Determinants and Differences of Grain Production Efficiency Between Main and Non-Main Producing Area in China

Abstract

This paper investigated the determinants, especially labor transformation, and differences of technical efficiency between main and non-main grain-producing area in China based on a panel data from 30 provinces in the period of 2001–2017. Stochastic frontier production function was used to estimate the level of technical efficiency and the marginal productivity of different inputs. The estimated results showed that land is the most important factor to improve China’s grain output, followed by fertilizers, labor, and machinery inputs. There was a significant 4.6 percent gap of production efficiency between main and non-main producing provinces. Influence of rural labor transformation was confirmed to be positive to improve technical efficiency.

1. Introduction

In the last two decades, benefited by the intensive use of traditional production input resources and improvement of production efficiency, China’s grain production output has achieved remarkable and successive growth. However, as the largest developing country with 1.4 billion population, satisfying food self-sufficiency and maintaining a substantial raise of total grain output is still under threat. Firstly, rapid industrialization and urbanization bring about the transformation of the rural labor force to the non-farm sector, which contributes to the decrease of the agricultural labor force in quantity and quality and the rising labor costs. Secondly, urban development requires a more proportion of fertile land, which implies that agriculture development is more severely constrained by limited land resources and it is not sustainable to increase grain production by expanding grain sown area. Thirdly, with the improvement of living standard, people have new demand of grain with higher quality and more quantity, the traditional way to facilitate grain output increase by adding input factors; however, failed to meet the long-term object. Lastly, the increase of fertilizer input not only weakens soil fertility but also results in serious damage to China’s rural environment. Therefore, raising the technical efficiency of grain production would be a thoughtful way to ensure food security.

Technical efficiency refers to the capacity of an economic unit to improve output as much as possible with limited resources. In this empirical study, technical efficiency was measured by the comparison of actual output to the possible maximum output of each economic unit obtained by frontier function with constant inputs. Thus, an inferior actual output to the estimated output denoted that the production practice of this economic unit was inefficient. As technical efficiency contributes a sustainable way to improve production output, researchers have conducted an in-depth study on this issue. Previous studies on China’s grain production efficiency were mainly focused on the early 21 century, and most of these studies attempted to measure technical efficiency with different methods and analyze the determinants of production efficiency based on farm practice at that time [1,2,3]. However, analysis of technical efficiency does not give a promising picture of China’s grain production. As China’s grain production has experienced a remarkable development over the years, these earlier studies are not able to reveal the new situation of China’ s production practice.

By collecting and combining numerous documents, we found that studies on the technical efficiency of agriculture fall on two parts. Part 1, all the studies concentrate on the calculation of technique efficiency by different methods [4,5] and the measurement of the proportion of technical efficiency to total factor productivity [6,7]. Ataboh used a stochastic frontier analysis (SFA) to analyze the determinants of technical efficiency among rice farmers in Kogi State, Nigeria, and the result showed 46 percent inefficiency in rice farmers [8]. Sherzod employed DEA (Data Envelope Analysis) model to study technical efficiency of wheat farms in Samarkand region, and the result presented that the mean value of technical efficiency of wheat-growing farmers were 0.79 and 0.82 under constant return to scale (CRS) and variable return to scale (VRS) assumptions [9]. Large differences are noted when efficiency measures are compared between parametric (SFA) and non-parametric (DEA) methods [10,11]. The econometric results suggest that stochastic frontier models generate lower mean TE estimates than non-parametric deterministic models, while parametric deterministic frontier models output lower estimates than the stochastic approach [12]. Part 2, all the studies concern about the determinants of technical efficiency from different aspects. Tan found that land fragmentation is one of the significant factors affecting technical efficiency of a rice farmer, and a larger average plot size increased TE (Technical Efficiency) [13]. Latruffe investigated the association between subsidies and farm technical efficiency, showing an uncertainty result [14]. Wang noticed the impact of global warming on agriculture and discovered that there was a significant relationship between surface temperature and grain production technical efficiency [15].

All the previous studies have, nevertheless, made a solid foundation on the selection of measuring methods and determinants of grain production technical efficiency for this research. While most of the researches concern about technical efficiency from aspects of natural conditions and economic development, few studies have noticed that rapid urban development has an impact on production efficiency by transforming rural labor force to the non-farm sector. One exception can be found in Pakapon [16], but they only considered the impact of age structure on technical efficiency and neglected the direct influence of labor outflow on technical efficiency. In this regard, this current paper differed from others in two major respects. Firstly, apart from investigating technical efficiency from the aspect of natural conditions and economic development, we added rural labor outflow as a key driver of technical efficiency. Secondly, we noticed the distinction of technical efficiency between main and non-main production areas in China. In other studies, the grain production practice of whole nation or provinces is the research object. However, according to the data from National Bureau of Statistics (NBS) of China, the total grain output of the whole nation in 2017 was 660.43 million ton, and the total grain output of 13 main grain production provinces was 521.38 million ton, which accounts for 78.95 percent of China’s grain output. There is a wide gap in the productivity between main and non-main production area in China.

Differences in grain output between main and non-main production area are reasonable and explainable. The main grain-producing area is defined by Chinese official based on the provincial comprehensive natural conditions. Most of these 13 provinces are located in plain or shallow hilly areas, with humid or semi-humid climate, abundant rainfall, good conditions of solar light, heat, and water resources, which are suitable for crop growth. Moreover, China’s grain production subsidy policy is more inclined to main grain production areas. Since the year 2004, the whole 13 main grain-producing provinces have implemented direct grain subsidies, while the others have implemented direct subsidies only for main grain-producing counties. Besides, the amount of subsidization in the main production province is higher than that of non-main grain production provinces. Thus, natural condition and government support on main grain producing areas contribute to a higher grain output. But how about technical efficiency? What kinds of factor contribute to this gap? What can we do to narrow this gap and to improve technical efficiency?

To help policymakers to identify the target areas for future improvement efforts, this paper estimated production efficiency by a stochastic frontier production function based on a panel data from 30 provinces in the period of 2001–2017. The purpose was to analyze the main determinants of China’s grain production efficiency, especially labor transformation, and the level of technical efficiency in particular areas. Thus, we were able to identify the potential areas to improve production efficiency and the direction of efforts to strike on. Meanwhile, output elasticities of each input factors were estimated by frontier function. Based on the information above, we could suggest to what area the input factors could expect an ideal output increase in a more sustainable way.

The rest of the paper was organized into four parts. Part 1 presents the model and data. Part 2 reports the empirical results and analyzes the elasticity of production factors. Part 3 discusses the determinants and differences of technical efficiency, and part 4 concludes.

2. Materials and Methods

Stochastic frontier production function has been used extensively to analyze technical efficiency since it was proposed by Aigner et al. [17] and Meeusen and van den Broeck [18]. It later was extended and applied in various areas. This paper adopted the single-stage estimation approach, proposed by Battese and Coelli [19], which can estimate technical efficiency and the determinants of its inefficiency in a simultaneous estimation procedure. The general form of the model for grain production is specified as:

$$Y_{it}={\beta }_0+\beta X_{it}+(V_{it}-U_{it})$$

(1)

where $Y_{it}$ is the production output; i and t denote the i^th province and t^th year. $X_{it}$ is a column vector of input variables. ${\beta }_s$ are the unknown parameters. $V_{it}$ is the error component representing statistical noise, such as weather and measurement error, and is assumed to follow a normal distribution with mean zero and variance ${\sigma }_v^2$; $U_{it}$ is the error component capturing systematic influences, which are attributed to the effect of technical inefficiency, and is assumed to follow a truncated normal distribution with mean $u_i$ and variance ${\sigma }_u^2$. Based on the stochastic frontier, we obtained, from the production function, that the technical efficiency of each province could be measured, and a function to analyze the determinants, which affect technical efficiency, is shown in Equation (2).

$$U_{it}={\delta }_0+\delta Z_{it}$$

(2)

where Z_it is a column vector of efficiency determinants, ${\delta }_s$ are the unknown parameters to be estimated. These parameters denote the impacts of variables in Z on technical inefficiency. Attention should be paid that a negative value in $\delta$ suggests a positive influence on technical inefficiency.

The technical efficiency index can be calculated as:

$$T{E}_{it}=\frac{E(Y_{it}|u_{it},X_{it})}{E(Y_{it}|u_{it}=0,X_{it})}=\exp (-U_{it})$$

(3)

where the numerator represents the actual grain output of i^th province in year t; the denominator represents the maximum possible grain output under current input circumstance, which means no inefficiency exists. Different from previous studies, which rely on Cobb-Douglas (C-D) function form, this paper adopted a flexible translog specification, and the estimated result was examined suitable for Chinese grain production. With four conventional inputs, the translog production frontier can be calculated as:

$$\begin{array}{l}\ln Y_{it}={\beta }_0+{\beta }_a\ln A_{it}+{\beta }_f\ln F_{it}+{\beta }_l\ln L_{it}+{\beta }_{t}T+{\beta }_{am}\ln A_{it}{M}_{it}+{\beta }_{af}\ln A_{it}\ln F_{it}\\ +{\beta }_{al}\ln A_{it}\ln L_{it}+{\beta }_{mf}\ln M_{it}\ln F_{it}+{\beta }_{ml}\ln M_{it}\ln L_{it}+{\beta }_{fl}\ln F_{it}\ln L_{it}\\ +1/2{\beta }_{aa}{(\ln A_{it})}^2+1/2{\beta }_{mm}{(\ln M_{it})}^2+1/2{\beta }_{ff}{(\ln F_{it})}^2\\ +1/2{\beta }_{ll}{(\ln L_{it})}^2+MP+(V_{it}-U_{it})\end{array}$$

(4)

where all the variables are natural logarithms. Y is total grain output, which is measured in ten thousand tons; A is total grain sown area, which is measured in thousand ha; M, F, and L are, respectively, defined as total machinery input (in million kilowatts), total fertilizer input (in ten thousand tons), and total labor input (in ten thousand people) in grain production. Due to the data on machinery, fertilizers and labors in grain production are not directly available from the Chinese official statistical sources; thus, we derived the data required with a special procedure [20]. Specifically, M and F were derived from the total power of agricultural machinery and pure contents of fertilizers for agriculture production by the proportion of total grain sown area to total crop sown area, respectively. L was derived from the total labor input in the primary industry employees, where we could obtain labor input of agriculture production from the agriculture value shares in the total output value of agriculture, forestry, animal husbandry, and fishery. Then, the labor input in grain production could be subtracted from the labor input of agriculture production in terms of the proportion of total grain sown area to total crop sown area. MP is a dummy variable, which stands for the main grain-producing province. When it comes to a main grain-producing province, the value of MP was 1, otherwise 0. This variable was set to investigate whether the main grain-producing provinces had higher technical efficiency. Apart from conventional inputs, time-trend variables (T) were included to account for technical progress.

According to the theoretical model (2), the specific model to measure determinants, which affect technical inefficiency, is given in Equation (5).

$$U_{it}={\delta }_0+{\delta }_{1}Per\_A{P}_{it}+{\delta }_{2}Out\_L_{it}+{\delta }_{3}AF{E}_{it}+{\delta }_{4}IR{R}_{it}+{\delta }_{5}D{I}_{it}+{\delta }_{5}D{I}_{it}+{\delta }_{6}Per\_GD{P}_{it}+{\delta }_{7}MC{I}_{it}$$

(5)

Given available data, we selected seven factors in the inefficiency function that might explain the inter-province and inter-period differences in technical efficiency. Per_AP is an agricultural product per capita of each province, measured by the ratio of the added value of the primary industry to the primary industry employees. It was expected to be negative to technical inefficiency. Out_L represents labor outflow. Due to data availability, the proportion of primary industry employees to total employment in all industries was used as a proxy of labor outflow, and it was assumed to have a positive effect on inefficiency. AFE stands for the share of agriculture financial expenditure in the general budget expenditure of each province. It suggested the government’s financial support on regional agriculture development and was expected to be negative to inefficiency. IRR is the effective irrigation rate, which is measured by the share of effectively irrigated area in total cultivated land area, and was assumed to have a negative effect on inefficiency. The disaster index (DI), is defined as the areas hit by natural calamities to the total crop sown area. It suggested the vulnerability of grain production to poor weather condition and was speculated to have a positive impact on inefficiency. Per_GDP, gross domestic product per capita in each province, was set to measure the impact of regional economic development to technical inefficiency and was assumed to have a negative relationship with inefficiency. Multiple crop index (MCI), stands for the ratio of the total crop sown area to total area under cultivation.

This paper would utilize Chinese provincial average statistical data from 2001 to 2017. Due to data availability, Hong Kong, Macau, Taiwan, Tibet were not included in the research sample. Apart from the primary industry employees, the data of all four conventional input variables and AFE, Per_GDP, and disaster area were obtained from the National Bureau of Statistics (NBS) of China. The values of the rest of the variables were obtained from their respective provincial statistical yearbook of China. To eliminate the effects of price changes, Per_GDP was deflated by the consumer price index of each province on a 2001 basis. It is worth to mention that this paper adopted a five-year moving average method to fill the blank of missing data.

The summary statistics of all variables required are presented in

Table 1. Mean value of grain output, explanatory variables by year by area.

Year	Area	Grain Output (10 kt)	Sown Area (000 ha)	Machinery Input (10 kW)	Fertilizer Use (10 kt)	Labor Input (10 kn)
2001	Non-main	752.17	1969.13	609.86	50.39	295.00
	Main	2490.66	5569.68	2066.84	152.22	631.75
	Total	1505.52	3529.36	1241.22	94.51	440.93
2006	Non-main	754.78	1721.53	730.24	55.20	248.64
	Main	2832.63	5809.24	2843.58	182.80	543.56
	Total	1655.18	3492.87	1646.02	110.49	376.44
2011	Non-main	800.34	1841.11	963.46	64.51	216.75
	Main	3340.12	6084.93	3820.98	208.25	484.02
	Total	1900.91	3680.10	2201.72	126.80	332.57
2016	Non-main	867.47	1843.48	917.25	67.62	203.61
	Main	3598.19	6270.18	3845.68	218.82	451.77
	Total	2050.78	3761.72	2186.24	133.14	311.15
2017	Non-main	818.58	1709.89	913.73	65.75	204.28
	Main	4010.62	6825.79	4153.60	226.40	481.58
	Total	2201.80	3926.78	2317.68	135.36	324.44
The growth rate between 2001 and 2017
2001–2017	0	8.83	−13.16	49.83	30.49	−30.75
	1	61.03	22.55	100.96	48.73	−23.77
	Total	46.25	11.26	86.73	43.22	−26.42

Note: Classification of provinces into the main grain-producing area is in Table 2. “Non-main” stands for the mean value of non-main producing area, and “Main” stands for the mean value of the main producing area. T = ton, ha = hectare, W = watt, n = number of work. Sources: National Bureau of Statistics (NBS), Chinese Statistical Yearbook (2002–2018).

. During 2001–2017, grain output in China grew by 46.25 percent. However, the non-main grain production area only contributed to 8.83 percent of grain output growth in this period. The growth rate in the 13 main grain production provinces was 61.03 percent. According to the preliminary analysis of the table, what contributed to such huge difference in growth rate of grain output was mainly the decline of grain sown area in non-main grain production area, the double growth rate of machinery input (49.83 percent in the non-main grain production area as compared to 100.96 percent in the main grain production provinces), and higher fertilizer use in main grain production area (30.49 percent in the non-main grain production area as compared to 48.73 percent in the main grain production provinces). The classification of main and non-main grain production provinces is based on Chinese official definition, and the classification is provided in

Table 2. Classification of provinces into the main grain production area.

Main Grain Production Area		Non-main Grain Production Area
Province	Abbreviation	Province	Abbreviation	Province	Abbreviation
Hebei	HEB	Beijing	BJ	Chongqin	CQ
Inner Mongolia	IM	Tianjing	TJ	Guizhou	GZ
Liaoning	LN	Shanxi	SX1	Yunnan	YN
Jilin	JL	Shanghai	SH	Shaanxi	SX2
Heilongjiang	HLJ	Zhejiang	ZJ	Gansu	GS
Jiangsu	JS	Fujian	FJ	Qinghai	QH
Anhui	AH	Guangdong	GD	Ningxia	NX
Jiangxi	JX	Guangxi	GX	Xinjiang	XJ
Shandong	SD	Hainan	HN
Henan	HEN
Hubei	HUB
Hunan	HUN
Sichuan	SC

Note: Classification of provinces into main grain production is according to State Administration of Grain (SAG).

.

3. Results and Discussion

This paper adopted a computer program FRONTIER (Version 4.1) (developed by Tim Coelli, Centre for Efficiency and Productivity Analysis, School of Economics, University of Queensland.Brisbane, QLD 4072, Australia) [21] to estimate Equations (4) and (5) in a simultaneous way. The results are presented in

Table 3. Results of the production frontier and inefficiency function.

Variables	Estimated Coefficients	Standard-Error	T-Values
Production Function
Constant	−6.204 ***	0.527	−11.765
Ln(A)	3.124 ***	0.253	12.370
Ln(M)	1.191 ***	0.190	6.256
Ln(F)	−4.056 ***	0.319	−12.724
Ln(L)	0.964 ***	0.230	4.200
T	0.009 ***	0.001	6.304
Ln(A) * Ln(M)	−0.559 ***	0.070	−8.018
Ln(A) * Ln(F)	1.145 ***	0.087	13.221
Ln(A) * Ln(L)	−0.585 ***	0.089	−6.566
Ln(M) * Ln(F)	0.147 ***	0.052	2.823
Ln(M) * Ln(L)	0.338 ***	0.046	7.431
Ln(F) * Ln(L)	−0.373 ***	0.050	−7.434
0.5 * Ln(A) * Ln(A)	−0.028	0.110	−0.257
0.5 * Ln(M) * Ln(M)	0.080	0.057	1.411
0.5 * Ln(F) * Ln(F)	−0.860 ***	0.086	−9.945
0.5 * Ln(L) * Ln(L)	0.543 ***	0.084	6.477
MP	0.201 ***	0.021	9.594
sigma-squared	0.011 ***	0.001	10.369
gamma	0.747 ***	0.060	12.517
Inefficiency Function
Constant	0.126 *	0.071	1.777
Per_AP	−0.093 ***	0.020	−4.745
Out_L	0.512 ***	0.110	4.657
AFE	0.514 *	0.264	1.946
Per_GDP	0.015 **	0.006	2.543
IRR	−0.395 ***	0.064	−6.204
DI	0.625 ***	0.078	7.983
MCI	−0.031	0.032	−0.941

Notes: These results are obtained by using Frontier 4.1, developed by Coelli [21]. The dependent variable is total grain output. ln(A), ln(M), ln(F) and ln(L) are, respectively, defined as total grain sown area, total machinery input, total fertilizer input, and total labor input in natural logarithms. MP is a dummy variable, which stands for the main grain-producing province. The negative coefficient in the inefficiency function represents a positive effect on technical efficiency and vice versa. “*” indicates the parameter was significant at 10% significance level, “**” for 5%, and “***” for 1%.

. We firstly examined the applicability of stochastic frontier production function to China’s grain production to ensure the credibility of estimated results. In other words, whether technical inefficiency existed in the grain production in China was examined. The tests of the hypothesis involving the parameters are provided in

Table 4. Tests of Hypothesis in the production model.

Diagnosis Statistics	Null Hypothesis	LR	Degree of Freedom	χ-Value	Decision
Testing the applicability of SFA	H0: γ = 0	397.25 *	9	16.919	Reject
Testing translog vs. C-D	H0: βaa = βmm = βff = βll = βam = βaf = βal = βmf = βml = βfl = 0	262.34 *	9	16.919	Reject
Testing technical change	H0: βt = 0	140.80 *	9	16.919	Reject

Notes: “*” indicates the parameter is significant at 10% significance level. LR: likelihood ratio; SFA: stochastic frontier analysis; C-D: Cobb-Douglas.

.

Apart from ${\beta }_{aa}$ and ${\beta }_{mm}$, all the estimated coefficients in the production function are significant at the five percent critical level. According to t-ratio of the value of $\gamma$, technical inefficiency does exist in China’s grain production, for the value of $\gamma$ significantly different from zero. We reconfirmed the applicability of SFA by LR (likelihood ratio) test; the result rejected the null hypothesis $\gamma =0$ as well. This, in turn, implied that traditional production function, which does not take technical inefficiency into consideration, is not suitable to analyze China’s grain production practice. Moreover, the coefficient of the time trend in frontier production function was significantly positive, indicating the production frontier shift of 0.9 percent per year. Further, the LR test for the applicability of translog form against C-D form rejected the null hypothesis. Thus, earlier research on China’s grain production with C-D function might not explain China’s grain production practice correctly.

As the model was estimated by translog function, respective elasticities of inputs with respect to total grain output had to be measured with a special procedure, which is calculating the derivative of the corresponding input variable in the production function. Tabulated in

Table 5. The elasticity of production factors by year.

Total	Land	Machinery	Fertilizer	Labor
2001	0.627	−0.125	0.194	0.169
2002	0.639	−0.122	0.182	0.170
2003	0.700	−0.138	0.182	0.138
2004	0.749	−0.135	0.153	0.119
2005	0.752	−0.138	0.161	0.114
2006	0.733	−0.095	0.087	0.162
2007	0.780	−0.111	0.098	0.129
2008	0.804	−0.131	0.126	0.101
2009	0.779	−0.122	0.123	0.119
2010	0.761	−0.113	0.116	0.135
2011	0.781	−0.123	0.128	0.118
2012	0.778	−0.117	0.118	0.126
2013	0.795	−0.118	0.111	0.118
2014	0.790	−0.116	0.110	0.124
2015	0.776	−0.114	0.115	0.133
2016	0.843	−0.131	0.111	0.086
2017	0.800	−0.109	0.088	0.128
average	0.758	−0.121	0.130	0.129

Notes: The elasticity, of production factors, was calculated by multiplying the partial derivatives of each input variables from frontier production function by the mean value of respective inputs by year. Elasticity means one extra unit of input would bring about the value of elasticity’s change to total grain output.

are input elasticities evaluated at the means of the variables.

The elasticities of various inputs differed from each other in trend and presented different importance to China’s grain production. According to the estimated elasticity, the land was the most important factor of grain production (0.758), followed by fertilizers (0.130) and labor (0.129). The elasticity of machinery inputs (−0.121) was small and displayed negative. However, this finding was different from what Jiang concluded by studying the grain technical efficiency in the Jiangsu province, that machinery inputs would increase grain output, while labor inputs would bring about the decline of grain output [4]. Apart from the possible data issue, for example, due to the phenomenon of farmers renting agricultural machinery from others that widely happens in farm practice, there may be a duplication of statistic data on total power of agricultural machinery, causing an illusion that agricultural machinery input in China’s agriculture practice is surplus; another possible reason that should be noted is that the development of China’s mechanization in grain production, which is meant to cut the rising production cost, starts in the early 21 century. Thus, the substitution of machinery to rural labor has a limited effect on improving grain output. Consequently, low or even negative elasticity of machinery inputs is expected.

To present the disparity in the elasticity of different inputs between main and non-main grain-producing area, we calculated their elasticity based on the estimated result of the production function, respectively. The details are presented in Figure 1. Generally, all the importance of production factors in the main grain-producing area was consistent with the whole nation, while the elasticity of labor was higher than a fertilizer in non-main grain-producing area. The average elasticity of land in the main grain-producing area was higher than the other. This, in turn, implied that a higher grain output could be expected when increasing grain sown area in the main grain-producing area. Moreover, the average elasticity of fertilizer was greatly higher in the main grain-producing province than the other. This finding suggested that fertilizer application to grain production had a great contribution to the 61.03 percent growth rate of grain output in the period of 2001–2017 in the main grain-producing area of China. With a low and even negative elasticity in recent years of fertilizer, the increasing fertilizer application in non-main grain-producing area would have limited or negative effect on improving grain output. As for the elasticity of labor, there was a descending trend over the years in the main grain-producing area and the whole nation, while it seemed stable in the non-main grain-producing area. The marginal productivity of labor in non-main grain-producing area was reported positive and higher than the whole nation, while it turned out to be negative in the main grain-producing area, suggesting that there is a serious redundancy of labor input in main grain-producing area.

Based on the results above, it is obvious that the utilization of labor and machinery to improve grain output in the main grain-producing province is not very promising under current farming practices. Application of more fertilizer and land could offer reasonable returns, but this is not so in the case of non-main grain-producing area. Further increase of land and labor inputs might be justifiable to improve grain output, while a higher proportion input of machinery and fertilizer in grain production would not promise a reasonable return.

Determinants and Differences in Technical Efficiency

The result of technical efficiency is reported in

Table 6. Production efficiency level by main and non-main grain-producing area.

Year	Non-Main Grain-Producing Area	Main Grain-Producing Area	Nation	Gap of Technical Efficiency
2001	0.746	0.769	0.756	0.023
2002	0.753	0.796	0.771	0.043
2003	0.772	0.766	0.770	−0.006
2004	0.791	0.828	0.807	0.037
2005	0.786	0.838	0.808	0.053
2006	0.799	0.838	0.816	0.039
2007	0.801	0.829	0.813	0.028
2008	0.814	0.872	0.839	0.058
2009	0.816	0.836	0.824	0.020
2010	0.809	0.860	0.831	0.052
2011	0.827	0.900	0.858	0.073
2012	0.844	0.911	0.873	0.067
2013	0.843	0.914	0.874	0.071
2014	0.847	0.901	0.870	0.053
2015	0.852	0.919	0.881	0.067
2016	0.852	0.902	0.874	0.051
2017	0.858	0.916	0.883	0.058
Average	0.812	0.858	0.832	0.046

. As shown in the table, we could easily find that the variations of production efficiencies between main and non-main grain-producing area were remarkable. Overall, the mean efficiency of the whole nation was 0.812, and the production efficiency of the main grain-producing provinces was 0.858, which was 0.046 higher than the non-main grain-producing province. Also, the production efficiencies of both area and the whole nation were found to be increased with years. During the period of study, the production efficiency of non-main grain-producing area rose from 0.746 to 0.858, meaning technical efficiency rose by 15.03 percent in the sample year; and in the main grain-producing area, efficiency rose from 0.769 to 0.916, contributing to 19.11 percent increase in technical efficiency. This might reflect the fact that significant changes in China’s grain production management practice had occurred over 2001–2017.

As for the disparity of technical efficiency between main and non-main grain-producing area, we found that the gap between them presented a rising trend over the years. For more detailed information, the growth path of this gap performed like an inverted ‘U’, which increased from 2001 to 2011, and when it attained the highest point, it decreased from 7.3 percent in 2011 to 5.8 percent in 2017. This implied a decreasing trend of the technical efficiency of the gap in the future. In general, both the rising scope and rising speed of technical efficiency in the main grain production area were higher than the other. Without doubt, one of the reasons, which contributed to this, was the benefits of natural condition on main grain-producing areas. Moreover, as the main grain production area plays a vital role in food security, the government puts more emphasis on this area and naturally leads to more government support on financial expenditure, new technical spread, and application.

To find out the determinants, which contribute to the disparity of production efficiency, we selected seven factors to estimate the inefficiency function. According to Table 3, technical inefficiencies were well explained by the explanatory variables in inefficiency function. Apart from multiple crop index, all other six variables had a significant impact on technical efficiency. The agricultural product per capita of each province (Per_AP_it) was founded to have a negative effect on inefficiency, which, in turn, means a higher agricultural product in a region and more efficient farming practice could be expected. As presented in Table 2, Per_AP of the whole nation increased from 0.54 percent to 2.50 percent, rose by 365.18 percent, contributing to the increment of production efficiency of the whole nation. Moreover, Per_AP in the main grain-producing province was 1.559 percent, which was 0.121 percent higher than the non-main grain-producing province. This was in line with our results, suggesting that higher Per_AP contributed to greater technical efficiency.

Labor outflow (Out_L_it) has been reported to have a positive relationship with technical inefficiency that is consistent with our expectation. A higher share of primary industry employees in total employment of all industry represents a lower degree of transformation of the rural labor force, which, in turn, implies a great technical inefficiency. This suggests that the transformation of the rural labor force does a great favor to technical efficiency. As shown from the descriptive statistics, the share of primary industry employees in total employment of all industry was dropped from 49.3 percent to 33.1 percent, which was dropped by 32.86 percent. This finding demonstrated that the greater degree of rural labor force outflow, the higher production efficiency would achieve. Especially, this result was consistent with the low and even negative elasticity of labor in the main grain production area. The negative marginal output of labor denotes that surplus labor exists in the main grain production area, and speeding up the labor outflow in this area could achieve higher technical efficiency.

Effective irrigation rate (IRR_it): the share of effectively irrigated area in the total cultivated land area was assumed to have a negative impact on inefficiency, and the empirical result confirmed our assumption. It suggested that a high effective irrigation rate contributed to the improvement of technical efficiency in grain production. From 2001 to 2017, the effective irrigation rate rose 6.72 percent for the whole nation, 4.86 percent and 9.20 percent, respectively, in the non-main and main grain-producing province. This justifies the fact that grain production efficiency is relatively higher in the region with higher effective irrigation rate. Multiple crop index (MCI_it) was found to have a negative effect on technical inefficiency, although insignificant in a statistical way. Thus, we could assume that areas with higher cropping index tend to have greater technical efficiency, for the reason that high cropping index represents better climate condition and farming facilities, a view shared by Yao [2].

In reverse, the disaster index (DI_it), which reflects the extent of vulnerability to natural calamities, produced a significantly positive effect on production inefficiency, indicating that areas with a lower disaster index tend to be more efficient. With the perfection of the disaster prevention system, the disaster index was reduced from 20.6 percent to 5.70 percent during the year of study, which was powerful evidence of our research result. The share of agriculture financial expenditure in the general budget expenditure of each province (AFE_it) was found to have a positive influence on technical efficiency, which was opposite to our assumption. Normally, higher financial support in agriculture means more capital input to agricultural business, suggesting an investment effect could be achieved through relaxing financial constraints, and a higher technical efficiency would be expected. However, the statistical result is not the case. One reason might be the lack of government supervision on financial expenditure. According to the statistical yearbook of China, the content of agriculture financial expenditure is divided into four parts: expenditure on policy-related subsidies, expenditure on capital construction, expenditure for three special items of science and technology promotion, and expenditure for relief funds in rural areas. The result of the complicated mixed financial support to promote technical efficiency has not been confirmed. Different type of financial expenditures may have a different association with production efficiency. Evidence can be found in the article of Latruffe [14], whose results showed that the effect of subsidies on technical efficiency might be positive, null, or negative.

Another unexpected result was the coefficient of Per_GDP_it, which turned out to be positive and statistically significant to inefficiency. One reasonable explanation is that high Per_GDP showed a great economic development situation of regions. However, economic development may have a certain negative impact on agricultural production, such as the occupation of agricultural land by non-agricultural industry development. Moreover, the share of agriculture in the total regional economy in the developed area is lower than the other, and the development of agriculture maybe not taken seriously in economically advanced place. Thus, a negative effect on technical efficiency of grain production is possible.

Consequently, to improve grain production technical efficiency in China and narrow the efficiency gap between non-main and main grain production area, effective measures can be considered from improving agricultural product per capita, encouraging labor transfer from agriculture to secondary and ternary industries, and enhancing effective irrigation rate. To some extent, the rising multiple crop index contributes to higher production efficiency. Moreover, improving the ability of the agricultural system to prevent grain production from disasters, such as strengthen the construction of irrigation and water conservancy, perfect irrigation and drainage system, is beneficial to enhance technical efficiency of grain production. The reinforcement of agriculture insurance work is also conductive to efficiency improvement by reducing production losses caused by natural disasters.

According to the previous study, the differences in production efficiency between main and non-main grain-producing area do exist in China’s grain production. To explore the provincial differences of technical efficiency, we plotted a chart of inter-provincial technical efficiency differences by Arcgis, as presented in Figure 2. We used dots to identify the main grain-producing provinces. Obviously, except Inner Mongolia, the production efficiency of the most main grain-producing province is relatively higher than the other. This seems to suggest that the current distribution of the main grain-producing province in China is justified as far as production efficiency is concerned. Among all the main grain-producing provinces, Hunan, Shandong, Jiangsu are very close to the frontier. Inner Mongolia is the only province that may have great potential for efficiency improvement, followed by Liaoning, Jilin, Hebei, Anhui, Hubei, Sichuan.

Other provinces with a high level of technical efficiency include Guangdong, Fujian, Zhejiang, Shanghai, Beijing, Tianjin, Xinjiang. Most of these efficient producers are located in the south-east part of China, economically advanced region. In reverse, provinces with inferior technical efficiency are located in north-west or south-west of China. This may have something to do with topographic influences.

4. Conclusions

In this paper, the empirical application of translog stochastic frontier production function was used to analyze the determinants and differences of technical efficiency between main and non-main producing area in China. Our results implied that land is the most important factor to improve the output of grain, followed by fertilizers, labors, and machinery inputs. In other words, higher grain output improvement could be expected when increasing one unit of land input than capital and labor input. Moreover, the marginal products of the land in the main grain-producing area were higher than the other, implying that a higher grain output could be expected when increasing grain sown area in the main grain-producing area. However, due to the limitation of land resources, China is unlikely to increase the output of all crops by expanding the sown area, but the optimal allocation of land resources among different crops could be achieved through structural adjustment, and land consolidation was approved to be effective in improving technical efficiency [22]. With a low and even negative elasticity of fertilizer, increasing fertilizer application in the non-main grain-producing was not found to be a promising way to improve grain output. This confirmed the grain production reality in China, that huge amounts of fertilizer inputs in grain production have caused enormous waste of resources [23]. The marginal products of labor in the main grain-producing area were reported to be negative, indicating that a serious redundancy of labor input exists in the main grain-producing area. Therefore, speeding up the labor transformation process would be a considerable way to improve production efficiency in the main grain-producing areas.

The average production efficiency of the main grain-producing provinces was 4.6 percent higher than the other, as approved in the article of Zeng [24]. The gap of production efficiency between main and non-main grain-producing provinces showed an expending trend in 2001–2011, while it is presenting a decreasing trend in recent years, implying that the expectation of narrowing the gap could be satisfied. In general, technical efficiency in China’s grain production presents a steady increasing trend over the years and a more balanced spatial development. The average level of technical efficiency of the whole nation was 16.8 percent below the frontier during the sample year, revealing that there is a great potential for grain output increase with relying on the improvement of production efficiency. As the variation of production efficiency across provinces is significant, the development efforts to satisfy China’s grain self-sufficiency should be concentrated on improving technical efficiency in those areas with large potentials, including the main grain-producing areas of Inner Mongolia, Liaoning, Jilin, Hebei, Anhui, Hubei, Sichuan and the non-main grain-producing areas of Shanxi, Shaanxi, Gansu, Guizhou, Yunnan. Effective measures to improve production efficiency and narrow the gap between main and non-main grain production area could be considered from improving agricultural product per capita, encouraging labor transfer from agriculture to secondary and ternary industries, enhancing effective irrigation rate, and improving the ability of the agricultural system to prevent grain production from disasters.