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In order to improve the production efficiency of maize in Henan, China, the HP (High-Pass) filter method is used to obtain the maize trend yield. Secondly, the Malmquist index method is used to analyze the changes of TFP (Total Factor Productivity) of maize in 18 cities in Henan Province in the past 11 years. Finally, the amount of slack in maize input and output is analyzed. The results show that the research and development level of advanced technology of maize production in Henan Province has been improved to some extent in recent years; the advanced technology in various regions has not been fully promoted and utilized; there is a certain degree of relaxation in the input of various elements of maize; the resource allocation is unreasonable, and there is a certain amount of space for saving.

Henan Province is located in the center of Huang-Huai Maize dominant industrial belt, and its light and heat resources are abundant, forming the cultivation system of wheat and maize cropping twice a year. Located in the continental monsoon climate zone, Henan Province is an important grain producing area in China. The summer maize planting area and output account for about 10% of the country, but the summer maize yield is high and unstable. As a big grain planting province, Henan planted 3316.86 thousand hectares of maize in 2016, with a total yield of 17.5297 million tons. In fact, the yield per unit area of maize in Henan Province is 5638 kg/ha in 2012 and decreased to 5285 kg/ha in 2016, while the planting area of maize in 2012 is 3100 thousand hectares, and by 2016 it had increased to 3316.86 thousand hectares. The input of other controllable elements is also in the state of growth; the input gradually increases and the output decreases, which indicates that the production efficiency of maize in Henan Province is low, so it is necessary to adjust the input of production factors to increase the yield of maize.

Data Envelopment Analysis (DEA), Malmquist Index Method, Stochastic Frontier Analysis (SFA), and DEA-Tobit models are widely used in productivity studies in the agricultural sector. Many scholars have studied the production efficiency of maize, and most scholars’ research mainly concentrates on the above methods to study the maize production efficiency in the country or in some provinces and cities, mainly the following parts.

For the study of maize production efficiency in China: Yang Guoqing et al. [

Studies on maize production efficiency in individual provinces and cities: Huang Yong [

The above scholars have used the actual production as the output index of maize, and the actual production of maize is affected by other factors, the actual yield could not be used as the exact output corresponding to the input of each element of maize. The analysis using actual production does not accurately reflect maize production efficiency. In this paper, the HP filter method is used to process the yield data of maize, and the trend yield is obtained as the output index of maize. The Malmquist index method of DEA is used to study the growth of maize TFP in 2006-2016 in various cities of Henan Province. The change of total factor productivity of maize is decomposed into technical efficiency and technological progress, and further decomposed into pure technical efficiency, scale efficiency and technological progress. Then the influence of efficiency change is analyzed concretely.

Data Envelopment Analysis (DEA) is first proposed by A.Charnes and W. W. Cooper [

The Malmquist productivity index is first proposed by Swedish economist and statistician Malmquist (1953) and can be used to investigate the variation of production efficiency in different periods. The nonparametric Malmquist exponent method based on data envelopment analysis defines the Malmquist exponent by the distance function (distance function) and calculates the total factor productivity (total factor productivity, (TFP) by using the mathematical linear programming model. Decompose the Malmquist index while analyzing the efficiency changes of production decision-making units in different periods to find the root cause of total factor productivity change [

M 0 t + 1 ( x t + 1 , y t + 1 , x t , y t ) = D 0 t + 1 ( x t + 1 , y t + 1 | V R S ) D 0 t ( x t , y t | V R S ) [ D 0 t + 1 ( x t + 1 , y t + 1 | C R S ) D 0 t ( x t , y t | C R S ) ⋅ D 0 t ( x t , y t | V R S ) D 0 t + 1 ( x t + 1 , y t + 1 | V R S ) ] ⋅ [ D 0 t ( x t + 1 , y t + 1 ) D 0 t + 1 ( x t + 1 , y t + 1 ) ⋅ D 0 t ( x t , y t ) D 0 t + 1 ( x t , y t ) ] 1 2 = pech × sech × techch (1)

Among them, D 0 t ( x t , y t ) and D 0 t + 1 ( x t + 1 , y t + 1 ) represent the distance function of two periods. M 0 t + 1 ( x t + 1 , y t + 1 , x t , y t ) > 1 , that is, TFP > 1, indicates that the total factor productivity is in the growth stage, and the resource allocation efficiency of maize is improved. M 0 t + 1 ( x t + 1 , y t + 1 , x t , y t ) < 1 , that is, TFP < 1, indicates that the total factor productivity is in the declining stage, and the resource allocation efficiency of maize is decreased. The change of technical efficiency is used to measure the ratio of the actual output to the theoretical maximum output under the same input condition or the ratio of the actual input to the theoretical maximum input under the same output condition, effch > 1, which indicates that the decision making unit is close to the technical frontier. Technological progress reflects the fact that during the implementation of the policy, through technological transformation or other means to achieve the same amount of output to reduce input or the same amount of input to improve output, pech > 1, indicating that the decision-making unit has technological progress or innovation.

The HP filtering method is a decomposition method of time series in state space. It assumes that the time series consists of two parts, namely: long-term trend component and short-term fluctuation component. The HP filter method can be considered as a high-pass filter, which can separates high-frequency components with periods below 8 years [

Maize yield sequence { y t } is divided into trend yield g t and fluctuating yield c t by HP filter, in which g t is a stable high frequency trend signal and c t is an unstable low frequency disturbance signal. The principle is to remove the low frequency signal c t by filtering, thereby detecting the high frequency signal g t from the production sequence. HP filter decomposes y t into: y t = g t + c t .

The detection method of high frequency signal g t is often defined as the solution of the following minimization formula, namely:

min { ∑ t = 1 T ( y t − g t ) + λ ∑ t = 1 T [ ( g t + 1 − g t ) − ( g t − g t − 1 ) ] 2 } (2)

In the formula, λ is the HP filter parameter. When λ = 0 , the minimized solution of the function is { y t } sequence. With the increase of λ value, the trend of minimum solution estimation is smoother. The general experience of λ is as follows:

λ = { 100 , annualdata 1600 , quarterlydata 14400 , monthlydata (3)

According to the scientificity, comprehensiveness and availability of data and the accuracy and rigor of data calculation, this paper selects the trend yield of maize per unit area (kg/ha), the number of people engaged in maize production (10,000 people), the effective irrigation area of maize (1000 ha), the sowing area of maize (1000 ha), the corn fertilizer application (ton), and the total power of maize machinery (10,000 kilowatts) in Henan Province from 2006 to 2016, data obtained from the Henan Provincial Bureau of Statistics [

Using DEAP2.1 software to calculate the overall situation of maize production efficiency during the period of 2006-2016 in Henan Province is shown in

Observing

2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Zhengzhou | 4969.27 | 4935.21 | 4900.85 | 4866.43 | 4831.83 | 4797.38 | 4763.37 | 4729.37 | 4695.52 | 4662.22 | 4628.57 |

Kaifeng | 5560.78 | 5551.61 | 5541.42 | 5529.64 | 5515.33 | 5496.57 | 5474.96 | 5450.85 | 5424.47 | 5396.69 | 5367.69 |

Luoyang | 5049.09 | 4984.07 | 4918.17 | 4852.78 | 4790.00 | 4732.85 | 4680.49 | 4631.31 | 4585.01 | 4542.53 | 4500.70 |

Pingdingshan | 4920.42 | 4876.89 | 4831.38 | 4782.33 | 4730.47 | 4676.18 | 4619.90 | 4562.23 | 4506.25 | 4457.83 | 4411.48 |

Anyang | 6456.62 | 6471.13 | 6482.48 | 6488.76 | 6490.05 | 6487.20 | 6480.74 | 6470.20 | 6455.76 | 6438.09 | 6417.97 |

Hebi | 6832.33 | 6865.44 | 6895.62 | 6921.14 | 6942.13 | 6959.32 | 6972.99 | 6982.87 | 6988.98 | 6992.31 | 6994.01 |

Xinxiang | 6048.98 | 6072.57 | 6093.78 | 6110.55 | 6121.47 | 6125.41 | 6120.87 | 6105.91 | 6080.80 | 6047.24 | 6008.41 |

Jiaozuo | 7323.62 | 7323.37 | 7321.33 | 7316.80 | 7309.13 | 7297.57 | 7281.18 | 7258.73 | 7230.56 | 7198.47 | 7164.22 |

Puyang | 6580.71 | 6579.54 | 6576.12 | 6569.27 | 6559.56 | 6547.90 | 6534.72 | 6519.34 | 6501.04 | 6477.37 | 6450.43 |

Xuchang | 6403.64 | 6387.96 | 6370.61 | 6348.99 | 6323.68 | 6295.58 | 6266.83 | 6238.26 | 6210.74 | 6185.63 | 6161.09 |

Luohe | 6215.70 | 6211.42 | 6209.28 | 6212.66 | 6224.70 | 6245.69 | 6274.00 | 6306.06 | 6340.04 | 6375.55 | 6411.91 |

Sanmenxia | 4528.95 | 4493.19 | 4455.89 | 4417.62 | 4378.75 | 4339.34 | 4299.33 | 4258.07 | 4216.21 | 4175.16 | 4134.48 |

Nanyang | 5550.92 | 5524.99 | 5496.50 | 5463.45 | 5424.54 | 5378.83 | 5325.77 | 5264.84 | 5197.75 | 5128.20 | 5057.20 |

Shangqiu | 6581.23 | 6587.49 | 6589.99 | 6586.03 | 6573.91 | 6553.04 | 6523.20 | 6484.98 | 6440.35 | 6392.01 | 6341.76 |

Xinyang | 4661.81 | 4606.40 | 4559.51 | 4533.03 | 4533.37 | 4564.72 | 4627.59 | 4720.70 | 4841.45 | 4984.98 | 5142.45 |

Zhoukou | 6127.30 | 6069.38 | 6017.31 | 5977.44 | 5954.25 | 5946.95 | 5950.13 | 5958.43 | 5969.71 | 5983.04 | 5996.11 |

Zhumadian | 5241.99 | 5221.88 | 5207.79 | 5203.07 | 5208.34 | 5221.91 | 5240.59 | 5261.22 | 5282.03 | 5302.66 | 5322.51 |

Jiyuan | 5214.63 | 5224.97 | 5233.02 | 5237.70 | 5239.02 | 5236.92 | 5231.04 | 5220.82 | 5206.82 | 5190.95 | 5174.11 |

Years | Comprehensive technical efficiency change index (Ech) | Technological progress change index (Tch) | Pure technical efficiency change index (PEch) | Scale efficiency change index (SEch) | Total factor productivity change index (TFPch) |
---|---|---|---|---|---|

2006-2007 | 0.961 | 1.035 | 0.962 | 0.999 | 0.994 |

2007-2008 | 0.941 | 0.948 | 0.919 | 1.024 | 0.892 |

2008-2009 | 1.002 | 0.966 | 1.018 | 0.984 | 0.968 |

2009-2010 | 0.996 | 0.965 | 0.990 | 1.006 | 0.961 |

2010-2011 | 0.943 | 1.025 | 0.963 | 0.980 | 0.967 |

2011-2012 | 1.003 | 0.967 | 0.993 | 1.011 | 0.970 |

2012-2013 | 0.994 | 0.991 | 0.982 | 1.012 | 0.986 |

2013-2014 | 0.995 | 0.978 | 0.996 | 0.999 | 0.974 |

2014-2015 | 0.953 | 1.026 | 0.974 | 0.979 | 0.978 |

2015-2016 | 0.915 | 1.074 | 0.960 | 0.952 | 0.982 |

Average | 0.970 | 0.997 | 0.975 | 0.994 | 0.967 |

value of each efficiency did not exceed 1, which indicated that these five efficiency have not improved. Among them, the average total factor productivity (TFP) decreased by 3.3% (the average index is 0.967, less than 1), indicating that the maize production efficiency in these 18 cities showed a downward trend in 2006-2016. Total factor productivity (TFP) of maize has been fluctuating from 2006 to 2016, which is mainly affected by the change of comprehensive technical efficiency (the overall technical efficiency has decreased by 3.0% annually), and the comprehensive technical efficiency is affected by pure technical efficiency and scale efficiency. Moreover, it is greatly affected by the pure technical efficiency (the average value of pure technical efficiency is 0.975, while the average efficiency of scale is 0.994). The reason for this phenomenon is that it fails to effectively promote the use of advanced technology or the unreasonable configuration of agricultural implements and low utilization efficiency.

From 2006 to 2016, the comprehensive technical efficiency change index of the annual maize production in 18 cities of Henan Province is greater than 1 in 2 time periods (2008-2009, 2011-2012), indicating that the input and output of these years are in the best allocation, and all resources have been fully utilized. The comprehensive technical efficiency change index of the remaining years is less than 1, especially in 2015-2016, the comprehensive technical efficiency change index is 0.915, which is the lowest level in the study period, and the allocation efficiency of input and output is the lowest during the study period.

From 2006 to 2016, the average value of technological progress in the studied cities is 0.997 (less than 1), and the technological progress of these years in 2006-2007, 2010-2011, 2014-2015, 2015-2016 is greater than 1, and is in a state of technological progress, and the progress is relatively large, 3.5%, 2.5%, 2.6% and 7.4%, while the technical progress changes of the remaining years are less than 1, indicating that these annual technologies have not improved.

The period of corn production pure technical efficiency change index greater than 1 is only in 2008-2009, and only the annual technology use efficiency is rising. The change in pure technical efficiency in 2013-2014 (0.996) basically tended to be 1, indicating that the efficiency of technology use in this year is basically the same as the previous year. The pure technical efficiency changes for the remaining years are all less than 1, indicating that the efficiency of technology use in these years has decreased from the previous year.

The average of maize production scale efficiency change in Henan Province is 0.994, and the scale efficiency change value of four time periods is greater than 1, which are 2007-2008 (1.024), 2009-2010 (1.006), 2011-2012 (1.011), 2012-2013 (1.012). These years scale returns are declining. In the remaining years, the scale efficiency change values are all less than 1, indicating that these years scale returns are increasing.

Using DEAP2.1 software to calculate the overall situation of maize production efficiency in the 18 cities of Henan Province during 2006-2016 is shown in

The total factor productivity of Hebi, Xinxiang, Jiaozuo, Puyang, Xuchang, Luohe, Sanmenxia, Shangqiu, Xinyang, Zhoukou and Jiyuan is much higher

Area | Comprehensive technical efficiency change index (Ech) | Technological progress change index (Tch) | Pure technical efficiency change index (PEch) | Scale efficiency change index (SEch) | Total factor productivity change index (TFPch) |
---|---|---|---|---|---|

Zhengzhou | 0.957 | 1.000 | 0.963 | 0.994 | 0.956 |

Kaifeng | 0.962 | 0.977 | 0.956 | 1.006 | 0.940 |

Luoyang | 0.957 | 1.000 | 0.967 | 0.989 | 0.956 |

Pingdingshan | 0.944 | 1.000 | 0.953 | 0.990 | 0.943 |

Anyang | 0.968 | 1.000 | 0.993 | 0.975 | 0.968 |

Hebi | 1.001 | 0.998 | 1.000 | 1.001 | 0.998 |

Xinxiang | 0.975 | 1.000 | 0.986 | 0.989 | 0.975 |

Jiaozuo | 0.984 | 1.000 | 1.000 | 0.984 | 0.984 |

Puyang | 0.972 | 1.000 | 0.964 | 1.008 | 0.972 |

Xuchang | 0.977 | 1.000 | 0.995 | 0.983 | 0.977 |

Luohe | 0.980 | 1.000 | 1.010 | 0.970 | 0.980 |

Sanmenxia | 0.973 | 1.000 | 0.981 | 0.992 | 0.973 |

Nanyang | 0.920 | 1.000 | 0.910 | 1.012 | 0.920 |

Shangqiu | 0.977 | 0.999 | 0.967 | 1.010 | 0.976 |

Xinyang | 0.997 | 0.981 | 0.987 | 1.011 | 0.978 |

Zhoukou | 0.969 | 1.000 | 0.970 | 0.999 | 0.969 |

Zhumadian | 0.947 | 1.000 | 0.958 | 0.989 | 0.947 |

Jiyuan | 1.000 | 0.993 | 1.000 | 1.000 | 0.993 |

Average | 0.970 | 0.997 | 0.975 | 0.994 | 0.967 |

than the average level, showing a positive growth, while Anyang (0.968) is basically the same as the average (0.967). Nanyang City (0.920) is well below the average level, and the rest of the cities are slightly below the average level. Total factor productivity is less than 1, indicating a negative growth.

In terms of technical efficiency, Hebi (1.001) is more than 1, Jiyuan is 1. The maize planting technical efficiency in these cities is relatively effective, the resources are fully utilized, the input and output are in the best allocation state. Xinxiang, Jiaozuo, Puyang, Xuchang, Luohe, Sanmenxia, Shangqiu and Xinyang are above the average level, Zhoukou (0.969) is close to the average level (0.970), Nanyang (0.920) is far below the average level, and the other cities are slightly lower than the average level. Below average, it indicates that the technical efficiency of maize planting in these areas is relatively ineffective, resources are not fully utilized, input and output allocation is unreasonable, and efficiency is low, so it needs to be improved.

In terms of technological progress, Zhengzhou, Luoyang, Pingdingshan, Anyang, Hebi, Xinxiang, Jiaozuo, Puyang, Xuchang, Luohe, Sanmenxia, Nanyang, Shangqiu, Zhoukou, Zhumadian is above the average level (0.997), indicating that these areas are in the leading level of Henan Province in the field of propaganda and application of advanced technology. The technological progress change indicators in other cities are lower than the average level, which indicates that these cities should strengthen the propaganda and application of advanced technology.

Among the 18 cities studied, 6 cities have scale efficiency values greater than 1. These cities have diminishing returns on scale, which should reduce the input of factors and avoid unnecessary waste to achieve the optimal scale. The scale efficiency value of Jiyuan is 1, which is in the optimal scale, while the remaining cities have a scale efficiency value of less than 1, in the case of increasing returns to scale, the input of factors should be increased to achieve optimal scale.

The pure technical efficiency of Hebi, Jiaozuo and Jiyuan is 1. The maize planting is in a technically effective state, and there is no input and output slack. The pure technical efficiency of the other areas is not equal to 1, indicating that the maize planting in these areas is in a technically inefficient state. There are different degrees of input and output irrational, and the input and output should be adjusted based on the effectiveness of DEA to achieve technical effectiveness.

If the comprehensive technical efficiency of maize in the cities of Henan Province is the best, the average yield of maize in 2016 can be increased by 176.099 kg/hm^{2}, and in 2006, the yield of maize can only increase by 107.978 kg/hm^{2}, which fully reflects the improvement of maize production technology in Henan Province in recent years.

In addition, there are some relaxations in the input factors of maize in Henan Province. If the technical efficiency is optimized while maintaining the same output, the input of factors can be saved to a certain extent.

Input of the number of maize producers

In 2006, the number of slack people engaged in maize production in Henan Province is 257170, but by 2016 it had fallen to 161640. This shows that the phenomenon of surplus labor input in Henan Province has been effectively alleviated, mainly because of the progress of science and technology, and the improvement of the mechanization level of maize production, which led to the accumulation of labor to the secondary and tertiary industries, thus reducing the slack in the production labor of maize. This is consistent with the research by Zhang Lina et al. [

Input of effective irrigation area and sowing area

The effective irrigation area of maize is 50.123 thousand hectares in 2006 and 37.855 thousand hectares in 2016, which indicated that the irrigation facilities of maize are fully and reasonably used, and the amount of relaxation is reduced. The maize sowing area increased from 8.911 thousand hectares in 2006 to 9.250 thousand hectares in 2016.

Input of chemical fertilizer application

The relaxation rate of chemical fertilizer application is 5511.475 tons in 2006 and increased to 7588.712 tons in 2016. This indicates that with the improvement of science and technology, the use cost of chemical fertilizers is lower, and the use of chemical fertilizers is gradually increasing, resulting in increased relaxation of chemical fertilizer application.

Input of total mechanical power

The total power input of agricultural machinery increased from 21.495 kilowatts in 2006 to 21.784 kilowatts in 2016, mainly due to the improvement of mechanization level and the increase in machinery investment in Henan Province, which resulted in a certain amount of relaxation in the total power of agricultural machinery.

From 2006 to 2016, the relaxation of various inputs in Henan Province is in an optimized state, mainly due to the advancement of science and technology, which resulted in a certain cost savings for maize production in Henan Province. It is of great significance to increase the enthusiasm of farmers to grow grain and ensure national food security.

In this paper, considering the effect of other factors on maize yield, the HP filter method is used to deal with the actual yield of maize, and the trend yield corresponding to the input of maize is obtained. The DEA Malmquist index method is used to analyze the efficiency of maize production in 18 cities of Henan Province from 2006 to 2016. The results show that: From the time dimension, the comprehensive technical efficiency change, the technological progress change, the pure technical efficiency change, the scale efficiency change and the total factor productivity change have not improved. From the perspective of spatial dimension, the total factor productivity of maize in all cities is less than 1, which is in the declining stage, showing negative growth, mainly because the production technology of each area is not reasonable and fully utilized. There is a certain degree of relaxation in the input and output of maize production factors, but the relaxation of input in 2016 is better than that in 2006, mainly due to the advancement of technology and the improvement of mechanization level. Strengthen the research and development and promotion of advanced agricultural technology, rationally adjust the allocation of production factors, improve the production efficiency of maize in Henan Province through technological progress and efficiency improvement, and ensure the food security of the country.

The authors are grateful to anonymous referees for their helpful and constructive comments on this paper. The work is supported by the Soft-science Foundation of Henan Province (172400410015), and the Philosophy and Social Program of Henan Province (2016BJJ022).

The authors declare no conflicts of interest regarding the publication of this paper.

Li, B.J. and Zhu, X.X. (2018) Analysis of Maize Production Efficiency Based on DEA-Malmquist Indexes: A Case Study of Henan Province. Journal of Agricultural Chemistry and Environment, 7, 176-187. https://doi.org/10.4236/jacen.2018.74015