2.3. Decoupling Index

Following Tapio’s decoupling elasticity coefficient [11], we define the decoupling index (DI) as Equation (4):

where DI_t indicates the change in one unit of CO₂ equivalents (C) with respect to G (value added in grain production) during base period t − 1 and last time t. C_t−1 and C_t represent agricultural carbon emissions at base time t − 1 and last phase t, respectively, and ΔC represents the change rate of agricultural carbon emissions between last phase t and base time t − 1. G_t−1 and G_t indicate the value added in grain production in base time t − 1 and last phase t, respectively, and ΔG represents the growth rate of value added in grain production from last phase t to base time t − 1. Data for calculating C_t, C_t−1, G_t, and G_t−1 are from the China Rural Statistical Yearbook (2001–2019) and the Heilongjiang Statistical Yearbook (2001–2019), and carbon emission coefficients appear in Table 1.

The relationship between grain production and agricultural carbon emissions is divided into six decoupling states on the basis of Equation (4): strong decoupling, strong coupling, weak decoupling, weak coupling, recessive decoupling, and expansive coupling (Table 2).

Degrees of decoupling states.

As shown in Table 2, strong decoupling means that the increase in agricultural carbon emissions becomes zero or negative as the value added in grain production increases; in other words, ΔC ≤ 0 and ΔG > 0, which indicates that grain production has broken away from the mode of high yield with high inputs and emissions. Strong coupling means a positive rate of change in agricultural carbon emissions (ΔC > 0), but a negative rate of change in value added in grain production (ΔG < 0). Weak decoupling means a state with positive change rates in both value added in grain production and agricultural carbon emissions, namely, ΔC > 0 and ΔG > 0, and DI ranges from 0 to 1. Weak coupling means that the rate of decline in agricultural carbon emissions is slower than the rate of decline in agricultural economy for the same period, namely, ΔC < 0 and ΔG < 0, and DI ranges from 0 to 1. Recessive decoupling means that agricultural carbon emissions decline faster than the value added in grain production declines for the same period (ΔC < 0 and ΔG < 0, and DI > 1), and expansive coupling means that value added in grain production rises at the cost of the increase in agricultural carbon emissions (ΔC > 0 and ΔG > 0, and DI > 1).