for a long time in the future. The Fifth Plenary Session of the 19th CPC Central Committee stressed that the quality and efficiency of China’s economic development are still not high, and the ecological environment protection still has a long way to go. The “Two Mountains Theory” enlightens us that we should adhere to protection in development and development in protection, so as to produce huge ecological, economic, and social benefits, and effectively improve China’s environmental total factor productivity. Environmental pollution, labor, capital, resources, and other factors are incorporated into the production function, and the total factor productivity obtained is the environmental total factor productivity.The Proposal of the CPC Central Committee on Formulating the 14th Five Year Plan for National Economic and Social Development and the Long-term Goals for 2005 points out that at present, China’s innovation ability does not meet the requirements of high-quality development, ecological and environmental protection has a long way to go, and it is necessary to unswervingly implement the new development concept of innovation, coordination, green, openness and sharing. Under the innovation driven development strategy, whether the growth of innovation investment can effectively promote the transformation and upgrading of economic structure, improve environmental total factor productivity, and achieve high-quality economic development is worthy of further study.Existing scholars have studied environmental total factor productivity from the perspectives of measurement methods and influencing factors.


### 1.1. On Measurement of Environmental Total Factor Productivity

H. Fujii, S. Kaneko, and S. Managi (2009) incorporated “bad” output into Luenberger productivity index, expanded and enriched Luenberger index, making it one of the mainstream methods for measuring environmental total factor productivity [1]. S. Chen (2015) used the SBM model to calculate China’s ecological total factor productivity from 1986 to 2012. The results show that the decline of economic growth is conducive for the development of ecological economy [2]. F. G. Shi (2015), R. H. Xie et al. (2017), X. H. Cui et al. (2019) calculated the industrial green total factor productivity by using SBM directional distance function and Luenberger productivity index, and found that the industrial green productivity showed an overall growth trend [3–5]. R. Moghaddasi R et al. (2016) used Solow residual method to study the relationship between agricultural total factor productivity growth and energy consumption in Iran, and found that there was a negative correlation between them [6]. J H. Hu Jianhui et al. (2016), J.X. Wu Jianxin et al. (2016), J. J. Miao et al. (2017), Q. Q. Fan et al. (2020), W. S. Meng et al. (2020) all used SBM directional distance function considering unexpected output and Luenberger productivity index method to measure China’s environmental total factor productivity, and decomposed and analyzed the environmental total factor productivity [7–11]. Based on the DEA Malmquist index method, X. Ma (2019) made a dynamic evaluation of the environmental total factor productivity of the sample countries from 1992 to 2014 and investigated the country differences in detail. It was found that although the level of environmental total factor productivity in most countries showed an upward trend, most of them were less than 1, indicating that there is still much room for improvement in the environmental efficiency of these countries [12]. P. Lin et al. (2020) took green total factor productivity as the research basis, used the transcendental logarithmic production function SFA model to empirically evaluate the green total factor productivity in Beijing-Tianjin-Hebei region, and found that there was significant regional heterogeneity in the growth rate of green total factor productivity in the region [13].


### 1.2. On the Influencing Factors of Environmental Total Factor Productivity

F. Rolf et al. (2016) conducted an empirical study based on the measurement results of GTFP and found that there was a significant positive correlation betweenR&D investment and GTFP [14]. L. Aldieri et al. (2019) conducted empirical analysis based on the unbalanced data sets of 85 regions in Russia from 2010 to 2015, and found that the impact of environmental innovation on total factor productivity is positive [15]. Q. Yin Qun et al. (2019) calculated the environmental total factor productivity of 30 provinces and cities in China based on the interprovincial panel data from 2008 to 2017, using SBM-DDF model and GML index. They found that innovation spillover can effectively promote the growth of environmental total factor productivity, in which technological progress is the main impact path [16]. J X. Wan et al. (2019) analyzed the impact of social capital on environmental total factor productivity by using the fixed effect model and found that there was little difference in environmental total factor productivity among provinces. Social capital promoted environmental technological progress but inhibited environmental technological efficiency. The network dimension of social capital had a positive impact on improving environmental total factor productivity [17]. L. M. Chen et al. (2020) used nonradial and nonangular SBM directional distance function and ML index to measure China’s GTFP, and found that foreign investment and environmental regulation have a significant impact on the growth of GTFP [18]. H. Chen Hao et al. (2020) and Y. Baolong et al. (2021) believed that there was a certain correlation between innovation investment and environmental total factor productivity [19, 20]. K. Guo et al. (2021) used the slack-based measurement model to calculate the environmental total factor productivity of China’s provinces from 2005 to 2017. It was found that the infrastructure construction level was positively correlated with the environmental total factor productivity, while the per capita GDP, financial development, and energy consumption intensity had a negative correlation impact on the environmental total factor productivity [21].Some scholars have studied the impact of innovation on total factor productivity. P. F. Ge et al. (2018) and Y. Zhou et al. (2019) found that both basic innovation and applied innovation have significantly promoted the improvement of green total factor productivity. The impact path of the former is technical efficiency, and the impact path of the latter includes technical efficiency and technological progress [22, 23]. S. Tang et al. (2019) believe that financial science and technology innovation helps to improve regional total factor productivity, and financial science and technology innovation can promote cross regional transmission of knowledge, that is, spatial knowledge spillover and promote the growth of total factor productivity in surrounding areas [24]. S. L. Liu et al. (2021) found that China’s regional innovation total factor productivity showed a positive growth trend as a whole, but its growth rate showed a fluctuating downward trend. The main driving factor of innovation total factor productivity growth changed from technological progress to the improvement of technological efficiency [25].To sum up, on the research of the measurement and influencing factors of environmental total factor productivity, domestic and foreign scholars mainly studied the action mechanism of different factors on environmental total factor productivity from the perspectives of industrial structure, urbanization, environmental regulation, FDI, financial development, opening to the outside world, and scientific and technological progress. In addition, a few scholars have studied the mechanism of innovation on total factor productivity and conducted relevant empirical research. Innovative investment can enhance environmental pollution control technology, reduce environmental treatment costs, reduce the negative environmental external effects of production, and improve environmental total factor productivity. The action mechanism of innovation investment on environmental total factor productivity is reflected through the following three effects: the spillover effect of external innovation capital, the technology spillover effect of pollution innovation and control investment, and the wage income and market demand effect of innovation. Under the guidance of the national innovation-driven strategy, it has gradually become the focus of research to study its impact on environmental total factor productivity from the perspective of innovation, and the existing research literature rarely brings innovation spillover and spatial connection into the unified analysis framework, which cannot intuitively quantify the spatial connection and strength between different regional units.Therefore, based on the relevant data of 30 provinces in China (except Tibet) from 2011 to 2019, this paper uses the Malmquist Luenberger (ML) index based on directional distance function (DDF) to measure environmental total factor productivity, and introduces a spatial econometric model to bring innovation spillovers and spatial linkages into the unified analysis framework, explore the innovation spillover level and spatial radiation capacity of different provinces, and empirically study the impact of innovation investment on environmental total factor productivity. Compared with the existing relevant research, the contribution of this paper is reflected in the following two points: (1) This paper takes innovation investment as the core explanatory variable to analyze the impact and spillover effect of innovation investment on environmental total factor productivity. (2) Considering the heterogeneity of geospatial dimensions, this paper introduces a spatial econometric model, brings innovation spillover and spatial linkages into a unified analysis framework, and uses the partial differential method of spatial regression model to further analyze the direct effect and spillover effect of innovation investment on environmental total factor productivity.The subsequent arrangement of this paper is as follows: the second part constructs the index system of environmental total factor productivity, and uses the ML index method to measure China’s environmental total factor productivity. The third part is the empirical research design, empirical results, and analysis. The fourth part is the main conclusions and recommendations.


## 1.1. On Measurement of Environmental Total Factor Productivity

H. Fujii, S. Kaneko, and S. Managi (2009) incorporated “bad” output into Luenberger productivity index, expanded and enriched Luenberger index, making it one of the mainstream methods for measuring environmental total factor productivity [1]. S. Chen (2015) used the SBM model to calculate China’s ecological total factor productivity from 1986 to 2012. The results show that the decline of economic growth is conducive for the development of ecological economy [2]. F. G. Shi (2015), R. H. Xie et al. (2017), X. H. Cui et al. (2019) calculated the industrial green total factor productivity by using SBM directional distance function and Luenberger productivity index, and found that the industrial green productivity showed an overall growth trend [3–5]. R. Moghaddasi R et al. (2016) used Solow residual method to study the relationship between agricultural total factor productivity growth and energy consumption in Iran, and found that there was a negative correlation between them [6]. J H. Hu Jianhui et al. (2016), J.X. Wu Jianxin et al. (2016), J. J. Miao et al. (2017), Q. Q. Fan et al. (2020), W. S. Meng et al. (2020) all used SBM directional distance function considering unexpected output and Luenberger productivity index method to measure China’s environmental total factor productivity, and decomposed and analyzed the environmental total factor productivity [7–11]. Based on the DEA Malmquist index method, X. Ma (2019) made a dynamic evaluation of the environmental total factor productivity of the sample countries from 1992 to 2014 and investigated the country differences in detail. It was found that although the level of environmental total factor productivity in most countries showed an upward trend, most of them were less than 1, indicating that there is still much room for improvement in the environmental efficiency of these countries [12]. P. Lin et al. (2020) took green total factor productivity as the research basis, used the transcendental logarithmic production function SFA model to empirically evaluate the green total factor productivity in Beijing-Tianjin-Hebei region, and found that there was significant regional heterogeneity in the growth rate of green total factor productivity in the region [13].


## 1.2. On the Influencing Factors of Environmental Total Factor Productivity

F. Rolf et al. (2016) conducted an empirical study based on the measurement results of GTFP and found that there was a significant positive correlation betweenR&D investment and GTFP [14]. L. Aldieri et al. (2019) conducted empirical analysis based on the unbalanced data sets of 85 regions in Russia from 2010 to 2015, and found that the impact of environmental innovation on total factor productivity is positive [15]. Q. Yin Qun et al. (2019) calculated the environmental total factor productivity of 30 provinces and cities in China based on the interprovincial panel data from 2008 to 2017, using SBM-DDF model and GML index. They found that innovation spillover can effectively promote the growth of environmental total factor productivity, in which technological progress is the main impact path [16]. J X. Wan et al. (2019) analyzed the impact of social capital on environmental total factor productivity by using the fixed effect model and found that there was little difference in environmental total factor productivity among provinces. Social capital promoted environmental technological progress but inhibited environmental technological efficiency. The network dimension of social capital had a positive impact on improving environmental total factor productivity [17]. L. M. Chen et al. (2020) used nonradial and nonangular SBM directional distance function and ML index to measure China’s GTFP, and found that foreign investment and environmental regulation have a significant impact on the growth of GTFP [18]. H. Chen Hao et al. (2020) and Y. Baolong et al. (2021) believed that there was a certain correlation between innovation investment and environmental total factor productivity [19, 20]. K. Guo et al. (2021) used the slack-based measurement model to calculate the environmental total factor productivity of China’s provinces from 2005 to 2017. It was found that the infrastructure construction level was positively correlated with the environmental total factor productivity, while the per capita GDP, financial development, and energy consumption intensity had a negative correlation impact on the environmental total factor productivity [21].Some scholars have studied the impact of innovation on total factor productivity. P. F. Ge et al. (2018) and Y. Zhou et al. (2019) found that both basic innovation and applied innovation have significantly promoted the improvement of green total factor productivity. The impact path of the former is technical efficiency, and the impact path of the latter includes technical efficiency and technological progress [22, 23]. S. Tang et al. (2019) believe that financial science and technology innovation helps to improve regional total factor productivity, and financial science and technology innovation can promote cross regional transmission of knowledge, that is, spatial knowledge spillover and promote the growth of total factor productivity in surrounding areas [24]. S. L. Liu et al. (2021) found that China’s regional innovation total factor productivity showed a positive growth trend as a whole, but its growth rate showed a fluctuating downward trend. The main driving factor of innovation total factor productivity growth changed from technological progress to the improvement of technological efficiency [25].To sum up, on the research of the measurement and influencing factors of environmental total factor productivity, domestic and foreign scholars mainly studied the action mechanism of different factors on environmental total factor productivity from the perspectives of industrial structure, urbanization, environmental regulation, FDI, financial development, opening to the outside world, and scientific and technological progress. In addition, a few scholars have studied the mechanism of innovation on total factor productivity and conducted relevant empirical research. Innovative investment can enhance environmental pollution control technology, reduce environmental treatment costs, reduce the negative environmental external effects of production, and improve environmental total factor productivity. The action mechanism of innovation investment on environmental total factor productivity is reflected through the following three effects: the spillover effect of external innovation capital, the technology spillover effect of pollution innovation and control investment, and the wage income and market demand effect of innovation. Under the guidance of the national innovation-driven strategy, it has gradually become the focus of research to study its impact on environmental total factor productivity from the perspective of innovation, and the existing research literature rarely brings innovation spillover and spatial connection into the unified analysis framework, which cannot intuitively quantify the spatial connection and strength between different regional units.Therefore, based on the relevant data of 30 provinces in China (except Tibet) from 2011 to 2019, this paper uses the Malmquist Luenberger (ML) index based on directional distance function (DDF) to measure environmental total factor productivity, and introduces a spatial econometric model to bring innovation spillovers and spatial linkages into the unified analysis framework, explore the innovation spillover level and spatial radiation capacity of different provinces, and empirically study the impact of innovation investment on environmental total factor productivity. Compared with the existing relevant research, the contribution of this paper is reflected in the following two points: (1) This paper takes innovation investment as the core explanatory variable to analyze the impact and spillover effect of innovation investment on environmental total factor productivity. (2) Considering the heterogeneity of geospatial dimensions, this paper introduces a spatial econometric model, brings innovation spillover and spatial linkages into a unified analysis framework, and uses the partial differential method of spatial regression model to further analyze the direct effect and spillover effect of innovation investment on environmental total factor productivity.The subsequent arrangement of this paper is as follows: the second part constructs the index system of environmental total factor productivity, and uses the ML index method to measure China’s environmental total factor productivity. The third part is the empirical research design, empirical results, and analysis. The fourth part is the main conclusions and recommendations.


## 2. Analysis of Environmental Total Factor Productivity

### 2.1. Index System of Environmental Total Factor Productivity

Based on the connotation of total factor productivity of environmental pollution factors, i.e., environmental total factor productivity, this paper constructs the index system of environmental total factor productivity from the perspective of economic performance and environmental pollution, using the construction method of environmental total factor productivity index by Y. Yan et al. (2020), in which economic performance is measured by input index and expected output index, and environmental pollution is measured by undesired output index. The definition of specific indicators is shown in Table1 [26].Table 1
Index system of environmental total factor productivity.
Primary indexSecondary indexTertiary indexInput indexCapitalTotal investment in fixed assetsLabor forceNumber of employees at the end of the yearEnergy consumptionTotal energy consumptionOutput indexEconomic growthRegional GDPUnexpected output indexThree industrial wastesWaste waterSulfur dioxideSolid waste


### 2.2. Measurement Method of Environmental Total Factor Productivity

According to the existing literature, the common methods used by previous scholars to measure total factor productivity include C-D production function regression method and Malmquist productivity index method based on DEA [27]. Malmquist productivity index method can reflect the dynamic changes of resource utilization efficiency in social and economic activities, but it cannot deal with expected output and unexpected output symmetrically. ML index method based on directional distance function solves this problem. It modifies the traditional Malmquist index, which can be used to measure total factor productivity in the presence of unexpected output. Therefore, based on the methods of Y. Chung et al. (1997) and S. Tang et al. (2019), this paper uses ML index based on directional distance function (DDF) to measure China’s environmental total factor productivity [24, 28].The ML index of environmental total factor productivity (ETFP growth rate) between phaset and phase t+1 is expressed by the following formula:(1)MLtt+1=1+D¯txt+1,yt+1,dt+1,gt+11+D¯txt,yt,dt,gt×1+D¯t+1xt+1,yt+1,dt+1,gt+11+D¯t+1xt,yt,dt,gt12.ML productivity index can be decomposed into the change in technical efficiency (MEC) and the change in technological progress (MTC), so as to explore the main reasons for the change of the productivity.(2)MLtt+1=MECtt+1×MTCtt+1,MLtt+1=1+D¯t+1xt+1,yt+1,dt+1,gt+11+D¯txt,yt,dt,gt,MTCtt+1=1+D¯txt+1,yt+1,dt+1,gt+11+D¯t+1xt+1,yt+1,dt+1,gt+1×1+D¯txt,yt,dt,gt1+D¯t+1xt,yt,dt,gt12,where x, y, d, and g represent input index, expected output, unexpected output, and direction vector, respectively. When ML productivity index is greater than 1, it indicates that the environmental total factor productivity has increased from phase t to phase t+1. When the ML productivity index is less than 1, it indicates that the environmental total factor productivity decreases from phase t to phase t+1. MEC indicates the change of technical efficiency. When MEC is greater than 1, it indicates that the technical efficiency has been improved from phase t to phase t+1; when MEC is less than 1, it indicates that the technical efficiency decreases from phase t to phase t+1. MTC indicates the change of technological progress. When MTC is greater than 1, it indicates the technological progress from phase t to phase t+1. On the contrary, the technology from phase t to phase t+1 will regress.


### 2.3. Measurement Results and Analysis of Environmental Total Factor Productivity

Using Matlab R2016a and the ML index, the environmental total factor productivity index (ML) and its decomposition index (MEC and MTC) of Chinese provinces under constant return to scale from 2012 to 2019 are calculated. Tables2–4, respectively, show the environmental total factor productivity and its decomposition of 30 provinces and cities in China during the sample period.Table 2
Environmental total factor productivity (ML).
Region20122013201420152016201720182019Beijing1.07021.11641.08401.11221.32381.09351.76481.2284Tianjin1.05601.05631.08711.03331.17831.12841.14821.0413Hebei1.00781.01091.03461.06161.07931.27831.03021.0290Shanxi1.01630.98101.02721.00021.04181.19981.10861.0200Mongolia1.04180.99261.07571.07641.07701.13031.12951.1108Liaoning1.03590.98251.06191.07711.19661.14321.11741.0598Jilin1.05000.96151.06291.02651.09341.07891.08941.0535Heilongjiang1.03531.04721.05121.00091.03871.05041.04501.0655Shanghai1.01351.00681.05661.04621.18851.25291.28300.9791Jiangsu1.04421.06401.03691.12401.13621.12261.13581.1351Zhejiang1.04201.07861.05211.10391.16691.09161.16941.0954Anhui1.05360.98441.08331.06961.12811.12941.01111.0974Fujian0.98421.05091.04871.04511.14421.02561.03941.0386Jiangxi1.04201.00091.05271.03421.12261.10941.20261.0532Shandong1.04490.98911.08211.09721.07151.08661.10491.2834Henan1.03740.94911.05791.05261.13071.12531.20641.0831Hubei1.08421.00901.09421.07661.12091.13921.21271.1006Hunan1.08871.05751.09481.11921.11681.11201.13521.0567Guangdong1.03290.86691.08381.10701.12221.09301.14921.0475Guangxi1.03250.99731.08821.08741.12091.08231.17281.0504Hainan1.04771.04931.05861.07291.17491.10391.11361.0611Chongqing1.07401.05111.07901.09461.13531.12391.13931.1183Sichuan1.07290.93831.11571.06821.10911.15371.24991.0803Guizhou1.03701.05371.10931.11091.07991.11401.13721.0459Yunnan1.04451.05591.10351.05471.06261.14311.10101.2305Shaanxi1.06290.96971.06251.02671.12001.11101.11781.2256Gansu1.02890.98531.03941.01531.06591.04031.03741.0478Qinghai1.02961.04631.08411.08021.10491.08861.07041.0499Ningxia0.98251.01701.04731.04451.11221.14451.14341.0410Xinjiang1.01971.02971.06800.98491.03511.10081.16341.0206Mean value1.04041.01331.06941.06351.12001.11991.15101.0850Table 3
The change in technical efficiency (MEC).
Region20122013201420152016201720182019Beijing1.00001.00001.00001.00001.00001.00001.00001.0000Tianjin1.03121.09111.04680.92671.00991.02181.02430.9930Hebei0.98221.40480.94670.93780.98611.16640.93310.9181Shanxi0.99901.08770.97380.92640.95781.13271.02901.0545Mongolia0.99571.57400.98430.94560.98331.03561.03571.0055Liaoning1.01291.04301.00120.98901.07661.04731.03751.1010Jilin1.02641.05671.02100.92850.97261.01001.03231.0116Heilongjiang1.01551.04501.01690.92280.93481.01991.02171.0416Shanghai1.00001.00001.00001.00001.00001.00001.00001.0000Jiangsu1.00001.00000.99691.00321.00001.00001.00001.0000Zhejiang1.00811.05140.99401.01520.98561.00771.04171.0369Anhui1.00911.27461.00000.95910.99631.00610.91840.9698Fujian0.93651.00060.99640.99581.00641.13570.94360.9663Jiangxi0.99861.11650.96160.94491.00141.01761.05080.9700Shandong1.00621.17451.00570.98990.98100.99061.01270.9772Henan1.00831.06021.00880.95520.99711.03261.11971.0086Hubei1.05241.07051.02070.97300.98121.03481.05881.0000Hunan1.05641.15011.00001.00001.00001.00001.00000.9616Guangdong1.00000.92430.99521.03470.97461.00290.95081.0277Guangxi1.00741.05901.02350.99040.98970.97561.02620.9642Hainan1.01811.01090.98640.99460.96010.97851.01701.0110Chongqing1.04731.10150.99591.01441.01491.03070.96901.0373Sichuan1.04250.95851.05370.97910.99301.05831.02381.0405Guizhou1.02161.09881.04551.01130.99361.02151.04030.9345Yunnan1.02321.08881.04330.96200.97231.05360.97041.1184Shaanxi1.03221.12970.98570.93221.00601.03081.04441.1664Gansu1.01391.00440.99730.96280.96301.04351.01081.0598Qinghai1.01321.09031.00000.96341.01631.01080.98670.9887Ningxia0.97191.45350.95830.91751.01261.04471.04760.9115Xinjiang1.00551.15231.00620.89710.94481.04151.09860.9708Mean value1.01121.10911.00220.96910.99041.03171.01481.0082Table 4
The change in technological progress (MTC).
Region20122013201420152016201720182019Beijing1.07021.11641.08401.11221.32381.09351.76481.2284Tianjin1.02410.96811.03841.11511.16681.10431.12101.0487Hebei1.02610.71961.09281.13201.09461.09601.10411.1209Shanxi1.01730.90191.05491.07981.08771.05921.07730.9673Mongolia1.04630.63071.09281.13841.09531.09141.09061.1048Liaoning1.02270.94201.06061.08911.11151.09161.07710.9626Jilin1.02310.90981.04101.10551.12431.06821.05531.0414Heilongjiang1.01951.00211.03371.08471.11111.02991.02291.0230Shanghai1.01351.00681.05661.04621.18851.25291.28300.9791Jiangsu1.04420.92001.04021.12051.13621.12261.13581.1351Zhejiang1.03361.02581.05841.08741.18391.08331.12271.0564Anhui1.04410.77231.08331.11511.13221.12251.10091.1316Fujian1.05101.05021.05251.04951.13690.90301.10151.0748Jiangxi1.04350.89641.09471.09451.12101.09021.14441.0857Shandong1.03850.84221.07601.10841.09221.09691.09101.0692Henan1.02880.89521.04871.10211.13411.08981.07751.0738Hubei1.03020.94261.07201.10641.14241.10091.14541.1006Hunan1.03060.91951.09481.11921.11681.11201.13521.0990Guangdong1.03290.93791.08901.06981.15141.08981.20861.0193Guangxi1.02490.94181.06321.09801.13261.10931.14281.0894Hainan1.02911.03791.07321.07881.22381.12831.09501.0495Chongqing1.02550.95421.08351.07921.11861.09041.17571.0780Sichuan1.02920.97891.05881.09101.11691.09011.22091.0382Guizhou1.01510.95891.06101.09841.08681.09051.09321.1193Yunnan1.02090.96981.05771.09641.09281.08491.13461.1003Shaanxi1.02970.85831.07791.10131.11341.07791.07021.0508Gansu1.01480.98101.04211.05461.10690.99701.02630.9886Qinghai1.01610.95961.08411.12121.08721.07701.08491.0619Ningxia1.01080.69971.09281.13841.09841.09551.09151.1421Xinjiang1.01410.89361.06141.09781.09551.05691.05901.0513Mean value1.02900.92111.06731.09771.13081.08651.13511.0697From the estimation results in Tables2–4, the following conclusions can be obtained.At the national level, the environmental total factor productivity index (ML) in China showed a fluctuating upward trend from 2012 to 2018, increasing from 1.03 in 2012 to 1.151 in 2018, with an average annual growth of 1.77%. In 2019, the environmental total factor productivity index decreased significantly, 5.77% lower than that of the previous year. In addition, the environmental total factor productivity index also decreased to some extent in 2013 and 2015. This reflects that when China pursues economic growth, the implementation of ecological and environmental protection policies is not in place and the protection effect is not satisfactory. From the decomposition index of environmental total factor productivity, the environmental technical efficiency index (MEC) increased from 1.0112 in 2012 to 1.1091 in 2013, an increase of 9.68%, and then it was in a downward trend until 1.0082 in 2019. The environmental technology progress index (MTC) decreased by 10.48% from 1.0290 in 2012 to 0.9211 in 2013, and then it was in a slow upward trend until 1.0697 in 2019. It can be seen that in recent years, technological progress has been the main driving force for the growth of China’s environmental total factor productivity.From the perspective of provincial data, the environmental total factor productivity of most provinces shows a growth trend. The fastest growing regions are Hebei, Beijing, and Yunnan, with growth rates of 0.246, 0.158, and 0.117, respectively, while the environmental total factor productivity of Shanghai, Hunan, Hainan, and Guizhou shows a slight negative growth. The provinces with the fastest growth of environmental technical efficiency index (MEC) are Yunnan, Guizhou, and Hubei, with growth rates of 13%, 9.30%, and 5.56%, respectively, while Hubei, Sichuan, and Tianjin showed significant negative growth. The provinces with the fastest growth in environmental technology progress index (MTC) are Jiangxi, Guizhou, and Yunnan, with growth rates of 22.82%, 17.81%, and 15.31%, respectively, while Heilongjiang, Hubei, and Beijing have negative growth. The reasons are as follows: the growth of environmental total factor productivity in Hebei, Beijing, and other regions is mainly due to technological progress. In the context of accelerating the construction of an innovative country, industries in these regions are more and more aware of the importance of scientific and technological innovation, have increased investment, attached importance to technological change, greatly promoted technological progress, and had a positive impact on the improvement of environmental total factor productivity. The environmental total factor productivity in Shanghai, Hunan, and other regions showed a slight decline, which may be due to the implementation of strict environmental regulation policies in these regions, resulting in increased costs and profit compression, resulting in the decline of environmental total factor productivity.


## 2.1. Index System of Environmental Total Factor Productivity

Based on the connotation of total factor productivity of environmental pollution factors, i.e., environmental total factor productivity, this paper constructs the index system of environmental total factor productivity from the perspective of economic performance and environmental pollution, using the construction method of environmental total factor productivity index by Y. Yan et al. (2020), in which economic performance is measured by input index and expected output index, and environmental pollution is measured by undesired output index. The definition of specific indicators is shown in Table1 [26].Table 1
Index system of environmental total factor productivity.
Primary indexSecondary indexTertiary indexInput indexCapitalTotal investment in fixed assetsLabor forceNumber of employees at the end of the yearEnergy consumptionTotal energy consumptionOutput indexEconomic growthRegional GDPUnexpected output indexThree industrial wastesWaste waterSulfur dioxideSolid waste


## 2.2. Measurement Method of Environmental Total Factor Productivity

According to the existing literature, the common methods used by previous scholars to measure total factor productivity include C-D production function regression method and Malmquist productivity index method based on DEA [27]. Malmquist productivity index method can reflect the dynamic changes of resource utilization efficiency in social and economic activities, but it cannot deal with expected output and unexpected output symmetrically. ML index method based on directional distance function solves this problem. It modifies the traditional Malmquist index, which can be used to measure total factor productivity in the presence of unexpected output. Therefore, based on the methods of Y. Chung et al. (1997) and S. Tang et al. (2019), this paper uses ML index based on directional distance function (DDF) to measure China’s environmental total factor productivity [24, 28].The ML index of environmental total factor productivity (ETFP growth rate) between phaset and phase t+1 is expressed by the following formula:(1)MLtt+1=1+D¯txt+1,yt+1,dt+1,gt+11+D¯txt,yt,dt,gt×1+D¯t+1xt+1,yt+1,dt+1,gt+11+D¯t+1xt,yt,dt,gt12.ML productivity index can be decomposed into the change in technical efficiency (MEC) and the change in technological progress (MTC), so as to explore the main reasons for the change of the productivity.(2)MLtt+1=MECtt+1×MTCtt+1,MLtt+1=1+D¯t+1xt+1,yt+1,dt+1,gt+11+D¯txt,yt,dt,gt,MTCtt+1=1+D¯txt+1,yt+1,dt+1,gt+11+D¯t+1xt+1,yt+1,dt+1,gt+1×1+D¯txt,yt,dt,gt1+D¯t+1xt,yt,dt,gt12,where x, y, d, and g represent input index, expected output, unexpected output, and direction vector, respectively. When ML productivity index is greater than 1, it indicates that the environmental total factor productivity has increased from phase t to phase t+1. When the ML productivity index is less than 1, it indicates that the environmental total factor productivity decreases from phase t to phase t+1. MEC indicates the change of technical efficiency. When MEC is greater than 1, it indicates that the technical efficiency has been improved from phase t to phase t+1; when MEC is less than 1, it indicates that the technical efficiency decreases from phase t to phase t+1. MTC indicates the change of technological progress. When MTC is greater than 1, it indicates the technological progress from phase t to phase t+1. On the contrary, the technology from phase t to phase t+1 will regress.


## 2.3. Measurement Results and Analysis of Environmental Total Factor Productivity

Using Matlab R2016a and the ML index, the environmental total factor productivity index (ML) and its decomposition index (MEC and MTC) of Chinese provinces under constant return to scale from 2012 to 2019 are calculated. Tables2–4, respectively, show the environmental total factor productivity and its decomposition of 30 provinces and cities in China during the sample period.Table 2
Environmental total factor productivity (ML).
Region20122013201420152016201720182019Beijing1.07021.11641.08401.11221.32381.09351.76481.2284Tianjin1.05601.05631.08711.03331.17831.12841.14821.0413Hebei1.00781.01091.03461.06161.07931.27831.03021.0290Shanxi1.01630.98101.02721.00021.04181.19981.10861.0200Mongolia1.04180.99261.07571.07641.07701.13031.12951.1108Liaoning1.03590.98251.06191.07711.19661.14321.11741.0598Jilin1.05000.96151.06291.02651.09341.07891.08941.0535Heilongjiang1.03531.04721.05121.00091.03871.05041.04501.0655Shanghai1.01351.00681.05661.04621.18851.25291.28300.9791Jiangsu1.04421.06401.03691.12401.13621.12261.13581.1351Zhejiang1.04201.07861.05211.10391.16691.09161.16941.0954Anhui1.05360.98441.08331.06961.12811.12941.01111.0974Fujian0.98421.05091.04871.04511.14421.02561.03941.0386Jiangxi1.04201.00091.05271.03421.12261.10941.20261.0532Shandong1.04490.98911.08211.09721.07151.08661.10491.2834Henan1.03740.94911.05791.05261.13071.12531.20641.0831Hubei1.08421.00901.09421.07661.12091.13921.21271.1006Hunan1.08871.05751.09481.11921.11681.11201.13521.0567Guangdong1.03290.86691.08381.10701.12221.09301.14921.0475Guangxi1.03250.99731.08821.08741.12091.08231.17281.0504Hainan1.04771.04931.05861.07291.17491.10391.11361.0611Chongqing1.07401.05111.07901.09461.13531.12391.13931.1183Sichuan1.07290.93831.11571.06821.10911.15371.24991.0803Guizhou1.03701.05371.10931.11091.07991.11401.13721.0459Yunnan1.04451.05591.10351.05471.06261.14311.10101.2305Shaanxi1.06290.96971.06251.02671.12001.11101.11781.2256Gansu1.02890.98531.03941.01531.06591.04031.03741.0478Qinghai1.02961.04631.08411.08021.10491.08861.07041.0499Ningxia0.98251.01701.04731.04451.11221.14451.14341.0410Xinjiang1.01971.02971.06800.98491.03511.10081.16341.0206Mean value1.04041.01331.06941.06351.12001.11991.15101.0850Table 3
The change in technical efficiency (MEC).
Region20122013201420152016201720182019Beijing1.00001.00001.00001.00001.00001.00001.00001.0000Tianjin1.03121.09111.04680.92671.00991.02181.02430.9930Hebei0.98221.40480.94670.93780.98611.16640.93310.9181Shanxi0.99901.08770.97380.92640.95781.13271.02901.0545Mongolia0.99571.57400.98430.94560.98331.03561.03571.0055Liaoning1.01291.04301.00120.98901.07661.04731.03751.1010Jilin1.02641.05671.02100.92850.97261.01001.03231.0116Heilongjiang1.01551.04501.01690.92280.93481.01991.02171.0416Shanghai1.00001.00001.00001.00001.00001.00001.00001.0000Jiangsu1.00001.00000.99691.00321.00001.00001.00001.0000Zhejiang1.00811.05140.99401.01520.98561.00771.04171.0369Anhui1.00911.27461.00000.95910.99631.00610.91840.9698Fujian0.93651.00060.99640.99581.00641.13570.94360.9663Jiangxi0.99861.11650.96160.94491.00141.01761.05080.9700Shandong1.00621.17451.00570.98990.98100.99061.01270.9772Henan1.00831.06021.00880.95520.99711.03261.11971.0086Hubei1.05241.07051.02070.97300.98121.03481.05881.0000Hunan1.05641.15011.00001.00001.00001.00001.00000.9616Guangdong1.00000.92430.99521.03470.97461.00290.95081.0277Guangxi1.00741.05901.02350.99040.98970.97561.02620.9642Hainan1.01811.01090.98640.99460.96010.97851.01701.0110Chongqing1.04731.10150.99591.01441.01491.03070.96901.0373Sichuan1.04250.95851.05370.97910.99301.05831.02381.0405Guizhou1.02161.09881.04551.01130.99361.02151.04030.9345Yunnan1.02321.08881.04330.96200.97231.05360.97041.1184Shaanxi1.03221.12970.98570.93221.00601.03081.04441.1664Gansu1.01391.00440.99730.96280.96301.04351.01081.0598Qinghai1.01321.09031.00000.96341.01631.01080.98670.9887Ningxia0.97191.45350.95830.91751.01261.04471.04760.9115Xinjiang1.00551.15231.00620.89710.94481.04151.09860.9708Mean value1.01121.10911.00220.96910.99041.03171.01481.0082Table 4
The change in technological progress (MTC).
Region20122013201420152016201720182019Beijing1.07021.11641.08401.11221.32381.09351.76481.2284Tianjin1.02410.96811.03841.11511.16681.10431.12101.0487Hebei1.02610.71961.09281.13201.09461.09601.10411.1209Shanxi1.01730.90191.05491.07981.08771.05921.07730.9673Mongolia1.04630.63071.09281.13841.09531.09141.09061.1048Liaoning1.02270.94201.06061.08911.11151.09161.07710.9626Jilin1.02310.90981.04101.10551.12431.06821.05531.0414Heilongjiang1.01951.00211.03371.08471.11111.02991.02291.0230Shanghai1.01351.00681.05661.04621.18851.25291.28300.9791Jiangsu1.04420.92001.04021.12051.13621.12261.13581.1351Zhejiang1.03361.02581.05841.08741.18391.08331.12271.0564Anhui1.04410.77231.08331.11511.13221.12251.10091.1316Fujian1.05101.05021.05251.04951.13690.90301.10151.0748Jiangxi1.04350.89641.09471.09451.12101.09021.14441.0857Shandong1.03850.84221.07601.10841.09221.09691.09101.0692Henan1.02880.89521.04871.10211.13411.08981.07751.0738Hubei1.03020.94261.07201.10641.14241.10091.14541.1006Hunan1.03060.91951.09481.11921.11681.11201.13521.0990Guangdong1.03290.93791.08901.06981.15141.08981.20861.0193Guangxi1.02490.94181.06321.09801.13261.10931.14281.0894Hainan1.02911.03791.07321.07881.22381.12831.09501.0495Chongqing1.02550.95421.08351.07921.11861.09041.17571.0780Sichuan1.02920.97891.05881.09101.11691.09011.22091.0382Guizhou1.01510.95891.06101.09841.08681.09051.09321.1193Yunnan1.02090.96981.05771.09641.09281.08491.13461.1003Shaanxi1.02970.85831.07791.10131.11341.07791.07021.0508Gansu1.01480.98101.04211.05461.10690.99701.02630.9886Qinghai1.01610.95961.08411.12121.08721.07701.08491.0619Ningxia1.01080.69971.09281.13841.09841.09551.09151.1421Xinjiang1.01410.89361.06141.09781.09551.05691.05901.0513Mean value1.02900.92111.06731.09771.13081.08651.13511.0697From the estimation results in Tables2–4, the following conclusions can be obtained.At the national level, the environmental total factor productivity index (ML) in China showed a fluctuating upward trend from 2012 to 2018, increasing from 1.03 in 2012 to 1.151 in 2018, with an average annual growth of 1.77%. In 2019, the environmental total factor productivity index decreased significantly, 5.77% lower than that of the previous year. In addition, the environmental total factor productivity index also decreased to some extent in 2013 and 2015. This reflects that when China pursues economic growth, the implementation of ecological and environmental protection policies is not in place and the protection effect is not satisfactory. From the decomposition index of environmental total factor productivity, the environmental technical efficiency index (MEC) increased from 1.0112 in 2012 to 1.1091 in 2013, an increase of 9.68%, and then it was in a downward trend until 1.0082 in 2019. The environmental technology progress index (MTC) decreased by 10.48% from 1.0290 in 2012 to 0.9211 in 2013, and then it was in a slow upward trend until 1.0697 in 2019. It can be seen that in recent years, technological progress has been the main driving force for the growth of China’s environmental total factor productivity.From the perspective of provincial data, the environmental total factor productivity of most provinces shows a growth trend. The fastest growing regions are Hebei, Beijing, and Yunnan, with growth rates of 0.246, 0.158, and 0.117, respectively, while the environmental total factor productivity of Shanghai, Hunan, Hainan, and Guizhou shows a slight negative growth. The provinces with the fastest growth of environmental technical efficiency index (MEC) are Yunnan, Guizhou, and Hubei, with growth rates of 13%, 9.30%, and 5.56%, respectively, while Hubei, Sichuan, and Tianjin showed significant negative growth. The provinces with the fastest growth in environmental technology progress index (MTC) are Jiangxi, Guizhou, and Yunnan, with growth rates of 22.82%, 17.81%, and 15.31%, respectively, while Heilongjiang, Hubei, and Beijing have negative growth. The reasons are as follows: the growth of environmental total factor productivity in Hebei, Beijing, and other regions is mainly due to technological progress. In the context of accelerating the construction of an innovative country, industries in these regions are more and more aware of the importance of scientific and technological innovation, have increased investment, attached importance to technological change, greatly promoted technological progress, and had a positive impact on the improvement of environmental total factor productivity. The environmental total factor productivity in Shanghai, Hunan, and other regions showed a slight decline, which may be due to the implementation of strict environmental regulation policies in these regions, resulting in increased costs and profit compression, resulting in the decline of environmental total factor productivity.


## 3. Econometric Analysis of the Impact of Innovation Investment on Environmental Total Factor Productivity

In view of the large temporal and spatial differences in innovation investment and environmental total factor productivity in various regions of China, it is necessary to consider the impact of geospatial factors on the research results. At the same time, there is a certain spatial correlation effect in the improvement of regional environmental total factor productivity, that is, the improvement of regional environmental total factor productivity may be affected by interregional factor flow and spillover effect. Therefore, this paper introduces a spatial econometric model to study the impact of innovation investment on environmental total factor productivity. Firstly, this paper uses Moran index to analyze the spatial correlation of environmental total factor productivity to test whether it is necessary to study the spatial effect. Secondly, the spatial Dobbin model is used to analyze whether there is a spatial effect of innovation investment on environmental total factor productivity, and the impact of innovation investment, economic development, energy structure, human capital, and foreign investment level on environmental total factor productivity is analyzed from the direct effect and spatial effect.


### 3.1. Spatial Correlation of Environmental Total Factor Productivity

Before estimating the spatial econometric model, this paper uses the global spatial autocorrelation Moran’s I index to test whether there is spatial correlation between regional environmental total factor productivity. Based on the data of 30 provinces in China from 2012 to 2019, this paper uses Moran’s I to analyze the global correlation effect of environmental total factor productivity. In order to make the analysis results more objective, two spatial weight matrices are used to calculate the global correlation of environmental total factor productivity. Moran index is calculated as follows:(3)Moran'SI=∑i=1n∑j=1nWijxi−x¯xj−x¯S2∑i=1n∑j=1nWij−1≤I≤1,where S2=∑i=1nxi−x¯/n is the sample variance; Wij is the spatial weight matrix, the reciprocal of distance 1/d is used as the index to measure the “geographical distance” between regions in the geographical distance matrix, and the difference of per capita GDP between regions 1/Y¯i−Y¯ji≠j is used as the index to measure the “economic distance” between regions in the economic distance matrix; ∑i=1n∑j=1nWij is the sum of all spatial weights.Based on the two spatial weight matrices, the Moran index of the environmental total factor productivity from 2012 to 2019 in China is calculated. The results are shown in Table5.Table 5
Moran Index of environmental total factor productivity.
Geographic distance matrixEconomic distance matrixYearI valueZ valueP valueYearI valueZ valueP value20120.041−0.1890.0252012−0.086−0.6960.55520130.0061.0120.0632013−0.0080.3650.00520140.0221.5800.00220140.0260.6740.012015−0.0140.5870.0922015−0.092−0.6350.05620160.0170.5480.00720160.0751.2920.00120170.0321.9410.05220170.1061.6440.10220180.069−1.3090.04420180.0801.7580.0792019−0.045−0.3000.7642019−0.177−1.6310.012It can be seen from Table5 that under the geographical distance matrix, the global Moran index of the environmental total factor productivity in all years except 2019 passed the significance test, and the global Moran index in all years except 2015 is positive, indicating that there is a significant global spatial positive correlation of the environmental total factor productivity in all provinces of China, that is, provinces with high level of environmental total factor productivity are adjacent to provinces with high level of environmental total factor productivity. Under the economic distance matrix, except 2012 and 2017, the global Moran index of the environmental total factor productivity in other years passed the significance test. Therefore, we cannot ignore the spatial characteristics of the environmental total factor productivity, and we need to analyze the impact of innovation investment on environmental total factor productivity from the spatial dimension.


### 3.2. Spatial Spillover Effect of Innovation Investment on Environmental Total Factor Productivity

The spatial econometric model is used to empirically study the impact of innovation investment on environmental total factor productivity. Firstly, regression analysis is carried out to explore the spatial relationship between innovation investment, economic development, energy structure, human capital, foreign investment level, and environmental total factor productivity. Secondly, the partial differential method of spatial regression model is introduced to decompose the impact of innovation investment on environmental total factor productivity, and analyze the direct effect and spatial spillover effect of innovation investment on environmental total factor productivity.


#### 3.2.1. Construction of Measurement Model

Through the above analysis, the environmental total factor productivity in China has significant spatial autocorrelation. Therefore, based on the model construction methods of W. P. Yang et al. (2020) and B. T. Li (2021) [29, 30], the following spatial econometric model is constructed:(4)Ti,t=α+λWTi,t−1+β1Ii,t+β2Ei,t+β3Si,t+β4Hi,t+β5Fi,t+γ1WIi,t+γ2WEi,t+γ3WSi,t+γ4WHi,t+γ5WFi,t+μi+vt+εi,t,where T represents environmental total factor productivity, I represents innovation investment, E represents economic development level, S represents energy structure, H represents human capital level, and F represents foreign investment level; i=1, …, 30; t=1, …, 8; α is the intercept term; λ measures the spillover effect of the level of Environmental Total Factor Productivity in the region affected by the level of Environmental Total Factor Productivity in the associated region (i.e. the elasticity of spatial spillover effect); γ1. ..., γ5 represents the contribution of innovation investment, economic development level, energy structure, human capital level, and foreign investment level to environmental total factor productivity, respectively; γ1. ..., γ5, respectively, represent the impact degree and direction of the corresponding variables in the adjacent areas on the regional environmental total factor productivity; μi and νt are individual fixed effect and time fixed effect, respectively; εi,t is random disturbance term; W = 30 × 30 spatial weight matrix.


#### 3.2.2. Variable Selection and Data Source

The core variables are innovation investment level, regional environmental total factor productivity, and the main control variables are economic development level, energy structure, human capital level, and foreign investment. The variable settings are as follows:(1)
Core Variables. ① Explained variable: the environmental total factor productivity index calculated above is used as the explanatory variable. ② Explanatory variables: from the influence mechanism of innovation investment on total factor productivity, it can be seen that innovation investment affects environmental total factor productivity through three effects: the spillover effect of external innovation capital, the technology spillover effect of pollution innovation governance investment, the wage income of innovation and the market demand effect, and the main factors affecting innovation efficiency are labor force and capital. Therefore, this paper starts from two aspects of innovation manpower investment and innovation capital investment, the full-time equivalent and expenditure of research and experimental development personnel in industrial enterprises above designated size are selected as explanatory variables.(2)
Main Control Variables. ① Economic development level: the level of regional economic development is measured by per capita GDP. ② Energy structure: the energy structure is expressed by the ratio of coal consumption to total energy consumption. ③ Human capital level: as the main body of promoting technological progress, human capital is very important for the improvement of environmental total factor productivity. Therefore, the level of human capital is measured by the number of students per 100000 people. ④ Foreign investment: the level of foreign investment is measured by the ratio of foreign direct investment to GDP.The data used in the demonstration are from China Statistical Yearbook from 2012 to 2019, China environmental database, and China economic and social big data platform and global EPS database. The per capita GDP, foreign direct investment, investment in fixed assets of the whole society, and other value indicators are subject to price reduction based on 2010. Individual missing data are filled with the average value of adjacent years, and the balance panel data from 2012 to 2019 are standardized to eliminate the dimensional impact between indicators.


#### 3.2.3. Basic Regression Analysis

Firstly, in order to judge whether the selected regression analysis model is a fixed effect model or a random effect model, this paper carries out the Hausmann test. The test results are significant at the level of 1%, so the fixed effect model is selected. Secondly, in order to further select the optimal model, we test the regional fixed effect, time fixed effect, and time-space double fixed effect, and reject the original hypothesis; so, we choose the double fixed effect model. Finally, the LR test is carried out. The results show that the spatial Dobbin model cannot be degenerated into SAR model or SEM model, so the double fixed effect spatial Dobbin model (SDM) is selected. The results of basic regression analysis are shown in Table6.Table 6
Estimation results of double fixed effect spatial Durbin model.
VariableGeographic distance matrixEconomic distance matrixλ0.565∗∗0.071∗(0.277)(0.102)I0.150∗0.018∗(−2.748)(2.491)E0.544∗∗∗0.278∗∗(7.794)(8.381)S−0.060−0.149∗∗(0.077)(0.074)H−0.142∗−0.115(−5.608)(−5.931)F0.049∗0.063∗(0.023)(0.024)W(I)2.268∗∗∗0.361(1.69)(8.301)W(E)1.262∗0.403∗(4.77)(2.1)W(S)−0.546∗−0.245∗(1.546)(0.2)W(H)−0.226∗−0.019(−0.001)(0.001)W(F)0.215∗−0.012(−0.173)(−0.064)Note.∗∗∗,∗∗,∗, respectively, mean passing the significance level test of 1%, 5%, and 10%. The values in brackets represent standard error.From the model estimation results in Table6, the following three conclusions are obtained.First, there is a positive spatial spillover effect in the improvement of Environmental Total Factor Productivity in all provinces. Under the two different spatial weight matrices of geographical distance matrix and economic distance matrix, spatial autoregressive coefficients are 0.565 and 0.071, respectively. The two coefficients pass the significance test at the level of 5% and 10%, respectively, which shows that the improvement of Environmental Total Factor Productivity in China’s provinces has a positive spatial spillover effect on itself, that is, the improvement of Environmental Total Factor Productivity in a region will promote the improvement of Environmental Total Factor Productivity in the surrounding areas of the region.Second, increasing investment in innovation has a positive effect on the improvement of Environmental Total Factor Productivity in the region and surrounding areas. Under two different spatial weight matrices, the spatial regression coefficients of innovation investment are 0.150 and 0.018, respectively, that is, every one percentage point increase in the level of innovation investment can bring 0.150 and 0.018 percentage points increase in Environmental Total Factor Productivity, respectively. The W(X) term can better explain the spatial transmission effect (X refers to I, E, S, H, and F in this paper). The coefficient of the exogenous interaction effect of innovation investment W(I) under the geographical distance matrix is 2.268, which indicates that the improvement of Environmental Total Factor Productivity in a region is affected by the level of innovation investment in the surrounding regions, and this impact is positive.Third, the coefficients of economic development and foreign investment are positive, and the coefficients of energy structure and human capital are negative, indicating that economic development and foreign investment promote the improvement of environmental total factor productivity, while energy structure and human capital inhibit the improvement of environmental total factor productivity. Under two different spatial weight matrices, there is a positive correlation between economic development and foreign investment level on the improvement of environmental total factor productivity. Among them, the spatial regression coefficients of economic development level are the largest, which are 0.544 and 0.278. respectively, and the spatial regression coefficients of foreign investment level are 0.049 and 0.063, respectively. The energy structure and human capital have a negative impact on the improvement of environmental total factor productivity. The spatial regression coefficients of energy structure are −0.060 and −0.149, respectively, and the spatial regression coefficients of human capital are −0.142 and −0.115, respectively. In item W(X), the exogenous interaction effect W(E) of economic development level is 1.262 and 0.403, respectively, while the exogenous interaction effect w (f) of foreign investment level passes the significance test under the geographical distance matrix, and its value is 0.215, indicating that the environmental total factor productivity level of a region is greatly affected by the economic development level of the surrounding region and relatively less affected by foreign investment in the surrounding region. The exogenous interaction effect W(S) of energy structure is −0.546 and −0.245, respectively, and the exogenous interaction effect W(H) of human capital is −0.226 under the geographical matrix, indicating that the current energy structure and human capital have a negative impact on the improvement of environmental total factor productivity, and there is still some room for adjustment in the future.


#### 3.2.4. Further Analysis

Considering that the spatial lag term of explanatory variables is added to the spatial Durbin model, and the original estimation coefficient cannot accurately characterize the impact of explanatory variables on the explained variables, this paper uses the experience of R. K. Pace et al. (2009) and H. J. Liu (2014) for reference, and uses the partial differential effect decomposition method to decompose the spatial effects into direct effects, indirect effects, and total effects [31, 32]. Using the partial differential method of spatial regression model, the n-order identity matrix is introduced to transform model (6), and the direct effect, indirect effect, and total effect of the rth explanatory variable of region j are obtained by calculating the partial derivative. The specific process is as follows:(5)In−λWT=αln+βX+γWX+ε,(6)T=∑r=1kSrWxr+VWlnα+VWε,(7)SrW=VWInβr+Wγr,VW=In−λW−1=In+λW+λ2W2+λ3W3+⋯λnWn,where In is the identity matrix of order n; k is the number of explanatory variables; xr is the rth explanatory variable; r=1,2,⋯k; βr is the regression coefficient of the rth explanatory variable in the explanatory variable vector X; and γr represents the estimation coefficient of the rth variable of WX.In order to explain the function ofSrW, equation (6) is written as (8), and Ti of a region ii=1,2,⋯n can be expressed as (9).(8)T1T2⋮Tn=∑r=1kSrW11SrW12…SrW1nSrW12SrW22…SrW2n⋮⋮⋮⋮SrW1nSrW2n⋯SrWnnx1rx2r⋮xnr+VWlnα+VWε,(9)Ti=∑r=1kSrWi1x1r+SrWi2x2r+⋯+SrWinxnr+VWα+VWiε,(10)∂Ti∂xjr=SrWij,(11)∂Ti∂xir=SrWii,where SrWij represents the influence degree of the rth explanatory variable of region j on the explained variable of region i; SrWii represents the influence degree of the rth explanatory variable of region i on the explained variable in this region.xjr represents the r-th explanatory variable in region j, and xir represents the r-th explanatory variable in region i. According to equations (9) and (10) is derived from the partial derivation of Ti to xjr, and equation (11) is derived from the partial derivation of Ti to xir.As can be seen from equations (10) and (11), in the spatial regression model, if j≠i, the partial derivative of Ti to xjr is usually not equal to 0 but depends on the i and j elements in matrix SrW. At the same time, the partial derivative of Ti to xir is usually not equal to βr. Therefore, the change of explanatory variables in a region will affect not only the explained variables in this region but also the explained variables in other regions. The former can be called direct effect, the latter is called indirect effect, and the sum of the two is the total effect [33]. See Table 7 for the effect decomposition results of Durbin model in double fixed effect space.Table 7
Estimation results of decomposition effect of Durbin model in double fixed effect space.
Direct effectIndirect effectTotal effectVariableGeographic distance matrixEconomic distance matrixVariableGeographic distance matrixEconomic distance matrixVariableGeographic distance matrixEconomic distance matrixI0.096∗0.174∗I1.453∗∗∗0.364∗I1.549∗∗∗0.381∗(2.747)(2.541)(1.076)(9.061)(1.150)(9.161)E0.517∗∗∗0.276∗∗E0.624∗0.449∗E1.141∗∗0.725∗∗(7.817)(8.171)(2.986)(2.331)(2.950)(2.321)S−0.068−0.140∗∗S−0.388∗−0.257∗S−0.320∗0.117∗(0.075)(0.073)(0.362)(0.245)(0.366)(0.281)H−0.147∗0.113H0.169∗0.041H−0.021∗−0.154(5.506)(5.901)(−0.001)(0.001)(−0.001)(0.001)F0.043∗0.062∗F0.149∗0.006F0.192∗0.069∗(−0.023)(−0.023)(0.107)(−0.071)(0.101)(0.075)According to the estimation results in Table7, the following conclusions can be drawn.The perspective of direct effect, innovation investment, economic development, and the level of foreign investment all promote the improvement of Environmental Total Factor Productivity in the region. Among them, the regression coefficient of economic development is the largest and its promotion effect is the most significant. Under the two distance matrices, the coefficients are 0.517 and 0.276, respectively, the coefficients of innovation investment are 0.096 and 0.174, respectively, and the regression coefficients of foreign investment are 0.043 and 0.062, respectively. This is because the improvement of innovation investment and foreign investment level will improve regional innovation ability, bring advanced technology, and improve resource utilization efficiency. At the same time, with the improvement of the economic development level, people pay more attention to the improvement of quality of life and the protection of ecological environment, so as to effectively improve environmental total factor productivity. The coefficients of energy structure and human capital level are negative, indicating that these two variables have a negative effect on the improvement of Environmental Total Factor Productivity in this region. The regression coefficient of energy structure passes the significance test under the economic distance matrix, and the value is −0.140. The regression coefficient of human capital passed the significance test under the geographical distance matrix, and the value was −0.147. The possible reasons are as follows: on the one hand, the current human structure cannot fully meet the needs of the development of green production technology, and the problem of talent structure still exists. On the other hand, the energy consumption in China is dominated by coal, which will produce a large number of polluting gases in the combustion process [34]. At the same time, enterprises have to invest a lot of economic resources to reduce pollution emissions, resulting in reduced production efficiency.In terms of indirect effects, innovation investment, economic development, human capital, and foreign investment have positive spatial spillover effects on the improvement of Environmental Total Factor Productivity in surrounding areas, and negative spatial spillover effects on energy structure. The regression coefficients of innovation investment were 1.453 and 0.364, respectively, and both passed the significance test; the regression coefficients of economic development were 0.624 and 0.449, respectively, and both passed the significance test. The regression coefficient of foreign investment passes the significance test under the geographical distance matrix, and its value is 0.149. The regression analysis coefficient of human capital passes the significance test under the geographical distance matrix, and its value is 0.169. This shows that compared with the direct effect, the spillover effect of human capital is more conducive to the improvement of environmental total factor productivity. This is because the regional flow of talents can solve the problem of insufficient Talent Investment in some regions, promote their rational distribution among industries and regions, and promote the improvement of labor productivity. The regression analysis coefficients of energy structure are −0.388 and −0.257, respectively, showing a negative spillover effect. The reason is that the energy consumption in China is mainly coal, and a large amount of pollution generated in the consumption process will have a certain impact on the surrounding environment, resulting in the decline of environmental quality and the impact of environmental total factor productivity [35].From the perspective of total effect, in addition to energy structure and human capital, all variables are conducive to the improvement of environmental total factor productivity. The regression coefficients of innovation investment are 1.549 and 0.381, respectively, indicating that increasing innovation investment by 1 percentage point will increase environmental total factor productivity by 1.549 and 0.381 percentage points. This is because increasing innovation investment can enable enterprises to quickly iterate production technology, improve independent innovation ability and scientific and technological level, so as to improve resource utilization efficiency, which has an obvious effect on the improvement of environmental total factor productivity. The regression coefficients of economic development level are 1.141 and 0.725, respectively, and both pass the significance test, indicating that it has a significant role in promoting the improvement of environmental total factor productivity. This is because, with the improvement of the level of economic development, people pursue a higher quality of living environment, forcing enterprises with serious pollution emissions to reduce unexpected output. The regression coefficients of foreign investment are 0.192 and 0.069, respectively, which are generally promoting. The reason is that foreign investment has brought advanced technology and management experience to improve production efficiency. The coefficient of energy structure under geographical distance matrix is −0.320 and the coefficient of human capital under geographical distance matrix is −0.021, indicating that these two variables hinder the further improvement of environmental total factor productivity.


## 3.1. Spatial Correlation of Environmental Total Factor Productivity

Before estimating the spatial econometric model, this paper uses the global spatial autocorrelation Moran’s I index to test whether there is spatial correlation between regional environmental total factor productivity. Based on the data of 30 provinces in China from 2012 to 2019, this paper uses Moran’s I to analyze the global correlation effect of environmental total factor productivity. In order to make the analysis results more objective, two spatial weight matrices are used to calculate the global correlation of environmental total factor productivity. Moran index is calculated as follows:(3)Moran'SI=∑i=1n∑j=1nWijxi−x¯xj−x¯S2∑i=1n∑j=1nWij−1≤I≤1,where S2=∑i=1nxi−x¯/n is the sample variance; Wij is the spatial weight matrix, the reciprocal of distance 1/d is used as the index to measure the “geographical distance” between regions in the geographical distance matrix, and the difference of per capita GDP between regions 1/Y¯i−Y¯ji≠j is used as the index to measure the “economic distance” between regions in the economic distance matrix; ∑i=1n∑j=1nWij is the sum of all spatial weights.Based on the two spatial weight matrices, the Moran index of the environmental total factor productivity from 2012 to 2019 in China is calculated. The results are shown in Table5.Table 5
Moran Index of environmental total factor productivity.
Geographic distance matrixEconomic distance matrixYearI valueZ valueP valueYearI valueZ valueP value20120.041−0.1890.0252012−0.086−0.6960.55520130.0061.0120.0632013−0.0080.3650.00520140.0221.5800.00220140.0260.6740.012015−0.0140.5870.0922015−0.092−0.6350.05620160.0170.5480.00720160.0751.2920.00120170.0321.9410.05220170.1061.6440.10220180.069−1.3090.04420180.0801.7580.0792019−0.045−0.3000.7642019−0.177−1.6310.012It can be seen from Table5 that under the geographical distance matrix, the global Moran index of the environmental total factor productivity in all years except 2019 passed the significance test, and the global Moran index in all years except 2015 is positive, indicating that there is a significant global spatial positive correlation of the environmental total factor productivity in all provinces of China, that is, provinces with high level of environmental total factor productivity are adjacent to provinces with high level of environmental total factor productivity. Under the economic distance matrix, except 2012 and 2017, the global Moran index of the environmental total factor productivity in other years passed the significance test. Therefore, we cannot ignore the spatial characteristics of the environmental total factor productivity, and we need to analyze the impact of innovation investment on environmental total factor productivity from the spatial dimension.


## 3.2. Spatial Spillover Effect of Innovation Investment on Environmental Total Factor Productivity

The spatial econometric model is used to empirically study the impact of innovation investment on environmental total factor productivity. Firstly, regression analysis is carried out to explore the spatial relationship between innovation investment, economic development, energy structure, human capital, foreign investment level, and environmental total factor productivity. Secondly, the partial differential method of spatial regression model is introduced to decompose the impact of innovation investment on environmental total factor productivity, and analyze the direct effect and spatial spillover effect of innovation investment on environmental total factor productivity.


### 3.2.1. Construction of Measurement Model

Through the above analysis, the environmental total factor productivity in China has significant spatial autocorrelation. Therefore, based on the model construction methods of W. P. Yang et al. (2020) and B. T. Li (2021) [29, 30], the following spatial econometric model is constructed:(4)Ti,t=α+λWTi,t−1+β1Ii,t+β2Ei,t+β3Si,t+β4Hi,t+β5Fi,t+γ1WIi,t+γ2WEi,t+γ3WSi,t+γ4WHi,t+γ5WFi,t+μi+vt+εi,t,where T represents environmental total factor productivity, I represents innovation investment, E represents economic development level, S represents energy structure, H represents human capital level, and F represents foreign investment level; i=1, …, 30; t=1, …, 8; α is the intercept term; λ measures the spillover effect of the level of Environmental Total Factor Productivity in the region affected by the level of Environmental Total Factor Productivity in the associated region (i.e. the elasticity of spatial spillover effect); γ1. ..., γ5 represents the contribution of innovation investment, economic development level, energy structure, human capital level, and foreign investment level to environmental total factor productivity, respectively; γ1. ..., γ5, respectively, represent the impact degree and direction of the corresponding variables in the adjacent areas on the regional environmental total factor productivity; μi and νt are individual fixed effect and time fixed effect, respectively; εi,t is random disturbance term; W = 30 × 30 spatial weight matrix.


### 3.2.2. Variable Selection and Data Source

The core variables are innovation investment level, regional environmental total factor productivity, and the main control variables are economic development level, energy structure, human capital level, and foreign investment. The variable settings are as follows:(1)
Core Variables. ① Explained variable: the environmental total factor productivity index calculated above is used as the explanatory variable. ② Explanatory variables: from the influence mechanism of innovation investment on total factor productivity, it can be seen that innovation investment affects environmental total factor productivity through three effects: the spillover effect of external innovation capital, the technology spillover effect of pollution innovation governance investment, the wage income of innovation and the market demand effect, and the main factors affecting innovation efficiency are labor force and capital. Therefore, this paper starts from two aspects of innovation manpower investment and innovation capital investment, the full-time equivalent and expenditure of research and experimental development personnel in industrial enterprises above designated size are selected as explanatory variables.(2)
Main Control Variables. ① Economic development level: the level of regional economic development is measured by per capita GDP. ② Energy structure: the energy structure is expressed by the ratio of coal consumption to total energy consumption. ③ Human capital level: as the main body of promoting technological progress, human capital is very important for the improvement of environmental total factor productivity. Therefore, the level of human capital is measured by the number of students per 100000 people. ④ Foreign investment: the level of foreign investment is measured by the ratio of foreign direct investment to GDP.The data used in the demonstration are from China Statistical Yearbook from 2012 to 2019, China environmental database, and China economic and social big data platform and global EPS database. The per capita GDP, foreign direct investment, investment in fixed assets of the whole society, and other value indicators are subject to price reduction based on 2010. Individual missing data are filled with the average value of adjacent years, and the balance panel data from 2012 to 2019 are standardized to eliminate the dimensional impact between indicators.


### 3.2.3. Basic Regression Analysis

Firstly, in order to judge whether the selected regression analysis model is a fixed effect model or a random effect model, this paper carries out the Hausmann test. The test results are significant at the level of 1%, so the fixed effect model is selected. Secondly, in order to further select the optimal model, we test the regional fixed effect, time fixed effect, and time-space double fixed effect, and reject the original hypothesis; so, we choose the double fixed effect model. Finally, the LR test is carried out. The results show that the spatial Dobbin model cannot be degenerated into SAR model or SEM model, so the double fixed effect spatial Dobbin model (SDM) is selected. The results of basic regression analysis are shown in Table6.Table 6
Estimation results of double fixed effect spatial Durbin model.
VariableGeographic distance matrixEconomic distance matrixλ0.565∗∗0.071∗(0.277)(0.102)I0.150∗0.018∗(−2.748)(2.491)E0.544∗∗∗0.278∗∗(7.794)(8.381)S−0.060−0.149∗∗(0.077)(0.074)H−0.142∗−0.115(−5.608)(−5.931)F0.049∗0.063∗(0.023)(0.024)W(I)2.268∗∗∗0.361(1.69)(8.301)W(E)1.262∗0.403∗(4.77)(2.1)W(S)−0.546∗−0.245∗(1.546)(0.2)W(H)−0.226∗−0.019(−0.001)(0.001)W(F)0.215∗−0.012(−0.173)(−0.064)Note.∗∗∗,∗∗,∗, respectively, mean passing the significance level test of 1%, 5%, and 10%. The values in brackets represent standard error.From the model estimation results in Table6, the following three conclusions are obtained.First, there is a positive spatial spillover effect in the improvement of Environmental Total Factor Productivity in all provinces. Under the two different spatial weight matrices of geographical distance matrix and economic distance matrix, spatial autoregressive coefficients are 0.565 and 0.071, respectively. The two coefficients pass the significance test at the level of 5% and 10%, respectively, which shows that the improvement of Environmental Total Factor Productivity in China’s provinces has a positive spatial spillover effect on itself, that is, the improvement of Environmental Total Factor Productivity in a region will promote the improvement of Environmental Total Factor Productivity in the surrounding areas of the region.Second, increasing investment in innovation has a positive effect on the improvement of Environmental Total Factor Productivity in the region and surrounding areas. Under two different spatial weight matrices, the spatial regression coefficients of innovation investment are 0.150 and 0.018, respectively, that is, every one percentage point increase in the level of innovation investment can bring 0.150 and 0.018 percentage points increase in Environmental Total Factor Productivity, respectively. The W(X) term can better explain the spatial transmission effect (X refers to I, E, S, H, and F in this paper). The coefficient of the exogenous interaction effect of innovation investment W(I) under the geographical distance matrix is 2.268, which indicates that the improvement of Environmental Total Factor Productivity in a region is affected by the level of innovation investment in the surrounding regions, and this impact is positive.Third, the coefficients of economic development and foreign investment are positive, and the coefficients of energy structure and human capital are negative, indicating that economic development and foreign investment promote the improvement of environmental total factor productivity, while energy structure and human capital inhibit the improvement of environmental total factor productivity. Under two different spatial weight matrices, there is a positive correlation between economic development and foreign investment level on the improvement of environmental total factor productivity. Among them, the spatial regression coefficients of economic development level are the largest, which are 0.544 and 0.278. respectively, and the spatial regression coefficients of foreign investment level are 0.049 and 0.063, respectively. The energy structure and human capital have a negative impact on the improvement of environmental total factor productivity. The spatial regression coefficients of energy structure are −0.060 and −0.149, respectively, and the spatial regression coefficients of human capital are −0.142 and −0.115, respectively. In item W(X), the exogenous interaction effect W(E) of economic development level is 1.262 and 0.403, respectively, while the exogenous interaction effect w (f) of foreign investment level passes the significance test under the geographical distance matrix, and its value is 0.215, indicating that the environmental total factor productivity level of a region is greatly affected by the economic development level of the surrounding region and relatively less affected by foreign investment in the surrounding region. The exogenous interaction effect W(S) of energy structure is −0.546 and −0.245, respectively, and the exogenous interaction effect W(H) of human capital is −0.226 under the geographical matrix, indicating that the current energy structure and human capital have a negative impact on the improvement of environmental total factor productivity, and there is still some room for adjustment in the future.


### 3.2.4. Further Analysis

Considering that the spatial lag term of explanatory variables is added to the spatial Durbin model, and the original estimation coefficient cannot accurately characterize the impact of explanatory variables on the explained variables, this paper uses the experience of R. K. Pace et al. (2009) and H. J. Liu (2014) for reference, and uses the partial differential effect decomposition method to decompose the spatial effects into direct effects, indirect effects, and total effects [31, 32]. Using the partial differential method of spatial regression model, the n-order identity matrix is introduced to transform model (6), and the direct effect, indirect effect, and total effect of the rth explanatory variable of region j are obtained by calculating the partial derivative. The specific process is as follows:(5)In−λWT=αln+βX+γWX+ε,(6)T=∑r=1kSrWxr+VWlnα+VWε,(7)SrW=VWInβr+Wγr,VW=In−λW−1=In+λW+λ2W2+λ3W3+⋯λnWn,where In is the identity matrix of order n; k is the number of explanatory variables; xr is the rth explanatory variable; r=1,2,⋯k; βr is the regression coefficient of the rth explanatory variable in the explanatory variable vector X; and γr represents the estimation coefficient of the rth variable of WX.In order to explain the function ofSrW, equation (6) is written as (8), and Ti of a region ii=1,2,⋯n can be expressed as (9).(8)T1T2⋮Tn=∑r=1kSrW11SrW12…SrW1nSrW12SrW22…SrW2n⋮⋮⋮⋮SrW1nSrW2n⋯SrWnnx1rx2r⋮xnr+VWlnα+VWε,(9)Ti=∑r=1kSrWi1x1r+SrWi2x2r+⋯+SrWinxnr+VWα+VWiε,(10)∂Ti∂xjr=SrWij,(11)∂Ti∂xir=SrWii,where SrWij represents the influence degree of the rth explanatory variable of region j on the explained variable of region i; SrWii represents the influence degree of the rth explanatory variable of region i on the explained variable in this region.xjr represents the r-th explanatory variable in region j, and xir represents the r-th explanatory variable in region i. According to equations (9) and (10) is derived from the partial derivation of Ti to xjr, and equation (11) is derived from the partial derivation of Ti to xir.As can be seen from equations (10) and (11), in the spatial regression model, if j≠i, the partial derivative of Ti to xjr is usually not equal to 0 but depends on the i and j elements in matrix SrW. At the same time, the partial derivative of Ti to xir is usually not equal to βr. Therefore, the change of explanatory variables in a region will affect not only the explained variables in this region but also the explained variables in other regions. The former can be called direct effect, the latter is called indirect effect, and the sum of the two is the total effect [33]. See Table 7 for the effect decomposition results of Durbin model in double fixed effect space.Table 7
Estimation results of decomposition effect of Durbin model in double fixed effect space.
Direct effectIndirect effectTotal effectVariableGeographic distance matrixEconomic distance matrixVariableGeographic distance matrixEconomic distance matrixVariableGeographic distance matrixEconomic distance matrixI0.096∗0.174∗I1.453∗∗∗0.364∗I1.549∗∗∗0.381∗(2.747)(2.541)(1.076)(9.061)(1.150)(9.161)E0.517∗∗∗0.276∗∗E0.624∗0.449∗E1.141∗∗0.725∗∗(7.817)(8.171)(2.986)(2.331)(2.950)(2.321)S−0.068−0.140∗∗S−0.388∗−0.257∗S−0.320∗0.117∗(0.075)(0.073)(0.362)(0.245)(0.366)(0.281)H−0.147∗0.113H0.169∗0.041H−0.021∗−0.154(5.506)(5.901)(−0.001)(0.001)(−0.001)(0.001)F0.043∗0.062∗F0.149∗0.006F0.192∗0.069∗(−0.023)(−0.023)(0.107)(−0.071)(0.101)(0.075)According to the estimation results in Table7, the following conclusions can be drawn.The perspective of direct effect, innovation investment, economic development, and the level of foreign investment all promote the improvement of Environmental Total Factor Productivity in the region. Among them, the regression coefficient of economic development is the largest and its promotion effect is the most significant. Under the two distance matrices, the coefficients are 0.517 and 0.276, respectively, the coefficients of innovation investment are 0.096 and 0.174, respectively, and the regression coefficients of foreign investment are 0.043 and 0.062, respectively. This is because the improvement of innovation investment and foreign investment level will improve regional innovation ability, bring advanced technology, and improve resource utilization efficiency. At the same time, with the improvement of the economic development level, people pay more attention to the improvement of quality of life and the protection of ecological environment, so as to effectively improve environmental total factor productivity. The coefficients of energy structure and human capital level are negative, indicating that these two variables have a negative effect on the improvement of Environmental Total Factor Productivity in this region. The regression coefficient of energy structure passes the significance test under the economic distance matrix, and the value is −0.140. The regression coefficient of human capital passed the significance test under the geographical distance matrix, and the value was −0.147. The possible reasons are as follows: on the one hand, the current human structure cannot fully meet the needs of the development of green production technology, and the problem of talent structure still exists. On the other hand, the energy consumption in China is dominated by coal, which will produce a large number of polluting gases in the combustion process [34]. At the same time, enterprises have to invest a lot of economic resources to reduce pollution emissions, resulting in reduced production efficiency.In terms of indirect effects, innovation investment, economic development, human capital, and foreign investment have positive spatial spillover effects on the improvement of Environmental Total Factor Productivity in surrounding areas, and negative spatial spillover effects on energy structure. The regression coefficients of innovation investment were 1.453 and 0.364, respectively, and both passed the significance test; the regression coefficients of economic development were 0.624 and 0.449, respectively, and both passed the significance test. The regression coefficient of foreign investment passes the significance test under the geographical distance matrix, and its value is 0.149. The regression analysis coefficient of human capital passes the significance test under the geographical distance matrix, and its value is 0.169. This shows that compared with the direct effect, the spillover effect of human capital is more conducive to the improvement of environmental total factor productivity. This is because the regional flow of talents can solve the problem of insufficient Talent Investment in some regions, promote their rational distribution among industries and regions, and promote the improvement of labor productivity. The regression analysis coefficients of energy structure are −0.388 and −0.257, respectively, showing a negative spillover effect. The reason is that the energy consumption in China is mainly coal, and a large amount of pollution generated in the consumption process will have a certain impact on the surrounding environment, resulting in the decline of environmental quality and the impact of environmental total factor productivity [35].From the perspective of total effect, in addition to energy structure and human capital, all variables are conducive to the improvement of environmental total factor productivity. The regression coefficients of innovation investment are 1.549 and 0.381, respectively, indicating that increasing innovation investment by 1 percentage point will increase environmental total factor productivity by 1.549 and 0.381 percentage points. This is because increasing innovation investment can enable enterprises to quickly iterate production technology, improve independent innovation ability and scientific and technological level, so as to improve resource utilization efficiency, which has an obvious effect on the improvement of environmental total factor productivity. The regression coefficients of economic development level are 1.141 and 0.725, respectively, and both pass the significance test, indicating that it has a significant role in promoting the improvement of environmental total factor productivity. This is because, with the improvement of the level of economic development, people pursue a higher quality of living environment, forcing enterprises with serious pollution emissions to reduce unexpected output. The regression coefficients of foreign investment are 0.192 and 0.069, respectively, which are generally promoting. The reason is that foreign investment has brought advanced technology and management experience to improve production efficiency. The coefficient of energy structure under geographical distance matrix is −0.320 and the coefficient of human capital under geographical distance matrix is −0.021, indicating that these two variables hinder the further improvement of environmental total factor productivity.


## 3.2.1. Construction of Measurement Model

Through the above analysis, the environmental total factor productivity in China has significant spatial autocorrelation. Therefore, based on the model construction methods of W. P. Yang et al. (2020) and B. T. Li (2021) [29, 30], the following spatial econometric model is constructed:(4)Ti,t=α+λWTi,t−1+β1Ii,t+β2Ei,t+β3Si,t+β4Hi,t+β5Fi,t+γ1WIi,t+γ2WEi,t+γ3WSi,t+γ4WHi,t+γ5WFi,t+μi+vt+εi,t,where T represents environmental total factor productivity, I represents innovation investment, E represents economic development level, S represents energy structure, H represents human capital level, and F represents foreign investment level; i=1, …, 30; t=1, …, 8; α is the intercept term; λ measures the spillover effect of the level of Environmental Total Factor Productivity in the region affected by the level of Environmental Total Factor Productivity in the associated region (i.e. the elasticity of spatial spillover effect); γ1. ..., γ5 represents the contribution of innovation investment, economic development level, energy structure, human capital level, and foreign investment level to environmental total factor productivity, respectively; γ1. ..., γ5, respectively, represent the impact degree and direction of the corresponding variables in the adjacent areas on the regional environmental total factor productivity; μi and νt are individual fixed effect and time fixed effect, respectively; εi,t is random disturbance term; W = 30 × 30 spatial weight matrix.


## 3.2.2. Variable Selection and Data Source

The core variables are innovation investment level, regional environmental total factor productivity, and the main control variables are economic development level, energy structure, human capital level, and foreign investment. The variable settings are as follows:(1)
Core Variables. ① Explained variable: the environmental total factor productivity index calculated above is used as the explanatory variable. ② Explanatory variables: from the influence mechanism of innovation investment on total factor productivity, it can be seen that innovation investment affects environmental total factor productivity through three effects: the spillover effect of external innovation capital, the technology spillover effect of pollution innovation governance investment, the wage income of innovation and the market demand effect, and the main factors affecting innovation efficiency are labor force and capital. Therefore, this paper starts from two aspects of innovation manpower investment and innovation capital investment, the full-time equivalent and expenditure of research and experimental development personnel in industrial enterprises above designated size are selected as explanatory variables.(2)
Main Control Variables. ① Economic development level: the level of regional economic development is measured by per capita GDP. ② Energy structure: the energy structure is expressed by the ratio of coal consumption to total energy consumption. ③ Human capital level: as the main body of promoting technological progress, human capital is very important for the improvement of environmental total factor productivity. Therefore, the level of human capital is measured by the number of students per 100000 people. ④ Foreign investment: the level of foreign investment is measured by the ratio of foreign direct investment to GDP.The data used in the demonstration are from China Statistical Yearbook from 2012 to 2019, China environmental database, and China economic and social big data platform and global EPS database. The per capita GDP, foreign direct investment, investment in fixed assets of the whole society, and other value indicators are subject to price reduction based on 2010. Individual missing data are filled with the average value of adjacent years, and the balance panel data from 2012 to 2019 are standardized to eliminate the dimensional impact between indicators.


## 3.2.3. Basic Regression Analysis

Firstly, in order to judge whether the selected regression analysis model is a fixed effect model or a random effect model, this paper carries out the Hausmann test. The test results are significant at the level of 1%, so the fixed effect model is selected. Secondly, in order to further select the optimal model, we test the regional fixed effect, time fixed effect, and time-space double fixed effect, and reject the original hypothesis; so, we choose the double fixed effect model. Finally, the LR test is carried out. The results show that the spatial Dobbin model cannot be degenerated into SAR model or SEM model, so the double fixed effect spatial Dobbin model (SDM) is selected. The results of basic regression analysis are shown in Table6.Table 6
Estimation results of double fixed effect spatial Durbin model.
VariableGeographic distance matrixEconomic distance matrixλ0.565∗∗0.071∗(0.277)(0.102)I0.150∗0.018∗(−2.748)(2.491)E0.544∗∗∗0.278∗∗(7.794)(8.381)S−0.060−0.149∗∗(0.077)(0.074)H−0.142∗−0.115(−5.608)(−5.931)F0.049∗0.063∗(0.023)(0.024)W(I)2.268∗∗∗0.361(1.69)(8.301)W(E)1.262∗0.403∗(4.77)(2.1)W(S)−0.546∗−0.245∗(1.546)(0.2)W(H)−0.226∗−0.019(−0.001)(0.001)W(F)0.215∗−0.012(−0.173)(−0.064)Note.∗∗∗,∗∗,∗, respectively, mean passing the significance level test of 1%, 5%, and 10%. The values in brackets represent standard error.From the model estimation results in Table6, the following three conclusions are obtained.First, there is a positive spatial spillover effect in the improvement of Environmental Total Factor Productivity in all provinces. Under the two different spatial weight matrices of geographical distance matrix and economic distance matrix, spatial autoregressive coefficients are 0.565 and 0.071, respectively. The two coefficients pass the significance test at the level of 5% and 10%, respectively, which shows that the improvement of Environmental Total Factor Productivity in China’s provinces has a positive spatial spillover effect on itself, that is, the improvement of Environmental Total Factor Productivity in a region will promote the improvement of Environmental Total Factor Productivity in the surrounding areas of the region.Second, increasing investment in innovation has a positive effect on the improvement of Environmental Total Factor Productivity in the region and surrounding areas. Under two different spatial weight matrices, the spatial regression coefficients of innovation investment are 0.150 and 0.018, respectively, that is, every one percentage point increase in the level of innovation investment can bring 0.150 and 0.018 percentage points increase in Environmental Total Factor Productivity, respectively. The W(X) term can better explain the spatial transmission effect (X refers to I, E, S, H, and F in this paper). The coefficient of the exogenous interaction effect of innovation investment W(I) under the geographical distance matrix is 2.268, which indicates that the improvement of Environmental Total Factor Productivity in a region is affected by the level of innovation investment in the surrounding regions, and this impact is positive.Third, the coefficients of economic development and foreign investment are positive, and the coefficients of energy structure and human capital are negative, indicating that economic development and foreign investment promote the improvement of environmental total factor productivity, while energy structure and human capital inhibit the improvement of environmental total factor productivity. Under two different spatial weight matrices, there is a positive correlation between economic development and foreign investment level on the improvement of environmental total factor productivity. Among them, the spatial regression coefficients of economic development level are the largest, which are 0.544 and 0.278. respectively, and the spatial regression coefficients of foreign investment level are 0.049 and 0.063, respectively. The energy structure and human capital have a negative impact on the improvement of environmental total factor productivity. The spatial regression coefficients of energy structure are −0.060 and −0.149, respectively, and the spatial regression coefficients of human capital are −0.142 and −0.115, respectively. In item W(X), the exogenous interaction effect W(E) of economic development level is 1.262 and 0.403, respectively, while the exogenous interaction effect w (f) of foreign investment level passes the significance test under the geographical distance matrix, and its value is 0.215, indicating that the environmental total factor productivity level of a region is greatly affected by the economic development level of the surrounding region and relatively less affected by foreign investment in the surrounding region. The exogenous interaction effect W(S) of energy structure is −0.546 and −0.245, respectively, and the exogenous interaction effect W(H) of human capital is −0.226 under the geographical matrix, indicating that the current energy structure and human capital have a negative impact on the improvement of environmental total factor productivity, and there is still some room for adjustment in the future.


## 3.2.4. Further Analysis

Considering that the spatial lag term of explanatory variables is added to the spatial Durbin model, and the original estimation coefficient cannot accurately characterize the impact of explanatory variables on the explained variables, this paper uses the experience of R. K. Pace et al. (2009) and H. J. Liu (2014) for reference, and uses the partial differential effect decomposition method to decompose the spatial effects into direct effects, indirect effects, and total effects [31, 32]. Using the partial differential method of spatial regression model, the n-order identity matrix is introduced to transform model (6), and the direct effect, indirect effect, and total effect of the rth explanatory variable of region j are obtained by calculating the partial derivative. The specific process is as follows:(5)In−λWT=αln+βX+γWX+ε,(6)T=∑r=1kSrWxr+VWlnα+VWε,(7)SrW=VWInβr+Wγr,VW=In−λW−1=In+λW+λ2W2+λ3W3+⋯λnWn,where In is the identity matrix of order n; k is the number of explanatory variables; xr is the rth explanatory variable; r=1,2,⋯k; βr is the regression coefficient of the rth explanatory variable in the explanatory variable vector X; and γr represents the estimation coefficient of the rth variable of WX.In order to explain the function ofSrW, equation (6) is written as (8), and Ti of a region ii=1,2,⋯n can be expressed as (9).(8)T1T2⋮Tn=∑r=1kSrW11SrW12…SrW1nSrW12SrW22…SrW2n⋮⋮⋮⋮SrW1nSrW2n⋯SrWnnx1rx2r⋮xnr+VWlnα+VWε,(9)Ti=∑r=1kSrWi1x1r+SrWi2x2r+⋯+SrWinxnr+VWα+VWiε,(10)∂Ti∂xjr=SrWij,(11)∂Ti∂xir=SrWii,where SrWij represents the influence degree of the rth explanatory variable of region j on the explained variable of region i; SrWii represents the influence degree of the rth explanatory variable of region i on the explained variable in this region.xjr represents the r-th explanatory variable in region j, and xir represents the r-th explanatory variable in region i. According to equations (9) and (10) is derived from the partial derivation of Ti to xjr, and equation (11) is derived from the partial derivation of Ti to xir.As can be seen from equations (10) and (11), in the spatial regression model, if j≠i, the partial derivative of Ti to xjr is usually not equal to 0 but depends on the i and j elements in matrix SrW. At the same time, the partial derivative of Ti to xir is usually not equal to βr. Therefore, the change of explanatory variables in a region will affect not only the explained variables in this region but also the explained variables in other regions. The former can be called direct effect, the latter is called indirect effect, and the sum of the two is the total effect [33]. See Table 7 for the effect decomposition results of Durbin model in double fixed effect space.Table 7
Estimation results of decomposition effect of Durbin model in double fixed effect space.
Direct effectIndirect effectTotal effectVariableGeographic distance matrixEconomic distance matrixVariableGeographic distance matrixEconomic distance matrixVariableGeographic distance matrixEconomic distance matrixI0.096∗0.174∗I1.453∗∗∗0.364∗I1.549∗∗∗0.381∗(2.747)(2.541)(1.076)(9.061)(1.150)(9.161)E0.517∗∗∗0.276∗∗E0.624∗0.449∗E1.141∗∗0.725∗∗(7.817)(8.171)(2.986)(2.331)(2.950)(2.321)S−0.068−0.140∗∗S−0.388∗−0.257∗S−0.320∗0.117∗(0.075)(0.073)(0.362)(0.245)(0.366)(0.281)H−0.147∗0.113H0.169∗0.041H−0.021∗−0.154(5.506)(5.901)(−0.001)(0.001)(−0.001)(0.001)F0.043∗0.062∗F0.149∗0.006F0.192∗0.069∗(−0.023)(−0.023)(0.107)(−0.071)(0.101)(0.075)According to the estimation results in Table7, the following conclusions can be drawn.The perspective of direct effect, innovation investment, economic development, and the level of foreign investment all promote the improvement of Environmental Total Factor Productivity in the region. Among them, the regression coefficient of economic development is the largest and its promotion effect is the most significant. Under the two distance matrices, the coefficients are 0.517 and 0.276, respectively, the coefficients of innovation investment are 0.096 and 0.174, respectively, and the regression coefficients of foreign investment are 0.043 and 0.062, respectively. This is because the improvement of innovation investment and foreign investment level will improve regional innovation ability, bring advanced technology, and improve resource utilization efficiency. At the same time, with the improvement of the economic development level, people pay more attention to the improvement of quality of life and the protection of ecological environment, so as to effectively improve environmental total factor productivity. The coefficients of energy structure and human capital level are negative, indicating that these two variables have a negative effect on the improvement of Environmental Total Factor Productivity in this region. The regression coefficient of energy structure passes the significance test under the economic distance matrix, and the value is −0.140. The regression coefficient of human capital passed the significance test under the geographical distance matrix, and the value was −0.147. The possible reasons are as follows: on the one hand, the current human structure cannot fully meet the needs of the development of green production technology, and the problem of talent structure still exists. On the other hand, the energy consumption in China is dominated by coal, which will produce a large number of polluting gases in the combustion process [34]. At the same time, enterprises have to invest a lot of economic resources to reduce pollution emissions, resulting in reduced production efficiency.In terms of indirect effects, innovation investment, economic development, human capital, and foreign investment have positive spatial spillover effects on the improvement of Environmental Total Factor Productivity in surrounding areas, and negative spatial spillover effects on energy structure. The regression coefficients of innovation investment were 1.453 and 0.364, respectively, and both passed the significance test; the regression coefficients of economic development were 0.624 and 0.449, respectively, and both passed the significance test. The regression coefficient of foreign investment passes the significance test under the geographical distance matrix, and its value is 0.149. The regression analysis coefficient of human capital passes the significance test under the geographical distance matrix, and its value is 0.169. This shows that compared with the direct effect, the spillover effect of human capital is more conducive to the improvement of environmental total factor productivity. This is because the regional flow of talents can solve the problem of insufficient Talent Investment in some regions, promote their rational distribution among industries and regions, and promote the improvement of labor productivity. The regression analysis coefficients of energy structure are −0.388 and −0.257, respectively, showing a negative spillover effect. The reason is that the energy consumption in China is mainly coal, and a large amount of pollution generated in the consumption process will have a certain impact on the surrounding environment, resulting in the decline of environmental quality and the impact of environmental total factor productivity [35].From the perspective of total effect, in addition to energy structure and human capital, all variables are conducive to the improvement of environmental total factor productivity. The regression coefficients of innovation investment are 1.549 and 0.381, respectively, indicating that increasing innovation investment by 1 percentage point will increase environmental total factor productivity by 1.549 and 0.381 percentage points. This is because increasing innovation investment can enable enterprises to quickly iterate production technology, improve independent innovation ability and scientific and technological level, so as to improve resource utilization efficiency, which has an obvious effect on the improvement of environmental total factor productivity. The regression coefficients of economic development level are 1.141 and 0.725, respectively, and both pass the significance test, indicating that it has a significant role in promoting the improvement of environmental total factor productivity. This is because, with the improvement of the level of economic development, people pursue a higher quality of living environment, forcing enterprises with serious pollution emissions to reduce unexpected output. The regression coefficients of foreign investment are 0.192 and 0.069, respectively, which are generally promoting. The reason is that foreign investment has brought advanced technology and management experience to improve production efficiency. The coefficient of energy structure under geographical distance matrix is −0.320 and the coefficient of human capital under geographical distance matrix is −0.021, indicating that these two variables hinder the further improvement of environmental total factor productivity.


## 4. Conclusions and Suggestions

### 4.1. Conclusion

Using the panel data of 30 provinces in China from 2012 to 2019, this paper empirically analyzes the impact of innovation investment on environmental total factor productivity by using spatial econometric analysis method, and obtains the following conclusions: (1) The overall environmental total factor productivity of all provinces showed a fluctuating upward trend from 2012 to 2019, and there were great differences among provinces, The decomposition index of environmental total factor productivity shows that the driving force of environmental total factor productivity growth mainly comes from technological progress. (2) There is spatial correlation and positive spatial spillover effect between environmental total factor productivity. (3) Innovation investment, economic development, and foreign investment can promote the improvement of environmental total factor productivity, but energy structure and human capital have a negative impact on the improvement of environmental total factor productivity. (4) Innovation investment, economic development, human capital, and foreign investment show a positive spillover effect on the improvement of Environmental Total Factor Productivity in the surrounding areas, while the energy structure shows a negative spillover effect.


### 4.2. Suggestions

In order to realize the coordinated development of economy, society, and environment, and improve the total factor productivity of environment, the following countermeasures and suggestions are taken:(1)
Encourage independent innovation and technology introduction, and narrow regional differences in environmental total factor productivity. The decomposition index of environmental total factor productivity shows that the driving force of environmental total factor productivity growth mainly comes from technological progress. Therefore, encouraging enterprises to actively innovate and strengthening technology introduction is one of the most effective ways to improve environmental total factor productivity. Specific measures are as follows: on the one hand, in order to reduce innovation costs and stimulate enterprises’ enthusiasm for independent innovation, local governments should adopt a series of positive government subsidy policies to help enterprises carry out independent innovation activities in a variety of ways. On the other hand, technology introduction can achieve technological progress in a short time and at a low cost [36]. Governments at all levels and relevant departments should actively build enterprise cooperation and exchange platforms, and create opportunities for enterprises to introduce advanced technology in combination with the actual development of local enterprises.(2)
Increase investment in innovation and give full play to the promotion and spillover effect of innovation investment on the improvement of environmental total factor productivity. According to the results of empirical analysis, innovation investment plays a very significant role in improving environmental total factor productivity. Only by strengthening enterprise innovation investment and innovating and upgrading the industrial chain can we improve environmental total factor productivity and truly achieve sustainable development. The specific measures are as follows: first, we should fully recognize the social innovation effect of innovation investment, increase innovation investment, and give full play to the role of technological innovation in ecological construction. Secondly, pay attention to the external technology absorption, introduction, and re-innovation of high-tech products, realize the coordinated innovation between internal independent innovation and external technology absorption, apply the achievements of scientific and technological innovation to practice, and give full play to the spatial spillover effect of innovation investment [37].(3)
Optimize the energy consumption structure and improve the efficiency of resource and energy utilization. According to the empirical results, the current energy consumption structure in China has a negative impact on the improvement of environmental total factor productivity [38]. Therefore, the energy consumption structure needs to be optimized and adjusted. In order to realize the coordinated development of energy, economy, society, and environment, on the one hand, we should comprehensively use economic, legal, and necessary administrative means to effectively control the total amount of energy consumption. On the other hand, we should focus on the promotion and application of clean energy, based on reality; adapt measures to local conditions; accelerate the adjustment of energy consumption structure; vigorously develop renewable clean energy; and explore the road of green and low-carbon development.


## 4.1. Conclusion

Using the panel data of 30 provinces in China from 2012 to 2019, this paper empirically analyzes the impact of innovation investment on environmental total factor productivity by using spatial econometric analysis method, and obtains the following conclusions: (1) The overall environmental total factor productivity of all provinces showed a fluctuating upward trend from 2012 to 2019, and there were great differences among provinces, The decomposition index of environmental total factor productivity shows that the driving force of environmental total factor productivity growth mainly comes from technological progress. (2) There is spatial correlation and positive spatial spillover effect between environmental total factor productivity. (3) Innovation investment, economic development, and foreign investment can promote the improvement of environmental total factor productivity, but energy structure and human capital have a negative impact on the improvement of environmental total factor productivity. (4) Innovation investment, economic development, human capital, and foreign investment show a positive spillover effect on the improvement of Environmental Total Factor Productivity in the surrounding areas, while the energy structure shows a negative spillover effect.


## 4.2. Suggestions

In order to realize the coordinated development of economy, society, and environment, and improve the total factor productivity of environment, the following countermeasures and suggestions are taken:(1)
Encourage independent innovation and technology introduction, and narrow regional differences in environmental total factor productivity. The decomposition index of environmental total factor productivity shows that the driving force of environmental total factor productivity growth mainly comes from technological progress. Therefore, encouraging enterprises to actively innovate and strengthening technology introduction is one of the most effective ways to improve environmental total factor productivity. Specific measures are as follows: on the one hand, in order to reduce innovation costs and stimulate enterprises’ enthusiasm for independent innovation, local governments should adopt a series of positive government subsidy policies to help enterprises carry out independent innovation activities in a variety of ways. On the other hand, technology introduction can achieve technological progress in a short time and at a low cost [36]. Governments at all levels and relevant departments should actively build enterprise cooperation and exchange platforms, and create opportunities for enterprises to introduce advanced technology in combination with the actual development of local enterprises.(2)
Increase investment in innovation and give full play to the promotion and spillover effect of innovation investment on the improvement of environmental total factor productivity. According to the results of empirical analysis, innovation investment plays a very significant role in improving environmental total factor productivity. Only by strengthening enterprise innovation investment and innovating and upgrading the industrial chain can we improve environmental total factor productivity and truly achieve sustainable development. The specific measures are as follows: first, we should fully recognize the social innovation effect of innovation investment, increase innovation investment, and give full play to the role of technological innovation in ecological construction. Secondly, pay attention to the external technology absorption, introduction, and re-innovation of high-tech products, realize the coordinated innovation between internal independent innovation and external technology absorption, apply the achievements of scientific and technological innovation to practice, and give full play to the spatial spillover effect of innovation investment [37].(3)
Optimize the energy consumption structure and improve the efficiency of resource and energy utilization. According to the empirical results, the current energy consumption structure in China has a negative impact on the improvement of environmental total factor productivity [38]. Therefore, the energy consumption structure needs to be optimized and adjusted. In order to realize the coordinated development of energy, economy, society, and environment, on the one hand, we should comprehensively use economic, legal, and necessary administrative means to effectively control the total amount of energy consumption. On the other hand, we should focus on the promotion and application of clean energy, based on reality; adapt measures to local conditions; accelerate the adjustment of energy consumption structure; vigorously develop renewable clean energy; and explore the road of green and low-carbon development.



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*Source: 3100174-2022-04-30.xml*