Abstract: Agricultural productive services is the related industry of grain production. In order to expand the ideas of food production development and grain yield improvement, this paper focuses on the impact of agricultural productive services on grain production.Firstly, this paper analyzes the impact of agricultural productive services on food production in terms of knowledge and technology through Romer′s endogenous growth theory;at the same time, capital is regarded as the link element between agricultural productive services and food production, the model of Romer′s endogenous growth theory is reformed, and the mechanism of agricultural productive services′ influence on food production in terms of capital is analyzed, and the research hypothesis is put forward according to the analysis results.Then, based on China′s provincial panel data from 2008 to 2017, through the establishment of a panel model, the System GMM method, differential GMM method and quantile regression method are used to test the research hypothesis.The results show that: the development of agricultural productive services can promote the improvement of grain production level:the grain yield per unit area will increase by 0.7 percentage points when the development level of agricultural servicesincreases by 1 percentage point; the impact of the development of different agricultural productive services on the improvement of grain production level is different, among which agricultural logistics has the greatest impact:every 1% increase in the development level of agricultural logistics industry will increase the grain yield by 1.1%.Therefore, (1) The development of agricultural productive services should take the development of food as the signal access point, and take the demand of farmers as the guidance. (2) At present, the agricultural logistics has the greatest impact on grain production, and should become the focus of the development strategy of agricultural productive services. (3) Regional coordination and policy coordination should be paid attention to in the development of agricultural productive services.

Key words: agricultural productive services, food production, Romer′s endogenous growth theory;GMM