The Influence of Government Subsidies on the Efficiency of Technological Innovation: A Panel Threshold Regression Approach

Abstract

As a typical technology-intensive industry, the renewable energy industry is a standard sample for scholars to study the R&D innovation of enterprises. At present, the industry is strongly supported by the government subsidy policy in China and has developed rapidly in recent years. Its own financing constraints and lack of innovation power are also the main problems for the development of renewable energy enterprises. Taking A-share renewable energy enterprises from 2016 to 2020 as the research object, this paper constructs a panel model to empirically study the relationship between government subsidies and enterprise innovation efficiency. The findings are as follows. First, government subsidies can significantly promote the innovation efficiency of enterprises; second, the government subsidy has an obvious double threshold effect on the innovation efficiency of enterprises, and when the government subsidy is in a certain range, the subsidy effect is the best; third, the government subsidy effect of non-state-owned renewable energy enterprises is better than that of state-owned enterprises; the effect of government subsidies for renewable energy enterprises in the central and western regions is better than that in the eastern region. The threshold effect of government subsidies on enterprise innovation efficiency is also quite different.

1. Introduction

Energy is the material basis supporting the progress of human civilization. It is an indispensable basic condition for the development of modern society. The environmental and health costs of fossil energy, especially coal, cannot be ignored. The energy issue is a prominent global challenge at present. It concerns the common interests of the international community and the future of the earth. The wide adoption of renewable energy and related technologies has become an essential solution. Renewable energy is an urgent need to cope with climate change and achieve sustainable development. At present, countries all over the world are engaged in research in the field of renewable energy development and utilization to solve the possible crisis of energy shortage [1]. In addition, the renewable energy industry has broad prospects. The development of the renewable energy industry can not only promote the development of this industry, but also greatly promote other industries in the industrial chain. Renewable energy can promote the technological development of transportation, manufacturing equipment and other industries, thus forming a large-scale industrial cluster. Wu et al. [2] believes that the renewable energy industry has the function of optimizing the energy consumption structure and reducing energy consumption, which will become a new growth point of the green economy, and can promote economic development and increase employment.

With the continuous development of the human economy and the continuous increase of energy consumption, natural resource issues have attracted more and more attention [3]. The energy that mankind depends on for survival is not inexhaustible [4]. At the national level, the development of the renewable energy industry is supported by government policies. Under the complex background of global environmental governance, the world energy structure has also been imperceptibly affected. Countries around the world have put forward a series of strategic plans for the important sector of renewable energy. Facing the new opportunities and challenges of China’s economic and social development in the 21st century, China attaches great importance to the renewable energy development strategy. In order to realize the transformation of economic development mode and industrial structure, China needs to take the renewable energy industry as an important driving force for economic development [5]. The renewable energy industry may become the backbone to solve the problem of China’s energy constraints on economic and social development. China strives to contribute to addressing global climate change and participating in global energy governance [6].

From the industry level, the renewable energy industry has a bright future. The renewable energy industry is the catalyst for industrial upgrading. Whether it is the energy-saving transformation of buildings or the treatment of sewage and garbage, it will form a new economic growth point. Photovoltaic power generation will eventually replace oil and coal as the main energy in the future. The transformation of energy structure is the general trend of modern sustainable development [7].

Nowadays, innovation is the main melody of economic development. The theme of innovation is also a research hotspot of scholars at home and abroad. Independent innovation is the source of power for enterprises to accelerate the pace of economic globalization and enhance international competitiveness. With the rapid development of science and technology, the market competition among enterprises in various countries is becoming increasingly fierce. In the process of industrialization, it also brings a series of problems, such as blind development, repeated construction and so on. Therefore, the fundamental way lies in “independent innovation”. In addition, there is a certain investment threshold for enterprise technological innovation. Only when the company prepares sufficient funds to purchase advanced instruments and equipment, and has key production factors such as high-tech R&D personnel, can it carry out technology R&D activities [8].

Insufficient investment in innovation is a major weakness restricting enterprises’ independent innovation. Compared with the technology oriented innovation of universities and scientific research institutions, the innovation activities of enterprises are more market-oriented. However, due to the existence of “market failure”, there are many difficulties in enterprise innovation, especially in small and medium-sized enterprises. In practice, many small enterprises and some non-state-owned enterprises have narrow financing channels and limited ability to resist risks, so it is difficult to undertake high initial R&D investment. Innovation activities have been severely inhibited. Renewable energy is an important component of the energy structure adjustment. Under the background of “double carbon” in China, renewable energy enterprises are facing broad development opportunities. The externalities of innovative activity lead to market failure, but government subsidies can alleviate this problem. The social value of innovative activities is usually greater than the private value. Without reasonable compensation, it is easy to weaken the innovation enthusiasm of enterprises. Government subsidies can share the risks that individual enterprises cannot bear. Government subsidies can also improve the return rate of technological innovation activities and accelerate the liquidity of enterprise R&D investment [9]. It is meaningful to investigate the relationship between government subsidies and enterprise innovation. Innovation can bring competitive advantages to enterprises, and independent innovation of enterprises can not be separated from the large amount of R&D investment. Especially for small and medium-sized enterprises and high-tech enterprises, R&D activities will inevitably encounter insufficient funds. In general, for the innovation activities of enterprises, government subsidy is a direct fiscal incentive policy [10]. In the field of technological innovation, knowledge spillovers and technology spillovers make it impossible for the R&D revenue to be fully occupied by private individuals. When R&D activities appear “market failure”, the market needs to be regulated with the help of the “visible hand” of the government [11]. At the same time, government subsidies not only provide direct R&D funding support for enterprises, but also play a supervisory role.

From an international perspective, there are also relevant documents to support it. In addition to China, this is also the case in South Korea. The author uses panel data from Korea Renewable Energy Technology Corporation to investigate how government policies affect innovation at the enterprise level. Finally, it shows that there is a positive two-way relationship between government policies and technological innovation of Korean enterprises. The government’s public R&D expenditure will increase by 1%, and the technological innovation of Korean enterprises will increase by 3.815% [12]. In order to explore whether the service enterprises receiving government subsidies are more involved in marketing and organizational innovation activities, the author analyzes subsidized and non subsidized innovation activities. The empirical data comes from Microdata Service of Germany Mannheim Innovation Group. The final conclusion is that public subsidies have a significant positive impact on marketing. Subsidized companies are more likely to organize innovation activities better than their competitors [13].

Although government subsidies can alleviate the financing problems of enterprises, they also have limitations. While government subsidies have shown initial results, they have also exposed many drawbacks. The problem of low-quality innovation has become increasingly prominent. Since the development strategy of building an “innovative country” was put forward in 2006, the Chinese government has continuously increased the intensity of subsidies for enterprise innovation. From 2006 to 2019, the national financial allocation for science and technology increased from 168.85 billion yuan to 107.74 billion yuan, an average annual increase of 64.492 billion yuan. However, compared with many countries, the average level of enterprise innovation investment is still low. For example, the proportion of enterprise R&D expenditure in GDP was only 1.72% in 2019, which is lower than the world average of 2.10%. From the perspective of subsidy structure, large enterprises are easy to obtain high subsidies, while relatively small entrepreneurial enterprises are difficult to obtain sufficient government subsidies [14].

The government needs to implement appropriate subsidy policies to deal with the problem of insufficient innovation motivation caused by market failure. This is also an important research direction in the field of government enterprise relations. But does the government subsidy improve the innovation efficiency of enterprises? Does the government subsidy achieve the expected goal of the government? Scientific government subsidies can ultimately optimize the allocation of resources and improve the innovation efficiency of enterprises. Guided by this, this study may have important reference value and significance for government management departments to formulate reasonable government subsidy policies.

The rest of the paper is as follows. Section 2 mainly summarizes an overview of the literature. Section 3 presents theoretical analysis and hypothesis. Section 4 focuses on the study of design. Section 5 describes data sources and sampling. Section 6 presents empirical estimation results and discussion. Section 7 shows our robustness test. Section 8 discusses the conclusion and policy recommendation.

2. Literature Review

As a key indicator to measure the transformation of innovation input into innovation output, enterprise innovation efficiency has been widely concerned by scholars [15,16]. With the deepening of economic globalization, enterprises are facing increasingly fierce international competition. The extensive production model is difficult to support the improvement of productivity. Innovation efficiency depends not only on the number of scientific and technological innovation achievements, but also on their transformation efficiency. The measurement of technological innovation efficiency can be divided into two categories: stochastic frontier analysis (SFA) and data envelopment analysis (DEA). Campos selected SFA to set the regulatory operating costs of 61 distribution utility companies. The results show that SFA is more flexible in dealing with outliers [17]. There are also many applications of DEA. In order to analyze energy efficiency, Zhang et al. [18] chose the three-stage slacks-based measure DEA (SBM-DEA) model to analyze the energy efficiency and influencing factors of 13 RCEP countries from 2000 to 2015.

The two measurement methods have their own characteristics. DEA sets a definite boundary and does not consider the existence of the measurement error, while SFA has advantages in the processing of measurement error and statistical interference. From the above points of view, the efficiency of technological innovation represents the ability of an enterprise to utilize and allocate resources. The lower the efficiency, the more resources will be wasted in the process of technological innovation activities. At present, government subsidies in the R&D field include direct R&D capital expenditure, tax relief, etc. Choi et al. believed that in most developed countries, governments often promote enterprise innovation efficiency through direct investment, tax incentives and other means. Government subsidies can stimulate enterprises to carry out R&D activities, and have a positive impact on enterprise innovation efficiency [19].

In recent years, the mechanism of government subsidies on social technological innovation activities has become one of the hotspots in theoretical research. On the issue of whether government subsidies can promote the efficiency of technological innovation of enterprises, there are great differences in academic circles. Due to the differences of samples, time and research methods, the conclusions are not consistent. There are two main conclusions. First, government subsidies can effectively improve the innovation efficiency of enterprises. Through R&D funding, project support, tax incentives and other policy tools, enterprise R&D expenditure can be increased. The main purpose of government intervention is to reduce the actual R&D costs of private enterprises. The government can guide enterprises to reasonably expand R&D expenditure. Therefore, the efficiency of national innovation activities has been improved [20].

Second, government subsidies may also inhibit innovation efficiency. There is a U-shaped relationship between government subsidies and innovation efficiency. This is because government subsidies may squeeze out the due R&D investment of enterprises. With the increase of the intensity of government subsidies, enterprises’ innovation investment is likely to decrease, resulting in the “crowding out” effect in final. The total R&D investment of enterprises will also be insufficient. To some extent, it creates the illusion of short-term profit increase [21]. In addition, because monopoly enterprises obtain government R&D funds through rent-seeking, R&D funds are not really used for enterprise technology research and development. This will eventually reduce the technological innovation efficiency of R&D activities [10]. If there is no corresponding incentive and supervision mechanism, it will lead to excessive reliance on government subsidies.

Scholars have also begun to be concerned about the influencing factors of government subsidies on technological innovation. Bai et al. discussed the government’s R&D subsidies for green innovation of energy intensive enterprises. The empirical results show that innovation investment, income and tax levels, enterprise size and ownership are the main factors for enterprises to obtain subsidies [11]. Aihua Wu selected the data of Chinese listed companies from 2009 to 2013. The conclusions are as follows: compared with non-state-owned enterprises, state-owned enterprises can get more government subsidies. However, for non-state-owned enterprises, the signal effect of government subsidies is better. Through government subsidies, enterprises can expand financing channels and ease the financing constraints [22].

According to the 2021 global innovation index report released by the world intellectual property organization (WIPO), China’s innovation index ranks only 12th in the world. In this context, it is of great practical significance to explore how government subsidies affect the innovation efficiency of enterprises. The characteristics of this study are as follows. First, in addition to basic regression, we add threshold effect. In this way, we can analyze whether there is an optimal range of government subsidies. Finally, it will help enterprises maximize innovation efficiency; secondly, from the perspective of different enterprise characteristics, such as the nature of property rights and regions, this paper evaluates the impact of different levels of government innovation subsidies on enterprise technological innovation. This will improve the scientificity and reliability of the evaluation of the effect of government subsidies.

To sum up, there are still some deficiencies in the analysis conclusions of existing literature on the impact of government subsidies on enterprise innovation efficiency. However, it also provides useful ideas for follow-up research. Deficiencies are as follows:

• Most literature uses the data at provincial and industrial levels for empirical research, while empirical evidence on the micro level is relatively lacking;
• The analysis of the impact of government subsidies on the innovation efficiency of enterprises is limited to being beneficial or unhelpful, without considering whether the difference in the effect of government subsidies originates from the threshold effect; The existing literature does not fully answer this question.

Therefore, based on previous research, this paper mainly carries out the following expansion: First of all, from the micro level of listed enterprises in Shanghai and Shenzhen A-shares, we investigate the impact of government subsidies on enterprise innovation efficiency. Then, on the basis of measuring innovation efficiency, this paper establishes a panel threshold model. In different subsidy intensities, the nonlinear impact of subsidies on innovation efficiency may have multiple characteristics, namely the threshold effect.

3. Theoretical Analysis and Hypothesis

3.1. The Relationship between Government Subsidies and Technological Innovation Efficiency

The efficiency of technological innovation is essentially the process of knowledge production. To some extent, it reflects the R&D and innovation capability of the company. In the process of enterprise development, technological innovation efficiency is an important factor in the core competitiveness of enterprises. Under ideal conditions, the same input will produce the same output. However, in reality, as an external environment, government subsidies will have a significant impact on the efficiency of technological innovation. The impact of government subsidies on the efficiency of technological innovation is complex. In view of the particularity of China’s economic system, the government plays a key role in economic development. The government balances the interests of various subjects and promotes the development of the market economy [23].

The impact mechanism of government subsidies on the technological innovation efficiency of renewable energy enterprises is mainly reflected in the following two points. The first is the promotion mechanism caused by the externality theory [24]. Second, because of Asymmetric Information theory, there is a restraining effect. Please see Figure 1. This theory has laid the economic theoretical foundation for the government to intervene in the R&D and innovation activities of enterprises. The attribute of R&D activities of enterprises is public goods. In other words, innovation has positive externality. Innovators cannot monopolize the benefits of innovation. Innovation activities require enterprises to invest a lot of R&D funds and human capital, especially for the renewable energy industry. The results of R&D activities are also uncertain, with great risks and uncertainties. In the face of this situation, the willingness of enterprises to carry out innovation activities gradually becomes low. At this point, government subsidies for innovation become a good remedy for market failure. Government subsidies are conducive to reducing the R&D costs of enterprises, thus stimulating enterprises to invest more funds.

According to the theory of information asymmetry, different subjects in market economic activities have different mastery of information. Compared with economic subjects with less information, subjects with more information are in a more favorable position. However, asymmetric information can easily induce adverse selection and moral hazards [25].

At the same time, due to the information asymmetry between the government and enterprises, it is not enough to rely on the government to screen enterprises that need subsidies. The asymmetric distribution of information among market entities is ubiquitous. However, without a scientific and reasonable evaluation and review system, it is difficult for enterprises to make reasonable use of government subsidy funds. Especially under the current fierce competition conditions, there is often a situation where the expected technological innovation results of enterprises are inconsistent with the actual results declared.

In this case, the actual effect of government subsidies deviates from the policy expectations. For example, some enterprises may carry out innovation activities only to obtain government subsidies. Once government subsidies are received, innovation activities will be stopped. Due to the existence of asymmetric information and other factors in the real economic environment, it is difficult to achieve optimal resource allocation. This paper mainly considers the information asymmetry between enterprises and external economic subjects. First, information asymmetry between enterprises and government. Limited by the lack of professional ability, the government can only know part of the information of some enterprises. Therefore, it is in a relatively disadvantageous position. The enterprise can master all the information of government subsidies and is in an information dominant position. Enterprises also have certain moral hazard after receiving subsidies, which destroys the efficiency of public resource allocation. The asymmetry of information makes it difficult for the government to choose the most supported enterprises. Secondly, the information asymmetry between enterprises and other investors. As external fund providers can not fully grasp the company’s development prospects, R&D projects and other information, they have weak motivation to invest in related enterprises. Finally, it affects the possibility of enterprise financing and technological innovation efficiency. Therefore, we propose the following assumptions:

Hypothesis 1 (H1). 

Government subsidies have a positive effect on technological innovation efficiency in renewable energy enterprises.

Hypothesis 2 (H2). 

Government subsidies have a negative effect on technological innovation efficiency in renewable energy enterprises.

3.2. Heterogeneity Analysis of Government Subsidies and Technological Innovation Efficiency

3.2.1. Property Rights Heterogeneity

The property right difference of renewable energy enterprises has an obvious regulatory effect on the efficiency of technological innovation. Most state-owned enterprises occupy a monopoly position in the industry, so there is little pressure for survival and development. The state-owned enterprises are lack of innovation motivation, and the decision-making behavior of leaders is easy to be short-term. Compared with state-owned enterprises, non-state-owned enterprises have insufficient congenital resource endowment conditions. Therefore, it is necessary to increase R&D investment to win market share. At this time, government subsidies and other external funds alleviate the financing pressure of enterprises and internal R&D risks. At the same time, the “endorsement” of the government effectively improves the confidence of enterprises in R&D. Finally, it improves the efficiency of technological innovation [26]. The nature of ownership represents the capital source background of the enterprise. China’s non-private enterprises are more sensitive to government subsidies, and the effect of unit subsidies is better. Therefore, we propose Hypothesis H3.

Hypothesis 3 (H3). 

Government subsidies have a greater positive effect on the technological innovation efficiency in state-owned renewable energy enterprises than in non-state-owned enterprises.

3.2.2. Regional Heterogeneity

The agglomeration of regional innovation resources will also have an important impact on the efficiency of technological innovation. The eastern coastal area, as an area with concentrated innovation resources in China, has convenient transportation and more talents. At the same time, the financial market also has obvious advantages. However, the eastern region has a high degree of internationalization and faces more fierce competition. In contrast, there is more room for enterprises in the central and western regions to improve their technological innovation efficiency. Therefore, enterprises have a stronger demand for government subsidies. This paper puts forward the following assumption:

Hypothesis 4 (H4). 

Government subsidies have a greater positive effect on the technological innovation efficiency of renewable energy enterprises in midwestern China than those in eastern China.

3.3. Threshold Effect

The original intention of government subsidies is to improve the efficiency of technological innovation of enterprises. However, excessive government subsidies will lead to the “swindle compensation” behavior of enterprises. Finally, the market operation environment becomes more and more chaotic. The threshold effect reflects that when the intensity of government subsidies is in different ranges, the influence coefficient of government subsidies on the efficiency of enterprise technological innovation will be different in stages. We find out the optimal input range of government subsidies, which will provide a good policy basis for encouraging enterprise innovation. Qing Li studied the effect of government innovation on technological innovation of enterprises. Finally, he came to the conclusion that only in a certain range can government subsidies play a role in promoting enterprise innovation. Government subsidies and enterprise technological innovation are complex non-linear relations [27]. Thus, we put forward Hypotheses H5–H7.

Hypothesis 5 (H5). 

The impact of government subsidies on the technological innovation efficiency of renewable energy enterprises has a threshold effect. When the intensity of government subsidies is in the optimal range, the positive effect of subsidies on the efficiency of technological innovation is the strongest.

Hypothesis 6 (H6). 

The differences in property rights characteristics of renewable energy enterprises may affect the threshold effect of government subsidies.

Hypothesis 7 (H7). 

The differences in regional characteristics of renewable energy enterprises may affect the threshold effect of government subsidies.

4. Research Methodology

By calculating the basic model regression, we can study the promotion or inhibition effect of government subsidies on enterprise innovation efficiency. Then, can too much or too little government subsidies can effectively improve enterprise innovation efficiency? In other words, whether government subsidies have a certain threshold effect on enterprise innovation efficiency, that is, whether government subsidies can improve enterprise innovation efficiency in a certain appropriate range. The strategy is presented in Figure 2.

4.1. The Three Stage DEA Model

This paper uses the Three-stage DEA model to evaluate the innovation efficiency of China’s renewable energy enterprises. The Three-stage DEA model will be introduced in detail below. Output variables are the number of patents granted to the company and the increase in intangible assets each year. Input variables are the total number of technical personnel and the total R&D investment each year. The Three-stage DEA model mainly includes the following three stages.

Stage I 

Initial DEA efficiency evaluation.

The efficiency evaluation at this stage uses the original input and output index data to measure the efficiency of the decision-making unit.

$$\begin{array}{c}\hfill S_{ni}=f\left(Z_i;{\beta }_n\right)+v_{ni}+{\mu }_{ni},i\in \mathcal{I};n\in \mathcal{N},\end{array}$$

(1)

where $S_{ni}$ represents the input relaxation variable, and $ni$ represents the i-th input of the n-th decision-making unit. ${\beta }_n$ represents the parameter to be estimated of the environmental variable. $f\left(Z_i;{\beta }_n\right)$ represents the influence of environmental variables on $S_{ni}$. $v_{ni}$ and ${\mu }_{ni}$ are the mixed error terms, indicating the interference of the error term on the innovation input and output of renewable energy enterprises. $\mathcal{I}=\{1,2,\cdots ,I\},\mathcal{N}=\{1,2,\cdots ,\mathrm{N}\}$.

Stage II 

Constructing SFA model.

Because the input or output slack variables obtained in the initial efficiency evaluation stage will be affected by the external environment and random errors, the SFA model is built to measure the above two influencing factors in this stage, and then eliminate the influence of these two factors. The SFA model is as follows:

$$\begin{array}{c}\hfill X_{ni}^A=X_{ni}+\left[max(f(Z_i;{\widehat{\beta }}_n))-f(Z_i;{\widehat{\beta }}_n)\right]+\left[max\left(v_{ni}\right)-v_{ni}\right],i\in \mathcal{I};n\in \mathcal{N},\end{array}$$

(2)

where $X_{ni}$ is the actual input value, and $X_{ni}^A$ is the adjusted input value. The former part of formula (2) indicates that all DMUs are adjusted to the same external environment, and the latter part indicates that all DMUs are adjusted to the same random error. In this case, all DMUs have the same environment.

Stage III 

DEA efficiency evaluation after adjustment.

The initial input index shall be adjusted according to the regression results of the above stages. Compared with the first stage, the efficiency value obtained in this stage excludes the influence of external environmental factors and random errors, so it is a more accurate efficiency value.

4.2. Panel Benchmark Model

In order to study the effect and path of government subsidies on innovation efficiency of renewable energy enterprises, we constructed a linear regression model between government subsidies and innovation efficiency. The innovation efficiency of renewable energy enterprises is calculated based on the Three-stage DEA model. It eliminates the interference of environmental factors and random errors, so it is more accurate. The regression model is as follows:

$$\begin{array}{cc}\hfill {\mathrm{CRSTE}}_{it}=& {\beta }_0+{\beta }_1{\mathrm{GOV}}_{it}+{\beta }_2\mathrm{T}\mathrm{O}\mathrm{P}+{\beta }_3{\mathrm{SIZE}}_{it}+{\beta }_4\mathrm{S}\mathrm{O}\mathrm{E}+{\beta }_5\mathrm{MARKET}+{\beta }_6\mathrm{EDU}\hfill \\ \hfill & +{\beta }_7\mathrm{SALARY}+{\beta }_8\mathrm{TOBINQ}+{\beta }_9\mathrm{C}\mathrm{A}\mathrm{S}\mathrm{H}+{\beta }_{10}\sum \mathrm{Y}\mathrm{E}\mathrm{A}\mathrm{R}+{\epsilon }_{it},\hfill \end{array}$$

(3)

where i and t represent the enterprise and year, respectively. The innovation efficiency of renewable energy enterprises (CRSTE) is calculated by Three-stage DEA. The control variables include ownership concentration (TOP), enterprise size (SIZE), enterprise property right (SOE), market competition level (MARKET), executive education level (EDU), employee salary level (SALARY), enterprise value index (TOBINQ), and cash asset ratio (CASH). ${\epsilon }_{it}$ is the random error term. The main variables in the regression model (3) are defined in

Table 1. The brief descriptions of the variables.

Category	Definition	Calculation/Valuation Method	Abbreviation
Explained variables	Technological innovation efficiency	Calculated by Three-stage DEA method	CRSTE
Explanatory variables	Government subsidies	Government subsidies/operating income	GOV
Control variables	Ownership concentration	Shareholding ratio of the top five shareholders	HERF
	Enterprise size	Natural logarithm of ending assets	SIZE
	Enterprise property right	According to the property right nature of the largest shareholder, listed companies are divided into state-owned and non-state-owned enterprises	PROP
	Market competition level	Percentage of main business income of each market competitor in the industry	MARKET
	Executive academic experience	Number of senior management with academic experience/total number of senior management team	ACAD
	Employee salary level	Per capita wage level	HUM
	Enterprise value index	Tobin Q	GROW
	Cash asset ratio	Cash assets/current assets	CASH

.

4.3. Threshold-Effect Model

Under different levels of government subsidies, the innovation efficiency of renewable energy enterprises is uncertain. The relationship between government subsidies and innovation efficiency of enterprises is not simply linear, and there may be an optimal range of subsidy intensity. This paper adopts the threshold panel data model referring to the article [28]. Through the threshold model, we can estimate the threshold value. Finally, the relationship between dependent variables and independent variables in each threshold interval is estimated. Taking the intensity of government subsidies as the threshold variable, we first consider the single threshold panel model.

$$\begin{array}{cc}\hfill {\mathrm{CRSTE}}_{it}=& {\beta }_0+{\beta }_1{\mathrm{GOV}}_{it}I\left({\mathrm{GOV}}_{it}\le \gamma \right)+{\beta }_2{\mathrm{GOV}}_{it}I\left({\mathrm{GOV}}_{it}>\gamma \right)+{\beta }^{*}X+{\epsilon }_{it},\hfill \end{array}$$

(4)

where $I(·)$ is a functional equation. When the conditions in brackets are met, the value is 1, otherwise it is 0. GOV is the threshold variable, and X is the set of control variables. Model (4) assumes that there is only one threshold. The setting of the double threshold model is shown in the following model:

$$\begin{array}{cc}\hfill {\mathrm{CRSTE}}_{it}=& {\beta }_0+{\beta }_1{\mathrm{GOV}}_{it}I({\mathrm{GOV}}_{it}\le {\gamma }_1)+{\beta }_2{\mathrm{GOV}}_{it}I({\gamma }_1<{\mathrm{GOV}}_{it}\le {\gamma }_2)\hfill \\ \hfill & +{\beta }_3{\mathrm{GOV}}_{it}I({\mathrm{GOV}}_{i}t>{\gamma }_2)+{\beta }^{*}X+{\epsilon }_{it}.\hfill \end{array}$$

(5)

Change model (4) into matrix form:

$$\begin{array}{c}\hfill \mathrm{CRSTE}=X\left(\gamma \right)\beta +\epsilon .\end{array}$$

(6)

Perform the least square estimation of formula (6). The residual sum of squares of the regression equation is:

$$\begin{array}{cc}\hfill \mathrm{SSE}\left(\gamma \right)=& {\widehat{\epsilon }}^{*}{\left(\gamma \right)}^{\prime }{\widehat{\epsilon }}^{*}\left(\gamma \right)\hfill \\ \hfill =& {CRSTE}^{{*}^{\prime }}\left[1-{CRSTE}^{*}{\left(\gamma \right)}^{\prime }{\left(X^{*}{\left(\gamma \right)}^{\prime }{X}^{*}\left(\gamma \right)\right)}^{-1}{X}^{*}{\left(\gamma \right)}^{\prime }\right]{\mathrm{CRSTE}}^{*}.\hfill \end{array}$$

(7)

The threshold estimator is

$$\begin{array}{c}\hfill \widehat{\gamma }=\underset{\gamma }{argmin}{SSE}_1\left(\gamma \right).\end{array}$$

(8)

The existence of threshold effect is assumed. The original assumption (H0) is ${\beta }_0={\beta }_1$, and the alternative Hypothesis H1 is ${\beta }_0\ne {\beta }_1$. In order to test the existence of threshold effect, the F statistic is established:

$$\begin{array}{c}\hfill F_1=\frac{{\mathrm{SSE}}_0-{\mathrm{SSE}}_1\left(\widehat{\gamma }\right)}{{\widehat{\sigma }}^2}.\end{array}$$

(9)

Because the distribution of F statistic is nonstandard, it is impossible to obtain the critical value of F statistic by looking up the table for hypothetical judgment. It is necessary to obtain the first-order asymptotic distribution of F statistics through “bootstrap”. Finally, the empirical P value is calculated to judge whether to reject the original hypothesis.

The threshold effect test can only determine whether there is a threshold value, but cannot determine whether the estimated threshold value is equal to the real threshold value. Therefore, we need to conduct an authenticity test. The original hypothesis and alternative hypothesis of the test are as follows:

• The original hypothesis (H0) is $\widehat{\gamma }={\gamma }_0$; the threshold estimate is equal to its true value.
• The alternative hypothesis (H1) is $\widehat{\gamma }\ne {\gamma }_0$; the threshold estimate is not equal to its true value.

  $$\begin{array}{c}\hfill \mathrm{LR}\left(\gamma \right)=\frac{{\mathrm{SSE}}_1-{\mathrm{SSE}}_2\left(\widehat{\gamma }\right)}{{\widehat{\sigma }}^2}.\end{array}$$

  (10)

This function is to judge whether to reject the original assumption, as shown in Equation (11):

$$c\left(\alpha \right)=-2\log \left(1-\sqrt[]{1-\alpha }\right).$$

(11)

When $\mathrm{LR}>c\left(\alpha \right)$, we reject the original hypothesis. That is, the threshold estimator is the real threshold.

5. Data Source and Sampling

The sample data selected in this paper comes from choice financial terminal and CSMAR database. Some data refer to the paper “The technological innovation efficiency of China’s renewable energy enterprises: An estimation based on a three-stage DEA model”. This paper deals with the data as follows:

(1)

Delete the samples of ST and *ST renewable energy enterprises;

(2)

Delete samples with incomplete or missing information disclosure;

(3)

In order to eliminate the adverse effects of outliers, the sample data were reduced to 1%; in view of data availability and completeness, the time span of the sample is 2016 to 2020.

Finally, we obtained a total of 1575 samples from 315 listed renewable energy companies.

5.1. Variable Definition

(1) Explained variables:

Innovation efficiency of renewable energy enterprises (CRSTE): The above Three-stage DEA model is adopted for measurement, which will not be repeated here.

(2) Explanatory variables:

Government subsidy intensity (GOV): It is expressed by the ratio of current government subsidies to operating income of renewable energy enterprises. Government subsidy policy is a way for the government to reallocate resources. As a macroeconomic means, government subsidy policy can stabilize and regulate the national economy. Through theoretical analysis, we find that the technological innovation effect of government subsidies may be related to the subsidy intensity. Therefore, government subsidies are both the main explanatory variable and the threshold variable in this paper.

(3) Control variables:

Ownership concentration (TOP): Major shareholders generally play a leading role in corporate decision-making. Major shareholders have two main functions: First, the right to appoint and remove personnel; Two, determining the development strategy of the company. The larger the shareholding ratio of major shareholders, they have more voice and decision-making power in the company. The shareholding ratio of shareholders means the weight of their decision-making in the company. The concentration of the ownership structure means that the decision-making power is in the hands of fewer people. Therefore, the lower the cost of a decision from formulation to implementation, including the innovation activities of renewable energy enterprises. On the contrary, the decentralization of ownership structure is not conducive to the stability of the company. Under the unstable situation of the company, it is difficult to carry out innovation activities. Based on this, this paper selects the shareholding ratio of the top ten shareholders as the control variable.

Enterprise size (SIZE): on the one hand, asset size is an important manifestation of the company’s strength. Enterprises of different sizes have different economic strength and anti risk ability, which obviously affects the innovation of enterprises. Large scale enterprises have more resources and strong economic strength, and their profitability may be relatively high. Companies with large assets tend to have good business prospects and will have strong competitiveness in the product market; On the other hand, the size of the enterprise is closely related to the R&D investment. The expansion of enterprise scale will convey that the enterprise has good profitability, development ability, operation ability and solvency. The large scale reflects that the enterprise has enough strength to carry out more independent R&D activities, which affects the R&D investment of the enterprise. The government may give different subsidies to renewable energy enterprises of different sizes. For large-scale enterprises, a more comprehensive and standardized R&D subsidy system will be formulated. When considering the effect of subsidies, the government will expect greater results, and often give priority to large-scale enterprises with more R&D economic support. Therefore, companies with large assets tend to have more employees and greater R&D investment. However, the management of large-scale enterprises is relatively complex, and their management costs are relatively high, which may also reduce the innovation benefits of enterprises. Therefore, this paper uses the logarithm of the total assets of listed companies at the end of the year to measure the size of enterprises.

Enterprise property right (SOE): the decision-making power of the company is also closely related to the property right nature of the enterprise. The different nature of property rights has a great impact on the company’s decision-making and business direction, thus indirectly affecting the innovation efficiency of renewable energy enterprises. It is mainly reflected in two aspects: (1) Based on the advantages of political connection, state-owned enterprises enjoy obvious advantages in resource acquisition; Most state-owned enterprises are large-scale, so they have a certain scale effect. (2) State owned enterprises bear a certain degree of social burden. Generally, employees cannot be dismissed easily, and employees are relatively lack of mobility. In addition, because state-owned enterprises are not completely market-oriented, their work efficiency may not be as high as that of private enterprises. Therefore, the type of ownership is also an important variable that affects the innovation behavior of enterprises. In China’s renewable energy industry, state-owned enterprises have absolute advantages in product competition and resource integration in the market. According to the different actual controllers of listed companies, this paper divides the property right nature of renewable energy listed companies into state-owned enterprises (controlled by the central or local governments) and non-state-owned enterprises (controlled by private individuals).

Market competition level (MARKET): the Herfindahl-Hirschman Index (HHI) is one of the better indicators for measuring market competition level in an industry. It is used more by the economic circles and government regulatory departments. The low Herfindahl-Hirschman Index indicates that there is little difference in operating income or assets between enterprises. The more enterprises of the same scale, the lower the market concentration, the more intense the competition among enterprises in the industry; On the contrary, the higher the Herfindahl-Hirschman Index, the greater the difference in operating income or assets between enterprises, the higher the market concentration and the smaller the competition intensity. The calculation method is the sum of the square of the percentage of the operating income of each market competitor in each industry in the total operating income of the industry. Fierce competition in the product market may increase the possibility of bankruptcy and liquidation of enterprises, and have an indirect impact on enterprise innovation.

Executive academic experience (EDU): It reflects the proportion of senior executives with academic experience in the senior management team. According to the high echelon theory, the top management team is the main body of business decision-making. Top management teams with different characteristics will affect the behavior and decision-making of enterprises to varying degrees [29]. In other words, the decisions and judgments made by senior executives are the result of filtering through individual thinking traits. The quality of top management team is an important factor influencing the internal governance and business decision-making of enterprises. Compared with other work experiences, academic research is characterized by strong exploration, creativity, high concentration and long investment period. As one of the important strategic decisions of enterprises, technological innovation is also influenced by the academic experience of senior executives.The academic experience of senior executives can increase the human capital of enterprises. The essence of academic experience is innovation, which enables executives to have good theoretical cultivation and scientific exploration spirit [30].

Employee salary level (SALARY): it is utilized to examine the impact of human wage changes on the innovation behavior of renewable energy enterprises. On the one hand, the wage level determined by the equilibrium of the labor market actually reflects the quality of human capital of the corresponding workers. A higher actual wage level can attract relatively better talents to serve the enterprise. Therefore, the relatively high actual wage level of enterprises means higher human capital quality in a dynamic sense, which increases the probability of successful innovation of enterprises. It provides greater incentives for enterprises to increase innovation expenditure. On the other hand, higher real wages can also improve work efficiency. In other words, a higher actual wage level can not only attract excellent talents, but also motivate them to work hard. In view of the availability of data, we assume that there is no friction in the labor market, employees of enterprises can flow freely among enterprises, and the actual wage level can fully reflect the quality of human capital of enterprises. Therefore, we use the actual wage level as a proxy variable for the quality of human capital. Specifically, we calculate the per capita income of employees.

Enterprise value index (TOBINQ): Tobin’s Q is the value indicator of an enterprise [31]. It is the ratio of the company’s market value to the replacement cost of assets. In the stock market, the market value of the company is represented by the market price of the stock. However, the stock market value is an absolute indicator, which is not suitable for judging the value of different companies. There are many kinds of relative indicators of the company’s market value, such as the entropy weight method. Entropy weight method is to measure and weight the profitability, debt repayment, operating capacity, development trend and other indicators of an enterprise respectively. However, this method is relatively cumbersome and is more used for ranking the market value of enterprises. Tobin’s Q value is often widely used to measure the value performance or growth of a company. Therefore, we also use Tobin’s Q-value index.

Cash asset ratio (CASH): It refers to the ratio of cash assets to current assets. Cash assets include cash, inter-bank deposits and deposits from the central bank. Current assets include cash assets and short-term marketable securities. The higher the cash ratio, the stronger the liquidity of the enterprise. Cash flow also represents the viability and growth ability of enterprises in the market to a large extent. The stronger the cash flow of an enterprise, the greater the vitality of the enterprise, and the greater the possibility and intensity of investment in scientific research projects. Only when enterprises strengthen cash flow management can they ensure that they have enough power to carry out scientific research and innovation. The liquidity of cash flow also determines the speed of enterprise innovation. Therefore, the higher the level of cash flow, the higher the level of enterprise innovation ability.

5.2. Descriptive Statistics on Samples

Before empirical analysis, it is necessary to make descriptive statistics on the relevant variables of the sample. We utilize stata15 for descriptive statistics. As shown in

Table 2. Descriptive statistics on variables of renewable energy enterprises.

Variable	N	Mean	Variance	Minimum	Maximum
CRSTE	1575	0.149	0.193	0.003	1
GOV	1575	0.0134	0.0145	0.000269	0.0827
TOP	1575	0.495	0.144	0.179	0.846
SIZE	1575	22.72	1.181	20.41	26.44
SOE	1575	0.314	0.464	0	1
MARKET	1575	0.00157	0.00304	2.56 × 10${}^{-5}$	0.0165
EDU	1575	0.0857	0.124	0	0.5
SALARY	1575	9.62	0.791	6.984	11.65
TOBINQ	1575	1.733	0.862	0.833	5.837
CASH	1575	0.119	0.0811	0.0112	0.422

, two points can be observed from the table:

• The maximum value of technological innovation efficiency (CRSTE) of renewable energy enterprises reaches 1, while the minimum value is 0.001 and the average value is 0.149. It shows that there are obvious differences in the level of technological innovation efficiency among different sample enterprises;
• The average value of government subsidy intensity (GOV) is 0.013, and the maximum and minimum values are 0.083 and 0.0003, respectively. This obviously implies that the subsidies obtained by different sample enterprises are very different.

Therefore, it is necessary for us to analyze the intensity of government subsidies in groups, which lays a foundation for analyzing the intensity of government subsidies as a threshold variable.

6. Empirical Estimation Results and Discussions

6.1. Multiple Regression of Governmental Subsidies on the Technological Innovation Efficiency

6.1.1. Basic Regression Analysis

In order to select a fixed effect or random effect model, Hausman test is required. The results demonstrate that the fixed effect model is selected for the three models.

Table 3. Regression results of governmental subsidies on the technological innovation efficiency.

Variable	Model (1)	Model (2)	Model (3)
Crste
Gov	0.744 *	1.711 ***	1.763 ***
	[1.808]	[5.209]	[5.661]
Top		0.071 **	0.062 **
		[2.561]	[2.245]
Size		0.080 ***	0.089 ***
		[15.880]	[17.526]
Market		15.659 ***	13.602 ***
		[7.323]	[6.447]
Edu			−0.004
			[−0.141]
Salary			0.018 ***
			[3.683]
Tobinq			0.010 ***
			[2.694]
Cash			0.073 *
			[1.798]
_cons	0.148 ***	−1.803 ***	−1.857 ***
	[5.301]	[−15.539]	[−13.512]
F	11.562	33.037	34.299
p	0	0	0
N	1575	1575	1575

Note: “*”, “**”, “***” indicate statistically significant when the correlation coefficient stands at 10%, 5%, and 1%.

presents the empirical results. The estimation results of models (1), (2) and (3) show that the coefficients of gov are significantly positive. That is, government subsidies can significantly promote the technological innovation efficiency of renewable energy enterprises. Specifically, model (1) is a regression result without control variables. It can be observed that government subsidies (GOV) have a positive impact on the efficiency of enterprise technological innovation. Every one percentage point increase in government subsidies will promote efficiency growth by 0.744 percentage points. Model (2) controls some of the variables, while model (3) controls all the variables. According to the model (3), the innovation efficiency of renewable energy enterprises is highly correlated with enterprise size, product market competition, human wage level and tobinq, all of which have passed the significance level of 1%. It means that these four control variables have played an important role in promoting the innovation efficiency of renewable energy enterprises by government subsidies. Equity concentration (TOP) and cash asset ratio (CASH) also promote the innovation efficiency of renewable energy enterprises. It passed the significance level of 5% and 10%, respectively. On the contrary, the innovation efficiency of renewable energy enterprises is not related to the academic experience of senior executives (EDU). Therefore, the initial Hypotheses H1 is tenable, but Hypotheses H2 is not valid.

6.1.2. The Property Rights Heterogeneity—Linear Regression Test

According to the nature of property rights, we divide renewable energy enterprises into state-owned enterprises and non-state-owned enterprises. The specific regression results are shown in

Table 4. Heterogeneity regression analysis results.

Variable	State-Owned Enterprises	Non-State-Owned Enterprises	Eastern Region	Central Region	Western Region
Crste
Gov	1.347 *	1.961 ***	1.763 ***	1.847 ***	1.829 **
	[1.962]	[5.343]	[4.563]	[3.123]	[2.426]
Top	−0.091	0.074 **	0.045	−0.053	0.280 **
	[−1.391]	[2.384]	[1.505]	[−0.655]	[2.327]
Size	0.110 ***	0.077 ***	0.073 ***	0.159 ***	0.134 ***
	[8.549]	[14.736]	[13.219]	[9.068]	[6.014]
Market	18.143 ***	13.092 ***	20.475 ***	4.927	3.724
	[3.512]	[4.480]	[8.060]	[0.290]	[0.401]
Edu	0.062	−0.034	−0.025	−0.013	−0.009
	[0.821]	[−1.319]	[−0.901]	[−0.124]	[−0.064]
Salary	0.022 *	0.018 ***	0.016 ***	−0.019	0.02
	[1.918]	[3.362]	[2.777]	[−1.553]	[1.200]
Tobinq	0.017	0.006	0.006	−0.005	0.047 **
	[1.549]	[1.630]	[1.452]	[−0.383]	[2.162]
Cash	0.085	0.017	0.028	0.273 ***	−0.510 ***
	[0.847]	[0.409]	[0.609]	[2.815]	[−2.953]
_cons	−2.259 ***	−1.635 ***	−1.523 ***	−2.997 ***	−2.989 ***
	[−6.833]	[−10.626]	[−9.346]	[−7.104]	[−4.679]
F	18.603	26.954	40.454	10.407	21.148
p	0	0	0	0	0
N	495	1080	1205	235	135

Note: “*”, “**”, “***” indicate statistically significant when the correlation coefficient stands at 10%, 5%, and 1%.

below. The regression coefficient of government subsidies on the technological innovation efficiency of non-state-owned enterprises is 1.96, with a significance of 1%; the regression coefficient of government subsidies on the technological innovation efficiency of state-owned enterprises is 1.35, with a significance of 10%. In other words, the positive impact of government subsidies on non-state-owned renewable energy enterprises is much stronger than that on state-owned enterprises. Therefore, Hypothesis H3 is verified.

6.1.3. The Regional Heterogeneity—Linear Regression Test

According to the province where the enterprise is located, the region in this paper is divided into eastern region, central region and western region. In 2011, the National Bureau of statistics divided China’s economic regions into three regions: Eastern, central and western regions. Among them, the eastern part includes Beijing, Tianjin, Hebei, Liaoning, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong and Hainan; the central part includes Shanxi, Jilin, Heilongjiang, Anhui, Jiangxi, Henan, Hubei and Hunan; The West includes Sichuan, Chongqing, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Inner Mongolia, Ningxia, Xinjiang and Guangxi. There are obvious differences in the level of economic development, government subsidies and industrial structure among different regions. In terms of the effect of government subsidies on the technological innovation efficiency of renewable energy enterprises, the enterprises in the three regions all have a positive impact. The central part has the greatest impact, followed by the west and then the east. The results are shown in Table 4. Therefore, the Hypothesis H4 is valid.

6.2. The Threshold Effect Test of Governmental Subsidies on the Technological Innovation Efficiency

6.2.1. Threshold Effect Test

After analyzing the possible threshold effect of government subsidies on the innovation efficiency of renewable energy enterprises, we further set different threshold models. The empirical validity test is carried out on the threshold effect and different heterogeneity factors.

Before the threshold model regression analysis, it is necessary to test the existence of threshold effect. We use the hypothesis test method to construct the F statistic, and then obtain the first-order asymptotic distribution of the F statistic by bootstrap. Finally, the p value is calculated to judge whether there is a threshold effect.

It can be observed from

Table 5. Threshold values estimation.

SAMPLE	The Whole Sample		Non-State-Owned		State-Owned		Eastern Region		Central Region		Western Region
Threshold Numbers	F Value	p Value	F Value	p Value	F Value	p Value	F Value	p Value	F Value	p Value	F Value	p Value
Single threshold	14.65	0.04	9.7	0.21	15.14	0.035	13.37	0.06	5.33	0.59	5.01	0.66
Double threshold	14.39	0.01	15.28	0.005	21.11	0.005	−0.29	0.9991	6.13	0.39	7.73	0.27
Triple threshold	1.66	0.965	10.79	0.14	1.93	0.96	2.64	0.925	4.43	0.79	4.28	0.635

that when the intensity of government subsidies is taken as the threshold variable, different enterprise samples have different threshold effects. According to the grouping of the whole sample, non-state-owned and state-owned enterprises, the p value under the single threshold and double threshold test is less than 0.05, and the p value corresponding to the triple threshold is greater than 0.1. It is concluded that the full sample, non-state-owned and state-owned renewable energy enterprises all have the double threshold effect under the 5% confidence level; in other words, among the full sample, non-state-owned and state-owned renewable energy enterprises, the impact of government subsidy intensity on the efficiency of enterprise technological innovation has a double threshold effect; Under the eastern grouping, the p value of the single threshold test is 0.06. That is, the renewable energy enterprises in the East have a single threshold effect under the 10% confidence level; on the contrary, there is no threshold effect in the central and western regions.

Table 6. Confidence interval estimation of thresholds.

SAMPLE	The Whole Sample		Non-State-Owned		State-Owned		Eastern Region
Threshold Numbers	Threshold Estimate	Confidence Interval	Threshold Estimate	Confidence Interval	Threshold Estimate	Confidence Interval	Threshold Estimate	Confidence Interval
Single threshold	0.0025	[0.0023,0.0025]	0.0031	[0.003,0.0031]	0.0018	[0.0017,0.0018]	0.0034	[0.0031,0.0034]
Double threshold	0.0037	[0.0037,0.0038]	0.0083	[0.0083,0.0083]	0.0037	[0.0037,0.0038]

shows the corresponding thresholds and confidence intervals of the full sample, state-owned enterprises, non-state-owned enterprises and eastern renewable energy enterprises.

6.2.2. Estimation of Threshold Effect

The regression results of the government subsidy intensity as a threshold variable are shown in

Table 7. Estimation of threshold effect based on government subsidy intensity.

SAMPLE	The Whole Sample		Non-State-Owned		State-Owned		Eastern Region
Variable	Coefficient	T Value	Coefficient	T Value	Coefficient	T Value	Coefficient	T Value
Top	0.157 ***	[2.871]	0.208 ***	[3.465]	0.063	[0.521]	0.164 **	[2.523]
Size	0.086 ***	[7.685]	0.084 ***	[7.509]	0.097 ***	[3.046]	0.070 ***	[5.809]
Market	19.726 ***	[5.043]	16.796 ***	[3.618]	24.368 ***	[3.315]	20.948 ***	[5.033]
Edu	−0.025	[−0.644]	−0.004	[−0.097]	−0.05	[−0.577]	−0.026	[−0.631]
Salary	0.004	[0.467]	0.007	[0.746]	−0.003	[−0.169]	0.003	[0.346]
Tobinq	−0.007	[−1.505]	−0.005	[−1.117]	−0.01	[−0.702]	−0.006	[−1.258]
Cash	−0.062	[−1.137]	−0.107 **	[−1.983]	0.04	[0.281]	−0.069	[−1.173]
th $\le {\mathcal{T}}_1$ 1	−8.522 **	[−2.360]	−0.547	[−0.381]	−15.020 **	[−2.046]	−13.551 ***	[−3.169]
${\mathcal{T}}_1$ < th ≤ ${\mathcal{T}}_2$	46.237 ***	[3.236]	22.470 ***	[3.439]	78.147 ***	[3.188]	0.103	[0.283]
th > ${\mathcal{T}}_2$ 1	0.383	[1.204]	0.791**	[2.253]	−0.295	[−0.449]
_cons	−1.975 ***	[−7.554]	−1.987 ***	[−7.383]	−1.985 ***	[−2.910]	−1.599 ***	[−5.453]
F	20.383		15.967		6.684		14.123
N	1575		1080		495		1205

Note: “**”, “***” indicate statistically significant when the correlation coefficient stands at 5%, and 1%. ¹ ${\mathcal{T}}_1$ is the first threshold value. ${\mathcal{T}}_2$ is the second threshold value.

. There is a significant double threshold effect of government subsidies on the innovation efficiency of renewable energy enterprises. When the government subsidies are less than or equal to 0.0025, the government subsidies inhibit the innovation efficiency of enterprises; when the government subsidy is between 0.0025 and 0.0037, the inhibition effect of the government subsidy on the innovation efficiency of enterprises turns to the promotion effect; when the government subsidy is greater than 0.0037, the effect becomes insignificant. Therefore, we verify the Hypothesis H5.

6.2.3. The Property Rights Heterogeneity—Threshold Effect Test

The above empirical test results of the basic panel model show that government subsidies have a significant promoting effect on enterprise innovation efficiency. However, through panel threshold model analysis, it is found that government subsidies have a threshold effect on enterprise innovation efficiency. Are there any differences between different enterprises at the property right nature and regional level? Therefore, this paper conducts a group test according to the nature of enterprise property rights and the heterogeneity of the region. We compare the threshold effect of government subsidies on innovation efficiency of different types of renewable energy enterprises.

In the samples of state-owned enterprises and non-state-owned enterprises, the impact of government subsidies on the innovation efficiency of renewable energy enterprises has a significant double threshold effect. Please see Table 7. For state-owned enterprises, when the government subsidy is less than or equal to 0.0018, there is a significant inhibition on the innovation efficiency of enterprises. Once the government subsidy exceeds 0.0018 and is less than 0.0037, the government subsidy can significantly promote the innovation efficiency of enterprises; when the government subsidy is greater than 0.0037, the inhibition effect occurs again. Similarly, for non-state-owned enterprises, the optimal promotion effect of government subsidies on the innovation efficiency of renewable energy enterprises is between 0.0031 and 0.0083. This shows that too much or too little government subsidies will hinder the improvement of enterprise innovation efficiency. Thus, Hypothesis H6 is verified.

6.2.4. The Regional Heterogeneity—Threshold Effect Test

Government subsidies have a single threshold effect on the innovation efficiency of renewable energy eastern enterprises. When the government subsidy increases continuously and crosses 0.0034, the impact of government subsidy on the innovation efficiency of eastern renewable energy enterprises changes from inhibition to insignificant. Therefore, Hypothesis H7 is verified.

7. Robustness Test

Since there may be a lag effect in the impact of government subsidies on the comprehensive technical efficiency of renewable energy enterprises, the robustness test is carried out with the lag first-order term of government subsidies as an independent variable. As shown in

Table 8. The robustness test results.

Variable	Model (1)	Model (2)	Model (3)
Crste
lGov	0.943 **	1.882 ***	1.828 ***
	[2.129]	[5.497]	[5.431]
Top		0.065 **	0.056 *
		[2.039]	[1.741]
Size		0.083 ***	0.085 ***
		[14.893]	[15.200]
Soe		0.019 **	0.018 *
		[1.974]	[1.959]
Market		14.407 ***	13.377 ***
		[6.268]	[5.900]
Edu			0.005
			[0.167]
Salary			0.020 ***
			[3.624]
Tobinq			0.010 **
			[2.412]
Cash			0.175 ***
			[3.761]
_cons	0.155 ***	−1.885 ***	-2.171 ***
	[5.036]	[−14.747]	[−15.552]
F	14.403	33.42	34.287
p	0.0000	0.0000	0.0000
N	1260	1260	1260

Note: “*”, “**”, “***” indicate statistically significant when the correlation coefficient stands at 10%, 5%, and 1%.

, the robustness test results are consistent with the full sample results above. It shows that the conclusion of this paper is robust and reliable.

8. Conclusions and Policy Recommendation

8.1. Key Findings

The development of society depends on the progress of technology. Technological progress is also inseparable from the technological innovation activities of enterprises. Technological innovation activities can not avoid the problem of market failure, but government subsidies can make up for market failure. Therefore, this paper takes the panel data of listed companies of renewable energy enterprises from 2016 to 2020 as a sample to study whether government subsidies can improve the technological innovation efficiency of renewable energy enterprises. We analyzed the threshold effect and effective range of government subsidies on technological innovation efficiency of renewable energy enterprises. This paper draws the following conclusions:

First, government subsidies can promote the technological innovation efficiency of renewable energy enterprises.

Second, government subsidies have different effects on technological innovation efficiency of renewable energy enterprises with different property rights. Compared with state-owned enterprises, government subsidies play a greater role in promoting the innovation efficiency of non-state-owned enterprises. In addition, this paper also analyzes the heterogeneity of the central, Eastern and western regions. Compared with the eastern region, the government subsidies in the central and western regions can better promote the technological innovation efficiency of renewable energy enterprises.

Third, there is not a simple linear relationship between government subsidies and technological innovation efficiency of renewable energy enterprises. When the intensity of government subsidies is taken as the threshold variable, there is a double threshold effect. There is an optimal subsidy range for the intensity of government subsidies $[0.0025,0.0037]$. When the government subsidy is too small, it will restrain the efficiency of technological innovation; when the government subsidy is too large, the effect becomes insignificant. Therefore, only when the government subsidy is in the optimal range can it stimulate the efficiency of technological innovation.

Fourth, enterprise ownership and regional characteristics will not affect the existence of threshold effect between government subsidies and technological innovation efficiency, but the number and size of threshold values will change due to different enterprise ownership and regions. Both state-owned and non-state-owned renewable energy enterprises have double thresholds. Eastern renewable energy enterprises are single threshold. Comparatively, renewable energy enterprises in the central and western regions have no threshold effect.

8.2. Policy Recommendations

Based on the above conclusions, in order to improve the effectiveness of government subsidies for the technological innovation efficiency of renewable energy enterprises, this paper puts forward the following policy recommendations.

First, optimize the government subsidy mechanism. The distribution of government subsidies should be more scientific and objective. We should consider that there is an optimal interval for the use efficiency of subsidies. The government should not blindly pursue the increase of subsidy scale. We should implement a policy of regional differences. The impact of government subsidies on innovation efficiency is heterogeneous in the eastern, central and western regions. The government should consider the specific R&D situation of local renewable energy enterprises. We can appropriately increase government subsidies to some non-state-owned renewable energy enterprises. This can better enhance the innovation ability of renewable energy enterprises.

When subsidizing different industries, the government should distinguish the links of technological innovation in the industry and subsidize them differently. In addition, from the perspective of subsidy projects, the government should consider the progressiveness and innovative nature of the project and screen out technologies with strong influence for support and guidance. Finally, from the perspective of enterprises, the government should make a comprehensive analysis according to the scale, innovation strength and asset status of enterprises. It cannot be determined by the ownership nature of the enterprise. The fairness of subsidies will directly affect the enthusiasm of enterprises’ technological innovation.

Second, improve the regulatory system of government subsidies. At present, the regulatory system of China’s government subsidy regulatory mechanism is not complete. To solve these problems, we should strengthen the information exchange between the government and enterprises. We should strictly supervise the distribution of government subsidies and implement a dynamic management mechanism. According to the effectiveness of government subsidies on technological innovation activities, the subsidy decline and exit policies shall be adopted in due time. Government regulators should accurately evaluate the indicators of enterprises to avoid local protectionism. Some enterprises with poor operating efficiency may have “subsidy fraud” behavior and use the funds from government subsidies to other irrelevant places. Therefore, the government should strengthen the examination of whether enterprises are qualified for subsidies.