Abstract: Environmental regulation and government R&D input are two difficult issues restricting the development of agriculture. Agricultural science and technology innovation has obvious externality, such as monopoly of R&D resources and information asymmetry which leads to the existence of “market failure”. Environmental regulation can effectively solve the market failure caused by science and technology innovation. The government works hard to realize the “win-win” between agricultural economic growth and environmental protection, of which the keys are to obtain the best intensity ranges of government R&D input and environmental regulation. The moderate environmental regulation has a leading-effect on government R&D investment and then produces the “compensation effect of innovation” to the agricultural science and technology innovation behavior. Thus, measuring the impact of environmental regulation and government R&D input on the efficiency of agricultural science and technology innovation is of great significance to study the sustainable development of modern agriculture. The paper has two research features. First, the paper considers simultaneously the effects of both environmental regulation and government R&D investment on the innovation efficiency of agricultural science and technology from the perspective of industry. Second, the super logarithm stochastic frontier approach is used to measure the efficiency of agricultural scientific and technological innovation, which is considered as the research object, and then the panel threshold model is applied to study the nonlinear effects of environmental regulation and government R&D on the efficiency of agricultural scientific and technological innovation to investigate the optimal ranges of environmental regulation and government R&D input. The structures of this paper are as follows: the first section is the introduction. The second section presents research design. The third section gives empirical analysis results. The main conclusions and policy implications are provided in section four.In this paper, 30 provincial panel data from 2004 to 2015 are used to measure the efficiency of agricultural science and technology innovation in China by using super-logarithmic SFA model. The results show that the government R&D investment and environmental regulation have significant effects on agricultural science and technology innovation at the 1% significant level, which indicates that the government R&D investment and environmental regulation have played important roles in promoting the efficiency of agricultural science and technology innovation. This is because that the government R&D investment has a leverage effect and the environmental regulation provides good production conditions and ecological environment for agricultural production, promoting the efficiency of agricultural science and technology innovation. Among the control variables, only the development level of agricultural productivity is not significant, the rest variables are significant, in which the abilities of infrastructure and innovation environment promoting the efficiency of agricultural science and technology innovation are much stronger than that of the human capital.Then, to play the role of environmental regulation and government R&D investment in promoting the efficiency of agricultural science and technology innovation in China, this paper uses the panel threshold model to test threshold effects of the two factors on the efficiency of agricultural innovation. Taking the government R&D input intensity and environmental regulation intensity as threshold variables, the threshold effects are further discussed to determine the optimal ranges of government R&D input intensity and environmental regulation intensity. The results show that the single threshold effect of government R&D investment, and the single, double and three threshold effect of environmental regulation are significant. The threshold effects on the efficiency of agricultural science and technology innovation are of great significance to improve the efficiency of agricultural science and technology innovation in China. The optimal interval of government R&D input intensity is above 0.11, and the influence coefficient is 0.194, which means the government R&D input can promote the efficiency of agricultural science and technology innovation continuously. The reason is that the private sector is unwilling to provide investment due to the greater externality and risk of the agricultural science and technology innovation, namely "market failure". The government acts as a powerful supporter for R&D, which needs to provide the necessary financial support for agricultural research and development. The excessive intensity of government R&D investment will also stimulate the investment in agricultural R&D resources and have a leverage effect, which will enable the government R&D funds to play the role of “accomplishing a great task with little effort by clever maneuvers”, and then improve the efficiency of agricultural science and technology innovation to maximize economic benefits. The optimal range of environmental regulation intensity is less than 0.62. Environmental regulation has a significant positive effect on the efficiency of agricultural science and technology innovation, and the influence coefficient is 0.798. The reason lies in the fact that in the aspect of controlling environmental pollution, the government has invested too much financial funds to improve the agricultural ecological environment leading to the agricultural scientific and technological innovation lack of sufficient fund motive force, and the efficiency of agricultural scientific and technological innovation reduced. Only when environmental regulation and government R&D input are in a reasonable range, can environmental regulation policy increase government R&D investment through “incentive effect”, affecting agricultural scientific and technological innovation behavior and producing “innovation compensation effect”, and can government effectively solve the dilemma of agriculture, improving the level of agricultural science and technology innovation, and promoting the sustainable development of agricultural economy.Therefore, in the environment of the environmental regulation, the government should play dominate role in the input of agricultural science and technology, and provide rich R&D funds and good innovation environment for agricultural scientific and technological innovation. First, the government should continue to expand the scale of government R&D investment so that it can reach the investment level of developed countries as far as possible.And it is necessary to prevent the low efficiency or inefficiency of government R&D investment by ensuring the intensity of government R&D input within a reasonable range. Second, in the aspect of environmental regulation, we should formulate feasible environmental regulation policies according to our national status. Neither increasing environmental costs blindly, nor ignoring the positive role played by environmental regulation policies is recommended. We should strengthen the depth and breadth of environmental regulation to promote the innovation of agricultural science and technology, and realize the “win-win” between agricultural economic development and environmental protection. Under the strict environmental regulation, adjusting the government R&D input intensity effectively and increasing the intensity of agricultural scientific and technological innovation greatly can promote the efficiency of agricultural scientific and technological innovation.

Key words: environmental regulation, government R&D input, agricultural technology innovation efficiency, threshold effect