# An Assessment of the Site-Specific Nutrient Management (SSNM) Strategy for Irrigated Rice in Asia

## Abstract

**:**

## 1. Introduction

- Is there evidence of complementary, von Liebig-type relationships among N, P, and K fertilizers?
- Does yield response to N fertilizer application depend on the initial state of the soil?

## 2. Background, Data Description and Empirical Model

#### 2.1. The SSNM Strategy for Rice

#### 2.2. Data Description

#### 2.3. The Empirical Model

^{2}) error term. The N, P, and K fertilizer application by farmers could be endogenous given the unobserved factors that affect yields. There were no good instruments available to address endogeneity concerns regarding the production function estimation. In the presence of heterogeneity, the polynomial and linear plus plateau approximations essentially converge, making the quadratic a viable alternative to the von Liebig and linear response plateau models [36]. Moreover, von Liebig models generally do not fit the data well and the actual estimation does not yield the right-angle isoquants described in its derivation [37].

_{0}cannot be rejected, $\frac{{\partial}^{2}y}{\partial {x}_{i}\partial {x}_{j}}\equiv \frac{\partial}{\partial {x}_{i}}\left(\frac{\partial y}{\partial {x}_{j}}\right)\equiv {\beta}_{ij}\equiv {\beta}_{ji}\equiv 0,$ then it indicates the independence of ${x}_{i}$ and ${x}_{j}$. The marginal productivity of ${x}_{j}$ is not affected by changes in the level of ${x}_{i}.$ If, however, ${H}_{0}$ is rejected, then nutrient interaction between ${x}_{i}$ and ${x}_{j}$ is present. If ${\beta}_{ij}\equiv {\beta}_{ji}>0$, then ${x}_{i}$ and ${x}_{j}$ are technically complementary. The marginal product of ${x}_{i}$ increases as ${x}_{j}$ increases. If ${\beta}_{ij}\equiv {\beta}_{ji}<0$, then ${x}_{i}$ and ${x}_{j}$ are technically substitutes. Increasing ${x}_{i}$ reduces the marginal productivity of ${x}_{j}$. Table 2 and Table 3 present the definition and summary of the statistics, respectively, for the regression variables.

## 3. Results and Discussion

#### 3.1. Marginal Physical Product and Output Elasticity

_{N}) fertilizer application was positive and the output elasticity value was less than one; both results were significant at the 1% level. The additional N fertilizer use had a significant positive influence on the yield in most plots in the sample. Henceforth, in this section, the term “N” refers to “N fertilizer applied” and “N fertilizer.” Similar interpretations are used for “P” and “K.” Nitrogen fertilizer application increases the height of leaves [41,42], the number of tillers/m

^{2}[41,43,44], and both the number and size of grain [45,46,47].

_{N}is decreasing in Aduthurai (India) (Figure 2), Sukamandi (Indonesia) (Figure 3), Nueva Ecija (Philippines) (Figure 4), and Ha Noi (Vietnam) (Figure 5), but increasing in Suphan Buri (Thailand) at all N rates (Figure 6). The increasing MPP

_{N}suggests a deficiency in N on most plots in the sample areas. Hence, use of an additional fertilizer could exert a positive influence on the yield. The maximum yield will be achieved at N rate where the MPP

_{N}= 0. These rates are 139 kg per ha in Aduthurai, 135 kg per ha in Sukamandi, 160 kg per ha in Nueva Ecija, and 100 kg per ha in Ha Noi. In Aduthurai, applying 139 kg per ha will result in almost 6 tons per ha of grain yield, given all the other factors are constant at the mean level. If more than 139 kg per ha is applied, MPP

_{N}will be negative. This is because excessive N promotes lodging and plants become more attractive to insects and diseases.

_{P}) was positive but the output elasticity is greater than one in Uttar Pradesh (India) (Table 7). The MPP

_{P}was positive and output elasticity was less than one in Sukamandi (Table 8), Can Tho (Vietnam), and Ha Noi (Table 9) at 1% significance level. The magnitude of the estimated coefficients of P reveals the significance of this nutrient in rice production, specifically in Vietnam. For example, a kilogram increase in P increases the yield by 136 kg per ha in Ha Noi.

_{P}and output elasticity at the mean level were negative in Nueva Ecija and Suphan Buri (Table 8), with both being statistically significant at 1% level. There is a possibility that most of the rice straw was retained in the field, and hence those soils were often saturated with P due to continuous P fertilizer application. The extractable Olsen-P level was relatively high for all farms in the sample areas [4]. No additional amount of P fertilizer is required to replenish the P removed with grain and straw. The additional P fertilizer application might result in overapplication. The overapplication of P fertilizer does not necessarily lead to environmental damage, but the ability of the soil to retain P is limited.

_{K}) varied across sites. The MPP

_{K}was positive and output elasticity was less than one at the mean level in Suphan Buri (Table 8). Potassium plays a key role in many metabolic processes in the plant. Meanwhile, a negative MPP

_{K}was observed in Can Tho (Table 9). With the current SSNM fertilizer algorithm, the doses of mineral fertilizers, including N-P-K fertilizers, are determined based on the target yield and the required nutritional needs of the plants. The K requirement of rice is sometimes supplied from plant residues that have been turned under and from K in irrigation water [48]. The SSNM approach takes into account the amount of K recycled from straw yield and the straw management level in the previous season when calculating K fertilizer requirements to avoid excessive K fertilizer use. However, it does not consider the abundance of digestible nutrients in the soil. The water from the Mekong River Delta has high contents of sediments that provide nutrients for crop. Additional K fertilizer would not be beneficial here and could result in overfertilization or negative MPP

_{K}. When fertilizer is overapplied, this may result in the formation of an excess of soluble fertilizer components in the soil and their increased leaching. This would burden the natural environment with a given nutrient, and at the same time reduce the effectiveness of the component application.

#### 3.2. Evidence of Complementarity Among N-P-K Fertilizers

_{N}is higher in absolute value than the direct effect of K on yield. Potassium must not be applied alone, but rather in combination with N. Given this, selective application of fertilizer, i.e., only applying N or K when farmers are faced with cash constraints, might cause more harm than good to the crop. The Wald test failed to reject the null hypothesis that there is no interaction between N and K fertilizers in Aduthurai, Thanjavur, Sukamandi, Nueva Ecija, Can Tho, and Ha Noi.

#### 3.3. Is Yield Response to N Fertilizer Dependent on the Ex Ante State of Soil?

_{N}was invariant to a C content level of approximately 13g/kg, at which point the MVP

_{N}increased up to a C content level of approximately 21 g/kg, after which the MVP

_{N}flattened out, with no further statistically significant growth in rice yield response to N fertilizer beyond that soil fertility level. On the other hand, the MVP

_{N}is rapidly increasing in all Philippine sample plots (Figure 11). The figure also suggests that a farmer with 15 g/kg of C content would get about PHP 84 (approximately USD 2) more profit than a farmer with 5 g/kg of C content, given that they apply the same level of N fertilizer at the mean level. The maximum yield will be achieved at the N rate where the MPP

_{OrgCN}= 0. The $M{R}_{N}$ in Ha Noi did not vary up to a C content level of approximately 17 g/kg, then it increased at an increasing rate up to a C content level of approximately 22 g/kg, after which it increased at a decreasing rate (Figure 12). If further investments are devoted to increasing the soil C content in Vietnam, N fertilizer application is expected to be profitable.

#### 3.4. Non-Nested Hypothesis Test Results

## 4. Conclusions and Policy Implications

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 3.**Marginal physical product of N (MPP

_{N}) at the mean level in Sukamandi, West Java, Indonesia.

**Figure 10.**Marginal value product of N (MVP

_{N}) based on the plot’s carbon content in Sukamand, Indonesia.

**Figure 11.**Marginal value product of N (MVP

_{N}) based on the plot’s carbon content in Nueva Ecija, Philippines.

**Figure 12.**Marginal value product of N (MVP

_{N}) based on the plot’s carbon content in Ha Noi, Vietnam.

**Figure 13.**Marginal value product of N (MVP

_{N}) based on the plot’s carbon content in Aduthurai, India.

Country | Region/Province | Rice Domain | NO. of Farmers | Cropping System | Climate | Years Included | Cropping Season ^{a} |
---|---|---|---|---|---|---|---|

India | Tamil Nadu | Aduthurai | 40 | Rice-rice | Tropical | 1997 | KR, TH |

Thanjavur | 19 | Rice-rice | Tropical | 1997,1999 | KR, TH | ||

Uttar Pradesh | Pantnagar | 23 | Rice-wheat | Sub-Tropical | 1997 | KH | |

Indonesia | West Java | Sukamandi | 30 | Rice-rice | Tropical | 1996,1998 | DS, WS |

Philippines | Nueva Ecija | Maligaya | 50 | Rice-rice | Tropical | 1995–1996 | DS, WS |

Thailand | Central Plain | Suphan Buri | 27 | Rice-rice | Tropical | 1995–1996 | DS, WS |

Vietnam | Mekong Delta | Can Tho | 32 | Rice-rice-rice | Tropical | 1996 | DS, WS |

Red River Delta | Hanoi | 24 | Rice-rice-maize | Sub-Tropical | 1997 | ER, LR |

^{a}High yielding season: KR—Kuruvai, DS—Dry Season, ER—Early Rice; Low yielding season: TH—Thaladi, WS—Wet Season, LR—Late Rice.

Variable | Description |
---|---|

Rice output (kg/ha) | Dependent variable (Y). |

Kilograms of rice harvested per hectare per season in a given year | |

Nitrogen applied (N/ha) | Kilogram of N per ha from fertilizers applied |

Phosphorus applied (P/ha) | Kilogram of P per ha from fertilizers applied |

Potassium (K/ha) | Kilogram of K per ha from fertilizers applied |

Org C | Amount of carbon content in the soil (g/kg) |

Age (year) | Age in years of the person responsible for production decisions on the plot |

Educ (year) | Total years of schooling completed by the farmer |

Farm area (ha) | Size of farm owned by the farmer |

High yielding season (HYS) | Dummy variable. |

HYS = 1; high yielding season | |

HYS = 0; low yielding season |

Site/Variable | No. of Observations | Mean | Standard Deviation |
---|---|---|---|

INDIA | |||

Aduthurai | |||

Rice output (kg/ha) | 1121 | 5128.03 | 1454.71 |

N applied (kg/ha) | 1121 | 52.87 | 64.9 |

P applied (kg/ha) | 1121 | 17.54 | 14.41 |

K applied (kg/ha) | 1121 | 32.95 | 30.87 |

Org C (g/kg) | 1121 | 9.04 | 1.25 |

Age (year) | 867 | 47.31 | 11.74 |

Educ (year) | 274 | 10.58 | 2.84 |

Farm area (ha) | 1121 | 0.3 | 0.08 |

HYS | 1121 | 0.37 | 0.48 |

Thanjavur | |||

Rice output (kg/ha) | 77 | 4632.96 | 1281.16 |

N applied (kg/ha) | 77 | 48.34 | 56.06 |

P applied (kg/ha) | 77 | 10.6 | 15.31 |

K applied (kg/ha) | 77 | 20.53 | 30.05 |

Org C (g/kg) | 77 | 71.15 | 7.88 |

Age (year) | - | - | - |

Educ (year) | - | - | - |

Farm area (ha) | 75 | 0.31 | 0.17 |

HYS | 77 | 0.92 | 0.27 |

Uttar Pradesh | |||

Rice output (kg/ha) | 84 | 5068.41 | 1190.91 |

N applied (kg/ha) | 84 | 62.97 | 72.61 |

P applied (kg/ha) | 84 | 24.64 | 8.44 |

K applied (kg/ha) | 84 | 30.05 | 21 |

Org C (g/kg) | 84 | 11.89 | 2.71 |

Age (year) | 80 | 50.35 | 11.6 |

Educ (year) | 40 | 11.1 | 3.37 |

Farm area (ha) | 84 | 0.36 | 0.08 |

HYS | 84 | 0 | 0 |

INDONESIA | |||

Sukamandi, West Java | |||

Rice output (kg/ha) | 480 | 4046.43 | 1372.89 |

N applied (kg/ha) | 480 | 55.36 | 66.03 |

P applied (kg/ha) | 480 | 11.24 | 12.77 |

K applied (kg/ha) | 480 | 17.37 | 23.83 |

Org C (g/kg) | 480 | 15.7 | 4.97 |

Age (year) | 435 | 43.3 | 13.81 |

Educ (year) | 142 | 6.92 | 3.28 |

Farm area (ha) | 480 | 0.99 | 1.18 |

HYS | 480 | 0.78 | 0.42 |

PHILIPPINES | |||

Nueva Ecija, Philippines | |||

Rice output (kg/ha) | 630 | 4760.10 | 1559.10 |

N applied (kg/ha) | 630 | 41.96 | 63.98 |

P applied (kg/ha) | 630 | 13.79 | 12.89 |

K applied (kg/ha) | 630 | 22.83 | 22.11 |

Org C (g/kg) | 630 | 10.39 | 2.78 |

Age (year) | 558 | 51.02 | 13.6 |

Educ (year) | 179 | 7.32 | 4.03 |

Farm area (ha) | 630 | 1.73 | 0.96 |

HYS | 630 | 1 | 0 |

THAILAND | |||

Suphan Buri, Thailand | |||

Rice output (kg/ha) | 660 | 3572.47 | 960.24 |

N applied (kg/ha) | 660 | 34.61 | 52.66 |

P applied (kg/ha) | 660 | 17.13 | 13.99 |

K applied (kg/ha) | 660 | 16.69 | 23.52 |

Org C (g/kg) | 660 | 10.49 | 6.67 |

Age (year) | 651 | 46.91 | 8.84 |

Educ (year) | 216 | 4.78 | 1.85 |

Farm area (ha) | 660 | 1.55 | 0.96 |

HYS | 660 | 0.65 | 0.48 |

VIETNAM | |||

Can Tho, Vietnam | |||

Rice output (kg/ha) | 591 | 3894.34 | 1415.28 |

N applied (kg/ha) | 591 | 32.22 | 54.18 |

P applied (kg/ha) | 591 | 15.38 | 13.82 |

K applied (kg/ha) | 591 | 19.2 | 22.38 |

Org C (g/kg) | 591 | 18.54 | 4.11 |

Age (year) | 591 | 47.8 | 11 |

Educ (year) | 591 | 6.86 | 3.65 |

Farm area (ha) | 591 | 0.81 | 0.67 |

HYS | 591 | 0.65 | 0.48 |

Ha Noi, Vietnam | |||

Rice output (kg/ha) | 96 | 5627.50 | 1389.42 |

N applied (kg/ha) | 96 | 48.12 | 50.67 |

P applied (kg/ha) | 96 | 24.25 | 8.1 |

K applied (kg/ha) | 96 | 51.05 | 14.71 |

Org C (g/kg) | 96 | 14.74 | 4.98 |

Age (year) | 48 | 47.75 | 9.15 |

Educ (year) | 24 | 7.08 | 2.65 |

Farm area (ha) | 96 | 0.08 | 0.02 |

HYS | 96 | 0.96 | 0.2 |

Variable | Aduthurai | Uttar Pradesh | Thankjavur | |||
---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 1 | Model 2 | Model 1 | Model 2 | |

Nitrogen (N) | 25.59 *** | 25.30 *** | −128.7 *** | −107.2 *** | −9.845 | −12.7 |

−5.618 | −5.634 | −36.95 | −35.31 | −29.23 | −30.46 | |

N-squared | −0.107 *** | −0.107 *** | 0.378 ** | 0.366 ** | −0.00907 | 0.0372 |

−0.0131 | −0.0131 | −0.156 | −0.15 | −0.108 | −0.121 | |

Phosphorus (P) | −19.97 | −17.67 | 1024.5 *** | 855.8** | 24.54 | 84.46 |

−15.7 | −15.78 | −345.6 | −328.7 | −99.92 | −120.9 | |

P-squared | 0.956 *** | 0.870 ** | −20.86 | −14.18 | 0.0359 | 0.353 |

−0.362 | −0.365 | −14.61 | −13.94 | −0.653 | −0.724 | |

Potassium (K) | 5.74 | 6.374 | −1054.7 ** | −840.8 ** | 53.90 ** | 34.73 |

−7.139 | −7.175 | −426.7 | −406.5 | −25.57 | −32.41 | |

K-squared | −0.114 *** | −0.111 *** | 2.721 | 2.866 | −0.122 | −0.0315 |

−0.0392 | −0.0392 | −2.452 | −2.308 | −0.159 | −0.177 | |

N × P | −0.221 * | −0.214 * | −1.34 | −1.914 | −0.0488 | −0.702 |

−0.118 | −0.118 | −2.173 | −2.085 | −1.18 | −1.381 | |

P × K | −0.0336 | −0.0489 | 19.93 | 12.39 | −1.109 | −1.474 * |

−0.149 | −0.149 | −17.24 | −16.41 | −0.735 | −0.84 | |

N × K | 0.0761 | 0.0727 | 4.566 *** | 4.102 *** | −0.141 | 0.0711 |

−0.0496 | −0.05 | −1.208 | −1.147 | −0.264 | −0.349 | |

Organic Carbon (OrgC) | 173.5 | 175.9 | −149.3 | −286.7 | 882.2 *** | 785.4 *** |

−217.4 | −218.4 | −200.5 | −209.5 | −233.3 | −261.8 | |

OrgC-squared | −7.558 | −8.079 | 5.506 | 10.39 | −5.941 *** | −5.296 *** |

−11.61 | −11.67 | −8.891 | −9.667 | −1.623 | −1.809 | |

OrgC × N | 0.618 | 0.629 | 0.537 | 0.485 | 0.283 | 0.24 |

−0.463 | −0.463 | −0.633 | −0.6 | −0.291 | −0.319 | |

High Yielding Season (HYS) | 138.1 * | - | 326.2 | |||

−71.63 | - | −588.4 | ||||

Farm area | 2250.2 | −21,061.1 ** | 448.5 | |||

−2518.3 | −8018.8 | −2741.9 | ||||

Farm area × farm area | −2860.5 | 40,513.2 *** | 359.8 | |||

−4017.7 | −13,753.9 | −2441.7 | ||||

Constant | 3310.8 *** | 2879.2 ** | 9308.7 *** | 11,624.0 *** | 2858.2 *** | 2550.6 *** |

−1013.8 | −1120.1 | −1756.9 | −1900.3 | −8317.3 | −9128.2 | |

No. of observations | 1121 | 1121 | 84 | 84 | 77 | 75 |

Adjusted R-squared | 0.408 | 0.409 | 0.51 | 0.567 | 0.642 | 0.629 |

Akaike Info Criteria | 18,934.8 | 18,935.5 | 1380.163 | 1371.333 | 1253.152 | 1226.733 |

Bayesian Info Criteria | 19,000.09 | 19,015.85 | 1411.763 | 1407.795 | 1283.622 | 1263.812 |

**Table 5.**Production function estimates using two versions of the quadratic model in Indonesia, Philippines, and Thailand.

Variable | West Java, Indonesia | Nueva Ecija, Phillippines | Suphan Buri, Thailand | |||
---|---|---|---|---|---|---|

Model 1 | Model 2 | Model 1 | Model 2 | Model 1 | Model 2 | |

N | 21.32 *** | 24.11 *** | 17.43 *** | 19.05 *** | −7.731 | −4.565 |

−3.732 | −3.209 | −6.287 | −6.297 | −5.871 | −5.694 | |

N-squared | −0.0881 *** | −0.0822 *** | −0.0662 *** | −0.0701 *** | 0.0864 ** | 0.0609 |

−0.0141 | −0.012 | −0.0187 | −0.0187 | −0.042 | −0.0412 | |

P | −10.75 | 8.973 | 22.36 | 25.85 | 78.79 *** | 74.12 *** |

−24.04 | −20.54 | −59.25 | −59.16 | −24.87 | −24.06 | |

P-squared | 0.448 | −0.474 | −1.052 | −1.19 | −0.476 | −0.446 |

−0.759 | −0.65 | −2.562 | −2.554 | −0.476 | −0.464 | |

K | −40.64 *** | −19.55 | −9.655 | −13.03 | - | −14.42 |

−14.04 | −12.06 | −29.42 | −29.77 | - | −13.62 | |

K-squared | 0.395 *** | 0.198 * | 0.841 * | 0.851 * | 7.279 | 7.653 * |

−0.127 | −0.109 | −0.456 | −0.454 | −4.674 | −4.559 | |

N × P | 0.255 * | 0.164 | 0.0975 | 0.0724 | −0.381 * | −0.334 |

−0.13 | −0.112 | −0.332 | −0.332 | −0.229 | −0.225 | |

P × K | 0.844 ** | 0.493 * | −0.837 | −0.727 | −13.41 * | −13.96 * |

−0.327 | −0.281 | −1.405 | −1.407 | −7.782 | −7.584 | |

N × K | 0.0532 | 0.0229 | −0.154 | −0.159 | 1.787 ** | 1.748 ** |

−0.0876 | −0.0748 | −0.19 | −0.191 | −0.893 | −0.867 | |

OrgC | 91.64 | 73.59 | 74.54 | 137.9 | −17.47 | 29.82 |

−72.39 | −63.72 | −124.2 | −126.3 | −19.83 | −28.79 | |

OrgC-squared | 2.32 | 1.48 | −3.101 | −5.42 | −0.0145 | −1.71 |

−2.208 | −1.927 | −5.713 | −5.765 | −0.983 | −1.222 | |

OrgC × N | −0.102 | −0.273 ** | 0.684 ** | 0.631 * | 0.0806 | 0.0412 |

−0.157 | −0.136 | −0.339 | −0.339 | −0.0952 | −0.0921 | |

HYS | 1402.6 *** | - | 533.7 *** | |||

−109.3 | - | −127.8 | ||||

Farm area | 620.2 *** | −474.5 ** | −8.541 | |||

−129 | −187.5 | −202.3 | ||||

Farm area × farm area | −122.3 *** | 103.1 ** | −0.913 | |||

−24.54 | −43.77 | −48.16 | ||||

Constant | 1338.7 ** | 449.1 | 3719.0 *** | 3744.8 *** | 3471.4 *** | 2901.3 *** |

−562.7 | −494.8 | −660.1 | −659.9 | −96.53 | −355.6 | |

No. of observations | 480 | 480 | 630 | 630 | 660 | 660 |

Adjusted R-squared | 0.469 | 0.615 | 0.287 | 0.292 | 0.2 | 0.256 |

Akaike Info Criteria | 8006.938 | 7855.506 | 10,851.17 | 10,848.61 | 10,802.13 | 10,757.67 |

Bayesian Info Criteria | 8061.198 | 7922.286 | 10,908.97 | 10,915.29 | 10,856.04 | 10,825.05 |

Variable | Can Tho | Ha Noi | ||
---|---|---|---|---|

Model 1 | Model 2 | Model 1 | Model 2 | |

N-squared | −8.633 | 16.94 ** | 83.23 | 69.25 |

−14.6 | −8.549 | −65.47 | −63.38 | |

Nsq | 0.064 | 0.0341 | −0.221 | −0.256 * |

−0.0948 | −0.0557 | −0.143 | −0.139 | |

P-squared | 235.8 *** | 57.89 | 231.9 | 204.3 |

−83.93 | −49.16 | −165.8 | −164.4 | |

Psq | −0.525 | 2.128 ** | 1.464 | 2.622 |

−1.514 | −0.878 | −2.66 | −2.611 | |

K-squared | −38.39 | −17.87 | −53.79 | −139.4 |

−81.27 | −47.03 | −140.9 | −139.4 | |

Ksq | 0.256 | −1.329 | 0.376 | 0.743 |

−1.673 | −0.967 | −0.577 | −0.579 | |

N × P | −1.147 | −1.209 ** | −2.550 ** | −2.741 *** |

−0.842 | −0.491 | −0.996 | −0.997 | |

P × K | −3.409 | 0.581 | −0.401 | −0.178 |

−3.233 | −1.878 | −1.505 | −1.527 | |

N × K | 0.861 | 0.233 | 0.175 | 0.639 |

−0.538 | −0.31 | −0.879 | −0.872 | |

OrgC | −521.1 *** | −446.2 *** | −205.1 | −265.4 |

−109.3 | −62.95 | −156.5 | −160.2 | |

OrgC-squared | 12.61 *** | 9.917 *** | 11.01 ** | 12.61 ** |

−2.761 | −1.592 | −4.798 | −4.834 | |

OrgC × N | −0.205 | −0.197 | 1.168 ** | 1.224 ** |

−0.277 | −0.159 | −0.526 | −0.514 | |

HYS | 2232.2 *** | 1122.1 * | ||

−68.55 | −568.4 | |||

Farm area | 507.6 *** | −73,770.9 ** | ||

−141.2 | −35,356.7 | |||

Farm area × farm area | −103.3 ** | 379,887.0 ** | ||

−45.94 | −178,261.7 | |||

Constant | 8650.2 *** | 6384.1 *** | 341.9 | 5167.6 |

−1052.8 | −616.5 | −7097.7 | −7221.5 | |

No. of observations | 591 | 591 | 96 | 96 |

Adjusted R-squared | 0.142 | 0.718 | 0.498 | 0.536 |

Akaike Info Criteria | 10,175.29 | 9520.387 | 1607.71 | 1602.749 |

Bayesian Info Criteria | 10,232.26 | 9590.496 | 1641.047 | 1643.778 |

Variable | Aduthurai | Thanjavur | Uttar Pradesh | |||
---|---|---|---|---|---|---|

MPP | Output Elasticity | MPP | Output Elasticity | MPP | Output Elasticity | |

Total N (kg) | 18.34 (1.36) *** | 0.19 (0.02) *** | 2.01 (12.85) | 0.02 (0.13) | 20.77 (22.67) | −0.09 (0.17) |

Total P (kg) | −0.04 (6.59) | −0.01 (0.02) | 27.77 (58.08) | 0.06 (0.13) | 408.94 (196.77) ** | 1.20 (0.87) ** |

Total K (Kg) | 2.05 (3.97) | 0.02 (0.02) | 21.25 (16.9) | 0.09 (0.07) | −104.99 (80.55) | −1.17 (0.49) ** |

Org C (g/kg) | 63.06 (30.72) ** | 0.12 (0.05) ** | 43.32 (13.75) *** | 0.66 (0.21) *** | −9.16 (47.81) | −0.02 (0.13) |

Farm area | 533.90 (472.02) | 0.02 (0.03) | 685.97 (1467.44) | 0.04 (0.10) | 918.68 (302.20) *** | 0.77 (0.25) *** |

**Table 8.**Marginal physical product (MPP) and output elasticity at the mean level in Indonesia, Philippines, and Thailand.

Variable | Sukamandi, West Java, Indonesia | Nueva Ecija, Philippines | Suphan Buri, Thailand | |||
---|---|---|---|---|---|---|

MPP | Output Elasticity | MPP | Output Elasticity | MPP | Output Elasticity | |

Total N (kg) | 12.96 (1.04) *** | 0.18 (0.01) *** | 17.10 (2.43) *** | 0.15 (0.02) *** | 36.27 (8.27) *** | 0.32 (0.08) *** |

Total P (kg) | 15.94 (7.68) ** | 0.04 (0.02) ** | −20.53 (21.89) | −0.06 (0.06) | −270.83 (64.42) *** | −0.70 (0.17) *** |

Total K (Kg) | −5.86 (5.06) | −0.02 (0.02) | 9.15 (13.36) | 0.04 (0.06) | 230.31 (54.44) *** | 0.48 (0.12) *** |

Org C (g/kg) | 104.96 (12.02) *** | 0.41 (0.05) *** | 51.82 (20.87) ** | 0.11 (0.05) ** | −3.98 (8.17) | −0.01 (0.02) |

Farm area | 380.40 (94.06) *** | 0.09 (0.02) *** | −123.87 (63.82) * | −0.04 (0.02) * | −11.78 (58.89) | −0.01 (0.03) |

Variable | Can Tho | Ha Noi | ||
---|---|---|---|---|

MPP | Output Elasticity | MPP | Output Elasticity | |

Total N (kg) | 1.36 (0.82) | 0.01 (0.05) | 28.81 (6.30) *** | 0.24 (0.05) *** |

Total P (kg) | 95.54 (24.34) *** | 0.38 (0.10) *** | 190.42 (55.69) *** | 0.82 (0.24) *** |

Total K (Kg) | −52.44 (15.45) *** | −0.26 (0.08) *** | −37.11 (46.42) | −0.33 (0.42) |

Org C (g/kg) | −84.76 (7.59) *** | −0.40 (0.04) *** | 165.18 (32.24) *** | 0.43 (0.08) *** |

Farm area | 340.30 (80.21) *** | 0.07 (0.02) *** | −575.38 (244.84) ** | −0.04 (0.03) * |

Hypothesis: Parameter β_{ij} | Aduthurai, India | Thanjavur, India | Uttar Pradesh, India | Sukamandi, WJ, Indonesia | ||||
---|---|---|---|---|---|---|---|---|

F Value | p-Value | F Value | p-Value | F Value | p-Value | F Value | p-Value | |

NP = 0 | 2.87 | 0.09 | 0.29 | 0.61 | 1.44 | 0.23 | 2.93 | 0.09 |

NP < 0 | 0.95 | 0.69 | 0.82 | 0.07 | ||||

NP > 0 | 0.04 | 0.31 | 0.18 | 0.93 | ||||

PK = 0 | 0.12 | 0.73 | 3.21 | 0.08 | 0.86 | 0.36 | 3.88 | 0.08 |

PK < 0 | 0.64 | 0.95 | 0.23 | 0.04 | ||||

PK > 0 | 0.36 | 0.05 | 0.77 | 0.96 | ||||

NK = 0 | 2.58 | 0.10 | 0.04 | 0.84 | 19.91 | 0.00 | 0.12 | 0.76 |

NK < 0 | 0.05 | 0.42 | 0.00 | 0.38 | ||||

NK > 0 | 0.95 | 0.58 | 0.99 | 0.62 | ||||

OrgCN = 0 | 1.78 | 0.18 | 0.74 | 0.45 | 0.69 | 0.42 | 4.76 | 0.04 |

OrgCN < 0 | 0.09 | 0.23 | 0.21 | 0.98 | ||||

OrgCN > 0 | 0.91 | 0.77 | 0.79 | 0.02 | ||||

Hypothesis: Parameter β_{ij} | Nueva Ecija, Philippines | Suphan Buri, Thailand | Can Tho, Vietnam | Hanoi, Vietnam | ||||

F Value | p-Value | F Value | p-Value | F Value | p-Value | F Value | p-Value | |

NP = 0 | 0.09 | 0.82 | 1.73 | 0.13 | 8.39 | 0.00 | 11.57 | 0.00 |

NP < 0 | 0.41 | 0.93 | 0.99 | 0.99 | ||||

NP > 0 | 0.59 | 0.07 | 0.01 | 0.01 | ||||

PK = 0 | 0.47 | 0.61 | 22.78 | 0.06 | 0.15 | 0.70 | 0.02 | 0.88 |

PK < 0 | 0.70 | 0.97 | 0.35 | 0.55 | ||||

PK > 0 | 0.30 | 0.03 | 0.65 | 0.45 | ||||

NK = 0 | 1.52 | 0.41 | 22.62 | 0.04 | 0.92 | 0.34 | 0.47 | 0.49 |

NK < 0 | 0.79 | 0.02 | 0.17 | 0.25 | ||||

NK > 0 | 0.21 | 0.98 | 0.83 | 0.75 | ||||

OrgCN = 0 | 3.97 | 0.06 | 0.22 | 0.65 | 2.09 | 0.15 | 3.05 | 0.08 |

OrgCN < 0 | 0.03 | 0.33 | 0.93 | 0.04 | ||||

OrgCN > 0 | 0.97 | 0.67 | 0.07 | 0.96 |

Site/ Alternative Hypothesis | Null Hypothesis | |||
---|---|---|---|---|

Linear Von Liebig | Squared | Square-Root | Non-Linear Von Liebig | |

India | ||||

Aduthurai | ||||

Linear von Liebig | - | 12.41 *** | 1.04 | 10.88 ** |

Squared | 1.12 | - | 0.03 | 1.66 |

Square-root | 0.78 | 9.84 *** | - | 1.7 |

Non-linear von Liebig | 21.57 *** | 13.74 *** | 3.81 * | - |

ALL | 3.10 ** | 6.59 *** | 2.91 ** | 0.64 |

Thanjavur | ||||

Linear von Liebig | - | 1.81 | 1.83 | 2.09 |

Squared | 5.11 ** | - | 0.94 | 3.14 * |

Square-root | 4.40 ** | 0 | - | 3.70 * |

Non-linear von Liebig | 69.16 *** | 4.13 ** | 7.48 ** | - |

ALL | 2.44 * | 1.34 | 2.04 | 1.33 |

Uttar Pradesh | ||||

Linear von Liebig | 0.15 | 1.87 | 0.8 | |

Squared | 3.84 * | 0.48 | 11.61 *** | |

Square-root | 3.47 * | 0.12 | 12.50 *** | |

Non-linear von Liebig | 6.94 *** | 0.26 | 0.83 | |

ALL | 1.54 | 0.12 | 1.09 | 4.35 *** |

West Java, Indonesia | ||||

Linear von Liebig | - | 0.1 | 2.46 | 89.54 *** |

Squared | 53.74 *** | - | 2.85* | 268.64 |

Square-root | 58.63 *** | 3.47 * | - | 14.80 *** |

Non-linear von Liebig | 51.36 *** | 0.68 | 0.06 | 260.41 *** |

ALL | 28.56 *** | 1.94 | 2.58 * | 91.48 *** |

Nueva Ecija, Philippines | ||||

Linear von Liebig | 0.05 | 0.69 | 3.22* | |

Squared | 23.17 *** | 2.86* | 0.47 | |

Square-root | 25.66 *** | 3.18 * | 0.7 | |

Non-linear von Liebig | 49.01 *** | 2.01 | 2.49 | |

ALL | 15.97 *** | 7.04 *** | 8.31 *** | 0.67 |

Site/Alternative Hypothesis | Null Hypothesis | |||

Linear von Liebig | Squared | Square-root | Non-linear von Liebig | |

Suphan Buri, Thailand | ||||

Linear von Liebig | 0.01 | 22.57 *** | 66.44 *** | |

Squared | 24.70 *** | 26.04 *** | 17.24 *** | |

Square-root | 28.87 *** | 6.66 ** | 17.81 *** | |

Non-linear von Liebig | 10.21 *** | 0.71 | 21.44 *** | |

ALL | 2.52 * | 18.31 *** | 6.09 *** | |

Vietnam | ||||

Can Tho | ||||

Linear von Liebig | - | 0.22 | 2 | 6.45 * |

Squared | 21.48 *** | - | 7.62 *** | 7.91 *** |

Square-root | 15.49 *** | 0.01 | - | 1.65 |

Non-linear von Liebig | 27.05 *** | 2.04 | 9.87 *** | - |

ALL | 10.31 *** | 1.98 | 6.46 *** | 4.55 *** |

Hanoi | ||||

Linear von Liebig | - | 0.13 | 6.41 ** | 0.16 |

Squared | 6.20 ** | - | 0.08 | 3.8 * |

Square-root | 5.46 ** | 6.3 7 ** | - | 3.30 * |

Non-linear von Liebig | 17.08 *** | 0.67 | 5.21 ** | - |

ALL | 4.88 *** | 1.45 | 2.35 * | 4.08 *** |

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**MDPI and ACS Style**

Rodriguez, D.G.P.
An Assessment of the Site-Specific Nutrient Management (SSNM) Strategy for Irrigated Rice in Asia. *Agriculture* **2020**, *10*, 559.
https://doi.org/10.3390/agriculture10110559

**AMA Style**

Rodriguez DGP.
An Assessment of the Site-Specific Nutrient Management (SSNM) Strategy for Irrigated Rice in Asia. *Agriculture*. 2020; 10(11):559.
https://doi.org/10.3390/agriculture10110559

**Chicago/Turabian Style**

Rodriguez, Divina Gracia P.
2020. "An Assessment of the Site-Specific Nutrient Management (SSNM) Strategy for Irrigated Rice in Asia" *Agriculture* 10, no. 11: 559.
https://doi.org/10.3390/agriculture10110559