Benefit Analysis of Chemical Fertilizer Input for Staple Grain Production Based on Threshold Panel Data Model

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Graduate School of Chinese Academy of Social Sciences, Beijing 102488, China

Abstract Based on the threshold panel data model, this paper analyzed the nonlinear relationship between chemical fertilizer input and grain output. At the provincial level, from the perspective of average and marginal net benefits, it compared the effects of chemical fertilizer input on farmers’ income. It reached the conclusion that the chemical fertilizer input efficiency has deviated from the optimal level. Thus, only by increasing the marginal productivity of chemical fertilizers, may it be able to increase farmers’ income.

Key words Chemical fertilizer, Threshold panel model, Nonlinear relationship, Net benefits, Productivity

1 Introduction

China is a country with large population but little land. Chemical fertilizer, as a "nutrient solution" for land, plays an important role in increasing grain yield in China. In the past 30 years, the chemical fertilizer input in China’s agricultural production has been increasing. Fig.1 illustrates the relationship between chemical fertilizer input (purity) and total grain growth from 1980 to 2015 taking 1980 as base year. It can be seen that grain yield nearly doubled, while chemical fertilizer input increased by nearly four times. In many provinces, the increase of chemical fertilizer input was greater, such as Jilin and Heilongjiang provinces, the chemical fertilizer input increased by more than six times in the past 30 years. From the perspective of the chemical fertilizer input per hectare, taking the average data of China’s three main staple grain crops (maize, wheat and rice) as an example, there has been no obvious growth trend in the past 20 years, and there have been fluctuations in this period. In 2015, the average yield of chemical fertilizers per hectare of these three kinds of crops was 361.65 kg, which was only 0.45 kg higher than that in 2014, and was 73.05 kg lower than that in 1998. At present, China’s chemical fertilizer input for staple grain per hectare is a stable period, it slowly grows at 340-370 kg/ha. Although the growth rate is low, it is still much higher than the world average (Fig.2). According to the statistics of the Ministry of Agriculture, the consumption of chemical fertilizers in China is 328.5 kg/ha, which is much higher than the world average (9 kg/ha), which is 2.6 times that of the United States and 2.5 times that of the European Union[1].

A method of measuring the input efficiency of a production factor is to divide the output by the amount the input factor. The value obtained can be called the productivity of the factor. We used the partial productivity of similar fertilizers to construct the chemical fertilizer productivity index, namely, the ratio of grain output to chemical fertilizer input, to evaluate the grain yield efficiency of chemical fertilizers. In addition, we calculated the ratio of total grain output value to chemical fertilizer input, reflecting the economic benefits of chemical fertilizer input. Fig.3 depicts the ratio of output and output value of three types of grain crops to chemical fertilizer input per hectare in the past 13 years (taking the price in 2015 as constant price). According to the ratio of grain output to chemical fertilizer input, the chemical fertilizer input required for unit grain output was relatively stable, in other words, the unit productivity of chemical fertilizers was relatively stable. From the point of view of the output value, after experiencing the rise in the first few years, the average output value of chemical fertilizer input started to return to a stable level (about 50 yuan/kg). This indicates that there has been no great change in the overall efficiency of chemical fertilizer input on the increase of grain yield and farmers’ income.

Therefore, through the output elasticity of chemical fertilizers, we try to explore the effects of chemical fertilizer input on economic benefits of farmers. Besides, through the introduction of chemical fertilizer productivity indicators, we try to explore the effects of chemical fertilizer input on economic benefits of grain production through the chemical fertilizer productivity.

Fig.1Relationshipbetweenthechemicalfertilizerinputandthegrainyieldincrease

Fig.2Convertedpureamountofchemicalfertilizerinputperhectareforthreestaplegraincropsin1998-2015

Fig.3Ratioofoutputandoutputvalueofthreestaplegraincropstochemicalfertilizerinput

2 Literature review

Foreign scholars have studied effects of chemical fertilizers on the land productivity long time ago. In the 1960s, countries such as Japan did not have enough agricultural land in the process of agricultural development. With the development of a series of agricultural technologies, especially the promotion and use of chemical fertilizers, the improvement of land productivity made up for the scarcity of land. Cristina Crisostomo David[2]also found that Japan, South Korea and Taiwan in China use a large amount of chemical fertilizers in agricultural production, which has led to a gradual increase in grain yield.

As regards the economic analysis of chemical fertilizer input, Huang Jikunetal.[3]analyzed the effects of chemical fertilizer input and structure on grain yield and economic benefits through constructing a production function between rice and chemical fertilizer use. They found that although chemical fertilizer input may increase the grain yield, it may not necessarily increase the income. Liu Runmeietal.[4]studied the relationship between the amount of chemical fertilizer application and chemical fertilizer productivity in maize of Yunnan Province, and pointed out that with the increase in the chemical fertilizer productivity, the chemical fertilizer productivity decreased with a negative exponential power. Shi Changliangetal.[5]analyzed the excess fertilizer input of staple grain crops through field survey data and national statistics.

3 Model building and data

3.1ModelintroductionIn order to accurately grasp the changes in the effects of chemical fertilizer input on the output at different stages, we selected the panel threshold regression model to explore the elastic change of chemical fertilizer input per hectare output. We carried out the analysis using the panel threshold regression method proposed by Hansen[6]and the panel fixed effect threshold regression method proposed by Wang Qunyong[7]. According to the model proposed by Hansen, the regression model of a single threshold is as follows:

Yit=μ+Xit(qit<γ)+Xit(qit≥γ)+μi+eit

(1)

The test of multiple thresholds is similar to the above.

3.2VariablesanddataIn the process of grain crop planting, the main input factors are labor, machinery, chemical fertilizer, pesticides and seeds. InChinaStatisticalYearbook, there is no data based on the factor input data per hectare, and it is difficult to accurately calculate the effects of chemical fertilizer input. Therefore, we selected the data of per capita input of japonica rice and wheat by region during 2006-2016[9], and used material inputs and capital inputs to represent factor inputs. The main variables include the grain output per hectare (Y) and factor input expressed in capital input (including seeds, machinery and pesticide input). Since the input factors have both material inputs and capital inputs, we adopted kg/ha and yuan/ha to represent the grain output and output value. The data sources are costs of seed, machinery and pesticide per hectare; labor input: the manpower per hectare, calculated by multiplying the number of labor per hectare by 8 h, the unit is the standard labor day; chemical fertilizer input: the amount of chemical fertilizer application per hectare (unit: kg) is also the threshold variable in this study.

The above variables are logarithmized when the model is built, and all capital inputs and prices are processed taking the 2015 value as the base data. In addition, we selected the chemical fertilizer productivity, that is, the ratio of grain output (unit: kg) to chemical fertilizer input (unit: kg) as the threshold value, to evaluate the effects of chemical fertilizer input on the grain output under different fertilizer productivity.

The independent and dependent variables are defined as follows:ydenotes the total output,czdenotes output,seedrefers to seed input,macdenotes the machinery input,nydenotes the pesticide input,fetdenotes the chemical fertilizer input, andlabdenotes the labor input.

4 Empirical test

4.1TestforpaneldataofjaponicariceBy constructing theF-value test, the test results rejected the mixed model. Considering the existence of heteroscedasticity, we used the random effect and fixed effect model tests based on the over-identification test method, the test results also rejected the selection of random effect models, so we adopted the fixed effect model for japonica rice data. The steps for wheat data test are the same as above, and the results are the same, indicating that we can use the method proposed by Wang Qunyong for threshold regression[7].

4.2DeterminationofthenumberofthresholdvariablesAs can be seen from Table 1 and Table 2, if the output is measured in material units, there are two threshold values for both models. If the output is measured in units of capital, there is no threshold in the model of japonica rice, and there are two thresholds in the model of wheat.

Table1Resultsofthethresholdeffecttestofthejaponicariceoutputmodel

Japonica rice outputNumber of thresholdsF valueBS times10% Critical value5% Critical value1% Critical valueY1135.31***30012.659 614.269 822.619 7242.53***30011.427 413.518 317.999 2340.3730061.053 266.780 577.662 0Y2110.223009.944 311.895 916.524 825.7230010.475 112.451 616.936 934.693009.567 010.895 712.880 5

Note:***means significant difference at 1% level, the same in following tables.

Table2Resultsofthethresholdeffecttestofthewheatoutputmodel

Wheat outputNumber of thresholdsF valueBS times10% Critical value5% Critical value1% Critical value Y1175.59***30017.397 234.209 850.690 7281.86***30022.828 526.716 746.464 8356.93300113.954 1122.566 5136.669 6Y2143.51***30017.717 722.569 027.616 9231.04***30011.590 613.929 918.241 8319.7630024.796 426.868 430.993 1

4.3ModelregressionresultsTakingY1as the dependent variable (model 1), we performed the threshold regression on japonica rice data; usingY1andY2as dependent variables (model 2, model 3), respectively, we performed the threshold regression on wheat data, the results are shown in Table 3. From the significance of the coefficients, the simulation effects of the three models are not perfect. However, from the perspective of the overall degree of interpretation of the model and the significance of the threshold variable, the model gave a good explanation of the nonlinear relationship between chemical fertilizer input and grain output. Considering that there are more significant variables in model 4 and the degree of explanation is not much different from that of model 3, so we selected model 1 and model 3 as the analysis objects. In model 1, the two threshold values are 16.709 9 and 21.199 2. When the chemical fertilizer productivity is lower than the first threshold, the chemical fertilizer input elasticity is 0.26. When it is in the range of the two thresholds, the chemical fertilizer input elasticity is 0.29, which is greater than the second threshold, and the chemical fertilizer input elasticity is 0.31. It indicates that when the chemical fertilizer productivity rises from 16.709 9 to 21.199 2, the grain output elasticity will increase by 19%. In model 3, the two threshold values are 9.701 9 and 16.693 4. When the chemical fertilizer productivity is lower than the first threshold, there is no data, so it is impossible to estimate. When it is in the range of the two thresholds, the chemical fertilizer input elasticity is 0.86, which is greater than the second threshold, and the chemical fertilizer input elasticity is 0.90. This also indicates that when the chemical fertilizer productivity rises from 9.701 9 to 16.693 4, the output elasticity of the grain output will increase by 4.7%.

From the perspective of elasticity alone, it is still impossible to know the specific changes in grain output value and material output brought about by 1 kg of fertilizer input under different fertilizer productivity. Thus, we analyzed what the economic benefits of the chemical fertilizers will ultimately give farmers. Based on the above models, we calculated the net income per hectare of chemical fertilizer input under different thresholds and under the same threshold. For the output of material input, the net incomes1is:s1= increase in grain output due to chemical fertilizer input × grain price - input of chemical fertilizer × price of chemical fertilizer; for output of capital input, net incomes2is:s2= increase in grain output due to chemical fertilizer input - input of chemical fertilizer × grain price, then we obtained the marginal net income of fertilizer inputs.

Table3Thresholdmodelregressionresults

Model 1lny1Model 2lny2Model 3lncz2lnseed0.057 2***-0.061 90.008 98(3.01)(-1.06)(0.12)lnmac-0.004 860.06 26***0.117***(-0.62)(2.14)(3.03)lnny-0.012 50.038 70.121***(-0.60)(1.02)(2.42)lnlab-0.083 6***0.044 6-0.010 8(-3.05)(0.91)(-0.17)Threshold variable coefficient 10.257***0.680***-(5.07)(8.05)-Threshold variable coefficient 20.286***0.751***0.856***(5.59)(8.95)(7.54)Threshold variable coefficient 30.313***0.799***0.897***(5.99)(9.36)(7.75)_cons5.365***3.273***3.132***(28.41)(9.94)(7.17)R-sq0.676 70.701 80.671 6N132143143

4.4AnalysisofjaponicariceoutputmodeldataFirst, there are different opinions about the fertilizer effect function. Assume that the fertilizer effect function is a quadratic function, the chemical fertilizer input conforms to the law of diminishing marginal utility, that is, the marginal benefit curve is an inverted U-shaped curve, then when the average benefit = marginal benefit, the chemical fertilizer input is the most efficient. Next, the chemical fertilizer is put in. Although the total income will continue to increase, the marginal net income of chemical fertilizer input will be less than the average income, indicating that the efficiency of chemical fertilizer input starts to decline. In the japonica rice sample, the average net income of fertilizersar1= (total income from chemical fertilizer inputs-costs of chemical fertilizer inputs)/chemical fertilizer input. Fig.4 illustrates the average net income and marginal net income of the japonica rice samples for all provinces. It can be seen that the difference between the two values is large. Especially in Hebei, Inner Mongolia and the three northeastern provinces, the difference is significantly larger than that of the southern provinces. It shows that using the net income to measure, the chemical input efficiency of China’s japonica rice is low, and the chemical input efficiency in the north is much lower than that in the south. Second, we listed data on chemical fertilizer inputs and marginal net income of all provinces in the japonica rice samples, expressed infet1andm1, as shown in Fig.5. It can be seen that the data of marginal net income is in the range of 0-20, and the amount of chemical fertilizer input is also fluctuating asynchronously. The amount of chemical fertilizer input does not mean that the marginal net income is also large, andviceversa. Although the trend of the two is not synchronized, the trend of marginal net income is more winding than the trend of chemical fertilizer input, which also shows that the effects of chemical fertilizer input on the marginal net income of japonica rice are not significant.

Through testing the relationship between chemical fertilizer productivity and marginal net income, the covariance of the two is 0.88, indicating a strong positive relationship between the two. For comparison purposes, we listed the statistical characteristics of the marginal net income data for different thresholds, as shown in Table 4. From the statistical characteristics of mean, minimum, maximum values,etc., when the chemical fertilizer productivity is lifted to a new stage, the marginal net income per unit of chemical fertilizer has been significantly improved.

Fig.4Marginalnetincomeandaveragenetincomeofchemicalfertilizerinjaponicariceoutputmodel

Fig.5Chemicalfertilizerinputanditsmarginalnetincomeinjaponicariceoutputmodel

Table4Statisticalcharacteristicsofmarginalnetincomedataunderdifferentchemicalfertilizerproductivityofjaponicarice

Chemical fertilizer productivity ofjaponica riceNumber ofsamplesMarginal net incomeAverage∥yuanStandard deviationMin.∥yuanMax.∥yuanLower than 16.709 9215.506 12.145 510.625 709.204 3616.709 9 - 21.199 2409.589 62.525 593.064 2514.203 35Higher than 21.199 27116.081 04.016 919.574 2129.362 12

4.5AnalysisofwheatoutputmodeldataThe average net income and marginal net income of all provinces in the wheat samples are shown in Fig.6. The relationship between the two is different from that of japonica rice, and it has undergone a process of overtaking. In 2009-2011, all provinces experienced an average net income of chemical fertilizer marginal net income, which is an inflection point of chemical fertilizer input efficiency. In all provinces, the chemical fertilizer input of wheat has changed from efficient to inefficient.

Fig.6Marginalnetincomeandaveragenetincomeofchemicalfertilizerinwheatoutputmodel

Fig.7 indicates data on chemical fertilizer inputs and marginal net income for all provinces in the wheat samples, expressed inm2andfet2, respectively. It can be seen that the marginal net income of wheat basically fluctuates in the range of 15-35. Compared with the trend of chemical fertilizer input, the fluctuation of marginal net income is larger. Besides, the trend of the two is also very inconsistent. For example, the fertilizer input in Shanxi and Inner Mongolia is slowly increasing, but the corresponding marginal net income is fluctuating. In addition, there is no obvious relationship between the peak value of chemical fertilizer input and the marginal net income, indicating that that the amount of chemical fertilizer input does not affect the marginal net income of chemical fertilizer.

Similarly, we tested the relationship between chemical fertilizer productivity and marginal net income. We first analyzed the covariance coefficient of the two, the value is 0.76, indicating that there is a strong positive relationship between them. As shown in Table 4, from the statistical characteristics of mean, minimum, maximum values,etc., when the chemical fertilizer productivity of wheat is increased, the marginal net income of grain is also greatly increased.

Fig.7Chemicalfertilizerinputanditsmarginalnetincomeinwheatoutputmodel

Table5Statisticalcharacteristicsofmarginalnetincomedataunderdifferentchemicalfertilizerproductivityofwheat

Chemical fertilizer productivityof wheatNumber ofsamplesMarginal net incomeAverage∥yuanStandard deviationMin.∥yuanMax.∥yuan9.701 9 -16.693 49923.440 772.935 2915.549 3 31.177 34Higher than 16.693 44429.871 033.253 9824.142 436.132 12

5 Conclusions

The marginal net income of chemical fertilizer input is lower than the average net income, especially the japonica rice shows higher deviation, indicating that the chemical fertilizer input efficiency deviates from the best. With the increase in the chemical fertilizer input, the total net income obtained by farmers is also increasing. However, the marginal net income will fluctuate within a certain range, and the relationship between this value and the amount of chemical fertilizer input is not obvious, and there is no obvious time trend. The increase in chemical fertilizer productivity is positively affecting the marginal net income of chemical fertilizer. Through increasing the unit output of chemical fertilizer, it is able to greatly increase the marginal net income of chemical fertilizer.