Land-use allocation

In general, policy analyses at the farm level can be grouped into mathematical programming (i.e., linear/nonlinear programming), econometric, and advanced programming techniques. This article uses the mathematical programming approach. This type of approach has several advantages that justify its recent increased use. For example, the approach allows the explicit representation of behavior that facilitates interdisciplinary research on agri-environmental interactions and agricultural systems’ environmental assessment (Ciaian et al. Reference Ciaian, Espinosa, Gomez y Paloma, Heckelei, Langrell, Louhichi, Sckokai, Thomas and Vard2013).

Following the modeling exercise of paddy farming in Sasaki (Reference Sasaki2012), land is divided into rectangular fields that are uniform in size and homogeneous in land quality (productivity: q) but heterogeneous between fields, an idea originally proposed by Lichtenberg (Reference Lichtenberg1989, Reference Lichtenberg, Gardner and Rausser2002). Each field is an assumed 0.1 ha, and the total surface area of cultivated land is 6 ha (60 fields). Japanese national statistics data on a 5–7 ha farm size are used in this study to estimate the profit function assuming a full-time commercial farmer. The structural transformation of Japanese agriculture toward more productive, profitable, and larger-scale farms has been a major policy goal. The area covered by farmers with more than 5 ha of farmland has been increasing in recent years, accounting for more than 60 percent in some regions.

In this study, the land-use allocation is assumed to include rice paddies, upland crops, and abandoned land (Figure 1). It is assumed that rice paddy is cultivated on the low q (productivity, drainage ability) land, and soy and wheat are cultivated on high q land. Most of Japan's land have been paddy fields, and the government is promoting shifting cultivation, such that the land with good “drainage conditions” and high productivity is now converted to wheat and soy cultivation. Compared with rice, the profit margins of soybeans and wheat are quite low.

Figure 1. Spatial Characteristics Assumed in the Model. The Land-Use Allocation Assumed to Include Rice Paddies, Upland Crops, and Abandoned Land.

There is some trade-off between paddy fields and upland crops in terms of environmental externalities. For example, although methane emissions from upland fields amount to zero, N₂O emissions are higher (Nishimura et al. Reference Nishimura, Sawamoto, Akiya, Sudo and Yagi2004). Consequently, it is beneficial to analyze rice paddy and the upland crop cultivation in a continuous analytical framework by formulating their main characteristics from both economic and environmental perspectives. It is assumed that land reforms in paddy fields (drainage canal and subsurface drainage) have already been initiated; this implies that a farmer may allocate land based only on the profit generated from each field; therefore, it is not necessary to incorporate “the land conversion cost” exogenously (OECD 2010).

Lichtenberg (Reference Lichtenberg1989, Reference Lichtenberg, Gardner and Rausser2002), Lankoski and Ollikainen (Reference Lankoski and Ollikainen2003), Lankoski, Lichtenberg, and Ollikainen (Reference Lankoski, Lichtenberg and Ollikainen2004), Lankoski, Ollikainen, and Uusitalo (Reference Lankoski, Ollikainen and Uusitalo2006), and developed a framework for analyzing the joint production of commodity and environmental outputs as well as negative externalities under heterogeneous land quality, which provides the foundation for the modeling in this study. Details of the theoretical framework are explained in the Annex.

Profit functions

Farmers’ profits from production in the absence of government intervention are:

(1) $${\rm \pi }^i = p_iy_i-cx_i-w_in_i-o_i\quad {\rm for}\;i = 1, \;2, \;3$$

where p _i refers to crops’ price, y _i to the yield/10a, c to the fertilizer (nitrogen) price, w _i to wage rate per hour, n_i to labor input, and o _i to other costs. The model employs a quadratic nitrogen response function, $y_i = a_i + {\rm \alpha }_ix_i + {\rm \beta }_ix_i^2$ , where x _i refers to the amount of N application (kg/10a) estimated for crop 1 (rice), crop 2 (wheat), and crop 3 (soy). When farmers consider the use of organic fertilizer application x _oi in addition to (or partially converting) chemical N fertilizer x _ci , the total amount of N application to the agricultural field is the summation of N fertilizer and N content of organic matter. Despite the recommended organic matter application amount (e.g., 1.0–1.5 t/10a for paddy fields in Japan), the implementation is inactive due to the following barriers: difficulties in realizing the manure application effects from the farmers’ viewpoint due to the diverseness of manure quality; a huge amount of the application is needed compared with the chemical one (high spreading cost); a lack of cooperation among crop and livestock farming (high transportation costs).

The average N content in organic fertilizer (cow manure) is set at 0.7 percent based on Sasaki (Reference Sasaki2012), and then the total amount of N application is expressed as:

(2) $$x_i = x_{ci} + 1, 000 \bullet x_{oi} \bullet 0.007$$

where 1,000 represents the conversion of the unit from tonne to kg.

Generally, N requirement * substitution rate (%) = the amount of organic fertilizer (kg/10a) * N content rate (%) * Fertilizer efficiency (%), where fertilizer efficiency is 30 percent.

Suppose that the positive effect for yield is expressed as Φ _i (x _oi ) and that of paddy is approximately 105 percent and that of wheat and soy 110 percent under the 1 t application, based on the several field survey data. The profits function is expressed as follows taking into consideration the additional cost for organic matter application:

(3) $${\rm \pi }^i = p_i( {a_i + {\rm \alpha }_ix_i + {\rm \beta }_ix_i^2 } ) \Phi _i( {x_{oi}} ) -cx_{ci}-( {c_{{\rm op}} + c_{{\rm ot}} + c_{{\rm os}}} ) x_{oi}-w_in_i-o_i \,{\rm for\ }i = 1, \;2, \;3$$

where c _op refers to the price of organic matter (JPY/tonne), c _ot to transportation cost (JPY/tonne), and c _os to the spreading cost (JPY/tonne).

The quadratic nitrogen response function of rice paddy was estimated using data from over 50 sample field surveys, which were collected by Toriyama (Reference Toriyama2002), and recently collected field experiment data in 12 field studies from the 1990s to 2010s:

(4) $$y_1 = 384.9 + 44.8x_1-2.4x_1^2 ( {{\rm R}^2 = 0.50} ) \;$$

Even without fertilizer, nutrition in irrigation water affects yield. It is generally said that the yield without fertilizer decreases only by 1/5 due to the paddy's high fertility. To reflect actual yield in paddy fields, a_i is given as a fixed value to exclude the effect of irrigation water, and then the land quality q is incorporated into the response function. The response function is expressed as:

(5) $$y_1 = 384.9 + ( {e_0 + e_1q} ) x_1-( {{\rm \mu }_0 + {\rm \mu }_1q} ) x_1^2 \;$$

Following the above field data, the yield spread is about 30 percent under the average N application amount. Thus, each of the parameters is obtained. Also, a positive yield effect Φ _i (x _oi ) of applying manure plays a significant role because the pros of manure application for farmers are expressed only by this positive yield effect in the model. In the model, a positive relationship between manure application and yield effect is expressed as quadratic equations based on field survey data (e.g., Shibahara et al. Reference Shibahara, Takehisa, Komatsu and Habe1999; NARO 2007). Then, Φ _i (x _oi ) is now expressed for rice paddy and wheat (=soy) as follows:

(6) $$\Phi _1( {x_{o1}} ) = {-}0.0274x_{o1}^2 + 0.0796x_{o1} + 1.0$$

(7) $$\Phi _2( {x_{o2}} ) = {-}0.0051x_{o1}^2 + 0.1518x_{o1} + 1.0.$$

The quadratic nitrogen response function of wheat (converted from rice paddy cultivation) was estimated using the National Agricultural Centre data sets (1989) and recently collected field experiment data of 14 field studies in Japan from the 2000s to 2010s:

(8) $$y_2 = 183.4 + 47.2x_2-1.8x_2^2 ( {{\rm R}^2 = 0.14} ) $$

The wheat response function to nitrogen is expressed as:

(9) $$y_2 = 183.4 + ( {h_0 + h_1q} ) x_2 + ( {{\rm \eta }_0 + {\rm \eta }_1q} ) x_2^2 \;$$

Since the yield spread is about 30 percent under the average N application amount, each parameter is obtained. In general, wheat yield is more responsive than paddy rice to nitrogen applications.

Soy's quadratic nitrogen response function is also estimated as follows based on data of 23 field studies in Japan from the 1980s to 2010s:

(10) $$y_3 = 289.4 + 7.33x_2-0.40x_2^2 ( {{\rm R}^2 = 0.99} ) $$

The soy response function to nitrogen is expressed as:

(11) $$y_3 = 289.4 + ( {h_0 + h_1q} ) x_2 + ( {{\rm \eta }_0 + {\rm \eta }_1q} ) x_2^2 $$

The spread using the average N application amount was assumed, and then each of the parameters was estimated to reflect the actual plotted yield data.

The parameters for the profit function are summarized in Table 1, and data sources used for the nitrogen response function are outlined in Table 2.

Table 1. Parameter values in the profit function

Source: 2016 MAFF stat.

Parameters to estimate the profit function, following OECD's (2010) and Sasaki (Reference Sasaki2012)'s specification.

Table 2. Data sources of the nitrogen response function

Nitrogen response function

It is difficult to formulate the relationship between N application and its impact by the easy-to-use way because N runoff from irrigation and meteoric water might affect the N balance in paddy fields. Generally, N runoff from paddy is explained as follows: [N runoff (surface runoff + subsurface flow)] = [The effect of irrigation water-load] + [The effect of meteoric water-load] + [The effect of N application]. We tried to estimate the relationship between N application and runoff by an exponential form (e.g., Tabuchi and Takamura Reference Tabuchi and Takamura1985, p. 70):

(12) $$z_i = {\rm \chi }_i{\rm exp}( {{\rm \delta }_ix_i} ) \;$$

where z _i refers to the amount of N runoff (surface and subsurface) and x _i is the amount of N application.

Paddy fields could be N removal sites or pollution sites depending on agricultural activities and irrigation water nitrogen concentration. It is well known that paddy fields and wetlands effectively improve water quality by removing nitrogen due to denitrification and absorption, which is effective only when irrigation water is highly concentrated.

Although the nitrogen movement in paddy is not simple, the relationship was estimated in Sasaki (Reference Sasaki2012) using available field survey data in Kunimatsu and Muraoka (Reference Kunimatsu and Muraoka1989). An exponential relation was found between the amount of N application and runoff.

(13) $$z_1 = 0.0062{\rm e}^{0.465x_1}-1.14( {{\rm R}^2 = 0.54} ) $$

In a precise sense, soil condition, crops, cropping season, and methodological condition could affect N runoff. Nevertheless, approximately 30 percent of applied N could runoff as the average in the Japanese condition. However, a linear function is not appropriate for optimization. Consequently, the exponential form was estimated based on Japanese field data, which were worked out by the National Institute for Agro-Environmental Science (NIAES), and the function was revised using new data as follows:

(14) $$z_2 = 2.614{\rm e}^{0.035x_2}( {{\rm R}^2 = 0.11} ) $$

where z ₂ refers to the amount of N runoff and x ₂ to the N application.

Due to the lack of observation and data, R² is not sufficiently high. The linear functions and general nitrogen runoff ratio were compared in to verify the robustness of the estimated exponential curve. There is consistency with the other estimation results under the average amount of N application, such as lower than 20 kg/10a.

GHG (CH₄, N₂O) emission and carbon sequestration function

Agriculture does not account for a high percentage of the total GHG emissions in Japan,Footnote ² although agriculture is an important anthropogenic source of CH₄ and N₂O emissions. GHG emissions from agricultural land (IPCC's 4C category rice cultivation and 4D category agricultural soils) derived from chemical and organic fertilizer applications account for approximately 80 percent of total emissions. In this analysis, therefore, fertilizer application amounts could be considered as control variables. Rice cultivation is a main anthropogenic source of CH₄ (methane) emissions. Fertilizer application and plowing of organic soil cause ammonium ions in the soil, and then N₂O is emitted. N₂O is also emitted via denitrification.

Since the amount of fertilizer application is the control variable in the profit function (nitrogen response function), it is possible to incorporate the CH₄, N₂O, and carbon sequestration function into the model; then, the net GHG emission (CO₂ equivalent) is explained by using the following equationFootnote ³ :

(15) $${\rm GHG}( {{\rm C}{\rm O}_ 2{\rm eq}} ) = 21 \bullet {\rm C}{\rm H}_4 + 310 \bullet {\rm N}_2{\rm O} + {\rm C}{\rm O}_ 2.\;$$

It is a fact that rice cultivation is a primary anthropogenic source of CH₄ emissions. Sasaki (Reference Sasaki2012) estimated the CH₄ emission (t CH₄/0.1 ha/year) equation based on IPCC guidelines as follows:

(16) $${\rm C}{\rm H}_4 = 0.001296 \times ( {1 + 1.4x_{oi}} ) ^{0.59}$$

Conversely, methane is not generated in other uplands because upland soils are normally oxidative and aerobic.

The fertilizer application and plowing of organic soil cause ammonium ions inside the soil. Then, N₂O is emitted in the process of oxidizing the ammonium ions into nitrate-nitrogen under aerobic conditions. Also, N₂O is emitted via denitrification. Sasaki (Reference Sasaki2012) estimated the N₂O emissions associated with fertilizer application as

(17) $${\rm N}_ 2{\rm O}_{{\rm direct}\_i} = \displaystyle{1 \over {1, \;000}} \times {\rm E}{\rm F}_{{\rm di}} \times x_i \times \displaystyle{{44} \over {28}}\;$$

where N₂O_{direct_i} refers to direct N₂O emissions derived from fertilizer application in land use i (t N₂O), 1/1,000 means the conversion of the unit from kg to tonne, EF_di to emission factors (kgN₂O-N/kgN) (for paddy: 0.0031 and upland crop: 0.0062), x_i to the amount of N application (kgN), and 44/28 means the conversion of N₂O-N emission to N₂O emission.

When E _adi is N₂O emissions associated with atmospheric deposition (kgN₂O) and E _li is emissions associated with nitrogen leaching and runoff (kgN₂O), indirect emission N₂O_{indirect_i} is expressed as follows:

(18) $${\rm N}_ 2{\rm O}_{{\rm indirect}\_i} = E_{{\rm adi}} + E_{{\rm li}}$$

Sasaki (Reference Sasaki2012) estimated emissions from atmospheric deposition as

(19) $$E_{{\rm adi}} = \displaystyle{1 \over {1, 000}} \times 0.01 \times {\rm RF} \times x_i \times \displaystyle{{44} \over {28}}$$

where E _adi refers to N₂O emissions from atmospheric deposition, 1/1,000 means the conversion of the unit from kg to tonne, 0.01 refers to emission factors (kgN₂O-N/kgN), RF is the rate of deposition from fertilizer (for chemical fertilizer: 0.1 and for organic fertilizer: 0.2), and x_i refers to the amount of nitrogen application.

Emissions from nitrogen leaching and runoff (E _li) are defined by Sasaki (Reference Sasaki2012) as

(20) $$E_{{\rm li}} = \displaystyle{1 \over {1, 000}} \times 0.0124 \times Z_i( {x_i} ) \times \displaystyle{{44} \over {28}}$$

where 1/1,000 means converting the unit from kg to tonne, 0.0124 is the emission factor from nitrogen leaching and runoff (kgN₂O-N/kgN), and Z_i refers to the runoff amount (kgN).

In addition to CH₄ and N₂O emissions, agriculture could significantly reduce the risk of climate change by taking carbon out of the atmosphere and storing it in the soil.Footnote ⁴ Japan has country-specific continuous survey data undertaken in 52 areas for paddy and 26 areas for upland crops. Soil samples are taken from the top surface up to 30 cm depth, and the amount of soil carbon is measured at the field level. Gray lowland soil and Gley soils for paddy and Andosols for upland crop data, the dominant soil types in Japan, are used in this study to reduce the uncertainty (of measurement depending on soil type).

The overall average data reveal that organic matter applications increase the amount of carbon sequestration: 1 t/10a manure application cause 40.6–77.4 kgC/10a sequestration in paddy fields, and 1.5 t/10a manure results in 37.3–170.9 kgC/10 sequestration in uplands. The amounts of carbon sequestration via organic matter application differ among soil types. These soil types are some of the representative soils widely found in Japan. Also, the use of the dominant soil type could permit extrapolation to a more spatially aggregate level.

The amount of carbon sequestration is expressed as follows:

(21) $$C_i = \sum {\rm Se}{\rm q}_i \bullet \displaystyle{{44} \over {12}}$$

Regarding specification of function form, since there is an upper bound for carbon sequestration capacity, polynomial functions are estimated using data from the MAFF, which include the amount of application per year and the increased amount of soil carbon in each soil type. Then, carbon sequestration is estimated for paddy and upland fields, respectively.

(22) $${\rm Se}{\rm q}_1 = {-}0.0062x_o^2 + 0.052x_o( {{\rm R}^2 = 0.80} ) $$

(23) $${\rm Se}{\rm q}_2 = {-}0.0013x_o^2 + 0.022x_o( {{\rm R}^2 = 0.69} ) \;$$

Biodiversity

This study examined the relationship between chemical fertilizer usage and biodiversity using empirical evidence from Japanese biologists’ field surveys. Katayama et al. (Reference Katayama, Osada, Mashiko, Baba, Tanaka, Kusumoto, Okubo, Ikeda and Natuhara2019) indicated a negative relationship between production intensity (conventional, environmentally friendly practice, and organic farming) and paddy fields’ many types of flora and fauna. Based on their study, the following relationship is derived when BD, defined using the Native Plants Species Richness Index for paddy fields, gives organic farming paddy fields a score of 100. Native plants data were used in this study because they are most heavily affected by farming practices.

(24) $${\rm B}{\rm D}_{{\rm paddy}} = \exp ( 4.605-0.02865x_{c1}) $$

In addition, Koshida and Katayama (Reference Koshida and Katayama2018) found that rice-field abandonment's effect on biodiversity was negative overall in a first comprehensive meta-analysis in Japan. Species richness decreased 56–72 percent after abandonment. This reduction is unlikely to recover and continues for plant species richness even 10–15 years further on from abandonment. These results suggest that rewilding (land renewal) may not be achieved by rice-field abandonment. The Native Plant Species Richness Index value of the abandoned area is expressed by using data recalculated from Koshida and Katayama (Reference Koshida and Katayama2018)Footnote ⁵ as:

(25) $${\rm B}{\rm D}_{{\rm abandoned}} = {\rm B}{\rm D}_{{\rm conventional}}\ast 0.66 = 49.92$$

where BD_conventional is 75.64, using the average chemical fertilizer application of conventional farming (Katayama et al. Reference Katayama, Osada, Mashiko, Baba, Tanaka, Kusumoto, Okubo, Ikeda and Natuhara2019).

The Native Plants Richness Index calculation for paddy fields is based on equations (24) and (25) (Figure 2). The summated biodiversity value BD in the baseline is normalized as 1 for easy comparison with the results of each simulation.

Figure 2. Native Plants Richness Index. The Native Plants Richness Index Calculation for Paddy Fields and Abandoned Area Based on Equations (24) and (25).

While surrounding environments might affect species richness in general, it is assumed that other arable lands and paddy fields do not usually affect each other's biodiversity. As the study considers a relatively large farm with a plain field, land-use diversity is not considered.

Data sources, data collection sites, and methods for the environmental impact estimation are summarized in Table 3.

Table 3. Data sources of the environmental impact estimation

Agricultural support policies

The study uses a benchmark scenario excluding the policy called “Baseline (market solution)” to compare the performance of individual policy instruments. Each support policy simulates payment increases or MPS equivalents by 10 percent of the value of each commodity and simultaneously applies these to the following commodities. Following this revenue-oriented rule, for example, MPS represents the price increase of rice, wheat, and soy by 5.5, 27, and 13 percent, respectively, to achieve a 10 percent revenue increase accounting for fertilizer application/yield changes before and after policy shocks. This MPS setting will encourage rice paddy's cultivation due to the high profitability. Prices in the mathematical programming model are given, and they change in scenarios; then changes in acreage/production will not impact prices. So, there are no indirect effects on policy scenario runs.

The individual policy instruments analyzed are:

• • market price support (MPS),

• • payment based on variable input (nitrogen fertilizer subsidy),

• • payment based on the noncurrent area (decouple payment),

• • agri-environmental payment for complying with fertilizer application constraint (50 percent) plus organic fertilizer (manure) application,

• • agri-environmental payment for complying with fertilizer application constraint (100 percent),

• • agri-environmental payment for complying with fertilizer application constraint (50 percent) plus cover crop (hairy vetch for paddy field, rye for arable land, and rotary tilling).

This revenue-oriented rule does not apply to “Payment based on variable input (nitrogen fertilizer subsidy)” since the nitrogen fertilizer price is low and does not significantly impact the profit function. The chemical fertilizer price reduction was technically unable to produce a 10 percent increase in revenue, so a 20 percent reduction of the chemical fertilizer price per kg is introduced as a reference. Details of these scenarios and parameter changes are summarized in Table 4.

Table 4. Details of policy scenarios

The baseline scenario specifies that rice paddy receives 75,000 JPY/0.1 ha, wheat receives 82,000 JPY/0.1 ha, and soy receives 62,000 JPY/0.1 ha as area payment. This subsidy is consistent with the Japanese government's introduction of a subsidy for arable crops to ensure competitive incomes with rice paddy. Also, this subsidy was designed to incentivize crop diversification so that farmers would shift from rice production to other crops (e.g., wheat and soybean), but the payment is assumed to depend on the production type, not on the production level. This direct payment for rice paddy was abolished in 2018. However, data in the profit function were extracted from 2016 national statistical data, so direct payment for rice paddy remains in the model.

Sensitivity analysis

To test the results’ robustness, we conducted sensitivity analyses for private optimum and MPS for organic fertilizer's positive effect on yield, chemical fertilizer price, and organic fertilizer cost by ±10 percent.

Sensitivity analyses were conducted to test the credibility and robustness for different assumptions and compare the baseline and MPS scenarios. It is difficult to test all parameters and combinations, so key parameters to determine chemical fertilizer and organic fertilizer application were assessed. The nitrogen application level and chemical/organic fertilizer combination are the fundamental drivers of net positive environmental outcomes in the model. Using Pannell's (Reference Pannell1997) and OECD's (2010) approach, we estimated the 10 percent shocks in chemical fertilizer prices, the organic fertilizer–related costs (collection, transportation, and spread), and the yield effect of organic fertilizer in the baseline and MPS scenarios. The results are presented in Table 7.

Table 7. Sensitivity analyses: ±10 percent shocks to chemical and organic fertilizer prices, and organic fertilizer's positive yield effect on productivity

Using Pannell's (Reference Pannell1997) and OECD's (2010) approach, we estimated the 10 percent shocks in chemical fertilizer prices, the organic fertilizer-related costs (collection, transportation, and spread), and the yield effect of organic fertilizer in the baseline and MPS scenarios.

The fertilizer price −10 percent shock indicates that nitrogen runoff becomes relatively intensive. Per 0.1 ha, nitrogen runoff for the crop has little effect on activity; the changes reflect shifting the land use to wheat. The functional form used for modeling nitrogen response implies low price elasticity. Under the MPS scenario, which is the same as the original scenario, the partial transition of chemical fertilizer to organic fertilizer has occurred, and nitrogen runoff and GHG emission decrease. In the case of a +10 percent shock, the nitrogen application and the environmental effect are, in contrast, less intensive.

A decrease in organic fertilizer cost will result in an increase in its application and reduced chemical fertilizer use, vice versa. A remarkable point here is that nitrogen runoff increases under the MPS scenario in contrast to the original scenario because land use is changed from soy to wheat, which requires more nitrogen. The last simulation relates the long-term application of organic fertilizer, which gives a positive yield effect change of +10 percent. Under the scenario of a 10 percent increase, all results continue to hold. Conversely, a −10 percent scenario results in a slight increase in nitrogen runoff due to land-use change from soy to wheat.

We found that key results from this study hold even after the sensitivity analysis, although results rely on assumptions used. Some key assumptions (e.g., combining chemical and organic fertilizer) would require caveats for model outcomes.