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Abstract China has achieved remarkable progress in grain production since 1978， in which yield increase played an important role. We can expect that future growth in grain output will highly depend on yield increase. Current literatures mainly adopt the productivity analysis to estimate the production potential， which assumes an identical production frontier in whole China and ignores the heterogeneities in agricultural policies， geography， and climates across regions. This paper sheds light on the club convergence in the yield of three main grains among provinces in China. With provincial yield data of rice， maize， and wheat from 1980 to 2012， we first investigate the yield convergence for China by using the conventional convergence tests. Contradictory results are found between β and σ convergence tests. In particular，β convergence test provides strong evidence that the yields of all three grains are converging， which is inconsistent with the data. On the contrary，σ convergence test finds that wheat yield is diverging， while no clear trend is found for rice and maize yields. Therefore，we further adopt a newly developed statistical method proposed by Phillips and Sul（2007） to re-test the convergence， which allows for different time paths and individual heterogeneity. Their methodology is particularly useful in measuring transition toward a long-run growth path or a common steady state. We first adopt this method to test the population convergence for the three grains. Results show that rice yield is converging into one club in whole China except for Shanxi Province. Moreover， maize yield is converging in whole China， while no population convergence is found for wheat yield. Instead， we find three convergent clubs for wheat yield: Beijing， Tianjin， Hebei， Shanxi， Inner Mongolia， Liaoning， Jilin， Heilongjiang， Shandong， Anhui， Jiangsu， Zhejiang， Fujian， Shaanxi， Xinjiang and Henan converge to the first club with the highest average yield; Hubei， Hunan， Guangdong， Sichuan， Gansu， Qinghai， Ningxia， Jiangxi and Shanghai converge to the second club with the middle average yield; Yunnan， Guangxi and Guizhou converge to the third club with the lowest yield; Tibet has the highest yield and diverges. A brief analysis indicates that convergence of rice and maize yields might be attributed to the popularization of high-yield variety and low dependence on natural condition， while wide heterogeneity in natural ecological condition， various seed variety， and great difference in input factors result in three convergence clubs for wheat. Furthermore， using the maximum yield in each club as the potential production frontier， we project the grain output for each year. Our results show that the gap between real output and potential output is shrinking over time. In particular， the gap between real output and potential output of wheat is the highest in the 1980s， which however experienced the largest decline in the past three decades， and dropped down to 11.76% in 2012. The potential output of the three main grains reaches 6.6 trillion tons in 2012， which is still 26% higher than the real output. Our results indicate that the potential increase of the three main grains will remain above 10% in the next 10-20 years．
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