| The source of agricultural growth has two aspects from the theory of economic growth, first is the increase in investment of resources, and second is the productivity improvement. The limited resources, especially the land decides the sustainability of agricultural growth can not depend on the unlimited increase of input, but the increase in productivity. That is, without the input increases quickly, the capacity of long-term agriculture growth needs to rely on the accumulation and improvement of productivity. China's economy has made remarkable achievements since reform and opening up, rural reform, which starts with the household contract responsibility system, also induces the development of agriculture, the main agricultural output continues to increase, such as crop, cotton, and so on, the income of farmers keeps increasing, living standards in rural areas also have been significantly improved. Whether this growth of agriculture production is due to its inputs increase or the productivity improvement? Whether this growth is sustainable and the productivity behind this growth can not be ignored. Regional difference has expanded with the overall agricultural output growing at the same time. If the differences is caused by the former, then the gap among regions can be resolved by a corresponding increase of agricultural production factors in the backward areas, but if the gap of agricultural production is mainly the productivity gap, which means the different ability of sustainable agricultural growth in different regions, then the trend of this capacity will also affect the future trend of regional disparity of agricultural production. Therefore, the agricultural productivity is a question worthy of our attention no matter from the promotion of the sustainability of agricultural growth perspective or from the sources of inter-regional differences in agricultural growth. Regarding the existing literature, the improvement of agricultural TFP which is brought by the reform of the institutions brought can explain most of the rapid growth of agricultural output from the reform and opening up to the early 80s. And the effect of institutional factors will gradually decrease over time, among the researches about the agricultural growth and regional differences after the mid-and late 80's, some scholars argued it was brought by the inputs of main factors, others believed it was caused by growth and regional differences of productivity. This paper starts from such a argument, designed to study whether the productivity dominates the regional differences of agricultural output and focus on the productivity level, study the trend of productivity differences, find the possibility of up or down trend of productivity of each province, as well as the impacts and effects of factors, such as space spillover, rural industrialization, human capital, the degree of opening, urbanization, market construction and regional R&D expenditures on agriculture, on agricultural productivity growth. This research will provide empirical evidence for improving productivity level of underdeveloped areas and reducing the regional differences.We use a long period panel data from 1985 to 2005 with Chinese 28 provinces and autonomous regions, agricultural production data, adopted growth accounting approach, non-parametric methods, the convergence test and spatial statistical methods, we get the following basic conclusions:1) The agricultural total factor productivity is the dominant factor of the regional differences agricultural output. First, we analyze the difference changes of the agricultural output of regions, the differences changes in factor inputs and total factor productivity since the reform and opening, find that regional differences in agricultural output expanding with the differences in factor inputs does not change obviously at the same time. The single-factor productivity, except for fertilizer productivity, is also gradually expanding when we combine the inputs and outputs together. Then we propose a hypothesis of statistical inference which is to be tested:difference in agricultural output comes from other factors besides the factor inputs.Then we try to figure out the source of this difference with quantitative analysis methods. The return of same factor varies in different regions and different periods when taking into account the 21 years are used in this long period of historical data, therefore we use the translog production function approach to calculate the output elasticity of the various regions in different periods. We decompose differences in output into the difference of productivity and factors based on the growth accounting approach, and use the Analysis of Variance (ANOVA) to the exam the major source of agricultural output difference within the period 1985-2005. From the traditional C-D function, we not only use the K-R method to decompose differences in output into input differences and the differences of productivity, but also the E-L method to decompose the difference of output into three parts:the input difference, difference of total factor productivity and interaction difference of factors and the productivity, based on the decomposition above. No matter which decomposition method is used, the results show that inter-regional difference in total factor productivity is the dominant source of the differences in agricultural output from 1985 to 2005; the total factor productivity difference at least contributes 55% of the differences of output even taking into account the interaction of factors and total factor productivity.2) The agricultural total factor productivity of all the 28 provinces shows no absolute convergence, nor conditional convergence and club convergence within the sample period, that is, there is no sign of regional disparities narrowing. Firstly, we conclude that the total factor productivity is the main source of the difference of provincial agricultural output, then we adopt a bilateral comparison method to calculate the level of the total factor productivity, which built the foundation for further research about the regional difference. Secondly, this paper uses a simple statistical analysis based on the panel data set of productivity levels; found that there is a consistence of the change in trends of differences in total factor productivity and the trends of differences in agricultural output, which can prove that total factor productivity is important to the differences in output. We also found that the growing trend of the difference of agricultural total factor productivity level and the differences in productivity growth through a simple statistical indicators.Finally, we use three types of convergence test in order to test whether there are narrowing trends of the level of differences in agricultural TFP, exam whether the regions who's TFP are grow faster than the higher areas. We get the following conclusion:the differences of the agricultural productivity will not be narrowing gradually over time but expanding from 1985 to 2005. The backward areas did not derive greater benefits through the technology spillover or achieve faster growth rate using the absoluteβconvergence test. The differences of agricultural productivity did not show the conditional convergence even we control the region and time fixed effects. Finally in accordance with the general district of China, we use the club convergence test which exams whether there is a narrowing trend of productivity level within the eastern, central and western three major economic zones, found that the internal productivity differences among province within the three regions has been expanded with the time, but the extent of expansion is different, the eastern region is the region with the highest productivity growth rates with the strongest trend of expansion of the internal differences among provinces. And through the absolute P convergence test, we did not find backward areas get faster growth within the three regions. The results of test prove that not only the difference among the three regions keeps expanding, but also there is no narrowing trend of the productivity level among the various provinces within the three regions.3) We try to find the spatial evidence of the club convergence, found that different province with different productivity level converge to different clubs, but internal disparities within each club have not narrowed, that is, there is no club convergence. Then by comparing the general spatial Markov chain and spatial Markov chain, we found that middle-high and high-level neighbors of a region can enhance the possibility of productivity increase. And the elements of these two Markov matrixes are different, which means the productivity of a province is affected by the neighbor's productivity levels, there is spatial dependence of productivity levels among regions. The elements with the same location in two chain matrixes are not equal, even the diagonal elements also have relatively large differences, indicating the productivity level of the region to which each province belongs has impacts on the upward or down change of its level of agricultural productivity, the changes of the level of regional productivity in each region is not independent, but a close relationship with the surrounding neighbors.4) We use spatial statistical and spatial econometric methods to find the causes of the convergence of agricultural productivity. Firstly, the spatial statistical analysis shows that there is local spatial correlation of agricultural total factor productivity level during the period range of the sample, thus we need to control the spatial factor during the study of the influencing factors.Then we introduce the six factors that may affect the productivity into the spatial econometric model one by one, the rural industrialization, human capital, openness, urbanization, market construction and agricultural R&D input, found that the rural industrialization improved the productivity significantly, the role of human capital is different in different sample period which may be relevant to the labor mobility. Urbanization promoted the productivity significantly, the opening and market construction are not significant. The variable which represents the agricultural R&D expenditure is not significant may be due to the index selection problem, and also reduces the explanatory capability of the model.
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