Objectives Chemical fertilizers play very important roles in the grain production of China, however, fertilizer quantity applied per unit area in China is far higher than other countries. Some field trials have shown that reducing fertilizer rate did not lead to a significant drop in grain production, some economists and grain producers remain cautious about reducing fertilizer rate. So it is important to scientifically evaluate the contribution rates of chemical fertilizers to the grain yields in China, and to make rational fertilizer application decision at the country level. The existing studies mainly analyzed the relationship between grain yield and fertilizer input as well as other factors using time series models, but the grain productivities varied from one province to the others, and the effect of fertilizers on grain yield changes is also dynamically changing. So this study chose panel data model to better depict input-output relationship of grain production in China, and reflect more accurately the contribution rates of fertilizers to grain yield changes in different stages.

Methods Grain input-output data of 30 provinces from 1995 to 2015 were collected respectively. Three kinds of panel regression models of grain production functions in the form of C-D and binomial functions were estimated. By using methods of fixed effect test and random effect test to evaluate different panel models, the random effects model was finally judged to be better than the mixed effects and fixed effects models. Based on the regression results of random effects model, the elastic coefficients of grain yield to fertilizer application quantity per unit area were calculated. Using the concept of total factor productivity, the contribution rates of fertilizers were calculated using grain production function and fertilizer elasticity coefficients to evaluate actual impact of fertilizers on grain production.

Results The empirical results showed that the elasticity coefficients were all significant, the fixed elastic coefficient was 0.17, and the variable elastic coefficients showed an obvious inverted U-shaped trend. It implied that the marginal fertilizer input had entered the stage of diminishing returns, continuing increase of fertilizer application quantity seemed unable to realize the increase of grain production. The elastic coefficient value of fertilizer application quantity was still high and bigger than other factors’, which demonstrated the unsubstitutability of fertilizer to grain production increase, on the other side. The contribution rates of fertilizers to grain yield increase showed that the contribution of fertilizers was diminishing and trended to zero. The input-output data analysis result of 2015 also indicated that appropriate reduction of fertilizer input would not lead to a sharp decrease in grain production, as the improvement of disaster prevention technology, agricultural mechanization degree and other elements had played greater roles in the increase of grain production.

Conclusions It is suggested that the rates of fertilizers should be strictly controlled at the county level, and the effect of fertilizer rate on yield increase should be improved by adjusting the way of fertilization and balancing the fertilization structure, meanwhile, contribution rates of technological factors to grain yields should be further promoted.